%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU693^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 10:46:16 AM UTC 2026
% Result : Theorem 70.39s 12.17s
% Output : CNFRefutation 12.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 46
% Number of leaves : 216
% Syntax : Number of formulae : 4074 (1392 unt; 0 typ; 215 def)
% Number of atoms : 33281 (13994 equ; 0 cnn)
% Maximal formula atoms : 212 ( 8 avg)
% Number of connectives : 70623 (14450 ~;13002 |; 39 &;42354 @)
% ( 14 <=>; 764 =>; 0 <=; 0 <~>)
% Maximal formula depth : 218 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2582 (2582 >; 0 *; 0 +; 0 <<)
% Number of symbols : 416 ( 413 usr; 217 con; 0-4 aty)
% Number of variables : 15367 (1444 ^;13887 !; 36 ?;15367 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_ap,type,
ap: $i > $i > $i > $i > $i ).
thf(tp_ap2p,type,
ap2p: $o ).
thf(tp_apProp,type,
apProp: $o ).
thf(tp_app,type,
app: $o ).
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_breln,type,
breln: $i > $i > $i > $o ).
thf(tp_brelnall1,type,
brelnall1: $o ).
thf(tp_brelnall2,type,
brelnall2: $o ).
thf(tp_bs114d,type,
bs114d: $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodfstin,type,
cartprodfstin: $o ).
thf(tp_cartprodfstpairEq,type,
cartprodfstpairEq: $o ).
thf(tp_cartprodmempair,type,
cartprodmempair: $o ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_cartprodmempaircEq,type,
cartprodmempaircEq: $o ).
thf(tp_cartprodpairin,type,
cartprodpairin: $o ).
thf(tp_cartprodpairmemEL,type,
cartprodpairmemEL: $o ).
thf(tp_cartprodpairmemER,type,
cartprodpairmemER: $o ).
thf(tp_cartprodpairsurjEq,type,
cartprodpairsurjEq: $o ).
thf(tp_cartprodsndin,type,
cartprodsndin: $o ).
thf(tp_cartprodsndpairEq,type,
cartprodsndpairEq: $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_dpsetconstr,type,
dpsetconstr: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_dpsetconstrEL1,type,
dpsetconstrEL1: $o ).
thf(tp_dpsetconstrEL2,type,
dpsetconstrEL2: $o ).
thf(tp_dpsetconstrER,type,
dpsetconstrER: $o ).
thf(tp_dpsetconstrERa,type,
dpsetconstrERa: $o ).
thf(tp_dpsetconstrI,type,
dpsetconstrI: $o ).
thf(tp_dpsetconstrSub,type,
dpsetconstrSub: $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_eqbreln,type,
eqbreln: $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_ex1E2,type,
ex1E2: $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_func,type,
func: $i > $i > $i > $o ).
thf(tp_funcGraphProp1,type,
funcGraphProp1: $o ).
thf(tp_funcGraphProp2,type,
funcGraphProp2: $o ).
thf(tp_funcGraphProp3,type,
funcGraphProp3: $o ).
thf(tp_funcGraphProp4,type,
funcGraphProp4: $o ).
thf(tp_funcImageSingleton,type,
funcImageSingleton: $o ).
thf(tp_funcSet,type,
funcSet: $i > $i > $i ).
thf(tp_funcext,type,
funcext: $o ).
thf(tp_funcext2,type,
funcext2: $o ).
thf(tp_funcextLem,type,
funcextLem: $o ).
thf(tp_funcinfuncset,type,
funcinfuncset: $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_infuncsetfunc,type,
infuncsetfunc: $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_kpairsurjEq,type,
kpairsurjEq: $o ).
thf(tp_ksnd,type,
ksnd: $i > $i ).
thf(tp_ksndpairEq,type,
ksndpairEq: $o ).
thf(tp_ksndsingleton,type,
ksndsingleton: $o ).
thf(tp_lam,type,
lam: $i > $i > ( $i > $i ) > $i ).
thf(tp_lam2p,type,
lam2p: $o ).
thf(tp_lamProp,type,
lamProp: $o ).
thf(tp_lamp,type,
lamp: $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_SY695,type,
sK100_SY695: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK101_SY705,type,
sK101_SY705: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK102_SY1069,type,
sK102_SY1069: $i > $i > $i > $i > $i ).
thf(tp_sK103_SY988,type,
sK103_SY988: $i > $i > $i > $i > $i ).
thf(tp_sK104_SY988,type,
sK104_SY988: $i > $i > $i > $i > $i ).
thf(tp_sK105_SY988,type,
sK105_SY988: $i > $i > $i > $i > $i ).
thf(tp_sK106_SY543,type,
sK106_SY543: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK107_SY705,type,
sK107_SY705: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK108_SY1084,type,
sK108_SY1084: $i > $i > $i > $i > $i ).
thf(tp_sK109_SY1085,type,
sK109_SY1085: $i > $i > $i > $i > $i ).
thf(tp_sK10_SY603,type,
sK10_SY603: $i > $i > $i ).
thf(tp_sK110_SY543,type,
sK110_SY543: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK111_SY543,type,
sK111_SY543: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK112_SY1012,type,
sK112_SY1012: $i > $i > $i > $i ).
thf(tp_sK113_SY705,type,
sK113_SY705: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK114_SY705,type,
sK114_SY705: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK115_SY1089,type,
sK115_SY1089: $i > $i > $i > $i > $i ).
thf(tp_sK116_SY1065,type,
sK116_SY1065: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK117_SY1066,type,
sK117_SY1066: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK118_SY543,type,
sK118_SY543: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK119_SY1012,type,
sK119_SY1012: $i > $i > $i > $i ).
thf(tp_sK11_SY633,type,
sK11_SY633: $i > $i > $i ).
thf(tp_sK120_SY705,type,
sK120_SY705: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK121_SY1070,type,
sK121_SY1070: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK122_SY1077,type,
sK122_SY1077: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK123_SY1078,type,
sK123_SY1078: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK124_SY1061,type,
sK124_SY1061: $i > $i > $i > $i ).
thf(tp_sK125_SY1102,type,
sK125_SY1102: $i > $i > $i > $i ).
thf(tp_sK126_SY768,type,
sK126_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK127_SY472,type,
sK127_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK128_SY1086,type,
sK128_SY1086: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK129_SY1116,type,
sK129_SY1116: $i > $i > $i > $i ).
thf(tp_sK12_SY640,type,
sK12_SY640: ( $i > $o ) > $i > $i ).
thf(tp_sK130_SY768,type,
sK130_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK131_SY472,type,
sK131_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK132_SY1087,type,
sK132_SY1087: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK133_SY1096,type,
sK133_SY1096: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK134_SY1097,type,
sK134_SY1097: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK135_SY1092,type,
sK135_SY1092: $i > $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK136_SY1110,type,
sK136_SY1110: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK137_SY1111,type,
sK137_SY1111: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK138_SY1112,type,
sK138_SY1112: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK139_SY1113,type,
sK139_SY1113: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK13_SY274,type,
sK13_SY274: $i > $i ).
thf(tp_sK140_SY1122,type,
sK140_SY1122: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK141_SY1123,type,
sK141_SY1123: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK142_SY1124,type,
sK142_SY1124: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK143_SY768,type,
sK143_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK144_SY472,type,
sK144_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK145_SY1125,type,
sK145_SY1125: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK146_SY768,type,
sK146_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK147_SY472,type,
sK147_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK148_SY768,type,
sK148_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK149_SY472,type,
sK149_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK14_SY681,type,
sK14_SY681: $i > $i > $i ).
thf(tp_sK150_SY768,type,
sK150_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK151_SY472,type,
sK151_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK152_SY768,type,
sK152_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK153_SY472,type,
sK153_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK154_SY768,type,
sK154_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK155_SY472,type,
sK155_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK156_SY768,type,
sK156_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK157_SY472,type,
sK157_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK158_SY768,type,
sK158_SY768: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK159_SY472,type,
sK159_SY472: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK15_SY684,type,
sK15_SY684: $i > $i > $i ).
thf(tp_sK160_SY1136,type,
sK160_SY1136: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK161_SY1137,type,
sK161_SY1137: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK162_SY1138,type,
sK162_SY1138: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK163_SY1139,type,
sK163_SY1139: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK164_SY1143,type,
sK164_SY1143: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK165_SY1144,type,
sK165_SY1144: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK166_SY1145,type,
sK166_SY1145: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK167_SY1153,type,
sK167_SY1153: $i > ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK16_SY692,type,
sK16_SY692: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK17_SY702,type,
sK17_SY702: ( $i > $o ) > $i > $i ).
thf(tp_sK18_SY747,type,
sK18_SY747: $i > $i > $i ).
thf(tp_sK19_SY438,type,
sK19_SY438: $i > $i ).
thf(tp_sK1_A,type,
sK1_A: $i ).
thf(tp_sK20_SY764,type,
sK20_SY764: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK21_SY950,type,
sK21_SY950: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK22_SY607,type,
sK22_SY607: $i > $i > $i ).
thf(tp_sK23_SY854,type,
sK23_SY854: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK24_SY857,type,
sK24_SY857: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK25_SY872,type,
sK25_SY872: $i > ( $i > $i ) > $i > $i ).
thf(tp_sK26_SY381,type,
sK26_SY381: $i > $i ).
thf(tp_sK27_SY433,type,
sK27_SY433: $i > $i ).
thf(tp_sK28_SY970,type,
sK28_SY970: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK29_SY537,type,
sK29_SY537: $i > $i > $i ).
thf(tp_sK2_SY2,type,
sK2_SY2: $i ).
thf(tp_sK30_SY944,type,
sK30_SY944: ( $i > $o ) > $i > $i ).
thf(tp_sK31_SY583,type,
sK31_SY583: ( $i > $o ) > $i > $i ).
thf(tp_sK32_SY951,type,
sK32_SY951: $i > ( $i > $o ) > $i ).
thf(tp_sK33_SY960,type,
sK33_SY960: ( $i > $o ) > $i > $i ).
thf(tp_sK34_SY893,type,
sK34_SY893: $i > $i > $i > $i ).
thf(tp_sK35_SY728,type,
sK35_SY728: ( $i > $o ) > $i > $i ).
thf(tp_sK36_SY237,type,
sK36_SY237: $i > $i > $i ).
thf(tp_sK37_SY957,type,
sK37_SY957: $o > $i > $i > $i ).
thf(tp_sK38_SX0,type,
sK38_SX0: $i > $i > $i ).
thf(tp_sK39_SX0,type,
sK39_SX0: $i > $i > $i ).
thf(tp_sK3_SY0,type,
sK3_SY0: $i ).
thf(tp_sK40_SY688,type,
sK40_SY688: $i > $i > $i ).
thf(tp_sK41_SY431,type,
sK41_SY431: $i > $i ).
thf(tp_sK42_SY979,type,
sK42_SY979: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK43_SY634,type,
sK43_SY634: $i > $i > $i ).
thf(tp_sK44_SY637,type,
sK44_SY637: $i > $i > $i ).
thf(tp_sK45_SY303,type,
sK45_SY303: $i > ( $i > $o ) > $i ).
thf(tp_sK46_SY695,type,
sK46_SY695: ( $i > $i > $o ) > $i > $i ).
thf(tp_sK47_SY993,type,
sK47_SY993: ( $i > $o ) > $i > $i > $i > $i ).
thf(tp_sK48_SY996,type,
sK48_SY996: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK49_SY817,type,
sK49_SY817: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK4_SY3,type,
sK4_SY3: $i ).
thf(tp_sK50_SY634,type,
sK50_SY634: $i > $i > $i ).
thf(tp_sK51_SY1020,type,
sK51_SY1020: $i > ( $i > $o ) > $i ).
thf(tp_sK52_SY717,type,
sK52_SY717: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK53_SY746,type,
sK53_SY746: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK54_SY1000,type,
sK54_SY1000: $i > $i > $i > $i > $i ).
thf(tp_sK55_SY943,type,
sK55_SY943: $i > ( $i > $o ) > $i ).
thf(tp_sK56_SY974,type,
sK56_SY974: $i > $i > $i > $i > $i ).
thf(tp_sK57_SY946,type,
sK57_SY946: $i > ( $i > $o ) > $i ).
thf(tp_sK58_SY949,type,
sK58_SY949: $i > ( $i > $o ) > $i ).
thf(tp_sK59_SY1019,type,
sK59_SY1019: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK5_SY153,type,
sK5_SY153: $i > $i ).
thf(tp_sK60_SY952,type,
sK60_SY952: $i > ( $i > $o ) > $i ).
thf(tp_sK61_SY953,type,
sK61_SY953: $i > ( $i > $o ) > $i ).
thf(tp_sK62_SY982,type,
sK62_SY982: $i > $i > $i > $i > $i ).
thf(tp_sK63_SY954,type,
sK63_SY954: $i > ( $i > $o ) > $i ).
thf(tp_sK64_SY983,type,
sK64_SY983: $i > $i > $i > $i > $i ).
thf(tp_sK65_SY986,type,
sK65_SY986: $i > $i > $i > $i > $i ).
thf(tp_sK66_SY992,type,
sK66_SY992: $i > $i > $i > $i > $i ).
thf(tp_sK67_SY1024,type,
sK67_SY1024: $i > $i > ( $i > $o ) > $i > $i ).
thf(tp_sK68_SY1025,type,
sK68_SY1025: $i > ( $i > $o ) > ( $i > $o ) > $i > $i ).
thf(tp_sK69_SY973,type,
sK69_SY973: $i > ( $i > $o ) > $i ).
thf(tp_sK6_SY54,type,
sK6_SY54: $i > $i ).
thf(tp_sK70_SY614,type,
sK70_SY614: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK71_SY1031,type,
sK71_SY1031: $i > $i > $i > $i > $i ).
thf(tp_sK72_SY1034,type,
sK72_SY1034: $i > $i > $i > $i > $i ).
thf(tp_sK73_SY1007,type,
sK73_SY1007: $i > $i > $i > $i ).
thf(tp_sK74_SY25,type,
sK74_SY25: $i > ( $i > $o ) > $i ).
thf(tp_sK75_SY556,type,
sK75_SY556: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK76_SY556,type,
sK76_SY556: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK77_SY1010,type,
sK77_SY1010: $i > $i > $i ).
thf(tp_sK78_SY220,type,
sK78_SY220: $i > ( $i > $o ) > $i ).
thf(tp_sK79_SY261,type,
sK79_SY261: $i > ( $i > $o ) > $i ).
thf(tp_sK7_SY243,type,
sK7_SY243: $i > $i ).
thf(tp_sK80_SY662,type,
sK80_SY662: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK81_SY305,type,
sK81_SY305: $i > ( $i > $o ) > $i ).
thf(tp_sK82_SY305,type,
sK82_SY305: $i > ( $i > $o ) > $i ).
thf(tp_sK83_SY1018,type,
sK83_SY1018: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK84_SY498,type,
sK84_SY498: $i > ( $i > $o ) > $i ).
thf(tp_sK85_SY25,type,
sK85_SY25: $i > ( $i > $o ) > $i ).
thf(tp_sK86_SY556,type,
sK86_SY556: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK87_SY139,type,
sK87_SY139: $i > ( $i > $o ) > $i ).
thf(tp_sK88_SY220,type,
sK88_SY220: $i > ( $i > $o ) > $i ).
thf(tp_sK89_SY261,type,
sK89_SY261: $i > ( $i > $o ) > $i ).
thf(tp_sK8_SY540,type,
sK8_SY540: ( $i > $o ) > $i > $i ).
thf(tp_sK90_SY305,type,
sK90_SY305: $i > ( $i > $o ) > $i ).
thf(tp_sK91_SY498,type,
sK91_SY498: $i > ( $i > $o ) > $i ).
thf(tp_sK92_SY139,type,
sK92_SY139: $i > ( $i > $o ) > $i ).
thf(tp_sK93_SY139,type,
sK93_SY139: $i > ( $i > $o ) > $i ).
thf(tp_sK94_SY988,type,
sK94_SY988: $i > $i > $i > $i > $i ).
thf(tp_sK95_SY139,type,
sK95_SY139: $i > ( $i > $o ) > $i ).
thf(tp_sK96_SY695,type,
sK96_SY695: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK97_SY543,type,
sK97_SY543: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK98_SY1035,type,
sK98_SY1035: ( $i > $o ) > $i > ( $i > $o ) > $i ).
thf(tp_sK99_SY1032,type,
sK99_SY1032: $i > ( $i > $i > $o ) > $i > $i ).
thf(tp_sK9_SY590,type,
sK9_SY590: ( $i > $o ) > ( $i > $o ) > $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_setOfPairsIsBReln,type,
setOfPairsIsBReln: $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_setukpairinjR,type,
setukpairinjR: $o ).
thf(tp_setukpairinjR1,type,
setukpairinjR1: $o ).
thf(tp_setukpairinjR11,type,
setukpairinjR11: $o ).
thf(tp_setukpairinjR12,type,
setukpairinjR12: $o ).
thf(tp_setukpairinjR2,type,
setukpairinjR2: $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_subbreln,type,
subbreln: $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_upairequniteq,type,
upairequniteq: $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(ap2p,definition,
( ap2p
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2p) ).
thf(apProp,definition,
( apProp
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in
@ ( setunion
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) )
@ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',apProp) ).
thf(app,definition,
( app
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( ap @ A @ B @ Xf @ Xx ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',app) ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',binunionRsub) ).
thf(breln,definition,
( breln
= ( ^ [A: $i,B: $i,C: $i] : ( subset @ C @ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',breln) ).
thf(brelnall1,definition,
( brelnall1
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall1) ).
thf(brelnall2,definition,
( brelnall2
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( Xphi @ ( kpair @ Xx @ Xy ) ) ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ R )
=> ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',brelnall2) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodfstpairEq,definition,
( cartprodfstpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodfstpairEq) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodmempaircEq,definition,
( cartprodmempaircEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( kpair @ Xx @ Xy )
= ( kpair @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodmempaircEq) ).
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/sandbox/benchmark/theBenchmark.p',cartprodpairin) ).
thf(cartprodpairmemEL,definition,
( cartprodpairmemEL
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemEL) ).
thf(cartprodpairmemER,definition,
( cartprodpairmemER
= ( ! [A: $i,B: $i,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairmemER) ).
thf(cartprodpairsurjEq,definition,
( cartprodpairsurjEq
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodpairsurjEq) ).
thf(cartprodsndin,definition,
( cartprodsndin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( ksnd @ Xu ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndin) ).
thf(cartprodsndpairEq,definition,
( cartprodsndpairEq
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cartprodsndpairEq) ).
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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(dpsetconstrEL1,definition,
( dpsetconstrEL1
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL1) ).
thf(dpsetconstrEL2,definition,
( dpsetconstrEL2
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( in @ Xy @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrEL2) ).
thf(dpsetconstrER,definition,
( dpsetconstrER
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i,Xy: $i] :
( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrER) ).
thf(dpsetconstrERa,definition,
( dpsetconstrERa
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) )
=> ( Xphi @ Xx @ Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrERa) ).
thf(dpsetconstrI,definition,
( dpsetconstrI
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xphi @ Xx @ Xy )
=> ( in @ ( kpair @ Xx @ Xy )
@ ( dpsetconstr @ A @ B
@ ^ [Xz: $i,Xu: $i] : ( Xphi @ Xz @ Xu ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrI) ).
thf(dpsetconstrSub,definition,
( dpsetconstrSub
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( subset
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) )
@ ( cartprod @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dpsetconstrSub) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dsetconstrI) ).
thf(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/sandbox/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/sandbox/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqbreln,definition,
( eqbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ S )
=> ( in @ ( kpair @ Xx @ Xy ) @ R ) ) ) )
=> ( R = S ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqbreln) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',eqinunit) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1E2,definition,
( ex1E2
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ex1E2) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',ex1I2) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',foundationAx) ).
thf(funcGraphProp1,definition,
( funcGraphProp1
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp1) ).
thf(funcGraphProp2,definition,
( funcGraphProp2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp2) ).
thf(funcGraphProp3,definition,
( funcGraphProp3
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( kpair @ Xx @ ( ap @ A @ B @ Xf @ Xx ) ) @ Xf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp3) ).
thf(funcGraphProp4,definition,
( funcGraphProp4
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xf )
=> ( ( ap @ A @ B @ Xf @ Xx )
= Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcGraphProp4) ).
thf(funcImageSingleton,definition,
( funcImageSingleton
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( singleton
@ ( dsetconstr @ B
@ ^ [Xy: $i] : ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcImageSingleton) ).
thf(funcext,definition,
( funcext
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext) ).
thf(funcext2,definition,
( funcext2
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xg: $i] :
( ( in @ Xg @ ( funcSet @ A @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ( Xf = Xg ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcext2) ).
thf(funcextLem,definition,
( funcextLem
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ! [Xg: $i] :
( ( func @ A @ B @ Xg )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xg @ Xx ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ Xg )
=> ( in @ ( kpair @ Xx @ Xy ) @ Xf ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcextLem) ).
thf(funcinfuncset,definition,
( funcinfuncset
= ( ! [A: $i,B: $i,Xf: $i] :
( ( func @ A @ B @ Xf )
=> ( in @ Xf @ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',funcinfuncset) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',inCongP) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',in__Cong) ).
thf(infuncsetfunc,definition,
( infuncsetfunc
= ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ( func @ A @ B @ Xf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infuncsetfunc) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairp) ).
thf(kpairsurjEq,definition,
( kpairsurjEq
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( ( kpair @ ( kfst @ Xu ) @ ( ksnd @ Xu ) )
= Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',kpairsurjEq) ).
thf(ksndpairEq,definition,
( ksndpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( ksnd @ ( kpair @ Xx @ Xy ) )
= Xy ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndpairEq) ).
thf(ksndsingleton,definition,
( ksndsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] :
( Xu
= ( kpair @ ( kfst @ Xu ) @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ksndsingleton) ).
thf(lam,definition,
( lam
= ( ^ [A: $i,B: $i,Xf: $i > $i] :
( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam) ).
thf(lam2p,definition,
( lam2p
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( in
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) )
@ ( funcSet @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lam2p) ).
thf(lamProp,definition,
( lamProp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] :
( ( Xf @ Xx )
= Xy ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamProp) ).
thf(lamp,definition,
( lamp
= ( ! [A: $i,B: $i,Xf: $i > $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( Xf @ Xx ) @ B ) )
=> ( func @ A @ B
@ ( lam @ A @ B
@ ^ [Xx: $i] : ( Xf @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',lamp) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetI1) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',sepSubset) ).
thf(setOfPairsIsBReln,definition,
( setOfPairsIsBReln
= ( ! [A: $i,B: $i,Xphi: $i > $i > $o] :
( breln @ A @ B
@ ( dpsetconstr @ A @ B
@ ^ [Xx: $i,Xy: $i] : ( Xphi @ Xx @ Xy ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setOfPairsIsBReln) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setextAx) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(setukpairinjR,definition,
( setukpairinjR
= ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( kpair @ Xx @ Xy )
= ( kpair @ Xz @ Xu ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR) ).
thf(setukpairinjR1,definition,
( setukpairinjR1
= ( ! [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 ) ) )
=> ( ( Xz = Xu )
=> ( Xy = Xu ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR1) ).
thf(setukpairinjR11,definition,
( setukpairinjR11
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR11) ).
thf(setukpairinjR12,definition,
( setukpairinjR12
= ( ! [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/sandbox/benchmark/theBenchmark.p',setukpairinjR12) ).
thf(setukpairinjR2,definition,
( setukpairinjR2
= ( ! [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 ) ) )
=> ( Xy = Xu ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setukpairinjR2) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionE) ).
thf(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singleton) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',singletonsswitch) ).
thf(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',singletonsuniq) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subPowSU) ).
thf(subbreln,definition,
( subbreln
= ( ! [A: $i,B: $i,R: $i] :
( ( breln @ A @ B @ R )
=> ! [S: $i] :
( ( breln @ A @ B @ S )
=> ( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( in @ ( kpair @ Xx @ Xy ) @ R )
=> ( in @ ( kpair @ Xx @ Xy ) @ S ) ) ) )
=> ( subset @ R @ S ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',subbreln) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/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/sandbox/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/sandbox/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairequniteq,definition,
( upairequniteq
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) )
= ( setadjoin @ Xz @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairequniteq) ).
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/sandbox/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/sandbox/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/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/sandbox/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',upairsetIR) ).
thf(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/sandbox/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( 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
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ap2apEq1) ).
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
=> ( setukpairinjR12
=> ( setukpairinjR1
=> ( upairequniteq
=> ( setukpairinjR2
=> ( setukpairinjR
=> ( ksndsingleton
=> ( ksndpairEq
=> ( kpairsurjEq
=> ( cartprodsndin
=> ( cartprodpairmemEL
=> ( cartprodpairmemER
=> ( cartprodmempaircEq
=> ( cartprodfstpairEq
=> ( cartprodsndpairEq
=> ( cartprodpairsurjEq
=> ( dpsetconstrI
=> ( dpsetconstrSub
=> ( setOfPairsIsBReln
=> ( dpsetconstrERa
=> ( dpsetconstrEL1
=> ( dpsetconstrEL2
=> ( dpsetconstrER
=> ( funcImageSingleton
=> ( apProp
=> ( app
=> ( infuncsetfunc
=> ( ap2p
=> ( funcinfuncset
=> ( lamProp
=> ( lamp
=> ( lam2p
=> ( brelnall1
=> ( brelnall2
=> ( ex1E2
=> ( funcGraphProp1
=> ( funcGraphProp3
=> ( funcGraphProp2
=> ( funcextLem
=> ( funcGraphProp4
=> ( subbreln
=> ( eqbreln
=> ( funcext
=> ( funcext2
=> ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
setextAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(4,plain,
emptysetAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(5,plain,
setadjoinAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(6,plain,
powersetAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(7,plain,
setunionAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(8,plain,
omega0Ax = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(9,plain,
omegaSAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(10,plain,
omegaIndAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(11,plain,
replAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(12,plain,
foundationAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(13,plain,
wellorderingAx = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(14,plain,
descrp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(15,plain,
dsetconstrI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(16,plain,
dsetconstrEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(17,plain,
dsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(18,plain,
exuE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(19,plain,
prop2setE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(20,plain,
emptysetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(21,plain,
emptysetimpfalse = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(22,plain,
notinemptyset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(23,plain,
exuE3e = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(24,plain,
setext = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(25,plain,
emptyI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(26,plain,
noeltsimpempty = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(27,plain,
setbeta = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(28,plain,
nonemptyE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(29,plain,
nonemptyI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(30,plain,
nonemptyI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(31,plain,
setadjoinIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(32,plain,
emptyinunitempty = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(33,plain,
setadjoinIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(34,plain,
setadjoinE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(35,plain,
setadjoinOr = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(36,plain,
setoftrueEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(37,plain,
powersetI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(38,plain,
emptyinPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(39,plain,
emptyInPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(40,plain,
powersetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(41,plain,
setunionI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(42,plain,
setunionE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(43,plain,
subPowSU = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(44,plain,
exuE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(45,plain,
nonemptyImpWitness = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(46,plain,
uniqinunit = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(47,plain,
notinsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(48,plain,
eqinunit = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(49,plain,
singletonsswitch = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(50,plain,
upairsetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(51,plain,
upairsetIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(52,plain,
upairsetIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(53,plain,
emptyE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(54,plain,
vacuousDall = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(55,plain,
quantDeMorgan1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(56,plain,
quantDeMorgan2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(57,plain,
quantDeMorgan3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(58,plain,
quantDeMorgan4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(59,plain,
prop2setI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(60,plain,
prop2set2propI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(61,plain,
notdexE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(62,plain,
notdallE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(63,plain,
exuI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(64,plain,
exuI3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(65,plain,
exuI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(66,plain,
inCongP = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(67,plain,
in__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(68,plain,
exuE3u = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(69,plain,
exu__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(70,plain,
emptyset__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(71,plain,
setadjoin__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(72,plain,
powerset__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(73,plain,
setunion__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(74,plain,
omega__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(75,plain,
exuEu = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(76,plain,
descr__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(77,plain,
dsetconstr__Cong = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(78,plain,
subsetI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(79,plain,
eqimpsubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(80,plain,
eqimpsubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(81,plain,
subsetI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(82,plain,
emptysetsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(83,plain,
subsetE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(84,plain,
subsetE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(85,plain,
notsubsetI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(86,plain,
notequalI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(87,plain,
notequalI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(88,plain,
subsetRefl = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(89,plain,
subsetTrans = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(90,plain,
setadjoinSub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(91,plain,
setadjoinSub2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(92,plain,
subset2powerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(93,plain,
setextsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(94,plain,
subsetemptysetimpeq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(95,plain,
powersetI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(96,plain,
powersetE1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(97,plain,
inPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(98,plain,
powersetsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(99,plain,
sepInPowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(100,plain,
sepSubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(101,plain,
binunionIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(102,plain,
upairset2IR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(103,plain,
binunionIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(104,plain,
binunionEcases = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(105,plain,
binunionE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(106,plain,
binunionLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(107,plain,
binunionRsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(108,plain,
binintersectI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(109,plain,
binintersectSubset5 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(110,plain,
binintersectEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(111,plain,
binintersectLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(112,plain,
binintersectSubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(113,plain,
binintersectSubset3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(114,plain,
binintersectER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(115,plain,
disjointsetsI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(116,plain,
binintersectRsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(117,plain,
binintersectSubset4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(118,plain,
binintersectSubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(119,plain,
bs114d = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(120,plain,
setminusI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(121,plain,
setminusEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(122,plain,
setminusER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(123,plain,
setminusSubset2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(124,plain,
setminusERneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(125,plain,
setminusELneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(126,plain,
setminusILneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(127,plain,
setminusIRneg = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(128,plain,
setminusLsub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(129,plain,
setminusSubset1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(130,plain,
symdiffE = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(131,plain,
symdiffI1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(132,plain,
symdiffI2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(133,plain,
symdiffIneg1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(134,plain,
symdiffIneg2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(135,plain,
secondinupair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(136,plain,
setukpairIL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(137,plain,
setukpairIR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(138,plain,
kpairiskpair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(139,plain,
kpairp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(140,plain,
singletonsubset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(141,plain,
singletoninpowerset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(142,plain,
singletoninpowunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(143,plain,
upairset2E = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(144,plain,
upairsubunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(145,plain,
upairinpowunion = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(146,plain,
ubforcartprodlem1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(147,plain,
ubforcartprodlem2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(148,plain,
ubforcartprodlem3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(149,plain,
cartprodpairin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(150,plain,
cartprodmempair1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(151,plain,
cartprodmempair = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(152,plain,
setunionE2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(153,plain,
setunionsingleton1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(154,plain,
setunionsingleton2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(155,plain,
setunionsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(156,plain,
singletonprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(157,plain,
ex1E1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(158,plain,
ex1I = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(159,plain,
ex1I2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(160,plain,
singletonsuniq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(161,plain,
setukpairinjL1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(162,plain,
kfstsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(163,plain,
theprop = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(164,plain,
kfstpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(165,plain,
cartprodfstin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(166,plain,
setukpairinjL2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(167,plain,
setukpairinjL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(168,plain,
setukpairinjR11 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(169,plain,
setukpairinjR12 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(170,plain,
setukpairinjR1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(171,plain,
upairequniteq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(172,plain,
setukpairinjR2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(173,plain,
setukpairinjR = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(174,plain,
ksndsingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(175,plain,
ksndpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(176,plain,
kpairsurjEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(177,plain,
cartprodsndin = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(178,plain,
cartprodpairmemEL = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(179,plain,
cartprodpairmemER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(180,plain,
cartprodmempaircEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(181,plain,
cartprodfstpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(182,plain,
cartprodsndpairEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(183,plain,
cartprodpairsurjEq = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(184,plain,
dpsetconstrI = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(185,plain,
dpsetconstrSub = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(186,plain,
setOfPairsIsBReln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(187,plain,
dpsetconstrERa = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(188,plain,
dpsetconstrEL1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(189,plain,
dpsetconstrEL2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(190,plain,
dpsetconstrER = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(191,plain,
funcImageSingleton = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(192,plain,
apProp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(193,plain,
app = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(194,plain,
infuncsetfunc = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(195,plain,
ap2p = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(196,plain,
funcinfuncset = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(197,plain,
lamProp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(198,plain,
lamp = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(199,plain,
lam2p = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(200,plain,
brelnall1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(201,plain,
brelnall2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(202,plain,
ex1E2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(203,plain,
funcGraphProp1 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(204,plain,
funcGraphProp3 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(205,plain,
funcGraphProp2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(206,plain,
funcextLem = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(207,plain,
funcGraphProp4 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(208,plain,
subbreln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(209,plain,
eqbreln = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(210,plain,
funcext = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(211,plain,
funcext2 = $true,
inference(standard_cnf,[status(thm)],[2]) ).
thf(212,plain,
( ( ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[2]) ).
thf(213,plain,
( ( ~ ! [A: $i,B: $i,Xf: $i] :
( ( in @ Xf @ ( funcSet @ A @ B ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( ( ap @ A @ B @ Xf @ Xx )
= ( ap @ A @ B @ Xf @ Xx ) ) ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[212]) ).
thf(214,plain,
( ( ( in @ sK4_SY3 @ ( funcSet @ sK1_A @ sK3_SY0 ) )
& ( in @ sK2_SY2 @ sK1_A )
& ~ $true )
= $true ),
inference(extcnf_combined,[status(esa)],[213]) ).
thf(215,plain,
funcext2 = $true,
inference(copy,[status(thm)],[211]) ).
thf(216,plain,
funcext = $true,
inference(copy,[status(thm)],[210]) ).
thf(217,plain,
eqbreln = $true,
inference(copy,[status(thm)],[209]) ).
thf(218,plain,
subbreln = $true,
inference(copy,[status(thm)],[208]) ).
thf(219,plain,
funcGraphProp4 = $true,
inference(copy,[status(thm)],[207]) ).
thf(220,plain,
funcextLem = $true,
inference(copy,[status(thm)],[206]) ).
thf(221,plain,
funcGraphProp2 = $true,
inference(copy,[status(thm)],[205]) ).
thf(222,plain,
funcGraphProp3 = $true,
inference(copy,[status(thm)],[204]) ).
thf(223,plain,
funcGraphProp1 = $true,
inference(copy,[status(thm)],[203]) ).
thf(224,plain,
ex1E2 = $true,
inference(copy,[status(thm)],[202]) ).
thf(225,plain,
brelnall2 = $true,
inference(copy,[status(thm)],[201]) ).
thf(226,plain,
brelnall1 = $true,
inference(copy,[status(thm)],[200]) ).
thf(227,plain,
lam2p = $true,
inference(copy,[status(thm)],[199]) ).
thf(228,plain,
lamp = $true,
inference(copy,[status(thm)],[198]) ).
thf(229,plain,
lamProp = $true,
inference(copy,[status(thm)],[197]) ).
thf(230,plain,
funcinfuncset = $true,
inference(copy,[status(thm)],[196]) ).
thf(231,plain,
ap2p = $true,
inference(copy,[status(thm)],[195]) ).
thf(232,plain,
infuncsetfunc = $true,
inference(copy,[status(thm)],[194]) ).
thf(233,plain,
app = $true,
inference(copy,[status(thm)],[193]) ).
thf(234,plain,
apProp = $true,
inference(copy,[status(thm)],[192]) ).
thf(235,plain,
funcImageSingleton = $true,
inference(copy,[status(thm)],[191]) ).
thf(236,plain,
dpsetconstrER = $true,
inference(copy,[status(thm)],[190]) ).
thf(237,plain,
dpsetconstrEL2 = $true,
inference(copy,[status(thm)],[189]) ).
thf(238,plain,
dpsetconstrEL1 = $true,
inference(copy,[status(thm)],[188]) ).
thf(239,plain,
dpsetconstrERa = $true,
inference(copy,[status(thm)],[187]) ).
thf(240,plain,
setOfPairsIsBReln = $true,
inference(copy,[status(thm)],[186]) ).
thf(241,plain,
dpsetconstrSub = $true,
inference(copy,[status(thm)],[185]) ).
thf(242,plain,
dpsetconstrI = $true,
inference(copy,[status(thm)],[184]) ).
thf(243,plain,
cartprodpairsurjEq = $true,
inference(copy,[status(thm)],[183]) ).
thf(244,plain,
cartprodsndpairEq = $true,
inference(copy,[status(thm)],[182]) ).
thf(245,plain,
cartprodfstpairEq = $true,
inference(copy,[status(thm)],[181]) ).
thf(246,plain,
cartprodmempaircEq = $true,
inference(copy,[status(thm)],[180]) ).
thf(247,plain,
cartprodpairmemER = $true,
inference(copy,[status(thm)],[179]) ).
thf(248,plain,
cartprodpairmemEL = $true,
inference(copy,[status(thm)],[178]) ).
thf(249,plain,
cartprodsndin = $true,
inference(copy,[status(thm)],[177]) ).
thf(250,plain,
kpairsurjEq = $true,
inference(copy,[status(thm)],[176]) ).
thf(251,plain,
ksndpairEq = $true,
inference(copy,[status(thm)],[175]) ).
thf(252,plain,
ksndsingleton = $true,
inference(copy,[status(thm)],[174]) ).
thf(253,plain,
setukpairinjR = $true,
inference(copy,[status(thm)],[173]) ).
thf(254,plain,
setukpairinjR2 = $true,
inference(copy,[status(thm)],[172]) ).
thf(255,plain,
upairequniteq = $true,
inference(copy,[status(thm)],[171]) ).
thf(256,plain,
setukpairinjR1 = $true,
inference(copy,[status(thm)],[170]) ).
thf(257,plain,
setukpairinjR12 = $true,
inference(copy,[status(thm)],[169]) ).
thf(258,plain,
setukpairinjR11 = $true,
inference(copy,[status(thm)],[168]) ).
thf(259,plain,
setukpairinjL = $true,
inference(copy,[status(thm)],[167]) ).
thf(260,plain,
setukpairinjL2 = $true,
inference(copy,[status(thm)],[166]) ).
thf(261,plain,
cartprodfstin = $true,
inference(copy,[status(thm)],[165]) ).
thf(262,plain,
kfstpairEq = $true,
inference(copy,[status(thm)],[164]) ).
thf(263,plain,
theprop = $true,
inference(copy,[status(thm)],[163]) ).
thf(264,plain,
kfstsingleton = $true,
inference(copy,[status(thm)],[162]) ).
thf(265,plain,
setukpairinjL1 = $true,
inference(copy,[status(thm)],[161]) ).
thf(266,plain,
singletonsuniq = $true,
inference(copy,[status(thm)],[160]) ).
thf(267,plain,
ex1I2 = $true,
inference(copy,[status(thm)],[159]) ).
thf(268,plain,
ex1I = $true,
inference(copy,[status(thm)],[158]) ).
thf(269,plain,
ex1E1 = $true,
inference(copy,[status(thm)],[157]) ).
thf(270,plain,
singletonprop = $true,
inference(copy,[status(thm)],[156]) ).
thf(271,plain,
setunionsingleton = $true,
inference(copy,[status(thm)],[155]) ).
thf(272,plain,
setunionsingleton2 = $true,
inference(copy,[status(thm)],[154]) ).
thf(273,plain,
setunionsingleton1 = $true,
inference(copy,[status(thm)],[153]) ).
thf(274,plain,
setunionE2 = $true,
inference(copy,[status(thm)],[152]) ).
thf(275,plain,
cartprodmempair = $true,
inference(copy,[status(thm)],[151]) ).
thf(276,plain,
cartprodmempair1 = $true,
inference(copy,[status(thm)],[150]) ).
thf(277,plain,
cartprodpairin = $true,
inference(copy,[status(thm)],[149]) ).
thf(278,plain,
ubforcartprodlem3 = $true,
inference(copy,[status(thm)],[148]) ).
thf(279,plain,
ubforcartprodlem2 = $true,
inference(copy,[status(thm)],[147]) ).
thf(280,plain,
ubforcartprodlem1 = $true,
inference(copy,[status(thm)],[146]) ).
thf(281,plain,
upairinpowunion = $true,
inference(copy,[status(thm)],[145]) ).
thf(282,plain,
upairsubunion = $true,
inference(copy,[status(thm)],[144]) ).
thf(283,plain,
upairset2E = $true,
inference(copy,[status(thm)],[143]) ).
thf(284,plain,
singletoninpowunion = $true,
inference(copy,[status(thm)],[142]) ).
thf(285,plain,
singletoninpowerset = $true,
inference(copy,[status(thm)],[141]) ).
thf(286,plain,
singletonsubset = $true,
inference(copy,[status(thm)],[140]) ).
thf(287,plain,
kpairp = $true,
inference(copy,[status(thm)],[139]) ).
thf(288,plain,
kpairiskpair = $true,
inference(copy,[status(thm)],[138]) ).
thf(289,plain,
setukpairIR = $true,
inference(copy,[status(thm)],[137]) ).
thf(290,plain,
setukpairIL = $true,
inference(copy,[status(thm)],[136]) ).
thf(291,plain,
secondinupair = $true,
inference(copy,[status(thm)],[135]) ).
thf(292,plain,
symdiffIneg2 = $true,
inference(copy,[status(thm)],[134]) ).
thf(293,plain,
symdiffIneg1 = $true,
inference(copy,[status(thm)],[133]) ).
thf(294,plain,
symdiffI2 = $true,
inference(copy,[status(thm)],[132]) ).
thf(295,plain,
symdiffI1 = $true,
inference(copy,[status(thm)],[131]) ).
thf(296,plain,
symdiffE = $true,
inference(copy,[status(thm)],[130]) ).
thf(297,plain,
setminusSubset1 = $true,
inference(copy,[status(thm)],[129]) ).
thf(298,plain,
setminusLsub = $true,
inference(copy,[status(thm)],[128]) ).
thf(299,plain,
setminusIRneg = $true,
inference(copy,[status(thm)],[127]) ).
thf(300,plain,
setminusILneg = $true,
inference(copy,[status(thm)],[126]) ).
thf(301,plain,
setminusELneg = $true,
inference(copy,[status(thm)],[125]) ).
thf(302,plain,
setminusERneg = $true,
inference(copy,[status(thm)],[124]) ).
thf(303,plain,
setminusSubset2 = $true,
inference(copy,[status(thm)],[123]) ).
thf(304,plain,
setminusER = $true,
inference(copy,[status(thm)],[122]) ).
thf(305,plain,
setminusEL = $true,
inference(copy,[status(thm)],[121]) ).
thf(306,plain,
setminusI = $true,
inference(copy,[status(thm)],[120]) ).
thf(307,plain,
bs114d = $true,
inference(copy,[status(thm)],[119]) ).
thf(308,plain,
binintersectSubset1 = $true,
inference(copy,[status(thm)],[118]) ).
thf(309,plain,
binintersectSubset4 = $true,
inference(copy,[status(thm)],[117]) ).
thf(310,plain,
binintersectRsub = $true,
inference(copy,[status(thm)],[116]) ).
thf(311,plain,
disjointsetsI1 = $true,
inference(copy,[status(thm)],[115]) ).
thf(312,plain,
binintersectER = $true,
inference(copy,[status(thm)],[114]) ).
thf(313,plain,
binintersectSubset3 = $true,
inference(copy,[status(thm)],[113]) ).
thf(314,plain,
binintersectSubset2 = $true,
inference(copy,[status(thm)],[112]) ).
thf(315,plain,
binintersectLsub = $true,
inference(copy,[status(thm)],[111]) ).
thf(316,plain,
binintersectEL = $true,
inference(copy,[status(thm)],[110]) ).
thf(317,plain,
binintersectSubset5 = $true,
inference(copy,[status(thm)],[109]) ).
thf(318,plain,
binintersectI = $true,
inference(copy,[status(thm)],[108]) ).
thf(319,plain,
binunionRsub = $true,
inference(copy,[status(thm)],[107]) ).
thf(320,plain,
binunionLsub = $true,
inference(copy,[status(thm)],[106]) ).
thf(321,plain,
binunionE = $true,
inference(copy,[status(thm)],[105]) ).
thf(322,plain,
binunionEcases = $true,
inference(copy,[status(thm)],[104]) ).
thf(323,plain,
binunionIR = $true,
inference(copy,[status(thm)],[103]) ).
thf(324,plain,
upairset2IR = $true,
inference(copy,[status(thm)],[102]) ).
thf(325,plain,
binunionIL = $true,
inference(copy,[status(thm)],[101]) ).
thf(326,plain,
sepSubset = $true,
inference(copy,[status(thm)],[100]) ).
thf(327,plain,
sepInPowerset = $true,
inference(copy,[status(thm)],[99]) ).
thf(328,plain,
powersetsubset = $true,
inference(copy,[status(thm)],[98]) ).
thf(329,plain,
inPowerset = $true,
inference(copy,[status(thm)],[97]) ).
thf(330,plain,
powersetE1 = $true,
inference(copy,[status(thm)],[96]) ).
thf(331,plain,
powersetI1 = $true,
inference(copy,[status(thm)],[95]) ).
thf(332,plain,
subsetemptysetimpeq = $true,
inference(copy,[status(thm)],[94]) ).
thf(333,plain,
setextsub = $true,
inference(copy,[status(thm)],[93]) ).
thf(334,plain,
subset2powerset = $true,
inference(copy,[status(thm)],[92]) ).
thf(335,plain,
setadjoinSub2 = $true,
inference(copy,[status(thm)],[91]) ).
thf(336,plain,
setadjoinSub = $true,
inference(copy,[status(thm)],[90]) ).
thf(337,plain,
subsetTrans = $true,
inference(copy,[status(thm)],[89]) ).
thf(338,plain,
subsetRefl = $true,
inference(copy,[status(thm)],[88]) ).
thf(339,plain,
notequalI2 = $true,
inference(copy,[status(thm)],[87]) ).
thf(340,plain,
notequalI1 = $true,
inference(copy,[status(thm)],[86]) ).
thf(341,plain,
notsubsetI = $true,
inference(copy,[status(thm)],[85]) ).
thf(342,plain,
subsetE2 = $true,
inference(copy,[status(thm)],[84]) ).
thf(343,plain,
subsetE = $true,
inference(copy,[status(thm)],[83]) ).
thf(344,plain,
emptysetsubset = $true,
inference(copy,[status(thm)],[82]) ).
thf(345,plain,
subsetI2 = $true,
inference(copy,[status(thm)],[81]) ).
thf(346,plain,
eqimpsubset1 = $true,
inference(copy,[status(thm)],[80]) ).
thf(347,plain,
eqimpsubset2 = $true,
inference(copy,[status(thm)],[79]) ).
thf(348,plain,
subsetI1 = $true,
inference(copy,[status(thm)],[78]) ).
thf(349,plain,
dsetconstr__Cong = $true,
inference(copy,[status(thm)],[77]) ).
thf(350,plain,
descr__Cong = $true,
inference(copy,[status(thm)],[76]) ).
thf(351,plain,
exuEu = $true,
inference(copy,[status(thm)],[75]) ).
thf(352,plain,
omega__Cong = $true,
inference(copy,[status(thm)],[74]) ).
thf(353,plain,
setunion__Cong = $true,
inference(copy,[status(thm)],[73]) ).
thf(354,plain,
powerset__Cong = $true,
inference(copy,[status(thm)],[72]) ).
thf(355,plain,
setadjoin__Cong = $true,
inference(copy,[status(thm)],[71]) ).
thf(356,plain,
emptyset__Cong = $true,
inference(copy,[status(thm)],[70]) ).
thf(357,plain,
exu__Cong = $true,
inference(copy,[status(thm)],[69]) ).
thf(358,plain,
exuE3u = $true,
inference(copy,[status(thm)],[68]) ).
thf(359,plain,
in__Cong = $true,
inference(copy,[status(thm)],[67]) ).
thf(360,plain,
inCongP = $true,
inference(copy,[status(thm)],[66]) ).
thf(361,plain,
exuI2 = $true,
inference(copy,[status(thm)],[65]) ).
thf(362,plain,
exuI3 = $true,
inference(copy,[status(thm)],[64]) ).
thf(363,plain,
exuI1 = $true,
inference(copy,[status(thm)],[63]) ).
thf(364,plain,
notdallE = $true,
inference(copy,[status(thm)],[62]) ).
thf(365,plain,
notdexE = $true,
inference(copy,[status(thm)],[61]) ).
thf(366,plain,
prop2set2propI = $true,
inference(copy,[status(thm)],[60]) ).
thf(367,plain,
prop2setI = $true,
inference(copy,[status(thm)],[59]) ).
thf(368,plain,
quantDeMorgan4 = $true,
inference(copy,[status(thm)],[58]) ).
thf(369,plain,
quantDeMorgan3 = $true,
inference(copy,[status(thm)],[57]) ).
thf(370,plain,
quantDeMorgan2 = $true,
inference(copy,[status(thm)],[56]) ).
thf(371,plain,
quantDeMorgan1 = $true,
inference(copy,[status(thm)],[55]) ).
thf(372,plain,
vacuousDall = $true,
inference(copy,[status(thm)],[54]) ).
thf(373,plain,
emptyE1 = $true,
inference(copy,[status(thm)],[53]) ).
thf(374,plain,
upairsetIR = $true,
inference(copy,[status(thm)],[52]) ).
thf(375,plain,
upairsetIL = $true,
inference(copy,[status(thm)],[51]) ).
thf(376,plain,
upairsetE = $true,
inference(copy,[status(thm)],[50]) ).
thf(377,plain,
singletonsswitch = $true,
inference(copy,[status(thm)],[49]) ).
thf(378,plain,
eqinunit = $true,
inference(copy,[status(thm)],[48]) ).
thf(379,plain,
notinsingleton = $true,
inference(copy,[status(thm)],[47]) ).
thf(380,plain,
uniqinunit = $true,
inference(copy,[status(thm)],[46]) ).
thf(381,plain,
nonemptyImpWitness = $true,
inference(copy,[status(thm)],[45]) ).
thf(382,plain,
exuE2 = $true,
inference(copy,[status(thm)],[44]) ).
thf(383,plain,
subPowSU = $true,
inference(copy,[status(thm)],[43]) ).
thf(384,plain,
setunionE = $true,
inference(copy,[status(thm)],[42]) ).
thf(385,plain,
setunionI = $true,
inference(copy,[status(thm)],[41]) ).
thf(386,plain,
powersetE = $true,
inference(copy,[status(thm)],[40]) ).
thf(387,plain,
emptyInPowerset = $true,
inference(copy,[status(thm)],[39]) ).
thf(388,plain,
emptyinPowerset = $true,
inference(copy,[status(thm)],[38]) ).
thf(389,plain,
powersetI = $true,
inference(copy,[status(thm)],[37]) ).
thf(390,plain,
setoftrueEq = $true,
inference(copy,[status(thm)],[36]) ).
thf(391,plain,
setadjoinOr = $true,
inference(copy,[status(thm)],[35]) ).
thf(392,plain,
setadjoinE = $true,
inference(copy,[status(thm)],[34]) ).
thf(393,plain,
setadjoinIR = $true,
inference(copy,[status(thm)],[33]) ).
thf(394,plain,
emptyinunitempty = $true,
inference(copy,[status(thm)],[32]) ).
thf(395,plain,
setadjoinIL = $true,
inference(copy,[status(thm)],[31]) ).
thf(396,plain,
nonemptyI1 = $true,
inference(copy,[status(thm)],[30]) ).
thf(397,plain,
nonemptyI = $true,
inference(copy,[status(thm)],[29]) ).
thf(398,plain,
nonemptyE1 = $true,
inference(copy,[status(thm)],[28]) ).
thf(399,plain,
setbeta = $true,
inference(copy,[status(thm)],[27]) ).
thf(400,plain,
noeltsimpempty = $true,
inference(copy,[status(thm)],[26]) ).
thf(401,plain,
emptyI = $true,
inference(copy,[status(thm)],[25]) ).
thf(402,plain,
setext = $true,
inference(copy,[status(thm)],[24]) ).
thf(403,plain,
exuE3e = $true,
inference(copy,[status(thm)],[23]) ).
thf(404,plain,
notinemptyset = $true,
inference(copy,[status(thm)],[22]) ).
thf(405,plain,
emptysetimpfalse = $true,
inference(copy,[status(thm)],[21]) ).
thf(406,plain,
emptysetE = $true,
inference(copy,[status(thm)],[20]) ).
thf(407,plain,
prop2setE = $true,
inference(copy,[status(thm)],[19]) ).
thf(408,plain,
exuE1 = $true,
inference(copy,[status(thm)],[18]) ).
thf(409,plain,
dsetconstrER = $true,
inference(copy,[status(thm)],[17]) ).
thf(410,plain,
dsetconstrEL = $true,
inference(copy,[status(thm)],[16]) ).
thf(411,plain,
dsetconstrI = $true,
inference(copy,[status(thm)],[15]) ).
thf(412,plain,
descrp = $true,
inference(copy,[status(thm)],[14]) ).
thf(413,plain,
wellorderingAx = $true,
inference(copy,[status(thm)],[13]) ).
thf(414,plain,
foundationAx = $true,
inference(copy,[status(thm)],[12]) ).
thf(415,plain,
replAx = $true,
inference(copy,[status(thm)],[11]) ).
thf(416,plain,
omegaIndAx = $true,
inference(copy,[status(thm)],[10]) ).
thf(417,plain,
omegaSAx = $true,
inference(copy,[status(thm)],[9]) ).
thf(418,plain,
omega0Ax = $true,
inference(copy,[status(thm)],[8]) ).
thf(419,plain,
setunionAx = $true,
inference(copy,[status(thm)],[7]) ).
thf(420,plain,
powersetAx = $true,
inference(copy,[status(thm)],[6]) ).
thf(421,plain,
setadjoinAx = $true,
inference(copy,[status(thm)],[5]) ).
thf(422,plain,
emptysetAx = $true,
inference(copy,[status(thm)],[4]) ).
thf(423,plain,
setextAx = $true,
inference(copy,[status(thm)],[3]) ).
thf(424,plain,
( ( ( in @ sK4_SY3 @ ( funcSet @ sK1_A @ sK3_SY0 ) )
& ( in @ sK2_SY2 @ sK1_A )
& ~ $true )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(425,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
( ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( in @ SX3 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[238,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(426,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( setadjoin @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[336,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(427,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ( SX0
!= ( setadjoin @ SX1 @ emptyset ) ) )
| ( in @ ( setunion @ SX0 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[263,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(428,plain,
( ( ! [SX0: $i,SX1: $i] : ( iskpair @ ( kpair @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[287,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(429,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[290,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(430,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ( func @ SX0 @ SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[232,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(431,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( in
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
@ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[327,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(432,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[248,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(433,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)],[265,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(434,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)],[408,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(435,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)],[282,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(436,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(437,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)],[260,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(438,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)],[267,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(439,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[255,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(440,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( powerset @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[278,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(441,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| ! [SX1: $o] : SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[406,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(442,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[300,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(443,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)],[410,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(444,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ ( setunion @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[383,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(445,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(446,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( kpair @ SX3 @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[223,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(447,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)],[268,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(448,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)],[322,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(449,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[304,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(450,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(451,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[347,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(452,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(453,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( func @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[220,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(454,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[299,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(455,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)],[360,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(456,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(457,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)],[351,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(458,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX2 )
| ( subset @ SX0 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[337,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(459,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)],[411,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(460,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
( ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( SX2 @ SX3 @ SX4 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[236,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(461,plain,
( ( ! [SX0: $i] :
( ~ ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 != emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[396,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(462,plain,
( ( ! [SX0: $i,SX1: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[288,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(463,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[346,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(464,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[341,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(465,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[422,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(466,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setadjoin @ SX0 @ emptyset )
!= ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[266,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(467,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ ( setadjoin @ SX2 @ emptyset ) @ ( powerset @ ( binunion @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[284,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(468,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)],[369,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(469,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[376,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,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)],[358,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(471,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)],[397,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(472,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[409,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(473,plain,
( ( omega = omega )
= $true ),
inference(unfold_def,[status(thm)],[352,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(474,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)],[350,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(475,plain,
( ( ! [SX0: $i] : ( in @ SX0 @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(476,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( in @ emptyset @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[367,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(477,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 ) ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[254,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(478,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)],[361,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(479,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( ( binintersect @ SX0 @ SX1 )
= SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(480,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[233,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(481,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[338,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(482,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[394,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(483,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( kfst @ SX2 ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[261,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(484,plain,
( ( ~ ( ~ ( in @ sK4_SY3 @ ( funcSet @ sK1_A @ sK3_SY0 ) )
| ~ ~ ( ~ ( in @ sK2_SY2 @ sK1_A )
| ~ ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(485,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)],[423,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(486,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ( SX0 != SX1 ) )
| ~ ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[379,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(487,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[325,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(488,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( setminus @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[298,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(489,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)],[413,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(490,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)],[281,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(491,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(unfold_def,[status(thm)],[418,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(492,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[274,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(493,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX1 @ ( binunion @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[319,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(494,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( ( kpair @ ( kfst @ SX2 ) @ ( ksnd @ SX2 ) )
= SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[243,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(495,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ emptyset )
| $false ) )
= $true ),
inference(unfold_def,[status(thm)],[405,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(496,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( ksnd @ ( kpair @ SX2 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[244,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(497,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)],[269,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(498,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ( func @ SX0 @ SX1
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] :
( ( SX2 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[228,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(499,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ( in
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] :
( ( SX2 @ SX3 )
= SX4 ) )
@ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[227,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(500,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ SX0 @ ( binunion @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[320,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(501,plain,
( ( ! [SX0: $i] :
( ( setunion @ ( setadjoin @ SX0 @ emptyset ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[271,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(502,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX0 = SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[259,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(503,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ( binintersect @ SX0 @ ( binunion @ SX1 @ SX2 ) )
= ( binunion @ ( binintersect @ SX0 @ SX1 ) @ ( binintersect @ SX0 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[307,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(504,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[225,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(505,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)],[296,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(506,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)],[412,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(507,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)],[402,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(508,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)],[382,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(509,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(510,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[323,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(511,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)],[419,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(512,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[343,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(513,plain,
( ( ! [SX0: $i] :
( ~ ( subset @ SX0 @ emptyset )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[332,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(514,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)],[370,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(515,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX2 )
| ( subset @ SX0 @ ( setadjoin @ SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[335,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(516,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)],[414,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(517,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( func @ SX0 @ SX1 @ SX3 )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[216,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(518,plain,
( ( ! [SX0: $i] :
( ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ( SX0 = emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(519,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( iskpair @ SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[275,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(520,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[378,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(521,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
= ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[258,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(522,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[301,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(523,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(524,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( SX2 @ SX3 @ SX4 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[239,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(525,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ~ ( subset @ SX0 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[340,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(526,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)],[363,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(527,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i] :
( ~ ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( SX2 @ SX3 ) @ SX1 ) )
| ( func @ SX0 @ SX1
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] :
( ( SX2 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[229,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(528,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[324,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(529,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ( ( kpair @ SX0 @ SX1 )
!= ( kpair @ SX2 @ SX3 ) )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[253,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(530,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) )
| ( SX2 = SX0 )
| ( SX2 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[283,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(531,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX2: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX2 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX2: $i] :
( SX0
= ( kpair @ ( kfst @ SX0 ) @ SX2 ) ) )
!= ( setadjoin @ SX1 @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[252,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(532,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)],[368,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(533,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[230,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(534,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)],[373,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(535,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ( subset @ SX2 @ SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[218,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(536,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[380,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(537,plain,
( ( ! [SX0: $i > $o,SX1: $i] :
( ~ ( in @ SX1 @ emptyset )
| ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[372,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(538,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] : ( SX2 @ SX3 @ SX4 ) )
@ ( cartprod @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[240,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(539,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[293,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(540,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in
@ ( setunion
@ ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 ) ) )
@ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[234,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(541,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)],[362,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(542,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[374,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(543,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 ) ) )
| ( SX2 != SX3 )
| ( SX1 = SX3 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[256,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(544,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)],[384,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(545,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[348,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(546,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[342,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(547,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX0 )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[308,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(548,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( binintersect @ SX0 @ SX1 )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[314,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(549,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[321,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(550,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[345,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(551,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( SX0 != SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[339,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(552,plain,
( ( ! [SX0: $i] : ( in @ emptyset @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[388,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(553,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX1 @ SX0 )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[331,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(554,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ ( ksnd @ SX2 ) @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[249,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(555,plain,
( ( ! [SX0: $i] :
( ( dsetconstr @ SX0
@ ^ [SX1: $i] : $true )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[390,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(556,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[375,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(557,plain,
( ( ! [SX0: $i] : ( subset @ emptyset @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[344,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(558,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)],[420,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(559,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)],[257,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(560,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)],[421,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(561,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kfst @ ( kpair @ SX2 @ SX3 ) )
= SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[245,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(562,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)],[415,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(563,plain,
( ( ! [SX0: $o,SX1: $i] :
( ~ ( in @ SX1 @ ( prop2set @ SX0 ) )
| SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[407,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(564,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)],[399,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(565,plain,
( ( ! [SX0: $i] : ( subset @ ( setunion @ ( setadjoin @ SX0 @ emptyset ) ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[273,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(566,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( in @ ( setadjoin @ SX1 @ emptyset ) @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[285,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(567,plain,
( ( emptyset = emptyset )
= $true ),
inference(unfold_def,[status(thm)],[356,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(568,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( ( setminus @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[303,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(569,plain,
( ( ! [SX0: $o] :
( ~ SX0
| ( set2prop @ ( prop2set @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[366,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(570,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)],[270,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(571,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( subset @ SX3 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 ) ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX3 )
| ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[217,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(572,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[291,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(573,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[277,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(574,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ( ( kpair @ ( kfst @ SX0 ) @ ( ksnd @ SX0 ) )
= SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[250,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(575,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ~ ( subset @ SX1 @ SX0 )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[333,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(576,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)],[371,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(577,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( binintersect @ SX0 @ SX1 ) @ SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[310,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(578,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[294,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(579,plain,
( ( ! [SX0: $i,SX1: $i] : ( subset @ ( binintersect @ SX0 @ SX1 ) @ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[315,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(580,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ( in @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[398,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(581,plain,
( ( ! [SX0: $i] : ( in @ emptyset @ ( powerset @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(582,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ omega )
| ( in @ ( setadjoin @ SX0 @ SX0 ) @ omega ) ) )
= $true ),
inference(unfold_def,[status(thm)],[417,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(583,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 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( SX1 @ SX3 )
| ( SX2 = SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[224,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(584,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ! [SX3: $i] :
~ ~ ( ~ ( in @ SX3 @ SX0 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SX1 )
| ( SX2
!= ( kpair @ SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[276,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(585,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[292,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(586,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)],[365,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(587,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)],[280,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(588,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)],[355,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(589,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ SX0 )
| ( subset @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[286,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(590,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( kpair @ SX3 @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) ) @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[222,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(591,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ ( funcSet @ SX0 @ SX1 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX4 )
= ( ap @ SX0 @ SX1 @ SX3 @ SX4 ) ) )
| ( SX2 = SX3 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[215,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(592,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ SX0 )
| ~ ( subset @ SX2 @ SX1 )
| ( subset @ SX2 @ ( binintersect @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(593,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)],[359,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(594,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(595,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ksnd @ ( kpair @ SX0 @ SX1 ) )
= SX1 ) )
= $true ),
inference(unfold_def,[status(thm)],[251,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(596,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX3: $i,SX4: $i] : ( SX2 @ SX3 @ SX4 ) )
@ ( cartprod @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[241,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(597,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)],[364,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(598,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX0 @ ( setadjoin @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[395,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(599,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( in @ SX0 @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[334,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(600,plain,
( ( ! [SX0: $i,SX1: $i] : ( in @ SX1 @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[289,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(601,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[389,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(602,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( kfst @ ( kpair @ SX0 @ SX1 ) )
= SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[262,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(603,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)],[416,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(604,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ emptyset ) )
= $true ),
inference(unfold_def,[status(thm)],[404,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(605,plain,
( ( ! [SX0: $i] :
( ~ ( ( SX0 != emptyset ) )
| ~ ! [SX1: $i] :
~ ~ ( ~ ( in @ SX1 @ SX0 )
| ~ $true ) ) )
= $true ),
inference(unfold_def,[status(thm)],[381,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(606,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( setunion @ SX0 )
= ( setunion @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(607,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( subset @ SX0 @ SX1 )
| ( subset @ ( powerset @ SX0 ) @ ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[328,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(608,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[295,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(609,plain,
( ( ! [SX0: $i] :
( ~ ( iskpair @ SX0 )
| ~ ! [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)],[264,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(610,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( binintersect @ SX0 @ SX1 )
!= SX1 )
| ( subset @ SX1 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[313,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(611,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( subset @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ! [SX3: $i > $o] :
( ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SX0 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SX1 )
| ~ ( in @ ( kpair @ SX4 @ SX5 ) @ SX2 )
| ( SX3 @ ( kpair @ SX4 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( SX3 @ SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[226,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(612,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)],[349,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(613,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(614,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)],[392,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(615,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( subset
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
@ SX0 ) )
= $true ),
inference(unfold_def,[status(thm)],[326,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(616,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( ( setminus @ SX0 @ SX1 )
!= emptyset )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[297,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(617,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)],[357,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(618,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)],[279,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(619,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX0 @ ( setadjoin @ SX1 @ emptyset ) )
| ( in @ SX1 @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[377,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(620,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i,SX3: $i] :
( ~ ( in @ ( kpair @ SX2 @ SX3 ) @ ( cartprod @ SX0 @ SX1 ) )
| ( in @ SX3 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[247,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(621,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i,SX4: $i] :
( ~ ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) )
| ( in @ SX4 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[237,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(622,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ( in @ ( ap @ SX0 @ SX1 @ SX2 @ SX3 ) @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[231,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(623,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i > $i > $o,SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( SX2 @ SX3 @ SX4 )
| ( in @ ( kpair @ SX3 @ SX4 )
@ ( dpsetconstr @ SX0 @ SX1
@ ^ [SX5: $i,SX6: $i] : ( SX2 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[242,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(624,plain,
( ( ! [SX0: $i > $o] :
( ~ ~ ! [SX1: $i] :
~ ~ ( ~ ( SX0 @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) )
| ~ ! [SX1: $i] :
~ ( SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(625,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[305,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(626,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( ( kpair @ SX2 @ SX3 )
= ( kpair @ SX2 @ SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[246,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(627,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4
@ ( dsetconstr @ SX1
@ ^ [SX5: $i] : ( in @ ( kpair @ SX3 @ SX5 ) @ SX2 ) ) )
| ( ( dsetconstr @ SX1
@ ^ [SX5: $i] : ( in @ ( kpair @ SX3 @ SX5 ) @ SX2 ) )
!= ( setadjoin @ SX4 @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[235,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(628,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[385,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(629,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( func @ SX0 @ SX1 @ SX2 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[221,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(630,plain,
( ( ! [SX0: $i] : ( subset @ SX0 @ ( setunion @ ( setadjoin @ SX0 @ emptyset ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[272,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(631,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( funcSet @ SX0 @ SX1 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX0 )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX1 )
| ~ ( in @ ( kpair @ SX3 @ SX4 ) @ SX2 )
| ( ( ap @ SX0 @ SX1 @ SX2 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[219,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(632,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ( ( powerset @ SX0 )
= ( powerset @ SX1 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[354,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(633,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ~ ( in @ SX2 @ ( setminus @ SX0 @ SX1 ) )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[302,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(634,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[386,ap2p,apProp,app,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,breln,brelnall1,brelnall2,bs114d,cartprodfstin,cartprodfstpairEq,cartprodmempair,cartprodmempair1,cartprodmempaircEq,cartprodpairin,cartprodpairmemEL,cartprodpairmemER,cartprodpairsurjEq,cartprodsndin,cartprodsndpairEq,descr__Cong,descrp,disjointsetsI1,dpsetconstrEL1,dpsetconstrEL2,dpsetconstrER,dpsetconstrERa,dpsetconstrI,dpsetconstrSub,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqbreln,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1E2,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,funcGraphProp1,funcGraphProp2,funcGraphProp3,funcGraphProp4,funcImageSingleton,funcext,funcext2,funcextLem,funcinfuncset,inCongP,inPowerset,in__Cong,infuncsetfunc,kfstpairEq,kfstsingleton,kpairiskpair,kpairp,kpairsurjEq,ksndpairEq,ksndsingleton,lam,lam2p,lamProp,lamp,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,setOfPairsIsBReln,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,setukpairinjR,setukpairinjR1,setukpairinjR11,setukpairinjR12,setukpairinjR2,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subbreln,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairequniteq,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(635,plain,
! [SV1: $i] :
( ( ! [SY4: $i,SY5: $i > $i > $o,SY6: $i,SY7: $i] :
( ~ ( in @ ( kpair @ SY6 @ SY7 )
@ ( dpsetconstr @ SV1 @ SY4
@ ^ [SX5: $i,SX6: $i] : ( SY5 @ SX5 @ SX6 ) ) )
| ( in @ SY6 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(636,plain,
! [SV2: $i] :
( ( ! [SY10: $i] : ( subset @ SY10 @ ( setadjoin @ SV2 @ SY10 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[426]) ).
thf(637,plain,
! [SV3: $i] :
( ( ~ ~ ! [SY11: $i] :
~ ~ ( ~ ( in @ SY11 @ SV3 )
| ( SV3
!= ( setadjoin @ SY11 @ emptyset ) ) )
| ( in @ ( setunion @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(638,plain,
! [SV4: $i] :
( ( ! [SY12: $i] : ( iskpair @ ( kpair @ SV4 @ SY12 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(639,plain,
! [SV5: $i] :
( ( ! [SY13: $i] : ( in @ SV5 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV5 @ ( setadjoin @ SY13 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(640,plain,
! [SV6: $i] :
( ( ! [SY14: $i,SY15: $i] :
( ~ ( in @ SY15 @ ( funcSet @ SV6 @ SY14 ) )
| ( func @ SV6 @ SY14 @ SY15 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(641,plain,
! [SV7: $i] :
( ( ! [SY16: $i > $o] :
( in
@ ( dsetconstr @ SV7
@ ^ [SX2: $i] : ( SY16 @ SX2 ) )
@ ( powerset @ SV7 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[431]) ).
thf(642,plain,
! [SV8: $i] :
( ( ! [SY18: $i,SY19: $i,SY20: $i] :
( ~ ( in @ ( kpair @ SY19 @ SY20 ) @ ( cartprod @ SV8 @ SY18 ) )
| ( in @ SY19 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(643,plain,
! [SV9: $i] :
( ( ! [SY21: $i,SY22: $i] :
( ~ ( in @ ( setadjoin @ SY22 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SY21 @ emptyset ) ) @ emptyset ) ) )
| ( SV9 = SY22 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(644,plain,
! [SV10: $i > $o] :
( ( ~ ~ ! [SY23: $i] :
~ ~ ( ~ ( SV10 @ SY23 )
| ~ ! [SY24: $i] :
( ~ ( SV10 @ SY24 )
| ( SY23 = SY24 ) ) )
| ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[434]) ).
thf(645,plain,
! [SV11: $i] :
( ( ! [SY27: $i,SY28: $i] :
( ~ ( in @ SY28 @ SV11 )
| ! [SY29: $i] :
( ~ ( in @ SY29 @ SY27 )
| ( subset @ ( setadjoin @ SY28 @ ( setadjoin @ SY29 @ emptyset ) ) @ ( binunion @ SV11 @ SY27 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(646,plain,
! [SV12: $i] :
( ( ! [SY30: $i] :
( ~ ~ ~ ! [SY31: $i] :
~ ~ ( ~ ( in @ SY31 @ SV12 )
| ~ ( in @ SY31 @ SY30 ) )
| ( ( binintersect @ SV12 @ SY30 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[436]) ).
thf(647,plain,
! [SV13: $i] :
( ( ! [SY32: $i,SY33: $i,SY34: $i] :
( ( ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SY32 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY33 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY33 @ ( setadjoin @ SY34 @ emptyset ) ) @ emptyset ) ) )
| ( SV13 = SY33 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(648,plain,
! [SV14: $i] :
( ( ! [SY35: $i > $o] :
( ~ ! [SY36: $i] :
( ~ ( in @ SY36 @ SV14 )
| ! [SY37: $i] :
( ~ ( in @ SY37 @ SV14 )
| ~ ( SY35 @ SY36 )
| ~ ( SY35 @ SY37 )
| ( SY36 = SY37 ) ) )
| ~ ~ ! [SY38: $i] :
~ ~ ( ~ ( in @ SY38 @ SV14 )
| ~ ( SY35 @ SY38 ) )
| ~ ! [SY39: $i] :
~ ~ ( ~ ( in @ SY39
@ ( dsetconstr @ SV14
@ ^ [SX3: $i] : ( SY35 @ SX3 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SX3: $i] : ( SY35 @ SX3 ) )
!= ( setadjoin @ SY39 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(649,plain,
! [SV15: $i] :
( ( ! [SY42: $i,SY43: $i] :
( ( ( setadjoin @ SV15 @ ( setadjoin @ SY42 @ emptyset ) )
!= ( setadjoin @ SY43 @ emptyset ) )
| ( SV15 = SY42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(650,plain,
! [SV16: $i] :
( ( ! [SY44: $i,SY45: $i] :
( ~ ( in @ SY45 @ SV16 )
| ! [SY46: $i] :
( ~ ( in @ SY46 @ SY44 )
| ( in @ ( kpair @ SY45 @ SY46 ) @ ( powerset @ ( powerset @ ( binunion @ SV16 @ SY44 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(651,plain,
! [SV17: $i] :
( ( ~ ( in @ SV17 @ emptyset )
| ! [SX1: $o] : SX1 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[441]) ).
thf(652,plain,
! [SV18: $i] :
( ( ! [SY48: $i,SY49: $i] :
( ~ ~ ( in @ SY49 @ SV18 )
| ~ ( in @ SY49 @ ( setminus @ SV18 @ SY48 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(653,plain,
! [SV19: $i] :
( ( ! [SY50: $i > $o,SY51: $i] :
( ~ ( in @ SY51
@ ( dsetconstr @ SV19
@ ^ [SX3: $i] : ( SY50 @ SX3 ) ) )
| ( in @ SY51 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(654,plain,
! [SV20: $i] :
( ( ! [SY53: $i] :
( ~ ( in @ SY53 @ SV20 )
| ( in @ SY53 @ ( powerset @ ( setunion @ SV20 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[444]) ).
thf(655,plain,
! [SV21: $i] :
( ( ~ ! [SY54: $i] :
~ ( in @ SY54 @ SV21 )
| ( SV21 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[445]) ).
thf(656,plain,
! [SV22: $i] :
( ( ! [SY55: $i,SY56: $i] :
( ~ ( func @ SV22 @ SY55 @ SY56 )
| ! [SY57: $i] :
( ~ ( in @ SY57 @ SV22 )
| ( in @ ( kpair @ SY57 @ ( ap @ SV22 @ SY55 @ SY56 @ SY57 ) ) @ SY56 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(657,plain,
! [SV23: $i] :
( ( ! [SY58: $i > $o,SY59: $i] :
( ~ ( in @ SY59 @ SV23 )
| ~ ( SY58 @ SY59 )
| ~ ! [SY60: $i] :
( ~ ( in @ SY60 @ SV23 )
| ~ ( SY58 @ SY60 )
| ( SY60 = SY59 ) )
| ~ ! [SY61: $i] :
~ ~ ( ~ ( in @ SY61
@ ( dsetconstr @ SV23
@ ^ [SX4: $i] : ( SY58 @ SX4 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SX4: $i] : ( SY58 @ SX4 ) )
!= ( setadjoin @ SY61 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(658,plain,
! [SV24: $i] :
( ( ! [SY64: $i,SY65: $i,SY66: $o] :
( ~ ( in @ SY65 @ ( binunion @ SV24 @ SY64 ) )
| ~ ( ~ ( in @ SY65 @ SV24 )
| SY66 )
| ~ ( ~ ( in @ SY65 @ SY64 )
| SY66 )
| SY66 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[448]) ).
thf(659,plain,
! [SV25: $i] :
( ( ! [SY67: $i,SY68: $i] :
( ~ ( in @ SY68 @ ( setminus @ SV25 @ SY67 ) )
| ~ ( in @ SY68 @ SY67 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[449]) ).
thf(660,plain,
! [SV26: $i] :
( ( ! [SY69: $i,SY70: $i] :
( ~ ( in @ SY70 @ ( binintersect @ SV26 @ SY69 ) )
| ( in @ SY70 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[450]) ).
thf(661,plain,
! [SV27: $i] :
( ( ! [SY71: $i] :
( ( SV27 != SY71 )
| ( subset @ SY71 @ SV27 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(662,plain,
! [SV28: $i] :
( ( ! [SY72: $i,SY73: $i] :
( ~ ( in @ SY73 @ ( binintersect @ SV28 @ SY72 ) )
| ( in @ SY73 @ SY72 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(663,plain,
! [SV29: $i] :
( ( ! [SY74: $i,SY75: $i] :
( ~ ( func @ SV29 @ SY74 @ SY75 )
| ! [SY76: $i] :
( ~ ( func @ SV29 @ SY74 @ SY76 )
| ~ ! [SY77: $i] :
( ~ ( in @ SY77 @ SV29 )
| ( ( ap @ SV29 @ SY74 @ SY75 @ SY77 )
= ( ap @ SV29 @ SY74 @ SY76 @ SY77 ) ) )
| ! [SY78: $i] :
( ~ ( in @ SY78 @ SV29 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY74 )
| ~ ( in @ ( kpair @ SY78 @ SX5 ) @ SY76 )
| ( in @ ( kpair @ SY78 @ SX5 ) @ SY75 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(664,plain,
! [SV30: $i] :
( ( ! [SY80: $i,SY81: $i] :
( ~ ( in @ SY81 @ SY80 )
| ~ ( in @ SY81 @ ( setminus @ SV30 @ SY80 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[454]) ).
thf(665,plain,
! [SV31: $i] :
( ( ! [SY82: $i] :
( ( SV31 != SY82 )
| ! [SY83: $i,SY84: $i] :
( ( SY83 != SY84 )
| ~ ( in @ SY83 @ SV31 )
| ( in @ SY84 @ SY82 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[455]) ).
thf(666,plain,
! [SV32: $i] :
( ( ! [SY85: $i,SY86: $i] :
( ~ ( in @ SY86 @ SY85 )
| ( in @ SY86 @ ( setadjoin @ SV32 @ SY85 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[456]) ).
thf(667,plain,
! [SV33: $i > $o] :
( ( ~ ~ ! [SY87: $i] :
~ ~ ( ~ ( SV33 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( SV33 @ SY88 )
| ( SY87 = SY88 ) ) )
| ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[457]) ).
thf(668,plain,
! [SV34: $i] :
( ( ! [SY91: $i,SY92: $i] :
( ~ ( subset @ SV34 @ SY91 )
| ~ ( subset @ SY91 @ SY92 )
| ( subset @ SV34 @ SY92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[458]) ).
thf(669,plain,
! [SV35: $i] :
( ( ! [SY93: $i > $o,SY94: $i] :
( ~ ( in @ SY94 @ SV35 )
| ~ ( SY93 @ SY94 )
| ( in @ SY94
@ ( dsetconstr @ SV35
@ ^ [SX3: $i] : ( SY93 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(670,plain,
! [SV36: $i] :
( ( ! [SY96: $i,SY97: $i > $i > $o,SY98: $i,SY99: $i] :
( ~ ( in @ ( kpair @ SY98 @ SY99 )
@ ( dpsetconstr @ SV36 @ SY96
@ ^ [SX5: $i,SX6: $i] : ( SY97 @ SX5 @ SX6 ) ) )
| ( SY97 @ SY98 @ SY99 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[460]) ).
thf(671,plain,
! [SV37: $i] :
( ( ~ ~ ! [SY102: $i] :
~ ( in @ SY102 @ SV37 )
| ( SV37 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[461]) ).
thf(672,plain,
! [SV38: $i] :
( ( ! [SY103: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ SV38 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV38 @ ( setadjoin @ SY103 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[462]) ).
thf(673,plain,
! [SV39: $i] :
( ( ! [SY104: $i] :
( ( SV39 != SY104 )
| ( subset @ SV39 @ SY104 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[463]) ).
thf(674,plain,
! [SV40: $i] :
( ( ! [SY105: $i,SY106: $i] :
( ~ ( in @ SY106 @ SV40 )
| ~ ~ ( in @ SY106 @ SY105 )
| ~ ( subset @ SV40 @ SY105 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(675,plain,
! [SV41: $i] :
( ( ~ ( in @ SV41 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[465]) ).
thf(676,plain,
! [SV42: $i] :
( ( ! [SY107: $i] :
( ( ( setadjoin @ SV42 @ emptyset )
!= ( setadjoin @ SY107 @ emptyset ) )
| ( SV42 = SY107 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[466]) ).
thf(677,plain,
! [SV43: $i] :
( ( ! [SY108: $i,SY109: $i] :
( ~ ( in @ SY109 @ SV43 )
| ( in @ ( setadjoin @ SY109 @ emptyset ) @ ( powerset @ ( binunion @ SV43 @ SY108 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(678,plain,
! [SV44: $i] :
( ( ! [SY110: $i > $o] :
( ~ ~ ~ ! [SY111: $i] :
~ ~ ( ~ ( in @ SY111 @ SV44 )
| ~ ( SY110 @ SY111 ) )
| ! [SY112: $i] :
( ~ ( in @ SY112 @ SV44 )
| ~ ( SY110 @ SY112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(679,plain,
! [SV45: $i] :
( ( ! [SY113: $i,SY114: $i] :
( ~ ( in @ SY114 @ ( setadjoin @ SV45 @ ( setadjoin @ SY113 @ emptyset ) ) )
| ( SY114 = SV45 )
| ( SY114 = SY113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[469]) ).
thf(680,plain,
! [SV46: $i > $o] :
( ( ~ ~ ! [SY115: $i] :
~ ~ ( ~ ( SV46 @ SY115 )
| ~ ! [SY116: $i] :
( ~ ( SV46 @ SY116 )
| ( SY115 = SY116 ) ) )
| ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(681,plain,
! [SV47: $i] :
( ( ! [SY119: $i > $o,SY120: $i] :
( ~ ( in @ SY120 @ SV47 )
| ~ ( SY119 @ SY120 )
| ( ( dsetconstr @ SV47
@ ^ [SX3: $i] : ( SY119 @ SX3 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(682,plain,
! [SV48: $i] :
( ( ! [SY122: $i > $o,SY123: $i] :
( ~ ( in @ SY123
@ ( dsetconstr @ SV48
@ ^ [SX3: $i] : ( SY122 @ SX3 ) ) )
| ( SY122 @ SY123 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(683,plain,
! [SV49: $i > $o] :
( ( ! [SY125: $i > $o] :
( ~ ! [SY126: $i,SY127: $i] :
( ( SY126 != SY127 )
| ~ ( ~ ( ~ ( SV49 @ SY126 )
| ( SY125 @ SY127 ) )
| ~ ( ~ ( SY125 @ SY127 )
| ( SV49 @ SY126 ) ) ) )
| ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY125 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY125 @ SX3 )
| ( SX2 = SX3 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SX2: $i] : ( SY125 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(684,plain,
! [SV50: $i] :
( ( in @ SV50 @ ( powerset @ SV50 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(685,plain,
! [SV51: $o] :
( ( ~ SV51
| ( in @ emptyset @ ( prop2set @ SV51 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[476]) ).
thf(686,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[476]) ).
thf(687,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[476]) ).
thf(688,plain,
! [SV52: $i] :
( ( ! [SY134: $i,SY135: $i,SY136: $i] :
( ( ( setadjoin @ ( setadjoin @ SV52 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV52 @ ( setadjoin @ SY134 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY135 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY135 @ ( setadjoin @ SY136 @ emptyset ) ) @ emptyset ) ) )
| ( SY134 = SY136 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(689,plain,
! [SV53: $i > $o] :
( ( ~ ~ ! [SY137: $i] :
~ ! [SY138: $i] :
~ ( ~ ( ~ ( SV53 @ SY138 )
| ( SY138 = SY137 ) )
| ~ ( ( SY138 != SY137 )
| ( SV53 @ SY138 ) ) )
| ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(690,plain,
! [SV54: $i] :
( ( ! [SY141: $i] :
( ~ ( subset @ SY141 @ SV54 )
| ( ( binintersect @ SV54 @ SY141 )
= SY141 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(691,plain,
! [SV55: $i] :
( ( ! [SY142: $i,SY143: $i] :
( ~ ( func @ SV55 @ SY142 @ SY143 )
| ! [SY144: $i] :
( ~ ( in @ SY144 @ SV55 )
| ( in @ ( ap @ SV55 @ SY142 @ SY143 @ SY144 ) @ SY142 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(692,plain,
! [SV56: $i] :
( ( subset @ SV56 @ SV56 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(693,plain,
! [SV57: $i] :
( ( ! [SY145: $i,SY146: $i] :
( ~ ( in @ SY146 @ ( cartprod @ SV57 @ SY145 ) )
| ( in @ ( kfst @ SY146 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(694,plain,
( ( ~ ( in @ sK4_SY3 @ ( funcSet @ sK1_A @ sK3_SY0 ) )
| ~ ~ ( ~ ( in @ sK2_SY2 @ sK1_A )
| ~ ~ $true ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[484]) ).
thf(695,plain,
! [SV58: $i] :
( ( ! [SY147: $i] :
( ~ ! [SY148: $i] :
~ ( ~ ( ~ ( in @ SY148 @ SV58 )
| ( in @ SY148 @ SY147 ) )
| ~ ( ~ ( in @ SY148 @ SY147 )
| ( in @ SY148 @ SV58 ) ) )
| ( SV58 = SY147 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(696,plain,
! [SV59: $i] :
( ( ! [SY149: $i] :
( ~ ( ( SV59 != SY149 ) )
| ~ ( in @ SY149 @ ( setadjoin @ SV59 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(697,plain,
! [SV60: $i] :
( ( ! [SY150: $i,SY151: $i] :
( ~ ( in @ SY151 @ SV60 )
| ( in @ SY151 @ ( binunion @ SV60 @ SY150 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(698,plain,
! [SV61: $i] :
( ( ! [SY152: $i] : ( subset @ ( setminus @ SV61 @ SY152 ) @ SV61 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(699,plain,
! [SV62: $i] :
( ( ~ ! [SY153: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY154: $i] :
( ~ ( in @ SY154 @ SY153 )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY154 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ~ ( ~ ( in @ SY156 @ SV62 )
| ~ ( in @ SY157 @ SV62 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY153 )
| ~ ( ~ ( ~ ( in @ SY156 @ SX4 )
| ( in @ SY157 @ SX4 ) )
| ~ ( ~ ( in @ SY157 @ SX4 )
| ( in @ SY156 @ SX4 ) ) ) )
| ( SY156 = SY157 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY153 )
| ~ ( in @ SX3 @ SY153 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY163: $i] :
( ~ ~ ( ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY163 )
| ( in @ SY164 @ SV62 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY163 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY153 )
| ~ ( in @ SX4 @ SY163 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY163 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY153 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(700,plain,
! [SV63: $i] :
( ( ! [SY171: $i,SY172: $i] :
( ~ ( in @ SY172 @ SV63 )
| ! [SY173: $i] :
( ~ ( in @ SY173 @ SY171 )
| ( in @ ( setadjoin @ SY172 @ ( setadjoin @ SY173 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SY171 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(701,plain,
! [SV64: $i] :
( ( ! [SY174: $i] :
( ~ ( in @ SY174 @ ( setunion @ SV64 ) )
| ~ ! [SY175: $i] :
~ ~ ( ~ ( in @ SY175 @ SV64 )
| ~ ( in @ SY174 @ SY175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(702,plain,
! [SV65: $i] :
( ( ! [SY176: $i] : ( subset @ SY176 @ ( binunion @ SV65 @ SY176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(703,plain,
! [SV66: $i] :
( ( ! [SY177: $i,SY178: $i] :
( ~ ( in @ SY178 @ ( cartprod @ SV66 @ SY177 ) )
| ( ( kpair @ ( kfst @ SY178 ) @ ( ksnd @ SY178 ) )
= SY178 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(704,plain,
! [SV67: $i] :
( ( ~ ( in @ SV67 @ emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(705,plain,
! [SV68: $i] :
( ( ! [SY179: $i,SY180: $i] :
( ~ ( in @ SY180 @ SV68 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY179 )
| ( ( ksnd @ ( kpair @ SY180 @ SX3 ) )
= SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[496]) ).
thf(706,plain,
! [SV69: $i] :
( ( ! [SY182: $i > $o] :
( ~ ~ ! [SY183: $i] :
~ ~ ( ~ ( in @ SY183
@ ( dsetconstr @ SV69
@ ^ [SX3: $i] : ( SY182 @ SX3 ) ) )
| ( ( dsetconstr @ SV69
@ ^ [SX3: $i] : ( SY182 @ SX3 ) )
!= ( setadjoin @ SY183 @ emptyset ) ) )
| ~ ! [SY186: $i] :
~ ~ ( ~ ( in @ SY186 @ SV69 )
| ~ ( SY182 @ SY186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(707,plain,
! [SV70: $i] :
( ( ! [SY187: $i,SY188: $i > $i] :
( ~ ! [SY189: $i] :
( ~ ( in @ SY189 @ SV70 )
| ( in @ ( SY188 @ SY189 ) @ SY187 ) )
| ( func @ SV70 @ SY187
@ ( dpsetconstr @ SV70 @ SY187
@ ^ [SX3: $i,SX4: $i] :
( ( SY188 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(708,plain,
! [SV71: $i] :
( ( ! [SY192: $i,SY193: $i > $i] :
( ~ ! [SY194: $i] :
( ~ ( in @ SY194 @ SV71 )
| ( in @ ( SY193 @ SY194 ) @ SY192 ) )
| ( in
@ ( dpsetconstr @ SV71 @ SY192
@ ^ [SX3: $i,SX4: $i] :
( ( SY193 @ SX3 )
= SX4 ) )
@ ( funcSet @ SV71 @ SY192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(709,plain,
! [SV72: $i] :
( ( ! [SY197: $i] : ( subset @ SV72 @ ( binunion @ SV72 @ SY197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[500]) ).
thf(710,plain,
! [SV73: $i] :
( ( ( setunion @ ( setadjoin @ SV73 @ emptyset ) )
= SV73 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(711,plain,
! [SV74: $i] :
( ( ! [SY198: $i,SY199: $i,SY200: $i] :
( ( ( kpair @ SV74 @ SY198 )
!= ( kpair @ SY199 @ SY200 ) )
| ( SV74 = SY199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(712,plain,
! [SV75: $i] :
( ( ! [SY201: $i,SY202: $i] :
( ( binintersect @ SV75 @ ( binunion @ SY201 @ SY202 ) )
= ( binunion @ ( binintersect @ SV75 @ SY201 ) @ ( binintersect @ SV75 @ SY202 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(713,plain,
! [SV76: $i] :
( ( ! [SY203: $i,SY204: $i] :
( ~ ( subset @ SY204 @ ( cartprod @ SV76 @ SY203 ) )
| ! [SY205: $i > $o] :
( ~ ! [SY206: $i] :
( ~ ( in @ SY206 @ SV76 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY203 )
| ~ ( in @ ( kpair @ SY206 @ SX5 ) @ SY204 )
| ( SY205 @ ( kpair @ SY206 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY204 )
| ( SY205 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(714,plain,
! [SV77: $i] :
( ( ! [SY209: $i,SY210: $i] :
( ~ ( in @ SY210 @ ( symdiff @ SV77 @ SY209 ) )
| ! [SY211: $o] :
( ~ ( ~ ( in @ SY210 @ SV77 )
| ~ ~ ( in @ SY210 @ SY209 )
| SY211 )
| ~ ( ~ ~ ( in @ SY210 @ SV77 )
| ~ ( in @ SY210 @ SY209 )
| SY211 )
| SY211 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(715,plain,
! [SV78: $i > $o] :
( ( ~ ~ ! [SY212: $i] :
~ ~ ( ~ ( SV78 @ SY212 )
| ~ ! [SY213: $i] :
( ~ ( SV78 @ SY213 )
| ( SY212 = SY213 ) ) )
| ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(716,plain,
! [SV79: $i] :
( ( ! [SY215: $i] :
( ~ ! [SY216: $i] :
( ~ ( in @ SY216 @ SV79 )
| ( in @ SY216 @ SY215 ) )
| ~ ! [SY217: $i] :
( ~ ( in @ SY217 @ SY215 )
| ( in @ SY217 @ SV79 ) )
| ( SV79 = SY215 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(717,plain,
! [SV80: $i > $o] :
( ( ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( SV80 @ SY218 )
| ~ ! [SY219: $i] :
( ~ ( SV80 @ SY219 )
| ( SY218 = SY219 ) ) )
| ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(718,plain,
! [SV81: $i] :
( ( ! [SY222: $i,SY223: $i] :
( ~ ( in @ SY223 @ SV81 )
| ~ ~ ( in @ SY223 @ SY222 )
| ( in @ SY223 @ ( setminus @ SV81 @ SY222 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(719,plain,
! [SV82: $i] :
( ( ! [SY224: $i,SY225: $i] :
( ~ ( in @ SY225 @ SY224 )
| ( in @ SY225 @ ( binunion @ SV82 @ SY224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(720,plain,
! [SV83: $i] :
( ( ! [SY226: $i] :
~ ( ~ ( ~ ( in @ SY226 @ ( setunion @ SV83 ) )
| ~ ! [SY227: $i] :
~ ~ ( ~ ( in @ SY226 @ SY227 )
| ~ ( in @ SY227 @ SV83 ) ) )
| ~ ( ~ ~ ! [SY228: $i] :
~ ~ ( ~ ( in @ SY226 @ SY228 )
| ~ ( in @ SY228 @ SV83 ) )
| ( in @ SY226 @ ( setunion @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(721,plain,
! [SV84: $i] :
( ( ! [SY229: $i,SY230: $i] :
( ~ ( subset @ SV84 @ SY229 )
| ~ ( in @ SY230 @ SV84 )
| ( in @ SY230 @ SY229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(722,plain,
! [SV85: $i] :
( ( ~ ( subset @ SV85 @ emptyset )
| ( SV85 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(723,plain,
! [SV86: $i] :
( ( ! [SY231: $i > $o] :
( ~ ! [SY232: $i] :
( ~ ( in @ SY232 @ SV86 )
| ~ ( SY231 @ SY232 ) )
| ~ ~ ! [SY233: $i] :
~ ~ ( ~ ( in @ SY233 @ SV86 )
| ~ ( SY231 @ SY233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(724,plain,
! [SV87: $i] :
( ( ! [SY234: $i,SY235: $i] :
( ~ ( subset @ SV87 @ SY235 )
| ( subset @ SV87 @ ( setadjoin @ SY234 @ SY235 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(725,plain,
! [SV88: $i] :
( ( ~ ~ ! [SY236: $i] :
~ ( in @ SY236 @ SV88 )
| ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY237 @ SV88 )
| ~ ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( in @ SY238 @ SV88 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(726,plain,
! [SV89: $i] :
( ( ! [SY239: $i,SY240: $i] :
( ~ ( func @ SV89 @ SY239 @ SY240 )
| ! [SY241: $i] :
( ~ ( func @ SV89 @ SY239 @ SY241 )
| ~ ! [SY242: $i] :
( ~ ( in @ SY242 @ SV89 )
| ( ( ap @ SV89 @ SY239 @ SY240 @ SY242 )
= ( ap @ SV89 @ SY239 @ SY241 @ SY242 ) ) )
| ( SY240 = SY241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[517]) ).
thf(727,plain,
! [SV90: $i] :
( ( ~ ! [SY243: $i] :
~ ( in @ SY243 @ SV90 )
| ( SV90 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(728,plain,
! [SV91: $i] :
( ( ! [SY244: $i,SY245: $i] :
( ~ ( in @ SY245 @ ( cartprod @ SV91 @ SY244 ) )
| ( iskpair @ SY245 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(729,plain,
! [SV92: $i] :
( ( ! [SY246: $i] :
( ( SV92 != SY246 )
| ( in @ SV92 @ ( setadjoin @ SY246 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[520]) ).
thf(730,plain,
! [SV93: $i] :
( ( ! [SY247: $i] :
( ( SV93 != SY247 )
| ( ( setadjoin @ SV93 @ ( setadjoin @ SY247 @ emptyset ) )
= ( setadjoin @ SV93 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[521]) ).
thf(731,plain,
! [SV94: $i] :
( ( ! [SY248: $i,SY249: $i] :
( ~ ~ ( in @ SY249 @ ( setminus @ SV94 @ SY248 ) )
| ~ ~ ( in @ SY249 @ SY248 )
| ~ ( in @ SY249 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[522]) ).
thf(732,plain,
! [SV95: $i] :
( ( ! [SY250: $i,SY251: $i] :
( ~ ( in @ SY251 @ SV95 )
| ~ ( in @ SY251 @ SY250 )
| ( in @ SY251 @ ( binintersect @ SV95 @ SY250 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(733,plain,
! [SV96: $i] :
( ( ! [SY252: $i,SY253: $i > $i > $o,SY254: $i] :
( ~ ( in @ SY254 @ SV96 )
| ! [SY255: $i] :
( ~ ( in @ SY255 @ SY252 )
| ~ ( in @ ( kpair @ SY254 @ SY255 )
@ ( dpsetconstr @ SV96 @ SY252
@ ^ [SX5: $i,SX6: $i] : ( SY253 @ SX5 @ SX6 ) ) )
| ( SY253 @ SY254 @ SY255 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(734,plain,
! [SV97: $i] :
( ( ! [SY258: $i] :
( ~ ~ ( subset @ SV97 @ SY258 )
| ( SV97 != SY258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(735,plain,
! [SV98: $i > $o] :
( ( ~ ~ ! [SY259: $i] :
~ ~ ( ~ ( SV98 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV98 @ SY260 )
| ( SY259 = SY260 ) ) )
| ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(736,plain,
! [SV99: $i] :
( ( ! [SY263: $i,SY264: $i > $i] :
( ~ ! [SY265: $i] :
( ~ ( in @ SY265 @ SV99 )
| ( in @ ( SY264 @ SY265 ) @ SY263 ) )
| ( func @ SV99 @ SY263
@ ( dpsetconstr @ SV99 @ SY263
@ ^ [SX3: $i,SX4: $i] :
( ( SY264 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(737,plain,
! [SV100: $i] :
( ( ! [SY268: $i] : ( in @ SY268 @ ( setadjoin @ SV100 @ ( setadjoin @ SY268 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(738,plain,
! [SV101: $i] :
( ( ! [SY269: $i,SY270: $i,SY271: $i] :
( ( ( kpair @ SV101 @ SY269 )
!= ( kpair @ SY270 @ SY271 ) )
| ( SY269 = SY271 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(739,plain,
! [SV102: $i] :
( ( ! [SY272: $i,SY273: $i] :
( ~ ( in @ SY273 @ ( setadjoin @ SV102 @ ( setadjoin @ SY272 @ emptyset ) ) )
| ( SY273 = SV102 )
| ( SY273 = SY272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(740,plain,
! [SV103: $i] :
( ( ~ ( iskpair @ SV103 )
| ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
!= ( setadjoin @ SY274 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(741,plain,
! [SV104: $i] :
( ( ! [SY277: $i > $o] :
( ~ ~ ! [SY278: $i] :
~ ~ ( ~ ( in @ SY278 @ SV104 )
| ~ ~ ( SY277 @ SY278 ) )
| ~ ! [SY279: $i] :
( ~ ( in @ SY279 @ SV104 )
| ( SY277 @ SY279 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(742,plain,
! [SV105: $i] :
( ( ! [SY280: $i,SY281: $i] :
( ~ ( func @ SV105 @ SY280 @ SY281 )
| ( in @ SY281 @ ( funcSet @ SV105 @ SY280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(743,plain,
! [SV106: $i] :
( ( ! [SY282: $i > $o] :
( ~ ~ ! [SY283: $i] :
~ ~ ( ~ ( in @ SY283 @ SV106 )
| ~ ( SY282 @ SY283 ) )
| ( ( dsetconstr @ SV106
@ ^ [SX2: $i] : ( SY282 @ SX2 ) )
!= emptyset )
| $false ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(744,plain,
! [SV107: $i] :
( ( ! [SY285: $i,SY286: $i] :
( ~ ( subset @ SY286 @ ( cartprod @ SV107 @ SY285 ) )
| ! [SY287: $i] :
( ~ ( subset @ SY287 @ ( cartprod @ SV107 @ SY285 ) )
| ~ ! [SY288: $i] :
( ~ ( in @ SY288 @ SV107 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY285 )
| ~ ( in @ ( kpair @ SY288 @ SX5 ) @ SY286 )
| ( in @ ( kpair @ SY288 @ SX5 ) @ SY287 ) ) )
| ( subset @ SY286 @ SY287 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(745,plain,
! [SV108: $i] :
( ( ! [SY290: $i] :
( ~ ( in @ SV108 @ ( setadjoin @ SY290 @ emptyset ) )
| ( SV108 = SY290 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(746,plain,
! [SV109: $i > $o] :
( ( ! [SY291: $i] :
( ~ ( in @ SY291 @ emptyset )
| ( SV109 @ SY291 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(747,plain,
! [SV110: $i] :
( ( ! [SY292: $i,SY293: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV110 @ SY292
@ ^ [SX3: $i,SX4: $i] : ( SY293 @ SX3 @ SX4 ) )
@ ( cartprod @ SV110 @ SY292 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(748,plain,
! [SV111: $i] :
( ( ! [SY296: $i,SY297: $i] :
( ~ ( in @ SY297 @ SV111 )
| ~ ( in @ SY297 @ SY296 )
| ~ ( in @ SY297 @ ( symdiff @ SV111 @ SY296 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(749,plain,
! [SV112: $i] :
( ( ! [SY298: $i,SY299: $i] :
( ~ ( func @ SV112 @ SY298 @ SY299 )
| ! [SY300: $i] :
( ~ ( in @ SY300 @ SV112 )
| ( in
@ ( setunion
@ ( dsetconstr @ SY298
@ ^ [SX4: $i] : ( in @ ( kpair @ SY300 @ SX4 ) @ SY299 ) ) )
@ SY298 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(750,plain,
! [SV113: $i > $o] :
( ( ~ ~ ! [SY302: $i] :
~ ( SV113 @ SY302 )
| ~ ! [SY303: $i,SY304: $i] :
( ~ ( SV113 @ SY303 )
| ~ ( SV113 @ SY304 )
| ( SY303 = SY304 ) )
| ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(751,plain,
! [SV114: $i] :
( ( ! [SY307: $i] : ( in @ SY307 @ ( setadjoin @ SV114 @ ( setadjoin @ SY307 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(752,plain,
! [SV115: $i] :
( ( ! [SY308: $i,SY309: $i,SY310: $i] :
( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SY308 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY309 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY309 @ ( setadjoin @ SY310 @ emptyset ) ) @ emptyset ) ) )
| ( SY309 != SY310 )
| ( SY308 = SY310 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(753,plain,
! [SV116: $i] :
( ( ! [SY311: $i] :
( ~ ( in @ SY311 @ ( setunion @ SV116 ) )
| ! [SY312: $o] :
( ~ ! [SY313: $i] :
( ~ ( in @ SY311 @ SY313 )
| ~ ( in @ SY313 @ SV116 )
| SY312 )
| SY312 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(754,plain,
! [SV117: $i] :
( ( ! [SY314: $i] :
( ~ ! [SY315: $i] :
( ~ ( in @ SY315 @ SV117 )
| ( in @ SY315 @ SY314 ) )
| ( subset @ SV117 @ SY314 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(755,plain,
! [SV118: $i] :
( ( ! [SY316: $i,SY317: $i] :
( ~ ( subset @ SV118 @ SY316 )
| ~ ~ ( in @ SY317 @ SY316 )
| ~ ( in @ SY317 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(756,plain,
! [SV119: $i] :
( ( ! [SY318: $i] :
( ( ( binintersect @ SV119 @ SY318 )
!= SV119 )
| ( subset @ SV119 @ SY318 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(757,plain,
! [SV120: $i] :
( ( ! [SY319: $i] :
( ~ ( subset @ SV120 @ SY319 )
| ( ( binintersect @ SV120 @ SY319 )
= SV120 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(758,plain,
! [SV121: $i] :
( ( ! [SY320: $i,SY321: $i] :
( ~ ( in @ SY321 @ ( binunion @ SV121 @ SY320 ) )
| ( in @ SY321 @ SV121 )
| ( in @ SY321 @ SY320 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(759,plain,
! [SV122: $i] :
( ( ! [SY322: $i] :
( ~ ! [SY323: $i] :
( ~ ( in @ SY323 @ SV122 )
| ( in @ SY323 @ SY322 ) )
| ( subset @ SV122 @ SY322 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(760,plain,
! [SV123: $i] :
( ( ! [SY324: $i,SY325: $i] :
( ~ ( in @ SY325 @ SV123 )
| ~ ~ ( in @ SY325 @ SY324 )
| ( SV123 != SY324 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(761,plain,
! [SV124: $i] :
( ( in @ emptyset @ ( powerset @ SV124 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(762,plain,
! [SV125: $i] :
( ( ! [SY326: $i] :
( ~ ( subset @ SY326 @ SV125 )
| ( in @ SY326 @ ( powerset @ SV125 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(763,plain,
! [SV126: $i] :
( ( ! [SY327: $i,SY328: $i] :
( ~ ( in @ SY328 @ ( cartprod @ SV126 @ SY327 ) )
| ( in @ ( ksnd @ SY328 ) @ SY327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(764,plain,
! [SV127: $i] :
( ( ( dsetconstr @ SV127
@ ^ [SX1: $i] : $true )
= SV127 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(765,plain,
! [SV128: $i] :
( ( ! [SY330: $i] : ( in @ SV128 @ ( setadjoin @ SV128 @ ( setadjoin @ SY330 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(766,plain,
! [SV129: $i] :
( ( subset @ emptyset @ SV129 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(767,plain,
! [SV130: $i] :
( ( ! [SY331: $i] :
~ ( ~ ( ~ ( in @ SY331 @ ( powerset @ SV130 ) )
| ! [SY332: $i] :
( ~ ( in @ SY332 @ SY331 )
| ( in @ SY332 @ SV130 ) ) )
| ~ ( ~ ! [SY333: $i] :
( ~ ( in @ SY333 @ SY331 )
| ( in @ SY333 @ SV130 ) )
| ( in @ SY331 @ ( powerset @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(768,plain,
! [SV131: $i] :
( ( ! [SY334: $i] :
( ( SV131 != SY334 )
| ( ( setadjoin @ ( setadjoin @ SV131 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV131 @ ( setadjoin @ SY334 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV131 @ emptyset ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(769,plain,
! [SV132: $i] :
( ( ! [SY335: $i,SY336: $i] :
~ ( ~ ( ~ ( in @ SY336 @ ( setadjoin @ SV132 @ SY335 ) )
| ( SY336 = SV132 )
| ( in @ SY336 @ SY335 ) )
| ~ ( ~ ( ( SY336 = SV132 )
| ( in @ SY336 @ SY335 ) )
| ( in @ SY336 @ ( setadjoin @ SV132 @ SY335 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(770,plain,
! [SV133: $i] :
( ( ! [SY337: $i,SY338: $i] :
( ~ ( in @ SY338 @ SV133 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY337 )
| ( ( kfst @ ( kpair @ SY338 @ SX3 ) )
= SY338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(771,plain,
! [SV134: $i > $i > $o] :
( ( ! [SY340: $i] :
( ~ ! [SY341: $i] :
( ~ ( in @ SY341 @ SY340 )
| ~ ! [SY342: $i] :
~ ~ ( ~ ( SV134 @ SY341 @ SY342 )
| ~ ! [SY343: $i] :
( ~ ( SV134 @ SY341 @ SY343 )
| ( SY342 = SY343 ) ) ) )
| ~ ! [SY344: $i] :
~ ! [SY345: $i] :
~ ( ~ ( ~ ( in @ SY345 @ SY344 )
| ~ ! [SY346: $i] :
~ ~ ( ~ ( in @ SY346 @ SY340 )
| ~ ( SV134 @ SY346 @ SY345 ) ) )
| ~ ( ~ ~ ! [SY347: $i] :
~ ~ ( ~ ( in @ SY347 @ SY340 )
| ~ ( SV134 @ SY347 @ SY345 ) )
| ( in @ SY345 @ SY344 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(772,plain,
! [SV135: $o] :
( ( ! [SY348: $i] :
( ~ ( in @ SY348 @ ( prop2set @ SV135 ) )
| SV135 ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[563]) ).
thf(773,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[563]) ).
thf(774,plain,
( ( ! [SX0: $i] :
( ~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[563]) ).
thf(775,plain,
! [SV136: $i] :
( ( ! [SY349: $i > $o,SY350: $i] :
( ~ ( in @ SY350 @ SV136 )
| ~ ( ~ ( ~ ( in @ SY350
@ ( dsetconstr @ SV136
@ ^ [SX3: $i] : ( SY349 @ SX3 ) ) )
| ( SY349 @ SY350 ) )
| ~ ( ~ ( SY349 @ SY350 )
| ( in @ SY350
@ ( dsetconstr @ SV136
@ ^ [SX3: $i] : ( SY349 @ SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(776,plain,
! [SV137: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV137 @ emptyset ) ) @ SV137 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(777,plain,
! [SV138: $i] :
( ( ! [SY353: $i] :
( ~ ( in @ SY353 @ SV138 )
| ( in @ ( setadjoin @ SY353 @ emptyset ) @ ( powerset @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(778,plain,
! [SV139: $i] :
( ( ! [SY354: $i] :
( ~ ( subset @ SV139 @ SY354 )
| ( ( setminus @ SV139 @ SY354 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(779,plain,
! [SV140: $o] :
( ( ~ SV140
| ( set2prop @ ( prop2set @ SV140 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[569]) ).
thf(780,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[569]) ).
thf(781,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[569]) ).
thf(782,plain,
! [SV141: $i] :
( ( ! [SY355: $i > $o] :
( ~ ! [SY356: $i] :
( ~ ( in @ SY356 @ SV141 )
| ! [SY357: $i] :
( ~ ( in @ SY357 @ SV141 )
| ~ ( SY355 @ SY356 )
| ~ ( SY355 @ SY357 )
| ( SY356 = SY357 ) ) )
| ~ ~ ! [SY358: $i] :
~ ~ ( ~ ( in @ SY358 @ SV141 )
| ~ ( SY355 @ SY358 ) )
| ~ ! [SY359: $i] :
~ ~ ( ~ ( in @ SY359
@ ( dsetconstr @ SV141
@ ^ [SX3: $i] : ( SY355 @ SX3 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SX3: $i] : ( SY355 @ SX3 ) )
!= ( setadjoin @ SY359 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[570]) ).
thf(783,plain,
! [SV142: $i] :
( ( ! [SY362: $i,SY363: $i] :
( ~ ( subset @ SY363 @ ( cartprod @ SV142 @ SY362 ) )
| ! [SY364: $i] :
( ~ ( subset @ SY364 @ ( cartprod @ SV142 @ SY362 ) )
| ~ ! [SY365: $i] :
( ~ ( in @ SY365 @ SV142 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY362 )
| ~ ( in @ ( kpair @ SY365 @ SX5 ) @ SY363 )
| ( in @ ( kpair @ SY365 @ SX5 ) @ SY364 ) ) )
| ~ ! [SY367: $i] :
( ~ ( in @ SY367 @ SV142 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY362 )
| ~ ( in @ ( kpair @ SY367 @ SX5 ) @ SY364 )
| ( in @ ( kpair @ SY367 @ SX5 ) @ SY363 ) ) )
| ( SY363 = SY364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(784,plain,
! [SV143: $i] :
( ( ! [SY369: $i] : ( in @ SY369 @ ( setadjoin @ SV143 @ ( setadjoin @ SY369 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(785,plain,
! [SV144: $i] :
( ( ! [SY370: $i,SY371: $i] :
( ~ ( in @ SY371 @ SV144 )
| ! [SY372: $i] :
( ~ ( in @ SY372 @ SY370 )
| ( in @ ( kpair @ SY371 @ SY372 ) @ ( cartprod @ SV144 @ SY370 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[573]) ).
thf(786,plain,
! [SV145: $i] :
( ( ~ ( iskpair @ SV145 )
| ( ( kpair @ ( kfst @ SV145 ) @ ( ksnd @ SV145 ) )
= SV145 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(787,plain,
! [SV146: $i] :
( ( ! [SY373: $i] :
( ~ ( subset @ SV146 @ SY373 )
| ~ ( subset @ SY373 @ SV146 )
| ( SV146 = SY373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(788,plain,
! [SV147: $i] :
( ( ! [SY374: $i > $o] :
( ~ ~ ! [SY375: $i] :
( ~ ( in @ SY375 @ SV147 )
| ( SY374 @ SY375 ) )
| ~ ! [SY376: $i] :
~ ~ ( ~ ( in @ SY376 @ SV147 )
| ~ ~ ( SY374 @ SY376 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(789,plain,
! [SV148: $i] :
( ( ! [SY377: $i] : ( subset @ ( binintersect @ SV148 @ SY377 ) @ SY377 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(790,plain,
! [SV149: $i] :
( ( ! [SY378: $i,SY379: $i] :
( ~ ~ ( in @ SY379 @ SV149 )
| ~ ( in @ SY379 @ SY378 )
| ( in @ SY379 @ ( symdiff @ SV149 @ SY378 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(791,plain,
! [SV150: $i] :
( ( ! [SY380: $i] : ( subset @ ( binintersect @ SV150 @ SY380 ) @ SV150 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[579]) ).
thf(792,plain,
! [SV151: $i] :
( ( ~ ( ( SV151 != emptyset ) )
| ~ ! [SY381: $i] :
~ ( in @ SY381 @ SV151 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(793,plain,
! [SV152: $i] :
( ( in @ emptyset @ ( powerset @ SV152 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(794,plain,
! [SV153: $i] :
( ( ~ ( in @ SV153 @ omega )
| ( in @ ( setadjoin @ SV153 @ SV153 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(795,plain,
! [SV154: $i] :
( ( ! [SY382: $i > $o] :
( ~ ~ ! [SY383: $i] :
~ ~ ( ~ ( in @ SY383
@ ( dsetconstr @ SV154
@ ^ [SX3: $i] : ( SY382 @ SX3 ) ) )
| ( ( dsetconstr @ SV154
@ ^ [SX3: $i] : ( SY382 @ SX3 ) )
!= ( setadjoin @ SY383 @ emptyset ) ) )
| ! [SY386: $i] :
( ~ ( in @ SY386 @ SV154 )
| ! [SY387: $i] :
( ~ ( in @ SY387 @ SV154 )
| ~ ( SY382 @ SY386 )
| ~ ( SY382 @ SY387 )
| ( SY386 = SY387 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(796,plain,
! [SV155: $i] :
( ( ! [SY388: $i,SY389: $i] :
( ~ ( in @ SY389 @ ( cartprod @ SV155 @ SY388 ) )
| ~ ! [SY390: $i] :
~ ~ ( ~ ( in @ SY390 @ SV155 )
| ~ ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4 @ SY388 )
| ( SY389
!= ( kpair @ SY390 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(797,plain,
! [SV156: $i] :
( ( ! [SY392: $i,SY393: $i] :
( ~ ~ ( in @ SY393 @ SV156 )
| ~ ~ ( in @ SY393 @ SY392 )
| ~ ( in @ SY393 @ ( symdiff @ SV156 @ SY392 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[585]) ).
thf(798,plain,
! [SV157: $i] :
( ( ! [SY394: $i > $o] :
( ~ ~ ~ ! [SY395: $i] :
~ ~ ( ~ ( in @ SY395 @ SV157 )
| ~ ( SY394 @ SY395 ) )
| ! [SY396: $i] :
( ~ ( in @ SY396 @ SV157 )
| ~ ( SY394 @ SY396 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(799,plain,
! [SV158: $i] :
( ( ! [SY397: $i,SY398: $i] :
( ~ ( in @ SY398 @ SV158 )
| ! [SY399: $i] :
( ~ ( in @ SY399 @ SY397 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY398 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY398 @ ( setadjoin @ SY399 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV158 @ SY397 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(800,plain,
! [SV159: $i] :
( ( ! [SY400: $i] :
( ( SV159 != SY400 )
| ! [SY401: $i,SY402: $i] :
( ( SY401 != SY402 )
| ( ( setadjoin @ SV159 @ SY401 )
= ( setadjoin @ SY400 @ SY402 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(801,plain,
! [SV160: $i] :
( ( ! [SY403: $i] :
( ~ ( in @ SY403 @ SV160 )
| ( subset @ ( setadjoin @ SY403 @ emptyset ) @ SV160 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(802,plain,
! [SV161: $i] :
( ( ! [SY404: $i,SY405: $i] :
( ~ ( in @ SY405 @ ( funcSet @ SV161 @ SY404 ) )
| ! [SY406: $i] :
( ~ ( in @ SY406 @ SV161 )
| ( in @ ( kpair @ SY406 @ ( ap @ SV161 @ SY404 @ SY405 @ SY406 ) ) @ SY405 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(803,plain,
! [SV162: $i] :
( ( ! [SY407: $i,SY408: $i] :
( ~ ( in @ SY408 @ ( funcSet @ SV162 @ SY407 ) )
| ! [SY409: $i] :
( ~ ( in @ SY409 @ ( funcSet @ SV162 @ SY407 ) )
| ~ ! [SY410: $i] :
( ~ ( in @ SY410 @ SV162 )
| ( ( ap @ SV162 @ SY407 @ SY408 @ SY410 )
= ( ap @ SV162 @ SY407 @ SY409 @ SY410 ) ) )
| ( SY408 = SY409 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(804,plain,
! [SV163: $i] :
( ( ! [SY411: $i,SY412: $i] :
( ~ ( subset @ SY412 @ SV163 )
| ~ ( subset @ SY412 @ SY411 )
| ( subset @ SY412 @ ( binintersect @ SV163 @ SY411 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[592]) ).
thf(805,plain,
! [SV164: $i] :
( ( ! [SY413: $i] :
( ( SV164 != SY413 )
| ! [SY414: $i,SY415: $i] :
( ( SY414 != SY415 )
| ~ ( ~ ( ~ ( in @ SY414 @ SV164 )
| ( in @ SY415 @ SY413 ) )
| ~ ( ~ ( in @ SY415 @ SY413 )
| ( in @ SY414 @ SV164 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[593]) ).
thf(806,plain,
! [SV165: $i] :
( ( ! [SY416: $i] :
( ~ ( in @ SY416 @ ( powerset @ SV165 ) )
| ( subset @ SY416 @ SV165 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[594]) ).
thf(807,plain,
! [SV166: $i] :
( ( ! [SY417: $i] :
( ( ksnd @ ( kpair @ SV166 @ SY417 ) )
= SY417 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[595]) ).
thf(808,plain,
! [SV167: $i] :
( ( ! [SY418: $i,SY419: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV167 @ SY418
@ ^ [SX3: $i,SX4: $i] : ( SY419 @ SX3 @ SX4 ) )
@ ( cartprod @ SV167 @ SY418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[596]) ).
thf(809,plain,
! [SV168: $i] :
( ( ! [SY422: $i > $o] :
( ~ ~ ! [SY423: $i] :
( ~ ( in @ SY423 @ SV168 )
| ( SY422 @ SY423 ) )
| ~ ! [SY424: $i] :
~ ~ ( ~ ( in @ SY424 @ SV168 )
| ~ ~ ( SY422 @ SY424 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[597]) ).
thf(810,plain,
! [SV169: $i] :
( ( ! [SY425: $i] : ( in @ SV169 @ ( setadjoin @ SV169 @ SY425 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(811,plain,
! [SV170: $i] :
( ( ! [SY426: $i] :
( ~ ( subset @ SV170 @ SY426 )
| ( in @ SV170 @ ( powerset @ SY426 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(812,plain,
! [SV171: $i] :
( ( ! [SY427: $i] : ( in @ SY427 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV171 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV171 @ ( setadjoin @ SY427 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(813,plain,
! [SV172: $i] :
( ( ! [SY428: $i] :
( ~ ! [SY429: $i] :
( ~ ( in @ SY429 @ SY428 )
| ( in @ SY429 @ SV172 ) )
| ( in @ SY428 @ ( powerset @ SV172 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(814,plain,
! [SV173: $i] :
( ( ! [SY430: $i] :
( ( kfst @ ( kpair @ SV173 @ SY430 ) )
= SV173 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(815,plain,
! [SV174: $i] :
( ( ~ ~ ( ~ ( in @ emptyset @ SV174 )
| ~ ! [SY431: $i] :
( ~ ~ ( ~ ( in @ SY431 @ omega )
| ~ ( in @ SY431 @ SV174 ) )
| ( in @ ( setadjoin @ SY431 @ SY431 ) @ SV174 ) ) )
| ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(816,plain,
! [SV175: $i] :
( ( ~ ( in @ SV175 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(817,plain,
! [SV176: $i] :
( ( ~ ( ( SV176 != emptyset ) )
| ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ SY433 @ SV176 )
| ~ $true ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(818,plain,
! [SV177: $i] :
( ( ! [SY434: $i] :
( ( SV177 != SY434 )
| ( ( setunion @ SV177 )
= ( setunion @ SY434 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(819,plain,
! [SV178: $i] :
( ( ! [SY435: $i] :
( ~ ( subset @ SV178 @ SY435 )
| ( subset @ ( powerset @ SV178 ) @ ( powerset @ SY435 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[607]) ).
thf(820,plain,
! [SV179: $i] :
( ( ! [SY436: $i,SY437: $i] :
( ~ ( in @ SY437 @ SV179 )
| ~ ~ ( in @ SY437 @ SY436 )
| ( in @ SY437 @ ( symdiff @ SV179 @ SY436 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(821,plain,
! [SV180: $i] :
( ( ~ ( iskpair @ SV180 )
| ~ ! [SY438: $i] :
~ ~ ( ~ ( in @ SY438
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) )
| ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
!= ( setadjoin @ SY438 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(822,plain,
! [SV181: $i] :
( ( ! [SY441: $i] :
( ( ( binintersect @ SV181 @ SY441 )
!= SY441 )
| ( subset @ SY441 @ SV181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(823,plain,
! [SV182: $i] :
( ( ! [SY442: $i,SY443: $i] :
( ~ ( subset @ SY443 @ ( cartprod @ SV182 @ SY442 ) )
| ! [SY444: $i > $o] :
( ~ ! [SY445: $i] :
( ~ ( in @ SY445 @ SV182 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY442 )
| ~ ( in @ ( kpair @ SY445 @ SX5 ) @ SY443 )
| ( SY444 @ ( kpair @ SY445 @ SX5 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY443 )
| ( SY444 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[611]) ).
thf(824,plain,
! [SV183: $i] :
( ( ! [SY448: $i] :
( ( SV183 != SY448 )
| ! [SY449: $i > $o,SY450: $i > $o] :
( ~ ! [SY451: $i] :
( ~ ( in @ SY451 @ SV183 )
| ! [SX5: $i] :
( ~ ( in @ SX5 @ SY448 )
| ( SY451 != SX5 )
| ~ ( ~ ( ~ ( SY449 @ SY451 )
| ( SY450 @ SX5 ) )
| ~ ( ~ ( SY450 @ SX5 )
| ( SY449 @ SY451 ) ) ) ) )
| ( ( dsetconstr @ SV183
@ ^ [SX4: $i] : ( SY449 @ SX4 ) )
= ( dsetconstr @ SY448
@ ^ [SX4: $i] : ( SY450 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[612]) ).
thf(825,plain,
! [SV184: $i] :
( ( ! [SY455: $i,SY456: $i] :
( ~ ( in @ SY456 @ ( setadjoin @ SV184 @ SY455 ) )
| ( SY456 = SV184 )
| ( in @ SY456 @ SY455 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[613]) ).
thf(826,plain,
! [SV185: $i] :
( ( ! [SY457: $i,SY458: $i] :
( ~ ( in @ SY458 @ ( setadjoin @ SV185 @ SY457 ) )
| ! [SY459: $o] :
( ~ ( ( SY458 != SV185 )
| SY459 )
| ~ ( ~ ( in @ SY458 @ SY457 )
| SY459 )
| SY459 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(827,plain,
! [SV186: $i] :
( ( ! [SY460: $i > $o] :
( subset
@ ( dsetconstr @ SV186
@ ^ [SX2: $i] : ( SY460 @ SX2 ) )
@ SV186 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(828,plain,
! [SV187: $i] :
( ( ! [SY462: $i] :
( ( ( setminus @ SV187 @ SY462 )
!= emptyset )
| ( subset @ SV187 @ SY462 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(829,plain,
! [SV188: $i > $o] :
( ( ! [SY463: $i > $o] :
( ~ ! [SY464: $i,SY465: $i] :
( ( SY464 != SY465 )
| ~ ( ~ ( ~ ( SV188 @ SY464 )
| ( SY463 @ SY465 ) )
| ~ ( ~ ( SY463 @ SY465 )
| ( SV188 @ SY464 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SX2: $i] :
~ ~ ( ~ ( SY463 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY463 @ SX3 )
| ( SX2 = SX3 ) ) ) )
| ~ ( ~ ~ ! [SX2: $i] :
~ ~ ( ~ ( SY463 @ SX2 )
| ~ ! [SX3: $i] :
( ~ ( SY463 @ SX3 )
| ( SX2 = SX3 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[617]) ).
thf(830,plain,
! [SV189: $i] :
( ( ! [SY474: $i,SY475: $i] :
( ~ ( in @ SY475 @ SV189 )
| ! [SY476: $i] :
( ~ ( in @ SY476 @ SY474 )
| ( in @ ( setadjoin @ ( setadjoin @ SY475 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY475 @ ( setadjoin @ SY476 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV189 @ SY474 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(831,plain,
! [SV190: $i] :
( ( ! [SY477: $i] :
( ~ ( in @ SV190 @ ( setadjoin @ SY477 @ emptyset ) )
| ( in @ SY477 @ ( setadjoin @ SV190 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[619]) ).
thf(832,plain,
! [SV191: $i] :
( ( ! [SY478: $i,SY479: $i,SY480: $i] :
( ~ ( in @ ( kpair @ SY479 @ SY480 ) @ ( cartprod @ SV191 @ SY478 ) )
| ( in @ SY480 @ SY478 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[620]) ).
thf(833,plain,
! [SV192: $i] :
( ( ! [SY481: $i,SY482: $i > $i > $o,SY483: $i,SY484: $i] :
( ~ ( in @ ( kpair @ SY483 @ SY484 )
@ ( dpsetconstr @ SV192 @ SY481
@ ^ [SX5: $i,SX6: $i] : ( SY482 @ SX5 @ SX6 ) ) )
| ( in @ SY484 @ SY481 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[621]) ).
thf(834,plain,
! [SV193: $i] :
( ( ! [SY487: $i,SY488: $i] :
( ~ ( in @ SY488 @ ( funcSet @ SV193 @ SY487 ) )
| ! [SY489: $i] :
( ~ ( in @ SY489 @ SV193 )
| ( in @ ( ap @ SV193 @ SY487 @ SY488 @ SY489 ) @ SY487 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[622]) ).
thf(835,plain,
! [SV194: $i] :
( ( ! [SY490: $i,SY491: $i > $i > $o,SY492: $i] :
( ~ ( in @ SY492 @ SV194 )
| ! [SY493: $i] :
( ~ ( in @ SY493 @ SY490 )
| ~ ( SY491 @ SY492 @ SY493 )
| ( in @ ( kpair @ SY492 @ SY493 )
@ ( dpsetconstr @ SV194 @ SY490
@ ^ [SX5: $i,SX6: $i] : ( SY491 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[623]) ).
thf(836,plain,
! [SV195: $i > $o] :
( ( ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( SV195 @ SY496 )
| ~ ! [SY497: $i] :
( ~ ( SV195 @ SY497 )
| ( SY496 = SY497 ) ) )
| ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(837,plain,
! [SV196: $i] :
( ( ! [SY499: $i,SY500: $i] :
( ~ ( in @ SY500 @ ( setminus @ SV196 @ SY499 ) )
| ( in @ SY500 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[625]) ).
thf(838,plain,
! [SV197: $i] :
( ( ! [SY501: $i,SY502: $i] :
( ~ ( in @ SY502 @ SV197 )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY501 )
| ( ( kpair @ SY502 @ SX3 )
= ( kpair @ SY502 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[626]) ).
thf(839,plain,
! [SV198: $i] :
( ( ! [SY504: $i,SY505: $i] :
( ~ ( func @ SV198 @ SY504 @ SY505 )
| ! [SY506: $i] :
( ~ ( in @ SY506 @ SV198 )
| ~ ! [SX4: $i] :
~ ~ ( ~ ( in @ SX4
@ ( dsetconstr @ SY504
@ ^ [SX5: $i] : ( in @ ( kpair @ SY506 @ SX5 ) @ SY505 ) ) )
| ( ( dsetconstr @ SY504
@ ^ [SX5: $i] : ( in @ ( kpair @ SY506 @ SX5 ) @ SY505 ) )
!= ( setadjoin @ SX4 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[627]) ).
thf(840,plain,
! [SV199: $i] :
( ( ! [SY510: $i,SY511: $i] :
( ~ ( in @ SY510 @ SY511 )
| ~ ( in @ SY511 @ SV199 )
| ( in @ SY510 @ ( setunion @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(841,plain,
! [SV200: $i] :
( ( ! [SY512: $i,SY513: $i] :
( ~ ( func @ SV200 @ SY512 @ SY513 )
| ! [SY514: $i] :
( ~ ( in @ SY514 @ SV200 )
| ! [SY515: $i] :
( ~ ( in @ SY515 @ SY512 )
| ~ ( in @ ( kpair @ SY514 @ SY515 ) @ SY513 )
| ( ( ap @ SV200 @ SY512 @ SY513 @ SY514 )
= SY515 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(842,plain,
! [SV201: $i] :
( ( subset @ SV201 @ ( setunion @ ( setadjoin @ SV201 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(843,plain,
! [SV202: $i] :
( ( ! [SY516: $i,SY517: $i] :
( ~ ( in @ SY517 @ ( funcSet @ SV202 @ SY516 ) )
| ! [SY518: $i] :
( ~ ( in @ SY518 @ SV202 )
| ! [SY519: $i] :
( ~ ( in @ SY519 @ SY516 )
| ~ ( in @ ( kpair @ SY518 @ SY519 ) @ SY517 )
| ( ( ap @ SV202 @ SY516 @ SY517 @ SY518 )
= SY519 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[631]) ).
thf(844,plain,
! [SV203: $i] :
( ( ! [SY520: $i] :
( ( SV203 != SY520 )
| ( ( powerset @ SV203 )
= ( powerset @ SY520 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[632]) ).
thf(845,plain,
! [SV204: $i] :
( ( ! [SY521: $i,SY522: $i] :
( ~ ~ ( in @ SY522 @ ( setminus @ SV204 @ SY521 ) )
| ~ ( in @ SY522 @ SV204 )
| ( in @ SY522 @ SY521 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(846,plain,
! [SV205: $i] :
( ( ! [SY523: $i,SY524: $i] :
( ~ ( in @ SY523 @ ( powerset @ SV205 ) )
| ~ ( in @ SY524 @ SY523 )
| ( in @ SY524 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[634]) ).
thf(847,plain,
! [SV206: $i,SV1: $i] :
( ( ! [SY525: $i > $i > $o,SY526: $i,SY527: $i] :
( ~ ( in @ ( kpair @ SY526 @ SY527 )
@ ( dpsetconstr @ SV1 @ SV206
@ ^ [SX5: $i,SX6: $i] : ( SY525 @ SX5 @ SX6 ) ) )
| ( in @ SY526 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[635]) ).
thf(848,plain,
! [SV2: $i,SV207: $i] :
( ( subset @ SV207 @ ( setadjoin @ SV2 @ SV207 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(849,plain,
! [SV3: $i] :
( ( ( ~ ~ ! [SY11: $i] :
~ ~ ( ~ ( in @ SY11 @ SV3 )
| ( SV3
!= ( setadjoin @ SY11 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[637]) ).
thf(850,plain,
! [SV208: $i,SV4: $i] :
( ( iskpair @ ( kpair @ SV4 @ SV208 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(851,plain,
! [SV209: $i,SV5: $i] :
( ( in @ SV5 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV5 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV5 @ ( setadjoin @ SV209 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[639]) ).
thf(852,plain,
! [SV210: $i,SV6: $i] :
( ( ! [SY530: $i] :
( ~ ( in @ SY530 @ ( funcSet @ SV6 @ SV210 ) )
| ( func @ SV6 @ SV210 @ SY530 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[640]) ).
thf(853,plain,
! [SV211: $i > $o,SV7: $i] :
( ( in
@ ( dsetconstr @ SV7
@ ^ [SY531: $i] : ( SV211 @ SY531 ) )
@ ( powerset @ SV7 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(854,plain,
! [SV212: $i,SV8: $i] :
( ( ! [SY532: $i,SY533: $i] :
( ~ ( in @ ( kpair @ SY532 @ SY533 ) @ ( cartprod @ SV8 @ SV212 ) )
| ( in @ SY532 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(855,plain,
! [SV213: $i,SV9: $i] :
( ( ! [SY534: $i] :
( ~ ( in @ ( setadjoin @ SY534 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) ) )
| ( SV9 = SY534 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[643]) ).
thf(856,plain,
! [SV10: $i > $o] :
( ( ( ~ ~ ! [SY23: $i] :
~ ~ ( ~ ( SV10 @ SY23 )
| ~ ! [SY24: $i] :
( ~ ( SV10 @ SY24 )
| ( SY23 = SY24 ) ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(857,plain,
! [SV214: $i,SV11: $i] :
( ( ! [SY535: $i] :
( ~ ( in @ SY535 @ SV11 )
| ! [SY536: $i] :
( ~ ( in @ SY536 @ SV214 )
| ( subset @ ( setadjoin @ SY535 @ ( setadjoin @ SY536 @ emptyset ) ) @ ( binunion @ SV11 @ SV214 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(858,plain,
! [SV215: $i,SV12: $i] :
( ( ~ ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV12 )
| ~ ( in @ SY537 @ SV215 ) )
| ( ( binintersect @ SV12 @ SV215 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(859,plain,
! [SV216: $i,SV13: $i] :
( ( ! [SY538: $i,SY539: $i] :
( ( ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY538 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY538 @ ( setadjoin @ SY539 @ emptyset ) ) @ emptyset ) ) )
| ( SV13 = SY538 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[647]) ).
thf(860,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ~ ! [SY540: $i] :
( ~ ( in @ SY540 @ SV14 )
| ! [SY541: $i] :
( ~ ( in @ SY541 @ SV14 )
| ~ ( SV217 @ SY540 )
| ~ ( SV217 @ SY541 )
| ( SY540 = SY541 ) ) )
| ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(861,plain,
! [SV218: $i,SV15: $i] :
( ( ! [SY546: $i] :
( ( ( setadjoin @ SV15 @ ( setadjoin @ SV218 @ emptyset ) )
!= ( setadjoin @ SY546 @ emptyset ) )
| ( SV15 = SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(862,plain,
! [SV219: $i,SV16: $i] :
( ( ! [SY547: $i] :
( ~ ( in @ SY547 @ SV16 )
| ! [SY548: $i] :
( ~ ( in @ SY548 @ SV219 )
| ( in @ ( kpair @ SY547 @ SY548 ) @ ( powerset @ ( powerset @ ( binunion @ SV16 @ SV219 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[650]) ).
thf(863,plain,
! [SV17: $i] :
( ( ( ~ ( in @ SV17 @ emptyset ) )
= $true )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[651]) ).
thf(864,plain,
! [SV220: $i,SV18: $i] :
( ( ! [SY549: $i] :
( ~ ~ ( in @ SY549 @ SV18 )
| ~ ( in @ SY549 @ ( setminus @ SV18 @ SV220 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[652]) ).
thf(865,plain,
! [SV221: $i > $o,SV19: $i] :
( ( ! [SY550: $i] :
( ~ ( in @ SY550
@ ( dsetconstr @ SV19
@ ^ [SY551: $i] : ( SV221 @ SY551 ) ) )
| ( in @ SY550 @ SV19 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[653]) ).
thf(866,plain,
! [SV20: $i,SV222: $i] :
( ( ~ ( in @ SV222 @ SV20 )
| ( in @ SV222 @ ( powerset @ ( setunion @ SV20 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[654]) ).
thf(867,plain,
! [SV21: $i] :
( ( ( ~ ! [SY54: $i] :
~ ( in @ SY54 @ SV21 ) )
= $true )
| ( ( SV21 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[655]) ).
thf(868,plain,
! [SV223: $i,SV22: $i] :
( ( ! [SY552: $i] :
( ~ ( func @ SV22 @ SV223 @ SY552 )
| ! [SY553: $i] :
( ~ ( in @ SY553 @ SV22 )
| ( in @ ( kpair @ SY553 @ ( ap @ SV22 @ SV223 @ SY552 @ SY553 ) ) @ SY552 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[656]) ).
thf(869,plain,
! [SV224: $i > $o,SV23: $i] :
( ( ! [SY554: $i] :
( ~ ( in @ SY554 @ SV23 )
| ~ ( SV224 @ SY554 )
| ~ ! [SY555: $i] :
( ~ ( in @ SY555 @ SV23 )
| ~ ( SV224 @ SY555 )
| ( SY555 = SY554 ) )
| ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(870,plain,
! [SV225: $i,SV24: $i] :
( ( ! [SY559: $i,SY560: $o] :
( ~ ( in @ SY559 @ ( binunion @ SV24 @ SV225 ) )
| ~ ( ~ ( in @ SY559 @ SV24 )
| SY560 )
| ~ ( ~ ( in @ SY559 @ SV225 )
| SY560 )
| SY560 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(871,plain,
! [SV226: $i,SV25: $i] :
( ( ! [SY561: $i] :
( ~ ( in @ SY561 @ ( setminus @ SV25 @ SV226 ) )
| ~ ( in @ SY561 @ SV226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[659]) ).
thf(872,plain,
! [SV227: $i,SV26: $i] :
( ( ! [SY562: $i] :
( ~ ( in @ SY562 @ ( binintersect @ SV26 @ SV227 ) )
| ( in @ SY562 @ SV26 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(873,plain,
! [SV228: $i,SV27: $i] :
( ( ( SV27 != SV228 )
| ( subset @ SV228 @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(874,plain,
! [SV229: $i,SV28: $i] :
( ( ! [SY563: $i] :
( ~ ( in @ SY563 @ ( binintersect @ SV28 @ SV229 ) )
| ( in @ SY563 @ SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[662]) ).
thf(875,plain,
! [SV230: $i,SV29: $i] :
( ( ! [SY564: $i] :
( ~ ( func @ SV29 @ SV230 @ SY564 )
| ! [SY565: $i] :
( ~ ( func @ SV29 @ SV230 @ SY565 )
| ~ ! [SY566: $i] :
( ~ ( in @ SY566 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SY564 @ SY566 )
= ( ap @ SV29 @ SV230 @ SY565 @ SY566 ) ) )
| ! [SY567: $i] :
( ~ ( in @ SY567 @ SV29 )
| ! [SY568: $i] :
( ~ ( in @ SY568 @ SV230 )
| ~ ( in @ ( kpair @ SY567 @ SY568 ) @ SY565 )
| ( in @ ( kpair @ SY567 @ SY568 ) @ SY564 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(876,plain,
! [SV30: $i,SV231: $i] :
( ( ! [SY569: $i] :
( ~ ( in @ SY569 @ SV231 )
| ~ ( in @ SY569 @ ( setminus @ SV30 @ SV231 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(877,plain,
! [SV232: $i,SV31: $i] :
( ( ( SV31 != SV232 )
| ! [SY570: $i,SY571: $i] :
( ( SY570 != SY571 )
| ~ ( in @ SY570 @ SV31 )
| ( in @ SY571 @ SV232 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(878,plain,
! [SV32: $i,SV233: $i] :
( ( ! [SY572: $i] :
( ~ ( in @ SY572 @ SV233 )
| ( in @ SY572 @ ( setadjoin @ SV32 @ SV233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[666]) ).
thf(879,plain,
! [SV33: $i > $o] :
( ( ( ~ ~ ! [SY87: $i] :
~ ~ ( ~ ( SV33 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( SV33 @ SY88 )
| ( SY87 = SY88 ) ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[667]) ).
thf(880,plain,
! [SV234: $i,SV34: $i] :
( ( ! [SY573: $i] :
( ~ ( subset @ SV34 @ SV234 )
| ~ ( subset @ SV234 @ SY573 )
| ( subset @ SV34 @ SY573 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(881,plain,
! [SV235: $i > $o,SV35: $i] :
( ( ! [SY574: $i] :
( ~ ( in @ SY574 @ SV35 )
| ~ ( SV235 @ SY574 )
| ( in @ SY574
@ ( dsetconstr @ SV35
@ ^ [SY575: $i] : ( SV235 @ SY575 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[669]) ).
thf(882,plain,
! [SV236: $i,SV36: $i] :
( ( ! [SY576: $i > $i > $o,SY577: $i,SY578: $i] :
( ~ ( in @ ( kpair @ SY577 @ SY578 )
@ ( dpsetconstr @ SV36 @ SV236
@ ^ [SX5: $i,SX6: $i] : ( SY576 @ SX5 @ SX6 ) ) )
| ( SY576 @ SY577 @ SY578 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[670]) ).
thf(883,plain,
! [SV37: $i] :
( ( ( ~ ~ ! [SY102: $i] :
~ ( in @ SY102 @ SV37 ) )
= $true )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[671]) ).
thf(884,plain,
! [SV237: $i,SV38: $i] :
( ( iskpair @ ( setadjoin @ ( setadjoin @ SV38 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV38 @ ( setadjoin @ SV237 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(885,plain,
! [SV238: $i,SV39: $i] :
( ( ( SV39 != SV238 )
| ( subset @ SV39 @ SV238 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(886,plain,
! [SV239: $i,SV40: $i] :
( ( ! [SY581: $i] :
( ~ ( in @ SY581 @ SV40 )
| ~ ~ ( in @ SY581 @ SV239 )
| ~ ( subset @ SV40 @ SV239 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[674]) ).
thf(887,plain,
! [SV41: $i] :
( ( in @ SV41 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[675]) ).
thf(888,plain,
! [SV240: $i,SV42: $i] :
( ( ( ( setadjoin @ SV42 @ emptyset )
!= ( setadjoin @ SV240 @ emptyset ) )
| ( SV42 = SV240 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(889,plain,
! [SV241: $i,SV43: $i] :
( ( ! [SY582: $i] :
( ~ ( in @ SY582 @ SV43 )
| ( in @ ( setadjoin @ SY582 @ emptyset ) @ ( powerset @ ( binunion @ SV43 @ SV241 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(890,plain,
! [SV242: $i > $o,SV44: $i] :
( ( ~ ~ ~ ! [SY583: $i] :
~ ~ ( ~ ( in @ SY583 @ SV44 )
| ~ ( SV242 @ SY583 ) )
| ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(891,plain,
! [SV243: $i,SV45: $i] :
( ( ! [SY585: $i] :
( ~ ( in @ SY585 @ ( setadjoin @ SV45 @ ( setadjoin @ SV243 @ emptyset ) ) )
| ( SY585 = SV45 )
| ( SY585 = SV243 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[679]) ).
thf(892,plain,
! [SV46: $i > $o] :
( ( ( ~ ~ ! [SY115: $i] :
~ ~ ( ~ ( SV46 @ SY115 )
| ~ ! [SY116: $i] :
( ~ ( SV46 @ SY116 )
| ( SY115 = SY116 ) ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[680]) ).
thf(893,plain,
! [SV244: $i > $o,SV47: $i] :
( ( ! [SY586: $i] :
( ~ ( in @ SY586 @ SV47 )
| ~ ( SV244 @ SY586 )
| ( ( dsetconstr @ SV47
@ ^ [SY587: $i] : ( SV244 @ SY587 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(894,plain,
! [SV245: $i > $o,SV48: $i] :
( ( ! [SY588: $i] :
( ~ ( in @ SY588
@ ( dsetconstr @ SV48
@ ^ [SY589: $i] : ( SV245 @ SY589 ) ) )
| ( SV245 @ SY588 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[682]) ).
thf(895,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ~ ! [SY590: $i,SY591: $i] :
( ( SY590 != SY591 )
| ~ ( ~ ( ~ ( SV49 @ SY590 )
| ( SV246 @ SY591 ) )
| ~ ( ~ ( SV246 @ SY591 )
| ( SV49 @ SY590 ) ) ) )
| ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(896,plain,
! [SV51: $o] :
( ( ( ~ SV51 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV51 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(897,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[686]) ).
thf(898,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[687]) ).
thf(899,plain,
! [SV247: $i,SV52: $i] :
( ( ! [SY598: $i,SY599: $i] :
( ( ( setadjoin @ ( setadjoin @ SV52 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV52 @ ( setadjoin @ SV247 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY598 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY598 @ ( setadjoin @ SY599 @ emptyset ) ) @ emptyset ) ) )
| ( SV247 = SY599 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(900,plain,
! [SV53: $i > $o] :
( ( ( ~ ~ ! [SY137: $i] :
~ ! [SY138: $i] :
~ ( ~ ( ~ ( SV53 @ SY138 )
| ( SY138 = SY137 ) )
| ~ ( ( SY138 != SY137 )
| ( SV53 @ SY138 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[689]) ).
thf(901,plain,
! [SV54: $i,SV248: $i] :
( ( ~ ( subset @ SV248 @ SV54 )
| ( ( binintersect @ SV54 @ SV248 )
= SV248 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(902,plain,
! [SV249: $i,SV55: $i] :
( ( ! [SY600: $i] :
( ~ ( func @ SV55 @ SV249 @ SY600 )
| ! [SY601: $i] :
( ~ ( in @ SY601 @ SV55 )
| ( in @ ( ap @ SV55 @ SV249 @ SY600 @ SY601 ) @ SV249 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(903,plain,
! [SV250: $i,SV57: $i] :
( ( ! [SY602: $i] :
( ~ ( in @ SY602 @ ( cartprod @ SV57 @ SV250 ) )
| ( in @ ( kfst @ SY602 ) @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(904,plain,
( ( ~ ( in @ sK4_SY3 @ ( funcSet @ sK1_A @ sK3_SY0 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(905,plain,
( ( ~ ~ ( ~ ( in @ sK2_SY2 @ sK1_A )
| ~ ~ $true ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[694]) ).
thf(906,plain,
! [SV251: $i,SV58: $i] :
( ( ~ ! [SY603: $i] :
~ ( ~ ( ~ ( in @ SY603 @ SV58 )
| ( in @ SY603 @ SV251 ) )
| ~ ( ~ ( in @ SY603 @ SV251 )
| ( in @ SY603 @ SV58 ) ) )
| ( SV58 = SV251 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[695]) ).
thf(907,plain,
! [SV252: $i,SV59: $i] :
( ( ~ ( ( SV59 != SV252 ) )
| ~ ( in @ SV252 @ ( setadjoin @ SV59 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[696]) ).
thf(908,plain,
! [SV253: $i,SV60: $i] :
( ( ! [SY604: $i] :
( ~ ( in @ SY604 @ SV60 )
| ( in @ SY604 @ ( binunion @ SV60 @ SV253 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[697]) ).
thf(909,plain,
! [SV254: $i,SV61: $i] :
( ( subset @ ( setminus @ SV61 @ SV254 ) @ SV61 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[698]) ).
thf(910,plain,
! [SV62: $i] :
( ( ! [SY153: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY154: $i] :
( ~ ( in @ SY154 @ SY153 )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY154 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY156: $i,SY157: $i] :
( ~ ~ ( ~ ( in @ SY156 @ SV62 )
| ~ ( in @ SY157 @ SV62 ) )
| ~ ! [SX4: $i] :
( ~ ( in @ SX4 @ SY153 )
| ~ ( ~ ( ~ ( in @ SY156 @ SX4 )
| ( in @ SY157 @ SX4 ) )
| ~ ( ~ ( in @ SY157 @ SX4 )
| ( in @ SY156 @ SX4 ) ) ) )
| ( SY156 = SY157 ) ) )
| ~ ! [SX2: $i,SX3: $i] :
( ~ ~ ( ~ ( in @ SX2 @ SY153 )
| ~ ( in @ SX3 @ SY153 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX2 )
| ( in @ SX4 @ SX3 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SX3 )
| ( in @ SX4 @ SX2 ) ) ) )
| ~ ! [SY163: $i] :
( ~ ~ ( ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY163 )
| ( in @ SY164 @ SV62 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY163 ) )
| ~ ! [SX3: $i] :
~ ~ ! [SX4: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SX3 @ SY153 )
| ~ ( in @ SX4 @ SY163 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SX3 )
| ~ ( in @ SX5 @ SY163 ) ) )
| ~ ! [SX5: $i] :
( ~ ( in @ SX5 @ SY153 )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SX5 )
| ( in @ SX6 @ SX3 ) )
| ( in @ SX4 @ SX5 ) ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[699]) ).
thf(911,plain,
! [SV255: $i,SV63: $i] :
( ( ! [SY605: $i] :
( ~ ( in @ SY605 @ SV63 )
| ! [SY606: $i] :
( ~ ( in @ SY606 @ SV255 )
| ( in @ ( setadjoin @ SY605 @ ( setadjoin @ SY606 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV255 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(912,plain,
! [SV64: $i,SV256: $i] :
( ( ~ ( in @ SV256 @ ( setunion @ SV64 ) )
| ~ ! [SY607: $i] :
~ ~ ( ~ ( in @ SY607 @ SV64 )
| ~ ( in @ SV256 @ SY607 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(913,plain,
! [SV65: $i,SV257: $i] :
( ( subset @ SV257 @ ( binunion @ SV65 @ SV257 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(914,plain,
! [SV258: $i,SV66: $i] :
( ( ! [SY608: $i] :
( ~ ( in @ SY608 @ ( cartprod @ SV66 @ SV258 ) )
| ( ( kpair @ ( kfst @ SY608 ) @ ( ksnd @ SY608 ) )
= SY608 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[703]) ).
thf(915,plain,
! [SV67: $i] :
( ( ( ~ ( in @ SV67 @ emptyset ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[704]) ).
thf(916,plain,
! [SV259: $i,SV68: $i] :
( ( ! [SY609: $i] :
( ~ ( in @ SY609 @ SV68 )
| ! [SY610: $i] :
( ~ ( in @ SY610 @ SV259 )
| ( ( ksnd @ ( kpair @ SY609 @ SY610 ) )
= SY610 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(917,plain,
! [SV260: $i > $o,SV69: $i] :
( ( ~ ~ ! [SY611: $i] :
~ ~ ( ~ ( in @ SY611
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
| ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SY611 @ emptyset ) ) )
| ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(918,plain,
! [SV261: $i,SV70: $i] :
( ( ! [SY615: $i > $i] :
( ~ ! [SY616: $i] :
( ~ ( in @ SY616 @ SV70 )
| ( in @ ( SY615 @ SY616 ) @ SV261 ) )
| ( func @ SV70 @ SV261
@ ( dpsetconstr @ SV70 @ SV261
@ ^ [SX3: $i,SX4: $i] :
( ( SY615 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(919,plain,
! [SV262: $i,SV71: $i] :
( ( ! [SY619: $i > $i] :
( ~ ! [SY620: $i] :
( ~ ( in @ SY620 @ SV71 )
| ( in @ ( SY619 @ SY620 ) @ SV262 ) )
| ( in
@ ( dpsetconstr @ SV71 @ SV262
@ ^ [SX3: $i,SX4: $i] :
( ( SY619 @ SX3 )
= SX4 ) )
@ ( funcSet @ SV71 @ SV262 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(920,plain,
! [SV263: $i,SV72: $i] :
( ( subset @ SV72 @ ( binunion @ SV72 @ SV263 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[709]) ).
thf(921,plain,
! [SV264: $i,SV74: $i] :
( ( ! [SY623: $i,SY624: $i] :
( ( ( kpair @ SV74 @ SV264 )
!= ( kpair @ SY623 @ SY624 ) )
| ( SV74 = SY623 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(922,plain,
! [SV265: $i,SV75: $i] :
( ( ! [SY625: $i] :
( ( binintersect @ SV75 @ ( binunion @ SV265 @ SY625 ) )
= ( binunion @ ( binintersect @ SV75 @ SV265 ) @ ( binintersect @ SV75 @ SY625 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(923,plain,
! [SV266: $i,SV76: $i] :
( ( ! [SY626: $i] :
( ~ ( subset @ SY626 @ ( cartprod @ SV76 @ SV266 ) )
| ! [SY627: $i > $o] :
( ~ ! [SY628: $i] :
( ~ ( in @ SY628 @ SV76 )
| ! [SY629: $i] :
( ~ ( in @ SY629 @ SV266 )
| ~ ( in @ ( kpair @ SY628 @ SY629 ) @ SY626 )
| ( SY627 @ ( kpair @ SY628 @ SY629 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY626 )
| ( SY627 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(924,plain,
! [SV267: $i,SV77: $i] :
( ( ! [SY631: $i] :
( ~ ( in @ SY631 @ ( symdiff @ SV77 @ SV267 ) )
| ! [SY632: $o] :
( ~ ( ~ ( in @ SY631 @ SV77 )
| ~ ~ ( in @ SY631 @ SV267 )
| SY632 )
| ~ ( ~ ~ ( in @ SY631 @ SV77 )
| ~ ( in @ SY631 @ SV267 )
| SY632 )
| SY632 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[714]) ).
thf(925,plain,
! [SV78: $i > $o] :
( ( ( ~ ~ ! [SY212: $i] :
~ ~ ( ~ ( SV78 @ SY212 )
| ~ ! [SY213: $i] :
( ~ ( SV78 @ SY213 )
| ( SY212 = SY213 ) ) ) )
= $true )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(926,plain,
! [SV268: $i,SV79: $i] :
( ( ~ ! [SY633: $i] :
( ~ ( in @ SY633 @ SV79 )
| ( in @ SY633 @ SV268 ) )
| ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) )
| ( SV79 = SV268 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[716]) ).
thf(927,plain,
! [SV80: $i > $o] :
( ( ( ~ ~ ! [SY218: $i] :
~ ~ ( ~ ( SV80 @ SY218 )
| ~ ! [SY219: $i] :
( ~ ( SV80 @ SY219 )
| ( SY218 = SY219 ) ) ) )
= $true )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[717]) ).
thf(928,plain,
! [SV269: $i,SV81: $i] :
( ( ! [SY635: $i] :
( ~ ( in @ SY635 @ SV81 )
| ~ ~ ( in @ SY635 @ SV269 )
| ( in @ SY635 @ ( setminus @ SV81 @ SV269 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[718]) ).
thf(929,plain,
! [SV82: $i,SV270: $i] :
( ( ! [SY636: $i] :
( ~ ( in @ SY636 @ SV270 )
| ( in @ SY636 @ ( binunion @ SV82 @ SV270 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[719]) ).
thf(930,plain,
! [SV83: $i,SV271: $i] :
( ( ~ ( ~ ( ~ ( in @ SV271 @ ( setunion @ SV83 ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SV271 @ SY637 )
| ~ ( in @ SY637 @ SV83 ) ) )
| ~ ( ~ ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SV271 @ SY638 )
| ~ ( in @ SY638 @ SV83 ) )
| ( in @ SV271 @ ( setunion @ SV83 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[720]) ).
thf(931,plain,
! [SV272: $i,SV84: $i] :
( ( ! [SY639: $i] :
( ~ ( subset @ SV84 @ SV272 )
| ~ ( in @ SY639 @ SV84 )
| ( in @ SY639 @ SV272 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(932,plain,
! [SV85: $i] :
( ( ( ~ ( subset @ SV85 @ emptyset ) )
= $true )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[722]) ).
thf(933,plain,
! [SV273: $i > $o,SV86: $i] :
( ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ SV86 )
| ~ ( SV273 @ SY640 ) )
| ~ ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(934,plain,
! [SV274: $i,SV87: $i] :
( ( ! [SY642: $i] :
( ~ ( subset @ SV87 @ SY642 )
| ( subset @ SV87 @ ( setadjoin @ SV274 @ SY642 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[724]) ).
thf(935,plain,
! [SV88: $i] :
( ( ( ~ ~ ! [SY236: $i] :
~ ( in @ SY236 @ SV88 ) )
= $true )
| ( ( ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY237 @ SV88 )
| ~ ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( in @ SY238 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[725]) ).
thf(936,plain,
! [SV275: $i,SV89: $i] :
( ( ! [SY643: $i] :
( ~ ( func @ SV89 @ SV275 @ SY643 )
| ! [SY644: $i] :
( ~ ( func @ SV89 @ SV275 @ SY644 )
| ~ ! [SY645: $i] :
( ~ ( in @ SY645 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SY643 @ SY645 )
= ( ap @ SV89 @ SV275 @ SY644 @ SY645 ) ) )
| ( SY643 = SY644 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(937,plain,
! [SV90: $i] :
( ( ( ~ ! [SY243: $i] :
~ ( in @ SY243 @ SV90 ) )
= $true )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[727]) ).
thf(938,plain,
! [SV276: $i,SV91: $i] :
( ( ! [SY646: $i] :
( ~ ( in @ SY646 @ ( cartprod @ SV91 @ SV276 ) )
| ( iskpair @ SY646 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[728]) ).
thf(939,plain,
! [SV277: $i,SV92: $i] :
( ( ( SV92 != SV277 )
| ( in @ SV92 @ ( setadjoin @ SV277 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(940,plain,
! [SV278: $i,SV93: $i] :
( ( ( SV93 != SV278 )
| ( ( setadjoin @ SV93 @ ( setadjoin @ SV278 @ emptyset ) )
= ( setadjoin @ SV93 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[730]) ).
thf(941,plain,
! [SV279: $i,SV94: $i] :
( ( ! [SY647: $i] :
( ~ ~ ( in @ SY647 @ ( setminus @ SV94 @ SV279 ) )
| ~ ~ ( in @ SY647 @ SV279 )
| ~ ( in @ SY647 @ SV94 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[731]) ).
thf(942,plain,
! [SV280: $i,SV95: $i] :
( ( ! [SY648: $i] :
( ~ ( in @ SY648 @ SV95 )
| ~ ( in @ SY648 @ SV280 )
| ( in @ SY648 @ ( binintersect @ SV95 @ SV280 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[732]) ).
thf(943,plain,
! [SV281: $i,SV96: $i] :
( ( ! [SY649: $i > $i > $o,SY650: $i] :
( ~ ( in @ SY650 @ SV96 )
| ! [SY651: $i] :
( ~ ( in @ SY651 @ SV281 )
| ~ ( in @ ( kpair @ SY650 @ SY651 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SX5: $i,SX6: $i] : ( SY649 @ SX5 @ SX6 ) ) )
| ( SY649 @ SY650 @ SY651 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[733]) ).
thf(944,plain,
! [SV282: $i,SV97: $i] :
( ( ~ ~ ( subset @ SV97 @ SV282 )
| ( SV97 != SV282 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[734]) ).
thf(945,plain,
! [SV98: $i > $o] :
( ( ( ~ ~ ! [SY259: $i] :
~ ~ ( ~ ( SV98 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV98 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[735]) ).
thf(946,plain,
! [SV283: $i,SV99: $i] :
( ( ! [SY654: $i > $i] :
( ~ ! [SY655: $i] :
( ~ ( in @ SY655 @ SV99 )
| ( in @ ( SY654 @ SY655 ) @ SV283 ) )
| ( func @ SV99 @ SV283
@ ( dpsetconstr @ SV99 @ SV283
@ ^ [SX3: $i,SX4: $i] :
( ( SY654 @ SX3 )
= SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[736]) ).
thf(947,plain,
! [SV100: $i,SV284: $i] :
( ( in @ SV284 @ ( setadjoin @ SV100 @ ( setadjoin @ SV284 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[737]) ).
thf(948,plain,
! [SV285: $i,SV101: $i] :
( ( ! [SY658: $i,SY659: $i] :
( ( ( kpair @ SV101 @ SV285 )
!= ( kpair @ SY658 @ SY659 ) )
| ( SV285 = SY659 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(949,plain,
! [SV286: $i,SV102: $i] :
( ( ! [SY660: $i] :
( ~ ( in @ SY660 @ ( setadjoin @ SV102 @ ( setadjoin @ SV286 @ emptyset ) ) )
| ( SY660 = SV102 )
| ( SY660 = SV286 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[739]) ).
thf(950,plain,
! [SV103: $i] :
( ( ( ~ ( iskpair @ SV103 ) )
= $true )
| ( ( ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
!= ( setadjoin @ SY274 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(951,plain,
! [SV287: $i > $o,SV104: $i] :
( ( ~ ~ ! [SY661: $i] :
~ ~ ( ~ ( in @ SY661 @ SV104 )
| ~ ~ ( SV287 @ SY661 ) )
| ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(952,plain,
! [SV288: $i,SV105: $i] :
( ( ! [SY663: $i] :
( ~ ( func @ SV105 @ SV288 @ SY663 )
| ( in @ SY663 @ ( funcSet @ SV105 @ SV288 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[742]) ).
thf(953,plain,
! [SV289: $i > $o,SV106: $i] :
( ( ~ ~ ! [SY664: $i] :
~ ~ ( ~ ( in @ SY664 @ SV106 )
| ~ ( SV289 @ SY664 ) )
| ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(954,plain,
! [SV290: $i,SV107: $i] :
( ( ! [SY666: $i] :
( ~ ( subset @ SY666 @ ( cartprod @ SV107 @ SV290 ) )
| ! [SY667: $i] :
( ~ ( subset @ SY667 @ ( cartprod @ SV107 @ SV290 ) )
| ~ ! [SY668: $i] :
( ~ ( in @ SY668 @ SV107 )
| ! [SY669: $i] :
( ~ ( in @ SY669 @ SV290 )
| ~ ( in @ ( kpair @ SY668 @ SY669 ) @ SY666 )
| ( in @ ( kpair @ SY668 @ SY669 ) @ SY667 ) ) )
| ( subset @ SY666 @ SY667 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[744]) ).
thf(955,plain,
! [SV291: $i,SV108: $i] :
( ( ~ ( in @ SV108 @ ( setadjoin @ SV291 @ emptyset ) )
| ( SV108 = SV291 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[745]) ).
thf(956,plain,
! [SV109: $i > $o,SV292: $i] :
( ( ~ ( in @ SV292 @ emptyset )
| ( SV109 @ SV292 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[746]) ).
thf(957,plain,
! [SV293: $i,SV110: $i] :
( ( ! [SY670: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV110 @ SV293
@ ^ [SX3: $i,SX4: $i] : ( SY670 @ SX3 @ SX4 ) )
@ ( cartprod @ SV110 @ SV293 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[747]) ).
thf(958,plain,
! [SV294: $i,SV111: $i] :
( ( ! [SY673: $i] :
( ~ ( in @ SY673 @ SV111 )
| ~ ( in @ SY673 @ SV294 )
| ~ ( in @ SY673 @ ( symdiff @ SV111 @ SV294 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[748]) ).
thf(959,plain,
! [SV295: $i,SV112: $i] :
( ( ! [SY674: $i] :
( ~ ( func @ SV112 @ SV295 @ SY674 )
| ! [SY675: $i] :
( ~ ( in @ SY675 @ SV112 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV295
@ ^ [SX4: $i] : ( in @ ( kpair @ SY675 @ SX4 ) @ SY674 ) ) )
@ SV295 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[749]) ).
thf(960,plain,
! [SV113: $i > $o] :
( ( ( ~ ~ ! [SY302: $i] :
~ ( SV113 @ SY302 ) )
= $true )
| ( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( SV113 @ SY303 )
| ~ ( SV113 @ SY304 )
| ( SY303 = SY304 ) )
| ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(961,plain,
! [SV114: $i,SV296: $i] :
( ( in @ SV296 @ ( setadjoin @ SV114 @ ( setadjoin @ SV296 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[751]) ).
thf(962,plain,
! [SV297: $i,SV115: $i] :
( ( ! [SY677: $i,SY678: $i] :
( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SY677 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY677 @ ( setadjoin @ SY678 @ emptyset ) ) @ emptyset ) ) )
| ( SY677 != SY678 )
| ( SV297 = SY678 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[752]) ).
thf(963,plain,
! [SV116: $i,SV298: $i] :
( ( ~ ( in @ SV298 @ ( setunion @ SV116 ) )
| ! [SY679: $o] :
( ~ ! [SY680: $i] :
( ~ ( in @ SV298 @ SY680 )
| ~ ( in @ SY680 @ SV116 )
| SY679 )
| SY679 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[753]) ).
thf(964,plain,
! [SV299: $i,SV117: $i] :
( ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV117 )
| ( in @ SY681 @ SV299 ) )
| ( subset @ SV117 @ SV299 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[754]) ).
thf(965,plain,
! [SV300: $i,SV118: $i] :
( ( ! [SY682: $i] :
( ~ ( subset @ SV118 @ SV300 )
| ~ ~ ( in @ SY682 @ SV300 )
| ~ ( in @ SY682 @ SV118 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[755]) ).
thf(966,plain,
! [SV301: $i,SV119: $i] :
( ( ( ( binintersect @ SV119 @ SV301 )
!= SV119 )
| ( subset @ SV119 @ SV301 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[756]) ).
thf(967,plain,
! [SV302: $i,SV120: $i] :
( ( ~ ( subset @ SV120 @ SV302 )
| ( ( binintersect @ SV120 @ SV302 )
= SV120 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[757]) ).
thf(968,plain,
! [SV303: $i,SV121: $i] :
( ( ! [SY683: $i] :
( ~ ( in @ SY683 @ ( binunion @ SV121 @ SV303 ) )
| ( in @ SY683 @ SV121 )
| ( in @ SY683 @ SV303 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[758]) ).
thf(969,plain,
! [SV304: $i,SV122: $i] :
( ( ~ ! [SY684: $i] :
( ~ ( in @ SY684 @ SV122 )
| ( in @ SY684 @ SV304 ) )
| ( subset @ SV122 @ SV304 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[759]) ).
thf(970,plain,
! [SV305: $i,SV123: $i] :
( ( ! [SY685: $i] :
( ~ ( in @ SY685 @ SV123 )
| ~ ~ ( in @ SY685 @ SV305 )
| ( SV123 != SV305 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[760]) ).
thf(971,plain,
! [SV125: $i,SV306: $i] :
( ( ~ ( subset @ SV306 @ SV125 )
| ( in @ SV306 @ ( powerset @ SV125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(972,plain,
! [SV307: $i,SV126: $i] :
( ( ! [SY686: $i] :
( ~ ( in @ SY686 @ ( cartprod @ SV126 @ SV307 ) )
| ( in @ ( ksnd @ SY686 ) @ SV307 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[763]) ).
thf(973,plain,
! [SV308: $i,SV128: $i] :
( ( in @ SV128 @ ( setadjoin @ SV128 @ ( setadjoin @ SV308 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[765]) ).
thf(974,plain,
! [SV130: $i,SV309: $i] :
( ( ~ ( ~ ( ~ ( in @ SV309 @ ( powerset @ SV130 ) )
| ! [SY687: $i] :
( ~ ( in @ SY687 @ SV309 )
| ( in @ SY687 @ SV130 ) ) )
| ~ ( ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV309 )
| ( in @ SY688 @ SV130 ) )
| ( in @ SV309 @ ( powerset @ SV130 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[767]) ).
thf(975,plain,
! [SV310: $i,SV131: $i] :
( ( ( SV131 != SV310 )
| ( ( setadjoin @ ( setadjoin @ SV131 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV131 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV131 @ emptyset ) @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[768]) ).
thf(976,plain,
! [SV311: $i,SV132: $i] :
( ( ! [SY689: $i] :
~ ( ~ ( ~ ( in @ SY689 @ ( setadjoin @ SV132 @ SV311 ) )
| ( SY689 = SV132 )
| ( in @ SY689 @ SV311 ) )
| ~ ( ~ ( ( SY689 = SV132 )
| ( in @ SY689 @ SV311 ) )
| ( in @ SY689 @ ( setadjoin @ SV132 @ SV311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(977,plain,
! [SV312: $i,SV133: $i] :
( ( ! [SY690: $i] :
( ~ ( in @ SY690 @ SV133 )
| ! [SY691: $i] :
( ~ ( in @ SY691 @ SV312 )
| ( ( kfst @ ( kpair @ SY690 @ SY691 ) )
= SY690 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[770]) ).
thf(978,plain,
! [SV134: $i > $i > $o,SV313: $i] :
( ( ~ ! [SY692: $i] :
( ~ ( in @ SY692 @ SV313 )
| ~ ! [SY342: $i] :
~ ~ ( ~ ( SV134 @ SY692 @ SY342 )
| ~ ! [SY343: $i] :
( ~ ( SV134 @ SY692 @ SY343 )
| ( SY342 = SY343 ) ) ) )
| ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(979,plain,
! [SV135: $o,SV314: $i] :
( ( ~ ( in @ SV314 @ ( prop2set @ SV135 ) )
| SV135 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(980,plain,
! [SV315: $i] :
( ( ~ ( in @ SV315 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[773]) ).
thf(981,plain,
! [SV316: $i] :
( ( ~ ( in @ SV316 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(982,plain,
! [SV317: $i > $o,SV136: $i] :
( ( ! [SY699: $i] :
( ~ ( in @ SY699 @ SV136 )
| ~ ( ~ ( ~ ( in @ SY699
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) )
| ( SV317 @ SY699 ) )
| ~ ( ~ ( SV317 @ SY699 )
| ( in @ SY699
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(983,plain,
! [SV138: $i,SV318: $i] :
( ( ~ ( in @ SV318 @ SV138 )
| ( in @ ( setadjoin @ SV318 @ emptyset ) @ ( powerset @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[777]) ).
thf(984,plain,
! [SV319: $i,SV139: $i] :
( ( ~ ( subset @ SV139 @ SV319 )
| ( ( setminus @ SV139 @ SV319 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[778]) ).
thf(985,plain,
! [SV140: $o] :
( ( ( ~ SV140 ) = $true )
| ( ( set2prop @ ( prop2set @ SV140 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[779]) ).
thf(986,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[780]) ).
thf(987,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[781]) ).
thf(988,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ~ ! [SY702: $i] :
( ~ ( in @ SY702 @ SV141 )
| ! [SY703: $i] :
( ~ ( in @ SY703 @ SV141 )
| ~ ( SV320 @ SY702 )
| ~ ( SV320 @ SY703 )
| ( SY702 = SY703 ) ) )
| ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(989,plain,
! [SV321: $i,SV142: $i] :
( ( ! [SY708: $i] :
( ~ ( subset @ SY708 @ ( cartprod @ SV142 @ SV321 ) )
| ! [SY709: $i] :
( ~ ( subset @ SY709 @ ( cartprod @ SV142 @ SV321 ) )
| ~ ! [SY710: $i] :
( ~ ( in @ SY710 @ SV142 )
| ! [SY711: $i] :
( ~ ( in @ SY711 @ SV321 )
| ~ ( in @ ( kpair @ SY710 @ SY711 ) @ SY708 )
| ( in @ ( kpair @ SY710 @ SY711 ) @ SY709 ) ) )
| ~ ! [SY712: $i] :
( ~ ( in @ SY712 @ SV142 )
| ! [SY713: $i] :
( ~ ( in @ SY713 @ SV321 )
| ~ ( in @ ( kpair @ SY712 @ SY713 ) @ SY709 )
| ( in @ ( kpair @ SY712 @ SY713 ) @ SY708 ) ) )
| ( SY708 = SY709 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(990,plain,
! [SV143: $i,SV322: $i] :
( ( in @ SV322 @ ( setadjoin @ SV143 @ ( setadjoin @ SV322 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(991,plain,
! [SV323: $i,SV144: $i] :
( ( ! [SY714: $i] :
( ~ ( in @ SY714 @ SV144 )
| ! [SY715: $i] :
( ~ ( in @ SY715 @ SV323 )
| ( in @ ( kpair @ SY714 @ SY715 ) @ ( cartprod @ SV144 @ SV323 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(992,plain,
! [SV145: $i] :
( ( ( ~ ( iskpair @ SV145 ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV145 ) @ ( ksnd @ SV145 ) )
= SV145 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[786]) ).
thf(993,plain,
! [SV324: $i,SV146: $i] :
( ( ~ ( subset @ SV146 @ SV324 )
| ~ ( subset @ SV324 @ SV146 )
| ( SV146 = SV324 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(994,plain,
! [SV325: $i > $o,SV147: $i] :
( ( ~ ~ ! [SY716: $i] :
( ~ ( in @ SY716 @ SV147 )
| ( SV325 @ SY716 ) )
| ~ ! [SY717: $i] :
~ ~ ( ~ ( in @ SY717 @ SV147 )
| ~ ~ ( SV325 @ SY717 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[788]) ).
thf(995,plain,
! [SV326: $i,SV148: $i] :
( ( subset @ ( binintersect @ SV148 @ SV326 ) @ SV326 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[789]) ).
thf(996,plain,
! [SV327: $i,SV149: $i] :
( ( ! [SY718: $i] :
( ~ ~ ( in @ SY718 @ SV149 )
| ~ ( in @ SY718 @ SV327 )
| ( in @ SY718 @ ( symdiff @ SV149 @ SV327 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[790]) ).
thf(997,plain,
! [SV328: $i,SV150: $i] :
( ( subset @ ( binintersect @ SV150 @ SV328 ) @ SV150 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[791]) ).
thf(998,plain,
! [SV151: $i] :
( ( ( ~ ( ( SV151 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY381: $i] :
~ ( in @ SY381 @ SV151 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[792]) ).
thf(999,plain,
! [SV153: $i] :
( ( ( ~ ( in @ SV153 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV153 @ SV153 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(1000,plain,
! [SV329: $i > $o,SV154: $i] :
( ( ~ ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
| ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SY719 @ emptyset ) ) )
| ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[795]) ).
thf(1001,plain,
! [SV330: $i,SV155: $i] :
( ( ! [SY724: $i] :
( ~ ( in @ SY724 @ ( cartprod @ SV155 @ SV330 ) )
| ~ ! [SY725: $i] :
~ ~ ( ~ ( in @ SY725 @ SV155 )
| ~ ~ ! [SY726: $i] :
~ ~ ( ~ ( in @ SY726 @ SV330 )
| ( SY724
!= ( kpair @ SY725 @ SY726 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[796]) ).
thf(1002,plain,
! [SV331: $i,SV156: $i] :
( ( ! [SY727: $i] :
( ~ ~ ( in @ SY727 @ SV156 )
| ~ ~ ( in @ SY727 @ SV331 )
| ~ ( in @ SY727 @ ( symdiff @ SV156 @ SV331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[797]) ).
thf(1003,plain,
! [SV332: $i > $o,SV157: $i] :
( ( ~ ~ ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV157 )
| ~ ( SV332 @ SY728 ) )
| ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[798]) ).
thf(1004,plain,
! [SV333: $i,SV158: $i] :
( ( ! [SY730: $i] :
( ~ ( in @ SY730 @ SV158 )
| ! [SY731: $i] :
( ~ ( in @ SY731 @ SV333 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY730 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY730 @ ( setadjoin @ SY731 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV158 @ SV333 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(1005,plain,
! [SV334: $i,SV159: $i] :
( ( ( SV159 != SV334 )
| ! [SY732: $i,SY733: $i] :
( ( SY732 != SY733 )
| ( ( setadjoin @ SV159 @ SY732 )
= ( setadjoin @ SV334 @ SY733 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[800]) ).
thf(1006,plain,
! [SV160: $i,SV335: $i] :
( ( ~ ( in @ SV335 @ SV160 )
| ( subset @ ( setadjoin @ SV335 @ emptyset ) @ SV160 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[801]) ).
thf(1007,plain,
! [SV336: $i,SV161: $i] :
( ( ! [SY734: $i] :
( ~ ( in @ SY734 @ ( funcSet @ SV161 @ SV336 ) )
| ! [SY735: $i] :
( ~ ( in @ SY735 @ SV161 )
| ( in @ ( kpair @ SY735 @ ( ap @ SV161 @ SV336 @ SY734 @ SY735 ) ) @ SY734 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(1008,plain,
! [SV337: $i,SV162: $i] :
( ( ! [SY736: $i] :
( ~ ( in @ SY736 @ ( funcSet @ SV162 @ SV337 ) )
| ! [SY737: $i] :
( ~ ( in @ SY737 @ ( funcSet @ SV162 @ SV337 ) )
| ~ ! [SY738: $i] :
( ~ ( in @ SY738 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SY736 @ SY738 )
= ( ap @ SV162 @ SV337 @ SY737 @ SY738 ) ) )
| ( SY736 = SY737 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(1009,plain,
! [SV338: $i,SV163: $i] :
( ( ! [SY739: $i] :
( ~ ( subset @ SY739 @ SV163 )
| ~ ( subset @ SY739 @ SV338 )
| ( subset @ SY739 @ ( binintersect @ SV163 @ SV338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[804]) ).
thf(1010,plain,
! [SV339: $i,SV164: $i] :
( ( ( SV164 != SV339 )
| ! [SY740: $i,SY741: $i] :
( ( SY740 != SY741 )
| ~ ( ~ ( ~ ( in @ SY740 @ SV164 )
| ( in @ SY741 @ SV339 ) )
| ~ ( ~ ( in @ SY741 @ SV339 )
| ( in @ SY740 @ SV164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[805]) ).
thf(1011,plain,
! [SV165: $i,SV340: $i] :
( ( ~ ( in @ SV340 @ ( powerset @ SV165 ) )
| ( subset @ SV340 @ SV165 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(1012,plain,
! [SV341: $i,SV166: $i] :
( ( ( ksnd @ ( kpair @ SV166 @ SV341 ) )
= SV341 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[807]) ).
thf(1013,plain,
! [SV342: $i,SV167: $i] :
( ( ! [SY742: $i > $i > $o] :
( subset
@ ( dpsetconstr @ SV167 @ SV342
@ ^ [SX3: $i,SX4: $i] : ( SY742 @ SX3 @ SX4 ) )
@ ( cartprod @ SV167 @ SV342 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(1014,plain,
! [SV343: $i > $o,SV168: $i] :
( ( ~ ~ ! [SY745: $i] :
( ~ ( in @ SY745 @ SV168 )
| ( SV343 @ SY745 ) )
| ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV168 )
| ~ ~ ( SV343 @ SY746 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(1015,plain,
! [SV344: $i,SV169: $i] :
( ( in @ SV169 @ ( setadjoin @ SV169 @ SV344 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[810]) ).
thf(1016,plain,
! [SV345: $i,SV170: $i] :
( ( ~ ( subset @ SV170 @ SV345 )
| ( in @ SV170 @ ( powerset @ SV345 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(1017,plain,
! [SV171: $i,SV346: $i] :
( ( in @ SV346 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV171 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV171 @ ( setadjoin @ SV346 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(1018,plain,
! [SV172: $i,SV347: $i] :
( ( ~ ! [SY747: $i] :
( ~ ( in @ SY747 @ SV347 )
| ( in @ SY747 @ SV172 ) )
| ( in @ SV347 @ ( powerset @ SV172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[813]) ).
thf(1019,plain,
! [SV348: $i,SV173: $i] :
( ( ( kfst @ ( kpair @ SV173 @ SV348 ) )
= SV173 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[814]) ).
thf(1020,plain,
! [SV174: $i] :
( ( ( ~ ~ ( ~ ( in @ emptyset @ SV174 )
| ~ ! [SY431: $i] :
( ~ ~ ( ~ ( in @ SY431 @ omega )
| ~ ( in @ SY431 @ SV174 ) )
| ( in @ ( setadjoin @ SY431 @ SY431 ) @ SV174 ) ) ) )
= $true )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[815]) ).
thf(1021,plain,
! [SV175: $i] :
( ( in @ SV175 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[816]) ).
thf(1022,plain,
! [SV176: $i] :
( ( ( ~ ( ( SV176 != emptyset ) ) )
= $true )
| ( ( ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ SY433 @ SV176 )
| ~ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(1023,plain,
! [SV349: $i,SV177: $i] :
( ( ( SV177 != SV349 )
| ( ( setunion @ SV177 )
= ( setunion @ SV349 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(1024,plain,
! [SV350: $i,SV178: $i] :
( ( ~ ( subset @ SV178 @ SV350 )
| ( subset @ ( powerset @ SV178 ) @ ( powerset @ SV350 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[819]) ).
thf(1025,plain,
! [SV351: $i,SV179: $i] :
( ( ! [SY748: $i] :
( ~ ( in @ SY748 @ SV179 )
| ~ ~ ( in @ SY748 @ SV351 )
| ( in @ SY748 @ ( symdiff @ SV179 @ SV351 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(1026,plain,
! [SV180: $i] :
( ( ( ~ ( iskpair @ SV180 ) )
= $true )
| ( ( ~ ! [SY438: $i] :
~ ~ ( ~ ( in @ SY438
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) )
| ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
!= ( setadjoin @ SY438 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[821]) ).
thf(1027,plain,
! [SV352: $i,SV181: $i] :
( ( ( ( binintersect @ SV181 @ SV352 )
!= SV352 )
| ( subset @ SV352 @ SV181 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[822]) ).
thf(1028,plain,
! [SV353: $i,SV182: $i] :
( ( ! [SY749: $i] :
( ~ ( subset @ SY749 @ ( cartprod @ SV182 @ SV353 ) )
| ! [SY750: $i > $o] :
( ~ ! [SY751: $i] :
( ~ ( in @ SY751 @ SV182 )
| ! [SY752: $i] :
( ~ ( in @ SY752 @ SV353 )
| ~ ( in @ ( kpair @ SY751 @ SY752 ) @ SY749 )
| ( SY750 @ ( kpair @ SY751 @ SY752 ) ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY749 )
| ( SY750 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[823]) ).
thf(1029,plain,
! [SV354: $i,SV183: $i] :
( ( ( SV183 != SV354 )
| ! [SY754: $i > $o,SY755: $i > $o] :
( ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV183 )
| ! [SY757: $i] :
( ~ ( in @ SY757 @ SV354 )
| ( SY756 != SY757 )
| ~ ( ~ ( ~ ( SY754 @ SY756 )
| ( SY755 @ SY757 ) )
| ~ ( ~ ( SY755 @ SY757 )
| ( SY754 @ SY756 ) ) ) ) )
| ( ( dsetconstr @ SV183
@ ^ [SX4: $i] : ( SY754 @ SX4 ) )
= ( dsetconstr @ SV354
@ ^ [SX4: $i] : ( SY755 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[824]) ).
thf(1030,plain,
! [SV355: $i,SV184: $i] :
( ( ! [SY760: $i] :
( ~ ( in @ SY760 @ ( setadjoin @ SV184 @ SV355 ) )
| ( SY760 = SV184 )
| ( in @ SY760 @ SV355 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[825]) ).
thf(1031,plain,
! [SV356: $i,SV185: $i] :
( ( ! [SY761: $i] :
( ~ ( in @ SY761 @ ( setadjoin @ SV185 @ SV356 ) )
| ! [SY762: $o] :
( ~ ( ( SY761 != SV185 )
| SY762 )
| ~ ( ~ ( in @ SY761 @ SV356 )
| SY762 )
| SY762 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[826]) ).
thf(1032,plain,
! [SV357: $i > $o,SV186: $i] :
( ( subset
@ ( dsetconstr @ SV186
@ ^ [SY763: $i] : ( SV357 @ SY763 ) )
@ SV186 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[827]) ).
thf(1033,plain,
! [SV358: $i,SV187: $i] :
( ( ( ( setminus @ SV187 @ SV358 )
!= emptyset )
| ( subset @ SV187 @ SV358 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(1034,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ~ ! [SY764: $i,SY765: $i] :
( ( SY764 != SY765 )
| ~ ( ~ ( ~ ( SV188 @ SY764 )
| ( SV359 @ SY765 ) )
| ~ ( ~ ( SV359 @ SY765 )
| ( SV188 @ SY764 ) ) ) )
| ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[829]) ).
thf(1035,plain,
! [SV360: $i,SV189: $i] :
( ( ! [SY774: $i] :
( ~ ( in @ SY774 @ SV189 )
| ! [SY775: $i] :
( ~ ( in @ SY775 @ SV360 )
| ( in @ ( setadjoin @ ( setadjoin @ SY774 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY774 @ ( setadjoin @ SY775 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV189 @ SV360 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[830]) ).
thf(1036,plain,
! [SV361: $i,SV190: $i] :
( ( ~ ( in @ SV190 @ ( setadjoin @ SV361 @ emptyset ) )
| ( in @ SV361 @ ( setadjoin @ SV190 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[831]) ).
thf(1037,plain,
! [SV362: $i,SV191: $i] :
( ( ! [SY776: $i,SY777: $i] :
( ~ ( in @ ( kpair @ SY776 @ SY777 ) @ ( cartprod @ SV191 @ SV362 ) )
| ( in @ SY777 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(1038,plain,
! [SV363: $i,SV192: $i] :
( ( ! [SY778: $i > $i > $o,SY779: $i,SY780: $i] :
( ~ ( in @ ( kpair @ SY779 @ SY780 )
@ ( dpsetconstr @ SV192 @ SV363
@ ^ [SX5: $i,SX6: $i] : ( SY778 @ SX5 @ SX6 ) ) )
| ( in @ SY780 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[833]) ).
thf(1039,plain,
! [SV364: $i,SV193: $i] :
( ( ! [SY783: $i] :
( ~ ( in @ SY783 @ ( funcSet @ SV193 @ SV364 ) )
| ! [SY784: $i] :
( ~ ( in @ SY784 @ SV193 )
| ( in @ ( ap @ SV193 @ SV364 @ SY783 @ SY784 ) @ SV364 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[834]) ).
thf(1040,plain,
! [SV365: $i,SV194: $i] :
( ( ! [SY785: $i > $i > $o,SY786: $i] :
( ~ ( in @ SY786 @ SV194 )
| ! [SY787: $i] :
( ~ ( in @ SY787 @ SV365 )
| ~ ( SY785 @ SY786 @ SY787 )
| ( in @ ( kpair @ SY786 @ SY787 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SX5: $i,SX6: $i] : ( SY785 @ SX5 @ SX6 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(1041,plain,
! [SV195: $i > $o] :
( ( ( ~ ~ ! [SY496: $i] :
~ ~ ( ~ ( SV195 @ SY496 )
| ~ ! [SY497: $i] :
( ~ ( SV195 @ SY497 )
| ( SY496 = SY497 ) ) ) )
= $true )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(1042,plain,
! [SV366: $i,SV196: $i] :
( ( ! [SY790: $i] :
( ~ ( in @ SY790 @ ( setminus @ SV196 @ SV366 ) )
| ( in @ SY790 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(1043,plain,
! [SV367: $i,SV197: $i] :
( ( ! [SY791: $i] :
( ~ ( in @ SY791 @ SV197 )
| ! [SY792: $i] :
( ~ ( in @ SY792 @ SV367 )
| ( ( kpair @ SY791 @ SY792 )
= ( kpair @ SY791 @ SY792 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[838]) ).
thf(1044,plain,
! [SV368: $i,SV198: $i] :
( ( ! [SY793: $i] :
( ~ ( func @ SV198 @ SV368 @ SY793 )
| ! [SY794: $i] :
( ~ ( in @ SY794 @ SV198 )
| ~ ! [SY795: $i] :
~ ~ ( ~ ( in @ SY795
@ ( dsetconstr @ SV368
@ ^ [SX5: $i] : ( in @ ( kpair @ SY794 @ SX5 ) @ SY793 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SX5: $i] : ( in @ ( kpair @ SY794 @ SX5 ) @ SY793 ) )
!= ( setadjoin @ SY795 @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[839]) ).
thf(1045,plain,
! [SV199: $i,SV369: $i] :
( ( ! [SY798: $i] :
( ~ ( in @ SV369 @ SY798 )
| ~ ( in @ SY798 @ SV199 )
| ( in @ SV369 @ ( setunion @ SV199 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(1046,plain,
! [SV370: $i,SV200: $i] :
( ( ! [SY799: $i] :
( ~ ( func @ SV200 @ SV370 @ SY799 )
| ! [SY800: $i] :
( ~ ( in @ SY800 @ SV200 )
| ! [SY801: $i] :
( ~ ( in @ SY801 @ SV370 )
| ~ ( in @ ( kpair @ SY800 @ SY801 ) @ SY799 )
| ( ( ap @ SV200 @ SV370 @ SY799 @ SY800 )
= SY801 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[841]) ).
thf(1047,plain,
! [SV371: $i,SV202: $i] :
( ( ! [SY802: $i] :
( ~ ( in @ SY802 @ ( funcSet @ SV202 @ SV371 ) )
| ! [SY803: $i] :
( ~ ( in @ SY803 @ SV202 )
| ! [SY804: $i] :
( ~ ( in @ SY804 @ SV371 )
| ~ ( in @ ( kpair @ SY803 @ SY804 ) @ SY802 )
| ( ( ap @ SV202 @ SV371 @ SY802 @ SY803 )
= SY804 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[843]) ).
thf(1048,plain,
! [SV372: $i,SV203: $i] :
( ( ( SV203 != SV372 )
| ( ( powerset @ SV203 )
= ( powerset @ SV372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[844]) ).
thf(1049,plain,
! [SV373: $i,SV204: $i] :
( ( ! [SY805: $i] :
( ~ ~ ( in @ SY805 @ ( setminus @ SV204 @ SV373 ) )
| ~ ( in @ SY805 @ SV204 )
| ( in @ SY805 @ SV373 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[845]) ).
thf(1050,plain,
! [SV205: $i,SV374: $i] :
( ( ! [SY806: $i] :
( ~ ( in @ SV374 @ ( powerset @ SV205 ) )
| ~ ( in @ SY806 @ SV374 )
| ( in @ SY806 @ SV205 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[846]) ).
thf(1051,plain,
! [SV375: $i > $i > $o,SV206: $i,SV1: $i] :
( ( ! [SY807: $i,SY808: $i] :
( ~ ( in @ ( kpair @ SY807 @ SY808 )
@ ( dpsetconstr @ SV1 @ SV206
@ ^ [SY809: $i,SY810: $i] : ( SV375 @ SY809 @ SY810 ) ) )
| ( in @ SY807 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[847]) ).
thf(1052,plain,
! [SV3: $i] :
( ( ( ~ ! [SY11: $i] :
~ ~ ( ~ ( in @ SY11 @ SV3 )
| ( SV3
!= ( setadjoin @ SY11 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[849]) ).
thf(1053,plain,
! [SV210: $i,SV6: $i,SV376: $i] :
( ( ~ ( in @ SV376 @ ( funcSet @ SV6 @ SV210 ) )
| ( func @ SV6 @ SV210 @ SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[852]) ).
thf(1054,plain,
! [SV212: $i,SV8: $i,SV377: $i] :
( ( ! [SY811: $i] :
( ~ ( in @ ( kpair @ SV377 @ SY811 ) @ ( cartprod @ SV8 @ SV212 ) )
| ( in @ SV377 @ SV8 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[854]) ).
thf(1055,plain,
! [SV213: $i,SV9: $i,SV378: $i] :
( ( ~ ( in @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) ) )
| ( SV9 = SV378 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[855]) ).
thf(1056,plain,
! [SV10: $i > $o] :
( ( ( ~ ! [SY23: $i] :
~ ~ ( ~ ( SV10 @ SY23 )
| ~ ! [SY24: $i] :
( ~ ( SV10 @ SY24 )
| ( SY23 = SY24 ) ) ) )
= $false )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[856]) ).
thf(1057,plain,
! [SV214: $i,SV11: $i,SV379: $i] :
( ( ~ ( in @ SV379 @ SV11 )
| ! [SY812: $i] :
( ~ ( in @ SY812 @ SV214 )
| ( subset @ ( setadjoin @ SV379 @ ( setadjoin @ SY812 @ emptyset ) ) @ ( binunion @ SV11 @ SV214 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[857]) ).
thf(1058,plain,
! [SV215: $i,SV12: $i] :
( ( ( ~ ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV12 )
| ~ ( in @ SY537 @ SV215 ) ) )
= $true )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(1059,plain,
! [SV380: $i,SV216: $i,SV13: $i] :
( ( ! [SY813: $i] :
( ( ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV380 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV380 @ ( setadjoin @ SY813 @ emptyset ) ) @ emptyset ) ) )
| ( SV13 = SV380 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[859]) ).
thf(1060,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ! [SY540: $i] :
( ~ ( in @ SY540 @ SV14 )
| ! [SY541: $i] :
( ~ ( in @ SY541 @ SV14 )
| ~ ( SV217 @ SY540 )
| ~ ( SV217 @ SY541 )
| ( SY540 = SY541 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[860]) ).
thf(1061,plain,
! [SV381: $i,SV218: $i,SV15: $i] :
( ( ( ( setadjoin @ SV15 @ ( setadjoin @ SV218 @ emptyset ) )
!= ( setadjoin @ SV381 @ emptyset ) )
| ( SV15 = SV218 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[861]) ).
thf(1062,plain,
! [SV219: $i,SV16: $i,SV382: $i] :
( ( ~ ( in @ SV382 @ SV16 )
| ! [SY814: $i] :
( ~ ( in @ SY814 @ SV219 )
| ( in @ ( kpair @ SV382 @ SY814 ) @ ( powerset @ ( powerset @ ( binunion @ SV16 @ SV219 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[862]) ).
thf(1063,plain,
! [SV17: $i] :
( ( ( in @ SV17 @ emptyset )
= $false )
| ( ( ! [SX1: $o] : SX1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[863]) ).
thf(1064,plain,
! [SV220: $i,SV18: $i,SV383: $i] :
( ( ~ ~ ( in @ SV383 @ SV18 )
| ~ ( in @ SV383 @ ( setminus @ SV18 @ SV220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[864]) ).
thf(1065,plain,
! [SV221: $i > $o,SV19: $i,SV384: $i] :
( ( ~ ( in @ SV384
@ ( dsetconstr @ SV19
@ ^ [SY551: $i] : ( SV221 @ SY551 ) ) )
| ( in @ SV384 @ SV19 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[865]) ).
thf(1066,plain,
! [SV20: $i,SV222: $i] :
( ( ( ~ ( in @ SV222 @ SV20 ) )
= $true )
| ( ( in @ SV222 @ ( powerset @ ( setunion @ SV20 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(1067,plain,
! [SV21: $i] :
( ( ( ! [SY54: $i] :
~ ( in @ SY54 @ SV21 ) )
= $false )
| ( ( SV21 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[867]) ).
thf(1068,plain,
! [SV385: $i,SV223: $i,SV22: $i] :
( ( ~ ( func @ SV22 @ SV223 @ SV385 )
| ! [SY816: $i] :
( ~ ( in @ SY816 @ SV22 )
| ( in @ ( kpair @ SY816 @ ( ap @ SV22 @ SV223 @ SV385 @ SY816 ) ) @ SV385 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[868]) ).
thf(1069,plain,
! [SV224: $i > $o,SV23: $i,SV386: $i] :
( ( ~ ( in @ SV386 @ SV23 )
| ~ ( SV224 @ SV386 )
| ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV23 )
| ~ ( SV224 @ SY817 )
| ( SY817 = SV386 ) )
| ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[869]) ).
thf(1070,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ! [SY821: $o] :
( ~ ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
| ~ ( ~ ( in @ SV387 @ SV24 )
| SY821 )
| ~ ( ~ ( in @ SV387 @ SV225 )
| SY821 )
| SY821 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[870]) ).
thf(1071,plain,
! [SV226: $i,SV25: $i,SV388: $i] :
( ( ~ ( in @ SV388 @ ( setminus @ SV25 @ SV226 ) )
| ~ ( in @ SV388 @ SV226 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[871]) ).
thf(1072,plain,
! [SV227: $i,SV26: $i,SV389: $i] :
( ( ~ ( in @ SV389 @ ( binintersect @ SV26 @ SV227 ) )
| ( in @ SV389 @ SV26 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[872]) ).
thf(1073,plain,
! [SV228: $i,SV27: $i] :
( ( ( SV27 != SV228 )
= $true )
| ( ( subset @ SV228 @ SV27 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[873]) ).
thf(1074,plain,
! [SV229: $i,SV28: $i,SV390: $i] :
( ( ~ ( in @ SV390 @ ( binintersect @ SV28 @ SV229 ) )
| ( in @ SV390 @ SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[874]) ).
thf(1075,plain,
! [SV391: $i,SV230: $i,SV29: $i] :
( ( ~ ( func @ SV29 @ SV230 @ SV391 )
| ! [SY822: $i] :
( ~ ( func @ SV29 @ SV230 @ SY822 )
| ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ SY823 )
= ( ap @ SV29 @ SV230 @ SY822 @ SY823 ) ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SV29 )
| ! [SY825: $i] :
( ~ ( in @ SY825 @ SV230 )
| ~ ( in @ ( kpair @ SY824 @ SY825 ) @ SY822 )
| ( in @ ( kpair @ SY824 @ SY825 ) @ SV391 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[875]) ).
thf(1076,plain,
! [SV30: $i,SV231: $i,SV392: $i] :
( ( ~ ( in @ SV392 @ SV231 )
| ~ ( in @ SV392 @ ( setminus @ SV30 @ SV231 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[876]) ).
thf(1077,plain,
! [SV232: $i,SV31: $i] :
( ( ( SV31 != SV232 )
= $true )
| ( ( ! [SY570: $i,SY571: $i] :
( ( SY570 != SY571 )
| ~ ( in @ SY570 @ SV31 )
| ( in @ SY571 @ SV232 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(1078,plain,
! [SV32: $i,SV233: $i,SV393: $i] :
( ( ~ ( in @ SV393 @ SV233 )
| ( in @ SV393 @ ( setadjoin @ SV32 @ SV233 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[878]) ).
thf(1079,plain,
! [SV33: $i > $o] :
( ( ( ~ ! [SY87: $i] :
~ ~ ( ~ ( SV33 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( SV33 @ SY88 )
| ( SY87 = SY88 ) ) ) )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[879]) ).
thf(1080,plain,
! [SV394: $i,SV234: $i,SV34: $i] :
( ( ~ ( subset @ SV34 @ SV234 )
| ~ ( subset @ SV234 @ SV394 )
| ( subset @ SV34 @ SV394 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[880]) ).
thf(1081,plain,
! [SV235: $i > $o,SV35: $i,SV395: $i] :
( ( ~ ( in @ SV395 @ SV35 )
| ~ ( SV235 @ SV395 )
| ( in @ SV395
@ ( dsetconstr @ SV35
@ ^ [SY575: $i] : ( SV235 @ SY575 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[881]) ).
thf(1082,plain,
! [SV396: $i > $i > $o,SV236: $i,SV36: $i] :
( ( ! [SY827: $i,SY828: $i] :
( ~ ( in @ ( kpair @ SY827 @ SY828 )
@ ( dpsetconstr @ SV36 @ SV236
@ ^ [SY829: $i,SY830: $i] : ( SV396 @ SY829 @ SY830 ) ) )
| ( SV396 @ SY827 @ SY828 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[882]) ).
thf(1083,plain,
! [SV37: $i] :
( ( ( ~ ! [SY102: $i] :
~ ( in @ SY102 @ SV37 ) )
= $false )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(1084,plain,
! [SV238: $i,SV39: $i] :
( ( ( SV39 != SV238 )
= $true )
| ( ( subset @ SV39 @ SV238 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[885]) ).
thf(1085,plain,
! [SV239: $i,SV40: $i,SV397: $i] :
( ( ~ ( in @ SV397 @ SV40 )
| ~ ~ ( in @ SV397 @ SV239 )
| ~ ( subset @ SV40 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[886]) ).
thf(1086,plain,
! [SV240: $i,SV42: $i] :
( ( ( ( setadjoin @ SV42 @ emptyset )
!= ( setadjoin @ SV240 @ emptyset ) )
= $true )
| ( ( SV42 = SV240 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[888]) ).
thf(1087,plain,
! [SV241: $i,SV43: $i,SV398: $i] :
( ( ~ ( in @ SV398 @ SV43 )
| ( in @ ( setadjoin @ SV398 @ emptyset ) @ ( powerset @ ( binunion @ SV43 @ SV241 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[889]) ).
thf(1088,plain,
! [SV242: $i > $o,SV44: $i] :
( ( ( ~ ~ ~ ! [SY583: $i] :
~ ~ ( ~ ( in @ SY583 @ SV44 )
| ~ ( SV242 @ SY583 ) ) )
= $true )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[890]) ).
thf(1089,plain,
! [SV243: $i,SV45: $i,SV399: $i] :
( ( ~ ( in @ SV399 @ ( setadjoin @ SV45 @ ( setadjoin @ SV243 @ emptyset ) ) )
| ( SV399 = SV45 )
| ( SV399 = SV243 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[891]) ).
thf(1090,plain,
! [SV46: $i > $o] :
( ( ( ~ ! [SY115: $i] :
~ ~ ( ~ ( SV46 @ SY115 )
| ~ ! [SY116: $i] :
( ~ ( SV46 @ SY116 )
| ( SY115 = SY116 ) ) ) )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(1091,plain,
! [SV244: $i > $o,SV47: $i,SV400: $i] :
( ( ~ ( in @ SV400 @ SV47 )
| ~ ( SV244 @ SV400 )
| ( ( dsetconstr @ SV47
@ ^ [SY587: $i] : ( SV244 @ SY587 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[893]) ).
thf(1092,plain,
! [SV245: $i > $o,SV48: $i,SV401: $i] :
( ( ~ ( in @ SV401
@ ( dsetconstr @ SV48
@ ^ [SY589: $i] : ( SV245 @ SY589 ) ) )
| ( SV245 @ SV401 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[894]) ).
thf(1093,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ! [SY590: $i,SY591: $i] :
( ( SY590 != SY591 )
| ~ ( ~ ( ~ ( SV49 @ SY590 )
| ( SV246 @ SY591 ) )
| ~ ( ~ ( SV246 @ SY591 )
| ( SV49 @ SY590 ) ) ) ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[895]) ).
thf(1094,plain,
! [SV51: $o] :
( ( SV51 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV51 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(1095,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(1096,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(1097,plain,
! [SV402: $i,SV247: $i,SV52: $i] :
( ( ! [SY833: $i] :
( ( ( setadjoin @ ( setadjoin @ SV52 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV52 @ ( setadjoin @ SV247 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV402 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV402 @ ( setadjoin @ SY833 @ emptyset ) ) @ emptyset ) ) )
| ( SV247 = SY833 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[899]) ).
thf(1098,plain,
! [SV53: $i > $o] :
( ( ( ~ ! [SY137: $i] :
~ ! [SY138: $i] :
~ ( ~ ( ~ ( SV53 @ SY138 )
| ( SY138 = SY137 ) )
| ~ ( ( SY138 != SY137 )
| ( SV53 @ SY138 ) ) ) )
= $false )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[900]) ).
thf(1099,plain,
! [SV54: $i,SV248: $i] :
( ( ( ~ ( subset @ SV248 @ SV54 ) )
= $true )
| ( ( ( binintersect @ SV54 @ SV248 )
= SV248 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[901]) ).
thf(1100,plain,
! [SV403: $i,SV249: $i,SV55: $i] :
( ( ~ ( func @ SV55 @ SV249 @ SV403 )
| ! [SY834: $i] :
( ~ ( in @ SY834 @ SV55 )
| ( in @ ( ap @ SV55 @ SV249 @ SV403 @ SY834 ) @ SV249 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[902]) ).
thf(1101,plain,
! [SV250: $i,SV57: $i,SV404: $i] :
( ( ~ ( in @ SV404 @ ( cartprod @ SV57 @ SV250 ) )
| ( in @ ( kfst @ SV404 ) @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[903]) ).
thf(1102,plain,
( ( in @ sK4_SY3 @ ( funcSet @ sK1_A @ sK3_SY0 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[904]) ).
thf(1103,plain,
( ( ~ ( ~ ( in @ sK2_SY2 @ sK1_A )
| ~ ~ $true ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[905]) ).
thf(1104,plain,
! [SV251: $i,SV58: $i] :
( ( ( ~ ! [SY603: $i] :
~ ( ~ ( ~ ( in @ SY603 @ SV58 )
| ( in @ SY603 @ SV251 ) )
| ~ ( ~ ( in @ SY603 @ SV251 )
| ( in @ SY603 @ SV58 ) ) ) )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[906]) ).
thf(1105,plain,
! [SV252: $i,SV59: $i] :
( ( ( ~ ( ( SV59 != SV252 ) ) )
= $true )
| ( ( ~ ( in @ SV252 @ ( setadjoin @ SV59 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[907]) ).
thf(1106,plain,
! [SV253: $i,SV60: $i,SV405: $i] :
( ( ~ ( in @ SV405 @ SV60 )
| ( in @ SV405 @ ( binunion @ SV60 @ SV253 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[908]) ).
thf(1107,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
| ~ ! [SY840: $i,SY841: $i] :
( ~ ~ ( ~ ( in @ SY840 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY841 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY840 )
| ( in @ SX4 @ SY841 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY841 )
| ( in @ SX4 @ SY840 ) ) ) )
| ~ ! [SY844: $i] :
( ~ ~ ( ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY844 )
| ( in @ SY164 @ SV62 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY844 ) )
| ~ ! [SY847: $i] :
~ ~ ! [SY848: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY847 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY848 @ SY844 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY847 )
| ~ ( in @ SX5 @ SY844 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY847 ) )
| ( in @ SY848 @ SY850 ) ) ) ) ) )
= $false ),
inference(extcnf_forall_neg,[status(esa)],[910]) ).
thf(1108,plain,
! [SV255: $i,SV63: $i,SV406: $i] :
( ( ~ ( in @ SV406 @ SV63 )
| ! [SY852: $i] :
( ~ ( in @ SY852 @ SV255 )
| ( in @ ( setadjoin @ SV406 @ ( setadjoin @ SY852 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV255 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[911]) ).
thf(1109,plain,
! [SV64: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ ( setunion @ SV64 ) ) )
= $true )
| ( ( ~ ! [SY607: $i] :
~ ~ ( ~ ( in @ SY607 @ SV64 )
| ~ ( in @ SV256 @ SY607 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[912]) ).
thf(1110,plain,
! [SV258: $i,SV66: $i,SV407: $i] :
( ( ~ ( in @ SV407 @ ( cartprod @ SV66 @ SV258 ) )
| ( ( kpair @ ( kfst @ SV407 ) @ ( ksnd @ SV407 ) )
= SV407 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[914]) ).
thf(1111,plain,
! [SV67: $i] :
( ( ( in @ SV67 @ emptyset )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(1112,plain,
! [SV259: $i,SV68: $i,SV408: $i] :
( ( ~ ( in @ SV408 @ SV68 )
| ! [SY853: $i] :
( ~ ( in @ SY853 @ SV259 )
| ( ( ksnd @ ( kpair @ SV408 @ SY853 ) )
= SY853 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[916]) ).
thf(1113,plain,
! [SV260: $i > $o,SV69: $i] :
( ( ( ~ ~ ! [SY611: $i] :
~ ~ ( ~ ( in @ SY611
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
| ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SY611 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1114,plain,
! [SV261: $i,SV409: $i > $i,SV70: $i] :
( ( ~ ! [SY854: $i] :
( ~ ( in @ SY854 @ SV70 )
| ( in @ ( SV409 @ SY854 ) @ SV261 ) )
| ( func @ SV70 @ SV261
@ ( dpsetconstr @ SV70 @ SV261
@ ^ [SY855: $i,SY856: $i] :
( ( SV409 @ SY855 )
= SY856 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[918]) ).
thf(1115,plain,
! [SV262: $i,SV410: $i > $i,SV71: $i] :
( ( ~ ! [SY857: $i] :
( ~ ( in @ SY857 @ SV71 )
| ( in @ ( SV410 @ SY857 ) @ SV262 ) )
| ( in
@ ( dpsetconstr @ SV71 @ SV262
@ ^ [SY858: $i,SY859: $i] :
( ( SV410 @ SY858 )
= SY859 ) )
@ ( funcSet @ SV71 @ SV262 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[919]) ).
thf(1116,plain,
! [SV411: $i,SV264: $i,SV74: $i] :
( ( ! [SY860: $i] :
( ( ( kpair @ SV74 @ SV264 )
!= ( kpair @ SV411 @ SY860 ) )
| ( SV74 = SV411 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[921]) ).
thf(1117,plain,
! [SV412: $i,SV265: $i,SV75: $i] :
( ( ( binintersect @ SV75 @ ( binunion @ SV265 @ SV412 ) )
= ( binunion @ ( binintersect @ SV75 @ SV265 ) @ ( binintersect @ SV75 @ SV412 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[922]) ).
thf(1118,plain,
! [SV266: $i,SV76: $i,SV413: $i] :
( ( ~ ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
| ! [SY861: $i > $o] :
( ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SV76 )
| ! [SY863: $i] :
( ~ ( in @ SY863 @ SV266 )
| ~ ( in @ ( kpair @ SY862 @ SY863 ) @ SV413 )
| ( SY861 @ ( kpair @ SY862 @ SY863 ) ) ) )
| ! [SY864: $i] :
( ~ ( in @ SY864 @ SV413 )
| ( SY861 @ SY864 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[923]) ).
thf(1119,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ~ ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
| ! [SY865: $o] :
( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| SY865 )
| ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SY865 )
| SY865 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[924]) ).
thf(1120,plain,
! [SV78: $i > $o] :
( ( ( ~ ! [SY212: $i] :
~ ~ ( ~ ( SV78 @ SY212 )
| ~ ! [SY213: $i] :
( ~ ( SV78 @ SY213 )
| ( SY212 = SY213 ) ) ) )
= $false )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[925]) ).
thf(1121,plain,
! [SV268: $i,SV79: $i] :
( ( ( ~ ! [SY633: $i] :
( ~ ( in @ SY633 @ SV79 )
| ( in @ SY633 @ SV268 ) ) )
= $true )
| ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) )
| ( SV79 = SV268 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1122,plain,
! [SV80: $i > $o] :
( ( ( ~ ! [SY218: $i] :
~ ~ ( ~ ( SV80 @ SY218 )
| ~ ! [SY219: $i] :
( ~ ( SV80 @ SY219 )
| ( SY218 = SY219 ) ) ) )
= $false )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[927]) ).
thf(1123,plain,
! [SV269: $i,SV81: $i,SV415: $i] :
( ( ~ ( in @ SV415 @ SV81 )
| ~ ~ ( in @ SV415 @ SV269 )
| ( in @ SV415 @ ( setminus @ SV81 @ SV269 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1124,plain,
! [SV82: $i,SV270: $i,SV416: $i] :
( ( ~ ( in @ SV416 @ SV270 )
| ( in @ SV416 @ ( binunion @ SV82 @ SV270 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[929]) ).
thf(1125,plain,
! [SV83: $i,SV271: $i] :
( ( ~ ( ~ ( in @ SV271 @ ( setunion @ SV83 ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SV271 @ SY637 )
| ~ ( in @ SY637 @ SV83 ) ) )
| ~ ( ~ ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SV271 @ SY638 )
| ~ ( in @ SY638 @ SV83 ) )
| ( in @ SV271 @ ( setunion @ SV83 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[930]) ).
thf(1126,plain,
! [SV417: $i,SV272: $i,SV84: $i] :
( ( ~ ( subset @ SV84 @ SV272 )
| ~ ( in @ SV417 @ SV84 )
| ( in @ SV417 @ SV272 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1127,plain,
! [SV85: $i] :
( ( ( subset @ SV85 @ emptyset )
= $false )
| ( ( SV85 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[932]) ).
thf(1128,plain,
! [SV273: $i > $o,SV86: $i] :
( ( ( ~ ! [SY640: $i] :
( ~ ( in @ SY640 @ SV86 )
| ~ ( SV273 @ SY640 ) ) )
= $true )
| ( ( ~ ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[933]) ).
thf(1129,plain,
! [SV274: $i,SV418: $i,SV87: $i] :
( ( ~ ( subset @ SV87 @ SV418 )
| ( subset @ SV87 @ ( setadjoin @ SV274 @ SV418 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1130,plain,
! [SV88: $i] :
( ( ( ~ ! [SY236: $i] :
~ ( in @ SY236 @ SV88 ) )
= $false )
| ( ( ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY237 @ SV88 )
| ~ ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( in @ SY238 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1131,plain,
! [SV419: $i,SV275: $i,SV89: $i] :
( ( ~ ( func @ SV89 @ SV275 @ SV419 )
| ! [SY866: $i] :
( ~ ( func @ SV89 @ SV275 @ SY866 )
| ~ ! [SY867: $i] :
( ~ ( in @ SY867 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ SY867 )
= ( ap @ SV89 @ SV275 @ SY866 @ SY867 ) ) )
| ( SV419 = SY866 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[936]) ).
thf(1132,plain,
! [SV90: $i] :
( ( ( ! [SY243: $i] :
~ ( in @ SY243 @ SV90 ) )
= $false )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1133,plain,
! [SV276: $i,SV91: $i,SV420: $i] :
( ( ~ ( in @ SV420 @ ( cartprod @ SV91 @ SV276 ) )
| ( iskpair @ SV420 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[938]) ).
thf(1134,plain,
! [SV277: $i,SV92: $i] :
( ( ( SV92 != SV277 )
= $true )
| ( ( in @ SV92 @ ( setadjoin @ SV277 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[939]) ).
thf(1135,plain,
! [SV278: $i,SV93: $i] :
( ( ( SV93 != SV278 )
= $true )
| ( ( ( setadjoin @ SV93 @ ( setadjoin @ SV278 @ emptyset ) )
= ( setadjoin @ SV93 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[940]) ).
thf(1136,plain,
! [SV279: $i,SV94: $i,SV421: $i] :
( ( ~ ~ ( in @ SV421 @ ( setminus @ SV94 @ SV279 ) )
| ~ ~ ( in @ SV421 @ SV279 )
| ~ ( in @ SV421 @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[941]) ).
thf(1137,plain,
! [SV280: $i,SV95: $i,SV422: $i] :
( ( ~ ( in @ SV422 @ SV95 )
| ~ ( in @ SV422 @ SV280 )
| ( in @ SV422 @ ( binintersect @ SV95 @ SV280 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[942]) ).
thf(1138,plain,
! [SV423: $i > $i > $o,SV281: $i,SV96: $i] :
( ( ! [SY868: $i] :
( ~ ( in @ SY868 @ SV96 )
| ! [SY869: $i] :
( ~ ( in @ SY869 @ SV281 )
| ~ ( in @ ( kpair @ SY868 @ SY869 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) )
| ( SV423 @ SY868 @ SY869 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[943]) ).
thf(1139,plain,
! [SV282: $i,SV97: $i] :
( ( ( ~ ~ ( subset @ SV97 @ SV282 ) )
= $true )
| ( ( SV97 != SV282 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[944]) ).
thf(1140,plain,
! [SV98: $i > $o] :
( ( ( ~ ! [SY259: $i] :
~ ~ ( ~ ( SV98 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV98 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $false )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1141,plain,
! [SV283: $i,SV424: $i > $i,SV99: $i] :
( ( ~ ! [SY872: $i] :
( ~ ( in @ SY872 @ SV99 )
| ( in @ ( SV424 @ SY872 ) @ SV283 ) )
| ( func @ SV99 @ SV283
@ ( dpsetconstr @ SV99 @ SV283
@ ^ [SY873: $i,SY874: $i] :
( ( SV424 @ SY873 )
= SY874 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[946]) ).
thf(1142,plain,
! [SV425: $i,SV285: $i,SV101: $i] :
( ( ! [SY875: $i] :
( ( ( kpair @ SV101 @ SV285 )
!= ( kpair @ SV425 @ SY875 ) )
| ( SV285 = SY875 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[948]) ).
thf(1143,plain,
! [SV286: $i,SV102: $i,SV426: $i] :
( ( ~ ( in @ SV426 @ ( setadjoin @ SV102 @ ( setadjoin @ SV286 @ emptyset ) ) )
| ( SV426 = SV102 )
| ( SV426 = SV286 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1144,plain,
! [SV103: $i] :
( ( ( iskpair @ SV103 )
= $false )
| ( ( ~ ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
!= ( setadjoin @ SY274 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[950]) ).
thf(1145,plain,
! [SV287: $i > $o,SV104: $i] :
( ( ( ~ ~ ! [SY661: $i] :
~ ~ ( ~ ( in @ SY661 @ SV104 )
| ~ ~ ( SV287 @ SY661 ) ) )
= $true )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1146,plain,
! [SV427: $i,SV288: $i,SV105: $i] :
( ( ~ ( func @ SV105 @ SV288 @ SV427 )
| ( in @ SV427 @ ( funcSet @ SV105 @ SV288 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[952]) ).
thf(1147,plain,
! [SV289: $i > $o,SV106: $i] :
( ( ( ~ ~ ! [SY664: $i] :
~ ~ ( ~ ( in @ SY664 @ SV106 )
| ~ ( SV289 @ SY664 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[953]) ).
thf(1148,plain,
! [SV290: $i,SV107: $i,SV428: $i] :
( ( ~ ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
| ! [SY876: $i] :
( ~ ( subset @ SY876 @ ( cartprod @ SV107 @ SV290 ) )
| ~ ! [SY877: $i] :
( ~ ( in @ SY877 @ SV107 )
| ! [SY878: $i] :
( ~ ( in @ SY878 @ SV290 )
| ~ ( in @ ( kpair @ SY877 @ SY878 ) @ SV428 )
| ( in @ ( kpair @ SY877 @ SY878 ) @ SY876 ) ) )
| ( subset @ SV428 @ SY876 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[954]) ).
thf(1149,plain,
! [SV291: $i,SV108: $i] :
( ( ( ~ ( in @ SV108 @ ( setadjoin @ SV291 @ emptyset ) ) )
= $true )
| ( ( SV108 = SV291 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1150,plain,
! [SV109: $i > $o,SV292: $i] :
( ( ( ~ ( in @ SV292 @ emptyset ) )
= $true )
| ( ( SV109 @ SV292 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[956]) ).
thf(1151,plain,
! [SV429: $i > $i > $o,SV293: $i,SV110: $i] :
( ( subset
@ ( dpsetconstr @ SV110 @ SV293
@ ^ [SY879: $i,SY880: $i] : ( SV429 @ SY879 @ SY880 ) )
@ ( cartprod @ SV110 @ SV293 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[957]) ).
thf(1152,plain,
! [SV294: $i,SV111: $i,SV430: $i] :
( ( ~ ( in @ SV430 @ SV111 )
| ~ ( in @ SV430 @ SV294 )
| ~ ( in @ SV430 @ ( symdiff @ SV111 @ SV294 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[958]) ).
thf(1153,plain,
! [SV431: $i,SV295: $i,SV112: $i] :
( ( ~ ( func @ SV112 @ SV295 @ SV431 )
| ! [SY881: $i] :
( ~ ( in @ SY881 @ SV112 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV295
@ ^ [SY882: $i] : ( in @ ( kpair @ SY881 @ SY882 ) @ SV431 ) ) )
@ SV295 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[959]) ).
thf(1154,plain,
! [SV113: $i > $o] :
( ( ( ~ ! [SY302: $i] :
~ ( SV113 @ SY302 ) )
= $false )
| ( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( SV113 @ SY303 )
| ~ ( SV113 @ SY304 )
| ( SY303 = SY304 ) )
| ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[960]) ).
thf(1155,plain,
! [SV432: $i,SV297: $i,SV115: $i] :
( ( ! [SY883: $i] :
( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV432 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV432 @ ( setadjoin @ SY883 @ emptyset ) ) @ emptyset ) ) )
| ( SV432 != SY883 )
| ( SV297 = SY883 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1156,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( setunion @ SV116 ) ) )
= $true )
| ( ( ! [SY679: $o] :
( ~ ! [SY680: $i] :
( ~ ( in @ SV298 @ SY680 )
| ~ ( in @ SY680 @ SV116 )
| SY679 )
| SY679 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[963]) ).
thf(1157,plain,
! [SV299: $i,SV117: $i] :
( ( ( ~ ! [SY681: $i] :
( ~ ( in @ SY681 @ SV117 )
| ( in @ SY681 @ SV299 ) ) )
= $true )
| ( ( subset @ SV117 @ SV299 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[964]) ).
thf(1158,plain,
! [SV433: $i,SV300: $i,SV118: $i] :
( ( ~ ( subset @ SV118 @ SV300 )
| ~ ~ ( in @ SV433 @ SV300 )
| ~ ( in @ SV433 @ SV118 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[965]) ).
thf(1159,plain,
! [SV301: $i,SV119: $i] :
( ( ( ( binintersect @ SV119 @ SV301 )
!= SV119 )
= $true )
| ( ( subset @ SV119 @ SV301 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[966]) ).
thf(1160,plain,
! [SV302: $i,SV120: $i] :
( ( ( ~ ( subset @ SV120 @ SV302 ) )
= $true )
| ( ( ( binintersect @ SV120 @ SV302 )
= SV120 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[967]) ).
thf(1161,plain,
! [SV303: $i,SV121: $i,SV434: $i] :
( ( ~ ( in @ SV434 @ ( binunion @ SV121 @ SV303 ) )
| ( in @ SV434 @ SV121 )
| ( in @ SV434 @ SV303 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[968]) ).
thf(1162,plain,
! [SV304: $i,SV122: $i] :
( ( ( ~ ! [SY684: $i] :
( ~ ( in @ SY684 @ SV122 )
| ( in @ SY684 @ SV304 ) ) )
= $true )
| ( ( subset @ SV122 @ SV304 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[969]) ).
thf(1163,plain,
! [SV305: $i,SV123: $i,SV435: $i] :
( ( ~ ( in @ SV435 @ SV123 )
| ~ ~ ( in @ SV435 @ SV305 )
| ( SV123 != SV305 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[970]) ).
thf(1164,plain,
! [SV125: $i,SV306: $i] :
( ( ( ~ ( subset @ SV306 @ SV125 ) )
= $true )
| ( ( in @ SV306 @ ( powerset @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[971]) ).
thf(1165,plain,
! [SV307: $i,SV126: $i,SV436: $i] :
( ( ~ ( in @ SV436 @ ( cartprod @ SV126 @ SV307 ) )
| ( in @ ( ksnd @ SV436 ) @ SV307 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[972]) ).
thf(1166,plain,
! [SV130: $i,SV309: $i] :
( ( ~ ( ~ ( in @ SV309 @ ( powerset @ SV130 ) )
| ! [SY687: $i] :
( ~ ( in @ SY687 @ SV309 )
| ( in @ SY687 @ SV130 ) ) )
| ~ ( ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV309 )
| ( in @ SY688 @ SV130 ) )
| ( in @ SV309 @ ( powerset @ SV130 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[974]) ).
thf(1167,plain,
! [SV310: $i,SV131: $i] :
( ( ( SV131 != SV310 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV131 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV131 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV131 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[975]) ).
thf(1168,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ~ ( ~ ( ~ ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
| ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
| ~ ( ~ ( ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
| ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[976]) ).
thf(1169,plain,
! [SV312: $i,SV133: $i,SV438: $i] :
( ( ~ ( in @ SV438 @ SV133 )
| ! [SY884: $i] :
( ~ ( in @ SY884 @ SV312 )
| ( ( kfst @ ( kpair @ SV438 @ SY884 ) )
= SV438 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[977]) ).
thf(1170,plain,
! [SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ! [SY692: $i] :
( ~ ( in @ SY692 @ SV313 )
| ~ ! [SY342: $i] :
~ ~ ( ~ ( SV134 @ SY692 @ SY342 )
| ~ ! [SY343: $i] :
( ~ ( SV134 @ SY692 @ SY343 )
| ( SY342 = SY343 ) ) ) ) )
= $true )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1171,plain,
! [SV135: $o,SV314: $i] :
( ( ( ~ ( in @ SV314 @ ( prop2set @ SV135 ) ) )
= $true )
| ( SV135 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[979]) ).
thf(1172,plain,
! [SV315: $i] :
( ( ( ~ ( in @ SV315 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[980]) ).
thf(1173,plain,
! [SV316: $i] :
( ( ( ~ ( in @ SV316 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[981]) ).
thf(1174,plain,
! [SV317: $i > $o,SV136: $i,SV439: $i] :
( ( ~ ( in @ SV439 @ SV136 )
| ~ ( ~ ( ~ ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) )
| ( SV317 @ SV439 ) )
| ~ ( ~ ( SV317 @ SV439 )
| ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[982]) ).
thf(1175,plain,
! [SV138: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV138 ) )
= $true )
| ( ( in @ ( setadjoin @ SV318 @ emptyset ) @ ( powerset @ SV138 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[983]) ).
thf(1176,plain,
! [SV319: $i,SV139: $i] :
( ( ( ~ ( subset @ SV139 @ SV319 ) )
= $true )
| ( ( ( setminus @ SV139 @ SV319 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[984]) ).
thf(1177,plain,
! [SV140: $o] :
( ( SV140 = $false )
| ( ( set2prop @ ( prop2set @ SV140 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1178,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[986]) ).
thf(1179,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1180,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ! [SY702: $i] :
( ~ ( in @ SY702 @ SV141 )
| ! [SY703: $i] :
( ~ ( in @ SY703 @ SV141 )
| ~ ( SV320 @ SY702 )
| ~ ( SV320 @ SY703 )
| ( SY702 = SY703 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[988]) ).
thf(1181,plain,
! [SV321: $i,SV142: $i,SV440: $i] :
( ( ~ ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
| ! [SY887: $i] :
( ~ ( subset @ SY887 @ ( cartprod @ SV142 @ SV321 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SV142 )
| ! [SY889: $i] :
( ~ ( in @ SY889 @ SV321 )
| ~ ( in @ ( kpair @ SY888 @ SY889 ) @ SV440 )
| ( in @ ( kpair @ SY888 @ SY889 ) @ SY887 ) ) )
| ~ ! [SY890: $i] :
( ~ ( in @ SY890 @ SV142 )
| ! [SY891: $i] :
( ~ ( in @ SY891 @ SV321 )
| ~ ( in @ ( kpair @ SY890 @ SY891 ) @ SY887 )
| ( in @ ( kpair @ SY890 @ SY891 ) @ SV440 ) ) )
| ( SV440 = SY887 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[989]) ).
thf(1182,plain,
! [SV323: $i,SV144: $i,SV441: $i] :
( ( ~ ( in @ SV441 @ SV144 )
| ! [SY892: $i] :
( ~ ( in @ SY892 @ SV323 )
| ( in @ ( kpair @ SV441 @ SY892 ) @ ( cartprod @ SV144 @ SV323 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[991]) ).
thf(1183,plain,
! [SV145: $i] :
( ( ( iskpair @ SV145 )
= $false )
| ( ( ( kpair @ ( kfst @ SV145 ) @ ( ksnd @ SV145 ) )
= SV145 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1184,plain,
! [SV324: $i,SV146: $i] :
( ( ( ~ ( subset @ SV146 @ SV324 ) )
= $true )
| ( ( ~ ( subset @ SV324 @ SV146 )
| ( SV146 = SV324 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[993]) ).
thf(1185,plain,
! [SV325: $i > $o,SV147: $i] :
( ( ( ~ ~ ! [SY716: $i] :
( ~ ( in @ SY716 @ SV147 )
| ( SV325 @ SY716 ) ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ~ ( ~ ( in @ SY717 @ SV147 )
| ~ ~ ( SV325 @ SY717 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[994]) ).
thf(1186,plain,
! [SV327: $i,SV149: $i,SV442: $i] :
( ( ~ ~ ( in @ SV442 @ SV149 )
| ~ ( in @ SV442 @ SV327 )
| ( in @ SV442 @ ( symdiff @ SV149 @ SV327 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[996]) ).
thf(1187,plain,
! [SV151: $i] :
( ( ( SV151 != emptyset )
= $false )
| ( ( ~ ! [SY381: $i] :
~ ( in @ SY381 @ SV151 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1188,plain,
! [SV153: $i] :
( ( ( in @ SV153 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV153 @ SV153 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[999]) ).
thf(1189,plain,
! [SV329: $i > $o,SV154: $i] :
( ( ( ~ ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
| ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SY719 @ emptyset ) ) ) )
= $true )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1000]) ).
thf(1190,plain,
! [SV330: $i,SV155: $i,SV443: $i] :
( ( ~ ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
| ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ SY893 @ SV155 )
| ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV330 )
| ( SV443
!= ( kpair @ SY893 @ SY894 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1001]) ).
thf(1191,plain,
! [SV331: $i,SV156: $i,SV444: $i] :
( ( ~ ~ ( in @ SV444 @ SV156 )
| ~ ~ ( in @ SV444 @ SV331 )
| ~ ( in @ SV444 @ ( symdiff @ SV156 @ SV331 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1002]) ).
thf(1192,plain,
! [SV332: $i > $o,SV157: $i] :
( ( ( ~ ~ ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV157 )
| ~ ( SV332 @ SY728 ) ) )
= $true )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1003]) ).
thf(1193,plain,
! [SV333: $i,SV158: $i,SV445: $i] :
( ( ~ ( in @ SV445 @ SV158 )
| ! [SY895: $i] :
( ~ ( in @ SY895 @ SV333 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV445 @ ( setadjoin @ SY895 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV158 @ SV333 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1004]) ).
thf(1194,plain,
! [SV334: $i,SV159: $i] :
( ( ( SV159 != SV334 )
= $true )
| ( ( ! [SY732: $i,SY733: $i] :
( ( SY732 != SY733 )
| ( ( setadjoin @ SV159 @ SY732 )
= ( setadjoin @ SV334 @ SY733 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1195,plain,
! [SV160: $i,SV335: $i] :
( ( ( ~ ( in @ SV335 @ SV160 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV335 @ emptyset ) @ SV160 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1006]) ).
thf(1196,plain,
! [SV336: $i,SV161: $i,SV446: $i] :
( ( ~ ( in @ SV446 @ ( funcSet @ SV161 @ SV336 ) )
| ! [SY896: $i] :
( ~ ( in @ SY896 @ SV161 )
| ( in @ ( kpair @ SY896 @ ( ap @ SV161 @ SV336 @ SV446 @ SY896 ) ) @ SV446 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1007]) ).
thf(1197,plain,
! [SV337: $i,SV162: $i,SV447: $i] :
( ( ~ ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
| ! [SY897: $i] :
( ~ ( in @ SY897 @ ( funcSet @ SV162 @ SV337 ) )
| ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ SY898 )
= ( ap @ SV162 @ SV337 @ SY897 @ SY898 ) ) )
| ( SV447 = SY897 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1008]) ).
thf(1198,plain,
! [SV338: $i,SV163: $i,SV448: $i] :
( ( ~ ( subset @ SV448 @ SV163 )
| ~ ( subset @ SV448 @ SV338 )
| ( subset @ SV448 @ ( binintersect @ SV163 @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1009]) ).
thf(1199,plain,
! [SV339: $i,SV164: $i] :
( ( ( SV164 != SV339 )
= $true )
| ( ( ! [SY740: $i,SY741: $i] :
( ( SY740 != SY741 )
| ~ ( ~ ( ~ ( in @ SY740 @ SV164 )
| ( in @ SY741 @ SV339 ) )
| ~ ( ~ ( in @ SY741 @ SV339 )
| ( in @ SY740 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1010]) ).
thf(1200,plain,
! [SV165: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ ( powerset @ SV165 ) ) )
= $true )
| ( ( subset @ SV340 @ SV165 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1011]) ).
thf(1201,plain,
! [SV449: $i > $i > $o,SV342: $i,SV167: $i] :
( ( subset
@ ( dpsetconstr @ SV167 @ SV342
@ ^ [SY899: $i,SY900: $i] : ( SV449 @ SY899 @ SY900 ) )
@ ( cartprod @ SV167 @ SV342 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1013]) ).
thf(1202,plain,
! [SV343: $i > $o,SV168: $i] :
( ( ( ~ ~ ! [SY745: $i] :
( ~ ( in @ SY745 @ SV168 )
| ( SV343 @ SY745 ) ) )
= $true )
| ( ( ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV168 )
| ~ ~ ( SV343 @ SY746 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1014]) ).
thf(1203,plain,
! [SV345: $i,SV170: $i] :
( ( ( ~ ( subset @ SV170 @ SV345 ) )
= $true )
| ( ( in @ SV170 @ ( powerset @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1016]) ).
thf(1204,plain,
! [SV172: $i,SV347: $i] :
( ( ( ~ ! [SY747: $i] :
( ~ ( in @ SY747 @ SV347 )
| ( in @ SY747 @ SV172 ) ) )
= $true )
| ( ( in @ SV347 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1018]) ).
thf(1205,plain,
! [SV174: $i] :
( ( ( ~ ( ~ ( in @ emptyset @ SV174 )
| ~ ! [SY431: $i] :
( ~ ~ ( ~ ( in @ SY431 @ omega )
| ~ ( in @ SY431 @ SV174 ) )
| ( in @ ( setadjoin @ SY431 @ SY431 ) @ SV174 ) ) ) )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1206,plain,
! [SV176: $i] :
( ( ( SV176 != emptyset )
= $false )
| ( ( ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ SY433 @ SV176 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1022]) ).
thf(1207,plain,
! [SV349: $i,SV177: $i] :
( ( ( SV177 != SV349 )
= $true )
| ( ( ( setunion @ SV177 )
= ( setunion @ SV349 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1023]) ).
thf(1208,plain,
! [SV350: $i,SV178: $i] :
( ( ( ~ ( subset @ SV178 @ SV350 ) )
= $true )
| ( ( subset @ ( powerset @ SV178 ) @ ( powerset @ SV350 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1209,plain,
! [SV351: $i,SV179: $i,SV450: $i] :
( ( ~ ( in @ SV450 @ SV179 )
| ~ ~ ( in @ SV450 @ SV351 )
| ( in @ SV450 @ ( symdiff @ SV179 @ SV351 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1025]) ).
thf(1210,plain,
! [SV180: $i] :
( ( ( iskpair @ SV180 )
= $false )
| ( ( ~ ! [SY438: $i] :
~ ~ ( ~ ( in @ SY438
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) )
| ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
!= ( setadjoin @ SY438 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1211,plain,
! [SV352: $i,SV181: $i] :
( ( ( ( binintersect @ SV181 @ SV352 )
!= SV352 )
= $true )
| ( ( subset @ SV352 @ SV181 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1027]) ).
thf(1212,plain,
! [SV353: $i,SV182: $i,SV451: $i] :
( ( ~ ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
| ! [SY901: $i > $o] :
( ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV182 )
| ! [SY903: $i] :
( ~ ( in @ SY903 @ SV353 )
| ~ ( in @ ( kpair @ SY902 @ SY903 ) @ SV451 )
| ( SY901 @ ( kpair @ SY902 @ SY903 ) ) ) )
| ! [SY904: $i] :
( ~ ( in @ SY904 @ SV451 )
| ( SY901 @ SY904 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1028]) ).
thf(1213,plain,
! [SV354: $i,SV183: $i] :
( ( ( SV183 != SV354 )
= $true )
| ( ( ! [SY754: $i > $o,SY755: $i > $o] :
( ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV183 )
| ! [SY757: $i] :
( ~ ( in @ SY757 @ SV354 )
| ( SY756 != SY757 )
| ~ ( ~ ( ~ ( SY754 @ SY756 )
| ( SY755 @ SY757 ) )
| ~ ( ~ ( SY755 @ SY757 )
| ( SY754 @ SY756 ) ) ) ) )
| ( ( dsetconstr @ SV183
@ ^ [SX4: $i] : ( SY754 @ SX4 ) )
= ( dsetconstr @ SV354
@ ^ [SX4: $i] : ( SY755 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1029]) ).
thf(1214,plain,
! [SV355: $i,SV184: $i,SV452: $i] :
( ( ~ ( in @ SV452 @ ( setadjoin @ SV184 @ SV355 ) )
| ( SV452 = SV184 )
| ( in @ SV452 @ SV355 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1030]) ).
thf(1215,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ~ ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
| ! [SY905: $o] :
( ~ ( ( SV453 != SV185 )
| SY905 )
| ~ ( ~ ( in @ SV453 @ SV356 )
| SY905 )
| SY905 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1216,plain,
! [SV358: $i,SV187: $i] :
( ( ( ( setminus @ SV187 @ SV358 )
!= emptyset )
= $true )
| ( ( subset @ SV187 @ SV358 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1033]) ).
thf(1217,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ! [SY764: $i,SY765: $i] :
( ( SY764 != SY765 )
| ~ ( ~ ( ~ ( SV188 @ SY764 )
| ( SV359 @ SY765 ) )
| ~ ( ~ ( SV359 @ SY765 )
| ( SV188 @ SY764 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1034]) ).
thf(1218,plain,
! [SV360: $i,SV189: $i,SV454: $i] :
( ( ~ ( in @ SV454 @ SV189 )
| ! [SY906: $i] :
( ~ ( in @ SY906 @ SV360 )
| ( in @ ( setadjoin @ ( setadjoin @ SV454 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV454 @ ( setadjoin @ SY906 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV189 @ SV360 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1035]) ).
thf(1219,plain,
! [SV361: $i,SV190: $i] :
( ( ( ~ ( in @ SV190 @ ( setadjoin @ SV361 @ emptyset ) ) )
= $true )
| ( ( in @ SV361 @ ( setadjoin @ SV190 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1036]) ).
thf(1220,plain,
! [SV362: $i,SV191: $i,SV455: $i] :
( ( ! [SY907: $i] :
( ~ ( in @ ( kpair @ SV455 @ SY907 ) @ ( cartprod @ SV191 @ SV362 ) )
| ( in @ SY907 @ SV362 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1221,plain,
! [SV456: $i > $i > $o,SV363: $i,SV192: $i] :
( ( ! [SY908: $i,SY909: $i] :
( ~ ( in @ ( kpair @ SY908 @ SY909 )
@ ( dpsetconstr @ SV192 @ SV363
@ ^ [SY910: $i,SY911: $i] : ( SV456 @ SY910 @ SY911 ) ) )
| ( in @ SY909 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1222,plain,
! [SV364: $i,SV193: $i,SV457: $i] :
( ( ~ ( in @ SV457 @ ( funcSet @ SV193 @ SV364 ) )
| ! [SY912: $i] :
( ~ ( in @ SY912 @ SV193 )
| ( in @ ( ap @ SV193 @ SV364 @ SV457 @ SY912 ) @ SV364 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1039]) ).
thf(1223,plain,
! [SV458: $i > $i > $o,SV365: $i,SV194: $i] :
( ( ! [SY913: $i] :
( ~ ( in @ SY913 @ SV194 )
| ! [SY914: $i] :
( ~ ( in @ SY914 @ SV365 )
| ~ ( SV458 @ SY913 @ SY914 )
| ( in @ ( kpair @ SY913 @ SY914 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1040]) ).
thf(1224,plain,
! [SV195: $i > $o] :
( ( ( ~ ! [SY496: $i] :
~ ~ ( ~ ( SV195 @ SY496 )
| ~ ! [SY497: $i] :
( ~ ( SV195 @ SY497 )
| ( SY496 = SY497 ) ) ) )
= $false )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1225,plain,
! [SV366: $i,SV196: $i,SV459: $i] :
( ( ~ ( in @ SV459 @ ( setminus @ SV196 @ SV366 ) )
| ( in @ SV459 @ SV196 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1042]) ).
thf(1226,plain,
! [SV367: $i,SV197: $i,SV460: $i] :
( ( ~ ( in @ SV460 @ SV197 )
| ! [SY917: $i] :
( ~ ( in @ SY917 @ SV367 )
| ( ( kpair @ SV460 @ SY917 )
= ( kpair @ SV460 @ SY917 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1043]) ).
thf(1227,plain,
! [SV461: $i,SV368: $i,SV198: $i] :
( ( ~ ( func @ SV198 @ SV368 @ SV461 )
| ! [SY918: $i] :
( ~ ( in @ SY918 @ SV198 )
| ~ ! [SY919: $i] :
~ ~ ( ~ ( in @ SY919
@ ( dsetconstr @ SV368
@ ^ [SY920: $i] : ( in @ ( kpair @ SY918 @ SY920 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY921: $i] : ( in @ ( kpair @ SY918 @ SY921 ) @ SV461 ) )
!= ( setadjoin @ SY919 @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1044]) ).
thf(1228,plain,
! [SV199: $i,SV462: $i,SV369: $i] :
( ( ~ ( in @ SV369 @ SV462 )
| ~ ( in @ SV462 @ SV199 )
| ( in @ SV369 @ ( setunion @ SV199 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1045]) ).
thf(1229,plain,
! [SV463: $i,SV370: $i,SV200: $i] :
( ( ~ ( func @ SV200 @ SV370 @ SV463 )
| ! [SY922: $i] :
( ~ ( in @ SY922 @ SV200 )
| ! [SY923: $i] :
( ~ ( in @ SY923 @ SV370 )
| ~ ( in @ ( kpair @ SY922 @ SY923 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SY922 )
= SY923 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1046]) ).
thf(1230,plain,
! [SV371: $i,SV202: $i,SV464: $i] :
( ( ~ ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
| ! [SY924: $i] :
( ~ ( in @ SY924 @ SV202 )
| ! [SY925: $i] :
( ~ ( in @ SY925 @ SV371 )
| ~ ( in @ ( kpair @ SY924 @ SY925 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SY924 )
= SY925 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1047]) ).
thf(1231,plain,
! [SV372: $i,SV203: $i] :
( ( ( SV203 != SV372 )
= $true )
| ( ( ( powerset @ SV203 )
= ( powerset @ SV372 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1048]) ).
thf(1232,plain,
! [SV373: $i,SV204: $i,SV465: $i] :
( ( ~ ~ ( in @ SV465 @ ( setminus @ SV204 @ SV373 ) )
| ~ ( in @ SV465 @ SV204 )
| ( in @ SV465 @ SV373 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1049]) ).
thf(1233,plain,
! [SV466: $i,SV205: $i,SV374: $i] :
( ( ~ ( in @ SV374 @ ( powerset @ SV205 ) )
| ~ ( in @ SV466 @ SV374 )
| ( in @ SV466 @ SV205 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1050]) ).
thf(1234,plain,
! [SV375: $i > $i > $o,SV206: $i,SV1: $i,SV467: $i] :
( ( ! [SY926: $i] :
( ~ ( in @ ( kpair @ SV467 @ SY926 )
@ ( dpsetconstr @ SV1 @ SV206
@ ^ [SY809: $i,SY810: $i] : ( SV375 @ SY809 @ SY810 ) ) )
| ( in @ SV467 @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1051]) ).
thf(1235,plain,
! [SV3: $i] :
( ( ( ! [SY11: $i] :
~ ~ ( ~ ( in @ SY11 @ SV3 )
| ( SV3
!= ( setadjoin @ SY11 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1052]) ).
thf(1236,plain,
! [SV210: $i,SV6: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ ( funcSet @ SV6 @ SV210 ) ) )
= $true )
| ( ( func @ SV6 @ SV210 @ SV376 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1053]) ).
thf(1237,plain,
! [SV212: $i,SV8: $i,SV468: $i,SV377: $i] :
( ( ~ ( in @ ( kpair @ SV377 @ SV468 ) @ ( cartprod @ SV8 @ SV212 ) )
| ( in @ SV377 @ SV8 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1054]) ).
thf(1238,plain,
! [SV213: $i,SV9: $i,SV378: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV9 = SV378 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1055]) ).
thf(1239,plain,
! [SV10: $i > $o] :
( ( ( ! [SY23: $i] :
~ ~ ( ~ ( SV10 @ SY23 )
| ~ ! [SY24: $i] :
( ~ ( SV10 @ SY24 )
| ( SY23 = SY24 ) ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1056]) ).
thf(1240,plain,
! [SV214: $i,SV11: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV11 ) )
= $true )
| ( ( ! [SY812: $i] :
( ~ ( in @ SY812 @ SV214 )
| ( subset @ ( setadjoin @ SV379 @ ( setadjoin @ SY812 @ emptyset ) ) @ ( binunion @ SV11 @ SV214 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1057]) ).
thf(1241,plain,
! [SV215: $i,SV12: $i] :
( ( ( ~ ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV12 )
| ~ ( in @ SY537 @ SV215 ) ) )
= $false )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1058]) ).
thf(1242,plain,
! [SV469: $i,SV380: $i,SV216: $i,SV13: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV380 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV380 @ ( setadjoin @ SV469 @ emptyset ) ) @ emptyset ) ) )
| ( SV13 = SV380 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1059]) ).
thf(1243,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ! [SY540: $i] :
( ~ ( in @ SY540 @ SV14 )
| ! [SY541: $i] :
( ~ ( in @ SY541 @ SV14 )
| ~ ( SV217 @ SY540 )
| ~ ( SV217 @ SY541 )
| ( SY540 = SY541 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1244,plain,
! [SV381: $i,SV218: $i,SV15: $i] :
( ( ( ( setadjoin @ SV15 @ ( setadjoin @ SV218 @ emptyset ) )
!= ( setadjoin @ SV381 @ emptyset ) )
= $true )
| ( ( SV15 = SV218 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1061]) ).
thf(1245,plain,
! [SV219: $i,SV16: $i,SV382: $i] :
( ( ( ~ ( in @ SV382 @ SV16 ) )
= $true )
| ( ( ! [SY814: $i] :
( ~ ( in @ SY814 @ SV219 )
| ( in @ ( kpair @ SV382 @ SY814 ) @ ( powerset @ ( powerset @ ( binunion @ SV16 @ SV219 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1246,plain,
! [SV17: $i,SV470: $o] :
( ( SV470 = $true )
| ( ( in @ SV17 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1063]) ).
thf(1247,plain,
! [SV17: $i] :
( ( $true = $true )
| ( ( in @ SV17 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1063]) ).
thf(1248,plain,
! [SV17: $i] :
( ( $false = $true )
| ( ( in @ SV17 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1063]) ).
thf(1249,plain,
! [SV220: $i,SV18: $i,SV383: $i] :
( ( ( ~ ~ ( in @ SV383 @ SV18 ) )
= $true )
| ( ( ~ ( in @ SV383 @ ( setminus @ SV18 @ SV220 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1064]) ).
thf(1250,plain,
! [SV221: $i > $o,SV19: $i,SV384: $i] :
( ( ( ~ ( in @ SV384
@ ( dsetconstr @ SV19
@ ^ [SY551: $i] : ( SV221 @ SY551 ) ) ) )
= $true )
| ( ( in @ SV384 @ SV19 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1065]) ).
thf(1251,plain,
! [SV20: $i,SV222: $i] :
( ( ( in @ SV222 @ SV20 )
= $false )
| ( ( in @ SV222 @ ( powerset @ ( setunion @ SV20 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1066]) ).
thf(1252,plain,
! [SV21: $i] :
( ( ( ~ ( in @ ( sK6_SY54 @ SV21 ) @ SV21 ) )
= $false )
| ( ( SV21 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1067]) ).
thf(1253,plain,
! [SV385: $i,SV223: $i,SV22: $i] :
( ( ( ~ ( func @ SV22 @ SV223 @ SV385 ) )
= $true )
| ( ( ! [SY816: $i] :
( ~ ( in @ SY816 @ SV22 )
| ( in @ ( kpair @ SY816 @ ( ap @ SV22 @ SV223 @ SV385 @ SY816 ) ) @ SV385 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1254,plain,
! [SV224: $i > $o,SV23: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ SV23 ) )
= $true )
| ( ( ~ ( SV224 @ SV386 )
| ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV23 )
| ~ ( SV224 @ SY817 )
| ( SY817 = SV386 ) )
| ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1069]) ).
thf(1255,plain,
! [SV471: $o,SV225: $i,SV24: $i,SV387: $i] :
( ( ~ ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
| ~ ( ~ ( in @ SV387 @ SV24 )
| SV471 )
| ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 )
| SV471 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1070]) ).
thf(1256,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ~ ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
| ~ ( ~ ( in @ SV387 @ SV24 )
| $true )
| ~ ( ~ ( in @ SV387 @ SV225 )
| $true )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1070]) ).
thf(1257,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ~ ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
| ~ ( ~ ( in @ SV387 @ SV24 )
| $false )
| ~ ( ~ ( in @ SV387 @ SV225 )
| $false )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[1070]) ).
thf(1258,plain,
! [SV226: $i,SV25: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ ( setminus @ SV25 @ SV226 ) ) )
= $true )
| ( ( ~ ( in @ SV388 @ SV226 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1071]) ).
thf(1259,plain,
! [SV227: $i,SV26: $i,SV389: $i] :
( ( ( ~ ( in @ SV389 @ ( binintersect @ SV26 @ SV227 ) ) )
= $true )
| ( ( in @ SV389 @ SV26 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1072]) ).
thf(1260,plain,
! [SV228: $i,SV27: $i] :
( ( ( SV27 = SV228 )
= $false )
| ( ( subset @ SV228 @ SV27 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1073]) ).
thf(1261,plain,
! [SV229: $i,SV28: $i,SV390: $i] :
( ( ( ~ ( in @ SV390 @ ( binintersect @ SV28 @ SV229 ) ) )
= $true )
| ( ( in @ SV390 @ SV229 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1074]) ).
thf(1262,plain,
! [SV391: $i,SV230: $i,SV29: $i] :
( ( ( ~ ( func @ SV29 @ SV230 @ SV391 ) )
= $true )
| ( ( ! [SY822: $i] :
( ~ ( func @ SV29 @ SV230 @ SY822 )
| ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ SY823 )
= ( ap @ SV29 @ SV230 @ SY822 @ SY823 ) ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SV29 )
| ! [SY825: $i] :
( ~ ( in @ SY825 @ SV230 )
| ~ ( in @ ( kpair @ SY824 @ SY825 ) @ SY822 )
| ( in @ ( kpair @ SY824 @ SY825 ) @ SV391 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1075]) ).
thf(1263,plain,
! [SV30: $i,SV231: $i,SV392: $i] :
( ( ( ~ ( in @ SV392 @ SV231 ) )
= $true )
| ( ( ~ ( in @ SV392 @ ( setminus @ SV30 @ SV231 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1076]) ).
thf(1264,plain,
! [SV232: $i,SV31: $i] :
( ( ( SV31 = SV232 )
= $false )
| ( ( ! [SY570: $i,SY571: $i] :
( ( SY570 != SY571 )
| ~ ( in @ SY570 @ SV31 )
| ( in @ SY571 @ SV232 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1077]) ).
thf(1265,plain,
! [SV32: $i,SV233: $i,SV393: $i] :
( ( ( ~ ( in @ SV393 @ SV233 ) )
= $true )
| ( ( in @ SV393 @ ( setadjoin @ SV32 @ SV233 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1078]) ).
thf(1266,plain,
! [SV33: $i > $o] :
( ( ( ! [SY87: $i] :
~ ~ ( ~ ( SV33 @ SY87 )
| ~ ! [SY88: $i] :
( ~ ( SV33 @ SY88 )
| ( SY87 = SY88 ) ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1079]) ).
thf(1267,plain,
! [SV394: $i,SV234: $i,SV34: $i] :
( ( ( ~ ( subset @ SV34 @ SV234 ) )
= $true )
| ( ( ~ ( subset @ SV234 @ SV394 )
| ( subset @ SV34 @ SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1080]) ).
thf(1268,plain,
! [SV235: $i > $o,SV35: $i,SV395: $i] :
( ( ( ~ ( in @ SV395 @ SV35 ) )
= $true )
| ( ( ~ ( SV235 @ SV395 )
| ( in @ SV395
@ ( dsetconstr @ SV35
@ ^ [SY575: $i] : ( SV235 @ SY575 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1081]) ).
thf(1269,plain,
! [SV396: $i > $i > $o,SV236: $i,SV36: $i,SV472: $i] :
( ( ! [SY929: $i] :
( ~ ( in @ ( kpair @ SV472 @ SY929 )
@ ( dpsetconstr @ SV36 @ SV236
@ ^ [SY829: $i,SY830: $i] : ( SV396 @ SY829 @ SY830 ) ) )
| ( SV396 @ SV472 @ SY929 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1082]) ).
thf(1270,plain,
! [SV37: $i] :
( ( ( ! [SY102: $i] :
~ ( in @ SY102 @ SV37 ) )
= $true )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1083]) ).
thf(1271,plain,
! [SV238: $i,SV39: $i] :
( ( ( SV39 = SV238 )
= $false )
| ( ( subset @ SV39 @ SV238 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1272,plain,
! [SV239: $i,SV40: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV40 ) )
= $true )
| ( ( ~ ~ ( in @ SV397 @ SV239 )
| ~ ( subset @ SV40 @ SV239 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1085]) ).
thf(1273,plain,
! [SV240: $i,SV42: $i] :
( ( ( ( setadjoin @ SV42 @ emptyset )
= ( setadjoin @ SV240 @ emptyset ) )
= $false )
| ( ( SV42 = SV240 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1086]) ).
thf(1274,plain,
! [SV241: $i,SV43: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ SV43 ) )
= $true )
| ( ( in @ ( setadjoin @ SV398 @ emptyset ) @ ( powerset @ ( binunion @ SV43 @ SV241 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1087]) ).
thf(1275,plain,
! [SV242: $i > $o,SV44: $i] :
( ( ( ~ ~ ! [SY583: $i] :
~ ~ ( ~ ( in @ SY583 @ SV44 )
| ~ ( SV242 @ SY583 ) ) )
= $false )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1088]) ).
thf(1276,plain,
! [SV243: $i,SV45: $i,SV399: $i] :
( ( ( ~ ( in @ SV399 @ ( setadjoin @ SV45 @ ( setadjoin @ SV243 @ emptyset ) ) ) )
= $true )
| ( ( ( SV399 = SV45 )
| ( SV399 = SV243 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1089]) ).
thf(1277,plain,
! [SV46: $i > $o] :
( ( ( ! [SY115: $i] :
~ ~ ( ~ ( SV46 @ SY115 )
| ~ ! [SY116: $i] :
( ~ ( SV46 @ SY116 )
| ( SY115 = SY116 ) ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1090]) ).
thf(1278,plain,
! [SV244: $i > $o,SV47: $i,SV400: $i] :
( ( ( ~ ( in @ SV400 @ SV47 ) )
= $true )
| ( ( ~ ( SV244 @ SV400 )
| ( ( dsetconstr @ SV47
@ ^ [SY587: $i] : ( SV244 @ SY587 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1091]) ).
thf(1279,plain,
! [SV245: $i > $o,SV48: $i,SV401: $i] :
( ( ( ~ ( in @ SV401
@ ( dsetconstr @ SV48
@ ^ [SY589: $i] : ( SV245 @ SY589 ) ) ) )
= $true )
| ( ( SV245 @ SV401 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1092]) ).
thf(1280,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ! [SY590: $i,SY591: $i] :
( ( SY590 != SY591 )
| ~ ( ~ ( ~ ( SV49 @ SY590 )
| ( SV246 @ SY591 ) )
| ~ ( ~ ( SV246 @ SY591 )
| ( SV49 @ SY590 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1093]) ).
thf(1281,plain,
! [SV473: $i,SV402: $i,SV247: $i,SV52: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV52 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV52 @ ( setadjoin @ SV247 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV402 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV402 @ ( setadjoin @ SV473 @ emptyset ) ) @ emptyset ) ) )
| ( SV247 = SV473 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1097]) ).
thf(1282,plain,
! [SV53: $i > $o] :
( ( ( ! [SY137: $i] :
~ ! [SY138: $i] :
~ ( ~ ( ~ ( SV53 @ SY138 )
| ( SY138 = SY137 ) )
| ~ ( ( SY138 != SY137 )
| ( SV53 @ SY138 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1098]) ).
thf(1283,plain,
! [SV54: $i,SV248: $i] :
( ( ( subset @ SV248 @ SV54 )
= $false )
| ( ( ( binintersect @ SV54 @ SV248 )
= SV248 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1099]) ).
thf(1284,plain,
! [SV403: $i,SV249: $i,SV55: $i] :
( ( ( ~ ( func @ SV55 @ SV249 @ SV403 ) )
= $true )
| ( ( ! [SY834: $i] :
( ~ ( in @ SY834 @ SV55 )
| ( in @ ( ap @ SV55 @ SV249 @ SV403 @ SY834 ) @ SV249 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1100]) ).
thf(1285,plain,
! [SV250: $i,SV57: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ ( cartprod @ SV57 @ SV250 ) ) )
= $true )
| ( ( in @ ( kfst @ SV404 ) @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1101]) ).
thf(1286,plain,
( ( ~ ( in @ sK2_SY2 @ sK1_A )
| ~ ~ $true )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1103]) ).
thf(1287,plain,
! [SV251: $i,SV58: $i] :
( ( ( ! [SY603: $i] :
~ ( ~ ( ~ ( in @ SY603 @ SV58 )
| ( in @ SY603 @ SV251 ) )
| ~ ( ~ ( in @ SY603 @ SV251 )
| ( in @ SY603 @ SV58 ) ) ) )
= $false )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1104]) ).
thf(1288,plain,
! [SV252: $i,SV59: $i] :
( ( ( SV59 != SV252 )
= $false )
| ( ( ~ ( in @ SV252 @ ( setadjoin @ SV59 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1105]) ).
thf(1289,plain,
! [SV253: $i,SV60: $i,SV405: $i] :
( ( ( ~ ( in @ SV405 @ SV60 ) )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV60 @ SV253 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1106]) ).
thf(1290,plain,
! [SV62: $i] :
( ( ~ ( ~ ~ ( ~ ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
| ~ ! [SY840: $i,SY841: $i] :
( ~ ~ ( ~ ( in @ SY840 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY841 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY840 )
| ( in @ SX4 @ SY841 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY841 )
| ( in @ SX4 @ SY840 ) ) ) )
| ~ ! [SY844: $i] :
( ~ ~ ( ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY844 )
| ( in @ SY164 @ SV62 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY844 ) )
| ~ ! [SY847: $i] :
~ ~ ! [SY848: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY847 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY848 @ SY844 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY847 )
| ~ ( in @ SX5 @ SY844 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY847 ) )
| ( in @ SY848 @ SY850 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1107]) ).
thf(1291,plain,
! [SV255: $i,SV63: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ SV63 ) )
= $true )
| ( ( ! [SY852: $i] :
( ~ ( in @ SY852 @ SV255 )
| ( in @ ( setadjoin @ SV406 @ ( setadjoin @ SY852 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV255 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1108]) ).
thf(1292,plain,
! [SV64: $i,SV256: $i] :
( ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false )
| ( ( ~ ! [SY607: $i] :
~ ~ ( ~ ( in @ SY607 @ SV64 )
| ~ ( in @ SV256 @ SY607 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1109]) ).
thf(1293,plain,
! [SV258: $i,SV66: $i,SV407: $i] :
( ( ( ~ ( in @ SV407 @ ( cartprod @ SV66 @ SV258 ) ) )
= $true )
| ( ( ( kpair @ ( kfst @ SV407 ) @ ( ksnd @ SV407 ) )
= SV407 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1110]) ).
thf(1294,plain,
! [SV259: $i,SV68: $i,SV408: $i] :
( ( ( ~ ( in @ SV408 @ SV68 ) )
= $true )
| ( ( ! [SY853: $i] :
( ~ ( in @ SY853 @ SV259 )
| ( ( ksnd @ ( kpair @ SV408 @ SY853 ) )
= SY853 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1295,plain,
! [SV260: $i > $o,SV69: $i] :
( ( ( ~ ! [SY611: $i] :
~ ~ ( ~ ( in @ SY611
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
| ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SY611 @ emptyset ) ) ) )
= $false )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1113]) ).
thf(1296,plain,
! [SV261: $i,SV409: $i > $i,SV70: $i] :
( ( ( ~ ! [SY854: $i] :
( ~ ( in @ SY854 @ SV70 )
| ( in @ ( SV409 @ SY854 ) @ SV261 ) ) )
= $true )
| ( ( func @ SV70 @ SV261
@ ( dpsetconstr @ SV70 @ SV261
@ ^ [SY855: $i,SY856: $i] :
( ( SV409 @ SY855 )
= SY856 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1114]) ).
thf(1297,plain,
! [SV262: $i,SV410: $i > $i,SV71: $i] :
( ( ( ~ ! [SY857: $i] :
( ~ ( in @ SY857 @ SV71 )
| ( in @ ( SV410 @ SY857 ) @ SV262 ) ) )
= $true )
| ( ( in
@ ( dpsetconstr @ SV71 @ SV262
@ ^ [SY858: $i,SY859: $i] :
( ( SV410 @ SY858 )
= SY859 ) )
@ ( funcSet @ SV71 @ SV262 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1115]) ).
thf(1298,plain,
! [SV474: $i,SV411: $i,SV264: $i,SV74: $i] :
( ( ( ( kpair @ SV74 @ SV264 )
!= ( kpair @ SV411 @ SV474 ) )
| ( SV74 = SV411 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1116]) ).
thf(1299,plain,
! [SV266: $i,SV76: $i,SV413: $i] :
( ( ( ~ ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) ) )
= $true )
| ( ( ! [SY861: $i > $o] :
( ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SV76 )
| ! [SY863: $i] :
( ~ ( in @ SY863 @ SV266 )
| ~ ( in @ ( kpair @ SY862 @ SY863 ) @ SV413 )
| ( SY861 @ ( kpair @ SY862 @ SY863 ) ) ) )
| ! [SY864: $i] :
( ~ ( in @ SY864 @ SV413 )
| ( SY861 @ SY864 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1118]) ).
thf(1300,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) ) )
= $true )
| ( ( ! [SY865: $o] :
( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| SY865 )
| ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SY865 )
| SY865 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1119]) ).
thf(1301,plain,
! [SV78: $i > $o] :
( ( ( ! [SY212: $i] :
~ ~ ( ~ ( SV78 @ SY212 )
| ~ ! [SY213: $i] :
( ~ ( SV78 @ SY213 )
| ( SY212 = SY213 ) ) ) )
= $true )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1120]) ).
thf(1302,plain,
! [SV268: $i,SV79: $i] :
( ( ( ! [SY633: $i] :
( ~ ( in @ SY633 @ SV79 )
| ( in @ SY633 @ SV268 ) ) )
= $false )
| ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) )
| ( SV79 = SV268 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1121]) ).
thf(1303,plain,
! [SV80: $i > $o] :
( ( ( ! [SY218: $i] :
~ ~ ( ~ ( SV80 @ SY218 )
| ~ ! [SY219: $i] :
( ~ ( SV80 @ SY219 )
| ( SY218 = SY219 ) ) ) )
= $true )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1122]) ).
thf(1304,plain,
! [SV269: $i,SV81: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ SV81 ) )
= $true )
| ( ( ~ ~ ( in @ SV415 @ SV269 )
| ( in @ SV415 @ ( setminus @ SV81 @ SV269 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1123]) ).
thf(1305,plain,
! [SV82: $i,SV270: $i,SV416: $i] :
( ( ( ~ ( in @ SV416 @ SV270 ) )
= $true )
| ( ( in @ SV416 @ ( binunion @ SV82 @ SV270 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1124]) ).
thf(1306,plain,
! [SV83: $i,SV271: $i] :
( ( ~ ( ~ ( in @ SV271 @ ( setunion @ SV83 ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SV271 @ SY637 )
| ~ ( in @ SY637 @ SV83 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1307,plain,
! [SV83: $i,SV271: $i] :
( ( ~ ( ~ ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SV271 @ SY638 )
| ~ ( in @ SY638 @ SV83 ) )
| ( in @ SV271 @ ( setunion @ SV83 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1125]) ).
thf(1308,plain,
! [SV417: $i,SV272: $i,SV84: $i] :
( ( ( ~ ( subset @ SV84 @ SV272 ) )
= $true )
| ( ( ~ ( in @ SV417 @ SV84 )
| ( in @ SV417 @ SV272 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1126]) ).
thf(1309,plain,
! [SV273: $i > $o,SV86: $i] :
( ( ( ! [SY640: $i] :
( ~ ( in @ SY640 @ SV86 )
| ~ ( SV273 @ SY640 ) ) )
= $false )
| ( ( ~ ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1128]) ).
thf(1310,plain,
! [SV274: $i,SV418: $i,SV87: $i] :
( ( ( ~ ( subset @ SV87 @ SV418 ) )
= $true )
| ( ( subset @ SV87 @ ( setadjoin @ SV274 @ SV418 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1129]) ).
thf(1311,plain,
! [SV88: $i] :
( ( ( ! [SY236: $i] :
~ ( in @ SY236 @ SV88 ) )
= $true )
| ( ( ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY237 @ SV88 )
| ~ ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( in @ SY238 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1130]) ).
thf(1312,plain,
! [SV419: $i,SV275: $i,SV89: $i] :
( ( ( ~ ( func @ SV89 @ SV275 @ SV419 ) )
= $true )
| ( ( ! [SY866: $i] :
( ~ ( func @ SV89 @ SV275 @ SY866 )
| ~ ! [SY867: $i] :
( ~ ( in @ SY867 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ SY867 )
= ( ap @ SV89 @ SV275 @ SY866 @ SY867 ) ) )
| ( SV419 = SY866 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1313,plain,
! [SV90: $i] :
( ( ( ~ ( in @ ( sK7_SY243 @ SV90 ) @ SV90 ) )
= $false )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1132]) ).
thf(1314,plain,
! [SV276: $i,SV91: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ ( cartprod @ SV91 @ SV276 ) ) )
= $true )
| ( ( iskpair @ SV420 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1315,plain,
! [SV277: $i,SV92: $i] :
( ( ( SV92 = SV277 )
= $false )
| ( ( in @ SV92 @ ( setadjoin @ SV277 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1316,plain,
! [SV278: $i,SV93: $i] :
( ( ( SV93 = SV278 )
= $false )
| ( ( ( setadjoin @ SV93 @ ( setadjoin @ SV278 @ emptyset ) )
= ( setadjoin @ SV93 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1135]) ).
thf(1317,plain,
! [SV279: $i,SV94: $i,SV421: $i] :
( ( ( ~ ~ ( in @ SV421 @ ( setminus @ SV94 @ SV279 ) ) )
= $true )
| ( ( ~ ~ ( in @ SV421 @ SV279 )
| ~ ( in @ SV421 @ SV94 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1136]) ).
thf(1318,plain,
! [SV280: $i,SV95: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV95 ) )
= $true )
| ( ( ~ ( in @ SV422 @ SV280 )
| ( in @ SV422 @ ( binintersect @ SV95 @ SV280 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1137]) ).
thf(1319,plain,
! [SV423: $i > $i > $o,SV281: $i,SV96: $i,SV475: $i] :
( ( ~ ( in @ SV475 @ SV96 )
| ! [SY932: $i] :
( ~ ( in @ SY932 @ SV281 )
| ~ ( in @ ( kpair @ SV475 @ SY932 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) )
| ( SV423 @ SV475 @ SY932 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1138]) ).
thf(1320,plain,
! [SV282: $i,SV97: $i] :
( ( ( ~ ( subset @ SV97 @ SV282 ) )
= $false )
| ( ( SV97 != SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1139]) ).
thf(1321,plain,
! [SV98: $i > $o] :
( ( ( ! [SY259: $i] :
~ ~ ( ~ ( SV98 @ SY259 )
| ~ ! [SY260: $i] :
( ~ ( SV98 @ SY260 )
| ( SY259 = SY260 ) ) ) )
= $true )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1140]) ).
thf(1322,plain,
! [SV283: $i,SV424: $i > $i,SV99: $i] :
( ( ( ~ ! [SY872: $i] :
( ~ ( in @ SY872 @ SV99 )
| ( in @ ( SV424 @ SY872 ) @ SV283 ) ) )
= $true )
| ( ( func @ SV99 @ SV283
@ ( dpsetconstr @ SV99 @ SV283
@ ^ [SY873: $i,SY874: $i] :
( ( SV424 @ SY873 )
= SY874 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1141]) ).
thf(1323,plain,
! [SV476: $i,SV425: $i,SV285: $i,SV101: $i] :
( ( ( ( kpair @ SV101 @ SV285 )
!= ( kpair @ SV425 @ SV476 ) )
| ( SV285 = SV476 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1142]) ).
thf(1324,plain,
! [SV286: $i,SV102: $i,SV426: $i] :
( ( ( ~ ( in @ SV426 @ ( setadjoin @ SV102 @ ( setadjoin @ SV286 @ emptyset ) ) ) )
= $true )
| ( ( ( SV426 = SV102 )
| ( SV426 = SV286 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1325,plain,
! [SV103: $i] :
( ( ( ! [SY274: $i] :
~ ~ ( ~ ( in @ SY274
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
!= ( setadjoin @ SY274 @ emptyset ) ) ) )
= $false )
| ( ( iskpair @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1144]) ).
thf(1326,plain,
! [SV287: $i > $o,SV104: $i] :
( ( ( ~ ! [SY661: $i] :
~ ~ ( ~ ( in @ SY661 @ SV104 )
| ~ ~ ( SV287 @ SY661 ) ) )
= $false )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1145]) ).
thf(1327,plain,
! [SV427: $i,SV288: $i,SV105: $i] :
( ( ( ~ ( func @ SV105 @ SV288 @ SV427 ) )
= $true )
| ( ( in @ SV427 @ ( funcSet @ SV105 @ SV288 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1146]) ).
thf(1328,plain,
! [SV289: $i > $o,SV106: $i] :
( ( ( ~ ! [SY664: $i] :
~ ~ ( ~ ( in @ SY664 @ SV106 )
| ~ ( SV289 @ SY664 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1147]) ).
thf(1329,plain,
! [SV290: $i,SV107: $i,SV428: $i] :
( ( ( ~ ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) ) )
= $true )
| ( ( ! [SY876: $i] :
( ~ ( subset @ SY876 @ ( cartprod @ SV107 @ SV290 ) )
| ~ ! [SY877: $i] :
( ~ ( in @ SY877 @ SV107 )
| ! [SY878: $i] :
( ~ ( in @ SY878 @ SV290 )
| ~ ( in @ ( kpair @ SY877 @ SY878 ) @ SV428 )
| ( in @ ( kpair @ SY877 @ SY878 ) @ SY876 ) ) )
| ( subset @ SV428 @ SY876 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1148]) ).
thf(1330,plain,
! [SV291: $i,SV108: $i] :
( ( ( in @ SV108 @ ( setadjoin @ SV291 @ emptyset ) )
= $false )
| ( ( SV108 = SV291 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1149]) ).
thf(1331,plain,
! [SV109: $i > $o,SV292: $i] :
( ( ( in @ SV292 @ emptyset )
= $false )
| ( ( SV109 @ SV292 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1150]) ).
thf(1332,plain,
! [SV294: $i,SV111: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV111 ) )
= $true )
| ( ( ~ ( in @ SV430 @ SV294 )
| ~ ( in @ SV430 @ ( symdiff @ SV111 @ SV294 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1333,plain,
! [SV431: $i,SV295: $i,SV112: $i] :
( ( ( ~ ( func @ SV112 @ SV295 @ SV431 ) )
= $true )
| ( ( ! [SY881: $i] :
( ~ ( in @ SY881 @ SV112 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV295
@ ^ [SY882: $i] : ( in @ ( kpair @ SY881 @ SY882 ) @ SV431 ) ) )
@ SV295 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1334,plain,
! [SV113: $i > $o] :
( ( ( ! [SY302: $i] :
~ ( SV113 @ SY302 ) )
= $true )
| ( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( SV113 @ SY303 )
| ~ ( SV113 @ SY304 )
| ( SY303 = SY304 ) )
| ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1154]) ).
thf(1335,plain,
! [SV477: $i,SV432: $i,SV297: $i,SV115: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV432 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV432 @ ( setadjoin @ SV477 @ emptyset ) ) @ emptyset ) ) )
| ( SV432 != SV477 )
| ( SV297 = SV477 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1336,plain,
! [SV116: $i,SV298: $i] :
( ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false )
| ( ( ! [SY679: $o] :
( ~ ! [SY680: $i] :
( ~ ( in @ SV298 @ SY680 )
| ~ ( in @ SY680 @ SV116 )
| SY679 )
| SY679 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1156]) ).
thf(1337,plain,
! [SV299: $i,SV117: $i] :
( ( ( ! [SY681: $i] :
( ~ ( in @ SY681 @ SV117 )
| ( in @ SY681 @ SV299 ) ) )
= $false )
| ( ( subset @ SV117 @ SV299 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1338,plain,
! [SV433: $i,SV300: $i,SV118: $i] :
( ( ( ~ ( subset @ SV118 @ SV300 ) )
= $true )
| ( ( ~ ~ ( in @ SV433 @ SV300 )
| ~ ( in @ SV433 @ SV118 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1339,plain,
! [SV301: $i,SV119: $i] :
( ( ( ( binintersect @ SV119 @ SV301 )
= SV119 )
= $false )
| ( ( subset @ SV119 @ SV301 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1159]) ).
thf(1340,plain,
! [SV302: $i,SV120: $i] :
( ( ( subset @ SV120 @ SV302 )
= $false )
| ( ( ( binintersect @ SV120 @ SV302 )
= SV120 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1160]) ).
thf(1341,plain,
! [SV303: $i,SV121: $i,SV434: $i] :
( ( ( ~ ( in @ SV434 @ ( binunion @ SV121 @ SV303 ) ) )
= $true )
| ( ( ( in @ SV434 @ SV121 )
| ( in @ SV434 @ SV303 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1342,plain,
! [SV304: $i,SV122: $i] :
( ( ( ! [SY684: $i] :
( ~ ( in @ SY684 @ SV122 )
| ( in @ SY684 @ SV304 ) ) )
= $false )
| ( ( subset @ SV122 @ SV304 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1162]) ).
thf(1343,plain,
! [SV305: $i,SV123: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ SV123 ) )
= $true )
| ( ( ~ ~ ( in @ SV435 @ SV305 )
| ( SV123 != SV305 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1163]) ).
thf(1344,plain,
! [SV125: $i,SV306: $i] :
( ( ( subset @ SV306 @ SV125 )
= $false )
| ( ( in @ SV306 @ ( powerset @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1164]) ).
thf(1345,plain,
! [SV307: $i,SV126: $i,SV436: $i] :
( ( ( ~ ( in @ SV436 @ ( cartprod @ SV126 @ SV307 ) ) )
= $true )
| ( ( in @ ( ksnd @ SV436 ) @ SV307 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1165]) ).
thf(1346,plain,
! [SV130: $i,SV309: $i] :
( ( ~ ( ~ ( in @ SV309 @ ( powerset @ SV130 ) )
| ! [SY687: $i] :
( ~ ( in @ SY687 @ SV309 )
| ( in @ SY687 @ SV130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1347,plain,
! [SV130: $i,SV309: $i] :
( ( ~ ( ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV309 )
| ( in @ SY688 @ SV130 ) )
| ( in @ SV309 @ ( powerset @ SV130 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1166]) ).
thf(1348,plain,
! [SV310: $i,SV131: $i] :
( ( ( SV131 = SV310 )
= $false )
| ( ( ( setadjoin @ ( setadjoin @ SV131 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV131 @ ( setadjoin @ SV310 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV131 @ emptyset ) @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1167]) ).
thf(1349,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ~ ( ~ ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
| ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
| ~ ( ~ ( ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
| ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1350,plain,
! [SV312: $i,SV133: $i,SV438: $i] :
( ( ( ~ ( in @ SV438 @ SV133 ) )
= $true )
| ( ( ! [SY884: $i] :
( ~ ( in @ SY884 @ SV312 )
| ( ( kfst @ ( kpair @ SV438 @ SY884 ) )
= SV438 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1351,plain,
! [SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY692: $i] :
( ~ ( in @ SY692 @ SV313 )
| ~ ! [SY342: $i] :
~ ~ ( ~ ( SV134 @ SY692 @ SY342 )
| ~ ! [SY343: $i] :
( ~ ( SV134 @ SY692 @ SY343 )
| ( SY342 = SY343 ) ) ) ) )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1170]) ).
thf(1352,plain,
! [SV135: $o,SV314: $i] :
( ( ( in @ SV314 @ ( prop2set @ SV135 ) )
= $false )
| ( SV135 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1171]) ).
thf(1353,plain,
! [SV315: $i] :
( ( ( in @ SV315 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1172]) ).
thf(1354,plain,
! [SV316: $i] :
( ( ( in @ SV316 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1355,plain,
! [SV317: $i > $o,SV136: $i,SV439: $i] :
( ( ( ~ ( in @ SV439 @ SV136 ) )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) )
| ( SV317 @ SV439 ) )
| ~ ( ~ ( SV317 @ SV439 )
| ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1174]) ).
thf(1356,plain,
! [SV138: $i,SV318: $i] :
( ( ( in @ SV318 @ SV138 )
= $false )
| ( ( in @ ( setadjoin @ SV318 @ emptyset ) @ ( powerset @ SV138 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1175]) ).
thf(1357,plain,
! [SV319: $i,SV139: $i] :
( ( ( subset @ SV139 @ SV319 )
= $false )
| ( ( ( setminus @ SV139 @ SV319 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1176]) ).
thf(1358,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ! [SY702: $i] :
( ~ ( in @ SY702 @ SV141 )
| ! [SY703: $i] :
( ~ ( in @ SY703 @ SV141 )
| ~ ( SV320 @ SY702 )
| ~ ( SV320 @ SY703 )
| ( SY702 = SY703 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1180]) ).
thf(1359,plain,
! [SV321: $i,SV142: $i,SV440: $i] :
( ( ( ~ ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) ) )
= $true )
| ( ( ! [SY887: $i] :
( ~ ( subset @ SY887 @ ( cartprod @ SV142 @ SV321 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SV142 )
| ! [SY889: $i] :
( ~ ( in @ SY889 @ SV321 )
| ~ ( in @ ( kpair @ SY888 @ SY889 ) @ SV440 )
| ( in @ ( kpair @ SY888 @ SY889 ) @ SY887 ) ) )
| ~ ! [SY890: $i] :
( ~ ( in @ SY890 @ SV142 )
| ! [SY891: $i] :
( ~ ( in @ SY891 @ SV321 )
| ~ ( in @ ( kpair @ SY890 @ SY891 ) @ SY887 )
| ( in @ ( kpair @ SY890 @ SY891 ) @ SV440 ) ) )
| ( SV440 = SY887 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1181]) ).
thf(1360,plain,
! [SV323: $i,SV144: $i,SV441: $i] :
( ( ( ~ ( in @ SV441 @ SV144 ) )
= $true )
| ( ( ! [SY892: $i] :
( ~ ( in @ SY892 @ SV323 )
| ( in @ ( kpair @ SV441 @ SY892 ) @ ( cartprod @ SV144 @ SV323 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1182]) ).
thf(1361,plain,
! [SV324: $i,SV146: $i] :
( ( ( subset @ SV146 @ SV324 )
= $false )
| ( ( ~ ( subset @ SV324 @ SV146 )
| ( SV146 = SV324 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1362,plain,
! [SV325: $i > $o,SV147: $i] :
( ( ( ~ ! [SY716: $i] :
( ~ ( in @ SY716 @ SV147 )
| ( SV325 @ SY716 ) ) )
= $false )
| ( ( ~ ! [SY717: $i] :
~ ~ ( ~ ( in @ SY717 @ SV147 )
| ~ ~ ( SV325 @ SY717 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1185]) ).
thf(1363,plain,
! [SV327: $i,SV149: $i,SV442: $i] :
( ( ( ~ ~ ( in @ SV442 @ SV149 ) )
= $true )
| ( ( ~ ( in @ SV442 @ SV327 )
| ( in @ SV442 @ ( symdiff @ SV149 @ SV327 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1186]) ).
thf(1364,plain,
! [SV151: $i] :
( ( ( SV151 = emptyset )
= $true )
| ( ( ~ ! [SY381: $i] :
~ ( in @ SY381 @ SV151 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1365,plain,
! [SV329: $i > $o,SV154: $i] :
( ( ( ~ ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
| ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SY719 @ emptyset ) ) ) )
= $false )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1366,plain,
! [SV330: $i,SV155: $i,SV443: $i] :
( ( ( ~ ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) ) )
= $true )
| ( ( ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ SY893 @ SV155 )
| ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV330 )
| ( SV443
!= ( kpair @ SY893 @ SY894 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1190]) ).
thf(1367,plain,
! [SV331: $i,SV156: $i,SV444: $i] :
( ( ( ~ ~ ( in @ SV444 @ SV156 ) )
= $true )
| ( ( ~ ~ ( in @ SV444 @ SV331 )
| ~ ( in @ SV444 @ ( symdiff @ SV156 @ SV331 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1191]) ).
thf(1368,plain,
! [SV332: $i > $o,SV157: $i] :
( ( ( ~ ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV157 )
| ~ ( SV332 @ SY728 ) ) )
= $false )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1192]) ).
thf(1369,plain,
! [SV333: $i,SV158: $i,SV445: $i] :
( ( ( ~ ( in @ SV445 @ SV158 ) )
= $true )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV333 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV445 @ ( setadjoin @ SY895 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV158 @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1193]) ).
thf(1370,plain,
! [SV334: $i,SV159: $i] :
( ( ( SV159 = SV334 )
= $false )
| ( ( ! [SY732: $i,SY733: $i] :
( ( SY732 != SY733 )
| ( ( setadjoin @ SV159 @ SY732 )
= ( setadjoin @ SV334 @ SY733 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1194]) ).
thf(1371,plain,
! [SV160: $i,SV335: $i] :
( ( ( in @ SV335 @ SV160 )
= $false )
| ( ( subset @ ( setadjoin @ SV335 @ emptyset ) @ SV160 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1195]) ).
thf(1372,plain,
! [SV336: $i,SV161: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ ( funcSet @ SV161 @ SV336 ) ) )
= $true )
| ( ( ! [SY896: $i] :
( ~ ( in @ SY896 @ SV161 )
| ( in @ ( kpair @ SY896 @ ( ap @ SV161 @ SV336 @ SV446 @ SY896 ) ) @ SV446 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1196]) ).
thf(1373,plain,
! [SV337: $i,SV162: $i,SV447: $i] :
( ( ( ~ ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) ) )
= $true )
| ( ( ! [SY897: $i] :
( ~ ( in @ SY897 @ ( funcSet @ SV162 @ SV337 ) )
| ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ SY898 )
= ( ap @ SV162 @ SV337 @ SY897 @ SY898 ) ) )
| ( SV447 = SY897 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1197]) ).
thf(1374,plain,
! [SV338: $i,SV163: $i,SV448: $i] :
( ( ( ~ ( subset @ SV448 @ SV163 ) )
= $true )
| ( ( ~ ( subset @ SV448 @ SV338 )
| ( subset @ SV448 @ ( binintersect @ SV163 @ SV338 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1375,plain,
! [SV339: $i,SV164: $i] :
( ( ( SV164 = SV339 )
= $false )
| ( ( ! [SY740: $i,SY741: $i] :
( ( SY740 != SY741 )
| ~ ( ~ ( ~ ( in @ SY740 @ SV164 )
| ( in @ SY741 @ SV339 ) )
| ~ ( ~ ( in @ SY741 @ SV339 )
| ( in @ SY740 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1199]) ).
thf(1376,plain,
! [SV165: $i,SV340: $i] :
( ( ( in @ SV340 @ ( powerset @ SV165 ) )
= $false )
| ( ( subset @ SV340 @ SV165 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1200]) ).
thf(1377,plain,
! [SV343: $i > $o,SV168: $i] :
( ( ( ~ ! [SY745: $i] :
( ~ ( in @ SY745 @ SV168 )
| ( SV343 @ SY745 ) ) )
= $false )
| ( ( ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV168 )
| ~ ~ ( SV343 @ SY746 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1202]) ).
thf(1378,plain,
! [SV345: $i,SV170: $i] :
( ( ( subset @ SV170 @ SV345 )
= $false )
| ( ( in @ SV170 @ ( powerset @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1203]) ).
thf(1379,plain,
! [SV172: $i,SV347: $i] :
( ( ( ! [SY747: $i] :
( ~ ( in @ SY747 @ SV347 )
| ( in @ SY747 @ SV172 ) ) )
= $false )
| ( ( in @ SV347 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1204]) ).
thf(1380,plain,
! [SV174: $i] :
( ( ( ~ ( in @ emptyset @ SV174 )
| ~ ! [SY431: $i] :
( ~ ~ ( ~ ( in @ SY431 @ omega )
| ~ ( in @ SY431 @ SV174 ) )
| ( in @ ( setadjoin @ SY431 @ SY431 ) @ SV174 ) ) )
= $true )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1381,plain,
! [SV176: $i] :
( ( ( SV176 = emptyset )
= $true )
| ( ( ~ ! [SY433: $i] :
~ ~ ( ~ ( in @ SY433 @ SV176 )
| ~ $true ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1382,plain,
! [SV349: $i,SV177: $i] :
( ( ( SV177 = SV349 )
= $false )
| ( ( ( setunion @ SV177 )
= ( setunion @ SV349 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1383,plain,
! [SV350: $i,SV178: $i] :
( ( ( subset @ SV178 @ SV350 )
= $false )
| ( ( subset @ ( powerset @ SV178 ) @ ( powerset @ SV350 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1208]) ).
thf(1384,plain,
! [SV351: $i,SV179: $i,SV450: $i] :
( ( ( ~ ( in @ SV450 @ SV179 ) )
= $true )
| ( ( ~ ~ ( in @ SV450 @ SV351 )
| ( in @ SV450 @ ( symdiff @ SV179 @ SV351 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1385,plain,
! [SV180: $i] :
( ( ( ! [SY438: $i] :
~ ~ ( ~ ( in @ SY438
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) )
| ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
!= ( setadjoin @ SY438 @ emptyset ) ) ) )
= $false )
| ( ( iskpair @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1210]) ).
thf(1386,plain,
! [SV352: $i,SV181: $i] :
( ( ( ( binintersect @ SV181 @ SV352 )
= SV352 )
= $false )
| ( ( subset @ SV352 @ SV181 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1211]) ).
thf(1387,plain,
! [SV353: $i,SV182: $i,SV451: $i] :
( ( ( ~ ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) ) )
= $true )
| ( ( ! [SY901: $i > $o] :
( ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV182 )
| ! [SY903: $i] :
( ~ ( in @ SY903 @ SV353 )
| ~ ( in @ ( kpair @ SY902 @ SY903 ) @ SV451 )
| ( SY901 @ ( kpair @ SY902 @ SY903 ) ) ) )
| ! [SY904: $i] :
( ~ ( in @ SY904 @ SV451 )
| ( SY901 @ SY904 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1212]) ).
thf(1388,plain,
! [SV354: $i,SV183: $i] :
( ( ( SV183 = SV354 )
= $false )
| ( ( ! [SY754: $i > $o,SY755: $i > $o] :
( ~ ! [SY756: $i] :
( ~ ( in @ SY756 @ SV183 )
| ! [SY757: $i] :
( ~ ( in @ SY757 @ SV354 )
| ( SY756 != SY757 )
| ~ ( ~ ( ~ ( SY754 @ SY756 )
| ( SY755 @ SY757 ) )
| ~ ( ~ ( SY755 @ SY757 )
| ( SY754 @ SY756 ) ) ) ) )
| ( ( dsetconstr @ SV183
@ ^ [SX4: $i] : ( SY754 @ SX4 ) )
= ( dsetconstr @ SV354
@ ^ [SX4: $i] : ( SY755 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1213]) ).
thf(1389,plain,
! [SV355: $i,SV184: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ ( setadjoin @ SV184 @ SV355 ) ) )
= $true )
| ( ( ( SV452 = SV184 )
| ( in @ SV452 @ SV355 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1214]) ).
thf(1390,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) ) )
= $true )
| ( ( ! [SY905: $o] :
( ~ ( ( SV453 != SV185 )
| SY905 )
| ~ ( ~ ( in @ SV453 @ SV356 )
| SY905 )
| SY905 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1215]) ).
thf(1391,plain,
! [SV358: $i,SV187: $i] :
( ( ( ( setminus @ SV187 @ SV358 )
= emptyset )
= $false )
| ( ( subset @ SV187 @ SV358 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1216]) ).
thf(1392,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY764: $i,SY765: $i] :
( ( SY764 != SY765 )
| ~ ( ~ ( ~ ( SV188 @ SY764 )
| ( SV359 @ SY765 ) )
| ~ ( ~ ( SV359 @ SY765 )
| ( SV188 @ SY764 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1217]) ).
thf(1393,plain,
! [SV360: $i,SV189: $i,SV454: $i] :
( ( ( ~ ( in @ SV454 @ SV189 ) )
= $true )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV360 )
| ( in @ ( setadjoin @ ( setadjoin @ SV454 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV454 @ ( setadjoin @ SY906 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV189 @ SV360 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1394,plain,
! [SV361: $i,SV190: $i] :
( ( ( in @ SV190 @ ( setadjoin @ SV361 @ emptyset ) )
= $false )
| ( ( in @ SV361 @ ( setadjoin @ SV190 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1219]) ).
thf(1395,plain,
! [SV362: $i,SV191: $i,SV478: $i,SV455: $i] :
( ( ~ ( in @ ( kpair @ SV455 @ SV478 ) @ ( cartprod @ SV191 @ SV362 ) )
| ( in @ SV478 @ SV362 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1220]) ).
thf(1396,plain,
! [SV456: $i > $i > $o,SV363: $i,SV192: $i,SV479: $i] :
( ( ! [SY935: $i] :
( ~ ( in @ ( kpair @ SV479 @ SY935 )
@ ( dpsetconstr @ SV192 @ SV363
@ ^ [SY910: $i,SY911: $i] : ( SV456 @ SY910 @ SY911 ) ) )
| ( in @ SY935 @ SV363 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1397,plain,
! [SV364: $i,SV193: $i,SV457: $i] :
( ( ( ~ ( in @ SV457 @ ( funcSet @ SV193 @ SV364 ) ) )
= $true )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ SV193 )
| ( in @ ( ap @ SV193 @ SV364 @ SV457 @ SY912 ) @ SV364 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1222]) ).
thf(1398,plain,
! [SV458: $i > $i > $o,SV365: $i,SV194: $i,SV480: $i] :
( ( ~ ( in @ SV480 @ SV194 )
| ! [SY938: $i] :
( ~ ( in @ SY938 @ SV365 )
| ~ ( SV458 @ SV480 @ SY938 )
| ( in @ ( kpair @ SV480 @ SY938 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1223]) ).
thf(1399,plain,
! [SV195: $i > $o] :
( ( ( ! [SY496: $i] :
~ ~ ( ~ ( SV195 @ SY496 )
| ~ ! [SY497: $i] :
( ~ ( SV195 @ SY497 )
| ( SY496 = SY497 ) ) ) )
= $true )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1400,plain,
! [SV366: $i,SV196: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( setminus @ SV196 @ SV366 ) ) )
= $true )
| ( ( in @ SV459 @ SV196 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1225]) ).
thf(1401,plain,
! [SV367: $i,SV197: $i,SV460: $i] :
( ( ( ~ ( in @ SV460 @ SV197 ) )
= $true )
| ( ( ! [SY917: $i] :
( ~ ( in @ SY917 @ SV367 )
| ( ( kpair @ SV460 @ SY917 )
= ( kpair @ SV460 @ SY917 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1226]) ).
thf(1402,plain,
! [SV461: $i,SV368: $i,SV198: $i] :
( ( ( ~ ( func @ SV198 @ SV368 @ SV461 ) )
= $true )
| ( ( ! [SY918: $i] :
( ~ ( in @ SY918 @ SV198 )
| ~ ! [SY919: $i] :
~ ~ ( ~ ( in @ SY919
@ ( dsetconstr @ SV368
@ ^ [SY920: $i] : ( in @ ( kpair @ SY918 @ SY920 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY921: $i] : ( in @ ( kpair @ SY918 @ SY921 ) @ SV461 ) )
!= ( setadjoin @ SY919 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1227]) ).
thf(1403,plain,
! [SV199: $i,SV462: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV462 ) )
= $true )
| ( ( ~ ( in @ SV462 @ SV199 )
| ( in @ SV369 @ ( setunion @ SV199 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1228]) ).
thf(1404,plain,
! [SV463: $i,SV370: $i,SV200: $i] :
( ( ( ~ ( func @ SV200 @ SV370 @ SV463 ) )
= $true )
| ( ( ! [SY922: $i] :
( ~ ( in @ SY922 @ SV200 )
| ! [SY923: $i] :
( ~ ( in @ SY923 @ SV370 )
| ~ ( in @ ( kpair @ SY922 @ SY923 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SY922 )
= SY923 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1229]) ).
thf(1405,plain,
! [SV371: $i,SV202: $i,SV464: $i] :
( ( ( ~ ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) ) )
= $true )
| ( ( ! [SY924: $i] :
( ~ ( in @ SY924 @ SV202 )
| ! [SY925: $i] :
( ~ ( in @ SY925 @ SV371 )
| ~ ( in @ ( kpair @ SY924 @ SY925 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SY924 )
= SY925 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1230]) ).
thf(1406,plain,
! [SV372: $i,SV203: $i] :
( ( ( SV203 = SV372 )
= $false )
| ( ( ( powerset @ SV203 )
= ( powerset @ SV372 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1231]) ).
thf(1407,plain,
! [SV373: $i,SV204: $i,SV465: $i] :
( ( ( ~ ~ ( in @ SV465 @ ( setminus @ SV204 @ SV373 ) ) )
= $true )
| ( ( ~ ( in @ SV465 @ SV204 )
| ( in @ SV465 @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1232]) ).
thf(1408,plain,
! [SV466: $i,SV205: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ ( powerset @ SV205 ) ) )
= $true )
| ( ( ~ ( in @ SV466 @ SV374 )
| ( in @ SV466 @ SV205 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1233]) ).
thf(1409,plain,
! [SV375: $i > $i > $o,SV206: $i,SV1: $i,SV481: $i,SV467: $i] :
( ( ~ ( in @ ( kpair @ SV467 @ SV481 )
@ ( dpsetconstr @ SV1 @ SV206
@ ^ [SY809: $i,SY810: $i] : ( SV375 @ SY809 @ SY810 ) ) )
| ( in @ SV467 @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1410,plain,
! [SV3: $i,SV482: $i] :
( ( ( ~ ~ ( ~ ( in @ SV482 @ SV3 )
| ( SV3
!= ( setadjoin @ SV482 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1235]) ).
thf(1411,plain,
! [SV210: $i,SV6: $i,SV376: $i] :
( ( ( in @ SV376 @ ( funcSet @ SV6 @ SV210 ) )
= $false )
| ( ( func @ SV6 @ SV210 @ SV376 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1236]) ).
thf(1412,plain,
! [SV212: $i,SV8: $i,SV468: $i,SV377: $i] :
( ( ( ~ ( in @ ( kpair @ SV377 @ SV468 ) @ ( cartprod @ SV8 @ SV212 ) ) )
= $true )
| ( ( in @ SV377 @ SV8 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1237]) ).
thf(1413,plain,
! [SV213: $i,SV9: $i,SV378: $i] :
( ( ( in @ ( setadjoin @ SV378 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV9 @ ( setadjoin @ SV213 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV9 = SV378 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1238]) ).
thf(1414,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ SV483 )
| ~ ! [SY943: $i] :
( ~ ( SV10 @ SY943 )
| ( SV483 = SY943 ) ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1239]) ).
thf(1415,plain,
! [SV214: $i,SV11: $i,SV379: $i] :
( ( ( in @ SV379 @ SV11 )
= $false )
| ( ( ! [SY812: $i] :
( ~ ( in @ SY812 @ SV214 )
| ( subset @ ( setadjoin @ SV379 @ ( setadjoin @ SY812 @ emptyset ) ) @ ( binunion @ SV11 @ SV214 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1240]) ).
thf(1416,plain,
! [SV215: $i,SV12: $i] :
( ( ( ~ ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV12 )
| ~ ( in @ SY537 @ SV215 ) ) )
= $true )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1241]) ).
thf(1417,plain,
! [SV469: $i,SV380: $i,SV216: $i,SV13: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV380 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV380 @ ( setadjoin @ SV469 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV13 = SV380 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1418,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ~ ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
| ! [SY944: $i] :
( ~ ( in @ SY944 @ SV14 )
| ~ ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
| ~ ( SV217 @ SY944 )
| ( ( sK8_SY540 @ SV217 @ SV14 )
= SY944 ) ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1243]) ).
thf(1419,plain,
! [SV381: $i,SV218: $i,SV15: $i] :
( ( ( ( setadjoin @ SV15 @ ( setadjoin @ SV218 @ emptyset ) )
= ( setadjoin @ SV381 @ emptyset ) )
= $false )
| ( ( SV15 = SV218 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1244]) ).
thf(1420,plain,
! [SV219: $i,SV16: $i,SV382: $i] :
( ( ( in @ SV382 @ SV16 )
= $false )
| ( ( ! [SY814: $i] :
( ~ ( in @ SY814 @ SV219 )
| ( in @ ( kpair @ SV382 @ SY814 ) @ ( powerset @ ( powerset @ ( binunion @ SV16 @ SV219 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1245]) ).
thf(1421,plain,
! [SV220: $i,SV18: $i,SV383: $i] :
( ( ( ~ ( in @ SV383 @ SV18 ) )
= $false )
| ( ( ~ ( in @ SV383 @ ( setminus @ SV18 @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1249]) ).
thf(1422,plain,
! [SV221: $i > $o,SV19: $i,SV384: $i] :
( ( ( in @ SV384
@ ( dsetconstr @ SV19
@ ^ [SY551: $i] : ( SV221 @ SY551 ) ) )
= $false )
| ( ( in @ SV384 @ SV19 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1423,plain,
! [SV21: $i] :
( ( ( in @ ( sK6_SY54 @ SV21 ) @ SV21 )
= $true )
| ( ( SV21 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1252]) ).
thf(1424,plain,
! [SV385: $i,SV223: $i,SV22: $i] :
( ( ( func @ SV22 @ SV223 @ SV385 )
= $false )
| ( ( ! [SY816: $i] :
( ~ ( in @ SY816 @ SV22 )
| ( in @ ( kpair @ SY816 @ ( ap @ SV22 @ SV223 @ SV385 @ SY816 ) ) @ SV385 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1253]) ).
thf(1425,plain,
! [SV224: $i > $o,SV23: $i,SV386: $i] :
( ( ( in @ SV386 @ SV23 )
= $false )
| ( ( ~ ( SV224 @ SV386 )
| ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV23 )
| ~ ( SV224 @ SY817 )
| ( SY817 = SV386 ) )
| ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1254]) ).
thf(1426,plain,
! [SV471: $o,SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| SV471 )
| ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 )
| SV471 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1255]) ).
thf(1427,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| $true )
| ~ ( ~ ( in @ SV387 @ SV225 )
| $true )
| $true )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1256]) ).
thf(1428,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| $false )
| ~ ( ~ ( in @ SV387 @ SV225 )
| $false )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1257]) ).
thf(1429,plain,
! [SV226: $i,SV25: $i,SV388: $i] :
( ( ( in @ SV388 @ ( setminus @ SV25 @ SV226 ) )
= $false )
| ( ( ~ ( in @ SV388 @ SV226 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1430,plain,
! [SV227: $i,SV26: $i,SV389: $i] :
( ( ( in @ SV389 @ ( binintersect @ SV26 @ SV227 ) )
= $false )
| ( ( in @ SV389 @ SV26 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1431,plain,
! [SV229: $i,SV28: $i,SV390: $i] :
( ( ( in @ SV390 @ ( binintersect @ SV28 @ SV229 ) )
= $false )
| ( ( in @ SV390 @ SV229 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1261]) ).
thf(1432,plain,
! [SV391: $i,SV230: $i,SV29: $i] :
( ( ( func @ SV29 @ SV230 @ SV391 )
= $false )
| ( ( ! [SY822: $i] :
( ~ ( func @ SV29 @ SV230 @ SY822 )
| ~ ! [SY823: $i] :
( ~ ( in @ SY823 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ SY823 )
= ( ap @ SV29 @ SV230 @ SY822 @ SY823 ) ) )
| ! [SY824: $i] :
( ~ ( in @ SY824 @ SV29 )
| ! [SY825: $i] :
( ~ ( in @ SY825 @ SV230 )
| ~ ( in @ ( kpair @ SY824 @ SY825 ) @ SY822 )
| ( in @ ( kpair @ SY824 @ SY825 ) @ SV391 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1433,plain,
! [SV30: $i,SV231: $i,SV392: $i] :
( ( ( in @ SV392 @ SV231 )
= $false )
| ( ( ~ ( in @ SV392 @ ( setminus @ SV30 @ SV231 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1434,plain,
! [SV232: $i,SV31: $i,SV484: $i] :
( ( ( ! [SY945: $i] :
( ( SV484 != SY945 )
| ~ ( in @ SV484 @ SV31 )
| ( in @ SY945 @ SV232 ) ) )
= $true )
| ( ( SV31 = SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1264]) ).
thf(1435,plain,
! [SV32: $i,SV233: $i,SV393: $i] :
( ( ( in @ SV393 @ SV233 )
= $false )
| ( ( in @ SV393 @ ( setadjoin @ SV32 @ SV233 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1436,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( ~ ~ ( ~ ( SV33 @ SV485 )
| ~ ! [SY946: $i] :
( ~ ( SV33 @ SY946 )
| ( SV485 = SY946 ) ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1266]) ).
thf(1437,plain,
! [SV394: $i,SV234: $i,SV34: $i] :
( ( ( subset @ SV34 @ SV234 )
= $false )
| ( ( ~ ( subset @ SV234 @ SV394 )
| ( subset @ SV34 @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1267]) ).
thf(1438,plain,
! [SV235: $i > $o,SV35: $i,SV395: $i] :
( ( ( in @ SV395 @ SV35 )
= $false )
| ( ( ~ ( SV235 @ SV395 )
| ( in @ SV395
@ ( dsetconstr @ SV35
@ ^ [SY575: $i] : ( SV235 @ SY575 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1268]) ).
thf(1439,plain,
! [SV396: $i > $i > $o,SV236: $i,SV36: $i,SV486: $i,SV472: $i] :
( ( ~ ( in @ ( kpair @ SV472 @ SV486 )
@ ( dpsetconstr @ SV36 @ SV236
@ ^ [SY829: $i,SY830: $i] : ( SV396 @ SY829 @ SY830 ) ) )
| ( SV396 @ SV472 @ SV486 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1269]) ).
thf(1440,plain,
! [SV37: $i,SV487: $i] :
( ( ( ~ ( in @ SV487 @ SV37 ) )
= $true )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1270]) ).
thf(1441,plain,
! [SV239: $i,SV40: $i,SV397: $i] :
( ( ( in @ SV397 @ SV40 )
= $false )
| ( ( ~ ~ ( in @ SV397 @ SV239 )
| ~ ( subset @ SV40 @ SV239 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1442,plain,
! [SV241: $i,SV43: $i,SV398: $i] :
( ( ( in @ SV398 @ SV43 )
= $false )
| ( ( in @ ( setadjoin @ SV398 @ emptyset ) @ ( powerset @ ( binunion @ SV43 @ SV241 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1443,plain,
! [SV242: $i > $o,SV44: $i] :
( ( ( ~ ! [SY583: $i] :
~ ~ ( ~ ( in @ SY583 @ SV44 )
| ~ ( SV242 @ SY583 ) ) )
= $true )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1275]) ).
thf(1444,plain,
! [SV243: $i,SV45: $i,SV399: $i] :
( ( ( in @ SV399 @ ( setadjoin @ SV45 @ ( setadjoin @ SV243 @ emptyset ) ) )
= $false )
| ( ( ( SV399 = SV45 )
| ( SV399 = SV243 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1445,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( ~ ~ ( ~ ( SV46 @ SV488 )
| ~ ! [SY949: $i] :
( ~ ( SV46 @ SY949 )
| ( SV488 = SY949 ) ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1277]) ).
thf(1446,plain,
! [SV244: $i > $o,SV47: $i,SV400: $i] :
( ( ( in @ SV400 @ SV47 )
= $false )
| ( ( ~ ( SV244 @ SV400 )
| ( ( dsetconstr @ SV47
@ ^ [SY587: $i] : ( SV244 @ SY587 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1278]) ).
thf(1447,plain,
! [SV245: $i > $o,SV48: $i,SV401: $i] :
( ( ( in @ SV401
@ ( dsetconstr @ SV48
@ ^ [SY589: $i] : ( SV245 @ SY589 ) ) )
= $false )
| ( ( SV245 @ SV401 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1279]) ).
thf(1448,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY950: $i] :
( ( ( sK9_SY590 @ SV246 @ SV49 )
!= SY950 )
| ~ ( ~ ( ~ ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
| ( SV246 @ SY950 ) )
| ~ ( ~ ( SV246 @ SY950 )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1280]) ).
thf(1449,plain,
! [SV473: $i,SV402: $i,SV247: $i,SV52: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV52 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV52 @ ( setadjoin @ SV247 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV402 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV402 @ ( setadjoin @ SV473 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( SV247 = SV473 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1281]) ).
thf(1450,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ! [SY951: $i] :
~ ( ~ ( ~ ( SV53 @ SY951 )
| ( SY951 = SV489 ) )
| ~ ( ( SY951 != SV489 )
| ( SV53 @ SY951 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1282]) ).
thf(1451,plain,
! [SV403: $i,SV249: $i,SV55: $i] :
( ( ( func @ SV55 @ SV249 @ SV403 )
= $false )
| ( ( ! [SY834: $i] :
( ~ ( in @ SY834 @ SV55 )
| ( in @ ( ap @ SV55 @ SV249 @ SV403 @ SY834 ) @ SV249 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1284]) ).
thf(1452,plain,
! [SV250: $i,SV57: $i,SV404: $i] :
( ( ( in @ SV404 @ ( cartprod @ SV57 @ SV250 ) )
= $false )
| ( ( in @ ( kfst @ SV404 ) @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1285]) ).
thf(1453,plain,
( ( ~ ( in @ sK2_SY2 @ sK1_A ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1454,plain,
( ( ~ ~ $true )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1286]) ).
thf(1455,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 ) )
| ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) ) ) )
= $false )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1287]) ).
thf(1456,plain,
! [SV252: $i,SV59: $i] :
( ( ( SV59 = SV252 )
= $true )
| ( ( ~ ( in @ SV252 @ ( setadjoin @ SV59 @ emptyset ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1288]) ).
thf(1457,plain,
! [SV253: $i,SV60: $i,SV405: $i] :
( ( ( in @ SV405 @ SV60 )
= $false )
| ( ( in @ SV405 @ ( binunion @ SV60 @ SV253 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1289]) ).
thf(1458,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
| ~ ! [SY840: $i,SY841: $i] :
( ~ ~ ( ~ ( in @ SY840 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY841 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY840 )
| ( in @ SX4 @ SY841 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY841 )
| ( in @ SX4 @ SY840 ) ) ) )
| ~ ! [SY844: $i] :
( ~ ~ ( ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY844 )
| ( in @ SY164 @ SV62 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY844 ) )
| ~ ! [SY847: $i] :
~ ~ ! [SY848: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY847 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY848 @ SY844 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY847 )
| ~ ( in @ SX5 @ SY844 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY847 ) )
| ( in @ SY848 @ SY850 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1290]) ).
thf(1459,plain,
! [SV255: $i,SV63: $i,SV406: $i] :
( ( ( in @ SV406 @ SV63 )
= $false )
| ( ( ! [SY852: $i] :
( ~ ( in @ SY852 @ SV255 )
| ( in @ ( setadjoin @ SV406 @ ( setadjoin @ SY852 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV255 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1460,plain,
! [SV256: $i,SV64: $i] :
( ( ( ! [SY607: $i] :
~ ~ ( ~ ( in @ SY607 @ SV64 )
| ~ ( in @ SV256 @ SY607 ) ) )
= $false )
| ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1292]) ).
thf(1461,plain,
! [SV258: $i,SV66: $i,SV407: $i] :
( ( ( in @ SV407 @ ( cartprod @ SV66 @ SV258 ) )
= $false )
| ( ( ( kpair @ ( kfst @ SV407 ) @ ( ksnd @ SV407 ) )
= SV407 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1293]) ).
thf(1462,plain,
! [SV259: $i,SV68: $i,SV408: $i] :
( ( ( in @ SV408 @ SV68 )
= $false )
| ( ( ! [SY853: $i] :
( ~ ( in @ SY853 @ SV259 )
| ( ( ksnd @ ( kpair @ SV408 @ SY853 ) )
= SY853 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1294]) ).
thf(1463,plain,
! [SV260: $i > $o,SV69: $i] :
( ( ( ! [SY611: $i] :
~ ~ ( ~ ( in @ SY611
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
| ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SY611 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1464,plain,
! [SV261: $i,SV409: $i > $i,SV70: $i] :
( ( ( ! [SY854: $i] :
( ~ ( in @ SY854 @ SV70 )
| ( in @ ( SV409 @ SY854 ) @ SV261 ) ) )
= $false )
| ( ( func @ SV70 @ SV261
@ ( dpsetconstr @ SV70 @ SV261
@ ^ [SY855: $i,SY856: $i] :
( ( SV409 @ SY855 )
= SY856 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1296]) ).
thf(1465,plain,
! [SV262: $i,SV410: $i > $i,SV71: $i] :
( ( ( ! [SY857: $i] :
( ~ ( in @ SY857 @ SV71 )
| ( in @ ( SV410 @ SY857 ) @ SV262 ) ) )
= $false )
| ( ( in
@ ( dpsetconstr @ SV71 @ SV262
@ ^ [SY858: $i,SY859: $i] :
( ( SV410 @ SY858 )
= SY859 ) )
@ ( funcSet @ SV71 @ SV262 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1297]) ).
thf(1466,plain,
! [SV474: $i,SV411: $i,SV264: $i,SV74: $i] :
( ( ( ( kpair @ SV74 @ SV264 )
!= ( kpair @ SV411 @ SV474 ) )
= $true )
| ( ( SV74 = SV411 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1298]) ).
thf(1467,plain,
! [SV266: $i,SV76: $i,SV413: $i] :
( ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false )
| ( ( ! [SY861: $i > $o] :
( ~ ! [SY862: $i] :
( ~ ( in @ SY862 @ SV76 )
| ! [SY863: $i] :
( ~ ( in @ SY863 @ SV266 )
| ~ ( in @ ( kpair @ SY862 @ SY863 ) @ SV413 )
| ( SY861 @ ( kpair @ SY862 @ SY863 ) ) ) )
| ! [SY864: $i] :
( ~ ( in @ SY864 @ SV413 )
| ( SY861 @ SY864 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1299]) ).
thf(1468,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false )
| ( ( ! [SY865: $o] :
( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| SY865 )
| ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SY865 )
| SY865 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1300]) ).
thf(1469,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( ~ ~ ( ~ ( SV78 @ SV490 )
| ~ ! [SY952: $i] :
( ~ ( SV78 @ SY952 )
| ( SV490 = SY952 ) ) ) )
= $true )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1301]) ).
thf(1470,plain,
! [SV79: $i,SV268: $i] :
( ( ( ~ ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 )
| ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV268 ) )
= $false )
| ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) )
| ( SV79 = SV268 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1302]) ).
thf(1471,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ~ ~ ( ~ ( SV80 @ SV491 )
| ~ ! [SY953: $i] :
( ~ ( SV80 @ SY953 )
| ( SV491 = SY953 ) ) ) )
= $true )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1303]) ).
thf(1472,plain,
! [SV269: $i,SV81: $i,SV415: $i] :
( ( ( in @ SV415 @ SV81 )
= $false )
| ( ( ~ ~ ( in @ SV415 @ SV269 )
| ( in @ SV415 @ ( setminus @ SV81 @ SV269 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1304]) ).
thf(1473,plain,
! [SV82: $i,SV270: $i,SV416: $i] :
( ( ( in @ SV416 @ SV270 )
= $false )
| ( ( in @ SV416 @ ( binunion @ SV82 @ SV270 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1305]) ).
thf(1474,plain,
! [SV83: $i,SV271: $i] :
( ( ~ ( in @ SV271 @ ( setunion @ SV83 ) )
| ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SV271 @ SY637 )
| ~ ( in @ SY637 @ SV83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1306]) ).
thf(1475,plain,
! [SV83: $i,SV271: $i] :
( ( ~ ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SV271 @ SY638 )
| ~ ( in @ SY638 @ SV83 ) )
| ( in @ SV271 @ ( setunion @ SV83 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1307]) ).
thf(1476,plain,
! [SV417: $i,SV272: $i,SV84: $i] :
( ( ( subset @ SV84 @ SV272 )
= $false )
| ( ( ~ ( in @ SV417 @ SV84 )
| ( in @ SV417 @ SV272 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1308]) ).
thf(1477,plain,
! [SV86: $i,SV273: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
| ~ ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) ) )
= $false )
| ( ( ~ ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1309]) ).
thf(1478,plain,
! [SV274: $i,SV418: $i,SV87: $i] :
( ( ( subset @ SV87 @ SV418 )
= $false )
| ( ( subset @ SV87 @ ( setadjoin @ SV274 @ SV418 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1310]) ).
thf(1479,plain,
! [SV88: $i,SV492: $i] :
( ( ( ~ ( in @ SV492 @ SV88 ) )
= $true )
| ( ( ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY237 @ SV88 )
| ~ ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( in @ SY238 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1311]) ).
thf(1480,plain,
! [SV419: $i,SV275: $i,SV89: $i] :
( ( ( func @ SV89 @ SV275 @ SV419 )
= $false )
| ( ( ! [SY866: $i] :
( ~ ( func @ SV89 @ SV275 @ SY866 )
| ~ ! [SY867: $i] :
( ~ ( in @ SY867 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ SY867 )
= ( ap @ SV89 @ SV275 @ SY866 @ SY867 ) ) )
| ( SV419 = SY866 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1312]) ).
thf(1481,plain,
! [SV90: $i] :
( ( ( in @ ( sK7_SY243 @ SV90 ) @ SV90 )
= $true )
| ( ( SV90 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1482,plain,
! [SV276: $i,SV91: $i,SV420: $i] :
( ( ( in @ SV420 @ ( cartprod @ SV91 @ SV276 ) )
= $false )
| ( ( iskpair @ SV420 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1314]) ).
thf(1483,plain,
! [SV279: $i,SV94: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ ( setminus @ SV94 @ SV279 ) ) )
= $false )
| ( ( ~ ~ ( in @ SV421 @ SV279 )
| ~ ( in @ SV421 @ SV94 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1317]) ).
thf(1484,plain,
! [SV280: $i,SV95: $i,SV422: $i] :
( ( ( in @ SV422 @ SV95 )
= $false )
| ( ( ~ ( in @ SV422 @ SV280 )
| ( in @ SV422 @ ( binintersect @ SV95 @ SV280 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1485,plain,
! [SV423: $i > $i > $o,SV281: $i,SV96: $i,SV475: $i] :
( ( ( ~ ( in @ SV475 @ SV96 ) )
= $true )
| ( ( ! [SY932: $i] :
( ~ ( in @ SY932 @ SV281 )
| ~ ( in @ ( kpair @ SV475 @ SY932 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) )
| ( SV423 @ SV475 @ SY932 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1319]) ).
thf(1486,plain,
! [SV282: $i,SV97: $i] :
( ( ( subset @ SV97 @ SV282 )
= $true )
| ( ( SV97 != SV282 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1320]) ).
thf(1487,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ~ ( ~ ( SV98 @ SV493 )
| ~ ! [SY954: $i] :
( ~ ( SV98 @ SY954 )
| ( SV493 = SY954 ) ) ) )
= $true )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1321]) ).
thf(1488,plain,
! [SV283: $i,SV424: $i > $i,SV99: $i] :
( ( ( ! [SY872: $i] :
( ~ ( in @ SY872 @ SV99 )
| ( in @ ( SV424 @ SY872 ) @ SV283 ) ) )
= $false )
| ( ( func @ SV99 @ SV283
@ ( dpsetconstr @ SV99 @ SV283
@ ^ [SY873: $i,SY874: $i] :
( ( SV424 @ SY873 )
= SY874 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1322]) ).
thf(1489,plain,
! [SV476: $i,SV425: $i,SV285: $i,SV101: $i] :
( ( ( ( kpair @ SV101 @ SV285 )
!= ( kpair @ SV425 @ SV476 ) )
= $true )
| ( ( SV285 = SV476 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1323]) ).
thf(1490,plain,
! [SV286: $i,SV102: $i,SV426: $i] :
( ( ( in @ SV426 @ ( setadjoin @ SV102 @ ( setadjoin @ SV286 @ emptyset ) ) )
= $false )
| ( ( ( SV426 = SV102 )
| ( SV426 = SV286 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1324]) ).
thf(1491,plain,
! [SV103: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK13_SY274 @ SV103 )
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
!= ( setadjoin @ ( sK13_SY274 @ SV103 ) @ emptyset ) ) ) )
= $false )
| ( ( iskpair @ SV103 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1325]) ).
thf(1492,plain,
! [SV287: $i > $o,SV104: $i] :
( ( ( ! [SY661: $i] :
~ ~ ( ~ ( in @ SY661 @ SV104 )
| ~ ~ ( SV287 @ SY661 ) ) )
= $true )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1326]) ).
thf(1493,plain,
! [SV427: $i,SV288: $i,SV105: $i] :
( ( ( func @ SV105 @ SV288 @ SV427 )
= $false )
| ( ( in @ SV427 @ ( funcSet @ SV105 @ SV288 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1327]) ).
thf(1494,plain,
! [SV289: $i > $o,SV106: $i] :
( ( ( ! [SY664: $i] :
~ ~ ( ~ ( in @ SY664 @ SV106 )
| ~ ( SV289 @ SY664 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1328]) ).
thf(1495,plain,
! [SV290: $i,SV107: $i,SV428: $i] :
( ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( ! [SY876: $i] :
( ~ ( subset @ SY876 @ ( cartprod @ SV107 @ SV290 ) )
| ~ ! [SY877: $i] :
( ~ ( in @ SY877 @ SV107 )
| ! [SY878: $i] :
( ~ ( in @ SY878 @ SV290 )
| ~ ( in @ ( kpair @ SY877 @ SY878 ) @ SV428 )
| ( in @ ( kpair @ SY877 @ SY878 ) @ SY876 ) ) )
| ( subset @ SV428 @ SY876 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1496,plain,
! [SV294: $i,SV111: $i,SV430: $i] :
( ( ( in @ SV430 @ SV111 )
= $false )
| ( ( ~ ( in @ SV430 @ SV294 )
| ~ ( in @ SV430 @ ( symdiff @ SV111 @ SV294 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1497,plain,
! [SV431: $i,SV295: $i,SV112: $i] :
( ( ( func @ SV112 @ SV295 @ SV431 )
= $false )
| ( ( ! [SY881: $i] :
( ~ ( in @ SY881 @ SV112 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV295
@ ^ [SY882: $i] : ( in @ ( kpair @ SY881 @ SY882 ) @ SV431 ) ) )
@ SV295 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1333]) ).
thf(1498,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ SV494 ) )
= $true )
| ( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( SV113 @ SY303 )
| ~ ( SV113 @ SY304 )
| ( SY303 = SY304 ) )
| ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1499,plain,
! [SV477: $i,SV432: $i,SV297: $i,SV115: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ SV432 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV432 @ ( setadjoin @ SV477 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ( SV432 != SV477 )
| ( SV297 = SV477 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1335]) ).
thf(1500,plain,
! [SV495: $o,SV116: $i,SV298: $i] :
( ( ( ~ ! [SY957: $i] :
( ~ ( in @ SV298 @ SY957 )
| ~ ( in @ SY957 @ SV116 )
| SV495 )
| SV495 )
= $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1336]) ).
thf(1501,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV298 @ SX0 )
| ~ ( in @ SX0 @ SV116 )
| $true )
| $true )
= $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1336]) ).
thf(1502,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV298 @ SX0 )
| ~ ( in @ SX0 @ SV116 )
| $false )
| $false )
= $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1336]) ).
thf(1503,plain,
! [SV117: $i,SV299: $i] :
( ( ( ~ ( in @ ( sK14_SY681 @ SV299 @ SV117 ) @ SV117 )
| ( in @ ( sK14_SY681 @ SV299 @ SV117 ) @ SV299 ) )
= $false )
| ( ( subset @ SV117 @ SV299 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1337]) ).
thf(1504,plain,
! [SV433: $i,SV300: $i,SV118: $i] :
( ( ( subset @ SV118 @ SV300 )
= $false )
| ( ( ~ ~ ( in @ SV433 @ SV300 )
| ~ ( in @ SV433 @ SV118 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1338]) ).
thf(1505,plain,
! [SV303: $i,SV121: $i,SV434: $i] :
( ( ( in @ SV434 @ ( binunion @ SV121 @ SV303 ) )
= $false )
| ( ( ( in @ SV434 @ SV121 )
| ( in @ SV434 @ SV303 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1341]) ).
thf(1506,plain,
! [SV122: $i,SV304: $i] :
( ( ( ~ ( in @ ( sK15_SY684 @ SV304 @ SV122 ) @ SV122 )
| ( in @ ( sK15_SY684 @ SV304 @ SV122 ) @ SV304 ) )
= $false )
| ( ( subset @ SV122 @ SV304 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1342]) ).
thf(1507,plain,
! [SV305: $i,SV123: $i,SV435: $i] :
( ( ( in @ SV435 @ SV123 )
= $false )
| ( ( ~ ~ ( in @ SV435 @ SV305 )
| ( SV123 != SV305 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1508,plain,
! [SV307: $i,SV126: $i,SV436: $i] :
( ( ( in @ SV436 @ ( cartprod @ SV126 @ SV307 ) )
= $false )
| ( ( in @ ( ksnd @ SV436 ) @ SV307 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1345]) ).
thf(1509,plain,
! [SV130: $i,SV309: $i] :
( ( ~ ( in @ SV309 @ ( powerset @ SV130 ) )
| ! [SY687: $i] :
( ~ ( in @ SY687 @ SV309 )
| ( in @ SY687 @ SV130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1346]) ).
thf(1510,plain,
! [SV130: $i,SV309: $i] :
( ( ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV309 )
| ( in @ SY688 @ SV130 ) )
| ( in @ SV309 @ ( powerset @ SV130 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1347]) ).
thf(1511,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ~ ( ~ ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
| ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1349]) ).
thf(1512,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ~ ( ~ ( ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
| ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1349]) ).
thf(1513,plain,
! [SV312: $i,SV133: $i,SV438: $i] :
( ( ( in @ SV438 @ SV133 )
= $false )
| ( ( ! [SY884: $i] :
( ~ ( in @ SY884 @ SV312 )
| ( ( kfst @ ( kpair @ SV438 @ SY884 ) )
= SV438 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1350]) ).
thf(1514,plain,
! [SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
| ~ ! [SY958: $i] :
~ ~ ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY958 )
| ~ ! [SY959: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY959 )
| ( SY958 = SY959 ) ) ) )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1351]) ).
thf(1515,plain,
! [SV317: $i > $o,SV136: $i,SV439: $i] :
( ( ( in @ SV439 @ SV136 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) )
| ( SV317 @ SV439 ) )
| ~ ( ~ ( SV317 @ SV439 )
| ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1355]) ).
thf(1516,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ~ ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
| ! [SY960: $i] :
( ~ ( in @ SY960 @ SV141 )
| ~ ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
| ~ ( SV320 @ SY960 )
| ( ( sK17_SY702 @ SV320 @ SV141 )
= SY960 ) ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1358]) ).
thf(1517,plain,
! [SV321: $i,SV142: $i,SV440: $i] :
( ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( ! [SY887: $i] :
( ~ ( subset @ SY887 @ ( cartprod @ SV142 @ SV321 ) )
| ~ ! [SY888: $i] :
( ~ ( in @ SY888 @ SV142 )
| ! [SY889: $i] :
( ~ ( in @ SY889 @ SV321 )
| ~ ( in @ ( kpair @ SY888 @ SY889 ) @ SV440 )
| ( in @ ( kpair @ SY888 @ SY889 ) @ SY887 ) ) )
| ~ ! [SY890: $i] :
( ~ ( in @ SY890 @ SV142 )
| ! [SY891: $i] :
( ~ ( in @ SY891 @ SV321 )
| ~ ( in @ ( kpair @ SY890 @ SY891 ) @ SY887 )
| ( in @ ( kpair @ SY890 @ SY891 ) @ SV440 ) ) )
| ( SV440 = SY887 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1518,plain,
! [SV323: $i,SV144: $i,SV441: $i] :
( ( ( in @ SV441 @ SV144 )
= $false )
| ( ( ! [SY892: $i] :
( ~ ( in @ SY892 @ SV323 )
| ( in @ ( kpair @ SV441 @ SY892 ) @ ( cartprod @ SV144 @ SV323 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1519,plain,
! [SV146: $i,SV324: $i] :
( ( ( ~ ( subset @ SV324 @ SV146 ) )
= $true )
| ( ( SV146 = SV324 )
= $true )
| ( ( subset @ SV146 @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1361]) ).
thf(1520,plain,
! [SV325: $i > $o,SV147: $i] :
( ( ( ! [SY716: $i] :
( ~ ( in @ SY716 @ SV147 )
| ( SV325 @ SY716 ) ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ~ ( ~ ( in @ SY717 @ SV147 )
| ~ ~ ( SV325 @ SY717 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1362]) ).
thf(1521,plain,
! [SV327: $i,SV149: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ SV149 ) )
= $false )
| ( ( ~ ( in @ SV442 @ SV327 )
| ( in @ SV442 @ ( symdiff @ SV149 @ SV327 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1522,plain,
! [SV151: $i] :
( ( ( ! [SY381: $i] :
~ ( in @ SY381 @ SV151 ) )
= $false )
| ( ( SV151 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1523,plain,
! [SV329: $i > $o,SV154: $i] :
( ( ( ! [SY719: $i] :
~ ~ ( ~ ( in @ SY719
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
| ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SY719 @ emptyset ) ) ) )
= $true )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1365]) ).
thf(1524,plain,
! [SV330: $i,SV155: $i,SV443: $i] :
( ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false )
| ( ( ~ ! [SY893: $i] :
~ ~ ( ~ ( in @ SY893 @ SV155 )
| ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV330 )
| ( SV443
!= ( kpair @ SY893 @ SY894 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1366]) ).
thf(1525,plain,
! [SV331: $i,SV156: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ SV156 ) )
= $false )
| ( ( ~ ~ ( in @ SV444 @ SV331 )
| ~ ( in @ SV444 @ ( symdiff @ SV156 @ SV331 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1367]) ).
thf(1526,plain,
! [SV332: $i > $o,SV157: $i] :
( ( ( ~ ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV157 )
| ~ ( SV332 @ SY728 ) ) )
= $true )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1368]) ).
thf(1527,plain,
! [SV333: $i,SV158: $i,SV445: $i] :
( ( ( in @ SV445 @ SV158 )
= $false )
| ( ( ! [SY895: $i] :
( ~ ( in @ SY895 @ SV333 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV445 @ ( setadjoin @ SY895 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV158 @ SV333 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1369]) ).
thf(1528,plain,
! [SV334: $i,SV159: $i,SV496: $i] :
( ( ( ! [SY961: $i] :
( ( SV496 != SY961 )
| ( ( setadjoin @ SV159 @ SV496 )
= ( setadjoin @ SV334 @ SY961 ) ) ) )
= $true )
| ( ( SV159 = SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1370]) ).
thf(1529,plain,
! [SV336: $i,SV161: $i,SV446: $i] :
( ( ( in @ SV446 @ ( funcSet @ SV161 @ SV336 ) )
= $false )
| ( ( ! [SY896: $i] :
( ~ ( in @ SY896 @ SV161 )
| ( in @ ( kpair @ SY896 @ ( ap @ SV161 @ SV336 @ SV446 @ SY896 ) ) @ SV446 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1372]) ).
thf(1530,plain,
! [SV337: $i,SV162: $i,SV447: $i] :
( ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false )
| ( ( ! [SY897: $i] :
( ~ ( in @ SY897 @ ( funcSet @ SV162 @ SV337 ) )
| ~ ! [SY898: $i] :
( ~ ( in @ SY898 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ SY898 )
= ( ap @ SV162 @ SV337 @ SY897 @ SY898 ) ) )
| ( SV447 = SY897 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1531,plain,
! [SV338: $i,SV163: $i,SV448: $i] :
( ( ( subset @ SV448 @ SV163 )
= $false )
| ( ( ~ ( subset @ SV448 @ SV338 )
| ( subset @ SV448 @ ( binintersect @ SV163 @ SV338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1532,plain,
! [SV339: $i,SV164: $i,SV497: $i] :
( ( ( ! [SY962: $i] :
( ( SV497 != SY962 )
| ~ ( ~ ( ~ ( in @ SV497 @ SV164 )
| ( in @ SY962 @ SV339 ) )
| ~ ( ~ ( in @ SY962 @ SV339 )
| ( in @ SV497 @ SV164 ) ) ) ) )
= $true )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1375]) ).
thf(1533,plain,
! [SV343: $i > $o,SV168: $i] :
( ( ( ! [SY745: $i] :
( ~ ( in @ SY745 @ SV168 )
| ( SV343 @ SY745 ) ) )
= $true )
| ( ( ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV168 )
| ~ ~ ( SV343 @ SY746 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1377]) ).
thf(1534,plain,
! [SV347: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK18_SY747 @ SV172 @ SV347 ) @ SV347 )
| ( in @ ( sK18_SY747 @ SV172 @ SV347 ) @ SV172 ) )
= $false )
| ( ( in @ SV347 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1379]) ).
thf(1535,plain,
! [SV174: $i] :
( ( ( ~ ( in @ emptyset @ SV174 ) )
= $true )
| ( ( ~ ! [SY431: $i] :
( ~ ~ ( ~ ( in @ SY431 @ omega )
| ~ ( in @ SY431 @ SV174 ) )
| ( in @ ( setadjoin @ SY431 @ SY431 ) @ SV174 ) ) )
= $true )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1380]) ).
thf(1536,plain,
! [SV176: $i] :
( ( ( ! [SY433: $i] :
~ ~ ( ~ ( in @ SY433 @ SV176 )
| ~ $true ) )
= $false )
| ( ( SV176 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1537,plain,
! [SV351: $i,SV179: $i,SV450: $i] :
( ( ( in @ SV450 @ SV179 )
= $false )
| ( ( ~ ~ ( in @ SV450 @ SV351 )
| ( in @ SV450 @ ( symdiff @ SV179 @ SV351 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1384]) ).
thf(1538,plain,
! [SV180: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK19_SY438 @ SV180 )
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) )
| ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
!= ( setadjoin @ ( sK19_SY438 @ SV180 ) @ emptyset ) ) ) )
= $false )
| ( ( iskpair @ SV180 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1385]) ).
thf(1539,plain,
! [SV353: $i,SV182: $i,SV451: $i] :
( ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false )
| ( ( ! [SY901: $i > $o] :
( ~ ! [SY902: $i] :
( ~ ( in @ SY902 @ SV182 )
| ! [SY903: $i] :
( ~ ( in @ SY903 @ SV353 )
| ~ ( in @ ( kpair @ SY902 @ SY903 ) @ SV451 )
| ( SY901 @ ( kpair @ SY902 @ SY903 ) ) ) )
| ! [SY904: $i] :
( ~ ( in @ SY904 @ SV451 )
| ( SY901 @ SY904 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1387]) ).
thf(1540,plain,
! [SV498: $i > $o,SV354: $i,SV183: $i] :
( ( ( ! [SY965: $i > $o] :
( ~ ! [SY966: $i] :
( ~ ( in @ SY966 @ SV183 )
| ! [SY967: $i] :
( ~ ( in @ SY967 @ SV354 )
| ( SY966 != SY967 )
| ~ ( ~ ( ~ ( SV498 @ SY966 )
| ( SY965 @ SY967 ) )
| ~ ( ~ ( SY965 @ SY967 )
| ( SV498 @ SY966 ) ) ) ) )
| ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SX4: $i] : ( SY965 @ SX4 ) ) ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1541,plain,
! [SV355: $i,SV184: $i,SV452: $i] :
( ( ( in @ SV452 @ ( setadjoin @ SV184 @ SV355 ) )
= $false )
| ( ( ( SV452 = SV184 )
| ( in @ SV452 @ SV355 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1389]) ).
thf(1542,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false )
| ( ( ! [SY905: $o] :
( ~ ( ( SV453 != SV185 )
| SY905 )
| ~ ( ~ ( in @ SV453 @ SV356 )
| SY905 )
| SY905 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1543,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY970: $i] :
( ( ( sK20_SY764 @ SV359 @ SV188 )
!= SY970 )
| ~ ( ~ ( ~ ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
| ( SV359 @ SY970 ) )
| ~ ( ~ ( SV359 @ SY970 )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1392]) ).
thf(1544,plain,
! [SV360: $i,SV189: $i,SV454: $i] :
( ( ( in @ SV454 @ SV189 )
= $false )
| ( ( ! [SY906: $i] :
( ~ ( in @ SY906 @ SV360 )
| ( in @ ( setadjoin @ ( setadjoin @ SV454 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV454 @ ( setadjoin @ SY906 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV189 @ SV360 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1393]) ).
thf(1545,plain,
! [SV362: $i,SV191: $i,SV478: $i,SV455: $i] :
( ( ( ~ ( in @ ( kpair @ SV455 @ SV478 ) @ ( cartprod @ SV191 @ SV362 ) ) )
= $true )
| ( ( in @ SV478 @ SV362 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1395]) ).
thf(1546,plain,
! [SV456: $i > $i > $o,SV363: $i,SV192: $i,SV499: $i,SV479: $i] :
( ( ~ ( in @ ( kpair @ SV479 @ SV499 )
@ ( dpsetconstr @ SV192 @ SV363
@ ^ [SY910: $i,SY911: $i] : ( SV456 @ SY910 @ SY911 ) ) )
| ( in @ SV499 @ SV363 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1396]) ).
thf(1547,plain,
! [SV364: $i,SV193: $i,SV457: $i] :
( ( ( in @ SV457 @ ( funcSet @ SV193 @ SV364 ) )
= $false )
| ( ( ! [SY912: $i] :
( ~ ( in @ SY912 @ SV193 )
| ( in @ ( ap @ SV193 @ SV364 @ SV457 @ SY912 ) @ SV364 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1548,plain,
! [SV458: $i > $i > $o,SV365: $i,SV194: $i,SV480: $i] :
( ( ( ~ ( in @ SV480 @ SV194 ) )
= $true )
| ( ( ! [SY938: $i] :
( ~ ( in @ SY938 @ SV365 )
| ~ ( SV458 @ SV480 @ SY938 )
| ( in @ ( kpair @ SV480 @ SY938 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1398]) ).
thf(1549,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ~ ~ ( ~ ( SV195 @ SV500 )
| ~ ! [SY973: $i] :
( ~ ( SV195 @ SY973 )
| ( SV500 = SY973 ) ) ) )
= $true )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1399]) ).
thf(1550,plain,
! [SV366: $i,SV196: $i,SV459: $i] :
( ( ( in @ SV459 @ ( setminus @ SV196 @ SV366 ) )
= $false )
| ( ( in @ SV459 @ SV196 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1400]) ).
thf(1551,plain,
! [SV367: $i,SV197: $i,SV460: $i] :
( ( ( in @ SV460 @ SV197 )
= $false )
| ( ( ! [SY917: $i] :
( ~ ( in @ SY917 @ SV367 )
| ( ( kpair @ SV460 @ SY917 )
= ( kpair @ SV460 @ SY917 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1401]) ).
thf(1552,plain,
! [SV461: $i,SV368: $i,SV198: $i] :
( ( ( func @ SV198 @ SV368 @ SV461 )
= $false )
| ( ( ! [SY918: $i] :
( ~ ( in @ SY918 @ SV198 )
| ~ ! [SY919: $i] :
~ ~ ( ~ ( in @ SY919
@ ( dsetconstr @ SV368
@ ^ [SY920: $i] : ( in @ ( kpair @ SY918 @ SY920 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY921: $i] : ( in @ ( kpair @ SY918 @ SY921 ) @ SV461 ) )
!= ( setadjoin @ SY919 @ emptyset ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1402]) ).
thf(1553,plain,
! [SV199: $i,SV462: $i,SV369: $i] :
( ( ( in @ SV369 @ SV462 )
= $false )
| ( ( ~ ( in @ SV462 @ SV199 )
| ( in @ SV369 @ ( setunion @ SV199 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1403]) ).
thf(1554,plain,
! [SV463: $i,SV370: $i,SV200: $i] :
( ( ( func @ SV200 @ SV370 @ SV463 )
= $false )
| ( ( ! [SY922: $i] :
( ~ ( in @ SY922 @ SV200 )
| ! [SY923: $i] :
( ~ ( in @ SY923 @ SV370 )
| ~ ( in @ ( kpair @ SY922 @ SY923 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SY922 )
= SY923 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1404]) ).
thf(1555,plain,
! [SV371: $i,SV202: $i,SV464: $i] :
( ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false )
| ( ( ! [SY924: $i] :
( ~ ( in @ SY924 @ SV202 )
| ! [SY925: $i] :
( ~ ( in @ SY925 @ SV371 )
| ~ ( in @ ( kpair @ SY924 @ SY925 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SY924 )
= SY925 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1405]) ).
thf(1556,plain,
! [SV373: $i,SV204: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ ( setminus @ SV204 @ SV373 ) ) )
= $false )
| ( ( ~ ( in @ SV465 @ SV204 )
| ( in @ SV465 @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1407]) ).
thf(1557,plain,
! [SV466: $i,SV205: $i,SV374: $i] :
( ( ( in @ SV374 @ ( powerset @ SV205 ) )
= $false )
| ( ( ~ ( in @ SV466 @ SV374 )
| ( in @ SV466 @ SV205 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1408]) ).
thf(1558,plain,
! [SV375: $i > $i > $o,SV206: $i,SV1: $i,SV481: $i,SV467: $i] :
( ( ( ~ ( in @ ( kpair @ SV467 @ SV481 )
@ ( dpsetconstr @ SV1 @ SV206
@ ^ [SY809: $i,SY810: $i] : ( SV375 @ SY809 @ SY810 ) ) ) )
= $true )
| ( ( in @ SV467 @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1409]) ).
thf(1559,plain,
! [SV3: $i,SV482: $i] :
( ( ( ~ ( ~ ( in @ SV482 @ SV3 )
| ( SV3
!= ( setadjoin @ SV482 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1560,plain,
! [SV212: $i,SV8: $i,SV468: $i,SV377: $i] :
( ( ( in @ ( kpair @ SV377 @ SV468 ) @ ( cartprod @ SV8 @ SV212 ) )
= $false )
| ( ( in @ SV377 @ SV8 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1412]) ).
thf(1561,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ SV483 )
| ~ ! [SY943: $i] :
( ~ ( SV10 @ SY943 )
| ( SV483 = SY943 ) ) ) )
= $false )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1562,plain,
! [SV11: $i,SV379: $i,SV214: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV214 )
| ( subset @ ( setadjoin @ SV379 @ ( setadjoin @ SV501 @ emptyset ) ) @ ( binunion @ SV11 @ SV214 ) ) )
= $true )
| ( ( in @ SV379 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1415]) ).
thf(1563,plain,
! [SV215: $i,SV12: $i] :
( ( ( ! [SY537: $i] :
~ ~ ( ~ ( in @ SY537 @ SV12 )
| ~ ( in @ SY537 @ SV215 ) ) )
= $false )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1564,plain,
! [SV469: $i,SV380: $i,SV216: $i,SV13: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV13 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV13 @ ( setadjoin @ SV216 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV380 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV380 @ ( setadjoin @ SV469 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV13 = SV380 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1565,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ~ ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1566,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ! [SY944: $i] :
( ~ ( in @ SY944 @ SV14 )
| ~ ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
| ~ ( SV217 @ SY944 )
| ( ( sK8_SY540 @ SV217 @ SV14 )
= SY944 ) ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1418]) ).
thf(1567,plain,
! [SV16: $i,SV382: $i,SV219: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ SV219 )
| ( in @ ( kpair @ SV382 @ SV502 ) @ ( powerset @ ( powerset @ ( binunion @ SV16 @ SV219 ) ) ) ) )
= $true )
| ( ( in @ SV382 @ SV16 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1420]) ).
thf(1568,plain,
! [SV220: $i,SV18: $i,SV383: $i] :
( ( ( in @ SV383 @ SV18 )
= $true )
| ( ( ~ ( in @ SV383 @ ( setminus @ SV18 @ SV220 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1421]) ).
thf(1569,plain,
! [SV385: $i,SV223: $i,SV22: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV22 )
| ( in @ ( kpair @ SV503 @ ( ap @ SV22 @ SV223 @ SV385 @ SV503 ) ) @ SV385 ) )
= $true )
| ( ( func @ SV22 @ SV223 @ SV385 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1424]) ).
thf(1570,plain,
! [SV23: $i,SV386: $i,SV224: $i > $o] :
( ( ( ~ ( SV224 @ SV386 ) )
= $true )
| ( ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV23 )
| ~ ( SV224 @ SY817 )
| ( SY817 = SV386 ) )
| ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1425]) ).
thf(1571,plain,
! [SV471: $o,SV225: $i,SV24: $i,SV387: $i] :
( ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| SV471 )
| ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 )
| SV471 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1426]) ).
thf(1572,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| $true )
| ~ ( ~ ( in @ SV387 @ SV225 )
| $true )
| $true )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1573,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| $false )
| ~ ( ~ ( in @ SV387 @ SV225 )
| $false )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1574,plain,
! [SV25: $i,SV226: $i,SV388: $i] :
( ( ( in @ SV388 @ SV226 )
= $false )
| ( ( in @ SV388 @ ( setminus @ SV25 @ SV226 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1575,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i] :
( ( ( ~ ( func @ SV29 @ SV230 @ SV504 )
| ~ ! [SY974: $i] :
( ~ ( in @ SY974 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ SY974 )
= ( ap @ SV29 @ SV230 @ SV504 @ SY974 ) ) )
| ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1432]) ).
thf(1576,plain,
! [SV231: $i,SV30: $i,SV392: $i] :
( ( ( in @ SV392 @ ( setminus @ SV30 @ SV231 ) )
= $false )
| ( ( in @ SV392 @ SV231 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1433]) ).
thf(1577,plain,
! [SV232: $i,SV31: $i,SV505: $i,SV484: $i] :
( ( ( ( SV484 != SV505 )
| ~ ( in @ SV484 @ SV31 )
| ( in @ SV505 @ SV232 ) )
= $true )
| ( ( SV31 = SV232 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1434]) ).
thf(1578,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( ~ ( ~ ( SV33 @ SV485 )
| ~ ! [SY946: $i] :
( ~ ( SV33 @ SY946 )
| ( SV485 = SY946 ) ) ) )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1436]) ).
thf(1579,plain,
! [SV34: $i,SV394: $i,SV234: $i] :
( ( ( ~ ( subset @ SV234 @ SV394 ) )
= $true )
| ( ( subset @ SV34 @ SV394 )
= $true )
| ( ( subset @ SV34 @ SV234 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1437]) ).
thf(1580,plain,
! [SV35: $i,SV395: $i,SV235: $i > $o] :
( ( ( ~ ( SV235 @ SV395 ) )
= $true )
| ( ( in @ SV395
@ ( dsetconstr @ SV35
@ ^ [SY575: $i] : ( SV235 @ SY575 ) ) )
= $true )
| ( ( in @ SV395 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1581,plain,
! [SV396: $i > $i > $o,SV236: $i,SV36: $i,SV486: $i,SV472: $i] :
( ( ( ~ ( in @ ( kpair @ SV472 @ SV486 )
@ ( dpsetconstr @ SV36 @ SV236
@ ^ [SY829: $i,SY830: $i] : ( SV396 @ SY829 @ SY830 ) ) ) )
= $true )
| ( ( SV396 @ SV472 @ SV486 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1582,plain,
! [SV37: $i,SV487: $i] :
( ( ( in @ SV487 @ SV37 )
= $false )
| ( ( SV37 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1440]) ).
thf(1583,plain,
! [SV40: $i,SV239: $i,SV397: $i] :
( ( ( ~ ~ ( in @ SV397 @ SV239 ) )
= $true )
| ( ( ~ ( subset @ SV40 @ SV239 ) )
= $true )
| ( ( in @ SV397 @ SV40 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1441]) ).
thf(1584,plain,
! [SV242: $i > $o,SV44: $i] :
( ( ( ! [SY583: $i] :
~ ~ ( ~ ( in @ SY583 @ SV44 )
| ~ ( SV242 @ SY583 ) ) )
= $false )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1443]) ).
thf(1585,plain,
! [SV243: $i,SV45: $i,SV399: $i] :
( ( ( SV399 = SV45 )
= $true )
| ( ( SV399 = SV243 )
= $true )
| ( ( in @ SV399 @ ( setadjoin @ SV45 @ ( setadjoin @ SV243 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1444]) ).
thf(1586,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( ~ ( ~ ( SV46 @ SV488 )
| ~ ! [SY949: $i] :
( ~ ( SV46 @ SY949 )
| ( SV488 = SY949 ) ) ) )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1587,plain,
! [SV47: $i,SV400: $i,SV244: $i > $o] :
( ( ( ~ ( SV244 @ SV400 ) )
= $true )
| ( ( ( dsetconstr @ SV47
@ ^ [SY587: $i] : ( SV244 @ SY587 ) )
!= emptyset )
= $true )
| ( ( in @ SV400 @ SV47 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1446]) ).
thf(1588,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( ( ( sK9_SY590 @ SV246 @ SV49 )
!= ( sK21_SY950 @ SV49 @ SV246 ) )
| ~ ( ~ ( ~ ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
| ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) ) )
| ~ ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1448]) ).
thf(1589,plain,
! [SV473: $i,SV402: $i,SV247: $i,SV52: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV52 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV52 @ ( setadjoin @ SV247 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV402 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV402 @ ( setadjoin @ SV473 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV247 = SV473 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1449]) ).
thf(1590,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY951: $i] :
~ ( ~ ( ~ ( SV53 @ SY951 )
| ( SY951 = SV489 ) )
| ~ ( ( SY951 != SV489 )
| ( SV53 @ SY951 ) ) ) )
= $false )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1450]) ).
thf(1591,plain,
! [SV403: $i,SV249: $i,SV55: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV55 )
| ( in @ ( ap @ SV55 @ SV249 @ SV403 @ SV506 ) @ SV249 ) )
= $true )
| ( ( func @ SV55 @ SV249 @ SV403 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1451]) ).
thf(1592,plain,
( ( in @ sK2_SY2 @ sK1_A )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1593,plain,
( ( ~ $true ) = $true ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1594,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 ) )
| ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1595,plain,
! [SV59: $i,SV252: $i] :
( ( ( in @ SV252 @ ( setadjoin @ SV59 @ emptyset ) )
= $false )
| ( ( SV59 = SV252 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1456]) ).
thf(1596,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
| ~ ! [SY840: $i,SY841: $i] :
( ~ ~ ( ~ ( in @ SY840 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY841 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY840 )
| ( in @ SX4 @ SY841 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY841 )
| ( in @ SX4 @ SY840 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1597,plain,
! [SV62: $i] :
( ( ~ ! [SY844: $i] :
( ~ ~ ( ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY844 )
| ( in @ SY164 @ SV62 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY844 ) )
| ~ ! [SY847: $i] :
~ ~ ! [SY848: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY847 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY848 @ SY844 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY847 )
| ~ ( in @ SX5 @ SY844 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY847 ) )
| ( in @ SY848 @ SY850 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1458]) ).
thf(1598,plain,
! [SV63: $i,SV406: $i,SV255: $i,SV507: $i] :
( ( ( ~ ( in @ SV507 @ SV255 )
| ( in @ ( setadjoin @ SV406 @ ( setadjoin @ SV507 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV255 ) ) ) )
= $true )
| ( ( in @ SV406 @ SV63 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1459]) ).
thf(1599,plain,
! [SV64: $i,SV256: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK22_SY607 @ SV256 @ SV64 ) @ SV64 )
| ~ ( in @ SV256 @ ( sK22_SY607 @ SV256 @ SV64 ) ) ) )
= $false )
| ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1460]) ).
thf(1600,plain,
! [SV68: $i,SV408: $i,SV259: $i,SV508: $i] :
( ( ( ~ ( in @ SV508 @ SV259 )
| ( ( ksnd @ ( kpair @ SV408 @ SV508 ) )
= SV508 ) )
= $true )
| ( ( in @ SV408 @ SV68 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1462]) ).
thf(1601,plain,
! [SV260: $i > $o,SV69: $i,SV509: $i] :
( ( ( ~ ~ ( ~ ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
| ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SV509 @ emptyset ) ) ) )
= $true )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1463]) ).
thf(1602,plain,
! [SV70: $i,SV409: $i > $i,SV261: $i] :
( ( ( ~ ( in @ ( sK23_SY854 @ SV261 @ SV409 @ SV70 ) @ SV70 )
| ( in @ ( SV409 @ ( sK23_SY854 @ SV261 @ SV409 @ SV70 ) ) @ SV261 ) )
= $false )
| ( ( func @ SV70 @ SV261
@ ( dpsetconstr @ SV70 @ SV261
@ ^ [SY855: $i,SY856: $i] :
( ( SV409 @ SY855 )
= SY856 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1464]) ).
thf(1603,plain,
! [SV71: $i,SV410: $i > $i,SV262: $i] :
( ( ( ~ ( in @ ( sK24_SY857 @ SV262 @ SV410 @ SV71 ) @ SV71 )
| ( in @ ( SV410 @ ( sK24_SY857 @ SV262 @ SV410 @ SV71 ) ) @ SV262 ) )
= $false )
| ( ( in
@ ( dpsetconstr @ SV71 @ SV262
@ ^ [SY858: $i,SY859: $i] :
( ( SV410 @ SY858 )
= SY859 ) )
@ ( funcSet @ SV71 @ SV262 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1465]) ).
thf(1604,plain,
! [SV474: $i,SV411: $i,SV264: $i,SV74: $i] :
( ( ( ( kpair @ SV74 @ SV264 )
= ( kpair @ SV411 @ SV474 ) )
= $false )
| ( ( SV74 = SV411 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1466]) ).
thf(1605,plain,
! [SV510: $i > $o,SV413: $i,SV266: $i,SV76: $i] :
( ( ( ~ ! [SY979: $i] :
( ~ ( in @ SY979 @ SV76 )
| ! [SY980: $i] :
( ~ ( in @ SY980 @ SV266 )
| ~ ( in @ ( kpair @ SY979 @ SY980 ) @ SV413 )
| ( SV510 @ ( kpair @ SY979 @ SY980 ) ) ) )
| ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1467]) ).
thf(1606,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| SV511 )
| ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1468]) ).
thf(1607,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| $true )
| ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1468]) ).
thf(1608,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| $false )
| ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1468]) ).
thf(1609,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( ~ ( ~ ( SV78 @ SV490 )
| ~ ! [SY952: $i] :
( ~ ( SV78 @ SY952 )
| ( SV490 = SY952 ) ) ) )
= $false )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1469]) ).
thf(1610,plain,
! [SV79: $i,SV268: $i] :
( ( ( ~ ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 ) )
= $false )
| ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) )
| ( SV79 = SV268 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1611,plain,
! [SV79: $i,SV268: $i] :
( ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV268 )
= $false )
| ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) )
| ( SV79 = SV268 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1470]) ).
thf(1612,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ~ ( ~ ( SV80 @ SV491 )
| ~ ! [SY953: $i] :
( ~ ( SV80 @ SY953 )
| ( SV491 = SY953 ) ) ) )
= $false )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1471]) ).
thf(1613,plain,
! [SV81: $i,SV269: $i,SV415: $i] :
( ( ( ~ ~ ( in @ SV415 @ SV269 ) )
= $true )
| ( ( in @ SV415 @ ( setminus @ SV81 @ SV269 ) )
= $true )
| ( ( in @ SV415 @ SV81 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1472]) ).
thf(1614,plain,
! [SV83: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ ( setunion @ SV83 ) ) )
= $true )
| ( ( ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SV271 @ SY637 )
| ~ ( in @ SY637 @ SV83 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1474]) ).
thf(1615,plain,
! [SV83: $i,SV271: $i] :
( ( ( ~ ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SV271 @ SY638 )
| ~ ( in @ SY638 @ SV83 ) ) )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1475]) ).
thf(1616,plain,
! [SV272: $i,SV84: $i,SV417: $i] :
( ( ( ~ ( in @ SV417 @ SV84 ) )
= $true )
| ( ( in @ SV417 @ SV272 )
= $true )
| ( ( subset @ SV84 @ SV272 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1476]) ).
thf(1617,plain,
! [SV86: $i,SV273: $i > $o] :
( ( ( ~ ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 ) )
= $false )
| ( ( ~ ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1618,plain,
! [SV86: $i,SV273: $i > $o] :
( ( ( ~ ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) ) )
= $false )
| ( ( ~ ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1477]) ).
thf(1619,plain,
! [SV88: $i,SV492: $i] :
( ( ( in @ SV492 @ SV88 )
= $false )
| ( ( ~ ! [SY237: $i] :
~ ~ ( ~ ( in @ SY237 @ SV88 )
| ~ ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( in @ SY238 @ SV88 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1479]) ).
thf(1620,plain,
! [SV419: $i,SV512: $i,SV275: $i,SV89: $i] :
( ( ( ~ ( func @ SV89 @ SV275 @ SV512 )
| ~ ! [SY982: $i] :
( ~ ( in @ SY982 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ SY982 )
= ( ap @ SV89 @ SV275 @ SV512 @ SY982 ) ) )
| ( SV419 = SV512 ) )
= $true )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1621,plain,
! [SV279: $i,SV94: $i,SV421: $i] :
( ( ( in @ SV421 @ ( setminus @ SV94 @ SV279 ) )
= $true )
| ( ( ~ ~ ( in @ SV421 @ SV279 )
| ~ ( in @ SV421 @ SV94 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1483]) ).
thf(1622,plain,
! [SV95: $i,SV280: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV280 ) )
= $true )
| ( ( in @ SV422 @ ( binintersect @ SV95 @ SV280 ) )
= $true )
| ( ( in @ SV422 @ SV95 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1623,plain,
! [SV423: $i > $i > $o,SV281: $i,SV96: $i,SV475: $i] :
( ( ( in @ SV475 @ SV96 )
= $false )
| ( ( ! [SY932: $i] :
( ~ ( in @ SY932 @ SV281 )
| ~ ( in @ ( kpair @ SV475 @ SY932 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) )
| ( SV423 @ SV475 @ SY932 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1485]) ).
thf(1624,plain,
! [SV282: $i,SV97: $i] :
( ( ( SV97 = SV282 )
= $false )
| ( ( subset @ SV97 @ SV282 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1486]) ).
thf(1625,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( ~ ( SV98 @ SV493 )
| ~ ! [SY954: $i] :
( ~ ( SV98 @ SY954 )
| ( SV493 = SY954 ) ) ) )
= $false )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1487]) ).
thf(1626,plain,
! [SV99: $i,SV424: $i > $i,SV283: $i] :
( ( ( ~ ( in @ ( sK25_SY872 @ SV283 @ SV424 @ SV99 ) @ SV99 )
| ( in @ ( SV424 @ ( sK25_SY872 @ SV283 @ SV424 @ SV99 ) ) @ SV283 ) )
= $false )
| ( ( func @ SV99 @ SV283
@ ( dpsetconstr @ SV99 @ SV283
@ ^ [SY873: $i,SY874: $i] :
( ( SV424 @ SY873 )
= SY874 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1488]) ).
thf(1627,plain,
! [SV476: $i,SV425: $i,SV285: $i,SV101: $i] :
( ( ( ( kpair @ SV101 @ SV285 )
= ( kpair @ SV425 @ SV476 ) )
= $false )
| ( ( SV285 = SV476 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1489]) ).
thf(1628,plain,
! [SV286: $i,SV102: $i,SV426: $i] :
( ( ( SV426 = SV102 )
= $true )
| ( ( SV426 = SV286 )
= $true )
| ( ( in @ SV426 @ ( setadjoin @ SV102 @ ( setadjoin @ SV286 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1490]) ).
thf(1629,plain,
! [SV103: $i] :
( ( ( ~ ( ~ ( in @ ( sK13_SY274 @ SV103 )
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
!= ( setadjoin @ ( sK13_SY274 @ SV103 ) @ emptyset ) ) ) )
= $true )
| ( ( iskpair @ SV103 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1491]) ).
thf(1630,plain,
! [SV287: $i > $o,SV104: $i,SV513: $i] :
( ( ( ~ ~ ( ~ ( in @ SV513 @ SV104 )
| ~ ~ ( SV287 @ SV513 ) ) )
= $true )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1492]) ).
thf(1631,plain,
! [SV289: $i > $o,SV106: $i,SV514: $i] :
( ( ( ~ ~ ( ~ ( in @ SV514 @ SV106 )
| ~ ( SV289 @ SV514 ) ) )
= $true )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1494]) ).
thf(1632,plain,
! [SV428: $i,SV290: $i,SV107: $i,SV515: $i] :
( ( ( ~ ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
| ~ ! [SY983: $i] :
( ~ ( in @ SY983 @ SV107 )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV290 )
| ~ ( in @ ( kpair @ SY983 @ SY984 ) @ SV428 )
| ( in @ ( kpair @ SY983 @ SY984 ) @ SV515 ) ) )
| ( subset @ SV428 @ SV515 ) )
= $true )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1495]) ).
thf(1633,plain,
! [SV111: $i,SV294: $i,SV430: $i] :
( ( ( ~ ( in @ SV430 @ SV294 ) )
= $true )
| ( ( ~ ( in @ SV430 @ ( symdiff @ SV111 @ SV294 ) ) )
= $true )
| ( ( in @ SV430 @ SV111 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1496]) ).
thf(1634,plain,
! [SV431: $i,SV295: $i,SV112: $i,SV516: $i] :
( ( ( ~ ( in @ SV516 @ SV112 )
| ( in
@ ( setunion
@ ( dsetconstr @ SV295
@ ^ [SY985: $i] : ( in @ ( kpair @ SV516 @ SY985 ) @ SV431 ) ) )
@ SV295 ) )
= $true )
| ( ( func @ SV112 @ SV295 @ SV431 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1497]) ).
thf(1635,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( SV113 @ SV494 )
= $false )
| ( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( SV113 @ SY303 )
| ~ ( SV113 @ SY304 )
| ( SY303 = SY304 ) )
| ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1498]) ).
thf(1636,plain,
! [SV477: $i,SV432: $i,SV297: $i,SV115: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV432 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV432 @ ( setadjoin @ SV477 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ( SV432 != SV477 )
| ( SV297 = SV477 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1637,plain,
! [SV495: $o,SV116: $i,SV298: $i] :
( ( ( ~ ! [SY957: $i] :
( ~ ( in @ SV298 @ SY957 )
| ~ ( in @ SY957 @ SV116 )
| SV495 ) )
= $true )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1500]) ).
thf(1638,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV298 @ SX0 )
| ~ ( in @ SX0 @ SV116 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1501]) ).
thf(1639,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ! [SX0: $i] :
( ~ ( in @ SV298 @ SX0 )
| ~ ( in @ SX0 @ SV116 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1502]) ).
thf(1640,plain,
! [SV117: $i,SV299: $i] :
( ( ( ~ ( in @ ( sK14_SY681 @ SV299 @ SV117 ) @ SV117 ) )
= $false )
| ( ( subset @ SV117 @ SV299 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1503]) ).
thf(1641,plain,
! [SV117: $i,SV299: $i] :
( ( ( in @ ( sK14_SY681 @ SV299 @ SV117 ) @ SV299 )
= $false )
| ( ( subset @ SV117 @ SV299 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1503]) ).
thf(1642,plain,
! [SV118: $i,SV300: $i,SV433: $i] :
( ( ( ~ ~ ( in @ SV433 @ SV300 ) )
= $true )
| ( ( ~ ( in @ SV433 @ SV118 ) )
= $true )
| ( ( subset @ SV118 @ SV300 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1643,plain,
! [SV303: $i,SV121: $i,SV434: $i] :
( ( ( in @ SV434 @ SV121 )
= $true )
| ( ( in @ SV434 @ SV303 )
= $true )
| ( ( in @ SV434 @ ( binunion @ SV121 @ SV303 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1644,plain,
! [SV122: $i,SV304: $i] :
( ( ( ~ ( in @ ( sK15_SY684 @ SV304 @ SV122 ) @ SV122 ) )
= $false )
| ( ( subset @ SV122 @ SV304 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1645,plain,
! [SV122: $i,SV304: $i] :
( ( ( in @ ( sK15_SY684 @ SV304 @ SV122 ) @ SV304 )
= $false )
| ( ( subset @ SV122 @ SV304 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1506]) ).
thf(1646,plain,
! [SV123: $i,SV305: $i,SV435: $i] :
( ( ( ~ ~ ( in @ SV435 @ SV305 ) )
= $true )
| ( ( SV123 != SV305 )
= $true )
| ( ( in @ SV435 @ SV123 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1507]) ).
thf(1647,plain,
! [SV130: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ ( powerset @ SV130 ) ) )
= $true )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV309 )
| ( in @ SY687 @ SV130 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1509]) ).
thf(1648,plain,
! [SV130: $i,SV309: $i] :
( ( ( ~ ! [SY688: $i] :
( ~ ( in @ SY688 @ SV309 )
| ( in @ SY688 @ SV130 ) ) )
= $true )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1510]) ).
thf(1649,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ~ ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
| ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1511]) ).
thf(1650,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ~ ( ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
| ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1651,plain,
! [SV133: $i,SV438: $i,SV312: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ SV312 )
| ( ( kfst @ ( kpair @ SV438 @ SV517 ) )
= SV438 ) )
= $true )
| ( ( in @ SV438 @ SV133 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1513]) ).
thf(1652,plain,
! [SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 ) )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1653,plain,
! [SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ! [SY958: $i] :
~ ~ ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY958 )
| ~ ! [SY959: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY959 )
| ( SY958 = SY959 ) ) ) )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1514]) ).
thf(1654,plain,
! [SV317: $i > $o,SV136: $i,SV439: $i] :
( ( ( ~ ( ~ ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) )
| ( SV317 @ SV439 ) )
| ~ ( ~ ( SV317 @ SV439 )
| ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) ) ) )
= $false )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1655,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ~ ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1516]) ).
thf(1656,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ! [SY960: $i] :
( ~ ( in @ SY960 @ SV141 )
| ~ ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
| ~ ( SV320 @ SY960 )
| ( ( sK17_SY702 @ SV320 @ SV141 )
= SY960 ) ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1516]) ).
thf(1657,plain,
! [SV440: $i,SV321: $i,SV142: $i,SV518: $i] :
( ( ( ~ ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
| ~ ! [SY986: $i] :
( ~ ( in @ SY986 @ SV142 )
| ! [SY987: $i] :
( ~ ( in @ SY987 @ SV321 )
| ~ ( in @ ( kpair @ SY986 @ SY987 ) @ SV440 )
| ( in @ ( kpair @ SY986 @ SY987 ) @ SV518 ) ) )
| ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1517]) ).
thf(1658,plain,
! [SV144: $i,SV441: $i,SV323: $i,SV519: $i] :
( ( ( ~ ( in @ SV519 @ SV323 )
| ( in @ ( kpair @ SV441 @ SV519 ) @ ( cartprod @ SV144 @ SV323 ) ) )
= $true )
| ( ( in @ SV441 @ SV144 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1518]) ).
thf(1659,plain,
! [SV146: $i,SV324: $i] :
( ( ( subset @ SV324 @ SV146 )
= $false )
| ( ( SV146 = SV324 )
= $true )
| ( ( subset @ SV146 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1519]) ).
thf(1660,plain,
! [SV325: $i > $o,SV147: $i,SV520: $i] :
( ( ( ~ ( in @ SV520 @ SV147 )
| ( SV325 @ SV520 ) )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ~ ( ~ ( in @ SY717 @ SV147 )
| ~ ~ ( SV325 @ SY717 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1661,plain,
! [SV327: $i,SV149: $i,SV442: $i] :
( ( ( in @ SV442 @ SV149 )
= $true )
| ( ( ~ ( in @ SV442 @ SV327 )
| ( in @ SV442 @ ( symdiff @ SV149 @ SV327 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1521]) ).
thf(1662,plain,
! [SV151: $i] :
( ( ( ~ ( in @ ( sK26_SY381 @ SV151 ) @ SV151 ) )
= $false )
| ( ( SV151 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1522]) ).
thf(1663,plain,
! [SV329: $i > $o,SV154: $i,SV521: $i] :
( ( ( ~ ~ ( ~ ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
| ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SV521 @ emptyset ) ) ) )
= $true )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1523]) ).
thf(1664,plain,
! [SV443: $i,SV330: $i,SV155: $i] :
( ( ( ! [SY893: $i] :
~ ~ ( ~ ( in @ SY893 @ SV155 )
| ~ ~ ! [SY894: $i] :
~ ~ ( ~ ( in @ SY894 @ SV330 )
| ( SV443
!= ( kpair @ SY893 @ SY894 ) ) ) ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1524]) ).
thf(1665,plain,
! [SV331: $i,SV156: $i,SV444: $i] :
( ( ( in @ SV444 @ SV156 )
= $true )
| ( ( ~ ~ ( in @ SV444 @ SV331 )
| ~ ( in @ SV444 @ ( symdiff @ SV156 @ SV331 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1666,plain,
! [SV332: $i > $o,SV157: $i] :
( ( ( ! [SY728: $i] :
~ ~ ( ~ ( in @ SY728 @ SV157 )
| ~ ( SV332 @ SY728 ) ) )
= $false )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1526]) ).
thf(1667,plain,
! [SV158: $i,SV445: $i,SV333: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV333 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV445 @ ( setadjoin @ SV522 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV158 @ SV333 ) ) ) )
= $true )
| ( ( in @ SV445 @ SV158 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1527]) ).
thf(1668,plain,
! [SV334: $i,SV159: $i,SV523: $i,SV496: $i] :
( ( ( ( SV496 != SV523 )
| ( ( setadjoin @ SV159 @ SV496 )
= ( setadjoin @ SV334 @ SV523 ) ) )
= $true )
| ( ( SV159 = SV334 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1528]) ).
thf(1669,plain,
! [SV446: $i,SV336: $i,SV161: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ SV161 )
| ( in @ ( kpair @ SV524 @ ( ap @ SV161 @ SV336 @ SV446 @ SV524 ) ) @ SV446 ) )
= $true )
| ( ( in @ SV446 @ ( funcSet @ SV161 @ SV336 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1529]) ).
thf(1670,plain,
! [SV447: $i,SV337: $i,SV162: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) )
| ~ ! [SY992: $i] :
( ~ ( in @ SY992 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ SY992 )
= ( ap @ SV162 @ SV337 @ SV525 @ SY992 ) ) )
| ( SV447 = SV525 ) )
= $true )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1671,plain,
! [SV163: $i,SV338: $i,SV448: $i] :
( ( ( ~ ( subset @ SV448 @ SV338 ) )
= $true )
| ( ( subset @ SV448 @ ( binintersect @ SV163 @ SV338 ) )
= $true )
| ( ( subset @ SV448 @ SV163 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1531]) ).
thf(1672,plain,
! [SV339: $i,SV164: $i,SV526: $i,SV497: $i] :
( ( ( ( SV497 != SV526 )
| ~ ( ~ ( ~ ( in @ SV497 @ SV164 )
| ( in @ SV526 @ SV339 ) )
| ~ ( ~ ( in @ SV526 @ SV339 )
| ( in @ SV497 @ SV164 ) ) ) )
= $true )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1532]) ).
thf(1673,plain,
! [SV343: $i > $o,SV168: $i,SV527: $i] :
( ( ( ~ ( in @ SV527 @ SV168 )
| ( SV343 @ SV527 ) )
= $true )
| ( ( ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV168 )
| ~ ~ ( SV343 @ SY746 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1533]) ).
thf(1674,plain,
! [SV347: $i,SV172: $i] :
( ( ( ~ ( in @ ( sK18_SY747 @ SV172 @ SV347 ) @ SV347 ) )
= $false )
| ( ( in @ SV347 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1675,plain,
! [SV347: $i,SV172: $i] :
( ( ( in @ ( sK18_SY747 @ SV172 @ SV347 ) @ SV172 )
= $false )
| ( ( in @ SV347 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1534]) ).
thf(1676,plain,
! [SV174: $i] :
( ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ~ ! [SY431: $i] :
( ~ ~ ( ~ ( in @ SY431 @ omega )
| ~ ( in @ SY431 @ SV174 ) )
| ( in @ ( setadjoin @ SY431 @ SY431 ) @ SV174 ) ) )
= $true )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1535]) ).
thf(1677,plain,
! [SV176: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK27_SY433 @ SV176 ) @ SV176 )
| ~ $true ) )
= $false )
| ( ( SV176 = emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1536]) ).
thf(1678,plain,
! [SV179: $i,SV351: $i,SV450: $i] :
( ( ( ~ ~ ( in @ SV450 @ SV351 ) )
= $true )
| ( ( in @ SV450 @ ( symdiff @ SV179 @ SV351 ) )
= $true )
| ( ( in @ SV450 @ SV179 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1537]) ).
thf(1679,plain,
! [SV180: $i] :
( ( ( ~ ( ~ ( in @ ( sK19_SY438 @ SV180 )
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) )
| ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
!= ( setadjoin @ ( sK19_SY438 @ SV180 ) @ emptyset ) ) ) )
= $true )
| ( ( iskpair @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1680,plain,
! [SV528: $i > $o,SV451: $i,SV353: $i,SV182: $i] :
( ( ( ~ ! [SY993: $i] :
( ~ ( in @ SY993 @ SV182 )
| ! [SY994: $i] :
( ~ ( in @ SY994 @ SV353 )
| ~ ( in @ ( kpair @ SY993 @ SY994 ) @ SV451 )
| ( SV528 @ ( kpair @ SY993 @ SY994 ) ) ) )
| ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1539]) ).
thf(1681,plain,
! [SV529: $i > $o,SV498: $i > $o,SV354: $i,SV183: $i] :
( ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ SV183 )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV354 )
| ( SY996 != SY997 )
| ~ ( ~ ( ~ ( SV498 @ SY996 )
| ( SV529 @ SY997 ) )
| ~ ( ~ ( SV529 @ SY997 )
| ( SV498 @ SY996 ) ) ) ) )
| ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1540]) ).
thf(1682,plain,
! [SV355: $i,SV184: $i,SV452: $i] :
( ( ( SV452 = SV184 )
= $true )
| ( ( in @ SV452 @ SV355 )
= $true )
| ( ( in @ SV452 @ ( setadjoin @ SV184 @ SV355 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1541]) ).
thf(1683,plain,
! [SV356: $i,SV530: $o,SV185: $i,SV453: $i] :
( ( ( ~ ( ( SV453 != SV185 )
| SV530 )
| ~ ( ~ ( in @ SV453 @ SV356 )
| SV530 )
| SV530 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1542]) ).
thf(1684,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( ~ ( ( SV453 != SV185 )
| $true )
| ~ ( ~ ( in @ SV453 @ SV356 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1542]) ).
thf(1685,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( ~ ( ( SV453 != SV185 )
| $false )
| ~ ( ~ ( in @ SV453 @ SV356 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1542]) ).
thf(1686,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ( ( sK20_SY764 @ SV359 @ SV188 )
!= ( sK28_SY970 @ SV188 @ SV359 ) )
| ~ ( ~ ( ~ ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
| ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) ) )
| ~ ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1543]) ).
thf(1687,plain,
! [SV189: $i,SV454: $i,SV360: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ SV360 )
| ( in @ ( setadjoin @ ( setadjoin @ SV454 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV454 @ ( setadjoin @ SV531 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV189 @ SV360 ) ) ) ) )
= $true )
| ( ( in @ SV454 @ SV189 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1544]) ).
thf(1688,plain,
! [SV362: $i,SV191: $i,SV478: $i,SV455: $i] :
( ( ( in @ ( kpair @ SV455 @ SV478 ) @ ( cartprod @ SV191 @ SV362 ) )
= $false )
| ( ( in @ SV478 @ SV362 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1545]) ).
thf(1689,plain,
! [SV456: $i > $i > $o,SV363: $i,SV192: $i,SV499: $i,SV479: $i] :
( ( ( ~ ( in @ ( kpair @ SV479 @ SV499 )
@ ( dpsetconstr @ SV192 @ SV363
@ ^ [SY910: $i,SY911: $i] : ( SV456 @ SY910 @ SY911 ) ) ) )
= $true )
| ( ( in @ SV499 @ SV363 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1546]) ).
thf(1690,plain,
! [SV457: $i,SV364: $i,SV193: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ SV193 )
| ( in @ ( ap @ SV193 @ SV364 @ SV457 @ SV532 ) @ SV364 ) )
= $true )
| ( ( in @ SV457 @ ( funcSet @ SV193 @ SV364 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1547]) ).
thf(1691,plain,
! [SV458: $i > $i > $o,SV365: $i,SV194: $i,SV480: $i] :
( ( ( in @ SV480 @ SV194 )
= $false )
| ( ( ! [SY938: $i] :
( ~ ( in @ SY938 @ SV365 )
| ~ ( SV458 @ SV480 @ SY938 )
| ( in @ ( kpair @ SV480 @ SY938 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1548]) ).
thf(1692,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ~ ( ~ ( SV195 @ SV500 )
| ~ ! [SY973: $i] :
( ~ ( SV195 @ SY973 )
| ( SV500 = SY973 ) ) ) )
= $false )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1549]) ).
thf(1693,plain,
! [SV197: $i,SV460: $i,SV367: $i,SV533: $i] :
( ( ( ~ ( in @ SV533 @ SV367 )
| ( ( kpair @ SV460 @ SV533 )
= ( kpair @ SV460 @ SV533 ) ) )
= $true )
| ( ( in @ SV460 @ SV197 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1551]) ).
thf(1694,plain,
! [SV461: $i,SV368: $i,SV198: $i,SV534: $i] :
( ( ( ~ ( in @ SV534 @ SV198 )
| ~ ! [SY1000: $i] :
~ ~ ( ~ ( in @ SY1000
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
!= ( setadjoin @ SY1000 @ emptyset ) ) ) )
= $true )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1695,plain,
! [SV369: $i,SV199: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ SV199 ) )
= $true )
| ( ( in @ SV369 @ ( setunion @ SV199 ) )
= $true )
| ( ( in @ SV369 @ SV462 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1553]) ).
thf(1696,plain,
! [SV463: $i,SV370: $i,SV200: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ SV200 )
| ! [SY1003: $i] :
( ~ ( in @ SY1003 @ SV370 )
| ~ ( in @ ( kpair @ SV535 @ SY1003 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SV535 )
= SY1003 ) ) )
= $true )
| ( ( func @ SV200 @ SV370 @ SV463 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1554]) ).
thf(1697,plain,
! [SV464: $i,SV371: $i,SV202: $i,SV536: $i] :
( ( ( ~ ( in @ SV536 @ SV202 )
| ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV371 )
| ~ ( in @ ( kpair @ SV536 @ SY1004 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SV536 )
= SY1004 ) ) )
= $true )
| ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1555]) ).
thf(1698,plain,
! [SV373: $i,SV204: $i,SV465: $i] :
( ( ( in @ SV465 @ ( setminus @ SV204 @ SV373 ) )
= $true )
| ( ( ~ ( in @ SV465 @ SV204 )
| ( in @ SV465 @ SV373 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1556]) ).
thf(1699,plain,
! [SV205: $i,SV374: $i,SV466: $i] :
( ( ( ~ ( in @ SV466 @ SV374 ) )
= $true )
| ( ( in @ SV466 @ SV205 )
= $true )
| ( ( in @ SV374 @ ( powerset @ SV205 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1557]) ).
thf(1700,plain,
! [SV375: $i > $i > $o,SV206: $i,SV1: $i,SV481: $i,SV467: $i] :
( ( ( in @ ( kpair @ SV467 @ SV481 )
@ ( dpsetconstr @ SV1 @ SV206
@ ^ [SY809: $i,SY810: $i] : ( SV375 @ SY809 @ SY810 ) ) )
= $false )
| ( ( in @ SV467 @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1558]) ).
thf(1701,plain,
! [SV3: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV3 )
| ( SV3
!= ( setadjoin @ SV482 @ emptyset ) ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1559]) ).
thf(1702,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV483 )
| ~ ! [SY943: $i] :
( ~ ( SV10 @ SY943 )
| ( SV483 = SY943 ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1561]) ).
thf(1703,plain,
! [SV11: $i,SV379: $i,SV214: $i,SV501: $i] :
( ( ( ~ ( in @ SV501 @ SV214 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV379 @ ( setadjoin @ SV501 @ emptyset ) ) @ ( binunion @ SV11 @ SV214 ) )
= $true )
| ( ( in @ SV379 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1562]) ).
thf(1704,plain,
! [SV12: $i,SV215: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV215 ) ) )
= $false )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1563]) ).
thf(1705,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1565]) ).
thf(1706,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
| ~ ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
| ~ ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
| ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1566]) ).
thf(1707,plain,
! [SV16: $i,SV382: $i,SV219: $i,SV502: $i] :
( ( ( ~ ( in @ SV502 @ SV219 ) )
= $true )
| ( ( in @ ( kpair @ SV382 @ SV502 ) @ ( powerset @ ( powerset @ ( binunion @ SV16 @ SV219 ) ) ) )
= $true )
| ( ( in @ SV382 @ SV16 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1567]) ).
thf(1708,plain,
! [SV220: $i,SV18: $i,SV383: $i] :
( ( ( in @ SV383 @ ( setminus @ SV18 @ SV220 ) )
= $false )
| ( ( in @ SV383 @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1568]) ).
thf(1709,plain,
! [SV385: $i,SV223: $i,SV22: $i,SV503: $i] :
( ( ( ~ ( in @ SV503 @ SV22 ) )
= $true )
| ( ( in @ ( kpair @ SV503 @ ( ap @ SV22 @ SV223 @ SV385 @ SV503 ) ) @ SV385 )
= $true )
| ( ( func @ SV22 @ SV223 @ SV385 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1569]) ).
thf(1710,plain,
! [SV23: $i,SV386: $i,SV224: $i > $o] :
( ( ( SV224 @ SV386 )
= $false )
| ( ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV23 )
| ~ ( SV224 @ SY817 )
| ( SY817 = SV386 ) )
| ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1570]) ).
thf(1711,plain,
! [SV225: $i,SV471: $o,SV24: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| SV471 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 )
| SV471 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1571]) ).
thf(1712,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $true )
| $true )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1572]) ).
thf(1713,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV24 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $false )
| $false )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1573]) ).
thf(1714,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i] :
( ( ( ~ ( func @ SV29 @ SV230 @ SV504 ) )
= $true )
| ( ( ~ ! [SY974: $i] :
( ~ ( in @ SY974 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ SY974 )
= ( ap @ SV29 @ SV230 @ SV504 @ SY974 ) ) )
| ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1575]) ).
thf(1715,plain,
! [SV232: $i,SV31: $i,SV505: $i,SV484: $i] :
( ( ( SV484 != SV505 )
= $true )
| ( ( ~ ( in @ SV484 @ SV31 )
| ( in @ SV505 @ SV232 ) )
= $true )
| ( ( SV31 = SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1716,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV485 )
| ~ ! [SY946: $i] :
( ~ ( SV33 @ SY946 )
| ( SV485 = SY946 ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1717,plain,
! [SV34: $i,SV394: $i,SV234: $i] :
( ( ( subset @ SV234 @ SV394 )
= $false )
| ( ( subset @ SV34 @ SV394 )
= $true )
| ( ( subset @ SV34 @ SV234 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1579]) ).
thf(1718,plain,
! [SV35: $i,SV395: $i,SV235: $i > $o] :
( ( ( SV235 @ SV395 )
= $false )
| ( ( in @ SV395
@ ( dsetconstr @ SV35
@ ^ [SY575: $i] : ( SV235 @ SY575 ) ) )
= $true )
| ( ( in @ SV395 @ SV35 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1580]) ).
thf(1719,plain,
! [SV396: $i > $i > $o,SV236: $i,SV36: $i,SV486: $i,SV472: $i] :
( ( ( in @ ( kpair @ SV472 @ SV486 )
@ ( dpsetconstr @ SV36 @ SV236
@ ^ [SY829: $i,SY830: $i] : ( SV396 @ SY829 @ SY830 ) ) )
= $false )
| ( ( SV396 @ SV472 @ SV486 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1720,plain,
! [SV487: $i,SV37: $i] :
( ( ( SV37 = emptyset )
= $false )
| ( ( in @ SV487 @ SV37 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1721,plain,
! [SV40: $i,SV239: $i,SV397: $i] :
( ( ( ~ ( in @ SV397 @ SV239 ) )
= $false )
| ( ( ~ ( subset @ SV40 @ SV239 ) )
= $true )
| ( ( in @ SV397 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1583]) ).
thf(1722,plain,
! [SV44: $i,SV242: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 )
| ~ ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) ) ) )
= $false )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1584]) ).
thf(1723,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV488 )
| ~ ! [SY949: $i] :
( ~ ( SV46 @ SY949 )
| ( SV488 = SY949 ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1586]) ).
thf(1724,plain,
! [SV47: $i,SV400: $i,SV244: $i > $o] :
( ( ( SV244 @ SV400 )
= $false )
| ( ( ( dsetconstr @ SV47
@ ^ [SY587: $i] : ( SV244 @ SY587 ) )
!= emptyset )
= $true )
| ( ( in @ SV400 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1587]) ).
thf(1725,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( ( sK9_SY590 @ SV246 @ SV49 )
!= ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1726,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
| ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) ) )
| ~ ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1588]) ).
thf(1727,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
| ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 ) )
| ~ ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) ) ) )
= $false )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1590]) ).
thf(1728,plain,
! [SV403: $i,SV249: $i,SV55: $i,SV506: $i] :
( ( ( ~ ( in @ SV506 @ SV55 ) )
= $true )
| ( ( in @ ( ap @ SV55 @ SV249 @ SV403 @ SV506 ) @ SV249 )
= $true )
| ( ( func @ SV55 @ SV249 @ SV403 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1729,plain,
$true = $false,
inference(extcnf_not_pos,[status(thm)],[1593]) ).
thf(1730,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1594]) ).
thf(1731,plain,
! [SV62: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
| ~ ! [SY840: $i,SY841: $i] :
( ~ ~ ( ~ ( in @ SY840 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY841 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY840 )
| ( in @ SX4 @ SY841 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY841 )
| ( in @ SX4 @ SY840 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1596]) ).
thf(1732,plain,
! [SV62: $i] :
( ( ! [SY844: $i] :
( ~ ~ ( ~ ! [SY164: $i] :
( ~ ( in @ SY164 @ SY844 )
| ( in @ SY164 @ SV62 ) )
| ~ ~ ! [SX3: $i] :
~ ( in @ SX3 @ SY844 ) )
| ~ ! [SY847: $i] :
~ ~ ! [SY848: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY847 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY848 @ SY844 ) )
| ~ ~ ~ ! [SX5: $i] :
~ ~ ( ~ ( in @ SX5 @ SY847 )
| ~ ( in @ SX5 @ SY844 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY847 ) )
| ( in @ SY848 @ SY850 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1597]) ).
thf(1733,plain,
! [SV63: $i,SV406: $i,SV255: $i,SV507: $i] :
( ( ( ~ ( in @ SV507 @ SV255 ) )
= $true )
| ( ( in @ ( setadjoin @ SV406 @ ( setadjoin @ SV507 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV255 ) ) )
= $true )
| ( ( in @ SV406 @ SV63 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1598]) ).
thf(1734,plain,
! [SV64: $i,SV256: $i] :
( ( ( ~ ( ~ ( in @ ( sK22_SY607 @ SV256 @ SV64 ) @ SV64 )
| ~ ( in @ SV256 @ ( sK22_SY607 @ SV256 @ SV64 ) ) ) )
= $true )
| ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1599]) ).
thf(1735,plain,
! [SV68: $i,SV408: $i,SV259: $i,SV508: $i] :
( ( ( ~ ( in @ SV508 @ SV259 ) )
= $true )
| ( ( ( ksnd @ ( kpair @ SV408 @ SV508 ) )
= SV508 )
= $true )
| ( ( in @ SV408 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1600]) ).
thf(1736,plain,
! [SV260: $i > $o,SV69: $i,SV509: $i] :
( ( ( ~ ( ~ ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
| ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SV509 @ emptyset ) ) ) )
= $false )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1601]) ).
thf(1737,plain,
! [SV70: $i,SV409: $i > $i,SV261: $i] :
( ( ( ~ ( in @ ( sK23_SY854 @ SV261 @ SV409 @ SV70 ) @ SV70 ) )
= $false )
| ( ( func @ SV70 @ SV261
@ ( dpsetconstr @ SV70 @ SV261
@ ^ [SY855: $i,SY856: $i] :
( ( SV409 @ SY855 )
= SY856 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1738,plain,
! [SV70: $i,SV261: $i,SV409: $i > $i] :
( ( ( in @ ( SV409 @ ( sK23_SY854 @ SV261 @ SV409 @ SV70 ) ) @ SV261 )
= $false )
| ( ( func @ SV70 @ SV261
@ ( dpsetconstr @ SV70 @ SV261
@ ^ [SY855: $i,SY856: $i] :
( ( SV409 @ SY855 )
= SY856 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1602]) ).
thf(1739,plain,
! [SV71: $i,SV410: $i > $i,SV262: $i] :
( ( ( ~ ( in @ ( sK24_SY857 @ SV262 @ SV410 @ SV71 ) @ SV71 ) )
= $false )
| ( ( in
@ ( dpsetconstr @ SV71 @ SV262
@ ^ [SY858: $i,SY859: $i] :
( ( SV410 @ SY858 )
= SY859 ) )
@ ( funcSet @ SV71 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1740,plain,
! [SV71: $i,SV262: $i,SV410: $i > $i] :
( ( ( in @ ( SV410 @ ( sK24_SY857 @ SV262 @ SV410 @ SV71 ) ) @ SV262 )
= $false )
| ( ( in
@ ( dpsetconstr @ SV71 @ SV262
@ ^ [SY858: $i,SY859: $i] :
( ( SV410 @ SY858 )
= SY859 ) )
@ ( funcSet @ SV71 @ SV262 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1741,plain,
! [SV510: $i > $o,SV413: $i,SV266: $i,SV76: $i] :
( ( ( ~ ! [SY979: $i] :
( ~ ( in @ SY979 @ SV76 )
| ! [SY980: $i] :
( ~ ( in @ SY980 @ SV266 )
| ~ ( in @ ( kpair @ SY979 @ SY980 ) @ SV413 )
| ( SV510 @ ( kpair @ SY979 @ SY980 ) ) ) ) )
= $true )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1605]) ).
thf(1742,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| SV511 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1606]) ).
thf(1743,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| $true ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1607]) ).
thf(1744,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| $false ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1608]) ).
thf(1745,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( ~ ( SV78 @ SV490 )
| ~ ! [SY952: $i] :
( ~ ( SV78 @ SY952 )
| ( SV490 = SY952 ) ) )
= $true )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1609]) ).
thf(1746,plain,
! [SV79: $i,SV268: $i] :
( ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 )
= $true )
| ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) )
| ( SV79 = SV268 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1610]) ).
thf(1747,plain,
! [SV79: $i,SV268: $i] :
( ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) ) )
= $true )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV268 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1611]) ).
thf(1748,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV491 )
| ~ ! [SY953: $i] :
( ~ ( SV80 @ SY953 )
| ( SV491 = SY953 ) ) )
= $true )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1612]) ).
thf(1749,plain,
! [SV81: $i,SV269: $i,SV415: $i] :
( ( ( ~ ( in @ SV415 @ SV269 ) )
= $false )
| ( ( in @ SV415 @ ( setminus @ SV81 @ SV269 ) )
= $true )
| ( ( in @ SV415 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1613]) ).
thf(1750,plain,
! [SV83: $i,SV271: $i] :
( ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false )
| ( ( ~ ! [SY637: $i] :
~ ~ ( ~ ( in @ SV271 @ SY637 )
| ~ ( in @ SY637 @ SV83 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1614]) ).
thf(1751,plain,
! [SV83: $i,SV271: $i] :
( ( ( ~ ! [SY638: $i] :
~ ~ ( ~ ( in @ SV271 @ SY638 )
| ~ ( in @ SY638 @ SV83 ) ) )
= $false )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1752,plain,
! [SV272: $i,SV84: $i,SV417: $i] :
( ( ( in @ SV417 @ SV84 )
= $false )
| ( ( in @ SV417 @ SV272 )
= $true )
| ( ( subset @ SV84 @ SV272 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1753,plain,
! [SV86: $i,SV273: $i > $o] :
( ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true )
| ( ( ~ ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1617]) ).
thf(1754,plain,
! [SV86: $i,SV273: $i > $o] :
( ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true )
| ( ( ~ ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1618]) ).
thf(1755,plain,
! [SV492: $i,SV88: $i] :
( ( ( ! [SY237: $i] :
~ ~ ( ~ ( in @ SY237 @ SV88 )
| ~ ~ ~ ! [SY238: $i] :
~ ~ ( ~ ( in @ SY238 @ SY237 )
| ~ ( in @ SY238 @ SV88 ) ) ) )
= $false )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1756,plain,
! [SV419: $i,SV512: $i,SV275: $i,SV89: $i] :
( ( ( ~ ( func @ SV89 @ SV275 @ SV512 ) )
= $true )
| ( ( ~ ! [SY982: $i] :
( ~ ( in @ SY982 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ SY982 )
= ( ap @ SV89 @ SV275 @ SV512 @ SY982 ) ) )
| ( SV419 = SV512 ) )
= $true )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1620]) ).
thf(1757,plain,
! [SV94: $i,SV279: $i,SV421: $i] :
( ( ( ~ ~ ( in @ SV421 @ SV279 ) )
= $true )
| ( ( ~ ( in @ SV421 @ SV94 ) )
= $true )
| ( ( in @ SV421 @ ( setminus @ SV94 @ SV279 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1621]) ).
thf(1758,plain,
! [SV95: $i,SV280: $i,SV422: $i] :
( ( ( in @ SV422 @ SV280 )
= $false )
| ( ( in @ SV422 @ ( binintersect @ SV95 @ SV280 ) )
= $true )
| ( ( in @ SV422 @ SV95 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1622]) ).
thf(1759,plain,
! [SV423: $i > $i > $o,SV96: $i,SV475: $i,SV281: $i,SV537: $i] :
( ( ( ~ ( in @ SV537 @ SV281 )
| ~ ( in @ ( kpair @ SV475 @ SV537 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) )
| ( SV423 @ SV475 @ SV537 ) )
= $true )
| ( ( in @ SV475 @ SV96 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1623]) ).
thf(1760,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV493 )
| ~ ! [SY954: $i] :
( ~ ( SV98 @ SY954 )
| ( SV493 = SY954 ) ) )
= $true )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1625]) ).
thf(1761,plain,
! [SV99: $i,SV424: $i > $i,SV283: $i] :
( ( ( ~ ( in @ ( sK25_SY872 @ SV283 @ SV424 @ SV99 ) @ SV99 ) )
= $false )
| ( ( func @ SV99 @ SV283
@ ( dpsetconstr @ SV99 @ SV283
@ ^ [SY873: $i,SY874: $i] :
( ( SV424 @ SY873 )
= SY874 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1762,plain,
! [SV99: $i,SV283: $i,SV424: $i > $i] :
( ( ( in @ ( SV424 @ ( sK25_SY872 @ SV283 @ SV424 @ SV99 ) ) @ SV283 )
= $false )
| ( ( func @ SV99 @ SV283
@ ( dpsetconstr @ SV99 @ SV283
@ ^ [SY873: $i,SY874: $i] :
( ( SV424 @ SY873 )
= SY874 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1626]) ).
thf(1763,plain,
! [SV103: $i] :
( ( ( ~ ( in @ ( sK13_SY274 @ SV103 )
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) )
| ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
!= ( setadjoin @ ( sK13_SY274 @ SV103 ) @ emptyset ) ) )
= $false )
| ( ( iskpair @ SV103 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1629]) ).
thf(1764,plain,
! [SV287: $i > $o,SV104: $i,SV513: $i] :
( ( ( ~ ( ~ ( in @ SV513 @ SV104 )
| ~ ~ ( SV287 @ SV513 ) ) )
= $false )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1765,plain,
! [SV289: $i > $o,SV106: $i,SV514: $i] :
( ( ( ~ ( ~ ( in @ SV514 @ SV106 )
| ~ ( SV289 @ SV514 ) ) )
= $false )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1631]) ).
thf(1766,plain,
! [SV428: $i,SV290: $i,SV107: $i,SV515: $i] :
( ( ( ~ ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) ) )
= $true )
| ( ( ~ ! [SY983: $i] :
( ~ ( in @ SY983 @ SV107 )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV290 )
| ~ ( in @ ( kpair @ SY983 @ SY984 ) @ SV428 )
| ( in @ ( kpair @ SY983 @ SY984 ) @ SV515 ) ) )
| ( subset @ SV428 @ SV515 ) )
= $true )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1632]) ).
thf(1767,plain,
! [SV111: $i,SV294: $i,SV430: $i] :
( ( ( in @ SV430 @ SV294 )
= $false )
| ( ( ~ ( in @ SV430 @ ( symdiff @ SV111 @ SV294 ) ) )
= $true )
| ( ( in @ SV430 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1633]) ).
thf(1768,plain,
! [SV431: $i,SV295: $i,SV112: $i,SV516: $i] :
( ( ( ~ ( in @ SV516 @ SV112 ) )
= $true )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV295
@ ^ [SY985: $i] : ( in @ ( kpair @ SV516 @ SY985 ) @ SV431 ) ) )
@ SV295 )
= $true )
| ( ( func @ SV112 @ SV295 @ SV431 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1634]) ).
thf(1769,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ! [SY303: $i,SY304: $i] :
( ~ ( SV113 @ SY303 )
| ~ ( SV113 @ SY304 )
| ( SY303 = SY304 ) ) )
= $true )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1635]) ).
thf(1770,plain,
! [SV115: $i,SV297: $i,SV477: $i,SV432: $i] :
( ( ( SV432 != SV477 )
= $true )
| ( ( SV297 = SV477 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV432 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV432 @ ( setadjoin @ SV477 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1636]) ).
thf(1771,plain,
! [SV495: $o,SV116: $i,SV298: $i] :
( ( ( ! [SY957: $i] :
( ~ ( in @ SV298 @ SY957 )
| ~ ( in @ SY957 @ SV116 )
| SV495 ) )
= $false )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1772,plain,
! [SV116: $i,SV298: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV298 @ SX0 )
| ~ ( in @ SX0 @ SV116 )
| $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1638]) ).
thf(1773,plain,
! [SV116: $i,SV298: $i] :
( ( ( ! [SX0: $i] :
( ~ ( in @ SV298 @ SX0 )
| ~ ( in @ SX0 @ SV116 )
| $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1774,plain,
! [SV117: $i,SV299: $i] :
( ( ( in @ ( sK14_SY681 @ SV299 @ SV117 ) @ SV117 )
= $true )
| ( ( subset @ SV117 @ SV299 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1640]) ).
thf(1775,plain,
! [SV118: $i,SV300: $i,SV433: $i] :
( ( ( ~ ( in @ SV433 @ SV300 ) )
= $false )
| ( ( ~ ( in @ SV433 @ SV118 ) )
= $true )
| ( ( subset @ SV118 @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1642]) ).
thf(1776,plain,
! [SV122: $i,SV304: $i] :
( ( ( in @ ( sK15_SY684 @ SV304 @ SV122 ) @ SV122 )
= $true )
| ( ( subset @ SV122 @ SV304 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1644]) ).
thf(1777,plain,
! [SV123: $i,SV305: $i,SV435: $i] :
( ( ( ~ ( in @ SV435 @ SV305 ) )
= $false )
| ( ( SV123 != SV305 )
= $true )
| ( ( in @ SV435 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1778,plain,
! [SV130: $i,SV309: $i] :
( ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $false )
| ( ( ! [SY687: $i] :
( ~ ( in @ SY687 @ SV309 )
| ( in @ SY687 @ SV130 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1647]) ).
thf(1779,plain,
! [SV130: $i,SV309: $i] :
( ( ( ! [SY688: $i] :
( ~ ( in @ SY688 @ SV309 )
| ( in @ SY688 @ SV130 ) ) )
= $false )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1648]) ).
thf(1780,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ( ~ ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) ) )
= $true )
| ( ( ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1781,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ( ~ ( ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) ) )
= $true )
| ( ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1782,plain,
! [SV133: $i,SV438: $i,SV312: $i,SV517: $i] :
( ( ( ~ ( in @ SV517 @ SV312 ) )
= $true )
| ( ( ( kfst @ ( kpair @ SV438 @ SV517 ) )
= SV438 )
= $true )
| ( ( in @ SV438 @ SV133 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1783,plain,
! [SV313: $i,SV134: $i > $i > $o] :
( ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1652]) ).
thf(1784,plain,
! [SV313: $i,SV134: $i > $i > $o] :
( ( ( ! [SY958: $i] :
~ ~ ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY958 )
| ~ ! [SY959: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY959 )
| ( SY958 = SY959 ) ) ) )
= $true )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1653]) ).
thf(1785,plain,
! [SV317: $i > $o,SV136: $i,SV439: $i] :
( ( ( ~ ( ~ ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) )
| ( SV317 @ SV439 ) ) )
= $false )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1786,plain,
! [SV136: $i,SV439: $i,SV317: $i > $o] :
( ( ( ~ ( ~ ( SV317 @ SV439 )
| ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) ) ) )
= $false )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1787,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1655]) ).
thf(1788,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ~ ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
| ~ ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
| ~ ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
| ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1656]) ).
thf(1789,plain,
! [SV440: $i,SV321: $i,SV142: $i,SV518: $i] :
( ( ( ~ ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) ) )
= $true )
| ( ( ~ ! [SY986: $i] :
( ~ ( in @ SY986 @ SV142 )
| ! [SY987: $i] :
( ~ ( in @ SY987 @ SV321 )
| ~ ( in @ ( kpair @ SY986 @ SY987 ) @ SV440 )
| ( in @ ( kpair @ SY986 @ SY987 ) @ SV518 ) ) )
| ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1657]) ).
thf(1790,plain,
! [SV144: $i,SV441: $i,SV323: $i,SV519: $i] :
( ( ( ~ ( in @ SV519 @ SV323 ) )
= $true )
| ( ( in @ ( kpair @ SV441 @ SV519 ) @ ( cartprod @ SV144 @ SV323 ) )
= $true )
| ( ( in @ SV441 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1658]) ).
thf(1791,plain,
! [SV325: $i > $o,SV147: $i,SV520: $i] :
( ( ( ~ ( in @ SV520 @ SV147 ) )
= $true )
| ( ( SV325 @ SV520 )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ~ ( ~ ( in @ SY717 @ SV147 )
| ~ ~ ( SV325 @ SY717 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1792,plain,
! [SV149: $i,SV327: $i,SV442: $i] :
( ( ( ~ ( in @ SV442 @ SV327 ) )
= $true )
| ( ( in @ SV442 @ ( symdiff @ SV149 @ SV327 ) )
= $true )
| ( ( in @ SV442 @ SV149 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1793,plain,
! [SV151: $i] :
( ( ( in @ ( sK26_SY381 @ SV151 ) @ SV151 )
= $true )
| ( ( SV151 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1662]) ).
thf(1794,plain,
! [SV329: $i > $o,SV154: $i,SV521: $i] :
( ( ( ~ ( ~ ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
| ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SV521 @ emptyset ) ) ) )
= $false )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1663]) ).
thf(1795,plain,
! [SV155: $i,SV330: $i,SV443: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SV155 )
| ~ ~ ! [SY1007: $i] :
~ ~ ( ~ ( in @ SY1007 @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SY1007 ) ) ) ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1664]) ).
thf(1796,plain,
! [SV156: $i,SV331: $i,SV444: $i] :
( ( ( ~ ~ ( in @ SV444 @ SV331 ) )
= $true )
| ( ( ~ ( in @ SV444 @ ( symdiff @ SV156 @ SV331 ) ) )
= $true )
| ( ( in @ SV444 @ SV156 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1665]) ).
thf(1797,plain,
! [SV157: $i,SV332: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 )
| ~ ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) ) ) )
= $false )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1666]) ).
thf(1798,plain,
! [SV158: $i,SV445: $i,SV333: $i,SV522: $i] :
( ( ( ~ ( in @ SV522 @ SV333 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV445 @ ( setadjoin @ SV522 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV158 @ SV333 ) ) )
= $true )
| ( ( in @ SV445 @ SV158 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1667]) ).
thf(1799,plain,
! [SV334: $i,SV159: $i,SV523: $i,SV496: $i] :
( ( ( SV496 != SV523 )
= $true )
| ( ( ( setadjoin @ SV159 @ SV496 )
= ( setadjoin @ SV334 @ SV523 ) )
= $true )
| ( ( SV159 = SV334 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1668]) ).
thf(1800,plain,
! [SV446: $i,SV336: $i,SV161: $i,SV524: $i] :
( ( ( ~ ( in @ SV524 @ SV161 ) )
= $true )
| ( ( in @ ( kpair @ SV524 @ ( ap @ SV161 @ SV336 @ SV446 @ SV524 ) ) @ SV446 )
= $true )
| ( ( in @ SV446 @ ( funcSet @ SV161 @ SV336 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1669]) ).
thf(1801,plain,
! [SV447: $i,SV337: $i,SV162: $i,SV525: $i] :
( ( ( ~ ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) ) )
= $true )
| ( ( ~ ! [SY992: $i] :
( ~ ( in @ SY992 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ SY992 )
= ( ap @ SV162 @ SV337 @ SV525 @ SY992 ) ) )
| ( SV447 = SV525 ) )
= $true )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1670]) ).
thf(1802,plain,
! [SV163: $i,SV338: $i,SV448: $i] :
( ( ( subset @ SV448 @ SV338 )
= $false )
| ( ( subset @ SV448 @ ( binintersect @ SV163 @ SV338 ) )
= $true )
| ( ( subset @ SV448 @ SV163 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1671]) ).
thf(1803,plain,
! [SV339: $i,SV164: $i,SV526: $i,SV497: $i] :
( ( ( SV497 != SV526 )
= $true )
| ( ( ~ ( ~ ( ~ ( in @ SV497 @ SV164 )
| ( in @ SV526 @ SV339 ) )
| ~ ( ~ ( in @ SV526 @ SV339 )
| ( in @ SV497 @ SV164 ) ) ) )
= $true )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1672]) ).
thf(1804,plain,
! [SV343: $i > $o,SV168: $i,SV527: $i] :
( ( ( ~ ( in @ SV527 @ SV168 ) )
= $true )
| ( ( SV343 @ SV527 )
= $true )
| ( ( ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV168 )
| ~ ~ ( SV343 @ SY746 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1673]) ).
thf(1805,plain,
! [SV347: $i,SV172: $i] :
( ( ( in @ ( sK18_SY747 @ SV172 @ SV347 ) @ SV347 )
= $true )
| ( ( in @ SV347 @ ( powerset @ SV172 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1674]) ).
thf(1806,plain,
! [SV174: $i] :
( ( ( ! [SY431: $i] :
( ~ ~ ( ~ ( in @ SY431 @ omega )
| ~ ( in @ SY431 @ SV174 ) )
| ( in @ ( setadjoin @ SY431 @ SY431 ) @ SV174 ) ) )
= $false )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1676]) ).
thf(1807,plain,
! [SV176: $i] :
( ( ( ~ ( ~ ( in @ ( sK27_SY433 @ SV176 ) @ SV176 )
| ~ $true ) )
= $true )
| ( ( SV176 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1677]) ).
thf(1808,plain,
! [SV179: $i,SV351: $i,SV450: $i] :
( ( ( ~ ( in @ SV450 @ SV351 ) )
= $false )
| ( ( in @ SV450 @ ( symdiff @ SV179 @ SV351 ) )
= $true )
| ( ( in @ SV450 @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1809,plain,
! [SV180: $i] :
( ( ( ~ ( in @ ( sK19_SY438 @ SV180 )
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) )
| ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
!= ( setadjoin @ ( sK19_SY438 @ SV180 ) @ emptyset ) ) )
= $false )
| ( ( iskpair @ SV180 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1810,plain,
! [SV528: $i > $o,SV451: $i,SV353: $i,SV182: $i] :
( ( ( ~ ! [SY993: $i] :
( ~ ( in @ SY993 @ SV182 )
| ! [SY994: $i] :
( ~ ( in @ SY994 @ SV353 )
| ~ ( in @ ( kpair @ SY993 @ SY994 ) @ SV451 )
| ( SV528 @ ( kpair @ SY993 @ SY994 ) ) ) ) )
= $true )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1680]) ).
thf(1811,plain,
! [SV529: $i > $o,SV498: $i > $o,SV354: $i,SV183: $i] :
( ( ( ~ ! [SY996: $i] :
( ~ ( in @ SY996 @ SV183 )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV354 )
| ( SY996 != SY997 )
| ~ ( ~ ( ~ ( SV498 @ SY996 )
| ( SV529 @ SY997 ) )
| ~ ( ~ ( SV529 @ SY997 )
| ( SV498 @ SY996 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1681]) ).
thf(1812,plain,
! [SV356: $i,SV530: $o,SV185: $i,SV453: $i] :
( ( ( ~ ( ( SV453 != SV185 )
| SV530 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| SV530 )
| SV530 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1683]) ).
thf(1813,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( ~ ( ( SV453 != SV185 )
| $true ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1684]) ).
thf(1814,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( ~ ( ( SV453 != SV185 )
| $false ) )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1685]) ).
thf(1815,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ( sK20_SY764 @ SV359 @ SV188 )
!= ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1816,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
| ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) ) )
| ~ ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1686]) ).
thf(1817,plain,
! [SV189: $i,SV454: $i,SV360: $i,SV531: $i] :
( ( ( ~ ( in @ SV531 @ SV360 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV454 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV454 @ ( setadjoin @ SV531 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV189 @ SV360 ) ) ) )
= $true )
| ( ( in @ SV454 @ SV189 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1818,plain,
! [SV456: $i > $i > $o,SV363: $i,SV192: $i,SV499: $i,SV479: $i] :
( ( ( in @ ( kpair @ SV479 @ SV499 )
@ ( dpsetconstr @ SV192 @ SV363
@ ^ [SY910: $i,SY911: $i] : ( SV456 @ SY910 @ SY911 ) ) )
= $false )
| ( ( in @ SV499 @ SV363 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1689]) ).
thf(1819,plain,
! [SV457: $i,SV364: $i,SV193: $i,SV532: $i] :
( ( ( ~ ( in @ SV532 @ SV193 ) )
= $true )
| ( ( in @ ( ap @ SV193 @ SV364 @ SV457 @ SV532 ) @ SV364 )
= $true )
| ( ( in @ SV457 @ ( funcSet @ SV193 @ SV364 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1690]) ).
thf(1820,plain,
! [SV194: $i,SV480: $i,SV458: $i > $i > $o,SV365: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ SV365 )
| ~ ( SV458 @ SV480 @ SV538 )
| ( in @ ( kpair @ SV480 @ SV538 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) ) )
= $true )
| ( ( in @ SV480 @ SV194 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1691]) ).
thf(1821,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ~ ( SV195 @ SV500 )
| ~ ! [SY973: $i] :
( ~ ( SV195 @ SY973 )
| ( SV500 = SY973 ) ) )
= $true )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1692]) ).
thf(1822,plain,
! [SV197: $i,SV460: $i,SV367: $i,SV533: $i] :
( ( ( ~ ( in @ SV533 @ SV367 ) )
= $true )
| ( ( ( kpair @ SV460 @ SV533 )
= ( kpair @ SV460 @ SV533 ) )
= $true )
| ( ( in @ SV460 @ SV197 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1693]) ).
thf(1823,plain,
! [SV461: $i,SV368: $i,SV198: $i,SV534: $i] :
( ( ( ~ ( in @ SV534 @ SV198 ) )
= $true )
| ( ( ~ ! [SY1000: $i] :
~ ~ ( ~ ( in @ SY1000
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
!= ( setadjoin @ SY1000 @ emptyset ) ) ) )
= $true )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1694]) ).
thf(1824,plain,
! [SV369: $i,SV199: $i,SV462: $i] :
( ( ( in @ SV462 @ SV199 )
= $false )
| ( ( in @ SV369 @ ( setunion @ SV199 ) )
= $true )
| ( ( in @ SV369 @ SV462 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1695]) ).
thf(1825,plain,
! [SV463: $i,SV370: $i,SV200: $i,SV535: $i] :
( ( ( ~ ( in @ SV535 @ SV200 ) )
= $true )
| ( ( ! [SY1003: $i] :
( ~ ( in @ SY1003 @ SV370 )
| ~ ( in @ ( kpair @ SV535 @ SY1003 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SV535 )
= SY1003 ) ) )
= $true )
| ( ( func @ SV200 @ SV370 @ SV463 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1696]) ).
thf(1826,plain,
! [SV464: $i,SV371: $i,SV202: $i,SV536: $i] :
( ( ( ~ ( in @ SV536 @ SV202 ) )
= $true )
| ( ( ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV371 )
| ~ ( in @ ( kpair @ SV536 @ SY1004 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SV536 )
= SY1004 ) ) )
= $true )
| ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1697]) ).
thf(1827,plain,
! [SV373: $i,SV204: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ SV204 ) )
= $true )
| ( ( in @ SV465 @ SV373 )
= $true )
| ( ( in @ SV465 @ ( setminus @ SV204 @ SV373 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1698]) ).
thf(1828,plain,
! [SV205: $i,SV374: $i,SV466: $i] :
( ( ( in @ SV466 @ SV374 )
= $false )
| ( ( in @ SV466 @ SV205 )
= $true )
| ( ( in @ SV374 @ ( powerset @ SV205 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1699]) ).
thf(1829,plain,
! [SV3: $i,SV482: $i] :
( ( ( ~ ( in @ SV482 @ SV3 ) )
= $true )
| ( ( SV3
!= ( setadjoin @ SV482 @ emptyset ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1701]) ).
thf(1830,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV483 ) )
= $true )
| ( ( ~ ! [SY943: $i] :
( ~ ( SV10 @ SY943 )
| ( SV483 = SY943 ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1702]) ).
thf(1831,plain,
! [SV11: $i,SV379: $i,SV214: $i,SV501: $i] :
( ( ( in @ SV501 @ SV214 )
= $false )
| ( ( subset @ ( setadjoin @ SV379 @ ( setadjoin @ SV501 @ emptyset ) ) @ ( binunion @ SV11 @ SV214 ) )
= $true )
| ( ( in @ SV379 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1703]) ).
thf(1832,plain,
! [SV12: $i,SV215: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV215 ) ) )
= $true )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1704]) ).
thf(1833,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1705]) ).
thf(1834,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ~ ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1706]) ).
thf(1835,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ~ ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
| ~ ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
| ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1706]) ).
thf(1836,plain,
! [SV16: $i,SV382: $i,SV219: $i,SV502: $i] :
( ( ( in @ SV502 @ SV219 )
= $false )
| ( ( in @ ( kpair @ SV382 @ SV502 ) @ ( powerset @ ( powerset @ ( binunion @ SV16 @ SV219 ) ) ) )
= $true )
| ( ( in @ SV382 @ SV16 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1707]) ).
thf(1837,plain,
! [SV385: $i,SV223: $i,SV22: $i,SV503: $i] :
( ( ( in @ SV503 @ SV22 )
= $false )
| ( ( in @ ( kpair @ SV503 @ ( ap @ SV22 @ SV223 @ SV385 @ SV503 ) ) @ SV385 )
= $true )
| ( ( func @ SV22 @ SV223 @ SV385 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1709]) ).
thf(1838,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ~ ! [SY817: $i] :
( ~ ( in @ SY817 @ SV23 )
| ~ ( SV224 @ SY817 )
| ( SY817 = SV386 ) ) )
= $true )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1710]) ).
thf(1839,plain,
! [SV225: $i,SV471: $o,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV24 )
| SV471 )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 )
| SV471 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1711]) ).
thf(1840,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV24 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $true )
| $true )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1712]) ).
thf(1841,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV24 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $false )
| $false )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1842,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i] :
( ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( ~ ! [SY974: $i] :
( ~ ( in @ SY974 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ SY974 )
= ( ap @ SV29 @ SV230 @ SV504 @ SY974 ) ) )
| ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1714]) ).
thf(1843,plain,
! [SV232: $i,SV31: $i,SV505: $i,SV484: $i] :
( ( ( SV484 = SV505 )
= $false )
| ( ( ~ ( in @ SV484 @ SV31 )
| ( in @ SV505 @ SV232 ) )
= $true )
| ( ( SV31 = SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1715]) ).
thf(1844,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV485 ) )
= $true )
| ( ( ~ ! [SY946: $i] :
( ~ ( SV33 @ SY946 )
| ( SV485 = SY946 ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1716]) ).
thf(1845,plain,
! [SV40: $i,SV239: $i,SV397: $i] :
( ( ( in @ SV397 @ SV239 )
= $true )
| ( ( ~ ( subset @ SV40 @ SV239 ) )
= $true )
| ( ( in @ SV397 @ SV40 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1721]) ).
thf(1846,plain,
! [SV44: $i,SV242: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 )
| ~ ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) ) ) )
= $true )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1722]) ).
thf(1847,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV488 ) )
= $true )
| ( ( ~ ! [SY949: $i] :
( ~ ( SV46 @ SY949 )
| ( SV488 = SY949 ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1723]) ).
thf(1848,plain,
! [SV400: $i,SV244: $i > $o,SV47: $i] :
( ( ( ( dsetconstr @ SV47
@ ^ [SY587: $i] : ( SV244 @ SY587 ) )
= emptyset )
= $false )
| ( ( SV244 @ SV400 )
= $false )
| ( ( in @ SV400 @ SV47 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1724]) ).
thf(1849,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1725]) ).
thf(1850,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
| ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) ) )
| ~ ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1851,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( ~ ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
| ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 ) )
| ~ ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1852,plain,
! [SV403: $i,SV249: $i,SV55: $i,SV506: $i] :
( ( ( in @ SV506 @ SV55 )
= $false )
| ( ( in @ ( ap @ SV55 @ SV249 @ SV403 @ SV506 ) @ SV249 )
= $true )
| ( ( func @ SV55 @ SV249 @ SV403 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1728]) ).
thf(1853,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1730]) ).
thf(1854,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
| ~ ! [SY840: $i,SY841: $i] :
( ~ ~ ( ~ ( in @ SY840 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY841 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY840 )
| ( in @ SX4 @ SY841 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY841 )
| ( in @ SX4 @ SY840 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1731]) ).
thf(1855,plain,
! [SV62: $i,SV539: $i] :
( ( ~ ~ ( ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV539 )
| ( in @ SY1010 @ SV62 ) )
| ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
| ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(1856,plain,
! [SV63: $i,SV406: $i,SV255: $i,SV507: $i] :
( ( ( in @ SV507 @ SV255 )
= $false )
| ( ( in @ ( setadjoin @ SV406 @ ( setadjoin @ SV507 @ emptyset ) ) @ ( powerset @ ( binunion @ SV63 @ SV255 ) ) )
= $true )
| ( ( in @ SV406 @ SV63 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1733]) ).
thf(1857,plain,
! [SV64: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK22_SY607 @ SV256 @ SV64 ) @ SV64 )
| ~ ( in @ SV256 @ ( sK22_SY607 @ SV256 @ SV64 ) ) )
= $false )
| ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1734]) ).
thf(1858,plain,
! [SV68: $i,SV408: $i,SV259: $i,SV508: $i] :
( ( ( in @ SV508 @ SV259 )
= $false )
| ( ( ( ksnd @ ( kpair @ SV408 @ SV508 ) )
= SV508 )
= $true )
| ( ( in @ SV408 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1735]) ).
thf(1859,plain,
! [SV260: $i > $o,SV69: $i,SV509: $i] :
( ( ( ~ ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
| ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SV509 @ emptyset ) ) )
= $true )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1736]) ).
thf(1860,plain,
! [SV70: $i,SV409: $i > $i,SV261: $i] :
( ( ( in @ ( sK23_SY854 @ SV261 @ SV409 @ SV70 ) @ SV70 )
= $true )
| ( ( func @ SV70 @ SV261
@ ( dpsetconstr @ SV70 @ SV261
@ ^ [SY855: $i,SY856: $i] :
( ( SV409 @ SY855 )
= SY856 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1737]) ).
thf(1861,plain,
! [SV71: $i,SV410: $i > $i,SV262: $i] :
( ( ( in @ ( sK24_SY857 @ SV262 @ SV410 @ SV71 ) @ SV71 )
= $true )
| ( ( in
@ ( dpsetconstr @ SV71 @ SV262
@ ^ [SY858: $i,SY859: $i] :
( ( SV410 @ SY858 )
= SY859 ) )
@ ( funcSet @ SV71 @ SV262 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1739]) ).
thf(1862,plain,
! [SV510: $i > $o,SV413: $i,SV266: $i,SV76: $i] :
( ( ( ! [SY979: $i] :
( ~ ( in @ SY979 @ SV76 )
| ! [SY980: $i] :
( ~ ( in @ SY980 @ SV266 )
| ~ ( in @ ( kpair @ SY979 @ SY980 ) @ SV413 )
| ( SV510 @ ( kpair @ SY979 @ SY980 ) ) ) ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1741]) ).
thf(1863,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| SV511 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1742]) ).
thf(1864,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1865,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 )
| ~ ~ ( in @ SV414 @ SV267 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1866,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( ~ ( SV78 @ SV490 ) )
= $true )
| ( ( ~ ! [SY952: $i] :
( ~ ( SV78 @ SY952 )
| ( SV490 = SY952 ) ) )
= $true )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1745]) ).
thf(1867,plain,
! [SV79: $i,SV268: $i] :
( ( ( ~ ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) ) )
= $true )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1746]) ).
thf(1868,plain,
! [SV79: $i,SV268: $i] :
( ( ( ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) ) )
= $false )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV268 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1747]) ).
thf(1869,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV491 ) )
= $true )
| ( ( ~ ! [SY953: $i] :
( ~ ( SV80 @ SY953 )
| ( SV491 = SY953 ) ) )
= $true )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1748]) ).
thf(1870,plain,
! [SV81: $i,SV269: $i,SV415: $i] :
( ( ( in @ SV415 @ SV269 )
= $true )
| ( ( in @ SV415 @ ( setminus @ SV81 @ SV269 ) )
= $true )
| ( ( in @ SV415 @ SV81 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1871,plain,
! [SV83: $i,SV271: $i] :
( ( ( ! [SY637: $i] :
~ ~ ( ~ ( in @ SV271 @ SY637 )
| ~ ( in @ SY637 @ SV83 ) ) )
= $false )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1750]) ).
thf(1872,plain,
! [SV83: $i,SV271: $i] :
( ( ( ! [SY638: $i] :
~ ~ ( ~ ( in @ SV271 @ SY638 )
| ~ ( in @ SY638 @ SV83 ) ) )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1873,plain,
! [SV273: $i > $o,SV86: $i] :
( ( ( ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $false )
| ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1753]) ).
thf(1874,plain,
! [SV273: $i > $o,SV86: $i] :
( ( ( ~ ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $false )
| ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1754]) ).
thf(1875,plain,
! [SV88: $i,SV492: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK36_SY237 @ SV492 @ SV88 ) @ SV88 )
| ~ ~ ~ ! [SY1017: $i] :
~ ~ ( ~ ( in @ SY1017 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SY1017 @ SV88 ) ) ) )
= $false )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1755]) ).
thf(1876,plain,
! [SV419: $i,SV512: $i,SV275: $i,SV89: $i] :
( ( ( func @ SV89 @ SV275 @ SV512 )
= $false )
| ( ( ~ ! [SY982: $i] :
( ~ ( in @ SY982 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ SY982 )
= ( ap @ SV89 @ SV275 @ SV512 @ SY982 ) ) )
| ( SV419 = SV512 ) )
= $true )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1877,plain,
! [SV94: $i,SV279: $i,SV421: $i] :
( ( ( ~ ( in @ SV421 @ SV279 ) )
= $false )
| ( ( ~ ( in @ SV421 @ SV94 ) )
= $true )
| ( ( in @ SV421 @ ( setminus @ SV94 @ SV279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1757]) ).
thf(1878,plain,
! [SV423: $i > $i > $o,SV96: $i,SV475: $i,SV281: $i,SV537: $i] :
( ( ( ~ ( in @ SV537 @ SV281 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV475 @ SV537 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) )
| ( SV423 @ SV475 @ SV537 ) )
= $true )
| ( ( in @ SV475 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1879,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV493 ) )
= $true )
| ( ( ~ ! [SY954: $i] :
( ~ ( SV98 @ SY954 )
| ( SV493 = SY954 ) ) )
= $true )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1760]) ).
thf(1880,plain,
! [SV99: $i,SV424: $i > $i,SV283: $i] :
( ( ( in @ ( sK25_SY872 @ SV283 @ SV424 @ SV99 ) @ SV99 )
= $true )
| ( ( func @ SV99 @ SV283
@ ( dpsetconstr @ SV99 @ SV283
@ ^ [SY873: $i,SY874: $i] :
( ( SV424 @ SY873 )
= SY874 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1761]) ).
thf(1881,plain,
! [SV103: $i] :
( ( ( ~ ( in @ ( sK13_SY274 @ SV103 )
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) ) )
= $false )
| ( ( iskpair @ SV103 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1882,plain,
! [SV103: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
!= ( setadjoin @ ( sK13_SY274 @ SV103 ) @ emptyset ) )
= $false )
| ( ( iskpair @ SV103 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1763]) ).
thf(1883,plain,
! [SV287: $i > $o,SV104: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV104 )
| ~ ~ ( SV287 @ SV513 ) )
= $true )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1764]) ).
thf(1884,plain,
! [SV289: $i > $o,SV106: $i,SV514: $i] :
( ( ( ~ ( in @ SV514 @ SV106 )
| ~ ( SV289 @ SV514 ) )
= $true )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1765]) ).
thf(1885,plain,
! [SV428: $i,SV290: $i,SV107: $i,SV515: $i] :
( ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( ~ ! [SY983: $i] :
( ~ ( in @ SY983 @ SV107 )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV290 )
| ~ ( in @ ( kpair @ SY983 @ SY984 ) @ SV428 )
| ( in @ ( kpair @ SY983 @ SY984 ) @ SV515 ) ) )
| ( subset @ SV428 @ SV515 ) )
= $true )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1766]) ).
thf(1886,plain,
! [SV294: $i,SV111: $i,SV430: $i] :
( ( ( in @ SV430 @ ( symdiff @ SV111 @ SV294 ) )
= $false )
| ( ( in @ SV430 @ SV294 )
= $false )
| ( ( in @ SV430 @ SV111 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1767]) ).
thf(1887,plain,
! [SV431: $i,SV295: $i,SV112: $i,SV516: $i] :
( ( ( in @ SV516 @ SV112 )
= $false )
| ( ( in
@ ( setunion
@ ( dsetconstr @ SV295
@ ^ [SY985: $i] : ( in @ ( kpair @ SV516 @ SY985 ) @ SV431 ) ) )
@ SV295 )
= $true )
| ( ( func @ SV112 @ SV295 @ SV431 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1768]) ).
thf(1888,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ! [SY303: $i,SY304: $i] :
( ~ ( SV113 @ SY303 )
| ~ ( SV113 @ SY304 )
| ( SY303 = SY304 ) ) )
= $false )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1769]) ).
thf(1889,plain,
! [SV115: $i,SV297: $i,SV477: $i,SV432: $i] :
( ( ( SV432 = SV477 )
= $false )
| ( ( SV297 = SV477 )
= $true )
| ( ( ( setadjoin @ ( setadjoin @ SV115 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV115 @ ( setadjoin @ SV297 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SV432 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV432 @ ( setadjoin @ SV477 @ emptyset ) ) @ emptyset ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1890,plain,
! [SV116: $i,SV495: $o,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( sK37_SY957 @ SV495 @ SV116 @ SV298 ) )
| ~ ( in @ ( sK37_SY957 @ SV495 @ SV116 @ SV298 ) @ SV116 )
| SV495 )
= $false )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1771]) ).
thf(1891,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( sK38_SX0 @ SV116 @ SV298 ) )
| ~ ( in @ ( sK38_SX0 @ SV116 @ SV298 ) @ SV116 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1772]) ).
thf(1892,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( sK39_SX0 @ SV116 @ SV298 ) )
| ~ ( in @ ( sK39_SX0 @ SV116 @ SV298 ) @ SV116 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1773]) ).
thf(1893,plain,
! [SV118: $i,SV300: $i,SV433: $i] :
( ( ( in @ SV433 @ SV300 )
= $true )
| ( ( ~ ( in @ SV433 @ SV118 ) )
= $true )
| ( ( subset @ SV118 @ SV300 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1775]) ).
thf(1894,plain,
! [SV123: $i,SV305: $i,SV435: $i] :
( ( ( in @ SV435 @ SV305 )
= $true )
| ( ( SV123 != SV305 )
= $true )
| ( ( in @ SV435 @ SV123 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1895,plain,
! [SV130: $i,SV309: $i,SV540: $i] :
( ( ( ~ ( in @ SV540 @ SV309 )
| ( in @ SV540 @ SV130 ) )
= $true )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(1896,plain,
! [SV309: $i,SV130: $i] :
( ( ( ~ ( in @ ( sK40_SY688 @ SV130 @ SV309 ) @ SV309 )
| ( in @ ( sK40_SY688 @ SV130 @ SV309 ) @ SV130 ) )
= $false )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1779]) ).
thf(1897,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
= $false )
| ( ( ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1780]) ).
thf(1898,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ( ( SV437 = SV132 )
| ( in @ SV437 @ SV311 ) )
= $false )
| ( ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1899,plain,
! [SV133: $i,SV438: $i,SV312: $i,SV517: $i] :
( ( ( in @ SV517 @ SV312 )
= $false )
| ( ( ( kfst @ ( kpair @ SV438 @ SV517 ) )
= SV438 )
= $true )
| ( ( in @ SV438 @ SV133 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1782]) ).
thf(1900,plain,
! [SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1783]) ).
thf(1901,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ~ ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
| ~ ! [SY1018: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY1018 )
| ( SV541 = SY1018 ) ) ) )
= $true )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1784]) ).
thf(1902,plain,
! [SV317: $i > $o,SV136: $i,SV439: $i] :
( ( ( ~ ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) )
| ( SV317 @ SV439 ) )
= $true )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1785]) ).
thf(1903,plain,
! [SV136: $i,SV439: $i,SV317: $i > $o] :
( ( ( ~ ( SV317 @ SV439 )
| ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) ) )
= $true )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1786]) ).
thf(1904,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1787]) ).
thf(1905,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ~ ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1906,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ~ ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
| ~ ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
| ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1788]) ).
thf(1907,plain,
! [SV440: $i,SV321: $i,SV142: $i,SV518: $i] :
( ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( ~ ! [SY986: $i] :
( ~ ( in @ SY986 @ SV142 )
| ! [SY987: $i] :
( ~ ( in @ SY987 @ SV321 )
| ~ ( in @ ( kpair @ SY986 @ SY987 ) @ SV440 )
| ( in @ ( kpair @ SY986 @ SY987 ) @ SV518 ) ) )
| ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1789]) ).
thf(1908,plain,
! [SV144: $i,SV441: $i,SV323: $i,SV519: $i] :
( ( ( in @ SV519 @ SV323 )
= $false )
| ( ( in @ ( kpair @ SV441 @ SV519 ) @ ( cartprod @ SV144 @ SV323 ) )
= $true )
| ( ( in @ SV441 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1790]) ).
thf(1909,plain,
! [SV325: $i > $o,SV147: $i,SV520: $i] :
( ( ( in @ SV520 @ SV147 )
= $false )
| ( ( SV325 @ SV520 )
= $true )
| ( ( ~ ! [SY717: $i] :
~ ~ ( ~ ( in @ SY717 @ SV147 )
| ~ ~ ( SV325 @ SY717 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1791]) ).
thf(1910,plain,
! [SV149: $i,SV327: $i,SV442: $i] :
( ( ( in @ SV442 @ SV327 )
= $false )
| ( ( in @ SV442 @ ( symdiff @ SV149 @ SV327 ) )
= $true )
| ( ( in @ SV442 @ SV149 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1792]) ).
thf(1911,plain,
! [SV329: $i > $o,SV154: $i,SV521: $i] :
( ( ( ~ ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
| ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SV521 @ emptyset ) ) )
= $true )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1794]) ).
thf(1912,plain,
! [SV155: $i,SV330: $i,SV443: $i] :
( ( ( ~ ( ~ ( in @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SV155 )
| ~ ~ ! [SY1007: $i] :
~ ~ ( ~ ( in @ SY1007 @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SY1007 ) ) ) ) )
= $true )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1913,plain,
! [SV156: $i,SV331: $i,SV444: $i] :
( ( ( ~ ( in @ SV444 @ SV331 ) )
= $false )
| ( ( ~ ( in @ SV444 @ ( symdiff @ SV156 @ SV331 ) ) )
= $true )
| ( ( in @ SV444 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1796]) ).
thf(1914,plain,
! [SV157: $i,SV332: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 )
| ~ ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) ) ) )
= $true )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1797]) ).
thf(1915,plain,
! [SV158: $i,SV445: $i,SV333: $i,SV522: $i] :
( ( ( in @ SV522 @ SV333 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV445 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV445 @ ( setadjoin @ SV522 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV158 @ SV333 ) ) )
= $true )
| ( ( in @ SV445 @ SV158 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1798]) ).
thf(1916,plain,
! [SV334: $i,SV159: $i,SV523: $i,SV496: $i] :
( ( ( SV496 = SV523 )
= $false )
| ( ( ( setadjoin @ SV159 @ SV496 )
= ( setadjoin @ SV334 @ SV523 ) )
= $true )
| ( ( SV159 = SV334 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1799]) ).
thf(1917,plain,
! [SV446: $i,SV336: $i,SV161: $i,SV524: $i] :
( ( ( in @ SV524 @ SV161 )
= $false )
| ( ( in @ ( kpair @ SV524 @ ( ap @ SV161 @ SV336 @ SV446 @ SV524 ) ) @ SV446 )
= $true )
| ( ( in @ SV446 @ ( funcSet @ SV161 @ SV336 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1800]) ).
thf(1918,plain,
! [SV447: $i,SV337: $i,SV162: $i,SV525: $i] :
( ( ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) )
= $false )
| ( ( ~ ! [SY992: $i] :
( ~ ( in @ SY992 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ SY992 )
= ( ap @ SV162 @ SV337 @ SV525 @ SY992 ) ) )
| ( SV447 = SV525 ) )
= $true )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1801]) ).
thf(1919,plain,
! [SV339: $i,SV164: $i,SV526: $i,SV497: $i] :
( ( ( SV497 = SV526 )
= $false )
| ( ( ~ ( ~ ( ~ ( in @ SV497 @ SV164 )
| ( in @ SV526 @ SV339 ) )
| ~ ( ~ ( in @ SV526 @ SV339 )
| ( in @ SV497 @ SV164 ) ) ) )
= $true )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1803]) ).
thf(1920,plain,
! [SV343: $i > $o,SV168: $i,SV527: $i] :
( ( ( in @ SV527 @ SV168 )
= $false )
| ( ( SV343 @ SV527 )
= $true )
| ( ( ~ ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV168 )
| ~ ~ ( SV343 @ SY746 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1804]) ).
thf(1921,plain,
! [SV174: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK41_SY431 @ SV174 ) @ omega )
| ~ ( in @ ( sK41_SY431 @ SV174 ) @ SV174 ) )
| ( in @ ( setadjoin @ ( sK41_SY431 @ SV174 ) @ ( sK41_SY431 @ SV174 ) ) @ SV174 ) )
= $false )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1806]) ).
thf(1922,plain,
! [SV176: $i] :
( ( ( ~ ( in @ ( sK27_SY433 @ SV176 ) @ SV176 )
| ~ $true )
= $false )
| ( ( SV176 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1807]) ).
thf(1923,plain,
! [SV179: $i,SV351: $i,SV450: $i] :
( ( ( in @ SV450 @ SV351 )
= $true )
| ( ( in @ SV450 @ ( symdiff @ SV179 @ SV351 ) )
= $true )
| ( ( in @ SV450 @ SV179 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1808]) ).
thf(1924,plain,
! [SV180: $i] :
( ( ( ~ ( in @ ( sK19_SY438 @ SV180 )
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) ) )
= $false )
| ( ( iskpair @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1809]) ).
thf(1925,plain,
! [SV180: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
!= ( setadjoin @ ( sK19_SY438 @ SV180 ) @ emptyset ) )
= $false )
| ( ( iskpair @ SV180 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1809]) ).
thf(1926,plain,
! [SV528: $i > $o,SV451: $i,SV353: $i,SV182: $i] :
( ( ( ! [SY993: $i] :
( ~ ( in @ SY993 @ SV182 )
| ! [SY994: $i] :
( ~ ( in @ SY994 @ SV353 )
| ~ ( in @ ( kpair @ SY993 @ SY994 ) @ SV451 )
| ( SV528 @ ( kpair @ SY993 @ SY994 ) ) ) ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1810]) ).
thf(1927,plain,
! [SV529: $i > $o,SV498: $i > $o,SV354: $i,SV183: $i] :
( ( ( ! [SY996: $i] :
( ~ ( in @ SY996 @ SV183 )
| ! [SY997: $i] :
( ~ ( in @ SY997 @ SV354 )
| ( SY996 != SY997 )
| ~ ( ~ ( ~ ( SV498 @ SY996 )
| ( SV529 @ SY997 ) )
| ~ ( ~ ( SV529 @ SY997 )
| ( SV498 @ SY996 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1928,plain,
! [SV356: $i,SV530: $o,SV185: $i,SV453: $i] :
( ( ( ( SV453 != SV185 )
| SV530 )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| SV530 )
| SV530 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1812]) ).
thf(1929,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( ( SV453 != SV185 )
| $true )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1813]) ).
thf(1930,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( ( SV453 != SV185 )
| $false )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1814]) ).
thf(1931,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1815]) ).
thf(1932,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
| ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) ) )
| ~ ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1816]) ).
thf(1933,plain,
! [SV189: $i,SV454: $i,SV360: $i,SV531: $i] :
( ( ( in @ SV531 @ SV360 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV454 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV454 @ ( setadjoin @ SV531 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV189 @ SV360 ) ) ) )
= $true )
| ( ( in @ SV454 @ SV189 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1934,plain,
! [SV457: $i,SV364: $i,SV193: $i,SV532: $i] :
( ( ( in @ SV532 @ SV193 )
= $false )
| ( ( in @ ( ap @ SV193 @ SV364 @ SV457 @ SV532 ) @ SV364 )
= $true )
| ( ( in @ SV457 @ ( funcSet @ SV193 @ SV364 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1819]) ).
thf(1935,plain,
! [SV194: $i,SV480: $i,SV458: $i > $i > $o,SV365: $i,SV538: $i] :
( ( ( ~ ( in @ SV538 @ SV365 ) )
= $true )
| ( ( ~ ( SV458 @ SV480 @ SV538 )
| ( in @ ( kpair @ SV480 @ SV538 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) ) )
= $true )
| ( ( in @ SV480 @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1820]) ).
thf(1936,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ~ ( SV195 @ SV500 ) )
= $true )
| ( ( ~ ! [SY973: $i] :
( ~ ( SV195 @ SY973 )
| ( SV500 = SY973 ) ) )
= $true )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1937,plain,
! [SV197: $i,SV460: $i,SV367: $i,SV533: $i] :
( ( ( in @ SV533 @ SV367 )
= $false )
| ( ( ( kpair @ SV460 @ SV533 )
= ( kpair @ SV460 @ SV533 ) )
= $true )
| ( ( in @ SV460 @ SV197 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1822]) ).
thf(1938,plain,
! [SV461: $i,SV368: $i,SV198: $i,SV534: $i] :
( ( ( in @ SV534 @ SV198 )
= $false )
| ( ( ~ ! [SY1000: $i] :
~ ~ ( ~ ( in @ SY1000
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
!= ( setadjoin @ SY1000 @ emptyset ) ) ) )
= $true )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1823]) ).
thf(1939,plain,
! [SV463: $i,SV370: $i,SV200: $i,SV535: $i] :
( ( ( in @ SV535 @ SV200 )
= $false )
| ( ( ! [SY1003: $i] :
( ~ ( in @ SY1003 @ SV370 )
| ~ ( in @ ( kpair @ SV535 @ SY1003 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SV535 )
= SY1003 ) ) )
= $true )
| ( ( func @ SV200 @ SV370 @ SV463 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1940,plain,
! [SV464: $i,SV371: $i,SV202: $i,SV536: $i] :
( ( ( in @ SV536 @ SV202 )
= $false )
| ( ( ! [SY1004: $i] :
( ~ ( in @ SY1004 @ SV371 )
| ~ ( in @ ( kpair @ SV536 @ SY1004 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SV536 )
= SY1004 ) ) )
= $true )
| ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1826]) ).
thf(1941,plain,
! [SV373: $i,SV204: $i,SV465: $i] :
( ( ( in @ SV465 @ SV204 )
= $false )
| ( ( in @ SV465 @ SV373 )
= $true )
| ( ( in @ SV465 @ ( setminus @ SV204 @ SV373 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1827]) ).
thf(1942,plain,
! [SV3: $i,SV482: $i] :
( ( ( in @ SV482 @ SV3 )
= $false )
| ( ( SV3
!= ( setadjoin @ SV482 @ emptyset ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1829]) ).
thf(1943,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( SV10 @ SV483 )
= $false )
| ( ( ~ ! [SY943: $i] :
( ~ ( SV10 @ SY943 )
| ( SV483 = SY943 ) ) )
= $true )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1830]) ).
thf(1944,plain,
! [SV12: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV12 )
| ~ ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV215 ) )
= $false )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1832]) ).
thf(1945,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1833]) ).
thf(1946,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1834]) ).
thf(1947,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ~ ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1948,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ~ ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
| ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1835]) ).
thf(1949,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ! [SY817: $i] :
( ~ ( in @ SY817 @ SV23 )
| ~ ( SV224 @ SY817 )
| ( SY817 = SV386 ) ) )
= $false )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1950,plain,
! [SV471: $o,SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 )
| SV471 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1951,plain,
! [SV24: $i,SV225: $i,SV387: $i,SV471: $o] :
( ( SV471 = $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 )
| SV471 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1839]) ).
thf(1952,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $true )
| $true )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1953,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $true )
| $true )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1840]) ).
thf(1954,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV24 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $false )
| $false )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1955,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $false )
| $false )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1841]) ).
thf(1956,plain,
! [SV504: $i,SV391: $i,SV230: $i,SV29: $i] :
( ( ( ~ ! [SY974: $i] :
( ~ ( in @ SY974 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ SY974 )
= ( ap @ SV29 @ SV230 @ SV504 @ SY974 ) ) ) )
= $true )
| ( ( ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1842]) ).
thf(1957,plain,
! [SV232: $i,SV505: $i,SV31: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ SV31 ) )
= $true )
| ( ( in @ SV505 @ SV232 )
= $true )
| ( ( SV484 = SV505 )
= $false )
| ( ( SV31 = SV232 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1843]) ).
thf(1958,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( SV33 @ SV485 )
= $false )
| ( ( ~ ! [SY946: $i] :
( ~ ( SV33 @ SY946 )
| ( SV485 = SY946 ) ) )
= $true )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1844]) ).
thf(1959,plain,
! [SV397: $i,SV239: $i,SV40: $i] :
( ( ( subset @ SV40 @ SV239 )
= $false )
| ( ( in @ SV397 @ SV239 )
= $true )
| ( ( in @ SV397 @ SV40 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1845]) ).
thf(1960,plain,
! [SV44: $i,SV242: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 )
| ~ ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) ) )
= $false )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1961,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( SV46 @ SV488 )
= $false )
| ( ( ~ ! [SY949: $i] :
( ~ ( SV46 @ SY949 )
| ( SV488 = SY949 ) ) )
= $true )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1847]) ).
thf(1962,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1849]) ).
thf(1963,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
| ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(1964,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( ~ ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
| ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 ) ) )
= $true )
| ( ( ~ ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1851]) ).
thf(1965,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(1966,plain,
! [SV58: $i,SV251: $i] :
( ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1853]) ).
thf(1967,plain,
! [SV62: $i] :
( ( ~ ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1854]) ).
thf(1968,plain,
! [SV62: $i] :
( ( ~ ! [SY840: $i,SY841: $i] :
( ~ ~ ( ~ ( in @ SY840 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY841 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY840 )
| ( in @ SX4 @ SY841 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY841 )
| ( in @ SX4 @ SY840 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1854]) ).
thf(1969,plain,
! [SV62: $i,SV539: $i] :
( ( ( ~ ~ ( ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV539 )
| ( in @ SY1010 @ SV62 ) )
| ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(1970,plain,
! [SV64: $i,SV256: $i] :
( ( ( ~ ( in @ ( sK22_SY607 @ SV256 @ SV64 ) @ SV64 ) )
= $false )
| ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1971,plain,
! [SV64: $i,SV256: $i] :
( ( ( ~ ( in @ SV256 @ ( sK22_SY607 @ SV256 @ SV64 ) ) )
= $false )
| ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1857]) ).
thf(1972,plain,
! [SV260: $i > $o,SV69: $i,SV509: $i] :
( ( ( ~ ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SV509 @ emptyset ) )
= $true )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1859]) ).
thf(1973,plain,
! [SV76: $i,SV266: $i,SV413: $i,SV510: $i > $o] :
( ( ( ~ ( in @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SV76 )
| ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV266 )
| ~ ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SY1019 ) @ SV413 )
| ( SV510 @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SY1019 ) ) ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1862]) ).
thf(1974,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1863]) ).
thf(1975,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV267 )
| SV511 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1863]) ).
thf(1976,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1864]) ).
thf(1977,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV267 )
| $true )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1864]) ).
thf(1978,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(1979,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV267 )
| $false )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1865]) ).
thf(1980,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( SV78 @ SV490 )
= $false )
| ( ( ~ ! [SY952: $i] :
( ~ ( SV78 @ SY952 )
| ( SV490 = SY952 ) ) )
= $true )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1866]) ).
thf(1981,plain,
! [SV79: $i,SV268: $i] :
( ( ( ! [SY634: $i] :
( ~ ( in @ SY634 @ SV268 )
| ( in @ SY634 @ SV79 ) ) )
= $false )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1867]) ).
thf(1982,plain,
! [SV268: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK43_SY634 @ SV79 @ SV268 ) @ SV268 )
| ( in @ ( sK43_SY634 @ SV79 @ SV268 ) @ SV79 ) )
= $false )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV268 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1868]) ).
thf(1983,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( SV80 @ SV491 )
= $false )
| ( ( ~ ! [SY953: $i] :
( ~ ( SV80 @ SY953 )
| ( SV491 = SY953 ) ) )
= $true )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1869]) ).
thf(1984,plain,
! [SV83: $i,SV271: $i] :
( ( ( ~ ~ ( ~ ( in @ SV271 @ ( sK44_SY637 @ SV83 @ SV271 ) )
| ~ ( in @ ( sK44_SY637 @ SV83 @ SV271 ) @ SV83 ) ) )
= $false )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1871]) ).
thf(1985,plain,
! [SV83: $i,SV542: $i,SV271: $i] :
( ( ( ~ ~ ( ~ ( in @ SV271 @ SV542 )
| ~ ( in @ SV542 @ SV83 ) ) )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1872]) ).
thf(1986,plain,
! [SV273: $i > $o,SV86: $i] :
( ( ( ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true )
| ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1873]) ).
thf(1987,plain,
! [SV273: $i > $o,SV86: $i] :
( ( ( ! [SY641: $i] :
~ ~ ( ~ ( in @ SY641 @ SV86 )
| ~ ( SV273 @ SY641 ) ) )
= $true )
| ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1874]) ).
thf(1988,plain,
! [SV88: $i,SV492: $i] :
( ( ( ~ ( ~ ( in @ ( sK36_SY237 @ SV492 @ SV88 ) @ SV88 )
| ~ ~ ~ ! [SY1017: $i] :
~ ~ ( ~ ( in @ SY1017 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SY1017 @ SV88 ) ) ) )
= $true )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1875]) ).
thf(1989,plain,
! [SV512: $i,SV419: $i,SV275: $i,SV89: $i] :
( ( ( ~ ! [SY982: $i] :
( ~ ( in @ SY982 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ SY982 )
= ( ap @ SV89 @ SV275 @ SV512 @ SY982 ) ) ) )
= $true )
| ( ( SV419 = SV512 )
= $true )
| ( ( func @ SV89 @ SV275 @ SV512 )
= $false )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(1990,plain,
! [SV94: $i,SV279: $i,SV421: $i] :
( ( ( in @ SV421 @ SV279 )
= $true )
| ( ( ~ ( in @ SV421 @ SV94 ) )
= $true )
| ( ( in @ SV421 @ ( setminus @ SV94 @ SV279 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1877]) ).
thf(1991,plain,
! [SV423: $i > $i > $o,SV96: $i,SV475: $i,SV281: $i,SV537: $i] :
( ( ( in @ SV537 @ SV281 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV475 @ SV537 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) )
| ( SV423 @ SV475 @ SV537 ) )
= $true )
| ( ( in @ SV475 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1878]) ).
thf(1992,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( SV98 @ SV493 )
= $false )
| ( ( ~ ! [SY954: $i] :
( ~ ( SV98 @ SY954 )
| ( SV493 = SY954 ) ) )
= $true )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1879]) ).
thf(1993,plain,
! [SV103: $i] :
( ( ( in @ ( sK13_SY274 @ SV103 )
@ ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY275: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY275 ) ) ) )
= $true )
| ( ( iskpair @ SV103 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1881]) ).
thf(1994,plain,
! [SV103: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV103 )
@ ^ [SY276: $i] :
( SV103
= ( kpair @ ( kfst @ SV103 ) @ SY276 ) ) )
= ( setadjoin @ ( sK13_SY274 @ SV103 ) @ emptyset ) )
= $true )
| ( ( iskpair @ SV103 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1882]) ).
thf(1995,plain,
! [SV287: $i > $o,SV104: $i,SV513: $i] :
( ( ( ~ ( in @ SV513 @ SV104 ) )
= $true )
| ( ( ~ ~ ( SV287 @ SV513 ) )
= $true )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1883]) ).
thf(1996,plain,
! [SV289: $i > $o,SV106: $i,SV514: $i] :
( ( ( ~ ( in @ SV514 @ SV106 ) )
= $true )
| ( ( ~ ( SV289 @ SV514 ) )
= $true )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1884]) ).
thf(1997,plain,
! [SV515: $i,SV428: $i,SV290: $i,SV107: $i] :
( ( ( ~ ! [SY983: $i] :
( ~ ( in @ SY983 @ SV107 )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV290 )
| ~ ( in @ ( kpair @ SY983 @ SY984 ) @ SV428 )
| ( in @ ( kpair @ SY983 @ SY984 ) @ SV515 ) ) ) )
= $true )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1885]) ).
thf(1998,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ! [SY1020: $i] :
( ~ ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
| ~ ( SV113 @ SY1020 )
| ( ( sK45_SY303 @ SV494 @ SV113 )
= SY1020 ) ) )
= $false )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1888]) ).
thf(1999,plain,
! [SV116: $i,SV495: $o,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( sK37_SY957 @ SV495 @ SV116 @ SV298 ) ) )
= $false )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2000,plain,
! [SV298: $i,SV116: $i,SV495: $o] :
( ( ( ~ ( in @ ( sK37_SY957 @ SV495 @ SV116 @ SV298 ) @ SV116 )
| SV495 )
= $false )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1890]) ).
thf(2001,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( sK38_SX0 @ SV116 @ SV298 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(2002,plain,
! [SV298: $i,SV116: $i] :
( ( ( ~ ( in @ ( sK38_SX0 @ SV116 @ SV298 ) @ SV116 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1891]) ).
thf(2003,plain,
! [SV116: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( sK39_SX0 @ SV116 @ SV298 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(2004,plain,
! [SV298: $i,SV116: $i] :
( ( ( ~ ( in @ ( sK39_SX0 @ SV116 @ SV298 ) @ SV116 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1892]) ).
thf(2005,plain,
! [SV300: $i,SV118: $i,SV433: $i] :
( ( ( in @ SV433 @ SV118 )
= $false )
| ( ( in @ SV433 @ SV300 )
= $true )
| ( ( subset @ SV118 @ SV300 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1893]) ).
thf(2006,plain,
! [SV435: $i,SV305: $i,SV123: $i] :
( ( ( SV123 = SV305 )
= $false )
| ( ( in @ SV435 @ SV305 )
= $true )
| ( ( in @ SV435 @ SV123 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(2007,plain,
! [SV130: $i,SV309: $i,SV540: $i] :
( ( ( ~ ( in @ SV540 @ SV309 ) )
= $true )
| ( ( in @ SV540 @ SV130 )
= $true )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1895]) ).
thf(2008,plain,
! [SV309: $i,SV130: $i] :
( ( ( ~ ( in @ ( sK40_SY688 @ SV130 @ SV309 ) @ SV309 ) )
= $false )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2009,plain,
! [SV309: $i,SV130: $i] :
( ( ( in @ ( sK40_SY688 @ SV130 @ SV309 ) @ SV130 )
= $false )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1896]) ).
thf(2010,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ( SV437 = SV132 )
= $true )
| ( ( in @ SV437 @ SV311 )
= $true )
| ( ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1897]) ).
thf(2011,plain,
! [SV311: $i,SV132: $i,SV437: $i] :
( ( ( SV437 = SV132 )
= $false )
| ( ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(2012,plain,
! [SV132: $i,SV311: $i,SV437: $i] :
( ( ( in @ SV437 @ SV311 )
= $false )
| ( ( in @ SV437 @ ( setadjoin @ SV132 @ SV311 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1898]) ).
thf(2013,plain,
! [SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ! [SY1021: $i] :
~ ( ~ ( ~ ( in @ SY1021 @ ( sK46_SY695 @ SV134 @ SV313 ) )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY1021 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY1021 ) )
| ( in @ SY1021 @ ( sK46_SY695 @ SV134 @ SV313 ) ) ) ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1900]) ).
thf(2014,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
| ~ ! [SY1018: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY1018 )
| ( SV541 = SY1018 ) ) ) )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1901]) ).
thf(2015,plain,
! [SV317: $i > $o,SV136: $i,SV439: $i] :
( ( ( ~ ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) ) )
= $true )
| ( ( SV317 @ SV439 )
= $true )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(2016,plain,
! [SV136: $i,SV439: $i,SV317: $i > $o] :
( ( ( ~ ( SV317 @ SV439 ) )
= $true )
| ( ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) )
= $true )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1903]) ).
thf(2017,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1904]) ).
thf(2018,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1905]) ).
thf(2019,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ~ ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2020,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ~ ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
| ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1906]) ).
thf(2021,plain,
! [SV518: $i,SV440: $i,SV321: $i,SV142: $i] :
( ( ( ~ ! [SY986: $i] :
( ~ ( in @ SY986 @ SV142 )
| ! [SY987: $i] :
( ~ ( in @ SY987 @ SV321 )
| ~ ( in @ ( kpair @ SY986 @ SY987 ) @ SV440 )
| ( in @ ( kpair @ SY986 @ SY987 ) @ SV518 ) ) ) )
= $true )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(2022,plain,
! [SV520: $i,SV325: $i > $o,SV147: $i] :
( ( ( ! [SY717: $i] :
~ ~ ( ~ ( in @ SY717 @ SV147 )
| ~ ~ ( SV325 @ SY717 ) ) )
= $false )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1909]) ).
thf(2023,plain,
! [SV329: $i > $o,SV154: $i,SV521: $i] :
( ( ( ~ ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SV521 @ emptyset ) )
= $true )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(2024,plain,
! [SV155: $i,SV330: $i,SV443: $i] :
( ( ( ~ ( in @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SV155 )
| ~ ~ ! [SY1007: $i] :
~ ~ ( ~ ( in @ SY1007 @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SY1007 ) ) ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1912]) ).
thf(2025,plain,
! [SV156: $i,SV331: $i,SV444: $i] :
( ( ( in @ SV444 @ SV331 )
= $true )
| ( ( ~ ( in @ SV444 @ ( symdiff @ SV156 @ SV331 ) ) )
= $true )
| ( ( in @ SV444 @ SV156 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1913]) ).
thf(2026,plain,
! [SV157: $i,SV332: $i > $o] :
( ( ( ~ ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 )
| ~ ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) ) )
= $false )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1914]) ).
thf(2027,plain,
! [SV525: $i,SV447: $i,SV337: $i,SV162: $i] :
( ( ( ~ ! [SY992: $i] :
( ~ ( in @ SY992 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ SY992 )
= ( ap @ SV162 @ SV337 @ SV525 @ SY992 ) ) ) )
= $true )
| ( ( SV447 = SV525 )
= $true )
| ( ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) )
= $false )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2028,plain,
! [SV339: $i,SV526: $i,SV164: $i,SV497: $i] :
( ( ( ~ ( ~ ( in @ SV497 @ SV164 )
| ( in @ SV526 @ SV339 ) )
| ~ ( ~ ( in @ SV526 @ SV339 )
| ( in @ SV497 @ SV164 ) ) )
= $false )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1919]) ).
thf(2029,plain,
! [SV527: $i,SV343: $i > $o,SV168: $i] :
( ( ( ! [SY746: $i] :
~ ~ ( ~ ( in @ SY746 @ SV168 )
| ~ ~ ( SV343 @ SY746 ) ) )
= $false )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1920]) ).
thf(2030,plain,
! [SV174: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK41_SY431 @ SV174 ) @ omega )
| ~ ( in @ ( sK41_SY431 @ SV174 ) @ SV174 ) ) )
= $false )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2031,plain,
! [SV174: $i] :
( ( ( in @ ( setadjoin @ ( sK41_SY431 @ SV174 ) @ ( sK41_SY431 @ SV174 ) ) @ SV174 )
= $false )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1921]) ).
thf(2032,plain,
! [SV176: $i] :
( ( ( ~ ( in @ ( sK27_SY433 @ SV176 ) @ SV176 ) )
= $false )
| ( ( SV176 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2033,plain,
! [SV176: $i] :
( ( ( ~ $true ) = $false )
| ( ( SV176 = emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1922]) ).
thf(2034,plain,
! [SV180: $i] :
( ( ( in @ ( sK19_SY438 @ SV180 )
@ ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY439: $i] : ( in @ ( setadjoin @ SY439 @ emptyset ) @ SV180 ) ) )
= $true )
| ( ( iskpair @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1924]) ).
thf(2035,plain,
! [SV180: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV180 )
@ ^ [SY440: $i] : ( in @ ( setadjoin @ SY440 @ emptyset ) @ SV180 ) )
= ( setadjoin @ ( sK19_SY438 @ SV180 ) @ emptyset ) )
= $true )
| ( ( iskpair @ SV180 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1925]) ).
thf(2036,plain,
! [SV182: $i,SV353: $i,SV451: $i,SV528: $i > $o] :
( ( ( ~ ( in @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SV182 )
| ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV353 )
| ~ ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SY1024 ) @ SV451 )
| ( SV528 @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SY1024 ) ) ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1926]) ).
thf(2037,plain,
! [SV183: $i,SV354: $i,SV498: $i > $o,SV529: $i > $o] :
( ( ( ~ ( in @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) @ SV183 )
| ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV354 )
| ( ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 )
!= SY1025 )
| ~ ( ~ ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
| ( SV529 @ SY1025 ) )
| ~ ( ~ ( SV529 @ SY1025 )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1927]) ).
thf(2038,plain,
! [SV530: $o,SV356: $i,SV185: $i,SV453: $i] :
( ( ( SV453 != SV185 )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| SV530 )
| SV530 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(2039,plain,
! [SV185: $i,SV356: $i,SV453: $i,SV530: $o] :
( ( SV530 = $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| SV530 )
| SV530 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1928]) ).
thf(2040,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( SV453 != SV185 )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2041,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1929]) ).
thf(2042,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( SV453 != SV185 )
= $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1930]) ).
thf(2043,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1930]) ).
thf(2044,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1931]) ).
thf(2045,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
| ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1932]) ).
thf(2046,plain,
! [SV194: $i,SV480: $i,SV458: $i > $i > $o,SV365: $i,SV538: $i] :
( ( ( in @ SV538 @ SV365 )
= $false )
| ( ( ~ ( SV458 @ SV480 @ SV538 )
| ( in @ ( kpair @ SV480 @ SV538 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) ) )
= $true )
| ( ( in @ SV480 @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1935]) ).
thf(2047,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( SV195 @ SV500 )
= $false )
| ( ( ~ ! [SY973: $i] :
( ~ ( SV195 @ SY973 )
| ( SV500 = SY973 ) ) )
= $true )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2048,plain,
! [SV198: $i,SV461: $i,SV534: $i,SV368: $i] :
( ( ( ! [SY1000: $i] :
~ ~ ( ~ ( in @ SY1000
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
!= ( setadjoin @ SY1000 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV534 @ SV198 )
= $false )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1938]) ).
thf(2049,plain,
! [SV200: $i,SV463: $i,SV535: $i,SV370: $i,SV543: $i] :
( ( ( ~ ( in @ SV543 @ SV370 )
| ~ ( in @ ( kpair @ SV535 @ SV543 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SV535 )
= SV543 ) )
= $true )
| ( ( in @ SV535 @ SV200 )
= $false )
| ( ( func @ SV200 @ SV370 @ SV463 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1939]) ).
thf(2050,plain,
! [SV202: $i,SV464: $i,SV536: $i,SV371: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ SV371 )
| ~ ( in @ ( kpair @ SV536 @ SV544 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SV536 )
= SV544 ) )
= $true )
| ( ( in @ SV536 @ SV202 )
= $false )
| ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1940]) ).
thf(2051,plain,
! [SV482: $i,SV3: $i] :
( ( ( SV3
= ( setadjoin @ SV482 @ emptyset ) )
= $false )
| ( ( in @ SV482 @ SV3 )
= $false )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1942]) ).
thf(2052,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ! [SY943: $i] :
( ~ ( SV10 @ SY943 )
| ( SV483 = SY943 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1943]) ).
thf(2053,plain,
! [SV12: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV12 ) )
= $false )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1944]) ).
thf(2054,plain,
! [SV12: $i,SV215: $i] :
( ( ( ~ ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV215 ) )
= $false )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1944]) ).
thf(2055,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1945]) ).
thf(2056,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1946]) ).
thf(2057,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1947]) ).
thf(2058,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ~ ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2059,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1948]) ).
thf(2060,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
| ~ ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
| ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 ) )
= $false )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1949]) ).
thf(2061,plain,
! [SV471: $o,SV225: $i,SV24: $i,SV387: $i] :
( ( ( in @ SV387 @ SV24 )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 )
| SV471 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1950]) ).
thf(2062,plain,
! [SV24: $i,SV471: $o,SV225: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 ) )
= $true )
| ( SV471 = $true )
| ( SV471 = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1951]) ).
thf(2063,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( in @ SV387 @ SV24 )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $true )
| $true )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2064,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1953]) ).
thf(2065,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( ( in @ SV387 @ SV24 )
= $true )
| ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $false )
| $false )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1954]) ).
thf(2066,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1955]) ).
thf(2067,plain,
! [SV504: $i,SV391: $i,SV230: $i,SV29: $i] :
( ( ( ! [SY974: $i] :
( ~ ( in @ SY974 @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ SY974 )
= ( ap @ SV29 @ SV230 @ SV504 @ SY974 ) ) ) )
= $false )
| ( ( ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2068,plain,
! [SV232: $i,SV505: $i,SV31: $i,SV484: $i] :
( ( ( in @ SV484 @ SV31 )
= $false )
| ( ( in @ SV505 @ SV232 )
= $true )
| ( ( SV484 = SV505 )
= $false )
| ( ( SV31 = SV232 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1957]) ).
thf(2069,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( ! [SY946: $i] :
( ~ ( SV33 @ SY946 )
| ( SV485 = SY946 ) ) )
= $false )
| ( ( SV33 @ SV485 )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1958]) ).
thf(2070,plain,
! [SV44: $i,SV242: $i > $o] :
( ( ( ~ ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 ) )
= $false )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1960]) ).
thf(2071,plain,
! [SV44: $i,SV242: $i > $o] :
( ( ( ~ ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) ) )
= $false )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1960]) ).
thf(2072,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( ! [SY949: $i] :
( ~ ( SV46 @ SY949 )
| ( SV488 = SY949 ) ) )
= $false )
| ( ( SV46 @ SV488 )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1961]) ).
thf(2073,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1962]) ).
thf(2074,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
| ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) ) )
= $false )
| ( ( ~ ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2075,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
| ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 ) )
= $false )
| ( ( ~ ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2076,plain,
! [SV58: $i,SV251: $i] :
( ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) ) )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1965]) ).
thf(2077,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
= $false )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1966]) ).
thf(2078,plain,
! [SV62: $i] :
( ( ~ ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1967]) ).
thf(2079,plain,
! [SV62: $i] :
( ( ! [SY840: $i,SY841: $i] :
( ~ ~ ( ~ ( in @ SY840 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY841 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY840 )
| ( in @ SX4 @ SY841 ) )
| ! [SX4: $i] :
( ~ ( in @ SX4 @ SY841 )
| ( in @ SX4 @ SY840 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1968]) ).
thf(2080,plain,
! [SV62: $i,SV539: $i] :
( ( ( ~ ( ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV539 )
| ( in @ SY1010 @ SV62 ) )
| ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) ) )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1969]) ).
thf(2081,plain,
! [SV64: $i,SV256: $i] :
( ( ( in @ ( sK22_SY607 @ SV256 @ SV64 ) @ SV64 )
= $true )
| ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1970]) ).
thf(2082,plain,
! [SV64: $i,SV256: $i] :
( ( ( in @ SV256 @ ( sK22_SY607 @ SV256 @ SV64 ) )
= $true )
| ( ( in @ SV256 @ ( setunion @ SV64 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1971]) ).
thf(2083,plain,
! [SV260: $i > $o,SV69: $i,SV509: $i] :
( ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
!= ( setadjoin @ SV509 @ emptyset ) )
= $true )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2084,plain,
! [SV76: $i,SV266: $i,SV413: $i,SV510: $i > $o] :
( ( ( ~ ( in @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SV76 ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(2085,plain,
! [SV76: $i,SV413: $i,SV510: $i > $o,SV266: $i] :
( ( ( ! [SY1019: $i] :
( ~ ( in @ SY1019 @ SV266 )
| ~ ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SY1019 ) @ SV413 )
| ( SV510 @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SY1019 ) ) ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1973]) ).
thf(2086,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1974]) ).
thf(2087,plain,
! [SV511: $o,SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2088,plain,
! [SV267: $i,SV77: $i,SV414: $i,SV511: $o] :
( ( SV511 = $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2089,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1976]) ).
thf(2090,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2091,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( $true = $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1977]) ).
thf(2092,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1978]) ).
thf(2093,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2094,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( $false = $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1979]) ).
thf(2095,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( ! [SY952: $i] :
( ~ ( SV78 @ SY952 )
| ( SV490 = SY952 ) ) )
= $false )
| ( ( SV78 @ SV490 )
= $false )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1980]) ).
thf(2096,plain,
! [SV268: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK50_SY634 @ SV79 @ SV268 ) @ SV268 )
| ( in @ ( sK50_SY634 @ SV79 @ SV268 ) @ SV79 ) )
= $false )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[1981]) ).
thf(2097,plain,
! [SV268: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK43_SY634 @ SV79 @ SV268 ) @ SV268 ) )
= $false )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV268 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2098,plain,
! [SV268: $i,SV79: $i] :
( ( ( in @ ( sK43_SY634 @ SV79 @ SV268 ) @ SV79 )
= $false )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV268 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1982]) ).
thf(2099,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ! [SY953: $i] :
( ~ ( SV80 @ SY953 )
| ( SV491 = SY953 ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1983]) ).
thf(2100,plain,
! [SV83: $i,SV271: $i] :
( ( ( ~ ( ~ ( in @ SV271 @ ( sK44_SY637 @ SV83 @ SV271 ) )
| ~ ( in @ ( sK44_SY637 @ SV83 @ SV271 ) @ SV83 ) ) )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2101,plain,
! [SV83: $i,SV542: $i,SV271: $i] :
( ( ( ~ ( ~ ( in @ SV271 @ SV542 )
| ~ ( in @ SV542 @ SV83 ) ) )
= $false )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1985]) ).
thf(2102,plain,
! [SV273: $i > $o,SV86: $i,SV545: $i] :
( ( ( ~ ~ ( ~ ( in @ SV545 @ SV86 )
| ~ ( SV273 @ SV545 ) ) )
= $true )
| ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1986]) ).
thf(2103,plain,
! [SV273: $i > $o,SV86: $i,SV546: $i] :
( ( ( ~ ~ ( ~ ( in @ SV546 @ SV86 )
| ~ ( SV273 @ SV546 ) ) )
= $true )
| ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1987]) ).
thf(2104,plain,
! [SV88: $i,SV492: $i] :
( ( ( ~ ( in @ ( sK36_SY237 @ SV492 @ SV88 ) @ SV88 )
| ~ ~ ~ ! [SY1017: $i] :
~ ~ ( ~ ( in @ SY1017 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SY1017 @ SV88 ) ) )
= $false )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1988]) ).
thf(2105,plain,
! [SV512: $i,SV419: $i,SV275: $i,SV89: $i] :
( ( ( ! [SY982: $i] :
( ~ ( in @ SY982 @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ SY982 )
= ( ap @ SV89 @ SV275 @ SV512 @ SY982 ) ) ) )
= $false )
| ( ( SV419 = SV512 )
= $true )
| ( ( func @ SV89 @ SV275 @ SV512 )
= $false )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1989]) ).
thf(2106,plain,
! [SV279: $i,SV94: $i,SV421: $i] :
( ( ( in @ SV421 @ SV94 )
= $false )
| ( ( in @ SV421 @ SV279 )
= $true )
| ( ( in @ SV421 @ ( setminus @ SV94 @ SV279 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1990]) ).
thf(2107,plain,
! [SV423: $i > $i > $o,SV281: $i,SV96: $i,SV537: $i,SV475: $i] :
( ( ( ~ ( in @ ( kpair @ SV475 @ SV537 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) ) )
= $true )
| ( ( SV423 @ SV475 @ SV537 )
= $true )
| ( ( in @ SV537 @ SV281 )
= $false )
| ( ( in @ SV475 @ SV96 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2108,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ! [SY954: $i] :
( ~ ( SV98 @ SY954 )
| ( SV493 = SY954 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1992]) ).
thf(2109,plain,
! [SV287: $i > $o,SV104: $i,SV513: $i] :
( ( ( in @ SV513 @ SV104 )
= $false )
| ( ( ~ ~ ( SV287 @ SV513 ) )
= $true )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2110,plain,
! [SV289: $i > $o,SV106: $i,SV514: $i] :
( ( ( in @ SV514 @ SV106 )
= $false )
| ( ( ~ ( SV289 @ SV514 ) )
= $true )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2111,plain,
! [SV515: $i,SV428: $i,SV290: $i,SV107: $i] :
( ( ( ! [SY983: $i] :
( ~ ( in @ SY983 @ SV107 )
| ! [SY984: $i] :
( ~ ( in @ SY984 @ SV290 )
| ~ ( in @ ( kpair @ SY983 @ SY984 ) @ SV428 )
| ( in @ ( kpair @ SY983 @ SY984 ) @ SV515 ) ) ) )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2112,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
| ~ ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
| ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) ) )
= $false )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[1998]) ).
thf(2113,plain,
! [SV116: $i,SV495: $o,SV298: $i] :
( ( ( in @ SV298 @ ( sK37_SY957 @ SV495 @ SV116 @ SV298 ) )
= $true )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1999]) ).
thf(2114,plain,
! [SV298: $i,SV116: $i,SV495: $o] :
( ( ( ~ ( in @ ( sK37_SY957 @ SV495 @ SV116 @ SV298 ) @ SV116 ) )
= $false )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2115,plain,
! [SV116: $i,SV298: $i,SV495: $o] :
( ( SV495 = $false )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2000]) ).
thf(2116,plain,
! [SV116: $i,SV298: $i] :
( ( ( in @ SV298 @ ( sK38_SX0 @ SV116 @ SV298 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2001]) ).
thf(2117,plain,
! [SV298: $i,SV116: $i] :
( ( ( ~ ( in @ ( sK38_SX0 @ SV116 @ SV298 ) @ SV116 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2002]) ).
thf(2118,plain,
! [SV116: $i,SV298: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2002]) ).
thf(2119,plain,
! [SV116: $i,SV298: $i] :
( ( ( in @ SV298 @ ( sK39_SX0 @ SV116 @ SV298 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2003]) ).
thf(2120,plain,
! [SV298: $i,SV116: $i] :
( ( ( ~ ( in @ ( sK39_SX0 @ SV116 @ SV298 ) @ SV116 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2121,plain,
! [SV116: $i,SV298: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2004]) ).
thf(2122,plain,
! [SV130: $i,SV309: $i,SV540: $i] :
( ( ( in @ SV540 @ SV309 )
= $false )
| ( ( in @ SV540 @ SV130 )
= $true )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2007]) ).
thf(2123,plain,
! [SV309: $i,SV130: $i] :
( ( ( in @ ( sK40_SY688 @ SV130 @ SV309 ) @ SV309 )
= $true )
| ( ( in @ SV309 @ ( powerset @ SV130 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2008]) ).
thf(2124,plain,
! [SV313: $i,SV134: $i > $i > $o] :
( ( ( ! [SY1021: $i] :
~ ( ~ ( ~ ( in @ SY1021 @ ( sK46_SY695 @ SV134 @ SV313 ) )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY1021 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY1021 ) )
| ( in @ SY1021 @ ( sK46_SY695 @ SV134 @ SV313 ) ) ) ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2013]) ).
thf(2125,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
| ~ ! [SY1018: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY1018 )
| ( SV541 = SY1018 ) ) )
= $true )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2014]) ).
thf(2126,plain,
! [SV317: $i > $o,SV136: $i,SV439: $i] :
( ( ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY700: $i] : ( SV317 @ SY700 ) ) )
= $false )
| ( ( SV317 @ SV439 )
= $true )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2127,plain,
! [SV136: $i,SV439: $i,SV317: $i > $o] :
( ( ( SV317 @ SV439 )
= $false )
| ( ( in @ SV439
@ ( dsetconstr @ SV136
@ ^ [SY701: $i] : ( SV317 @ SY701 ) ) )
= $true )
| ( ( in @ SV439 @ SV136 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2016]) ).
thf(2128,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2017]) ).
thf(2129,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2018]) ).
thf(2130,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2019]) ).
thf(2131,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ~ ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2020]) ).
thf(2132,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2020]) ).
thf(2133,plain,
! [SV518: $i,SV440: $i,SV321: $i,SV142: $i] :
( ( ( ! [SY986: $i] :
( ~ ( in @ SY986 @ SV142 )
| ! [SY987: $i] :
( ~ ( in @ SY987 @ SV321 )
| ~ ( in @ ( kpair @ SY986 @ SY987 ) @ SV440 )
| ( in @ ( kpair @ SY986 @ SY987 ) @ SV518 ) ) ) )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2021]) ).
thf(2134,plain,
! [SV147: $i,SV325: $i > $o,SV520: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) @ SV147 )
| ~ ~ ( SV325 @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) ) ) )
= $false )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2022]) ).
thf(2135,plain,
! [SV329: $i > $o,SV154: $i,SV521: $i] :
( ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
!= ( setadjoin @ SV521 @ emptyset ) )
= $true )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2023]) ).
thf(2136,plain,
! [SV155: $i,SV330: $i,SV443: $i] :
( ( ( ~ ( in @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SV155 ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2024]) ).
thf(2137,plain,
! [SV155: $i,SV443: $i,SV330: $i] :
( ( ( ~ ~ ! [SY1007: $i] :
~ ~ ( ~ ( in @ SY1007 @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SY1007 ) ) ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2024]) ).
thf(2138,plain,
! [SV331: $i,SV156: $i,SV444: $i] :
( ( ( in @ SV444 @ ( symdiff @ SV156 @ SV331 ) )
= $false )
| ( ( in @ SV444 @ SV331 )
= $true )
| ( ( in @ SV444 @ SV156 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2025]) ).
thf(2139,plain,
! [SV157: $i,SV332: $i > $o] :
( ( ( ~ ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 ) )
= $false )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2026]) ).
thf(2140,plain,
! [SV157: $i,SV332: $i > $o] :
( ( ( ~ ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) ) )
= $false )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2026]) ).
thf(2141,plain,
! [SV525: $i,SV447: $i,SV337: $i,SV162: $i] :
( ( ( ! [SY992: $i] :
( ~ ( in @ SY992 @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ SY992 )
= ( ap @ SV162 @ SV337 @ SV525 @ SY992 ) ) ) )
= $false )
| ( ( SV447 = SV525 )
= $true )
| ( ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) )
= $false )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2142,plain,
! [SV339: $i,SV526: $i,SV164: $i,SV497: $i] :
( ( ( ~ ( ~ ( in @ SV497 @ SV164 )
| ( in @ SV526 @ SV339 ) ) )
= $false )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2028]) ).
thf(2143,plain,
! [SV164: $i,SV497: $i,SV339: $i,SV526: $i] :
( ( ( ~ ( ~ ( in @ SV526 @ SV339 )
| ( in @ SV497 @ SV164 ) ) )
= $false )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2028]) ).
thf(2144,plain,
! [SV168: $i,SV343: $i > $o,SV527: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) @ SV168 )
| ~ ~ ( SV343 @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) ) ) )
= $false )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2029]) ).
thf(2145,plain,
! [SV174: $i] :
( ( ( ~ ( ~ ( in @ ( sK41_SY431 @ SV174 ) @ omega )
| ~ ( in @ ( sK41_SY431 @ SV174 ) @ SV174 ) ) )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2030]) ).
thf(2146,plain,
! [SV174: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ omega )
| ( in @ SV547 @ SV174 ) )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( setadjoin @ ( sK41_SY431 @ SV174 ) @ ( sK41_SY431 @ SV174 ) ) @ SV174 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2031]) ).
thf(2147,plain,
! [SV176: $i] :
( ( ( in @ ( sK27_SY433 @ SV176 ) @ SV176 )
= $true )
| ( ( SV176 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2148,plain,
! [SV176: $i] :
( ( $true = $true )
| ( ( SV176 = emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2149,plain,
! [SV182: $i,SV353: $i,SV451: $i,SV528: $i > $o] :
( ( ( ~ ( in @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SV182 ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2150,plain,
! [SV182: $i,SV451: $i,SV528: $i > $o,SV353: $i] :
( ( ( ! [SY1024: $i] :
( ~ ( in @ SY1024 @ SV353 )
| ~ ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SY1024 ) @ SV451 )
| ( SV528 @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SY1024 ) ) ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2036]) ).
thf(2151,plain,
! [SV183: $i,SV354: $i,SV498: $i > $o,SV529: $i > $o] :
( ( ( ~ ( in @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) @ SV183 ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2152,plain,
! [SV183: $i,SV498: $i > $o,SV529: $i > $o,SV354: $i] :
( ( ( ! [SY1025: $i] :
( ~ ( in @ SY1025 @ SV354 )
| ( ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 )
!= SY1025 )
| ~ ( ~ ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
| ( SV529 @ SY1025 ) )
| ~ ( ~ ( SV529 @ SY1025 )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2037]) ).
thf(2153,plain,
! [SV530: $o,SV356: $i,SV185: $i,SV453: $i] :
( ( ( SV453 = SV185 )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| SV530 )
| SV530 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2038]) ).
thf(2154,plain,
! [SV185: $i,SV530: $o,SV356: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| SV530 ) )
= $true )
| ( SV530 = $true )
| ( SV530 = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2039]) ).
thf(2155,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( SV453 = SV185 )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $true )
| $true )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2040]) ).
thf(2156,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2157,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( ( SV453 = SV185 )
= $true )
| ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $false )
| $false )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2158,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2043]) ).
thf(2159,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2044]) ).
thf(2160,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2044]) ).
thf(2161,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
| ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) ) )
= $false )
| ( ( ~ ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2045]) ).
thf(2162,plain,
! [SV365: $i,SV194: $i,SV538: $i,SV480: $i,SV458: $i > $i > $o] :
( ( ( ~ ( SV458 @ SV480 @ SV538 ) )
= $true )
| ( ( in @ ( kpair @ SV480 @ SV538 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) )
= $true )
| ( ( in @ SV538 @ SV365 )
= $false )
| ( ( in @ SV480 @ SV194 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2163,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ! [SY973: $i] :
( ~ ( SV195 @ SY973 )
| ( SV500 = SY973 ) ) )
= $false )
| ( ( SV195 @ SV500 )
= $false )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2047]) ).
thf(2164,plain,
! [SV368: $i,SV534: $i,SV461: $i,SV198: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 )
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
!= ( setadjoin @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV534 @ SV198 )
= $false )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2048]) ).
thf(2165,plain,
! [SV200: $i,SV463: $i,SV535: $i,SV370: $i,SV543: $i] :
( ( ( ~ ( in @ SV543 @ SV370 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV535 @ SV543 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SV535 )
= SV543 ) )
= $true )
| ( ( in @ SV535 @ SV200 )
= $false )
| ( ( func @ SV200 @ SV370 @ SV463 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2049]) ).
thf(2166,plain,
! [SV202: $i,SV464: $i,SV536: $i,SV371: $i,SV544: $i] :
( ( ( ~ ( in @ SV544 @ SV371 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV536 @ SV544 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SV536 )
= SV544 ) )
= $true )
| ( ( in @ SV536 @ SV202 )
= $false )
| ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2050]) ).
thf(2167,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
| ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2052]) ).
thf(2168,plain,
! [SV12: $i,SV215: $i] :
( ( ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV12 )
= $true )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2053]) ).
thf(2169,plain,
! [SV12: $i,SV215: $i] :
( ( ( in @ ( sK29_SY537 @ SV215 @ SV12 ) @ SV215 )
= $true )
| ( ( ( binintersect @ SV12 @ SV215 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2054]) ).
thf(2170,plain,
! [SV217: $i > $o,SV14: $i,SV548: $i] :
( ( ( ~ ~ ( ~ ( in @ SV548 @ SV14 )
| ~ ( SV217 @ SV548 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2055]) ).
thf(2171,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2172,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2057]) ).
thf(2173,plain,
! [SV14: $i,SV217: $i > $o] :
( ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true )
| ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) )
| ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2058]) ).
thf(2174,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2059]) ).
thf(2175,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 ) )
= $false )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2060]) ).
thf(2176,plain,
! [SV23: $i,SV386: $i,SV224: $i > $o] :
( ( ( ~ ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
| ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 ) )
= $false )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2060]) ).
thf(2177,plain,
! [SV24: $i,SV471: $o,SV225: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| SV471 ) )
= $true )
| ( SV471 = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2061]) ).
thf(2178,plain,
! [SV24: $i,SV471: $o,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 )
| SV471 )
= $false )
| ( SV471 = $true )
| ( SV471 = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2062]) ).
thf(2179,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2063]) ).
thf(2180,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2064]) ).
thf(2181,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( ~ ( in @ SV387 @ SV225 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2065]) ).
thf(2182,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2066]) ).
thf(2183,plain,
! [SV29: $i,SV230: $i,SV391: $i,SV504: $i] :
( ( ( ~ ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
| ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) ) )
= $false )
| ( ( ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2067]) ).
thf(2184,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) )
| ( SV485
= ( sK57_SY946 @ SV485 @ SV33 ) ) )
= $false )
| ( ( SV33 @ SV485 )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2069]) ).
thf(2185,plain,
! [SV44: $i,SV242: $i > $o] :
( ( ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 )
= $true )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2186,plain,
! [SV44: $i,SV242: $i > $o] :
( ( ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) )
= $true )
| ( ( ! [SY584: $i] :
( ~ ( in @ SY584 @ SV44 )
| ~ ( SV242 @ SY584 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2071]) ).
thf(2187,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) )
| ( SV488
= ( sK58_SY949 @ SV488 @ SV46 ) ) )
= $false )
| ( ( SV46 @ SV488 )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2072]) ).
thf(2188,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2073]) ).
thf(2189,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) )
= $false )
| ( ( ~ ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2074]) ).
thf(2190,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( ~ ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2074]) ).
thf(2191,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) )
= $false )
| ( ( ~ ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2075]) ).
thf(2192,plain,
! [SV53: $i > $o,SV489: $i] :
( ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ~ ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2075]) ).
thf(2193,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
| ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 ) )
= $false )
| ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2194,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 ) )
= $false )
| ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
= $false )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2195,plain,
! [SV58: $i,SV251: $i] :
( ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
= $false )
| ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
= $false )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2077]) ).
thf(2196,plain,
! [SV62: $i] :
( ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) )
| ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[2078]) ).
thf(2197,plain,
! [SV62: $i,SV549: $i] :
( ( ! [SY1028: $i] :
( ~ ~ ( ~ ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1028 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SY1029: $i] :
( ~ ( in @ SY1029 @ SV549 )
| ( in @ SY1029 @ SY1028 ) )
| ! [SY1030: $i] :
( ~ ( in @ SY1030 @ SY1028 )
| ( in @ SY1030 @ SV549 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2079]) ).
thf(2198,plain,
! [SV62: $i,SV539: $i] :
( ( ( ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV539 )
| ( in @ SY1010 @ SV62 ) )
| ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2080]) ).
thf(2199,plain,
! [SV509: $i,SV260: $i > $o,SV69: $i] :
( ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ~ ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2083]) ).
thf(2200,plain,
! [SV76: $i,SV266: $i,SV413: $i,SV510: $i > $o] :
( ( ( in @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SV76 )
= $true )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2084]) ).
thf(2201,plain,
! [SV266: $i,SV510: $i > $o,SV413: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) @ SV266 )
| ~ ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) @ SV413 )
| ( SV510 @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2085]) ).
thf(2202,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 ) )
= $true )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2203,plain,
! [SV511: $o,SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2087]) ).
thf(2204,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 ) )
= $true )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2205,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2089]) ).
thf(2206,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2090]) ).
thf(2207,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2091]) ).
thf(2208,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2092]) ).
thf(2209,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $true )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2210,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2094]) ).
thf(2211,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( ~ ( SV78 @ ( sK60_SY952 @ SV490 @ SV78 ) )
| ( SV490
= ( sK60_SY952 @ SV490 @ SV78 ) ) )
= $false )
| ( ( SV78 @ SV490 )
= $false )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2095]) ).
thf(2212,plain,
! [SV268: $i,SV79: $i] :
( ( ( ~ ( in @ ( sK50_SY634 @ SV79 @ SV268 ) @ SV268 ) )
= $false )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2096]) ).
thf(2213,plain,
! [SV268: $i,SV79: $i] :
( ( ( in @ ( sK50_SY634 @ SV79 @ SV268 ) @ SV79 )
= $false )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2096]) ).
thf(2214,plain,
! [SV268: $i,SV79: $i] :
( ( ( in @ ( sK43_SY634 @ SV79 @ SV268 ) @ SV268 )
= $true )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV268 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2097]) ).
thf(2215,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
| ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2099]) ).
thf(2216,plain,
! [SV83: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ ( sK44_SY637 @ SV83 @ SV271 ) )
| ~ ( in @ ( sK44_SY637 @ SV83 @ SV271 ) @ SV83 ) )
= $false )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2100]) ).
thf(2217,plain,
! [SV83: $i,SV542: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV542 )
| ~ ( in @ SV542 @ SV83 ) )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2101]) ).
thf(2218,plain,
! [SV273: $i > $o,SV86: $i,SV545: $i] :
( ( ( ~ ( ~ ( in @ SV545 @ SV86 )
| ~ ( SV273 @ SV545 ) ) )
= $false )
| ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2102]) ).
thf(2219,plain,
! [SV273: $i > $o,SV86: $i,SV546: $i] :
( ( ( ~ ( ~ ( in @ SV546 @ SV86 )
| ~ ( SV273 @ SV546 ) ) )
= $false )
| ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2103]) ).
thf(2220,plain,
! [SV88: $i,SV492: $i] :
( ( ( ~ ( in @ ( sK36_SY237 @ SV492 @ SV88 ) @ SV88 ) )
= $false )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2221,plain,
! [SV88: $i,SV492: $i] :
( ( ( ~ ~ ~ ! [SY1017: $i] :
~ ~ ( ~ ( in @ SY1017 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SY1017 @ SV88 ) ) )
= $false )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2104]) ).
thf(2222,plain,
! [SV89: $i,SV275: $i,SV419: $i,SV512: $i] :
( ( ( ~ ( in @ ( sK62_SY982 @ SV512 @ SV419 @ SV275 @ SV89 ) @ SV89 )
| ( ( ap @ SV89 @ SV275 @ SV419 @ ( sK62_SY982 @ SV512 @ SV419 @ SV275 @ SV89 ) )
= ( ap @ SV89 @ SV275 @ SV512 @ ( sK62_SY982 @ SV512 @ SV419 @ SV275 @ SV89 ) ) ) )
= $false )
| ( ( SV419 = SV512 )
= $true )
| ( ( func @ SV89 @ SV275 @ SV512 )
= $false )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2105]) ).
thf(2223,plain,
! [SV423: $i > $i > $o,SV281: $i,SV96: $i,SV537: $i,SV475: $i] :
( ( ( in @ ( kpair @ SV475 @ SV537 )
@ ( dpsetconstr @ SV96 @ SV281
@ ^ [SY870: $i,SY871: $i] : ( SV423 @ SY870 @ SY871 ) ) )
= $false )
| ( ( SV423 @ SV475 @ SV537 )
= $true )
| ( ( in @ SV537 @ SV281 )
= $false )
| ( ( in @ SV475 @ SV96 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2107]) ).
thf(2224,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
| ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2108]) ).
thf(2225,plain,
! [SV104: $i,SV513: $i,SV287: $i > $o] :
( ( ( ~ ( SV287 @ SV513 ) )
= $false )
| ( ( in @ SV513 @ SV104 )
= $false )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2109]) ).
thf(2226,plain,
! [SV106: $i,SV514: $i,SV289: $i > $o] :
( ( ( SV289 @ SV514 )
= $false )
| ( ( in @ SV514 @ SV106 )
= $false )
| ( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
| $false )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2110]) ).
thf(2227,plain,
! [SV107: $i,SV290: $i,SV428: $i,SV515: $i] :
( ( ( ~ ( in @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ SV107 )
| ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV290 )
| ~ ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ SY1031 ) @ SV428 )
| ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ SY1031 ) @ SV515 ) ) )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2111]) ).
thf(2228,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) ) )
= $false )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2229,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
| ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) ) )
= $false )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2112]) ).
thf(2230,plain,
! [SV298: $i,SV116: $i,SV495: $o] :
( ( ( in @ ( sK37_SY957 @ SV495 @ SV116 @ SV298 ) @ SV116 )
= $true )
| ( SV495 = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2231,plain,
! [SV298: $i,SV116: $i] :
( ( ( in @ ( sK38_SX0 @ SV116 @ SV298 ) @ SV116 )
= $true )
| ( $true = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2117]) ).
thf(2232,plain,
! [SV298: $i,SV116: $i] :
( ( ( in @ ( sK39_SX0 @ SV116 @ SV298 ) @ SV116 )
= $true )
| ( $false = $true )
| ( ( in @ SV298 @ ( setunion @ SV116 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2120]) ).
thf(2233,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
| ~ ! [SY1032: $i] :
~ ~ ( ~ ( in @ SY1032 @ SV313 )
| ~ ( SV134 @ SY1032 @ SV550 ) ) )
| ~ ( ~ ~ ! [SY1033: $i] :
~ ~ ( ~ ( in @ SY1033 @ SV313 )
| ~ ( SV134 @ SY1033 @ SV550 ) )
| ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) ) ) ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2124]) ).
thf(2234,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 ) )
= $true )
| ( ( ~ ! [SY1018: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY1018 )
| ( SV541 = SY1018 ) ) )
= $true )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2125]) ).
thf(2235,plain,
! [SV320: $i > $o,SV141: $i,SV551: $i] :
( ( ( ~ ~ ( ~ ( in @ SV551 @ SV141 )
| ~ ( SV320 @ SV551 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2128]) ).
thf(2236,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2129]) ).
thf(2237,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2130]) ).
thf(2238,plain,
! [SV141: $i,SV320: $i > $o] :
( ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true )
| ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) )
| ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2131]) ).
thf(2239,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2240,plain,
! [SV142: $i,SV321: $i,SV440: $i,SV518: $i] :
( ( ( ~ ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
| ! [SY1034: $i] :
( ~ ( in @ SY1034 @ SV321 )
| ~ ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SY1034 ) @ SV440 )
| ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SY1034 ) @ SV518 ) ) )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2133]) ).
thf(2241,plain,
! [SV147: $i,SV325: $i > $o,SV520: $i] :
( ( ( ~ ( ~ ( in @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) @ SV147 )
| ~ ~ ( SV325 @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) ) ) )
= $true )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2134]) ).
thf(2242,plain,
! [SV521: $i,SV329: $i > $o,SV154: $i] :
( ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ! [SY722: $i] :
( ~ ( in @ SY722 @ SV154 )
| ! [SY723: $i] :
( ~ ( in @ SY723 @ SV154 )
| ~ ( SV329 @ SY722 )
| ~ ( SV329 @ SY723 )
| ( SY722 = SY723 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2135]) ).
thf(2243,plain,
! [SV155: $i,SV330: $i,SV443: $i] :
( ( ( in @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SV155 )
= $true )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2136]) ).
thf(2244,plain,
! [SV155: $i,SV443: $i,SV330: $i] :
( ( ( ~ ! [SY1007: $i] :
~ ~ ( ~ ( in @ SY1007 @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SY1007 ) ) ) )
= $true )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2137]) ).
thf(2245,plain,
! [SV157: $i,SV332: $i > $o] :
( ( ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 )
= $true )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2139]) ).
thf(2246,plain,
! [SV157: $i,SV332: $i > $o] :
( ( ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) )
= $true )
| ( ( ! [SY729: $i] :
( ~ ( in @ SY729 @ SV157 )
| ~ ( SV332 @ SY729 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2140]) ).
thf(2247,plain,
! [SV162: $i,SV337: $i,SV447: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK66_SY992 @ SV525 @ SV447 @ SV337 @ SV162 ) @ SV162 )
| ( ( ap @ SV162 @ SV337 @ SV447 @ ( sK66_SY992 @ SV525 @ SV447 @ SV337 @ SV162 ) )
= ( ap @ SV162 @ SV337 @ SV525 @ ( sK66_SY992 @ SV525 @ SV447 @ SV337 @ SV162 ) ) ) )
= $false )
| ( ( SV447 = SV525 )
= $true )
| ( ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) )
= $false )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2141]) ).
thf(2248,plain,
! [SV339: $i,SV526: $i,SV164: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ SV164 )
| ( in @ SV526 @ SV339 ) )
= $true )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2142]) ).
thf(2249,plain,
! [SV164: $i,SV497: $i,SV339: $i,SV526: $i] :
( ( ( ~ ( in @ SV526 @ SV339 )
| ( in @ SV497 @ SV164 ) )
= $true )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2143]) ).
thf(2250,plain,
! [SV168: $i,SV343: $i > $o,SV527: $i] :
( ( ( ~ ( ~ ( in @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) @ SV168 )
| ~ ~ ( SV343 @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) ) ) )
= $true )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2144]) ).
thf(2251,plain,
! [SV174: $i] :
( ( ( ~ ( in @ ( sK41_SY431 @ SV174 ) @ omega )
| ~ ( in @ ( sK41_SY431 @ SV174 ) @ SV174 ) )
= $false )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2145]) ).
thf(2252,plain,
! [SV174: $i,SV547: $i] :
( ( ( ~ ( in @ SV547 @ omega ) )
= $true )
| ( ( in @ SV547 @ SV174 )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( setadjoin @ ( sK41_SY431 @ SV174 ) @ ( sK41_SY431 @ SV174 ) ) @ SV174 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2146]) ).
thf(2253,plain,
! [SV182: $i,SV353: $i,SV451: $i,SV528: $i > $o] :
( ( ( in @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SV182 )
= $true )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2254,plain,
! [SV353: $i,SV528: $i > $o,SV451: $i,SV182: $i] :
( ( ( ~ ( in @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) @ SV353 )
| ~ ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) @ SV451 )
| ( SV528 @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2150]) ).
thf(2255,plain,
! [SV183: $i,SV354: $i,SV498: $i > $o,SV529: $i > $o] :
( ( ( in @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) @ SV183 )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2151]) ).
thf(2256,plain,
! [SV354: $i,SV529: $i > $o,SV498: $i > $o,SV183: $i] :
( ( ( ~ ( in @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) @ SV354 )
| ( ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 )
!= ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ~ ( ~ ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
| ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) ) )
| ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2152]) ).
thf(2257,plain,
! [SV185: $i,SV530: $o,SV356: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| SV530 ) )
= $true )
| ( SV530 = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2258,plain,
! [SV185: $i,SV530: $o,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 )
| SV530 )
= $false )
| ( SV530 = $true )
| ( SV530 = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2154]) ).
thf(2259,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2155]) ).
thf(2260,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2261,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( ~ ( in @ SV453 @ SV356 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2262,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2158]) ).
thf(2263,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2159]) ).
thf(2264,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2160]) ).
thf(2265,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) )
= $false )
| ( ( ~ ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2266,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( ~ ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2161]) ).
thf(2267,plain,
! [SV365: $i,SV194: $i,SV538: $i,SV480: $i,SV458: $i > $i > $o] :
( ( ( SV458 @ SV480 @ SV538 )
= $false )
| ( ( in @ ( kpair @ SV480 @ SV538 )
@ ( dpsetconstr @ SV194 @ SV365
@ ^ [SY915: $i,SY916: $i] : ( SV458 @ SY915 @ SY916 ) ) )
= $true )
| ( ( in @ SV538 @ SV365 )
= $false )
| ( ( in @ SV480 @ SV194 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2162]) ).
thf(2268,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ~ ( SV195 @ ( sK69_SY973 @ SV500 @ SV195 ) )
| ( SV500
= ( sK69_SY973 @ SV500 @ SV195 ) ) )
= $false )
| ( ( SV195 @ SV500 )
= $false )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2163]) ).
thf(2269,plain,
! [SV368: $i,SV534: $i,SV461: $i,SV198: $i] :
( ( ( ~ ( ~ ( in @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 )
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
!= ( setadjoin @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV534 @ SV198 )
= $false )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2164]) ).
thf(2270,plain,
! [SV200: $i,SV463: $i,SV535: $i,SV370: $i,SV543: $i] :
( ( ( in @ SV543 @ SV370 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV535 @ SV543 ) @ SV463 )
| ( ( ap @ SV200 @ SV370 @ SV463 @ SV535 )
= SV543 ) )
= $true )
| ( ( in @ SV535 @ SV200 )
= $false )
| ( ( func @ SV200 @ SV370 @ SV463 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2165]) ).
thf(2271,plain,
! [SV202: $i,SV464: $i,SV536: $i,SV371: $i,SV544: $i] :
( ( ( in @ SV544 @ SV371 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV536 @ SV544 ) @ SV464 )
| ( ( ap @ SV202 @ SV371 @ SV464 @ SV536 )
= SV544 ) )
= $true )
| ( ( in @ SV536 @ SV202 )
= $false )
| ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2166]) ).
thf(2272,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2167]) ).
thf(2273,plain,
! [SV10: $i > $o,SV483: $i] :
( ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2167]) ).
thf(2274,plain,
! [SV217: $i > $o,SV14: $i,SV548: $i] :
( ( ( ~ ( ~ ( in @ SV548 @ SV14 )
| ~ ( SV217 @ SV548 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2170]) ).
thf(2275,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2171]) ).
thf(2276,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2172]) ).
thf(2277,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2173]) ).
thf(2278,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2174]) ).
thf(2279,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2175]) ).
thf(2280,plain,
! [SV23: $i,SV386: $i,SV224: $i > $o] :
( ( ( ~ ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) ) )
= $false )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2176]) ).
thf(2281,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2176]) ).
thf(2282,plain,
! [SV24: $i,SV471: $o,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 )
| SV471 )
= $false )
| ( SV471 = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2177]) ).
thf(2283,plain,
! [SV24: $i,SV471: $o,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 ) )
= $false )
| ( SV471 = $true )
| ( SV471 = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2178]) ).
thf(2284,plain,
! [SV225: $i,SV24: $i,SV387: $i,SV471: $o] :
( ( SV471 = $false )
| ( SV471 = $true )
| ( SV471 = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2178]) ).
thf(2285,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2286,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2287,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2180]) ).
thf(2288,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2289,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2290,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2182]) ).
thf(2291,plain,
! [SV29: $i,SV230: $i,SV391: $i,SV504: $i] :
( ( ( ~ ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 ) )
= $false )
| ( ( ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2183]) ).
thf(2292,plain,
! [SV504: $i,SV391: $i,SV230: $i,SV29: $i] :
( ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2183]) ).
thf(2293,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) ) )
= $false )
| ( ( SV33 @ SV485 )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2184]) ).
thf(2294,plain,
! [SV33: $i > $o,SV485: $i] :
( ( ( SV485
= ( sK57_SY946 @ SV485 @ SV33 ) )
= $false )
| ( ( SV33 @ SV485 )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2184]) ).
thf(2295,plain,
! [SV242: $i > $o,SV44: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ SV44 )
| ~ ( SV242 @ SV552 ) )
= $true )
| ( ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2296,plain,
! [SV242: $i > $o,SV44: $i,SV553: $i] :
( ( ( ~ ( in @ SV553 @ SV44 )
| ~ ( SV242 @ SV553 ) )
= $true )
| ( ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2186]) ).
thf(2297,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) ) )
= $false )
| ( ( SV46 @ SV488 )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2187]) ).
thf(2298,plain,
! [SV46: $i > $o,SV488: $i] :
( ( ( SV488
= ( sK58_SY949 @ SV488 @ SV46 ) )
= $false )
| ( ( SV46 @ SV488 )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2187]) ).
thf(2299,plain,
! [SV246: $i > $o,SV554: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ SV554 )
| ~ ! [SY1035: $i] :
( ~ ( SV49 @ SY1035 )
| ( SV554 = SY1035 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2188]) ).
thf(2300,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( ~ ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2189]) ).
thf(2301,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2190]) ).
thf(2302,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ~ ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2191]) ).
thf(2303,plain,
! [SV53: $i > $o,SV489: $i] :
( ( ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2192]) ).
thf(2304,plain,
! [SV58: $i,SV251: $i] :
( ( ( ~ ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 ) )
= $false )
| ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2305,plain,
! [SV58: $i,SV251: $i] :
( ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
= $false )
| ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2193]) ).
thf(2306,plain,
! [SV58: $i,SV251: $i] :
( ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
= $true )
| ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
= $false )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2194]) ).
thf(2307,plain,
! [SV62: $i] :
( ( ~ ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2308,plain,
! [SV62: $i] :
( ( ~ ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[2196]) ).
thf(2309,plain,
! [SV555: $i,SV62: $i,SV549: $i] :
( ( ~ ~ ( ~ ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SV555 @ ( sK5_SY153 @ SV62 ) ) )
| ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV549 )
| ( in @ SY1036 @ SV555 ) )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2197]) ).
thf(2310,plain,
! [SV62: $i,SV539: $i] :
( ( ( ~ ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV539 )
| ( in @ SY1010 @ SV62 ) ) )
= $true )
| ( ( ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2198]) ).
thf(2311,plain,
! [SV509: $i,SV260: $i > $o,SV69: $i] :
( ( ( ! [SY614: $i] :
~ ~ ( ~ ( in @ SY614 @ SV69 )
| ~ ( SV260 @ SY614 ) ) )
= $false )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2312,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV556: $i] :
( ( ( ~ ( in @ SV556 @ SV413 )
| ( SV510 @ SV556 ) )
= $true )
| ( ( in @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SV76 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2313,plain,
! [SV266: $i,SV510: $i > $o,SV413: $i,SV76: $i] :
( ( ( ~ ( in @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) @ SV266 ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2314,plain,
! [SV76: $i,SV266: $i,SV413: $i,SV510: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) @ SV413 )
| ( SV510 @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2201]) ).
thf(2315,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2202]) ).
thf(2316,plain,
! [SV511: $o,SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
| SV511 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2203]) ).
thf(2317,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
= $false )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2318,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2205]) ).
thf(2319,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
| $true )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2206]) ).
thf(2320,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2207]) ).
thf(2321,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2208]) ).
thf(2322,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $false )
| ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
| $false )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2209]) ).
thf(2323,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2210]) ).
thf(2324,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( ~ ( SV78 @ ( sK60_SY952 @ SV490 @ SV78 ) ) )
= $false )
| ( ( SV78 @ SV490 )
= $false )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2325,plain,
! [SV78: $i > $o,SV490: $i] :
( ( ( SV490
= ( sK60_SY952 @ SV490 @ SV78 ) )
= $false )
| ( ( SV78 @ SV490 )
= $false )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2211]) ).
thf(2326,plain,
! [SV268: $i,SV79: $i] :
( ( ( in @ ( sK50_SY634 @ SV79 @ SV268 ) @ SV268 )
= $true )
| ( ( SV79 = SV268 )
= $true )
| ( ( in @ ( sK11_SY633 @ SV268 @ SV79 ) @ SV79 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2327,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2328,plain,
! [SV80: $i > $o,SV491: $i] :
( ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2215]) ).
thf(2329,plain,
! [SV83: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ ( sK44_SY637 @ SV83 @ SV271 ) ) )
= $false )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2330,plain,
! [SV271: $i,SV83: $i] :
( ( ( ~ ( in @ ( sK44_SY637 @ SV83 @ SV271 ) @ SV83 ) )
= $false )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2216]) ).
thf(2331,plain,
! [SV83: $i,SV542: $i,SV271: $i] :
( ( ( ~ ( in @ SV271 @ SV542 ) )
= $true )
| ( ( ~ ( in @ SV542 @ SV83 ) )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2217]) ).
thf(2332,plain,
! [SV273: $i > $o,SV86: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ SV86 )
| ~ ( SV273 @ SV545 ) )
= $true )
| ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2218]) ).
thf(2333,plain,
! [SV273: $i > $o,SV86: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ SV86 )
| ~ ( SV273 @ SV546 ) )
= $true )
| ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2219]) ).
thf(2334,plain,
! [SV88: $i,SV492: $i] :
( ( ( in @ ( sK36_SY237 @ SV492 @ SV88 ) @ SV88 )
= $true )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2220]) ).
thf(2335,plain,
! [SV88: $i,SV492: $i] :
( ( ( ~ ~ ! [SY1017: $i] :
~ ~ ( ~ ( in @ SY1017 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SY1017 @ SV88 ) ) )
= $true )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2221]) ).
thf(2336,plain,
! [SV89: $i,SV275: $i,SV419: $i,SV512: $i] :
( ( ( ~ ( in @ ( sK62_SY982 @ SV512 @ SV419 @ SV275 @ SV89 ) @ SV89 ) )
= $false )
| ( ( SV419 = SV512 )
= $true )
| ( ( func @ SV89 @ SV275 @ SV512 )
= $false )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2222]) ).
thf(2337,plain,
! [SV512: $i,SV419: $i,SV275: $i,SV89: $i] :
( ( ( ( ap @ SV89 @ SV275 @ SV419 @ ( sK62_SY982 @ SV512 @ SV419 @ SV275 @ SV89 ) )
= ( ap @ SV89 @ SV275 @ SV512 @ ( sK62_SY982 @ SV512 @ SV419 @ SV275 @ SV89 ) ) )
= $false )
| ( ( SV419 = SV512 )
= $true )
| ( ( func @ SV89 @ SV275 @ SV512 )
= $false )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2222]) ).
thf(2338,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2339,plain,
! [SV98: $i > $o,SV493: $i] :
( ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2224]) ).
thf(2340,plain,
! [SV104: $i,SV513: $i,SV287: $i > $o] :
( ( ( SV287 @ SV513 )
= $true )
| ( ( in @ SV513 @ SV104 )
= $false )
| ( ( ~ ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2225]) ).
thf(2341,plain,
! [SV514: $i,SV289: $i > $o,SV106: $i] :
( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
!= emptyset )
= $true )
| ( $false = $true )
| ( ( in @ SV514 @ SV106 )
= $false )
| ( ( SV289 @ SV514 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2226]) ).
thf(2342,plain,
! [SV107: $i,SV290: $i,SV428: $i,SV515: $i] :
( ( ( ~ ( in @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ SV107 ) )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2227]) ).
thf(2343,plain,
! [SV107: $i,SV428: $i,SV515: $i,SV290: $i] :
( ( ( ! [SY1031: $i] :
( ~ ( in @ SY1031 @ SV290 )
| ~ ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ SY1031 ) @ SV428 )
| ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ SY1031 ) @ SV515 ) ) )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2227]) ).
thf(2344,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2228]) ).
thf(2345,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) ) )
= $false )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2229]) ).
thf(2346,plain,
! [SV113: $i > $o,SV494: $i] :
( ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2229]) ).
thf(2347,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ( ~ ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
| ~ ! [SY1032: $i] :
~ ~ ( ~ ( in @ SY1032 @ SV313 )
| ~ ( SV134 @ SY1032 @ SV550 ) ) )
| ~ ( ~ ~ ! [SY1033: $i] :
~ ~ ( ~ ( in @ SY1033 @ SV313 )
| ~ ( SV134 @ SY1033 @ SV550 ) )
| ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2233]) ).
thf(2348,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( ~ ! [SY1018: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY1018 )
| ( SV541 = SY1018 ) ) )
= $true )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2234]) ).
thf(2349,plain,
! [SV320: $i > $o,SV141: $i,SV551: $i] :
( ( ( ~ ( ~ ( in @ SV551 @ SV141 )
| ~ ( SV320 @ SV551 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2235]) ).
thf(2350,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2236]) ).
thf(2351,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2352,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2353,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2239]) ).
thf(2354,plain,
! [SV142: $i,SV321: $i,SV440: $i,SV518: $i] :
( ( ( ~ ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 ) )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2240]) ).
thf(2355,plain,
! [SV142: $i,SV440: $i,SV518: $i,SV321: $i] :
( ( ( ! [SY1034: $i] :
( ~ ( in @ SY1034 @ SV321 )
| ~ ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SY1034 ) @ SV440 )
| ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SY1034 ) @ SV518 ) ) )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2240]) ).
thf(2356,plain,
! [SV147: $i,SV325: $i > $o,SV520: $i] :
( ( ( ~ ( in @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) @ SV147 )
| ~ ~ ( SV325 @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) ) )
= $false )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2241]) ).
thf(2357,plain,
! [SV521: $i,SV329: $i > $o,SV154: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ SV154 )
| ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SV154 )
| ~ ( SV329 @ SV557 )
| ~ ( SV329 @ SY1038 )
| ( SV557 = SY1038 ) ) )
= $true )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2242]) ).
thf(2358,plain,
! [SV155: $i,SV443: $i,SV330: $i] :
( ( ( ! [SY1007: $i] :
~ ~ ( ~ ( in @ SY1007 @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ SY1007 ) ) ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2359,plain,
! [SV332: $i > $o,SV157: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ SV157 )
| ~ ( SV332 @ SV558 ) )
= $true )
| ( ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2245]) ).
thf(2360,plain,
! [SV332: $i > $o,SV157: $i,SV559: $i] :
( ( ( ~ ( in @ SV559 @ SV157 )
| ~ ( SV332 @ SV559 ) )
= $true )
| ( ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2246]) ).
thf(2361,plain,
! [SV162: $i,SV337: $i,SV447: $i,SV525: $i] :
( ( ( ~ ( in @ ( sK66_SY992 @ SV525 @ SV447 @ SV337 @ SV162 ) @ SV162 ) )
= $false )
| ( ( SV447 = SV525 )
= $true )
| ( ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) )
= $false )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2362,plain,
! [SV525: $i,SV447: $i,SV337: $i,SV162: $i] :
( ( ( ( ap @ SV162 @ SV337 @ SV447 @ ( sK66_SY992 @ SV525 @ SV447 @ SV337 @ SV162 ) )
= ( ap @ SV162 @ SV337 @ SV525 @ ( sK66_SY992 @ SV525 @ SV447 @ SV337 @ SV162 ) ) )
= $false )
| ( ( SV447 = SV525 )
= $true )
| ( ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) )
= $false )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2247]) ).
thf(2363,plain,
! [SV339: $i,SV526: $i,SV164: $i,SV497: $i] :
( ( ( ~ ( in @ SV497 @ SV164 ) )
= $true )
| ( ( in @ SV526 @ SV339 )
= $true )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2248]) ).
thf(2364,plain,
! [SV164: $i,SV497: $i,SV339: $i,SV526: $i] :
( ( ( ~ ( in @ SV526 @ SV339 ) )
= $true )
| ( ( in @ SV497 @ SV164 )
= $true )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2249]) ).
thf(2365,plain,
! [SV168: $i,SV343: $i > $o,SV527: $i] :
( ( ( ~ ( in @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) @ SV168 )
| ~ ~ ( SV343 @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) ) )
= $false )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2250]) ).
thf(2366,plain,
! [SV174: $i] :
( ( ( ~ ( in @ ( sK41_SY431 @ SV174 ) @ omega ) )
= $false )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2251]) ).
thf(2367,plain,
! [SV174: $i] :
( ( ( ~ ( in @ ( sK41_SY431 @ SV174 ) @ SV174 ) )
= $false )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2251]) ).
thf(2368,plain,
! [SV174: $i,SV547: $i] :
( ( ( in @ SV547 @ omega )
= $false )
| ( ( in @ SV547 @ SV174 )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( setadjoin @ ( sK41_SY431 @ SV174 ) @ ( sK41_SY431 @ SV174 ) ) @ SV174 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2252]) ).
thf(2369,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV560: $i] :
( ( ( ~ ( in @ SV560 @ SV451 )
| ( SV528 @ SV560 ) )
= $true )
| ( ( in @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SV182 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2253]) ).
thf(2370,plain,
! [SV353: $i,SV528: $i > $o,SV451: $i,SV182: $i] :
( ( ( ~ ( in @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) @ SV353 ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2254]) ).
thf(2371,plain,
! [SV182: $i,SV353: $i,SV451: $i,SV528: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) @ SV451 )
| ( SV528 @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2254]) ).
thf(2372,plain,
! [SV354: $i,SV529: $i > $o,SV498: $i > $o,SV183: $i] :
( ( ( ~ ( in @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) @ SV354 ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2256]) ).
thf(2373,plain,
! [SV183: $i,SV354: $i,SV498: $i > $o,SV529: $i > $o] :
( ( ( ( ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 )
!= ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ~ ( ~ ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
| ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) ) )
| ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2256]) ).
thf(2374,plain,
! [SV185: $i,SV530: $o,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 )
| SV530 )
= $false )
| ( SV530 = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2257]) ).
thf(2375,plain,
! [SV185: $i,SV530: $o,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 ) )
= $false )
| ( SV530 = $true )
| ( SV530 = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2258]) ).
thf(2376,plain,
! [SV356: $i,SV185: $i,SV453: $i,SV530: $o] :
( ( SV530 = $false )
| ( SV530 = $true )
| ( SV530 = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2258]) ).
thf(2377,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 )
| $true )
= $false )
| ( $true = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2259]) ).
thf(2378,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2379,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2260]) ).
thf(2380,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 )
| $false )
= $false )
| ( $false = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2261]) ).
thf(2381,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2382,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2262]) ).
thf(2383,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2263]) ).
thf(2384,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2385,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( ~ ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2265]) ).
thf(2386,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2266]) ).
thf(2387,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ~ ( SV195 @ ( sK69_SY973 @ SV500 @ SV195 ) ) )
= $false )
| ( ( SV195 @ SV500 )
= $false )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2268]) ).
thf(2388,plain,
! [SV195: $i > $o,SV500: $i] :
( ( ( SV500
= ( sK69_SY973 @ SV500 @ SV195 ) )
= $false )
| ( ( SV195 @ SV500 )
= $false )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2268]) ).
thf(2389,plain,
! [SV368: $i,SV534: $i,SV461: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 )
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) )
| ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
!= ( setadjoin @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV534 @ SV198 )
= $false )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2390,plain,
! [SV370: $i,SV200: $i,SV463: $i,SV543: $i,SV535: $i] :
( ( ( ~ ( in @ ( kpair @ SV535 @ SV543 ) @ SV463 ) )
= $true )
| ( ( ( ap @ SV200 @ SV370 @ SV463 @ SV535 )
= SV543 )
= $true )
| ( ( in @ SV543 @ SV370 )
= $false )
| ( ( in @ SV535 @ SV200 )
= $false )
| ( ( func @ SV200 @ SV370 @ SV463 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2270]) ).
thf(2391,plain,
! [SV371: $i,SV202: $i,SV464: $i,SV544: $i,SV536: $i] :
( ( ( ~ ( in @ ( kpair @ SV536 @ SV544 ) @ SV464 ) )
= $true )
| ( ( ( ap @ SV202 @ SV371 @ SV464 @ SV536 )
= SV544 )
= $true )
| ( ( in @ SV544 @ SV371 )
= $false )
| ( ( in @ SV536 @ SV202 )
= $false )
| ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2271]) ).
thf(2392,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( ~ ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2272]) ).
thf(2393,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2273]) ).
thf(2394,plain,
! [SV217: $i > $o,SV14: $i,SV548: $i] :
( ( ( ~ ( in @ SV548 @ SV14 )
| ~ ( SV217 @ SV548 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2274]) ).
thf(2395,plain,
! [SV217: $i > $o,SV14: $i,SV561: $i] :
( ( ( ~ ~ ( ~ ( in @ SV561 @ SV14 )
| ~ ( SV217 @ SV561 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2275]) ).
thf(2396,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2276]) ).
thf(2397,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ~ ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2277]) ).
thf(2398,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2278]) ).
thf(2399,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $false )
| ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2279]) ).
thf(2400,plain,
! [SV23: $i,SV386: $i,SV224: $i > $o] :
( ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( ~ ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2280]) ).
thf(2401,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $false )
| ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2402,plain,
! [SV24: $i,SV471: $o,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 ) )
= $false )
| ( SV471 = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2403,plain,
! [SV225: $i,SV24: $i,SV387: $i,SV471: $o] :
( ( SV471 = $false )
| ( SV471 = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2282]) ).
thf(2404,plain,
! [SV24: $i,SV471: $o,SV225: $i,SV387: $i] :
( ( ( in @ SV387 @ SV225 )
= $true )
| ( SV471 = $true )
| ( SV471 = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2283]) ).
thf(2405,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2285]) ).
thf(2406,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2285]) ).
thf(2407,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( in @ SV387 @ SV225 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2286]) ).
thf(2408,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV225 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2288]) ).
thf(2409,plain,
! [SV225: $i,SV24: $i,SV387: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2288]) ).
thf(2410,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( in @ SV387 @ SV225 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2289]) ).
thf(2411,plain,
! [SV29: $i,SV230: $i,SV391: $i,SV504: $i] :
( ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( ! [SY975: $i] :
( ~ ( in @ SY975 @ SV29 )
| ! [SY976: $i] :
( ~ ( in @ SY976 @ SV230 )
| ~ ( in @ ( kpair @ SY975 @ SY976 ) @ SV504 )
| ( in @ ( kpair @ SY975 @ SY976 ) @ SV391 ) ) ) )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2291]) ).
thf(2412,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i,SV562: $i] :
( ( ( ~ ( in @ SV562 @ SV29 )
| ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV230 )
| ~ ( in @ ( kpair @ SV562 @ SY1039 ) @ SV504 )
| ( in @ ( kpair @ SV562 @ SY1039 ) @ SV391 ) ) )
= $true )
| ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2292]) ).
thf(2413,plain,
! [SV485: $i,SV33: $i > $o] :
( ( ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( ! [SY89: $i,SY90: $i] :
( ~ ( SV33 @ SY89 )
| ~ ( SV33 @ SY90 )
| ( SY89 = SY90 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2293]) ).
thf(2414,plain,
! [SV485: $i,SV563: $i,SV33: $i > $o] :
( ( ( ! [SY1040: $i] :
( ~ ( SV33 @ SV563 )
| ~ ( SV33 @ SY1040 )
| ( SV563 = SY1040 ) ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV485
= ( sK57_SY946 @ SV485 @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2294]) ).
thf(2415,plain,
! [SV242: $i > $o,SV44: $i,SV552: $i] :
( ( ( ~ ( in @ SV552 @ SV44 ) )
= $true )
| ( ( ~ ( SV242 @ SV552 ) )
= $true )
| ( ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2295]) ).
thf(2416,plain,
! [SV242: $i > $o,SV44: $i,SV553: $i] :
( ( ( ~ ( in @ SV553 @ SV44 ) )
= $true )
| ( ( ~ ( SV242 @ SV553 ) )
= $true )
| ( ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2296]) ).
thf(2417,plain,
! [SV488: $i,SV46: $i > $o] :
( ( ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( ! [SY117: $i,SY118: $i] :
( ~ ( SV46 @ SY117 )
| ~ ( SV46 @ SY118 )
| ( SY117 = SY118 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2297]) ).
thf(2418,plain,
! [SV488: $i,SV564: $i,SV46: $i > $o] :
( ( ( ! [SY1041: $i] :
( ~ ( SV46 @ SV564 )
| ~ ( SV46 @ SY1041 )
| ( SV564 = SY1041 ) ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV488
= ( sK58_SY949 @ SV488 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2298]) ).
thf(2419,plain,
! [SV246: $i > $o,SV554: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ SV554 )
| ~ ! [SY1035: $i] :
( ~ ( SV49 @ SY1035 )
| ( SV554 = SY1035 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2299]) ).
thf(2420,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
| ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2421,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2301]) ).
thf(2422,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2301]) ).
thf(2423,plain,
! [SV53: $i > $o,SV489: $i] :
( ( ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
| ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2302]) ).
thf(2424,plain,
! [SV53: $i > $o,SV489: $i] :
( ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2425,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2303]) ).
thf(2426,plain,
! [SV58: $i,SV251: $i] :
( ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV251 )
= $true )
| ( ( in @ ( sK10_SY603 @ SV251 @ SV58 ) @ SV58 )
= $true )
| ( ( SV58 = SV251 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2304]) ).
thf(2427,plain,
! [SV62: $i] :
( ( ! [SY835: $i] :
( ~ ( in @ SY835 @ ( sK5_SY153 @ SV62 ) )
| ! [SY155: $i] :
( ~ ( in @ SY155 @ SY835 )
| ( in @ SY155 @ SV62 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2307]) ).
thf(2428,plain,
! [SV62: $i] :
( ( ! [SY837: $i,SY838: $i] :
( ~ ~ ( ~ ( in @ SY837 @ SV62 )
| ~ ( in @ SY838 @ SV62 ) )
| ~ ! [SY839: $i] :
( ~ ( in @ SY839 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SY837 @ SY839 )
| ( in @ SY838 @ SY839 ) )
| ~ ( ~ ( in @ SY838 @ SY839 )
| ( in @ SY837 @ SY839 ) ) ) )
| ( SY837 = SY838 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[2308]) ).
thf(2429,plain,
! [SV555: $i,SV62: $i,SV549: $i] :
( ( ( ~ ~ ( ~ ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SV555 @ ( sK5_SY153 @ SV62 ) ) ) )
= $true )
| ( ( ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV549 )
| ( in @ SY1036 @ SV555 ) )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2309]) ).
thf(2430,plain,
! [SV62: $i,SV539: $i] :
( ( ( ! [SY1010: $i] :
( ~ ( in @ SY1010 @ SV539 )
| ( in @ SY1010 @ SV62 ) ) )
= $false )
| ( ( ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2310]) ).
thf(2431,plain,
! [SV69: $i,SV260: $i > $o,SV509: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) @ SV69 )
| ~ ( SV260 @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) ) ) )
= $false )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2311]) ).
thf(2432,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV556: $i] :
( ( ( ~ ( in @ SV556 @ SV413 ) )
= $true )
| ( ( SV510 @ SV556 )
= $true )
| ( ( in @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SV76 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2312]) ).
thf(2433,plain,
! [SV266: $i,SV510: $i > $o,SV413: $i,SV76: $i] :
( ( ( in @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) @ SV266 )
= $true )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2313]) ).
thf(2434,plain,
! [SV76: $i,SV266: $i,SV413: $i,SV510: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) @ SV413 ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2435,plain,
! [SV76: $i,SV266: $i,SV413: $i,SV510: $i > $o] :
( ( ( SV510 @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) )
= $false )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2314]) ).
thf(2436,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2437,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| SV511 )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2315]) ).
thf(2438,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 ) )
= $true )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2316]) ).
thf(2439,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2317]) ).
thf(2440,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| SV511 )
= $false )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2317]) ).
thf(2441,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2318]) ).
thf(2442,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2318]) ).
thf(2443,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2319]) ).
thf(2444,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2320]) ).
thf(2445,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| $true )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2320]) ).
thf(2446,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2447,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2321]) ).
thf(2448,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2322]) ).
thf(2449,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2323]) ).
thf(2450,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| $false )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2323]) ).
thf(2451,plain,
! [SV490: $i,SV78: $i > $o] :
( ( ( SV78 @ ( sK60_SY952 @ SV490 @ SV78 ) )
= $true )
| ( ( SV78 @ SV490 )
= $false )
| ( ( SV78
@ ( descr
@ ^ [SY214: $i] : ( SV78 @ SY214 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2324]) ).
thf(2452,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( ~ ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2327]) ).
thf(2453,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2328]) ).
thf(2454,plain,
! [SV83: $i,SV271: $i] :
( ( ( in @ SV271 @ ( sK44_SY637 @ SV83 @ SV271 ) )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2329]) ).
thf(2455,plain,
! [SV271: $i,SV83: $i] :
( ( ( in @ ( sK44_SY637 @ SV83 @ SV271 ) @ SV83 )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2330]) ).
thf(2456,plain,
! [SV83: $i,SV542: $i,SV271: $i] :
( ( ( in @ SV271 @ SV542 )
= $false )
| ( ( ~ ( in @ SV542 @ SV83 ) )
= $true )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2331]) ).
thf(2457,plain,
! [SV273: $i > $o,SV86: $i,SV545: $i] :
( ( ( ~ ( in @ SV545 @ SV86 ) )
= $true )
| ( ( ~ ( SV273 @ SV545 ) )
= $true )
| ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2458,plain,
! [SV273: $i > $o,SV86: $i,SV546: $i] :
( ( ( ~ ( in @ SV546 @ SV86 ) )
= $true )
| ( ( ~ ( SV273 @ SV546 ) )
= $true )
| ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2459,plain,
! [SV88: $i,SV492: $i] :
( ( ( ~ ! [SY1017: $i] :
~ ~ ( ~ ( in @ SY1017 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SY1017 @ SV88 ) ) )
= $false )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2460,plain,
! [SV89: $i,SV275: $i,SV419: $i,SV512: $i] :
( ( ( in @ ( sK62_SY982 @ SV512 @ SV419 @ SV275 @ SV89 ) @ SV89 )
= $true )
| ( ( SV419 = SV512 )
= $true )
| ( ( func @ SV89 @ SV275 @ SV512 )
= $false )
| ( ( func @ SV89 @ SV275 @ SV419 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2336]) ).
thf(2461,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( ~ ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2462,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2339]) ).
thf(2463,plain,
! [SV513: $i,SV287: $i > $o,SV104: $i] :
( ( ( ! [SY662: $i] :
( ~ ( in @ SY662 @ SV104 )
| ( SV287 @ SY662 ) ) )
= $false )
| ( ( in @ SV513 @ SV104 )
= $false )
| ( ( SV287 @ SV513 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2340]) ).
thf(2464,plain,
! [SV514: $i,SV289: $i > $o,SV106: $i] :
( ( ( ( dsetconstr @ SV106
@ ^ [SY665: $i] : ( SV289 @ SY665 ) )
= emptyset )
= $false )
| ( $false = $true )
| ( ( in @ SV514 @ SV106 )
= $false )
| ( ( SV289 @ SV514 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2465,plain,
! [SV107: $i,SV290: $i,SV428: $i,SV515: $i] :
( ( ( in @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ SV107 )
= $true )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2466,plain,
! [SV290: $i,SV515: $i,SV428: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) @ SV290 )
| ~ ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) ) @ SV428 )
| ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) ) @ SV515 ) )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2343]) ).
thf(2467,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $false )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2344]) ).
thf(2468,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( ~ ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2469,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $false )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2346]) ).
thf(2470,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ( ~ ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
| ~ ! [SY1032: $i] :
~ ~ ( ~ ( in @ SY1032 @ SV313 )
| ~ ( SV134 @ SY1032 @ SV550 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2347]) ).
thf(2471,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ( ~ ~ ! [SY1033: $i] :
~ ~ ( ~ ( in @ SY1033 @ SV313 )
| ~ ( SV134 @ SY1033 @ SV550 ) )
| ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) ) ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2347]) ).
thf(2472,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( ! [SY1018: $i] :
( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SY1018 )
| ( SV541 = SY1018 ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2348]) ).
thf(2473,plain,
! [SV320: $i > $o,SV141: $i,SV551: $i] :
( ( ( ~ ( in @ SV551 @ SV141 )
| ~ ( SV320 @ SV551 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2349]) ).
thf(2474,plain,
! [SV320: $i > $o,SV141: $i,SV565: $i] :
( ( ( ~ ~ ( ~ ( in @ SV565 @ SV141 )
| ~ ( SV320 @ SV565 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2350]) ).
thf(2475,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2351]) ).
thf(2476,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ~ ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2352]) ).
thf(2477,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2478,plain,
! [SV142: $i,SV321: $i,SV440: $i,SV518: $i] :
( ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2354]) ).
thf(2479,plain,
! [SV321: $i,SV518: $i,SV440: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
| ~ ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
| ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 ) )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2355]) ).
thf(2480,plain,
! [SV147: $i,SV325: $i > $o,SV520: $i] :
( ( ( ~ ( in @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) @ SV147 ) )
= $false )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2481,plain,
! [SV147: $i,SV520: $i,SV325: $i > $o] :
( ( ( ~ ~ ( SV325 @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) ) )
= $false )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2356]) ).
thf(2482,plain,
! [SV521: $i,SV329: $i > $o,SV154: $i,SV557: $i] :
( ( ( ~ ( in @ SV557 @ SV154 ) )
= $true )
| ( ( ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SV154 )
| ~ ( SV329 @ SV557 )
| ~ ( SV329 @ SY1038 )
| ( SV557 = SY1038 ) ) )
= $true )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2357]) ).
thf(2483,plain,
! [SV330: $i,SV443: $i,SV155: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) ) ) ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2358]) ).
thf(2484,plain,
! [SV332: $i > $o,SV157: $i,SV558: $i] :
( ( ( ~ ( in @ SV558 @ SV157 ) )
= $true )
| ( ( ~ ( SV332 @ SV558 ) )
= $true )
| ( ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2359]) ).
thf(2485,plain,
! [SV332: $i > $o,SV157: $i,SV559: $i] :
( ( ( ~ ( in @ SV559 @ SV157 ) )
= $true )
| ( ( ~ ( SV332 @ SV559 ) )
= $true )
| ( ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2360]) ).
thf(2486,plain,
! [SV162: $i,SV337: $i,SV447: $i,SV525: $i] :
( ( ( in @ ( sK66_SY992 @ SV525 @ SV447 @ SV337 @ SV162 ) @ SV162 )
= $true )
| ( ( SV447 = SV525 )
= $true )
| ( ( in @ SV525 @ ( funcSet @ SV162 @ SV337 ) )
= $false )
| ( ( in @ SV447 @ ( funcSet @ SV162 @ SV337 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2361]) ).
thf(2487,plain,
! [SV339: $i,SV526: $i,SV164: $i,SV497: $i] :
( ( ( in @ SV497 @ SV164 )
= $false )
| ( ( in @ SV526 @ SV339 )
= $true )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2363]) ).
thf(2488,plain,
! [SV164: $i,SV497: $i,SV339: $i,SV526: $i] :
( ( ( in @ SV526 @ SV339 )
= $false )
| ( ( in @ SV497 @ SV164 )
= $true )
| ( ( SV497 = SV526 )
= $false )
| ( ( SV164 = SV339 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2364]) ).
thf(2489,plain,
! [SV168: $i,SV343: $i > $o,SV527: $i] :
( ( ( ~ ( in @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) @ SV168 ) )
= $false )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2365]) ).
thf(2490,plain,
! [SV168: $i,SV527: $i,SV343: $i > $o] :
( ( ( ~ ~ ( SV343 @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) ) )
= $false )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2365]) ).
thf(2491,plain,
! [SV174: $i] :
( ( ( in @ ( sK41_SY431 @ SV174 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2366]) ).
thf(2492,plain,
! [SV174: $i] :
( ( ( in @ ( sK41_SY431 @ SV174 ) @ SV174 )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( ! [SY432: $i] :
( ~ ( in @ SY432 @ omega )
| ( in @ SY432 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2367]) ).
thf(2493,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV560: $i] :
( ( ( ~ ( in @ SV560 @ SV451 ) )
= $true )
| ( ( SV528 @ SV560 )
= $true )
| ( ( in @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SV182 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2369]) ).
thf(2494,plain,
! [SV353: $i,SV528: $i > $o,SV451: $i,SV182: $i] :
( ( ( in @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) @ SV353 )
= $true )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2495,plain,
! [SV182: $i,SV353: $i,SV451: $i,SV528: $i > $o] :
( ( ( ~ ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) @ SV451 ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2371]) ).
thf(2496,plain,
! [SV182: $i,SV353: $i,SV451: $i,SV528: $i > $o] :
( ( ( SV528 @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) )
= $false )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2371]) ).
thf(2497,plain,
! [SV354: $i,SV529: $i > $o,SV498: $i > $o,SV183: $i] :
( ( ( in @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) @ SV354 )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2498,plain,
! [SV183: $i,SV354: $i,SV498: $i > $o,SV529: $i > $o] :
( ( ( ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 )
!= ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2373]) ).
thf(2499,plain,
! [SV183: $i,SV354: $i,SV529: $i > $o,SV498: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
| ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) ) )
| ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2373]) ).
thf(2500,plain,
! [SV185: $i,SV530: $o,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 ) )
= $false )
| ( SV530 = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2501,plain,
! [SV356: $i,SV185: $i,SV453: $i,SV530: $o] :
( ( SV530 = $false )
| ( SV530 = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2374]) ).
thf(2502,plain,
! [SV185: $i,SV530: $o,SV356: $i,SV453: $i] :
( ( ( in @ SV453 @ SV356 )
= $true )
| ( SV530 = $true )
| ( SV530 = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2375]) ).
thf(2503,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 ) )
= $false )
| ( $true = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2504,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2377]) ).
thf(2505,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( in @ SV453 @ SV356 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2378]) ).
thf(2506,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( ~ ( in @ SV453 @ SV356 ) )
= $false )
| ( $false = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2380]) ).
thf(2507,plain,
! [SV356: $i,SV185: $i,SV453: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2380]) ).
thf(2508,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( in @ SV453 @ SV356 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2381]) ).
thf(2509,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2383]) ).
thf(2510,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2384]) ).
thf(2511,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
| ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2385]) ).
thf(2512,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2386]) ).
thf(2513,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2386]) ).
thf(2514,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( SV195 @ ( sK69_SY973 @ SV500 @ SV195 ) )
= $true )
| ( ( SV195 @ SV500 )
= $false )
| ( ( ~ ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2387]) ).
thf(2515,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $false )
| ( ( SV195 @ SV500 )
= $false )
| ( ( SV500
= ( sK69_SY973 @ SV500 @ SV195 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2516,plain,
! [SV368: $i,SV534: $i,SV461: $i,SV198: $i] :
( ( ( ~ ( in @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 )
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) ) )
= $false )
| ( ( in @ SV534 @ SV198 )
= $false )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2517,plain,
! [SV198: $i,SV461: $i,SV534: $i,SV368: $i] :
( ( ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
!= ( setadjoin @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 ) @ emptyset ) )
= $false )
| ( ( in @ SV534 @ SV198 )
= $false )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2389]) ).
thf(2518,plain,
! [SV370: $i,SV200: $i,SV463: $i,SV543: $i,SV535: $i] :
( ( ( in @ ( kpair @ SV535 @ SV543 ) @ SV463 )
= $false )
| ( ( ( ap @ SV200 @ SV370 @ SV463 @ SV535 )
= SV543 )
= $true )
| ( ( in @ SV543 @ SV370 )
= $false )
| ( ( in @ SV535 @ SV200 )
= $false )
| ( ( func @ SV200 @ SV370 @ SV463 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2519,plain,
! [SV371: $i,SV202: $i,SV464: $i,SV544: $i,SV536: $i] :
( ( ( in @ ( kpair @ SV536 @ SV544 ) @ SV464 )
= $false )
| ( ( ( ap @ SV202 @ SV371 @ SV464 @ SV536 )
= SV544 )
= $true )
| ( ( in @ SV544 @ SV371 )
= $false )
| ( ( in @ SV536 @ SV202 )
= $false )
| ( ( in @ SV464 @ ( funcSet @ SV202 @ SV371 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2520,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ! [SY25: $i] :
~ ~ ( ~ ( SV10 @ SY25 )
| ~ ! [SY26: $i] :
( ~ ( SV10 @ SY26 )
| ( SY25 = SY26 ) ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2521,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK74_SY25 @ SV483 @ SV10 ) )
| ~ ! [SY1042: $i] :
( ~ ( SV10 @ SY1042 )
| ( ( sK74_SY25 @ SV483 @ SV10 )
= SY1042 ) ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2393]) ).
thf(2522,plain,
! [SV217: $i > $o,SV14: $i,SV548: $i] :
( ( ( ~ ( in @ SV548 @ SV14 ) )
= $true )
| ( ( ~ ( SV217 @ SV548 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2394]) ).
thf(2523,plain,
! [SV217: $i > $o,SV14: $i,SV561: $i] :
( ( ( ~ ( ~ ( in @ SV561 @ SV14 )
| ~ ( SV217 @ SV561 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2395]) ).
thf(2524,plain,
! [SV217: $i > $o,SV14: $i,SV566: $i] :
( ( ( ~ ~ ( ~ ( in @ SV566 @ SV14 )
| ~ ( SV217 @ SV566 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2396]) ).
thf(2525,plain,
! [SV217: $i > $o,SV14: $i] :
( ( ( ! [SY542: $i] :
~ ~ ( ~ ( in @ SY542 @ SV14 )
| ~ ( SV217 @ SY542 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2397]) ).
thf(2526,plain,
! [SV217: $i > $o,SV14: $i,SV567: $i] :
( ( ( ~ ~ ( ~ ( in @ SV567 @ SV14 )
| ~ ( SV217 @ SV567 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2398]) ).
thf(2527,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2399]) ).
thf(2528,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ! [SY556: $i] :
~ ~ ( ~ ( in @ SY556
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ SY556 @ emptyset ) ) ) )
= $false )
| ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2400]) ).
thf(2529,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) ) )
= $false )
| ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2401]) ).
thf(2530,plain,
! [SV24: $i,SV471: $o,SV225: $i,SV387: $i] :
( ( ( in @ SV387 @ SV225 )
= $true )
| ( SV471 = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2402]) ).
thf(2531,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( in @ SV387 @ SV225 )
= $true )
| ( $true = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2405]) ).
thf(2532,plain,
! [SV24: $i,SV225: $i,SV387: $i] :
( ( ( in @ SV387 @ SV225 )
= $true )
| ( $false = $true )
| ( ( in @ SV387 @ SV24 )
= $true )
| ( ( in @ SV387 @ ( binunion @ SV24 @ SV225 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2408]) ).
thf(2533,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i,SV568: $i] :
( ( ( ~ ( in @ SV568 @ SV29 )
| ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV230 )
| ~ ( in @ ( kpair @ SV568 @ SY1047 ) @ SV504 )
| ( in @ ( kpair @ SV568 @ SY1047 ) @ SV391 ) ) )
= $true )
| ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2411]) ).
thf(2534,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i,SV562: $i] :
( ( ( ~ ( in @ SV562 @ SV29 ) )
= $true )
| ( ( ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV230 )
| ~ ( in @ ( kpair @ SV562 @ SY1039 ) @ SV504 )
| ( in @ ( kpair @ SV562 @ SY1039 ) @ SV391 ) ) )
= $true )
| ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2535,plain,
! [SV485: $i,SV569: $i,SV33: $i > $o] :
( ( ( ! [SY1048: $i] :
( ~ ( SV33 @ SV569 )
| ~ ( SV33 @ SY1048 )
| ( SV569 = SY1048 ) ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2413]) ).
thf(2536,plain,
! [SV485: $i,SV570: $i,SV563: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV563 )
| ~ ( SV33 @ SV570 )
| ( SV563 = SV570 ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV485
= ( sK57_SY946 @ SV485 @ SV33 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2414]) ).
thf(2537,plain,
! [SV242: $i > $o,SV44: $i,SV552: $i] :
( ( ( in @ SV552 @ SV44 )
= $false )
| ( ( ~ ( SV242 @ SV552 ) )
= $true )
| ( ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2415]) ).
thf(2538,plain,
! [SV242: $i > $o,SV44: $i,SV553: $i] :
( ( ( in @ SV553 @ SV44 )
= $false )
| ( ( ~ ( SV242 @ SV553 ) )
= $true )
| ( ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2416]) ).
thf(2539,plain,
! [SV488: $i,SV571: $i,SV46: $i > $o] :
( ( ( ! [SY1049: $i] :
( ~ ( SV46 @ SV571 )
| ~ ( SV46 @ SY1049 )
| ( SV571 = SY1049 ) ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2417]) ).
thf(2540,plain,
! [SV488: $i,SV572: $i,SV564: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV564 )
| ~ ( SV46 @ SV572 )
| ( SV564 = SV572 ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV488
= ( sK58_SY949 @ SV488 @ SV46 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2418]) ).
thf(2541,plain,
! [SV246: $i > $o,SV554: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV554 )
| ~ ! [SY1035: $i] :
( ~ ( SV49 @ SY1035 )
| ( SV554 = SY1035 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2419]) ).
thf(2542,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2420]) ).
thf(2543,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2420]) ).
thf(2544,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2421]) ).
thf(2545,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2422]) ).
thf(2546,plain,
! [SV53: $i > $o,SV489: $i] :
( ( ( ( sK32_SY951 @ SV489 @ SV53 )
!= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2547,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2423]) ).
thf(2548,plain,
! [SV53: $i > $o,SV489: $i] :
( ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2424]) ).
thf(2549,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2425]) ).
thf(2550,plain,
! [SV62: $i,SV573: $i] :
( ( ~ ( in @ SV573 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV573 )
| ( in @ SY1050 @ SV62 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2427]) ).
thf(2551,plain,
! [SV62: $i,SV574: $i] :
( ( ! [SY1051: $i] :
( ~ ~ ( ~ ( in @ SV574 @ SV62 )
| ~ ( in @ SY1051 @ SV62 ) )
| ~ ! [SY1052: $i] :
( ~ ( in @ SY1052 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1052 )
| ( in @ SY1051 @ SY1052 ) )
| ~ ( ~ ( in @ SY1051 @ SY1052 )
| ( in @ SV574 @ SY1052 ) ) ) )
| ( SV574 = SY1051 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2428]) ).
thf(2552,plain,
! [SV555: $i,SV62: $i,SV549: $i] :
( ( ( ~ ( ~ ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SV555 @ ( sK5_SY153 @ SV62 ) ) ) )
= $false )
| ( ( ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV549 )
| ( in @ SY1036 @ SV555 ) )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2429]) ).
thf(2553,plain,
! [SV539: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
| ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 ) )
= $false )
| ( ( ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2430]) ).
thf(2554,plain,
! [SV69: $i,SV260: $i > $o,SV509: $i] :
( ( ( ~ ( ~ ( in @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) @ SV69 )
| ~ ( SV260 @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) ) ) )
= $true )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2431]) ).
thf(2555,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV556: $i] :
( ( ( in @ SV556 @ SV413 )
= $false )
| ( ( SV510 @ SV556 )
= $true )
| ( ( in @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ SV76 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2432]) ).
thf(2556,plain,
! [SV266: $i,SV76: $i,SV510: $i > $o,SV413: $i,SV575: $i] :
( ( ( ~ ( in @ SV575 @ SV413 )
| ( SV510 @ SV575 ) )
= $true )
| ( ( in @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) @ SV266 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2433]) ).
thf(2557,plain,
! [SV76: $i,SV266: $i,SV413: $i,SV510: $i > $o] :
( ( ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) @ SV413 )
= $true )
| ( ( ! [SY981: $i] :
( ~ ( in @ SY981 @ SV413 )
| ( SV510 @ SY981 ) ) )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2434]) ).
thf(2558,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV576: $i] :
( ( ( ~ ( in @ SV576 @ SV413 )
| ( SV510 @ SV576 ) )
= $true )
| ( ( SV510 @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) )
= $false )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2435]) ).
thf(2559,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2436]) ).
thf(2560,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2437]) ).
thf(2561,plain,
! [SV267: $i,SV77: $i,SV414: $i,SV511: $o] :
( ( SV511 = $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2437]) ).
thf(2562,plain,
! [SV511: $o,SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| SV511 )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2563,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2439]) ).
thf(2564,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2440]) ).
thf(2565,plain,
! [SV267: $i,SV77: $i,SV414: $i,SV511: $o] :
( ( SV511 = $false )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2440]) ).
thf(2566,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2441]) ).
thf(2567,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2442]) ).
thf(2568,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2442]) ).
thf(2569,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2443]) ).
thf(2570,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2444]) ).
thf(2571,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2445]) ).
thf(2572,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2445]) ).
thf(2573,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2446]) ).
thf(2574,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2447]) ).
thf(2575,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2447]) ).
thf(2576,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 )
| ~ ( in @ SV414 @ SV267 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2448]) ).
thf(2577,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2449]) ).
thf(2578,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2579,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2450]) ).
thf(2580,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ! [SY220: $i] :
~ ! [SY221: $i] :
~ ( ~ ( ~ ( SV80 @ SY221 )
| ( SY221 = SY220 ) )
| ~ ( ( SY221 != SY220 )
| ( SV80 @ SY221 ) ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2581,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ~ ! [SY1053: $i] :
~ ( ~ ( ~ ( SV80 @ SY1053 )
| ( SY1053
= ( sK78_SY220 @ SV491 @ SV80 ) ) )
| ~ ( ( SY1053
!= ( sK78_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SY1053 ) ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2453]) ).
thf(2582,plain,
! [SV271: $i,SV83: $i,SV542: $i] :
( ( ( in @ SV542 @ SV83 )
= $false )
| ( ( in @ SV271 @ SV542 )
= $false )
| ( ( in @ SV271 @ ( setunion @ SV83 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2456]) ).
thf(2583,plain,
! [SV273: $i > $o,SV86: $i,SV545: $i] :
( ( ( in @ SV545 @ SV86 )
= $false )
| ( ( ~ ( SV273 @ SV545 ) )
= $true )
| ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2457]) ).
thf(2584,plain,
! [SV273: $i > $o,SV86: $i,SV546: $i] :
( ( ( in @ SV546 @ SV86 )
= $false )
| ( ( ~ ( SV273 @ SV546 ) )
= $true )
| ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2458]) ).
thf(2585,plain,
! [SV88: $i,SV492: $i] :
( ( ( ! [SY1017: $i] :
~ ~ ( ~ ( in @ SY1017 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SY1017 @ SV88 ) ) )
= $true )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2459]) ).
thf(2586,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ! [SY261: $i] :
~ ~ ( ~ ( SV98 @ SY261 )
| ~ ! [SY262: $i] :
( ~ ( SV98 @ SY262 )
| ( SY261 = SY262 ) ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2461]) ).
thf(2587,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ~ ( ~ ( SV98 @ ( sK79_SY261 @ SV493 @ SV98 ) )
| ~ ! [SY1054: $i] :
( ~ ( SV98 @ SY1054 )
| ( ( sK79_SY261 @ SV493 @ SV98 )
= SY1054 ) ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2462]) ).
thf(2588,plain,
! [SV104: $i,SV287: $i > $o,SV513: $i] :
( ( ( ~ ( in @ ( sK80_SY662 @ SV513 @ SV287 @ SV104 ) @ SV104 )
| ( SV287 @ ( sK80_SY662 @ SV513 @ SV287 @ SV104 ) ) )
= $false )
| ( ( in @ SV513 @ SV104 )
= $false )
| ( ( SV287 @ SV513 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2463]) ).
thf(2589,plain,
! [SV290: $i,SV515: $i,SV428: $i,SV107: $i] :
( ( ( ~ ( in @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2590,plain,
! [SV107: $i,SV290: $i,SV428: $i,SV515: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) ) @ SV428 )
| ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) ) @ SV515 ) )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2466]) ).
thf(2591,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ~ ( ~ ( SV113 @ ( sK81_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1055: $i] :
( ~ ( SV113 @ SY1055 )
| ( ( sK81_SY305 @ SV494 @ SV113 )
= SY1055 ) ) ) )
= $false )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2467]) ).
thf(2592,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ! [SY305: $i] :
~ ~ ( ~ ( SV113 @ SY305 )
| ~ ! [SY306: $i] :
( ~ ( SV113 @ SY306 )
| ( SY305 = SY306 ) ) ) )
= $false )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2593,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ~ ( ~ ( SV113 @ ( sK82_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1056: $i] :
( ~ ( SV113 @ SY1056 )
| ( ( sK82_SY305 @ SV494 @ SV113 )
= SY1056 ) ) ) )
= $false )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2469]) ).
thf(2594,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
| ~ ! [SY1032: $i] :
~ ~ ( ~ ( in @ SY1032 @ SV313 )
| ~ ( SV134 @ SY1032 @ SV550 ) ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2470]) ).
thf(2595,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ~ ! [SY1033: $i] :
~ ~ ( ~ ( in @ SY1033 @ SV313 )
| ~ ( SV134 @ SY1033 @ SV550 ) )
| ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2471]) ).
thf(2596,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
| ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2472]) ).
thf(2597,plain,
! [SV320: $i > $o,SV141: $i,SV551: $i] :
( ( ( ~ ( in @ SV551 @ SV141 ) )
= $true )
| ( ( ~ ( SV320 @ SV551 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2473]) ).
thf(2598,plain,
! [SV320: $i > $o,SV141: $i,SV565: $i] :
( ( ( ~ ( ~ ( in @ SV565 @ SV141 )
| ~ ( SV320 @ SV565 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2474]) ).
thf(2599,plain,
! [SV320: $i > $o,SV141: $i,SV577: $i] :
( ( ( ~ ~ ( ~ ( in @ SV577 @ SV141 )
| ~ ( SV320 @ SV577 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2475]) ).
thf(2600,plain,
! [SV320: $i > $o,SV141: $i] :
( ( ( ! [SY704: $i] :
~ ~ ( ~ ( in @ SY704 @ SV141 )
| ~ ( SV320 @ SY704 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2476]) ).
thf(2601,plain,
! [SV320: $i > $o,SV141: $i,SV578: $i] :
( ( ( ~ ~ ( ~ ( in @ SV578 @ SV141 )
| ~ ( SV320 @ SV578 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2477]) ).
thf(2602,plain,
! [SV440: $i,SV518: $i,SV321: $i,SV142: $i] :
( ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) ) )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2478]) ).
thf(2603,plain,
! [SV321: $i,SV518: $i,SV440: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 ) )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2604,plain,
! [SV142: $i,SV321: $i,SV440: $i,SV518: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
| ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 ) )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2479]) ).
thf(2605,plain,
! [SV147: $i,SV325: $i > $o,SV520: $i] :
( ( ( in @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) @ SV147 )
= $true )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2480]) ).
thf(2606,plain,
! [SV147: $i,SV520: $i,SV325: $i > $o] :
( ( ( ~ ( SV325 @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) ) )
= $true )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2481]) ).
thf(2607,plain,
! [SV521: $i,SV329: $i > $o,SV154: $i,SV557: $i] :
( ( ( in @ SV557 @ SV154 )
= $false )
| ( ( ! [SY1038: $i] :
( ~ ( in @ SY1038 @ SV154 )
| ~ ( SV329 @ SV557 )
| ~ ( SV329 @ SY1038 )
| ( SV557 = SY1038 ) ) )
= $true )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2482]) ).
thf(2608,plain,
! [SV330: $i,SV443: $i,SV155: $i] :
( ( ( ~ ( ~ ( in @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) ) ) ) )
= $true )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2609,plain,
! [SV332: $i > $o,SV157: $i,SV558: $i] :
( ( ( in @ SV558 @ SV157 )
= $false )
| ( ( ~ ( SV332 @ SV558 ) )
= $true )
| ( ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2484]) ).
thf(2610,plain,
! [SV332: $i > $o,SV157: $i,SV559: $i] :
( ( ( in @ SV559 @ SV157 )
= $false )
| ( ( ~ ( SV332 @ SV559 ) )
= $true )
| ( ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(2611,plain,
! [SV168: $i,SV343: $i > $o,SV527: $i] :
( ( ( in @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) @ SV168 )
= $true )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2489]) ).
thf(2612,plain,
! [SV168: $i,SV527: $i,SV343: $i > $o] :
( ( ( ~ ( SV343 @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) ) )
= $true )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2490]) ).
thf(2613,plain,
! [SV174: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ omega )
| ( in @ SV579 @ SV174 ) )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( sK41_SY431 @ SV174 ) @ omega )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2491]) ).
thf(2614,plain,
! [SV174: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ omega )
| ( in @ SV580 @ SV174 ) )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( sK41_SY431 @ SV174 ) @ SV174 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2492]) ).
thf(2615,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV560: $i] :
( ( ( in @ SV560 @ SV451 )
= $false )
| ( ( SV528 @ SV560 )
= $true )
| ( ( in @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ SV182 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2493]) ).
thf(2616,plain,
! [SV353: $i,SV182: $i,SV528: $i > $o,SV451: $i,SV581: $i] :
( ( ( ~ ( in @ SV581 @ SV451 )
| ( SV528 @ SV581 ) )
= $true )
| ( ( in @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) @ SV353 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2494]) ).
thf(2617,plain,
! [SV182: $i,SV353: $i,SV451: $i,SV528: $i > $o] :
( ( ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) @ SV451 )
= $true )
| ( ( ! [SY995: $i] :
( ~ ( in @ SY995 @ SV451 )
| ( SV528 @ SY995 ) ) )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2495]) ).
thf(2618,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV582: $i] :
( ( ( ~ ( in @ SV582 @ SV451 )
| ( SV528 @ SV582 ) )
= $true )
| ( ( SV528 @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) )
= $false )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2496]) ).
thf(2619,plain,
! [SV183: $i,SV354: $i,SV498: $i > $o,SV529: $i > $o] :
( ( ( ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 )
= ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2498]) ).
thf(2620,plain,
! [SV183: $i,SV354: $i,SV529: $i > $o,SV498: $i > $o] :
( ( ( ~ ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
| ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) ) )
| ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2499]) ).
thf(2621,plain,
! [SV185: $i,SV530: $o,SV356: $i,SV453: $i] :
( ( ( in @ SV453 @ SV356 )
= $true )
| ( SV530 = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2500]) ).
thf(2622,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( in @ SV453 @ SV356 )
= $true )
| ( $true = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2503]) ).
thf(2623,plain,
! [SV185: $i,SV356: $i,SV453: $i] :
( ( ( in @ SV453 @ SV356 )
= $true )
| ( $false = $true )
| ( ( SV453 = SV185 )
= $true )
| ( ( in @ SV453 @ ( setadjoin @ SV185 @ SV356 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2506]) ).
thf(2624,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2509]) ).
thf(2625,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2510]) ).
thf(2626,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2511]) ).
thf(2627,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2511]) ).
thf(2628,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2512]) ).
thf(2629,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2513]) ).
thf(2630,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ! [SY498: $i] :
~ ( SV195 @ SY498 ) )
= $false )
| ( ( SV195 @ SV500 )
= $false )
| ( ( SV195 @ ( sK69_SY973 @ SV500 @ SV195 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2631,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ~ ( SV195 @ ( sK84_SY498 @ SV500 @ SV195 ) ) )
= $false )
| ( ( SV195 @ SV500 )
= $false )
| ( ( SV500
= ( sK69_SY973 @ SV500 @ SV195 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2515]) ).
thf(2632,plain,
! [SV368: $i,SV534: $i,SV461: $i,SV198: $i] :
( ( ( in @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 )
@ ( dsetconstr @ SV368
@ ^ [SY1001: $i] : ( in @ ( kpair @ SV534 @ SY1001 ) @ SV461 ) ) )
= $true )
| ( ( in @ SV534 @ SV198 )
= $false )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2516]) ).
thf(2633,plain,
! [SV198: $i,SV461: $i,SV534: $i,SV368: $i] :
( ( ( ( dsetconstr @ SV368
@ ^ [SY1002: $i] : ( in @ ( kpair @ SV534 @ SY1002 ) @ SV461 ) )
= ( setadjoin @ ( sK54_SY1000 @ SV198 @ SV461 @ SV534 @ SV368 ) @ emptyset ) )
= $true )
| ( ( in @ SV534 @ SV198 )
= $false )
| ( ( func @ SV198 @ SV368 @ SV461 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2517]) ).
thf(2634,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ~ ( ~ ( SV10 @ ( sK85_SY25 @ SV483 @ SV10 ) )
| ~ ! [SY1057: $i] :
( ~ ( SV10 @ SY1057 )
| ( ( sK85_SY25 @ SV483 @ SV10 )
= SY1057 ) ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2520]) ).
thf(2635,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK74_SY25 @ SV483 @ SV10 ) )
| ~ ! [SY1042: $i] :
( ~ ( SV10 @ SY1042 )
| ( ( sK74_SY25 @ SV483 @ SV10 )
= SY1042 ) ) ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2521]) ).
thf(2636,plain,
! [SV217: $i > $o,SV14: $i,SV548: $i] :
( ( ( in @ SV548 @ SV14 )
= $false )
| ( ( ~ ( SV217 @ SV548 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2522]) ).
thf(2637,plain,
! [SV217: $i > $o,SV14: $i,SV561: $i] :
( ( ( ~ ( in @ SV561 @ SV14 )
| ~ ( SV217 @ SV561 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2523]) ).
thf(2638,plain,
! [SV217: $i > $o,SV14: $i,SV566: $i] :
( ( ( ~ ( ~ ( in @ SV566 @ SV14 )
| ~ ( SV217 @ SV566 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2639,plain,
! [SV217: $i > $o,SV14: $i,SV583: $i] :
( ( ( ~ ~ ( ~ ( in @ SV583 @ SV14 )
| ~ ( SV217 @ SV583 ) ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2525]) ).
thf(2640,plain,
! [SV217: $i > $o,SV14: $i,SV567: $i] :
( ( ( ~ ( ~ ( in @ SV567 @ SV14 )
| ~ ( SV217 @ SV567 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2526]) ).
thf(2641,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( ~ ( in @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2527]) ).
thf(2642,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) ) )
= $false )
| ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2528]) ).
thf(2643,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( ~ ( in @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) ) )
= $true )
| ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2529]) ).
thf(2644,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i,SV568: $i] :
( ( ( ~ ( in @ SV568 @ SV29 ) )
= $true )
| ( ( ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV230 )
| ~ ( in @ ( kpair @ SV568 @ SY1047 ) @ SV504 )
| ( in @ ( kpair @ SV568 @ SY1047 ) @ SV391 ) ) )
= $true )
| ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2533]) ).
thf(2645,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i,SV562: $i] :
( ( ( in @ SV562 @ SV29 )
= $false )
| ( ( ! [SY1039: $i] :
( ~ ( in @ SY1039 @ SV230 )
| ~ ( in @ ( kpair @ SV562 @ SY1039 ) @ SV504 )
| ( in @ ( kpair @ SV562 @ SY1039 ) @ SV391 ) ) )
= $true )
| ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2646,plain,
! [SV485: $i,SV584: $i,SV569: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV569 )
| ~ ( SV33 @ SV584 )
| ( SV569 = SV584 ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2535]) ).
thf(2647,plain,
! [SV485: $i,SV570: $i,SV563: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV563 ) )
= $true )
| ( ( ~ ( SV33 @ SV570 )
| ( SV563 = SV570 ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV485
= ( sK57_SY946 @ SV485 @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2536]) ).
thf(2648,plain,
! [SV44: $i,SV552: $i,SV242: $i > $o] :
( ( ( SV242 @ SV552 )
= $false )
| ( ( in @ SV552 @ SV44 )
= $false )
| ( ( in @ ( sK31_SY583 @ SV242 @ SV44 ) @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2537]) ).
thf(2649,plain,
! [SV44: $i,SV553: $i,SV242: $i > $o] :
( ( ( SV242 @ SV553 )
= $false )
| ( ( in @ SV553 @ SV44 )
= $false )
| ( ( SV242 @ ( sK31_SY583 @ SV242 @ SV44 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2538]) ).
thf(2650,plain,
! [SV488: $i,SV585: $i,SV571: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV571 )
| ~ ( SV46 @ SV585 )
| ( SV571 = SV585 ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2539]) ).
thf(2651,plain,
! [SV488: $i,SV572: $i,SV564: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV564 ) )
= $true )
| ( ( ~ ( SV46 @ SV572 )
| ( SV564 = SV572 ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV488
= ( sK58_SY949 @ SV488 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2540]) ).
thf(2652,plain,
! [SV246: $i > $o,SV554: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV554 ) )
= $true )
| ( ( ~ ! [SY1035: $i] :
( ~ ( SV49 @ SY1035 )
| ( SV554 = SY1035 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2541]) ).
thf(2653,plain,
! [SV49: $i > $o,SV246: $i > $o] :
( ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) )
| ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2542]) ).
thf(2654,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2543]) ).
thf(2655,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2544]) ).
thf(2656,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2545]) ).
thf(2657,plain,
! [SV53: $i > $o,SV489: $i] :
( ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ~ ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2546]) ).
thf(2658,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2547]) ).
thf(2659,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2548]) ).
thf(2660,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ~ ( ~ ( SV53 @ ( sK87_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1060: $i] :
( ~ ( SV53 @ SY1060 )
| ( ( sK87_SY139 @ SV489 @ SV53 )
= SY1060 ) ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2549]) ).
thf(2661,plain,
! [SV62: $i,SV573: $i] :
( ( ( ~ ( in @ SV573 @ ( sK5_SY153 @ SV62 ) ) )
= $true )
| ( ( ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV573 )
| ( in @ SY1050 @ SV62 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2550]) ).
thf(2662,plain,
! [SV586: $i,SV62: $i,SV574: $i] :
( ( ~ ~ ( ~ ( in @ SV574 @ SV62 )
| ~ ( in @ SV586 @ SV62 ) )
| ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) )
| ( SV574 = SV586 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[2551]) ).
thf(2663,plain,
! [SV555: $i,SV62: $i,SV549: $i] :
( ( ( ~ ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SV555 @ ( sK5_SY153 @ SV62 ) ) )
= $true )
| ( ( ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV549 )
| ( in @ SY1036 @ SV555 ) )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2552]) ).
thf(2664,plain,
! [SV539: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 ) )
= $false )
| ( ( ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2665,plain,
! [SV539: $i,SV62: $i] :
( ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2553]) ).
thf(2666,plain,
! [SV69: $i,SV260: $i > $o,SV509: $i] :
( ( ( ~ ( in @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) @ SV69 )
| ~ ( SV260 @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) ) )
= $false )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2667,plain,
! [SV266: $i,SV76: $i,SV510: $i > $o,SV413: $i,SV575: $i] :
( ( ( ~ ( in @ SV575 @ SV413 ) )
= $true )
| ( ( SV510 @ SV575 )
= $true )
| ( ( in @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) @ SV266 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2556]) ).
thf(2668,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV413 )
| ( SV510 @ SV587 ) )
= $true )
| ( ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) @ SV413 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2557]) ).
thf(2669,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV576: $i] :
( ( ( ~ ( in @ SV576 @ SV413 ) )
= $true )
| ( ( SV510 @ SV576 )
= $true )
| ( ( SV510 @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) )
= $false )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2558]) ).
thf(2670,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2559]) ).
thf(2671,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2560]) ).
thf(2672,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2562]) ).
thf(2673,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| SV511 )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2562]) ).
thf(2674,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2563]) ).
thf(2675,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( SV511 = $true )
| ( SV511 = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2676,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2566]) ).
thf(2677,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( $true = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2567]) ).
thf(2678,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2679,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| $true )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2569]) ).
thf(2680,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2570]) ).
thf(2681,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2571]) ).
thf(2682,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2573]) ).
thf(2683,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( $false = $true )
| ( ( in @ SV414 @ SV77 )
= $true )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2574]) ).
thf(2684,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ~ ( in @ SV414 @ SV77 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2576]) ).
thf(2685,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 )
| $false )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2576]) ).
thf(2686,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2577]) ).
thf(2687,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2578]) ).
thf(2688,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ~ ! [SY1062: $i] :
~ ( ~ ( ~ ( SV80 @ SY1062 )
| ( SY1062
= ( sK88_SY220 @ SV491 @ SV80 ) ) )
| ~ ( ( SY1062
!= ( sK88_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SY1062 ) ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2580]) ).
thf(2689,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ! [SY1053: $i] :
~ ( ~ ( ~ ( SV80 @ SY1053 )
| ( SY1053
= ( sK78_SY220 @ SV491 @ SV80 ) ) )
| ~ ( ( SY1053
!= ( sK78_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SY1053 ) ) ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2581]) ).
thf(2690,plain,
! [SV86: $i,SV545: $i,SV273: $i > $o] :
( ( ( SV273 @ SV545 )
= $false )
| ( ( in @ SV545 @ SV86 )
= $false )
| ( ( in @ ( sK12_SY640 @ SV273 @ SV86 ) @ SV86 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2583]) ).
thf(2691,plain,
! [SV86: $i,SV546: $i,SV273: $i > $o] :
( ( ( SV273 @ SV546 )
= $false )
| ( ( in @ SV546 @ SV86 )
= $false )
| ( ( SV273 @ ( sK12_SY640 @ SV273 @ SV86 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2584]) ).
thf(2692,plain,
! [SV88: $i,SV492: $i,SV588: $i] :
( ( ( ~ ~ ( ~ ( in @ SV588 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SV588 @ SV88 ) ) )
= $true )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2585]) ).
thf(2693,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ~ ( ~ ( SV98 @ ( sK89_SY261 @ SV493 @ SV98 ) )
| ~ ! [SY1063: $i] :
( ~ ( SV98 @ SY1063 )
| ( ( sK89_SY261 @ SV493 @ SV98 )
= SY1063 ) ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2586]) ).
thf(2694,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( ~ ( SV98 @ ( sK79_SY261 @ SV493 @ SV98 ) )
| ~ ! [SY1054: $i] :
( ~ ( SV98 @ SY1054 )
| ( ( sK79_SY261 @ SV493 @ SV98 )
= SY1054 ) ) ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2587]) ).
thf(2695,plain,
! [SV104: $i,SV287: $i > $o,SV513: $i] :
( ( ( ~ ( in @ ( sK80_SY662 @ SV513 @ SV287 @ SV104 ) @ SV104 ) )
= $false )
| ( ( in @ SV513 @ SV104 )
= $false )
| ( ( SV287 @ SV513 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2588]) ).
thf(2696,plain,
! [SV104: $i,SV513: $i,SV287: $i > $o] :
( ( ( SV287 @ ( sK80_SY662 @ SV513 @ SV287 @ SV104 ) )
= $false )
| ( ( in @ SV513 @ SV104 )
= $false )
| ( ( SV287 @ SV513 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2588]) ).
thf(2697,plain,
! [SV290: $i,SV515: $i,SV428: $i,SV107: $i] :
( ( ( in @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) @ SV290 )
= $true )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2589]) ).
thf(2698,plain,
! [SV107: $i,SV290: $i,SV428: $i,SV515: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) ) @ SV428 ) )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2699,plain,
! [SV107: $i,SV290: $i,SV428: $i,SV515: $i] :
( ( ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) ) @ SV515 )
= $false )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2590]) ).
thf(2700,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( ~ ( SV113 @ ( sK81_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1055: $i] :
( ~ ( SV113 @ SY1055 )
| ( ( sK81_SY305 @ SV494 @ SV113 )
= SY1055 ) ) ) )
= $true )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2701,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ~ ( ~ ( SV113 @ ( sK90_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1064: $i] :
( ~ ( SV113 @ SY1064 )
| ( ( sK90_SY305 @ SV494 @ SV113 )
= SY1064 ) ) ) )
= $false )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2592]) ).
thf(2702,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( ~ ( SV113 @ ( sK82_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1056: $i] :
( ~ ( SV113 @ SY1056 )
| ( ( sK82_SY305 @ SV494 @ SV113 )
= SY1056 ) ) ) )
= $true )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2593]) ).
thf(2703,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) ) )
= $true )
| ( ( ~ ! [SY1032: $i] :
~ ~ ( ~ ( in @ SY1032 @ SV313 )
| ~ ( SV134 @ SY1032 @ SV550 ) ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2594]) ).
thf(2704,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ~ ! [SY1033: $i] :
~ ~ ( ~ ( in @ SY1033 @ SV313 )
| ~ ( SV134 @ SY1033 @ SV550 ) ) )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2595]) ).
thf(2705,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( ~ ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2596]) ).
thf(2706,plain,
! [SV134: $i > $i > $o,SV313: $i,SV541: $i] :
( ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2596]) ).
thf(2707,plain,
! [SV320: $i > $o,SV141: $i,SV551: $i] :
( ( ( in @ SV551 @ SV141 )
= $false )
| ( ( ~ ( SV320 @ SV551 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2597]) ).
thf(2708,plain,
! [SV320: $i > $o,SV141: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ SV141 )
| ~ ( SV320 @ SV565 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2709,plain,
! [SV320: $i > $o,SV141: $i,SV577: $i] :
( ( ( ~ ( ~ ( in @ SV577 @ SV141 )
| ~ ( SV320 @ SV577 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2599]) ).
thf(2710,plain,
! [SV320: $i > $o,SV141: $i,SV589: $i] :
( ( ( ~ ~ ( ~ ( in @ SV589 @ SV141 )
| ~ ( SV320 @ SV589 ) ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2600]) ).
thf(2711,plain,
! [SV320: $i > $o,SV141: $i,SV578: $i] :
( ( ( ~ ( ~ ( in @ SV578 @ SV141 )
| ~ ( SV320 @ SV578 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2712,plain,
! [SV440: $i,SV518: $i,SV321: $i,SV142: $i] :
( ( ( ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2713,plain,
! [SV321: $i,SV518: $i,SV440: $i,SV142: $i] :
( ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2714,plain,
! [SV142: $i,SV321: $i,SV440: $i,SV518: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2604]) ).
thf(2715,plain,
! [SV142: $i,SV321: $i,SV440: $i,SV518: $i] :
( ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2604]) ).
thf(2716,plain,
! [SV147: $i,SV520: $i,SV325: $i > $o] :
( ( ( SV325 @ ( sK52_SY717 @ SV520 @ SV325 @ SV147 ) )
= $false )
| ( ( SV325 @ SV520 )
= $true )
| ( ( in @ SV520 @ SV147 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2606]) ).
thf(2717,plain,
! [SV521: $i,SV557: $i,SV329: $i > $o,SV154: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ SV154 )
| ~ ( SV329 @ SV557 )
| ~ ( SV329 @ SV590 )
| ( SV557 = SV590 ) )
= $true )
| ( ( in @ SV557 @ SV154 )
= $false )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2607]) ).
thf(2718,plain,
! [SV330: $i,SV443: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) @ SV330 )
| ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) ) ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2608]) ).
thf(2719,plain,
! [SV157: $i,SV558: $i,SV332: $i > $o] :
( ( ( SV332 @ SV558 )
= $false )
| ( ( in @ SV558 @ SV157 )
= $false )
| ( ( in @ ( sK35_SY728 @ SV332 @ SV157 ) @ SV157 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2609]) ).
thf(2720,plain,
! [SV157: $i,SV559: $i,SV332: $i > $o] :
( ( ( SV332 @ SV559 )
= $false )
| ( ( in @ SV559 @ SV157 )
= $false )
| ( ( SV332 @ ( sK35_SY728 @ SV332 @ SV157 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2610]) ).
thf(2721,plain,
! [SV168: $i,SV527: $i,SV343: $i > $o] :
( ( ( SV343 @ ( sK53_SY746 @ SV527 @ SV343 @ SV168 ) )
= $false )
| ( ( SV343 @ SV527 )
= $true )
| ( ( in @ SV527 @ SV168 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2612]) ).
thf(2722,plain,
! [SV174: $i,SV579: $i] :
( ( ( ~ ( in @ SV579 @ omega ) )
= $true )
| ( ( in @ SV579 @ SV174 )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( sK41_SY431 @ SV174 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2613]) ).
thf(2723,plain,
! [SV174: $i,SV580: $i] :
( ( ( ~ ( in @ SV580 @ omega ) )
= $true )
| ( ( in @ SV580 @ SV174 )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( sK41_SY431 @ SV174 ) @ SV174 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2724,plain,
! [SV353: $i,SV182: $i,SV528: $i > $o,SV451: $i,SV581: $i] :
( ( ( ~ ( in @ SV581 @ SV451 ) )
= $true )
| ( ( SV528 @ SV581 )
= $true )
| ( ( in @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) @ SV353 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2616]) ).
thf(2725,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV591: $i] :
( ( ( ~ ( in @ SV591 @ SV451 )
| ( SV528 @ SV591 ) )
= $true )
| ( ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) @ SV451 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2617]) ).
thf(2726,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV582: $i] :
( ( ( ~ ( in @ SV582 @ SV451 ) )
= $true )
| ( ( SV528 @ SV582 )
= $true )
| ( ( SV528 @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) )
= $false )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2618]) ).
thf(2727,plain,
! [SV183: $i,SV354: $i,SV529: $i > $o,SV498: $i > $o] :
( ( ( ~ ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
| ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2620]) ).
thf(2728,plain,
! [SV359: $i > $o,SV592: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ SV592 )
| ~ ! [SY1065: $i] :
( ~ ( SV188 @ SY1065 )
| ( SV592 = SY1065 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2624]) ).
thf(2729,plain,
! [SV188: $i > $o,SV593: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ SV593 )
| ~ ! [SY1066: $i] :
( ~ ( SV359 @ SY1066 )
| ( SV593 = SY1066 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2625]) ).
thf(2730,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( ~ ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2626]) ).
thf(2731,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2732,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(2733,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2629]) ).
thf(2734,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2629]) ).
thf(2735,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( ~ ( SV195 @ ( sK91_SY498 @ SV500 @ SV195 ) ) )
= $false )
| ( ( SV195 @ SV500 )
= $false )
| ( ( SV195 @ ( sK69_SY973 @ SV500 @ SV195 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2630]) ).
thf(2736,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( SV195 @ ( sK84_SY498 @ SV500 @ SV195 ) )
= $true )
| ( ( SV195 @ SV500 )
= $false )
| ( ( SV500
= ( sK69_SY973 @ SV500 @ SV195 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2631]) ).
thf(2737,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( ~ ( SV10 @ ( sK85_SY25 @ SV483 @ SV10 ) )
| ~ ! [SY1057: $i] :
( ~ ( SV10 @ SY1057 )
| ( ( sK85_SY25 @ SV483 @ SV10 )
= SY1057 ) ) ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2634]) ).
thf(2738,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK74_SY25 @ SV483 @ SV10 ) )
| ~ ! [SY1042: $i] :
( ~ ( SV10 @ SY1042 )
| ( ( sK74_SY25 @ SV483 @ SV10 )
= SY1042 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2739,plain,
! [SV14: $i,SV548: $i,SV217: $i > $o] :
( ( ( SV217 @ SV548 )
= $false )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2636]) ).
thf(2740,plain,
! [SV217: $i > $o,SV14: $i,SV561: $i] :
( ( ( ~ ( in @ SV561 @ SV14 ) )
= $true )
| ( ( ~ ( SV217 @ SV561 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2637]) ).
thf(2741,plain,
! [SV217: $i > $o,SV14: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ SV14 )
| ~ ( SV217 @ SV566 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2638]) ).
thf(2742,plain,
! [SV217: $i > $o,SV14: $i,SV583: $i] :
( ( ( ~ ( ~ ( in @ SV583 @ SV14 )
| ~ ( SV217 @ SV583 ) ) )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2639]) ).
thf(2743,plain,
! [SV217: $i > $o,SV14: $i,SV567: $i] :
( ( ( ~ ( in @ SV567 @ SV14 )
| ~ ( SV217 @ SV567 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2640]) ).
thf(2744,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( in @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) )
= $false )
| ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2745,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( ~ ( in @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) ) )
= $true )
| ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2642]) ).
thf(2746,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( in @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) )
= $false )
| ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2747,plain,
! [SV391: $i,SV504: $i,SV230: $i,SV29: $i,SV568: $i] :
( ( ( in @ SV568 @ SV29 )
= $false )
| ( ( ! [SY1047: $i] :
( ~ ( in @ SY1047 @ SV230 )
| ~ ( in @ ( kpair @ SV568 @ SY1047 ) @ SV504 )
| ( in @ ( kpair @ SV568 @ SY1047 ) @ SV391 ) ) )
= $true )
| ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2748,plain,
! [SV29: $i,SV391: $i,SV504: $i,SV562: $i,SV230: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV230 )
| ~ ( in @ ( kpair @ SV562 @ SV594 ) @ SV504 )
| ( in @ ( kpair @ SV562 @ SV594 ) @ SV391 ) )
= $true )
| ( ( in @ SV562 @ SV29 )
= $false )
| ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2645]) ).
thf(2749,plain,
! [SV485: $i,SV584: $i,SV569: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV569 ) )
= $true )
| ( ( ~ ( SV33 @ SV584 )
| ( SV569 = SV584 ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2646]) ).
thf(2750,plain,
! [SV485: $i,SV570: $i,SV563: $i,SV33: $i > $o] :
( ( ( SV33 @ SV563 )
= $false )
| ( ( ~ ( SV33 @ SV570 )
| ( SV563 = SV570 ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV485
= ( sK57_SY946 @ SV485 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2647]) ).
thf(2751,plain,
! [SV488: $i,SV585: $i,SV571: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV571 ) )
= $true )
| ( ( ~ ( SV46 @ SV585 )
| ( SV571 = SV585 ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2650]) ).
thf(2752,plain,
! [SV488: $i,SV572: $i,SV564: $i,SV46: $i > $o] :
( ( ( SV46 @ SV564 )
= $false )
| ( ( ~ ( SV46 @ SV572 )
| ( SV564 = SV572 ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV488
= ( sK58_SY949 @ SV488 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2651]) ).
thf(2753,plain,
! [SV246: $i > $o,SV554: $i,SV49: $i > $o] :
( ( ( SV49 @ SV554 )
= $false )
| ( ( ~ ! [SY1035: $i] :
( ~ ( SV49 @ SY1035 )
| ( SV554 = SY1035 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2652]) ).
thf(2754,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2653]) ).
thf(2755,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2654]) ).
thf(2756,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2757,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2656]) ).
thf(2758,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY139: $i] :
~ ~ ( ~ ( SV53 @ SY139 )
| ~ ! [SY140: $i] :
( ~ ( SV53 @ SY140 )
| ( SY139 = SY140 ) ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2657]) ).
thf(2759,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ~ ( ~ ( SV53 @ ( sK92_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1067: $i] :
( ~ ( SV53 @ SY1067 )
| ( ( sK92_SY139 @ SV489 @ SV53 )
= SY1067 ) ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2658]) ).
thf(2760,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ~ ( ~ ( SV53 @ ( sK93_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1068: $i] :
( ~ ( SV53 @ SY1068 )
| ( ( sK93_SY139 @ SV489 @ SV53 )
= SY1068 ) ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2659]) ).
thf(2761,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( ~ ( SV53 @ ( sK87_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1060: $i] :
( ~ ( SV53 @ SY1060 )
| ( ( sK87_SY139 @ SV489 @ SV53 )
= SY1060 ) ) ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2660]) ).
thf(2762,plain,
! [SV62: $i,SV573: $i] :
( ( ( in @ SV573 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( ! [SY1050: $i] :
( ~ ( in @ SY1050 @ SV573 )
| ( in @ SY1050 @ SV62 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2661]) ).
thf(2763,plain,
! [SV586: $i,SV62: $i,SV574: $i] :
( ( ( ~ ~ ( ~ ( in @ SV574 @ SV62 )
| ~ ( in @ SV586 @ SV62 ) ) )
= $true )
| ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) )
| ( SV574 = SV586 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2662]) ).
thf(2764,plain,
! [SV555: $i,SV62: $i,SV549: $i] :
( ( ( ~ ( in @ SV549 @ ( sK5_SY153 @ SV62 ) ) )
= $true )
| ( ( ~ ( in @ SV555 @ ( sK5_SY153 @ SV62 ) ) )
= $true )
| ( ( ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV549 )
| ( in @ SY1036 @ SV555 ) )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2663]) ).
thf(2765,plain,
! [SV539: $i,SV62: $i] :
( ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( ~ ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2664]) ).
thf(2766,plain,
! [SV62: $i,SV539: $i] :
( ( ( ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2665]) ).
thf(2767,plain,
! [SV69: $i,SV260: $i > $o,SV509: $i] :
( ( ( ~ ( in @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) @ SV69 ) )
= $false )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2666]) ).
thf(2768,plain,
! [SV69: $i,SV509: $i,SV260: $i > $o] :
( ( ( ~ ( SV260 @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) ) )
= $false )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2666]) ).
thf(2769,plain,
! [SV266: $i,SV76: $i,SV510: $i > $o,SV413: $i,SV575: $i] :
( ( ( in @ SV575 @ SV413 )
= $false )
| ( ( SV510 @ SV575 )
= $true )
| ( ( in @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) @ SV266 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2667]) ).
thf(2770,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV587: $i] :
( ( ( ~ ( in @ SV587 @ SV413 ) )
= $true )
| ( ( SV510 @ SV587 )
= $true )
| ( ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) @ SV413 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2668]) ).
thf(2771,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV576: $i] :
( ( ( in @ SV576 @ SV413 )
= $false )
| ( ( SV510 @ SV576 )
= $true )
| ( ( SV510 @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) )
= $false )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2772,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2672]) ).
thf(2773,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2774,plain,
! [SV77: $i,SV267: $i,SV414: $i,SV511: $o] :
( ( SV511 = $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2673]) ).
thf(2775,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2678]) ).
thf(2776,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2679]) ).
thf(2777,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2679]) ).
thf(2778,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV77 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2684]) ).
thf(2779,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV267 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2685]) ).
thf(2780,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2685]) ).
thf(2781,plain,
! [SV491: $i,SV80: $i > $o] :
( ( ( ! [SY1062: $i] :
~ ( ~ ( ~ ( SV80 @ SY1062 )
| ( SY1062
= ( sK88_SY220 @ SV491 @ SV80 ) ) )
| ~ ( ( SY1062
!= ( sK88_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SY1062 ) ) ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2688]) ).
thf(2782,plain,
! [SV491: $i,SV595: $i,SV80: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV80 @ SV595 )
| ( SV595
= ( sK78_SY220 @ SV491 @ SV80 ) ) )
| ~ ( ( SV595
!= ( sK78_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SV595 ) ) ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2689]) ).
thf(2783,plain,
! [SV88: $i,SV492: $i,SV588: $i] :
( ( ( ~ ( ~ ( in @ SV588 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SV588 @ SV88 ) ) )
= $false )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2692]) ).
thf(2784,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( ~ ( SV98 @ ( sK89_SY261 @ SV493 @ SV98 ) )
| ~ ! [SY1063: $i] :
( ~ ( SV98 @ SY1063 )
| ( ( sK89_SY261 @ SV493 @ SV98 )
= SY1063 ) ) ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2693]) ).
thf(2785,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK79_SY261 @ SV493 @ SV98 ) )
| ~ ! [SY1054: $i] :
( ~ ( SV98 @ SY1054 )
| ( ( sK79_SY261 @ SV493 @ SV98 )
= SY1054 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2694]) ).
thf(2786,plain,
! [SV104: $i,SV287: $i > $o,SV513: $i] :
( ( ( in @ ( sK80_SY662 @ SV513 @ SV287 @ SV104 ) @ SV104 )
= $true )
| ( ( in @ SV513 @ SV104 )
= $false )
| ( ( SV287 @ SV513 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2695]) ).
thf(2787,plain,
! [SV107: $i,SV290: $i,SV428: $i,SV515: $i] :
( ( ( in @ ( kpair @ ( sK64_SY983 @ SV515 @ SV428 @ SV290 @ SV107 ) @ ( sK71_SY1031 @ SV107 @ SV428 @ SV515 @ SV290 ) ) @ SV428 )
= $true )
| ( ( subset @ SV428 @ SV515 )
= $true )
| ( ( subset @ SV515 @ ( cartprod @ SV107 @ SV290 ) )
= $false )
| ( ( subset @ SV428 @ ( cartprod @ SV107 @ SV290 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2698]) ).
thf(2788,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK81_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1055: $i] :
( ~ ( SV113 @ SY1055 )
| ( ( sK81_SY305 @ SV494 @ SV113 )
= SY1055 ) ) )
= $false )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2700]) ).
thf(2789,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( ~ ( SV113 @ ( sK90_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1064: $i] :
( ~ ( SV113 @ SY1064 )
| ( ( sK90_SY305 @ SV494 @ SV113 )
= SY1064 ) ) ) )
= $true )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2701]) ).
thf(2790,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK82_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1056: $i] :
( ~ ( SV113 @ SY1056 )
| ( ( sK82_SY305 @ SV494 @ SV113 )
= SY1056 ) ) )
= $false )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2702]) ).
thf(2791,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( ~ ! [SY1032: $i] :
~ ~ ( ~ ( in @ SY1032 @ SV313 )
| ~ ( SV134 @ SY1032 @ SV550 ) ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2703]) ).
thf(2792,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ! [SY1033: $i] :
~ ~ ( ~ ( in @ SY1033 @ SV313 )
| ~ ( SV134 @ SY1033 @ SV550 ) ) )
= $false )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2704]) ).
thf(2793,plain,
! [SV541: $i,SV313: $i,SV134: $i > $i > $o] :
( ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( ~ ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2705]) ).
thf(2794,plain,
! [SV541: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2706]) ).
thf(2795,plain,
! [SV141: $i,SV551: $i,SV320: $i > $o] :
( ( ( SV320 @ SV551 )
= $false )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2707]) ).
thf(2796,plain,
! [SV320: $i > $o,SV141: $i,SV565: $i] :
( ( ( ~ ( in @ SV565 @ SV141 ) )
= $true )
| ( ( ~ ( SV320 @ SV565 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2708]) ).
thf(2797,plain,
! [SV320: $i > $o,SV141: $i,SV577: $i] :
( ( ( ~ ( in @ SV577 @ SV141 )
| ~ ( SV320 @ SV577 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2709]) ).
thf(2798,plain,
! [SV320: $i > $o,SV141: $i,SV589: $i] :
( ( ( ~ ( ~ ( in @ SV589 @ SV141 )
| ~ ( SV320 @ SV589 ) ) )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2710]) ).
thf(2799,plain,
! [SV320: $i > $o,SV141: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV141 )
| ~ ( SV320 @ SV578 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2711]) ).
thf(2800,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 )
| ! [SY1069: $i] :
( ~ ( in @ SY1069 @ SV321 )
| ~ ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1069 ) @ SV518 )
| ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1069 ) @ SV440 ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2712]) ).
thf(2801,plain,
! [SV440: $i,SV518: $i,SV321: $i,SV142: $i] :
( ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) ) )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2713]) ).
thf(2802,plain,
! [SV142: $i,SV321: $i,SV440: $i,SV518: $i] :
( ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) )
| ( SV440 = SV518 ) )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2714]) ).
thf(2803,plain,
! [SV440: $i,SV518: $i,SV321: $i,SV142: $i] :
( ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) ) )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2715]) ).
thf(2804,plain,
! [SV521: $i,SV557: $i,SV329: $i > $o,SV154: $i,SV590: $i] :
( ( ( ~ ( in @ SV590 @ SV154 ) )
= $true )
| ( ( ~ ( SV329 @ SV557 )
| ~ ( SV329 @ SV590 )
| ( SV557 = SV590 ) )
= $true )
| ( ( in @ SV557 @ SV154 )
= $false )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2717]) ).
thf(2805,plain,
! [SV330: $i,SV443: $i,SV155: $i] :
( ( ( ~ ( in @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) @ SV330 ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2806,plain,
! [SV155: $i,SV330: $i,SV443: $i] :
( ( ( SV443
!= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) ) )
= $false )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2718]) ).
thf(2807,plain,
! [SV174: $i,SV579: $i] :
( ( ( in @ SV579 @ omega )
= $false )
| ( ( in @ SV579 @ SV174 )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( sK41_SY431 @ SV174 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2722]) ).
thf(2808,plain,
! [SV174: $i,SV580: $i] :
( ( ( in @ SV580 @ omega )
= $false )
| ( ( in @ SV580 @ SV174 )
= $true )
| ( ( in @ emptyset @ SV174 )
= $false )
| ( ( in @ ( sK41_SY431 @ SV174 ) @ SV174 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2723]) ).
thf(2809,plain,
! [SV353: $i,SV182: $i,SV528: $i > $o,SV451: $i,SV581: $i] :
( ( ( in @ SV581 @ SV451 )
= $false )
| ( ( SV528 @ SV581 )
= $true )
| ( ( in @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) @ SV353 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2724]) ).
thf(2810,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV591: $i] :
( ( ( ~ ( in @ SV591 @ SV451 ) )
= $true )
| ( ( SV528 @ SV591 )
= $true )
| ( ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) @ SV451 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2725]) ).
thf(2811,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV582: $i] :
( ( ( in @ SV582 @ SV451 )
= $false )
| ( ( SV528 @ SV582 )
= $true )
| ( ( SV528 @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) )
= $false )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2726]) ).
thf(2812,plain,
! [SV183: $i,SV354: $i,SV529: $i > $o,SV498: $i > $o] :
( ( ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
| ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) ) )
= $false )
| ( ( ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2727]) ).
thf(2813,plain,
! [SV359: $i > $o,SV592: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ SV592 )
| ~ ! [SY1065: $i] :
( ~ ( SV188 @ SY1065 )
| ( SV592 = SY1065 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2728]) ).
thf(2814,plain,
! [SV188: $i > $o,SV593: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ SV593 )
| ~ ! [SY1066: $i] :
( ~ ( SV359 @ SY1066 )
| ( SV593 = SY1066 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2729]) ).
thf(2815,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
| ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2730]) ).
thf(2816,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2731]) ).
thf(2817,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2731]) ).
thf(2818,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2819,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2732]) ).
thf(2820,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2733]) ).
thf(2821,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2734]) ).
thf(2822,plain,
! [SV500: $i,SV195: $i > $o] :
( ( ( SV195 @ ( sK91_SY498 @ SV500 @ SV195 ) )
= $true )
| ( ( SV195 @ SV500 )
= $false )
| ( ( SV195 @ ( sK69_SY973 @ SV500 @ SV195 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2735]) ).
thf(2823,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK85_SY25 @ SV483 @ SV10 ) )
| ~ ! [SY1057: $i] :
( ~ ( SV10 @ SY1057 )
| ( ( sK85_SY25 @ SV483 @ SV10 )
= SY1057 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2737]) ).
thf(2824,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK74_SY25 @ SV483 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2738]) ).
thf(2825,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ! [SY1042: $i] :
( ~ ( SV10 @ SY1042 )
| ( ( sK74_SY25 @ SV483 @ SV10 )
= SY1042 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2738]) ).
thf(2826,plain,
! [SV548: $i,SV217: $i > $o,SV14: $i] :
( ( ( ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( SV217 @ SV548 )
= $false )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2739]) ).
thf(2827,plain,
! [SV217: $i > $o,SV14: $i,SV561: $i] :
( ( ( in @ SV561 @ SV14 )
= $false )
| ( ( ~ ( SV217 @ SV561 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2740]) ).
thf(2828,plain,
! [SV217: $i > $o,SV14: $i,SV566: $i] :
( ( ( ~ ( in @ SV566 @ SV14 ) )
= $true )
| ( ( ~ ( SV217 @ SV566 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2741]) ).
thf(2829,plain,
! [SV217: $i > $o,SV14: $i,SV583: $i] :
( ( ( ~ ( in @ SV583 @ SV14 )
| ~ ( SV217 @ SV583 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2742]) ).
thf(2830,plain,
! [SV217: $i > $o,SV14: $i,SV567: $i] :
( ( ( ~ ( in @ SV567 @ SV14 ) )
= $true )
| ( ( ~ ( SV217 @ SV567 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2743]) ).
thf(2831,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( in @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) ) )
= $false )
| ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2832,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) )
= $false )
| ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2744]) ).
thf(2833,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( in @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
| ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) ) )
= $false )
| ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2745]) ).
thf(2834,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( in @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) ) )
= $false )
| ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2746]) ).
thf(2835,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) )
= $false )
| ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2746]) ).
thf(2836,plain,
! [SV29: $i,SV391: $i,SV504: $i,SV568: $i,SV230: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ SV230 )
| ~ ( in @ ( kpair @ SV568 @ SV596 ) @ SV504 )
| ( in @ ( kpair @ SV568 @ SV596 ) @ SV391 ) )
= $true )
| ( ( in @ SV568 @ SV29 )
= $false )
| ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2747]) ).
thf(2837,plain,
! [SV29: $i,SV391: $i,SV504: $i,SV562: $i,SV230: $i,SV594: $i] :
( ( ( ~ ( in @ SV594 @ SV230 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV562 @ SV594 ) @ SV504 )
| ( in @ ( kpair @ SV562 @ SV594 ) @ SV391 ) )
= $true )
| ( ( in @ SV562 @ SV29 )
= $false )
| ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2748]) ).
thf(2838,plain,
! [SV485: $i,SV584: $i,SV569: $i,SV33: $i > $o] :
( ( ( SV33 @ SV569 )
= $false )
| ( ( ~ ( SV33 @ SV584 )
| ( SV569 = SV584 ) )
= $true )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2749]) ).
thf(2839,plain,
! [SV485: $i,SV563: $i,SV570: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV570 ) )
= $true )
| ( ( SV563 = SV570 )
= $true )
| ( ( SV33 @ SV563 )
= $false )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV485
= ( sK57_SY946 @ SV485 @ SV33 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2750]) ).
thf(2840,plain,
! [SV488: $i,SV585: $i,SV571: $i,SV46: $i > $o] :
( ( ( SV46 @ SV571 )
= $false )
| ( ( ~ ( SV46 @ SV585 )
| ( SV571 = SV585 ) )
= $true )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2751]) ).
thf(2841,plain,
! [SV488: $i,SV564: $i,SV572: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV572 ) )
= $true )
| ( ( SV564 = SV572 )
= $true )
| ( ( SV46 @ SV564 )
= $false )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV488
= ( sK58_SY949 @ SV488 @ SV46 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2752]) ).
thf(2842,plain,
! [SV246: $i > $o,SV554: $i,SV49: $i > $o] :
( ( ( ! [SY1035: $i] :
( ~ ( SV49 @ SY1035 )
| ( SV554 = SY1035 ) ) )
= $false )
| ( ( SV49 @ SV554 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2753]) ).
thf(2843,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2754]) ).
thf(2844,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2755]) ).
thf(2845,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2756]) ).
thf(2846,plain,
! [SV246: $i > $o,SV597: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ SV597 )
| ~ ! [SY1070: $i] :
( ~ ( SV49 @ SY1070 )
| ( SV597 = SY1070 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2757]) ).
thf(2847,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ~ ( ~ ( SV53 @ ( sK95_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1071: $i] :
( ~ ( SV53 @ SY1071 )
| ( ( sK95_SY139 @ SV489 @ SV53 )
= SY1071 ) ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2758]) ).
thf(2848,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( ~ ( SV53 @ ( sK92_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1067: $i] :
( ~ ( SV53 @ SY1067 )
| ( ( sK92_SY139 @ SV489 @ SV53 )
= SY1067 ) ) ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2759]) ).
thf(2849,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( ~ ( SV53 @ ( sK93_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1068: $i] :
( ~ ( SV53 @ SY1068 )
| ( ( sK93_SY139 @ SV489 @ SV53 )
= SY1068 ) ) ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2760]) ).
thf(2850,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK87_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1060: $i] :
( ~ ( SV53 @ SY1060 )
| ( ( sK87_SY139 @ SV489 @ SV53 )
= SY1060 ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2761]) ).
thf(2851,plain,
! [SV62: $i,SV573: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV573 )
| ( in @ SV598 @ SV62 ) )
= $true )
| ( ( in @ SV573 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2762]) ).
thf(2852,plain,
! [SV586: $i,SV62: $i,SV574: $i] :
( ( ( ~ ( ~ ( in @ SV574 @ SV62 )
| ~ ( in @ SV586 @ SV62 ) ) )
= $false )
| ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) )
| ( SV574 = SV586 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2763]) ).
thf(2853,plain,
! [SV555: $i,SV62: $i,SV549: $i] :
( ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( ~ ( in @ SV555 @ ( sK5_SY153 @ SV62 ) ) )
= $true )
| ( ( ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV549 )
| ( in @ SY1036 @ SV555 ) )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2764]) ).
thf(2854,plain,
! [SV62: $i,SV539: $i] :
( ( ( ~ ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2765]) ).
thf(2855,plain,
! [SV62: $i,SV539: $i] :
( ( ( ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2766]) ).
thf(2856,plain,
! [SV69: $i,SV260: $i > $o,SV509: $i] :
( ( ( in @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) @ SV69 )
= $true )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2767]) ).
thf(2857,plain,
! [SV69: $i,SV509: $i,SV260: $i > $o] :
( ( ( SV260 @ ( sK70_SY614 @ SV509 @ SV260 @ SV69 ) )
= $true )
| ( ( in @ SV509
@ ( dsetconstr @ SV69
@ ^ [SY612: $i] : ( SV260 @ SY612 ) ) )
= $false )
| ( ( ( dsetconstr @ SV69
@ ^ [SY613: $i] : ( SV260 @ SY613 ) )
= ( setadjoin @ SV509 @ emptyset ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2768]) ).
thf(2858,plain,
! [SV76: $i,SV266: $i,SV510: $i > $o,SV413: $i,SV587: $i] :
( ( ( in @ SV587 @ SV413 )
= $false )
| ( ( SV510 @ SV587 )
= $true )
| ( ( in @ ( kpair @ ( sK42_SY979 @ SV510 @ SV413 @ SV266 @ SV76 ) @ ( sK59_SY1019 @ SV76 @ SV413 @ SV510 @ SV266 ) ) @ SV413 )
= $true )
| ( ( subset @ SV413 @ ( cartprod @ SV76 @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2770]) ).
thf(2859,plain,
! [SV267: $i,SV511: $o,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2772]) ).
thf(2860,plain,
! [SV77: $i,SV511: $o,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( SV511 = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2773]) ).
thf(2861,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2775]) ).
thf(2862,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( $true = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2776]) ).
thf(2863,plain,
! [SV267: $i,SV77: $i,SV414: $i] :
( ( ( in @ SV414 @ SV77 )
= $false )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2778]) ).
thf(2864,plain,
! [SV77: $i,SV267: $i,SV414: $i] :
( ( ( in @ SV414 @ SV267 )
= $true )
| ( $false = $true )
| ( ( in @ SV414 @ SV267 )
= $false )
| ( ( in @ SV414 @ ( symdiff @ SV77 @ SV267 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2779]) ).
thf(2865,plain,
! [SV491: $i,SV599: $i,SV80: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV80 @ SV599 )
| ( SV599
= ( sK88_SY220 @ SV491 @ SV80 ) ) )
| ~ ( ( SV599
!= ( sK88_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SV599 ) ) ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2781]) ).
thf(2866,plain,
! [SV491: $i,SV595: $i,SV80: $i > $o] :
( ( ( ~ ( ~ ( SV80 @ SV595 )
| ( SV595
= ( sK78_SY220 @ SV491 @ SV80 ) ) )
| ~ ( ( SV595
!= ( sK78_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SV595 ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2782]) ).
thf(2867,plain,
! [SV88: $i,SV492: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ ( sK36_SY237 @ SV492 @ SV88 ) )
| ~ ( in @ SV588 @ SV88 ) )
= $true )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2783]) ).
thf(2868,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK89_SY261 @ SV493 @ SV98 ) )
| ~ ! [SY1063: $i] :
( ~ ( SV98 @ SY1063 )
| ( ( sK89_SY261 @ SV493 @ SV98 )
= SY1063 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2784]) ).
thf(2869,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK79_SY261 @ SV493 @ SV98 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2785]) ).
thf(2870,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ! [SY1054: $i] :
( ~ ( SV98 @ SY1054 )
| ( ( sK79_SY261 @ SV493 @ SV98 )
= SY1054 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2785]) ).
thf(2871,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK81_SY305 @ SV494 @ SV113 ) ) )
= $false )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2788]) ).
thf(2872,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ! [SY1055: $i] :
( ~ ( SV113 @ SY1055 )
| ( ( sK81_SY305 @ SV494 @ SV113 )
= SY1055 ) ) )
= $false )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2788]) ).
thf(2873,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK90_SY305 @ SV494 @ SV113 ) )
| ~ ! [SY1064: $i] :
( ~ ( SV113 @ SY1064 )
| ( ( sK90_SY305 @ SV494 @ SV113 )
= SY1064 ) ) )
= $false )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2789]) ).
thf(2874,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK82_SY305 @ SV494 @ SV113 ) ) )
= $false )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2790]) ).
thf(2875,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ! [SY1056: $i] :
( ~ ( SV113 @ SY1056 )
| ( ( sK82_SY305 @ SV494 @ SV113 )
= SY1056 ) ) )
= $false )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2790]) ).
thf(2876,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY1032: $i] :
~ ~ ( ~ ( in @ SY1032 @ SV313 )
| ~ ( SV134 @ SY1032 @ SV550 ) ) )
= $false )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2791]) ).
thf(2877,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY1033: $i] :
~ ~ ( ~ ( in @ SY1033 @ SV313 )
| ~ ( SV134 @ SY1033 @ SV550 ) ) )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2792]) ).
thf(2878,plain,
! [SV541: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY695: $i] :
~ ! [SY696: $i] :
~ ( ~ ( ~ ( in @ SY696 @ SY695 )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY696 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY696 ) )
| ( in @ SY696 @ SY695 ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2793]) ).
thf(2879,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i] :
( ( ( ~ ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY1072 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY1072 ) )
| ( in @ SY1072 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2794]) ).
thf(2880,plain,
! [SV551: $i,SV320: $i > $o,SV141: $i] :
( ( ( ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( SV320 @ SV551 )
= $false )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2795]) ).
thf(2881,plain,
! [SV320: $i > $o,SV141: $i,SV565: $i] :
( ( ( in @ SV565 @ SV141 )
= $false )
| ( ( ~ ( SV320 @ SV565 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2796]) ).
thf(2882,plain,
! [SV320: $i > $o,SV141: $i,SV577: $i] :
( ( ( ~ ( in @ SV577 @ SV141 ) )
= $true )
| ( ( ~ ( SV320 @ SV577 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2797]) ).
thf(2883,plain,
! [SV320: $i > $o,SV141: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV141 )
| ~ ( SV320 @ SV589 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2798]) ).
thf(2884,plain,
! [SV320: $i > $o,SV141: $i,SV578: $i] :
( ( ( ~ ( in @ SV578 @ SV141 ) )
= $true )
| ( ( ~ ( SV320 @ SV578 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2799]) ).
thf(2885,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2886,plain,
! [SV142: $i,SV518: $i,SV440: $i,SV321: $i] :
( ( ( ! [SY1069: $i] :
( ~ ( in @ SY1069 @ SV321 )
| ~ ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1069 ) @ SV518 )
| ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1069 ) @ SV440 ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2800]) ).
thf(2887,plain,
! [SV440: $i,SV518: $i,SV321: $i,SV142: $i] :
( ( ( ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2801]) ).
thf(2888,plain,
! [SV440: $i,SV518: $i,SV321: $i,SV142: $i] :
( ( ( ~ ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) ) )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2802]) ).
thf(2889,plain,
! [SV440: $i,SV518: $i,SV321: $i,SV142: $i] :
( ( ( ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2803]) ).
thf(2890,plain,
! [SV521: $i,SV557: $i,SV329: $i > $o,SV154: $i,SV590: $i] :
( ( ( in @ SV590 @ SV154 )
= $false )
| ( ( ~ ( SV329 @ SV557 )
| ~ ( SV329 @ SV590 )
| ( SV557 = SV590 ) )
= $true )
| ( ( in @ SV557 @ SV154 )
= $false )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2804]) ).
thf(2891,plain,
! [SV330: $i,SV443: $i,SV155: $i] :
( ( ( in @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) @ SV330 )
= $true )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2805]) ).
thf(2892,plain,
! [SV155: $i,SV330: $i,SV443: $i] :
( ( ( SV443
= ( kpair @ ( sK34_SY893 @ SV443 @ SV330 @ SV155 ) @ ( sK73_SY1007 @ SV155 @ SV443 @ SV330 ) ) )
= $true )
| ( ( in @ SV443 @ ( cartprod @ SV155 @ SV330 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2806]) ).
thf(2893,plain,
! [SV182: $i,SV353: $i,SV528: $i > $o,SV451: $i,SV591: $i] :
( ( ( in @ SV591 @ SV451 )
= $false )
| ( ( SV528 @ SV591 )
= $true )
| ( ( in @ ( kpair @ ( sK47_SY993 @ SV528 @ SV451 @ SV353 @ SV182 ) @ ( sK67_SY1024 @ SV182 @ SV451 @ SV528 @ SV353 ) ) @ SV451 )
= $true )
| ( ( subset @ SV451 @ ( cartprod @ SV182 @ SV353 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2810]) ).
thf(2894,plain,
! [SV183: $i,SV354: $i,SV529: $i > $o,SV498: $i > $o] :
( ( ( ~ ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) )
= $false )
| ( ( ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2812]) ).
thf(2895,plain,
! [SV354: $i,SV498: $i > $o,SV183: $i,SV529: $i > $o] :
( ( ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $false )
| ( ( ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2812]) ).
thf(2896,plain,
! [SV359: $i > $o,SV592: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV592 )
| ~ ! [SY1065: $i] :
( ~ ( SV188 @ SY1065 )
| ( SV592 = SY1065 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2813]) ).
thf(2897,plain,
! [SV188: $i > $o,SV593: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV593 )
| ~ ! [SY1066: $i] :
( ~ ( SV359 @ SY1066 )
| ( SV593 = SY1066 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2814]) ).
thf(2898,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2815]) ).
thf(2899,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2815]) ).
thf(2900,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2816]) ).
thf(2901,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2817]) ).
thf(2902,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2818]) ).
thf(2903,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2819]) ).
thf(2904,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2820]) ).
thf(2905,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2821]) ).
thf(2906,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ ( sK85_SY25 @ SV483 @ SV10 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2823]) ).
thf(2907,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ~ ! [SY1057: $i] :
( ~ ( SV10 @ SY1057 )
| ( ( sK85_SY25 @ SV483 @ SV10 )
= SY1057 ) ) )
= $false )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2823]) ).
thf(2908,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK74_SY25 @ SV483 @ SV10 ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2824]) ).
thf(2909,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ! [SY1042: $i] :
( ~ ( SV10 @ SY1042 )
| ( ( sK74_SY25 @ SV483 @ SV10 )
= SY1042 ) ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2825]) ).
thf(2910,plain,
! [SV14: $i,SV217: $i > $o,SV548: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( SV217 @ SV548 )
= $false )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2826]) ).
thf(2911,plain,
! [SV14: $i,SV561: $i,SV217: $i > $o] :
( ( ( SV217 @ SV561 )
= $false )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2827]) ).
thf(2912,plain,
! [SV217: $i > $o,SV14: $i,SV566: $i] :
( ( ( in @ SV566 @ SV14 )
= $false )
| ( ( ~ ( SV217 @ SV566 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2828]) ).
thf(2913,plain,
! [SV217: $i > $o,SV14: $i,SV583: $i] :
( ( ( ~ ( in @ SV583 @ SV14 ) )
= $true )
| ( ( ~ ( SV217 @ SV583 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2829]) ).
thf(2914,plain,
! [SV217: $i > $o,SV14: $i,SV567: $i] :
( ( ( in @ SV567 @ SV14 )
= $false )
| ( ( ~ ( SV217 @ SV567 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2830]) ).
thf(2915,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( in @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
= $true )
| ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2831]) ).
thf(2916,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
= ( setadjoin @ ( sK75_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) )
= $true )
| ( ( in @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) @ SV23 )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2832]) ).
thf(2917,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( ~ ( in @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) ) )
= $false )
| ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2833]) ).
thf(2918,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
!= ( setadjoin @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) )
= $false )
| ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2833]) ).
thf(2919,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( in @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
= $true )
| ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2834]) ).
thf(2920,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
= ( setadjoin @ ( sK76_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) )
= $true )
| ( ( ( sK49_SY817 @ SV386 @ SV224 @ SV23 )
= SV386 )
= $false )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2835]) ).
thf(2921,plain,
! [SV29: $i,SV391: $i,SV504: $i,SV568: $i,SV230: $i,SV596: $i] :
( ( ( ~ ( in @ SV596 @ SV230 ) )
= $true )
| ( ( ~ ( in @ ( kpair @ SV568 @ SV596 ) @ SV504 )
| ( in @ ( kpair @ SV568 @ SV596 ) @ SV391 ) )
= $true )
| ( ( in @ SV568 @ SV29 )
= $false )
| ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2836]) ).
thf(2922,plain,
! [SV29: $i,SV391: $i,SV504: $i,SV562: $i,SV230: $i,SV594: $i] :
( ( ( in @ SV594 @ SV230 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV562 @ SV594 ) @ SV504 )
| ( in @ ( kpair @ SV562 @ SV594 ) @ SV391 ) )
= $true )
| ( ( in @ SV562 @ SV29 )
= $false )
| ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2837]) ).
thf(2923,plain,
! [SV485: $i,SV569: $i,SV584: $i,SV33: $i > $o] :
( ( ( ~ ( SV33 @ SV584 ) )
= $true )
| ( ( SV569 = SV584 )
= $true )
| ( ( SV33 @ SV569 )
= $false )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2838]) ).
thf(2924,plain,
! [SV485: $i,SV563: $i,SV570: $i,SV33: $i > $o] :
( ( ( SV33 @ SV570 )
= $false )
| ( ( SV563 = SV570 )
= $true )
| ( ( SV33 @ SV563 )
= $false )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV485
= ( sK57_SY946 @ SV485 @ SV33 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2839]) ).
thf(2925,plain,
! [SV488: $i,SV571: $i,SV585: $i,SV46: $i > $o] :
( ( ( ~ ( SV46 @ SV585 ) )
= $true )
| ( ( SV571 = SV585 )
= $true )
| ( ( SV46 @ SV571 )
= $false )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2840]) ).
thf(2926,plain,
! [SV488: $i,SV564: $i,SV572: $i,SV46: $i > $o] :
( ( ( SV46 @ SV572 )
= $false )
| ( ( SV564 = SV572 )
= $true )
| ( ( SV46 @ SV564 )
= $false )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV488
= ( sK58_SY949 @ SV488 @ SV46 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2841]) ).
thf(2927,plain,
! [SV554: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
| ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV554 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2842]) ).
thf(2928,plain,
! [SV246: $i > $o,SV49: $i > $o] :
( ( ( ! [SY128: $i] :
~ ~ ( ~ ( SV49 @ SY128 )
| ~ ! [SY129: $i] :
( ~ ( SV49 @ SY129 )
| ( SY128 = SY129 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2843]) ).
thf(2929,plain,
! [SV246: $i > $o,SV600: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ SV600 )
| ~ ! [SY1077: $i] :
( ~ ( SV49 @ SY1077 )
| ( SV600 = SY1077 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2844]) ).
thf(2930,plain,
! [SV246: $i > $o,SV601: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ SV601 )
| ~ ! [SY1078: $i] :
( ~ ( SV49 @ SY1078 )
| ( SV601 = SY1078 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2845]) ).
thf(2931,plain,
! [SV246: $i > $o,SV597: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ SV597 )
| ~ ! [SY1070: $i] :
( ~ ( SV49 @ SY1070 )
| ( SV597 = SY1070 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2846]) ).
thf(2932,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( ~ ( SV53 @ ( sK95_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1071: $i] :
( ~ ( SV53 @ SY1071 )
| ( ( sK95_SY139 @ SV489 @ SV53 )
= SY1071 ) ) ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2847]) ).
thf(2933,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK92_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1067: $i] :
( ~ ( SV53 @ SY1067 )
| ( ( sK92_SY139 @ SV489 @ SV53 )
= SY1067 ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2848]) ).
thf(2934,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK93_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1068: $i] :
( ~ ( SV53 @ SY1068 )
| ( ( sK93_SY139 @ SV489 @ SV53 )
= SY1068 ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2849]) ).
thf(2935,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK87_SY139 @ SV489 @ SV53 ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2850]) ).
thf(2936,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ! [SY1060: $i] :
( ~ ( SV53 @ SY1060 )
| ( ( sK87_SY139 @ SV489 @ SV53 )
= SY1060 ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2850]) ).
thf(2937,plain,
! [SV62: $i,SV573: $i,SV598: $i] :
( ( ( ~ ( in @ SV598 @ SV573 ) )
= $true )
| ( ( in @ SV598 @ SV62 )
= $true )
| ( ( in @ SV573 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2851]) ).
thf(2938,plain,
! [SV586: $i,SV62: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ SV62 )
| ~ ( in @ SV586 @ SV62 ) )
= $true )
| ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) )
| ( SV574 = SV586 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2852]) ).
thf(2939,plain,
! [SV549: $i,SV62: $i,SV555: $i] :
( ( ( in @ SV555 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV549 )
| ( in @ SY1036 @ SV555 ) )
| ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2853]) ).
thf(2940,plain,
! [SV62: $i,SV539: $i] :
( ( ( ! [SY1011: $i] :
~ ( in @ SY1011 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2854]) ).
thf(2941,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ( in @ SV602 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2855]) ).
thf(2942,plain,
! [SV491: $i,SV599: $i,SV80: $i > $o] :
( ( ( ~ ( ~ ( SV80 @ SV599 )
| ( SV599
= ( sK88_SY220 @ SV491 @ SV80 ) ) )
| ~ ( ( SV599
!= ( sK88_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SV599 ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2865]) ).
thf(2943,plain,
! [SV491: $i,SV595: $i,SV80: $i > $o] :
( ( ( ~ ( ~ ( SV80 @ SV595 )
| ( SV595
= ( sK78_SY220 @ SV491 @ SV80 ) ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2866]) ).
thf(2944,plain,
! [SV80: $i > $o,SV491: $i,SV595: $i] :
( ( ( ~ ( ( SV595
!= ( sK78_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SV595 ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2866]) ).
thf(2945,plain,
! [SV88: $i,SV492: $i,SV588: $i] :
( ( ( ~ ( in @ SV588 @ ( sK36_SY237 @ SV492 @ SV88 ) ) )
= $true )
| ( ( ~ ( in @ SV588 @ SV88 ) )
= $true )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2867]) ).
thf(2946,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ ( sK89_SY261 @ SV493 @ SV98 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2868]) ).
thf(2947,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ~ ! [SY1063: $i] :
( ~ ( SV98 @ SY1063 )
| ( ( sK89_SY261 @ SV493 @ SV98 )
= SY1063 ) ) )
= $false )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2868]) ).
thf(2948,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( SV98 @ ( sK79_SY261 @ SV493 @ SV98 ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2869]) ).
thf(2949,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ! [SY1054: $i] :
( ~ ( SV98 @ SY1054 )
| ( ( sK79_SY261 @ SV493 @ SV98 )
= SY1054 ) ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2870]) ).
thf(2950,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( SV113 @ ( sK81_SY305 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2871]) ).
thf(2951,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ! [SY1055: $i] :
( ~ ( SV113 @ SY1055 )
| ( ( sK81_SY305 @ SV494 @ SV113 )
= SY1055 ) ) )
= $true )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2872]) ).
thf(2952,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ ( sK90_SY305 @ SV494 @ SV113 ) ) )
= $false )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2873]) ).
thf(2953,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ~ ! [SY1064: $i] :
( ~ ( SV113 @ SY1064 )
| ( ( sK90_SY305 @ SV494 @ SV113 )
= SY1064 ) ) )
= $false )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2873]) ).
thf(2954,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( SV113 @ ( sK82_SY305 @ SV494 @ SV113 ) )
= $true )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2874]) ).
thf(2955,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ! [SY1056: $i] :
( ~ ( SV113 @ SY1056 )
| ( ( sK82_SY305 @ SV494 @ SV113 )
= SY1056 ) ) )
= $true )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2875]) ).
thf(2956,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV550 ) ) )
= $false )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2876]) ).
thf(2957,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i,SV603: $i] :
( ( ( ~ ~ ( ~ ( in @ SV603 @ SV313 )
| ~ ( SV134 @ SV603 @ SV550 ) ) )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2877]) ).
thf(2958,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i] :
( ( ( ~ ! [SY1079: $i] :
~ ( ~ ( ~ ( in @ SY1079 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY1079 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY1079 ) )
| ( in @ SY1079 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2878]) ).
thf(2959,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i] :
( ( ( ! [SY1072: $i] :
~ ( ~ ( ~ ( in @ SY1072 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY1072 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY1072 ) )
| ( in @ SY1072 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) ) ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2879]) ).
thf(2960,plain,
! [SV141: $i,SV320: $i > $o,SV551: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( SV320 @ SV551 )
= $false )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2880]) ).
thf(2961,plain,
! [SV141: $i,SV565: $i,SV320: $i > $o] :
( ( ( SV320 @ SV565 )
= $false )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2881]) ).
thf(2962,plain,
! [SV320: $i > $o,SV141: $i,SV577: $i] :
( ( ( in @ SV577 @ SV141 )
= $false )
| ( ( ~ ( SV320 @ SV577 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2882]) ).
thf(2963,plain,
! [SV320: $i > $o,SV141: $i,SV589: $i] :
( ( ( ~ ( in @ SV589 @ SV141 ) )
= $true )
| ( ( ~ ( SV320 @ SV589 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2883]) ).
thf(2964,plain,
! [SV320: $i > $o,SV141: $i,SV578: $i] :
( ( ( in @ SV578 @ SV141 )
= $false )
| ( ( ~ ( SV320 @ SV578 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2884]) ).
thf(2965,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2885]) ).
thf(2966,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 )
| ~ ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
| ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2886]) ).
thf(2967,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 )
| ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV321 )
| ~ ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1084 ) @ SV518 )
| ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1084 ) @ SV440 ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2887]) ).
thf(2968,plain,
! [SV440: $i,SV518: $i,SV321: $i,SV142: $i] :
( ( ( ! [SY988: $i] :
( ~ ( in @ SY988 @ SV142 )
| ! [SY989: $i] :
( ~ ( in @ SY989 @ SV321 )
| ~ ( in @ ( kpair @ SY988 @ SY989 ) @ SV518 )
| ( in @ ( kpair @ SY988 @ SY989 ) @ SV440 ) ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2888]) ).
thf(2969,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 )
| ! [SY1085: $i] :
( ~ ( in @ SY1085 @ SV321 )
| ~ ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1085 ) @ SV518 )
| ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1085 ) @ SV440 ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2889]) ).
thf(2970,plain,
! [SV521: $i,SV154: $i,SV590: $i,SV557: $i,SV329: $i > $o] :
( ( ( ~ ( SV329 @ SV557 ) )
= $true )
| ( ( ~ ( SV329 @ SV590 )
| ( SV557 = SV590 ) )
= $true )
| ( ( in @ SV590 @ SV154 )
= $false )
| ( ( in @ SV557 @ SV154 )
= $false )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2890]) ).
thf(2971,plain,
! [SV183: $i,SV354: $i,SV529: $i > $o,SV498: $i > $o] :
( ( ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
= $true )
| ( ( ~ ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2894]) ).
thf(2972,plain,
! [SV354: $i,SV498: $i > $o,SV183: $i,SV529: $i > $o] :
( ( ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) )
= $false )
| ( ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2895]) ).
thf(2973,plain,
! [SV359: $i > $o,SV592: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV592 ) )
= $true )
| ( ( ~ ! [SY1065: $i] :
( ~ ( SV188 @ SY1065 )
| ( SV592 = SY1065 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2896]) ).
thf(2974,plain,
! [SV188: $i > $o,SV593: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV593 ) )
= $true )
| ( ( ~ ! [SY1066: $i] :
( ~ ( SV359 @ SY1066 )
| ( SV593 = SY1066 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2897]) ).
thf(2975,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) )
| ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2898]) ).
thf(2976,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) )
| ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2899]) ).
thf(2977,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2900]) ).
thf(2978,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2901]) ).
thf(2979,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2902]) ).
thf(2980,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2903]) ).
thf(2981,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2904]) ).
thf(2982,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2905]) ).
thf(2983,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( SV10 @ ( sK85_SY25 @ SV483 @ SV10 ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2906]) ).
thf(2984,plain,
! [SV483: $i,SV10: $i > $o] :
( ( ( ! [SY1057: $i] :
( ~ ( SV10 @ SY1057 )
| ( ( sK85_SY25 @ SV483 @ SV10 )
= SY1057 ) ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2907]) ).
thf(2985,plain,
! [SV483: $i,SV604: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV604 )
| ( ( sK74_SY25 @ SV483 @ SV10 )
= SV604 ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2909]) ).
thf(2986,plain,
! [SV14: $i,SV217: $i > $o,SV548: $i] :
( ( ( ~ ( ~ ( in @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( SV217 @ SV548 )
= $false )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2910]) ).
thf(2987,plain,
! [SV561: $i,SV217: $i > $o,SV14: $i] :
( ( ( ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( SV217 @ SV561 )
= $false )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2911]) ).
thf(2988,plain,
! [SV14: $i,SV566: $i,SV217: $i > $o] :
( ( ( SV217 @ SV566 )
= $false )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2912]) ).
thf(2989,plain,
! [SV217: $i > $o,SV14: $i,SV583: $i] :
( ( ( in @ SV583 @ SV14 )
= $false )
| ( ( ~ ( SV217 @ SV583 ) )
= $true )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2913]) ).
thf(2990,plain,
! [SV14: $i,SV567: $i,SV217: $i > $o] :
( ( ( SV217 @ SV567 )
= $false )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2914]) ).
thf(2991,plain,
! [SV23: $i,SV224: $i > $o,SV386: $i] :
( ( ( in @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 )
@ ( dsetconstr @ SV23
@ ^ [SY557: $i] : ( SV224 @ SY557 ) ) )
= $true )
| ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2917]) ).
thf(2992,plain,
! [SV386: $i,SV224: $i > $o,SV23: $i] :
( ( ( ( dsetconstr @ SV23
@ ^ [SY558: $i] : ( SV224 @ SY558 ) )
= ( setadjoin @ ( sK86_SY556 @ SV386 @ SV224 @ SV23 ) @ emptyset ) )
= $true )
| ( ( SV224 @ ( sK49_SY817 @ SV386 @ SV224 @ SV23 ) )
= $true )
| ( ( SV224 @ SV386 )
= $false )
| ( ( in @ SV386 @ SV23 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2918]) ).
thf(2993,plain,
! [SV29: $i,SV391: $i,SV504: $i,SV568: $i,SV230: $i,SV596: $i] :
( ( ( in @ SV596 @ SV230 )
= $false )
| ( ( ~ ( in @ ( kpair @ SV568 @ SV596 ) @ SV504 )
| ( in @ ( kpair @ SV568 @ SV596 ) @ SV391 ) )
= $true )
| ( ( in @ SV568 @ SV29 )
= $false )
| ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2921]) ).
thf(2994,plain,
! [SV29: $i,SV230: $i,SV391: $i,SV504: $i,SV594: $i,SV562: $i] :
( ( ( ~ ( in @ ( kpair @ SV562 @ SV594 ) @ SV504 ) )
= $true )
| ( ( in @ ( kpair @ SV562 @ SV594 ) @ SV391 )
= $true )
| ( ( in @ SV594 @ SV230 )
= $false )
| ( ( in @ SV562 @ SV29 )
= $false )
| ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2922]) ).
thf(2995,plain,
! [SV485: $i,SV569: $i,SV584: $i,SV33: $i > $o] :
( ( ( SV33 @ SV584 )
= $false )
| ( ( SV569 = SV584 )
= $true )
| ( ( SV33 @ SV569 )
= $false )
| ( ( SV33 @ SV485 )
= $false )
| ( ( SV33 @ ( sK57_SY946 @ SV485 @ SV33 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2923]) ).
thf(2996,plain,
! [SV488: $i,SV571: $i,SV585: $i,SV46: $i > $o] :
( ( ( SV46 @ SV585 )
= $false )
| ( ( SV571 = SV585 )
= $true )
| ( ( SV46 @ SV571 )
= $false )
| ( ( SV46 @ SV488 )
= $false )
| ( ( SV46 @ ( sK58_SY949 @ SV488 @ SV46 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2925]) ).
thf(2997,plain,
! [SV554: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV554 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2927]) ).
thf(2998,plain,
! [SV49: $i > $o,SV246: $i > $o,SV554: $i] :
( ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( SV49 @ SV554 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2927]) ).
thf(2999,plain,
! [SV246: $i > $o,SV605: $i,SV49: $i > $o] :
( ( ( ~ ~ ( ~ ( SV49 @ SV605 )
| ~ ! [SY1086: $i] :
( ~ ( SV49 @ SY1086 )
| ( SV605 = SY1086 ) ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2928]) ).
thf(3000,plain,
! [SV246: $i > $o,SV600: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ SV600 )
| ~ ! [SY1077: $i] :
( ~ ( SV49 @ SY1077 )
| ( SV600 = SY1077 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2929]) ).
thf(3001,plain,
! [SV246: $i > $o,SV601: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ SV601 )
| ~ ! [SY1078: $i] :
( ~ ( SV49 @ SY1078 )
| ( SV601 = SY1078 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2930]) ).
thf(3002,plain,
! [SV246: $i > $o,SV597: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV597 )
| ~ ! [SY1070: $i] :
( ~ ( SV49 @ SY1070 )
| ( SV597 = SY1070 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2931]) ).
thf(3003,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK95_SY139 @ SV489 @ SV53 ) )
| ~ ! [SY1071: $i] :
( ~ ( SV53 @ SY1071 )
| ( ( sK95_SY139 @ SV489 @ SV53 )
= SY1071 ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2932]) ).
thf(3004,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK92_SY139 @ SV489 @ SV53 ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3005,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ! [SY1067: $i] :
( ~ ( SV53 @ SY1067 )
| ( ( sK92_SY139 @ SV489 @ SV53 )
= SY1067 ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2933]) ).
thf(3006,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK93_SY139 @ SV489 @ SV53 ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2934]) ).
thf(3007,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ! [SY1068: $i] :
( ~ ( SV53 @ SY1068 )
| ( ( sK93_SY139 @ SV489 @ SV53 )
= SY1068 ) ) )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2934]) ).
thf(3008,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( SV53 @ ( sK87_SY139 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2935]) ).
thf(3009,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY1060: $i] :
( ~ ( SV53 @ SY1060 )
| ( ( sK87_SY139 @ SV489 @ SV53 )
= SY1060 ) ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2936]) ).
thf(3010,plain,
! [SV62: $i,SV573: $i,SV598: $i] :
( ( ( in @ SV598 @ SV573 )
= $false )
| ( ( in @ SV598 @ SV62 )
= $true )
| ( ( in @ SV573 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2937]) ).
thf(3011,plain,
! [SV586: $i,SV62: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ SV62 ) )
= $true )
| ( ( ~ ( in @ SV586 @ SV62 ) )
= $true )
| ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) )
| ( SV574 = SV586 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2938]) ).
thf(3012,plain,
! [SV62: $i,SV555: $i,SV549: $i] :
( ( ( ! [SY1036: $i] :
( ~ ( in @ SY1036 @ SV549 )
| ( in @ SY1036 @ SV555 ) ) )
= $true )
| ( ( ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true )
| ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ SV555 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2939]) ).
thf(3013,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ( in @ SV606 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2940]) ).
thf(3014,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( in @ SV602 @ SV539 )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2941]) ).
thf(3015,plain,
! [SV491: $i,SV599: $i,SV80: $i > $o] :
( ( ( ~ ( ~ ( SV80 @ SV599 )
| ( SV599
= ( sK88_SY220 @ SV491 @ SV80 ) ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2942]) ).
thf(3016,plain,
! [SV80: $i > $o,SV491: $i,SV599: $i] :
( ( ( ~ ( ( SV599
!= ( sK88_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SV599 ) ) )
= $false )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2942]) ).
thf(3017,plain,
! [SV491: $i,SV595: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV595 )
| ( SV595
= ( sK78_SY220 @ SV491 @ SV80 ) ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2943]) ).
thf(3018,plain,
! [SV80: $i > $o,SV491: $i,SV595: $i] :
( ( ( ( SV595
!= ( sK78_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SV595 ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2944]) ).
thf(3019,plain,
! [SV88: $i,SV492: $i,SV588: $i] :
( ( ( in @ SV588 @ ( sK36_SY237 @ SV492 @ SV88 ) )
= $false )
| ( ( ~ ( in @ SV588 @ SV88 ) )
= $true )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2945]) ).
thf(3020,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( SV98 @ ( sK89_SY261 @ SV493 @ SV98 ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2946]) ).
thf(3021,plain,
! [SV493: $i,SV98: $i > $o] :
( ( ( ! [SY1063: $i] :
( ~ ( SV98 @ SY1063 )
| ( ( sK89_SY261 @ SV493 @ SV98 )
= SY1063 ) ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2947]) ).
thf(3022,plain,
! [SV493: $i,SV607: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV607 )
| ( ( sK79_SY261 @ SV493 @ SV98 )
= SV607 ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2949]) ).
thf(3023,plain,
! [SV494: $i,SV608: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ SV608 )
| ( ( sK81_SY305 @ SV494 @ SV113 )
= SV608 ) )
= $true )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2951]) ).
thf(3024,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( SV113 @ ( sK90_SY305 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2952]) ).
thf(3025,plain,
! [SV494: $i,SV113: $i > $o] :
( ( ( ! [SY1064: $i] :
( ~ ( SV113 @ SY1064 )
| ( ( sK90_SY305 @ SV494 @ SV113 )
= SY1064 ) ) )
= $true )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2953]) ).
thf(3026,plain,
! [SV494: $i,SV609: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ SV609 )
| ( ( sK82_SY305 @ SV494 @ SV113 )
= SV609 ) )
= $true )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2955]) ).
thf(3027,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ( ~ ( in @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV550 ) ) )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2956]) ).
thf(3028,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i,SV603: $i] :
( ( ( ~ ( ~ ( in @ SV603 @ SV313 )
| ~ ( SV134 @ SV603 @ SV550 ) ) )
= $false )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2957]) ).
thf(3029,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i] :
( ( ( ! [SY1079: $i] :
~ ( ~ ( ~ ( in @ SY1079 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY697: $i] :
~ ~ ( ~ ( in @ SY697 @ SV313 )
| ~ ( SV134 @ SY697 @ SY1079 ) ) )
| ~ ( ~ ~ ! [SY698: $i] :
~ ~ ( ~ ( in @ SY698 @ SV313 )
| ~ ( SV134 @ SY698 @ SY1079 ) )
| ( in @ SY1079 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) ) ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2958]) ).
thf(3030,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV610: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY1087: $i] :
~ ~ ( ~ ( in @ SY1087 @ SV313 )
| ~ ( SV134 @ SY1087 @ SV610 ) ) )
| ~ ( ~ ~ ! [SY1088: $i] :
~ ~ ( ~ ( in @ SY1088 @ SV313 )
| ~ ( SV134 @ SY1088 @ SV610 ) )
| ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) ) ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2959]) ).
thf(3031,plain,
! [SV141: $i,SV320: $i > $o,SV551: $i] :
( ( ( ~ ( ~ ( in @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( SV320 @ SV551 )
= $false )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2960]) ).
thf(3032,plain,
! [SV565: $i,SV320: $i > $o,SV141: $i] :
( ( ( ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( SV320 @ SV565 )
= $false )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2961]) ).
thf(3033,plain,
! [SV141: $i,SV577: $i,SV320: $i > $o] :
( ( ( SV320 @ SV577 )
= $false )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2962]) ).
thf(3034,plain,
! [SV320: $i > $o,SV141: $i,SV589: $i] :
( ( ( in @ SV589 @ SV141 )
= $false )
| ( ( ~ ( SV320 @ SV589 ) )
= $true )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2963]) ).
thf(3035,plain,
! [SV141: $i,SV578: $i,SV320: $i > $o] :
( ( ( SV320 @ SV578 )
= $false )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2964]) ).
thf(3036,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3037,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
| ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2966]) ).
thf(3038,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2967]) ).
thf(3039,plain,
! [SV142: $i,SV518: $i,SV440: $i,SV321: $i] :
( ( ( ! [SY1084: $i] :
( ~ ( in @ SY1084 @ SV321 )
| ~ ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1084 ) @ SV518 )
| ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1084 ) @ SV440 ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2967]) ).
thf(3040,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 )
| ! [SY1089: $i] :
( ~ ( in @ SY1089 @ SV321 )
| ~ ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1089 ) @ SV518 )
| ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1089 ) @ SV440 ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[2968]) ).
thf(3041,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2969]) ).
thf(3042,plain,
! [SV142: $i,SV518: $i,SV440: $i,SV321: $i] :
( ( ( ! [SY1085: $i] :
( ~ ( in @ SY1085 @ SV321 )
| ~ ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1085 ) @ SV518 )
| ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1085 ) @ SV440 ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2969]) ).
thf(3043,plain,
! [SV521: $i,SV154: $i,SV590: $i,SV557: $i,SV329: $i > $o] :
( ( ( SV329 @ SV557 )
= $false )
| ( ( ~ ( SV329 @ SV590 )
| ( SV557 = SV590 ) )
= $true )
| ( ( in @ SV590 @ SV154 )
= $false )
| ( ( in @ SV557 @ SV154 )
= $false )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2970]) ).
thf(3044,plain,
! [SV354: $i,SV498: $i > $o,SV183: $i,SV529: $i > $o] :
( ( ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
| ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) ) )
= $false )
| ( ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2971]) ).
thf(3045,plain,
! [SV354: $i,SV498: $i > $o,SV183: $i,SV529: $i > $o] :
( ( ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) ) )
= $false )
| ( ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2972]) ).
thf(3046,plain,
! [SV183: $i,SV354: $i,SV529: $i > $o,SV498: $i > $o] :
( ( ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
= $false )
| ( ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2972]) ).
thf(3047,plain,
! [SV359: $i > $o,SV592: $i,SV188: $i > $o] :
( ( ( SV188 @ SV592 )
= $false )
| ( ( ~ ! [SY1065: $i] :
( ~ ( SV188 @ SY1065 )
| ( SV592 = SY1065 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2973]) ).
thf(3048,plain,
! [SV188: $i > $o,SV593: $i,SV359: $i > $o] :
( ( ( SV359 @ SV593 )
= $false )
| ( ( ~ ! [SY1066: $i] :
( ~ ( SV359 @ SY1066 )
| ( SV593 = SY1066 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2974]) ).
thf(3049,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2975]) ).
thf(3050,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2976]) ).
thf(3051,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2977]) ).
thf(3052,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2978]) ).
thf(3053,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2979]) ).
thf(3054,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2980]) ).
thf(3055,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2981]) ).
thf(3056,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2982]) ).
thf(3057,plain,
! [SV483: $i,SV611: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV611 )
| ( ( sK85_SY25 @ SV483 @ SV10 )
= SV611 ) )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2984]) ).
thf(3058,plain,
! [SV483: $i,SV604: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV604 ) )
= $true )
| ( ( ( sK74_SY25 @ SV483 @ SV10 )
= SV604 )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2985]) ).
thf(3059,plain,
! [SV14: $i,SV217: $i > $o,SV548: $i] :
( ( ( ~ ( in @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( SV217 @ SV548 )
= $false )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2986]) ).
thf(3060,plain,
! [SV14: $i,SV217: $i > $o,SV561: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( SV217 @ SV561 )
= $false )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[2987]) ).
thf(3061,plain,
! [SV566: $i,SV217: $i > $o,SV14: $i] :
( ( ( ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( SV217 @ SV566 )
= $false )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2988]) ).
thf(3062,plain,
! [SV14: $i,SV583: $i,SV217: $i > $o] :
( ( ( SV217 @ SV583 )
= $false )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( ~ ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $true )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2989]) ).
thf(3063,plain,
! [SV567: $i,SV217: $i > $o,SV14: $i] :
( ( ( ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( SV217 @ SV567 )
= $false )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2990]) ).
thf(3064,plain,
! [SV29: $i,SV230: $i,SV391: $i,SV504: $i,SV596: $i,SV568: $i] :
( ( ( ~ ( in @ ( kpair @ SV568 @ SV596 ) @ SV504 ) )
= $true )
| ( ( in @ ( kpair @ SV568 @ SV596 ) @ SV391 )
= $true )
| ( ( in @ SV596 @ SV230 )
= $false )
| ( ( in @ SV568 @ SV29 )
= $false )
| ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2993]) ).
thf(3065,plain,
! [SV29: $i,SV230: $i,SV391: $i,SV504: $i,SV594: $i,SV562: $i] :
( ( ( in @ ( kpair @ SV562 @ SV594 ) @ SV504 )
= $false )
| ( ( in @ ( kpair @ SV562 @ SV594 ) @ SV391 )
= $true )
| ( ( in @ SV594 @ SV230 )
= $false )
| ( ( in @ SV562 @ SV29 )
= $false )
| ( ( ( ap @ SV29 @ SV230 @ SV391 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) )
= ( ap @ SV29 @ SV230 @ SV504 @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) ) )
= $false )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2994]) ).
thf(3066,plain,
! [SV554: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2997]) ).
thf(3067,plain,
! [SV554: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2998]) ).
thf(3068,plain,
! [SV246: $i > $o,SV605: $i,SV49: $i > $o] :
( ( ( ~ ( ~ ( SV49 @ SV605 )
| ~ ! [SY1086: $i] :
( ~ ( SV49 @ SY1086 )
| ( SV605 = SY1086 ) ) ) )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2999]) ).
thf(3069,plain,
! [SV246: $i > $o,SV600: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV600 )
| ~ ! [SY1077: $i] :
( ~ ( SV49 @ SY1077 )
| ( SV600 = SY1077 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3000]) ).
thf(3070,plain,
! [SV246: $i > $o,SV601: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV601 )
| ~ ! [SY1078: $i] :
( ~ ( SV49 @ SY1078 )
| ( SV601 = SY1078 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3001]) ).
thf(3071,plain,
! [SV246: $i > $o,SV597: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV597 ) )
= $true )
| ( ( ~ ! [SY1070: $i] :
( ~ ( SV49 @ SY1070 )
| ( SV597 = SY1070 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3002]) ).
thf(3072,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ ( sK95_SY139 @ SV489 @ SV53 ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3003]) ).
thf(3073,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ~ ! [SY1071: $i] :
( ~ ( SV53 @ SY1071 )
| ( ( sK95_SY139 @ SV489 @ SV53 )
= SY1071 ) ) )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3003]) ).
thf(3074,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( SV53 @ ( sK92_SY139 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3004]) ).
thf(3075,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY1067: $i] :
( ~ ( SV53 @ SY1067 )
| ( ( sK92_SY139 @ SV489 @ SV53 )
= SY1067 ) ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3005]) ).
thf(3076,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( SV53 @ ( sK93_SY139 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3006]) ).
thf(3077,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY1068: $i] :
( ~ ( SV53 @ SY1068 )
| ( ( sK93_SY139 @ SV489 @ SV53 )
= SY1068 ) ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3007]) ).
thf(3078,plain,
! [SV489: $i,SV612: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ SV612 )
| ( ( sK87_SY139 @ SV489 @ SV53 )
= SV612 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3009]) ).
thf(3079,plain,
! [SV586: $i,SV62: $i,SV574: $i] :
( ( ( in @ SV574 @ SV62 )
= $false )
| ( ( ~ ( in @ SV586 @ SV62 ) )
= $true )
| ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) )
| ( SV574 = SV586 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3011]) ).
thf(3080,plain,
! [SV62: $i,SV555: $i,SV549: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV549 )
| ( in @ SV613 @ SV555 ) )
= $true )
| ( ( ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true )
| ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ SV555 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3012]) ).
thf(3081,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( in @ SV606 @ SV539 )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( ~ ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3013]) ).
thf(3082,plain,
! [SV602: $i,SV539: $i,SV62: $i] :
( ( ( ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3014]) ).
thf(3083,plain,
! [SV491: $i,SV599: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV599 )
| ( SV599
= ( sK88_SY220 @ SV491 @ SV80 ) ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3015]) ).
thf(3084,plain,
! [SV80: $i > $o,SV491: $i,SV599: $i] :
( ( ( ( SV599
!= ( sK88_SY220 @ SV491 @ SV80 ) )
| ( SV80 @ SV599 ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3016]) ).
thf(3085,plain,
! [SV491: $i,SV595: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV595 ) )
= $true )
| ( ( SV595
= ( sK78_SY220 @ SV491 @ SV80 ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3017]) ).
thf(3086,plain,
! [SV80: $i > $o,SV491: $i,SV595: $i] :
( ( ( SV595
!= ( sK78_SY220 @ SV491 @ SV80 ) )
= $true )
| ( ( SV80 @ SV595 )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3018]) ).
thf(3087,plain,
! [SV492: $i,SV88: $i,SV588: $i] :
( ( ( in @ SV588 @ SV88 )
= $false )
| ( ( in @ SV588 @ ( sK36_SY237 @ SV492 @ SV88 ) )
= $false )
| ( ( in @ SV492 @ SV88 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3019]) ).
thf(3088,plain,
! [SV493: $i,SV614: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV614 )
| ( ( sK89_SY261 @ SV493 @ SV98 )
= SV614 ) )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3021]) ).
thf(3089,plain,
! [SV493: $i,SV607: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV607 ) )
= $true )
| ( ( ( sK79_SY261 @ SV493 @ SV98 )
= SV607 )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3022]) ).
thf(3090,plain,
! [SV494: $i,SV608: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ SV608 ) )
= $true )
| ( ( ( sK81_SY305 @ SV494 @ SV113 )
= SV608 )
= $true )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3023]) ).
thf(3091,plain,
! [SV494: $i,SV615: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ SV615 )
| ( ( sK90_SY305 @ SV494 @ SV113 )
= SV615 ) )
= $true )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3025]) ).
thf(3092,plain,
! [SV494: $i,SV609: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ SV609 ) )
= $true )
| ( ( ( sK82_SY305 @ SV494 @ SV113 )
= SV609 )
= $true )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3026]) ).
thf(3093,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ( in @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV550 ) )
= $false )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3027]) ).
thf(3094,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ SV313 )
| ~ ( SV134 @ SV603 @ SV550 ) )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3028]) ).
thf(3095,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV616: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY1092: $i] :
~ ~ ( ~ ( in @ SY1092 @ SV313 )
| ~ ( SV134 @ SY1092 @ SV616 ) ) )
| ~ ( ~ ~ ! [SY1093: $i] :
~ ~ ( ~ ( in @ SY1093 @ SV313 )
| ~ ( SV134 @ SY1093 @ SV616 ) )
| ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) ) ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3029]) ).
thf(3096,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV610: $i] :
( ( ( ~ ( ~ ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY1087: $i] :
~ ~ ( ~ ( in @ SY1087 @ SV313 )
| ~ ( SV134 @ SY1087 @ SV610 ) ) )
| ~ ( ~ ~ ! [SY1088: $i] :
~ ~ ( ~ ( in @ SY1088 @ SV313 )
| ~ ( SV134 @ SY1088 @ SV610 ) )
| ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3030]) ).
thf(3097,plain,
! [SV141: $i,SV320: $i > $o,SV551: $i] :
( ( ( ~ ( in @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( SV320 @ SV551 )
= $false )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3031]) ).
thf(3098,plain,
! [SV141: $i,SV320: $i > $o,SV565: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( SV320 @ SV565 )
= $false )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3032]) ).
thf(3099,plain,
! [SV577: $i,SV320: $i > $o,SV141: $i] :
( ( ( ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( SV320 @ SV577 )
= $false )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3033]) ).
thf(3100,plain,
! [SV141: $i,SV589: $i,SV320: $i > $o] :
( ( ( SV320 @ SV589 )
= $false )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( ~ ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $true )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3034]) ).
thf(3101,plain,
! [SV578: $i,SV320: $i > $o,SV141: $i] :
( ( ( ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( SV320 @ SV578 )
= $false )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3035]) ).
thf(3102,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( in @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3036]) ).
thf(3103,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3104,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3037]) ).
thf(3105,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3038]) ).
thf(3106,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 )
| ~ ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
| ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3039]) ).
thf(3107,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3040]) ).
thf(3108,plain,
! [SV142: $i,SV518: $i,SV440: $i,SV321: $i] :
( ( ( ! [SY1089: $i] :
( ~ ( in @ SY1089 @ SV321 )
| ~ ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1089 ) @ SV518 )
| ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SY1089 ) @ SV440 ) ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3040]) ).
thf(3109,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3041]) ).
thf(3110,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 )
| ~ ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
| ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3042]) ).
thf(3111,plain,
! [SV521: $i,SV154: $i,SV557: $i,SV590: $i,SV329: $i > $o] :
( ( ( ~ ( SV329 @ SV590 ) )
= $true )
| ( ( SV557 = SV590 )
= $true )
| ( ( SV329 @ SV557 )
= $false )
| ( ( in @ SV590 @ SV154 )
= $false )
| ( ( in @ SV557 @ SV154 )
= $false )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3043]) ).
thf(3112,plain,
! [SV354: $i,SV498: $i > $o,SV183: $i,SV529: $i > $o] :
( ( ( ~ ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) ) )
= $false )
| ( ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3113,plain,
! [SV183: $i,SV354: $i,SV529: $i > $o,SV498: $i > $o] :
( ( ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
= $false )
| ( ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3044]) ).
thf(3114,plain,
! [SV354: $i,SV498: $i > $o,SV183: $i,SV529: $i > $o] :
( ( ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $true )
| ( ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $false )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3045]) ).
thf(3115,plain,
! [SV359: $i > $o,SV592: $i,SV188: $i > $o] :
( ( ( ! [SY1065: $i] :
( ~ ( SV188 @ SY1065 )
| ( SV592 = SY1065 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3047]) ).
thf(3116,plain,
! [SV188: $i > $o,SV593: $i,SV359: $i > $o] :
( ( ( ! [SY1066: $i] :
( ~ ( SV359 @ SY1066 )
| ( SV593 = SY1066 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3048]) ).
thf(3117,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3049]) ).
thf(3118,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3050]) ).
thf(3119,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3051]) ).
thf(3120,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3052]) ).
thf(3121,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3053]) ).
thf(3122,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3054]) ).
thf(3123,plain,
! [SV359: $i > $o,SV617: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ SV617 )
| ~ ! [SY1096: $i] :
( ~ ( SV188 @ SY1096 )
| ( SV617 = SY1096 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3055]) ).
thf(3124,plain,
! [SV188: $i > $o,SV618: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ SV618 )
| ~ ! [SY1097: $i] :
( ~ ( SV359 @ SY1097 )
| ( SV618 = SY1097 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3056]) ).
thf(3125,plain,
! [SV483: $i,SV611: $i,SV10: $i > $o] :
( ( ( ~ ( SV10 @ SV611 ) )
= $true )
| ( ( ( sK85_SY25 @ SV483 @ SV10 )
= SV611 )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3057]) ).
thf(3126,plain,
! [SV483: $i,SV604: $i,SV10: $i > $o] :
( ( ( SV10 @ SV604 )
= $false )
| ( ( ( sK74_SY25 @ SV483 @ SV10 )
= SV604 )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV483
= ( sK55_SY943 @ SV483 @ SV10 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3058]) ).
thf(3127,plain,
! [SV14: $i,SV217: $i > $o,SV548: $i] :
( ( ( ~ ( in @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) ) )
= $false )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( SV217 @ SV548 )
= $false )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3128,plain,
! [SV548: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 ) @ emptyset ) )
= $false )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( SV217 @ SV548 )
= $false )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3059]) ).
thf(3129,plain,
! [SV14: $i,SV217: $i > $o,SV561: $i] :
( ( ( ~ ( ~ ( in @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( SV217 @ SV561 )
= $false )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3060]) ).
thf(3130,plain,
! [SV14: $i,SV217: $i > $o,SV566: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( SV217 @ SV566 )
= $false )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3061]) ).
thf(3131,plain,
! [SV583: $i,SV217: $i > $o,SV14: $i] :
( ( ( ! [SY543: $i] :
~ ~ ( ~ ( in @ SY543
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ SY543 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( SV217 @ SV583 )
= $false )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3062]) ).
thf(3132,plain,
! [SV14: $i,SV217: $i > $o,SV567: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( SV217 @ SV567 )
= $false )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3063]) ).
thf(3133,plain,
! [SV29: $i,SV230: $i,SV391: $i,SV504: $i,SV596: $i,SV568: $i] :
( ( ( in @ ( kpair @ SV568 @ SV596 ) @ SV504 )
= $false )
| ( ( in @ ( kpair @ SV568 @ SV596 ) @ SV391 )
= $true )
| ( ( in @ SV596 @ SV230 )
= $false )
| ( ( in @ SV568 @ SV29 )
= $false )
| ( ( in @ ( sK56_SY974 @ SV504 @ SV391 @ SV230 @ SV29 ) @ SV29 )
= $true )
| ( ( func @ SV29 @ SV230 @ SV504 )
= $false )
| ( ( func @ SV29 @ SV230 @ SV391 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3064]) ).
thf(3134,plain,
! [SV554: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3066]) ).
thf(3135,plain,
! [SV554: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3067]) ).
thf(3136,plain,
! [SV246: $i > $o,SV605: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV605 )
| ~ ! [SY1086: $i] :
( ~ ( SV49 @ SY1086 )
| ( SV605 = SY1086 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3068]) ).
thf(3137,plain,
! [SV246: $i > $o,SV600: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV600 ) )
= $true )
| ( ( ~ ! [SY1077: $i] :
( ~ ( SV49 @ SY1077 )
| ( SV600 = SY1077 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3069]) ).
thf(3138,plain,
! [SV246: $i > $o,SV601: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV601 ) )
= $true )
| ( ( ~ ! [SY1078: $i] :
( ~ ( SV49 @ SY1078 )
| ( SV601 = SY1078 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3070]) ).
thf(3139,plain,
! [SV246: $i > $o,SV597: $i,SV49: $i > $o] :
( ( ( SV49 @ SV597 )
= $false )
| ( ( ~ ! [SY1070: $i] :
( ~ ( SV49 @ SY1070 )
| ( SV597 = SY1070 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3071]) ).
thf(3140,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( SV53 @ ( sK95_SY139 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3072]) ).
thf(3141,plain,
! [SV489: $i,SV53: $i > $o] :
( ( ( ! [SY1071: $i] :
( ~ ( SV53 @ SY1071 )
| ( ( sK95_SY139 @ SV489 @ SV53 )
= SY1071 ) ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3073]) ).
thf(3142,plain,
! [SV489: $i,SV619: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ SV619 )
| ( ( sK92_SY139 @ SV489 @ SV53 )
= SV619 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3075]) ).
thf(3143,plain,
! [SV489: $i,SV620: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ SV620 )
| ( ( sK93_SY139 @ SV489 @ SV53 )
= SV620 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3077]) ).
thf(3144,plain,
! [SV489: $i,SV612: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ SV612 ) )
= $true )
| ( ( ( sK87_SY139 @ SV489 @ SV53 )
= SV612 )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3078]) ).
thf(3145,plain,
! [SV574: $i,SV62: $i,SV586: $i] :
( ( ( in @ SV586 @ SV62 )
= $false )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) )
| ( SV574 = SV586 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3079]) ).
thf(3146,plain,
! [SV62: $i,SV555: $i,SV549: $i,SV613: $i] :
( ( ( ~ ( in @ SV613 @ SV549 ) )
= $true )
| ( ( in @ SV613 @ SV555 )
= $true )
| ( ( ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true )
| ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ SV555 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3080]) ).
thf(3147,plain,
! [SV606: $i,SV539: $i,SV62: $i] :
( ( ( ! [SY1012: $i] :
~ ~ ! [SY1013: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ SY1012 @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1013 @ SV539 ) )
| ~ ~ ~ ! [SY1014: $i] :
~ ~ ( ~ ( in @ SY1014 @ SY1012 )
| ~ ( in @ SY1014 @ SV539 ) ) )
| ~ ! [SY850: $i] :
( ~ ( in @ SY850 @ ( sK5_SY153 @ SV62 ) )
| ! [SX6: $i] :
( ~ ( in @ SX6 @ SY850 )
| ( in @ SX6 @ SY1012 ) )
| ( in @ SY1013 @ SY850 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3081]) ).
thf(3148,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ~ ! [SY1102: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1102 @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
| ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SY1104 )
| ( in @ SY1105 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ SY1102 @ SY1104 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3082]) ).
thf(3149,plain,
! [SV491: $i,SV599: $i,SV80: $i > $o] :
( ( ( ~ ( SV80 @ SV599 ) )
= $true )
| ( ( SV599
= ( sK88_SY220 @ SV491 @ SV80 ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3083]) ).
thf(3150,plain,
! [SV80: $i > $o,SV491: $i,SV599: $i] :
( ( ( SV599
!= ( sK88_SY220 @ SV491 @ SV80 ) )
= $true )
| ( ( SV80 @ SV599 )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3084]) ).
thf(3151,plain,
! [SV491: $i,SV595: $i,SV80: $i > $o] :
( ( ( SV80 @ SV595 )
= $false )
| ( ( SV595
= ( sK78_SY220 @ SV491 @ SV80 ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3085]) ).
thf(3152,plain,
! [SV80: $i > $o,SV491: $i,SV595: $i] :
( ( ( SV595
= ( sK78_SY220 @ SV491 @ SV80 ) )
= $false )
| ( ( SV80 @ SV595 )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV491
= ( sK61_SY953 @ SV491 @ SV80 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3086]) ).
thf(3153,plain,
! [SV493: $i,SV614: $i,SV98: $i > $o] :
( ( ( ~ ( SV98 @ SV614 ) )
= $true )
| ( ( ( sK89_SY261 @ SV493 @ SV98 )
= SV614 )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3088]) ).
thf(3154,plain,
! [SV493: $i,SV607: $i,SV98: $i > $o] :
( ( ( SV98 @ SV607 )
= $false )
| ( ( ( sK79_SY261 @ SV493 @ SV98 )
= SV607 )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV493
= ( sK63_SY954 @ SV493 @ SV98 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3089]) ).
thf(3155,plain,
! [SV494: $i,SV608: $i,SV113: $i > $o] :
( ( ( SV113 @ SV608 )
= $false )
| ( ( ( sK81_SY305 @ SV494 @ SV113 )
= SV608 )
= $true )
| ( ( SV113 @ ( sK45_SY303 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3090]) ).
thf(3156,plain,
! [SV494: $i,SV615: $i,SV113: $i > $o] :
( ( ( ~ ( SV113 @ SV615 ) )
= $true )
| ( ( ( sK90_SY305 @ SV494 @ SV113 )
= SV615 )
= $true )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3091]) ).
thf(3157,plain,
! [SV494: $i,SV609: $i,SV113: $i > $o] :
( ( ( SV113 @ SV609 )
= $false )
| ( ( ( sK82_SY305 @ SV494 @ SV113 )
= SV609 )
= $true )
| ( ( ( sK45_SY303 @ SV494 @ SV113 )
= ( sK51_SY1020 @ SV494 @ SV113 ) )
= $false )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3092]) ).
thf(3158,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( ~ ( in @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV313 ) )
= $false )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3093]) ).
thf(3159,plain,
! [SV313: $i,SV550: $i,SV134: $i > $i > $o] :
( ( ( ~ ( SV134 @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV550 ) )
= $false )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3093]) ).
thf(3160,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i,SV603: $i] :
( ( ( ~ ( in @ SV603 @ SV313 ) )
= $true )
| ( ( ~ ( SV134 @ SV603 @ SV550 ) )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3094]) ).
thf(3161,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV616: $i] :
( ( ( ~ ( ~ ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY1092: $i] :
~ ~ ( ~ ( in @ SY1092 @ SV313 )
| ~ ( SV134 @ SY1092 @ SV616 ) ) )
| ~ ( ~ ~ ! [SY1093: $i] :
~ ~ ( ~ ( in @ SY1093 @ SV313 )
| ~ ( SV134 @ SY1093 @ SV616 ) )
| ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3095]) ).
thf(3162,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV610: $i] :
( ( ( ~ ( ~ ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY1087: $i] :
~ ~ ( ~ ( in @ SY1087 @ SV313 )
| ~ ( SV134 @ SY1087 @ SV610 ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3163,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ( ~ ~ ! [SY1088: $i] :
~ ~ ( ~ ( in @ SY1088 @ SV313 )
| ~ ( SV134 @ SY1088 @ SV610 ) )
| ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3096]) ).
thf(3164,plain,
! [SV141: $i,SV320: $i > $o,SV551: $i] :
( ( ( ~ ( in @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) ) )
= $false )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( SV320 @ SV551 )
= $false )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3165,plain,
! [SV551: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 ) @ emptyset ) )
= $false )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( SV320 @ SV551 )
= $false )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3097]) ).
thf(3166,plain,
! [SV141: $i,SV320: $i > $o,SV565: $i] :
( ( ( ~ ( ~ ( in @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( SV320 @ SV565 )
= $false )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3098]) ).
thf(3167,plain,
! [SV141: $i,SV320: $i > $o,SV577: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( SV320 @ SV577 )
= $false )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3099]) ).
thf(3168,plain,
! [SV589: $i,SV320: $i > $o,SV141: $i] :
( ( ( ! [SY705: $i] :
~ ~ ( ~ ( in @ SY705
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ SY705 @ emptyset ) ) ) )
= $false )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( SV320 @ SV589 )
= $false )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3100]) ).
thf(3169,plain,
! [SV141: $i,SV320: $i > $o,SV578: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( SV320 @ SV578 )
= $false )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3101]) ).
thf(3170,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( kpair @ ( sK94_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK102_SY1069 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3103]) ).
thf(3171,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3172,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
| ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3106]) ).
thf(3173,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ SV142 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3107]) ).
thf(3174,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 )
| ~ ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
| ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3108]) ).
thf(3175,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3176,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
| ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3110]) ).
thf(3177,plain,
! [SV521: $i,SV154: $i,SV557: $i,SV590: $i,SV329: $i > $o] :
( ( ( SV329 @ SV590 )
= $false )
| ( ( SV557 = SV590 )
= $true )
| ( ( SV329 @ SV557 )
= $false )
| ( ( in @ SV590 @ SV154 )
= $false )
| ( ( in @ SV557 @ SV154 )
= $false )
| ( ( in @ SV521
@ ( dsetconstr @ SV154
@ ^ [SY720: $i] : ( SV329 @ SY720 ) ) )
= $false )
| ( ( ( dsetconstr @ SV154
@ ^ [SY721: $i] : ( SV329 @ SY721 ) )
= ( setadjoin @ SV521 @ emptyset ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3111]) ).
thf(3178,plain,
! [SV354: $i,SV498: $i > $o,SV183: $i,SV529: $i > $o] :
( ( ( SV529 @ ( sK68_SY1025 @ SV183 @ SV498 @ SV529 @ SV354 ) )
= $true )
| ( ( SV498 @ ( sK48_SY996 @ SV529 @ SV498 @ SV354 @ SV183 ) )
= $true )
| ( ( ( dsetconstr @ SV183
@ ^ [SY968: $i] : ( SV498 @ SY968 ) )
= ( dsetconstr @ SV354
@ ^ [SY999: $i] : ( SV529 @ SY999 ) ) )
= $true )
| ( ( SV183 = SV354 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3112]) ).
thf(3179,plain,
! [SV592: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
| ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3115]) ).
thf(3180,plain,
! [SV593: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
| ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3116]) ).
thf(3181,plain,
! [SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY466: $i] :
~ ~ ( ~ ( SV188 @ SY466 )
| ~ ! [SY467: $i] :
( ~ ( SV188 @ SY467 )
| ( SY466 = SY467 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3117]) ).
thf(3182,plain,
! [SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY770: $i] :
~ ~ ( ~ ( SV359 @ SY770 )
| ~ ! [SY771: $i] :
( ~ ( SV359 @ SY771 )
| ( SY770 = SY771 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3118]) ).
thf(3183,plain,
! [SV359: $i > $o,SV621: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ SV621 )
| ~ ! [SY1110: $i] :
( ~ ( SV188 @ SY1110 )
| ( SV621 = SY1110 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3119]) ).
thf(3184,plain,
! [SV188: $i > $o,SV622: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ SV622 )
| ~ ! [SY1111: $i] :
( ~ ( SV359 @ SY1111 )
| ( SV622 = SY1111 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3120]) ).
thf(3185,plain,
! [SV359: $i > $o,SV623: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ SV623 )
| ~ ! [SY1112: $i] :
( ~ ( SV188 @ SY1112 )
| ( SV623 = SY1112 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3121]) ).
thf(3186,plain,
! [SV188: $i > $o,SV624: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ SV624 )
| ~ ! [SY1113: $i] :
( ~ ( SV359 @ SY1113 )
| ( SV624 = SY1113 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3122]) ).
thf(3187,plain,
! [SV359: $i > $o,SV617: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ SV617 )
| ~ ! [SY1096: $i] :
( ~ ( SV188 @ SY1096 )
| ( SV617 = SY1096 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3123]) ).
thf(3188,plain,
! [SV188: $i > $o,SV618: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ SV618 )
| ~ ! [SY1097: $i] :
( ~ ( SV359 @ SY1097 )
| ( SV618 = SY1097 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3124]) ).
thf(3189,plain,
! [SV483: $i,SV611: $i,SV10: $i > $o] :
( ( ( SV10 @ SV611 )
= $false )
| ( ( ( sK85_SY25 @ SV483 @ SV10 )
= SV611 )
= $true )
| ( ( SV10 @ SV483 )
= $false )
| ( ( SV10 @ ( sK55_SY943 @ SV483 @ SV10 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3125]) ).
thf(3190,plain,
! [SV14: $i,SV217: $i > $o,SV548: $i] :
( ( ( in @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
= $true )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( SV217 @ SV548 )
= $false )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3127]) ).
thf(3191,plain,
! [SV548: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
= ( setadjoin @ ( sK97_SY543 @ SV548 @ SV217 @ SV14 ) @ emptyset ) )
= $true )
| ( ( in @ SV548 @ SV14 )
= $false )
| ( ( SV217 @ SV548 )
= $false )
| ( ( in @ ( sK8_SY540 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3128]) ).
thf(3192,plain,
! [SV14: $i,SV217: $i > $o,SV561: $i] :
( ( ( ~ ( in @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( SV217 @ SV561 )
= $false )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3129]) ).
thf(3193,plain,
! [SV14: $i,SV217: $i > $o,SV566: $i] :
( ( ( ~ ( ~ ( in @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( SV217 @ SV566 )
= $false )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3130]) ).
thf(3194,plain,
! [SV14: $i,SV217: $i > $o,SV583: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( SV217 @ SV583 )
= $false )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3131]) ).
thf(3195,plain,
! [SV14: $i,SV217: $i > $o,SV567: $i] :
( ( ( ~ ( ~ ( in @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( SV217 @ SV567 )
= $false )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3132]) ).
thf(3196,plain,
! [SV554: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3134]) ).
thf(3197,plain,
! [SV554: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3135]) ).
thf(3198,plain,
! [SV246: $i > $o,SV605: $i,SV49: $i > $o] :
( ( ( ~ ( SV49 @ SV605 ) )
= $true )
| ( ( ~ ! [SY1086: $i] :
( ~ ( SV49 @ SY1086 )
| ( SV605 = SY1086 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3136]) ).
thf(3199,plain,
! [SV246: $i > $o,SV600: $i,SV49: $i > $o] :
( ( ( SV49 @ SV600 )
= $false )
| ( ( ~ ! [SY1077: $i] :
( ~ ( SV49 @ SY1077 )
| ( SV600 = SY1077 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3137]) ).
thf(3200,plain,
! [SV246: $i > $o,SV601: $i,SV49: $i > $o] :
( ( ( SV49 @ SV601 )
= $false )
| ( ( ~ ! [SY1078: $i] :
( ~ ( SV49 @ SY1078 )
| ( SV601 = SY1078 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3138]) ).
thf(3201,plain,
! [SV246: $i > $o,SV597: $i,SV49: $i > $o] :
( ( ( ! [SY1070: $i] :
( ~ ( SV49 @ SY1070 )
| ( SV597 = SY1070 ) ) )
= $false )
| ( ( SV49 @ SV597 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3139]) ).
thf(3202,plain,
! [SV489: $i,SV625: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ SV625 )
| ( ( sK95_SY139 @ SV489 @ SV53 )
= SV625 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3141]) ).
thf(3203,plain,
! [SV489: $i,SV619: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ SV619 ) )
= $true )
| ( ( ( sK92_SY139 @ SV489 @ SV53 )
= SV619 )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3142]) ).
thf(3204,plain,
! [SV489: $i,SV620: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ SV620 ) )
= $true )
| ( ( ( sK93_SY139 @ SV489 @ SV53 )
= SV620 )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3143]) ).
thf(3205,plain,
! [SV489: $i,SV612: $i,SV53: $i > $o] :
( ( ( SV53 @ SV612 )
= $false )
| ( ( ( sK87_SY139 @ SV489 @ SV53 )
= SV612 )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3144]) ).
thf(3206,plain,
! [SV586: $i,SV574: $i,SV62: $i] :
( ( ( ~ ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3145]) ).
thf(3207,plain,
! [SV62: $i,SV555: $i,SV549: $i,SV613: $i] :
( ( ( in @ SV613 @ SV549 )
= $false )
| ( ( in @ SV613 @ SV555 )
= $true )
| ( ( ! [SY1037: $i] :
( ~ ( in @ SY1037 @ SV555 )
| ( in @ SY1037 @ SV549 ) ) )
= $true )
| ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ SV555 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3146]) ).
thf(3208,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ~ ! [SY1116: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1116 @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
| ~ ! [SY1118: $i] :
( ~ ( in @ SY1118 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1119: $i] :
( ~ ( in @ SY1119 @ SY1118 )
| ( in @ SY1119 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ SY1116 @ SY1118 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3147]) ).
thf(3209,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ! [SY1102: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1102 @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
| ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SY1104 )
| ( in @ SY1105 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ SY1102 @ SY1104 ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3148]) ).
thf(3210,plain,
! [SV491: $i,SV599: $i,SV80: $i > $o] :
( ( ( SV80 @ SV599 )
= $false )
| ( ( SV599
= ( sK88_SY220 @ SV491 @ SV80 ) )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3149]) ).
thf(3211,plain,
! [SV80: $i > $o,SV491: $i,SV599: $i] :
( ( ( SV599
= ( sK88_SY220 @ SV491 @ SV80 ) )
= $false )
| ( ( SV80 @ SV599 )
= $true )
| ( ( SV80 @ SV491 )
= $false )
| ( ( SV80 @ ( sK61_SY953 @ SV491 @ SV80 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3150]) ).
thf(3212,plain,
! [SV493: $i,SV614: $i,SV98: $i > $o] :
( ( ( SV98 @ SV614 )
= $false )
| ( ( ( sK89_SY261 @ SV493 @ SV98 )
= SV614 )
= $true )
| ( ( SV98 @ SV493 )
= $false )
| ( ( SV98 @ ( sK63_SY954 @ SV493 @ SV98 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3153]) ).
thf(3213,plain,
! [SV494: $i,SV615: $i,SV113: $i > $o] :
( ( ( SV113 @ SV615 )
= $false )
| ( ( ( sK90_SY305 @ SV494 @ SV113 )
= SV615 )
= $true )
| ( ( SV113 @ ( sK51_SY1020 @ SV494 @ SV113 ) )
= $true )
| ( ( SV113 @ SV494 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3156]) ).
thf(3214,plain,
! [SV313: $i,SV134: $i > $i > $o,SV550: $i] :
( ( ( in @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV313 )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3158]) ).
thf(3215,plain,
! [SV313: $i,SV550: $i,SV134: $i > $i > $o] :
( ( ( SV134 @ ( sK99_SY1032 @ SV550 @ SV134 @ SV313 ) @ SV550 )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $false )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3159]) ).
thf(3216,plain,
! [SV550: $i,SV134: $i > $i > $o,SV313: $i,SV603: $i] :
( ( ( in @ SV603 @ SV313 )
= $false )
| ( ( ~ ( SV134 @ SV603 @ SV550 ) )
= $true )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3160]) ).
thf(3217,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV616: $i] :
( ( ( ~ ( ~ ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY1092: $i] :
~ ~ ( ~ ( in @ SY1092 @ SV313 )
| ~ ( SV134 @ SY1092 @ SV616 ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3218,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ( ~ ~ ! [SY1093: $i] :
~ ~ ( ~ ( in @ SY1093 @ SV313 )
| ~ ( SV134 @ SY1093 @ SV616 ) )
| ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) ) ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3161]) ).
thf(3219,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY1087: $i] :
~ ~ ( ~ ( in @ SY1087 @ SV313 )
| ~ ( SV134 @ SY1087 @ SV610 ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3162]) ).
thf(3220,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ~ ! [SY1088: $i] :
~ ~ ( ~ ( in @ SY1088 @ SV313 )
| ~ ( SV134 @ SY1088 @ SV610 ) )
| ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3163]) ).
thf(3221,plain,
! [SV141: $i,SV320: $i > $o,SV551: $i] :
( ( ( in @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
= $true )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( SV320 @ SV551 )
= $false )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3164]) ).
thf(3222,plain,
! [SV551: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
= ( setadjoin @ ( sK101_SY705 @ SV551 @ SV320 @ SV141 ) @ emptyset ) )
= $true )
| ( ( in @ SV551 @ SV141 )
= $false )
| ( ( SV320 @ SV551 )
= $false )
| ( ( in @ ( sK17_SY702 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3165]) ).
thf(3223,plain,
! [SV141: $i,SV320: $i > $o,SV565: $i] :
( ( ( ~ ( in @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( SV320 @ SV565 )
= $false )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3166]) ).
thf(3224,plain,
! [SV141: $i,SV320: $i > $o,SV577: $i] :
( ( ( ~ ( ~ ( in @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( SV320 @ SV577 )
= $false )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3167]) ).
thf(3225,plain,
! [SV141: $i,SV320: $i > $o,SV589: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $false )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( SV320 @ SV589 )
= $false )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3168]) ).
thf(3226,plain,
! [SV141: $i,SV320: $i > $o,SV578: $i] :
( ( ( ~ ( ~ ( in @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( SV320 @ SV578 )
= $false )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3169]) ).
thf(3227,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( in @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3171]) ).
thf(3228,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3172]) ).
thf(3229,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3172]) ).
thf(3230,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( ~ ( in @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3231,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
| ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3174]) ).
thf(3232,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( in @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3175]) ).
thf(3233,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3176]) ).
thf(3234,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3176]) ).
thf(3235,plain,
! [SV592: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3179]) ).
thf(3236,plain,
! [SV188: $i > $o,SV359: $i > $o,SV592: $i] :
( ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3179]) ).
thf(3237,plain,
! [SV593: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3180]) ).
thf(3238,plain,
! [SV359: $i > $o,SV188: $i > $o,SV593: $i] :
( ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3180]) ).
thf(3239,plain,
! [SV359: $i > $o,SV626: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ SV626 )
| ~ ! [SY1122: $i] :
( ~ ( SV188 @ SY1122 )
| ( SV626 = SY1122 ) ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3181]) ).
thf(3240,plain,
! [SV188: $i > $o,SV627: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ SV627 )
| ~ ! [SY1123: $i] :
( ~ ( SV359 @ SY1123 )
| ( SV627 = SY1123 ) ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3182]) ).
thf(3241,plain,
! [SV359: $i > $o,SV621: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ SV621 )
| ~ ! [SY1110: $i] :
( ~ ( SV188 @ SY1110 )
| ( SV621 = SY1110 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3183]) ).
thf(3242,plain,
! [SV188: $i > $o,SV622: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ SV622 )
| ~ ! [SY1111: $i] :
( ~ ( SV359 @ SY1111 )
| ( SV622 = SY1111 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3184]) ).
thf(3243,plain,
! [SV359: $i > $o,SV623: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ SV623 )
| ~ ! [SY1112: $i] :
( ~ ( SV188 @ SY1112 )
| ( SV623 = SY1112 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3185]) ).
thf(3244,plain,
! [SV188: $i > $o,SV624: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ SV624 )
| ~ ! [SY1113: $i] :
( ~ ( SV359 @ SY1113 )
| ( SV624 = SY1113 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3186]) ).
thf(3245,plain,
! [SV359: $i > $o,SV617: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV617 )
| ~ ! [SY1096: $i] :
( ~ ( SV188 @ SY1096 )
| ( SV617 = SY1096 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3187]) ).
thf(3246,plain,
! [SV188: $i > $o,SV618: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV618 )
| ~ ! [SY1097: $i] :
( ~ ( SV359 @ SY1097 )
| ( SV618 = SY1097 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3188]) ).
thf(3247,plain,
! [SV14: $i,SV217: $i > $o,SV561: $i] :
( ( ( ~ ( in @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) ) )
= $false )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( SV217 @ SV561 )
= $false )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3248,plain,
! [SV561: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 ) @ emptyset ) )
= $false )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( SV217 @ SV561 )
= $false )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3192]) ).
thf(3249,plain,
! [SV14: $i,SV217: $i > $o,SV566: $i] :
( ( ( ~ ( in @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( SV217 @ SV566 )
= $false )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3193]) ).
thf(3250,plain,
! [SV14: $i,SV217: $i > $o,SV583: $i] :
( ( ( ~ ( ~ ( in @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( SV217 @ SV583 )
= $false )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3194]) ).
thf(3251,plain,
! [SV14: $i,SV217: $i > $o,SV567: $i] :
( ( ( ~ ( in @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( SV217 @ SV567 )
= $false )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3195]) ).
thf(3252,plain,
! [SV554: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3196]) ).
thf(3253,plain,
! [SV554: $i,SV49: $i > $o,SV628: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV628 )
| ~ ! [SY1124: $i] :
( ~ ( SV246 @ SY1124 )
| ( SV628 = SY1124 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3197]) ).
thf(3254,plain,
! [SV246: $i > $o,SV605: $i,SV49: $i > $o] :
( ( ( SV49 @ SV605 )
= $false )
| ( ( ~ ! [SY1086: $i] :
( ~ ( SV49 @ SY1086 )
| ( SV605 = SY1086 ) ) )
= $true )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3198]) ).
thf(3255,plain,
! [SV246: $i > $o,SV600: $i,SV49: $i > $o] :
( ( ( ! [SY1077: $i] :
( ~ ( SV49 @ SY1077 )
| ( SV600 = SY1077 ) ) )
= $false )
| ( ( SV49 @ SV600 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3199]) ).
thf(3256,plain,
! [SV246: $i > $o,SV601: $i,SV49: $i > $o] :
( ( ( ! [SY1078: $i] :
( ~ ( SV49 @ SY1078 )
| ( SV601 = SY1078 ) ) )
= $false )
| ( ( SV49 @ SV601 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3200]) ).
thf(3257,plain,
! [SV597: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
| ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV597 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3201]) ).
thf(3258,plain,
! [SV489: $i,SV625: $i,SV53: $i > $o] :
( ( ( ~ ( SV53 @ SV625 ) )
= $true )
| ( ( ( sK95_SY139 @ SV489 @ SV53 )
= SV625 )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3202]) ).
thf(3259,plain,
! [SV489: $i,SV619: $i,SV53: $i > $o] :
( ( ( SV53 @ SV619 )
= $false )
| ( ( ( sK92_SY139 @ SV489 @ SV53 )
= SV619 )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3203]) ).
thf(3260,plain,
! [SV489: $i,SV620: $i,SV53: $i > $o] :
( ( ( SV53 @ SV620 )
= $false )
| ( ( ( sK93_SY139 @ SV489 @ SV53 )
= SV620 )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $false )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3204]) ).
thf(3261,plain,
! [SV586: $i,SV574: $i,SV62: $i] :
( ( ( ! [SY1061: $i] :
( ~ ( in @ SY1061 @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ SY1061 )
| ( in @ SV586 @ SY1061 ) )
| ~ ( ~ ( in @ SV586 @ SY1061 )
| ( in @ SV574 @ SY1061 ) ) ) ) )
= $false )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3206]) ).
thf(3262,plain,
! [SV62: $i,SV613: $i,SV549: $i,SV555: $i,SV629: $i] :
( ( ( ~ ( in @ SV629 @ SV555 )
| ( in @ SV629 @ SV549 ) )
= $true )
| ( ( in @ SV613 @ SV555 )
= $true )
| ( ( in @ SV613 @ SV549 )
= $false )
| ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ SV555 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3207]) ).
thf(3263,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ! [SY1116: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1116 @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
| ~ ! [SY1118: $i] :
( ~ ( in @ SY1118 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1119: $i] :
( ~ ( in @ SY1119 @ SY1118 )
| ( in @ SY1119 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ SY1116 @ SY1118 ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3208]) ).
thf(3264,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ! [SY1102: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1102 @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
| ~ ! [SY1104: $i] :
( ~ ( in @ SY1104 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SY1104 )
| ( in @ SY1105 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ SY1102 @ SY1104 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3209]) ).
thf(3265,plain,
! [SV313: $i,SV550: $i,SV603: $i,SV134: $i > $i > $o] :
( ( ( SV134 @ SV603 @ SV550 )
= $false )
| ( ( in @ SV603 @ SV313 )
= $false )
| ( ( in @ SV550 @ ( sK46_SY695 @ SV134 @ SV313 ) )
= $true )
| ( ( in @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV313 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3216]) ).
thf(3266,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
| ~ ! [SY1092: $i] :
~ ~ ( ~ ( in @ SY1092 @ SV313 )
| ~ ( SV134 @ SY1092 @ SV616 ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3217]) ).
thf(3267,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ~ ! [SY1093: $i] :
~ ~ ( ~ ( in @ SY1093 @ SV313 )
| ~ ( SV134 @ SY1093 @ SV616 ) )
| ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3218]) ).
thf(3268,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV610: $i] :
( ( ( ~ ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) ) )
= $true )
| ( ( ~ ! [SY1087: $i] :
~ ~ ( ~ ( in @ SY1087 @ SV313 )
| ~ ( SV134 @ SY1087 @ SV610 ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3219]) ).
thf(3269,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ~ ! [SY1088: $i] :
~ ~ ( ~ ( in @ SY1088 @ SV313 )
| ~ ( SV134 @ SY1088 @ SV610 ) ) )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3220]) ).
thf(3270,plain,
! [SV141: $i,SV320: $i > $o,SV565: $i] :
( ( ( ~ ( in @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) ) )
= $false )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( SV320 @ SV565 )
= $false )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3223]) ).
thf(3271,plain,
! [SV565: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 ) @ emptyset ) )
= $false )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( SV320 @ SV565 )
= $false )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3223]) ).
thf(3272,plain,
! [SV141: $i,SV320: $i > $o,SV577: $i] :
( ( ( ~ ( in @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( SV320 @ SV577 )
= $false )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3224]) ).
thf(3273,plain,
! [SV141: $i,SV320: $i > $o,SV589: $i] :
( ( ( ~ ( ~ ( in @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 ) @ emptyset ) ) ) )
= $true )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( SV320 @ SV589 )
= $false )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3225]) ).
thf(3274,plain,
! [SV141: $i,SV320: $i > $o,SV578: $i] :
( ( ( ~ ( in @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( SV320 @ SV578 )
= $false )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3226]) ).
thf(3275,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( kpair @ ( sK103_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK108_SY1084 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) @ SV321 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3228]) ).
thf(3276,plain,
! [SV321: $i,SV440: $i,SV518: $i,SV142: $i] :
( ( ( in @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) @ SV321 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3230]) ).
thf(3277,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( ~ ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 ) )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3231]) ).
thf(3278,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV440 )
= $false )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3231]) ).
thf(3279,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( kpair @ ( sK104_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK109_SY1085 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV518 )
= $false )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3233]) ).
thf(3280,plain,
! [SV592: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3235]) ).
thf(3281,plain,
! [SV592: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3236]) ).
thf(3282,plain,
! [SV593: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3237]) ).
thf(3283,plain,
! [SV593: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3238]) ).
thf(3284,plain,
! [SV359: $i > $o,SV626: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ SV626 )
| ~ ! [SY1122: $i] :
( ~ ( SV188 @ SY1122 )
| ( SV626 = SY1122 ) ) ) )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3239]) ).
thf(3285,plain,
! [SV188: $i > $o,SV627: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ SV627 )
| ~ ! [SY1123: $i] :
( ~ ( SV359 @ SY1123 )
| ( SV627 = SY1123 ) ) ) )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3240]) ).
thf(3286,plain,
! [SV359: $i > $o,SV621: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV621 )
| ~ ! [SY1110: $i] :
( ~ ( SV188 @ SY1110 )
| ( SV621 = SY1110 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3241]) ).
thf(3287,plain,
! [SV188: $i > $o,SV622: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV622 )
| ~ ! [SY1111: $i] :
( ~ ( SV359 @ SY1111 )
| ( SV622 = SY1111 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3242]) ).
thf(3288,plain,
! [SV359: $i > $o,SV623: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV623 )
| ~ ! [SY1112: $i] :
( ~ ( SV188 @ SY1112 )
| ( SV623 = SY1112 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3243]) ).
thf(3289,plain,
! [SV188: $i > $o,SV624: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV624 )
| ~ ! [SY1113: $i] :
( ~ ( SV359 @ SY1113 )
| ( SV624 = SY1113 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3244]) ).
thf(3290,plain,
! [SV359: $i > $o,SV617: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV617 ) )
= $true )
| ( ( ~ ! [SY1096: $i] :
( ~ ( SV188 @ SY1096 )
| ( SV617 = SY1096 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3245]) ).
thf(3291,plain,
! [SV188: $i > $o,SV618: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV618 ) )
= $true )
| ( ( ~ ! [SY1097: $i] :
( ~ ( SV359 @ SY1097 )
| ( SV618 = SY1097 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3246]) ).
thf(3292,plain,
! [SV14: $i,SV217: $i > $o,SV561: $i] :
( ( ( in @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
= $true )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( SV217 @ SV561 )
= $false )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3247]) ).
thf(3293,plain,
! [SV561: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
= ( setadjoin @ ( sK106_SY543 @ SV561 @ SV217 @ SV14 ) @ emptyset ) )
= $true )
| ( ( in @ SV561 @ SV14 )
= $false )
| ( ( SV217 @ SV561 )
= $false )
| ( ( in @ ( sK30_SY944 @ SV217 @ SV14 ) @ SV14 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3248]) ).
thf(3294,plain,
! [SV14: $i,SV217: $i > $o,SV566: $i] :
( ( ( ~ ( in @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) ) )
= $false )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( SV217 @ SV566 )
= $false )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3249]) ).
thf(3295,plain,
! [SV566: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 ) @ emptyset ) )
= $false )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( SV217 @ SV566 )
= $false )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3249]) ).
thf(3296,plain,
! [SV14: $i,SV217: $i > $o,SV583: $i] :
( ( ( ~ ( in @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
| ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( SV217 @ SV583 )
= $false )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3250]) ).
thf(3297,plain,
! [SV14: $i,SV217: $i > $o,SV567: $i] :
( ( ( ~ ( in @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) ) )
= $false )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( SV217 @ SV567 )
= $false )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3251]) ).
thf(3298,plain,
! [SV567: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 ) @ emptyset ) )
= $false )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( SV217 @ SV567 )
= $false )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3251]) ).
thf(3299,plain,
! [SV554: $i,SV49: $i > $o,SV630: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV630 )
| ~ ! [SY1125: $i] :
( ~ ( SV246 @ SY1125 )
| ( SV630 = SY1125 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3252]) ).
thf(3300,plain,
! [SV554: $i,SV49: $i > $o,SV628: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV628 )
| ~ ! [SY1124: $i] :
( ~ ( SV246 @ SY1124 )
| ( SV628 = SY1124 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3253]) ).
thf(3301,plain,
! [SV246: $i > $o,SV605: $i,SV49: $i > $o] :
( ( ( ! [SY1086: $i] :
( ~ ( SV49 @ SY1086 )
| ( SV605 = SY1086 ) ) )
= $false )
| ( ( SV49 @ SV605 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3254]) ).
thf(3302,plain,
! [SV600: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
| ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV600 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3255]) ).
thf(3303,plain,
! [SV601: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
| ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV601 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3256]) ).
thf(3304,plain,
! [SV597: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV597 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3257]) ).
thf(3305,plain,
! [SV49: $i > $o,SV246: $i > $o,SV597: $i] :
( ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV49 @ SV597 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3257]) ).
thf(3306,plain,
! [SV489: $i,SV625: $i,SV53: $i > $o] :
( ( ( SV53 @ SV625 )
= $false )
| ( ( ( sK95_SY139 @ SV489 @ SV53 )
= SV625 )
= $true )
| ( ( SV53 @ ( sK32_SY951 @ SV489 @ SV53 ) )
= $true )
| ( ( ( sK32_SY951 @ SV489 @ SV53 )
= SV489 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3258]) ).
thf(3307,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( ~ ( in @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( ~ ( ~ ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
| ~ ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) ) )
= $false )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3261]) ).
thf(3308,plain,
! [SV62: $i,SV613: $i,SV549: $i,SV555: $i,SV629: $i] :
( ( ( ~ ( in @ SV629 @ SV555 ) )
= $true )
| ( ( in @ SV629 @ SV549 )
= $true )
| ( ( in @ SV613 @ SV555 )
= $true )
| ( ( in @ SV613 @ SV549 )
= $false )
| ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ SV555 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3262]) ).
thf(3309,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ! [SY1116: $i] :
~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ SY1116 @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
| ~ ! [SY1118: $i] :
( ~ ( in @ SY1118 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1119: $i] :
( ~ ( in @ SY1119 @ SY1118 )
| ( in @ SY1119 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ SY1116 @ SY1118 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3263]) ).
thf(3310,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
| ~ ! [SY1127: $i] :
( ~ ( in @ SY1127 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SY1127 )
| ( in @ SY1105 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SY1127 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3264]) ).
thf(3311,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV616: $i] :
( ( ( ~ ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) ) )
= $true )
| ( ( ~ ! [SY1092: $i] :
~ ~ ( ~ ( in @ SY1092 @ SV313 )
| ~ ( SV134 @ SY1092 @ SV616 ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3266]) ).
thf(3312,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ~ ! [SY1093: $i] :
~ ~ ( ~ ( in @ SY1093 @ SV313 )
| ~ ( SV134 @ SY1093 @ SV616 ) ) )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3267]) ).
thf(3313,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV610: $i] :
( ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( ~ ! [SY1087: $i] :
~ ~ ( ~ ( in @ SY1087 @ SV313 )
| ~ ( SV134 @ SY1087 @ SV610 ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3268]) ).
thf(3314,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ! [SY1088: $i] :
~ ~ ( ~ ( in @ SY1088 @ SV313 )
| ~ ( SV134 @ SY1088 @ SV610 ) ) )
= $false )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3269]) ).
thf(3315,plain,
! [SV141: $i,SV320: $i > $o,SV565: $i] :
( ( ( in @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
= $true )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( SV320 @ SV565 )
= $false )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3270]) ).
thf(3316,plain,
! [SV565: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
= ( setadjoin @ ( sK107_SY705 @ SV565 @ SV320 @ SV141 ) @ emptyset ) )
= $true )
| ( ( in @ SV565 @ SV141 )
= $false )
| ( ( SV320 @ SV565 )
= $false )
| ( ( in @ ( sK33_SY960 @ SV320 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3271]) ).
thf(3317,plain,
! [SV141: $i,SV320: $i > $o,SV577: $i] :
( ( ( ~ ( in @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) ) )
= $false )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( SV320 @ SV577 )
= $false )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3272]) ).
thf(3318,plain,
! [SV577: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 ) @ emptyset ) )
= $false )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( SV320 @ SV577 )
= $false )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3272]) ).
thf(3319,plain,
! [SV141: $i,SV320: $i > $o,SV589: $i] :
( ( ( ~ ( in @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
| ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 ) @ emptyset ) ) )
= $false )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( SV320 @ SV589 )
= $false )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3273]) ).
thf(3320,plain,
! [SV141: $i,SV320: $i > $o,SV578: $i] :
( ( ( ~ ( in @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) ) )
= $false )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( SV320 @ SV578 )
= $false )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3321,plain,
! [SV578: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 ) @ emptyset ) )
= $false )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( SV320 @ SV578 )
= $false )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3274]) ).
thf(3322,plain,
! [SV142: $i,SV321: $i,SV518: $i,SV440: $i] :
( ( ( in @ ( kpair @ ( sK105_SY988 @ SV440 @ SV518 @ SV321 @ SV142 ) @ ( sK115_SY1089 @ SV142 @ SV518 @ SV440 @ SV321 ) ) @ SV518 )
= $true )
| ( ( SV440 = SV518 )
= $true )
| ( ( in @ ( kpair @ ( sK65_SY986 @ SV518 @ SV440 @ SV321 @ SV142 ) @ ( sK72_SY1034 @ SV142 @ SV440 @ SV518 @ SV321 ) ) @ SV440 )
= $true )
| ( ( subset @ SV518 @ ( cartprod @ SV142 @ SV321 ) )
= $false )
| ( ( subset @ SV440 @ ( cartprod @ SV142 @ SV321 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3277]) ).
thf(3323,plain,
! [SV592: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3280]) ).
thf(3324,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK126_SY768 @ SV592 @ SV188 @ SV359 ) )
| ~ ! [SY1129: $i] :
( ~ ( SV359 @ SY1129 )
| ( ( sK126_SY768 @ SV592 @ SV188 @ SV359 )
= SY1129 ) ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3281]) ).
thf(3325,plain,
! [SV593: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3282]) ).
thf(3326,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK127_SY472 @ SV593 @ SV359 @ SV188 ) )
| ~ ! [SY1130: $i] :
( ~ ( SV188 @ SY1130 )
| ( ( sK127_SY472 @ SV593 @ SV359 @ SV188 )
= SY1130 ) ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3283]) ).
thf(3327,plain,
! [SV359: $i > $o,SV626: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV626 )
| ~ ! [SY1122: $i] :
( ~ ( SV188 @ SY1122 )
| ( SV626 = SY1122 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3284]) ).
thf(3328,plain,
! [SV188: $i > $o,SV627: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV627 )
| ~ ! [SY1123: $i] :
( ~ ( SV359 @ SY1123 )
| ( SV627 = SY1123 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3285]) ).
thf(3329,plain,
! [SV359: $i > $o,SV621: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV621 ) )
= $true )
| ( ( ~ ! [SY1110: $i] :
( ~ ( SV188 @ SY1110 )
| ( SV621 = SY1110 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3286]) ).
thf(3330,plain,
! [SV188: $i > $o,SV622: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV622 ) )
= $true )
| ( ( ~ ! [SY1111: $i] :
( ~ ( SV359 @ SY1111 )
| ( SV622 = SY1111 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3287]) ).
thf(3331,plain,
! [SV359: $i > $o,SV623: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV623 ) )
= $true )
| ( ( ~ ! [SY1112: $i] :
( ~ ( SV188 @ SY1112 )
| ( SV623 = SY1112 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3288]) ).
thf(3332,plain,
! [SV188: $i > $o,SV624: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV624 ) )
= $true )
| ( ( ~ ! [SY1113: $i] :
( ~ ( SV359 @ SY1113 )
| ( SV624 = SY1113 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3289]) ).
thf(3333,plain,
! [SV359: $i > $o,SV617: $i,SV188: $i > $o] :
( ( ( SV188 @ SV617 )
= $false )
| ( ( ~ ! [SY1096: $i] :
( ~ ( SV188 @ SY1096 )
| ( SV617 = SY1096 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3290]) ).
thf(3334,plain,
! [SV188: $i > $o,SV618: $i,SV359: $i > $o] :
( ( ( SV359 @ SV618 )
= $false )
| ( ( ~ ! [SY1097: $i] :
( ~ ( SV359 @ SY1097 )
| ( SV618 = SY1097 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3291]) ).
thf(3335,plain,
! [SV14: $i,SV217: $i > $o,SV566: $i] :
( ( ( in @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
= $true )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( SV217 @ SV566 )
= $false )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3294]) ).
thf(3336,plain,
! [SV566: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
= ( setadjoin @ ( sK110_SY543 @ SV566 @ SV217 @ SV14 ) @ emptyset ) )
= $true )
| ( ( in @ SV566 @ SV14 )
= $false )
| ( ( SV217 @ SV566 )
= $false )
| ( ( SV217 @ ( sK8_SY540 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3295]) ).
thf(3337,plain,
! [SV14: $i,SV217: $i > $o,SV583: $i] :
( ( ( ~ ( in @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) ) )
= $false )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( SV217 @ SV583 )
= $false )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3296]) ).
thf(3338,plain,
! [SV583: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
!= ( setadjoin @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 ) @ emptyset ) )
= $false )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( SV217 @ SV583 )
= $false )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3296]) ).
thf(3339,plain,
! [SV14: $i,SV217: $i > $o,SV567: $i] :
( ( ( in @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
= $true )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( SV217 @ SV567 )
= $false )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3297]) ).
thf(3340,plain,
! [SV567: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
= ( setadjoin @ ( sK111_SY543 @ SV567 @ SV217 @ SV14 ) @ emptyset ) )
= $true )
| ( ( in @ SV567 @ SV14 )
= $false )
| ( ( SV217 @ SV567 )
= $false )
| ( ( ( sK8_SY540 @ SV217 @ SV14 )
= ( sK30_SY944 @ SV217 @ SV14 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3298]) ).
thf(3341,plain,
! [SV554: $i,SV49: $i > $o,SV630: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV630 )
| ~ ! [SY1125: $i] :
( ~ ( SV246 @ SY1125 )
| ( SV630 = SY1125 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3299]) ).
thf(3342,plain,
! [SV554: $i,SV49: $i > $o,SV628: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV628 )
| ~ ! [SY1124: $i] :
( ~ ( SV246 @ SY1124 )
| ( SV628 = SY1124 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3300]) ).
thf(3343,plain,
! [SV605: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
| ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV605 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3301]) ).
thf(3344,plain,
! [SV600: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV600 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3345,plain,
! [SV49: $i > $o,SV246: $i > $o,SV600: $i] :
( ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ SV600 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3302]) ).
thf(3346,plain,
! [SV601: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV601 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3303]) ).
thf(3347,plain,
! [SV49: $i > $o,SV246: $i > $o,SV601: $i] :
( ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV49 @ SV601 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3303]) ).
thf(3348,plain,
! [SV597: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3304]) ).
thf(3349,plain,
! [SV597: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3305]) ).
thf(3350,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( ~ ( in @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) @ ( sK5_SY153 @ SV62 ) ) )
= $false )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3307]) ).
thf(3351,plain,
! [SV62: $i,SV586: $i,SV574: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
| ~ ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) ) )
= $false )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3307]) ).
thf(3352,plain,
! [SV62: $i,SV613: $i,SV549: $i,SV555: $i,SV629: $i] :
( ( ( in @ SV629 @ SV555 )
= $false )
| ( ( in @ SV629 @ SV549 )
= $true )
| ( ( in @ SV613 @ SV555 )
= $true )
| ( ( in @ SV613 @ SV549 )
= $false )
| ( ( in @ SV549 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ SV555 @ ( sK5_SY153 @ SV62 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3308]) ).
thf(3353,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
| ~ ! [SY1132: $i] :
( ~ ( in @ SY1132 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1119: $i] :
( ~ ( in @ SY1119 @ SY1132 )
| ( in @ SY1119 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SY1132 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3309]) ).
thf(3354,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
| ~ ! [SY1127: $i] :
( ~ ( in @ SY1127 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SY1127 )
| ( in @ SY1105 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SY1127 ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3310]) ).
thf(3355,plain,
! [SV313: $i,SV134: $i > $i > $o,SV541: $i,SV616: $i] :
( ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( ~ ! [SY1092: $i] :
~ ~ ( ~ ( in @ SY1092 @ SV313 )
| ~ ( SV134 @ SY1092 @ SV616 ) ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3311]) ).
thf(3356,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ~ ! [SY1093: $i] :
~ ~ ( ~ ( in @ SY1093 @ SV313 )
| ~ ( SV134 @ SY1093 @ SV616 ) ) )
= $false )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3312]) ).
thf(3357,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY1087: $i] :
~ ~ ( ~ ( in @ SY1087 @ SV313 )
| ~ ( SV134 @ SY1087 @ SV610 ) ) )
= $false )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3313]) ).
thf(3358,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY1088: $i] :
~ ~ ( ~ ( in @ SY1088 @ SV313 )
| ~ ( SV134 @ SY1088 @ SV610 ) ) )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3314]) ).
thf(3359,plain,
! [SV141: $i,SV320: $i > $o,SV577: $i] :
( ( ( in @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
= $true )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( SV320 @ SV577 )
= $false )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3317]) ).
thf(3360,plain,
! [SV577: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
= ( setadjoin @ ( sK113_SY705 @ SV577 @ SV320 @ SV141 ) @ emptyset ) )
= $true )
| ( ( in @ SV577 @ SV141 )
= $false )
| ( ( SV320 @ SV577 )
= $false )
| ( ( SV320 @ ( sK17_SY702 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3318]) ).
thf(3361,plain,
! [SV141: $i,SV320: $i > $o,SV589: $i] :
( ( ( ~ ( in @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) ) )
= $false )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( SV320 @ SV589 )
= $false )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3319]) ).
thf(3362,plain,
! [SV589: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
!= ( setadjoin @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 ) @ emptyset ) )
= $false )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( SV320 @ SV589 )
= $false )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3319]) ).
thf(3363,plain,
! [SV141: $i,SV320: $i > $o,SV578: $i] :
( ( ( in @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
= $true )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( SV320 @ SV578 )
= $false )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3320]) ).
thf(3364,plain,
! [SV578: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
= ( setadjoin @ ( sK114_SY705 @ SV578 @ SV320 @ SV141 ) @ emptyset ) )
= $true )
| ( ( in @ SV578 @ SV141 )
= $false )
| ( ( SV320 @ SV578 )
= $false )
| ( ( ( sK17_SY702 @ SV320 @ SV141 )
= ( sK33_SY960 @ SV320 @ SV141 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3321]) ).
thf(3365,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK130_SY768 @ SV592 @ SV188 @ SV359 ) )
| ~ ! [SY1134: $i] :
( ~ ( SV359 @ SY1134 )
| ( ( sK130_SY768 @ SV592 @ SV188 @ SV359 )
= SY1134 ) ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3323]) ).
thf(3366,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK126_SY768 @ SV592 @ SV188 @ SV359 ) )
| ~ ! [SY1129: $i] :
( ~ ( SV359 @ SY1129 )
| ( ( sK126_SY768 @ SV592 @ SV188 @ SV359 )
= SY1129 ) ) ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3324]) ).
thf(3367,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK131_SY472 @ SV593 @ SV359 @ SV188 ) )
| ~ ! [SY1135: $i] :
( ~ ( SV188 @ SY1135 )
| ( ( sK131_SY472 @ SV593 @ SV359 @ SV188 )
= SY1135 ) ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3325]) ).
thf(3368,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK127_SY472 @ SV593 @ SV359 @ SV188 ) )
| ~ ! [SY1130: $i] :
( ~ ( SV188 @ SY1130 )
| ( ( sK127_SY472 @ SV593 @ SV359 @ SV188 )
= SY1130 ) ) ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3326]) ).
thf(3369,plain,
! [SV359: $i > $o,SV626: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV626 ) )
= $true )
| ( ( ~ ! [SY1122: $i] :
( ~ ( SV188 @ SY1122 )
| ( SV626 = SY1122 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3327]) ).
thf(3370,plain,
! [SV188: $i > $o,SV627: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV627 ) )
= $true )
| ( ( ~ ! [SY1123: $i] :
( ~ ( SV359 @ SY1123 )
| ( SV627 = SY1123 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3328]) ).
thf(3371,plain,
! [SV359: $i > $o,SV621: $i,SV188: $i > $o] :
( ( ( SV188 @ SV621 )
= $false )
| ( ( ~ ! [SY1110: $i] :
( ~ ( SV188 @ SY1110 )
| ( SV621 = SY1110 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3329]) ).
thf(3372,plain,
! [SV188: $i > $o,SV622: $i,SV359: $i > $o] :
( ( ( SV359 @ SV622 )
= $false )
| ( ( ~ ! [SY1111: $i] :
( ~ ( SV359 @ SY1111 )
| ( SV622 = SY1111 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3330]) ).
thf(3373,plain,
! [SV359: $i > $o,SV623: $i,SV188: $i > $o] :
( ( ( SV188 @ SV623 )
= $false )
| ( ( ~ ! [SY1112: $i] :
( ~ ( SV188 @ SY1112 )
| ( SV623 = SY1112 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3331]) ).
thf(3374,plain,
! [SV188: $i > $o,SV624: $i,SV359: $i > $o] :
( ( ( SV359 @ SV624 )
= $false )
| ( ( ~ ! [SY1113: $i] :
( ~ ( SV359 @ SY1113 )
| ( SV624 = SY1113 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3332]) ).
thf(3375,plain,
! [SV359: $i > $o,SV617: $i,SV188: $i > $o] :
( ( ( ! [SY1096: $i] :
( ~ ( SV188 @ SY1096 )
| ( SV617 = SY1096 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3333]) ).
thf(3376,plain,
! [SV188: $i > $o,SV618: $i,SV359: $i > $o] :
( ( ( ! [SY1097: $i] :
( ~ ( SV359 @ SY1097 )
| ( SV618 = SY1097 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3334]) ).
thf(3377,plain,
! [SV14: $i,SV217: $i > $o,SV583: $i] :
( ( ( in @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 )
@ ( dsetconstr @ SV14
@ ^ [SY544: $i] : ( SV217 @ SY544 ) ) )
= $true )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( SV217 @ SV583 )
= $false )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3337]) ).
thf(3378,plain,
! [SV583: $i,SV217: $i > $o,SV14: $i] :
( ( ( ( dsetconstr @ SV14
@ ^ [SY545: $i] : ( SV217 @ SY545 ) )
= ( setadjoin @ ( sK118_SY543 @ SV583 @ SV217 @ SV14 ) @ emptyset ) )
= $true )
| ( ( in @ SV583 @ SV14 )
= $false )
| ( ( SV217 @ SV583 )
= $false )
| ( ( SV217 @ ( sK30_SY944 @ SV217 @ SV14 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3338]) ).
thf(3379,plain,
! [SV554: $i,SV49: $i > $o,SV630: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV630 )
| ~ ! [SY1125: $i] :
( ~ ( SV246 @ SY1125 )
| ( SV630 = SY1125 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3341]) ).
thf(3380,plain,
! [SV554: $i,SV49: $i > $o,SV628: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV628 ) )
= $true )
| ( ( ~ ! [SY1124: $i] :
( ~ ( SV246 @ SY1124 )
| ( SV628 = SY1124 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3342]) ).
thf(3381,plain,
! [SV605: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( ~ ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) ) )
= $false )
| ( ( SV49 @ SV605 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3343]) ).
thf(3382,plain,
! [SV49: $i > $o,SV246: $i > $o,SV605: $i] :
( ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ SV605 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3343]) ).
thf(3383,plain,
! [SV600: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3344]) ).
thf(3384,plain,
! [SV600: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3345]) ).
thf(3385,plain,
! [SV601: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3346]) ).
thf(3386,plain,
! [SV601: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3347]) ).
thf(3387,plain,
! [SV597: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3348]) ).
thf(3388,plain,
! [SV597: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3349]) ).
thf(3389,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( in @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3350]) ).
thf(3390,plain,
! [SV62: $i,SV586: $i,SV574: $i] :
( ( ( ~ ( ~ ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
| ~ ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3351]) ).
thf(3391,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
| ~ ! [SY1132: $i] :
( ~ ( in @ SY1132 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1119: $i] :
( ~ ( in @ SY1119 @ SY1132 )
| ( in @ SY1119 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SY1132 ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3353]) ).
thf(3392,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
| ~ ! [SY1127: $i] :
( ~ ( in @ SY1127 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SY1127 )
| ( in @ SY1105 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SY1127 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3354]) ).
thf(3393,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY1092: $i] :
~ ~ ( ~ ( in @ SY1092 @ SV313 )
| ~ ( SV134 @ SY1092 @ SV616 ) ) )
= $false )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3355]) ).
thf(3394,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i] :
( ( ( ! [SY1093: $i] :
~ ~ ( ~ ( in @ SY1093 @ SV313 )
| ~ ( SV134 @ SY1093 @ SV616 ) ) )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3356]) ).
thf(3395,plain,
! [SV313: $i,SV134: $i > $i > $o,SV610: $i,SV541: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV610 ) ) )
= $false )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3357]) ).
thf(3396,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i,SV631: $i] :
( ( ( ~ ~ ( ~ ( in @ SV631 @ SV313 )
| ~ ( SV134 @ SV631 @ SV610 ) ) )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3358]) ).
thf(3397,plain,
! [SV141: $i,SV320: $i > $o,SV589: $i] :
( ( ( in @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 )
@ ( dsetconstr @ SV141
@ ^ [SY706: $i] : ( SV320 @ SY706 ) ) )
= $true )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( SV320 @ SV589 )
= $false )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3361]) ).
thf(3398,plain,
! [SV589: $i,SV320: $i > $o,SV141: $i] :
( ( ( ( dsetconstr @ SV141
@ ^ [SY707: $i] : ( SV320 @ SY707 ) )
= ( setadjoin @ ( sK120_SY705 @ SV589 @ SV320 @ SV141 ) @ emptyset ) )
= $true )
| ( ( in @ SV589 @ SV141 )
= $false )
| ( ( SV320 @ SV589 )
= $false )
| ( ( SV320 @ ( sK33_SY960 @ SV320 @ SV141 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3362]) ).
thf(3399,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK130_SY768 @ SV592 @ SV188 @ SV359 ) )
| ~ ! [SY1134: $i] :
( ~ ( SV359 @ SY1134 )
| ( ( sK130_SY768 @ SV592 @ SV188 @ SV359 )
= SY1134 ) ) ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3365]) ).
thf(3400,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK126_SY768 @ SV592 @ SV188 @ SV359 ) )
| ~ ! [SY1129: $i] :
( ~ ( SV359 @ SY1129 )
| ( ( sK126_SY768 @ SV592 @ SV188 @ SV359 )
= SY1129 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3366]) ).
thf(3401,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK131_SY472 @ SV593 @ SV359 @ SV188 ) )
| ~ ! [SY1135: $i] :
( ~ ( SV188 @ SY1135 )
| ( ( sK131_SY472 @ SV593 @ SV359 @ SV188 )
= SY1135 ) ) ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3367]) ).
thf(3402,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK127_SY472 @ SV593 @ SV359 @ SV188 ) )
| ~ ! [SY1130: $i] :
( ~ ( SV188 @ SY1130 )
| ( ( sK127_SY472 @ SV593 @ SV359 @ SV188 )
= SY1130 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3368]) ).
thf(3403,plain,
! [SV359: $i > $o,SV626: $i,SV188: $i > $o] :
( ( ( SV188 @ SV626 )
= $false )
| ( ( ~ ! [SY1122: $i] :
( ~ ( SV188 @ SY1122 )
| ( SV626 = SY1122 ) ) )
= $true )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3369]) ).
thf(3404,plain,
! [SV188: $i > $o,SV627: $i,SV359: $i > $o] :
( ( ( SV359 @ SV627 )
= $false )
| ( ( ~ ! [SY1123: $i] :
( ~ ( SV359 @ SY1123 )
| ( SV627 = SY1123 ) ) )
= $true )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3370]) ).
thf(3405,plain,
! [SV359: $i > $o,SV621: $i,SV188: $i > $o] :
( ( ( ! [SY1110: $i] :
( ~ ( SV188 @ SY1110 )
| ( SV621 = SY1110 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3371]) ).
thf(3406,plain,
! [SV188: $i > $o,SV622: $i,SV359: $i > $o] :
( ( ( ! [SY1111: $i] :
( ~ ( SV359 @ SY1111 )
| ( SV622 = SY1111 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3372]) ).
thf(3407,plain,
! [SV359: $i > $o,SV623: $i,SV188: $i > $o] :
( ( ( ! [SY1112: $i] :
( ~ ( SV188 @ SY1112 )
| ( SV623 = SY1112 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3373]) ).
thf(3408,plain,
! [SV188: $i > $o,SV624: $i,SV359: $i > $o] :
( ( ( ! [SY1113: $i] :
( ~ ( SV359 @ SY1113 )
| ( SV624 = SY1113 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3374]) ).
thf(3409,plain,
! [SV617: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
| ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3375]) ).
thf(3410,plain,
! [SV618: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
| ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3376]) ).
thf(3411,plain,
! [SV554: $i,SV49: $i > $o,SV630: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV630 ) )
= $true )
| ( ( ~ ! [SY1125: $i] :
( ~ ( SV246 @ SY1125 )
| ( SV630 = SY1125 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3379]) ).
thf(3412,plain,
! [SV554: $i,SV49: $i > $o,SV628: $i,SV246: $i > $o] :
( ( ( SV246 @ SV628 )
= $false )
| ( ( ~ ! [SY1124: $i] :
( ~ ( SV246 @ SY1124 )
| ( SV628 = SY1124 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3380]) ).
thf(3413,plain,
! [SV605: $i,SV246: $i > $o,SV49: $i > $o] :
( ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) )
| ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3381]) ).
thf(3414,plain,
! [SV605: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3382]) ).
thf(3415,plain,
! [SV600: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3383]) ).
thf(3416,plain,
! [SV600: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3384]) ).
thf(3417,plain,
! [SV601: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3385]) ).
thf(3418,plain,
! [SV601: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3386]) ).
thf(3419,plain,
! [SV597: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3387]) ).
thf(3420,plain,
! [SV597: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3388]) ).
thf(3421,plain,
! [SV62: $i,SV586: $i,SV574: $i] :
( ( ( ~ ( ~ ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3390]) ).
thf(3422,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
| ~ ! [SY1132: $i] :
( ~ ( in @ SY1132 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1119: $i] :
( ~ ( in @ SY1119 @ SY1132 )
| ( in @ SY1119 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SY1132 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3391]) ).
thf(3423,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3392]) ).
thf(3424,plain,
! [SV539: $i,SV602: $i,SV62: $i] :
( ( ( ~ ! [SY1127: $i] :
( ~ ( in @ SY1127 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SY1127 )
| ( in @ SY1105 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SY1127 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3392]) ).
thf(3425,plain,
! [SV313: $i,SV134: $i > $i > $o,SV616: $i,SV541: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV616 ) ) )
= $false )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3393]) ).
thf(3426,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i,SV632: $i] :
( ( ( ~ ~ ( ~ ( in @ SV632 @ SV313 )
| ~ ( SV134 @ SV632 @ SV616 ) ) )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3394]) ).
thf(3427,plain,
! [SV313: $i,SV134: $i > $i > $o,SV610: $i,SV541: $i] :
( ( ( ~ ( ~ ( in @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV610 ) ) )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3395]) ).
thf(3428,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i,SV631: $i] :
( ( ( ~ ( ~ ( in @ SV631 @ SV313 )
| ~ ( SV134 @ SV631 @ SV610 ) ) )
= $false )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3396]) ).
thf(3429,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK130_SY768 @ SV592 @ SV188 @ SV359 ) )
| ~ ! [SY1134: $i] :
( ~ ( SV359 @ SY1134 )
| ( ( sK130_SY768 @ SV592 @ SV188 @ SV359 )
= SY1134 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3399]) ).
thf(3430,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK126_SY768 @ SV592 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3400]) ).
thf(3431,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1129: $i] :
( ~ ( SV359 @ SY1129 )
| ( ( sK126_SY768 @ SV592 @ SV188 @ SV359 )
= SY1129 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3400]) ).
thf(3432,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK131_SY472 @ SV593 @ SV359 @ SV188 ) )
| ~ ! [SY1135: $i] :
( ~ ( SV188 @ SY1135 )
| ( ( sK131_SY472 @ SV593 @ SV359 @ SV188 )
= SY1135 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3401]) ).
thf(3433,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK127_SY472 @ SV593 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3402]) ).
thf(3434,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1130: $i] :
( ~ ( SV188 @ SY1130 )
| ( ( sK127_SY472 @ SV593 @ SV359 @ SV188 )
= SY1130 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3402]) ).
thf(3435,plain,
! [SV359: $i > $o,SV626: $i,SV188: $i > $o] :
( ( ( ! [SY1122: $i] :
( ~ ( SV188 @ SY1122 )
| ( SV626 = SY1122 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3403]) ).
thf(3436,plain,
! [SV188: $i > $o,SV627: $i,SV359: $i > $o] :
( ( ( ! [SY1123: $i] :
( ~ ( SV359 @ SY1123 )
| ( SV627 = SY1123 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3404]) ).
thf(3437,plain,
! [SV621: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
| ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3405]) ).
thf(3438,plain,
! [SV622: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
| ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3406]) ).
thf(3439,plain,
! [SV623: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
| ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3407]) ).
thf(3440,plain,
! [SV624: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
| ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3408]) ).
thf(3441,plain,
! [SV617: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3409]) ).
thf(3442,plain,
! [SV188: $i > $o,SV359: $i > $o,SV617: $i] :
( ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3409]) ).
thf(3443,plain,
! [SV618: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3410]) ).
thf(3444,plain,
! [SV359: $i > $o,SV188: $i > $o,SV618: $i] :
( ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3410]) ).
thf(3445,plain,
! [SV554: $i,SV49: $i > $o,SV630: $i,SV246: $i > $o] :
( ( ( SV246 @ SV630 )
= $false )
| ( ( ~ ! [SY1125: $i] :
( ~ ( SV246 @ SY1125 )
| ( SV630 = SY1125 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3411]) ).
thf(3446,plain,
! [SV554: $i,SV49: $i > $o,SV628: $i,SV246: $i > $o] :
( ( ( ! [SY1124: $i] :
( ~ ( SV246 @ SY1124 )
| ( SV628 = SY1124 ) ) )
= $false )
| ( ( SV246 @ SV628 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3412]) ).
thf(3447,plain,
! [SV605: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3413]) ).
thf(3448,plain,
! [SV605: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3414]) ).
thf(3449,plain,
! [SV600: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3415]) ).
thf(3450,plain,
! [SV600: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3416]) ).
thf(3451,plain,
! [SV601: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3417]) ).
thf(3452,plain,
! [SV601: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3418]) ).
thf(3453,plain,
! [SV597: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3419]) ).
thf(3454,plain,
! [SV597: $i,SV49: $i > $o,SV633: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV633 )
| ~ ! [SY1136: $i] :
( ~ ( SV246 @ SY1136 )
| ( SV633 = SY1136 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3420]) ).
thf(3455,plain,
! [SV62: $i,SV586: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3421]) ).
thf(3456,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3422]) ).
thf(3457,plain,
! [SV539: $i,SV606: $i,SV62: $i] :
( ( ( ~ ! [SY1132: $i] :
( ~ ( in @ SY1132 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1119: $i] :
( ~ ( in @ SY1119 @ SY1132 )
| ( in @ SY1119 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SY1132 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3422]) ).
thf(3458,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3423]) ).
thf(3459,plain,
! [SV539: $i,SV602: $i,SV62: $i] :
( ( ( ! [SY1127: $i] :
( ~ ( in @ SY1127 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1105: $i] :
( ~ ( in @ SY1105 @ SY1127 )
| ( in @ SY1105 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SY1127 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3424]) ).
thf(3460,plain,
! [SV313: $i,SV134: $i > $i > $o,SV616: $i,SV541: $i] :
( ( ( ~ ( ~ ( in @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV616 ) ) )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3425]) ).
thf(3461,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i,SV632: $i] :
( ( ( ~ ( ~ ( in @ SV632 @ SV313 )
| ~ ( SV134 @ SV632 @ SV616 ) ) )
= $false )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3426]) ).
thf(3462,plain,
! [SV313: $i,SV134: $i > $i > $o,SV610: $i,SV541: $i] :
( ( ( ~ ( in @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV610 ) )
= $false )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3427]) ).
thf(3463,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ SV313 )
| ~ ( SV134 @ SV631 @ SV610 ) )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3428]) ).
thf(3464,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK130_SY768 @ SV592 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3429]) ).
thf(3465,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1134: $i] :
( ~ ( SV359 @ SY1134 )
| ( ( sK130_SY768 @ SV592 @ SV188 @ SV359 )
= SY1134 ) ) )
= $false )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3429]) ).
thf(3466,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK126_SY768 @ SV592 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3430]) ).
thf(3467,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ! [SY1129: $i] :
( ~ ( SV359 @ SY1129 )
| ( ( sK126_SY768 @ SV592 @ SV188 @ SV359 )
= SY1129 ) ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3431]) ).
thf(3468,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK131_SY472 @ SV593 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3469,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1135: $i] :
( ~ ( SV188 @ SY1135 )
| ( ( sK131_SY472 @ SV593 @ SV359 @ SV188 )
= SY1135 ) ) )
= $false )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3432]) ).
thf(3470,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK127_SY472 @ SV593 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3433]) ).
thf(3471,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ! [SY1130: $i] :
( ~ ( SV188 @ SY1130 )
| ( ( sK127_SY472 @ SV593 @ SV359 @ SV188 )
= SY1130 ) ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3434]) ).
thf(3472,plain,
! [SV626: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
| ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3435]) ).
thf(3473,plain,
! [SV627: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
| ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3436]) ).
thf(3474,plain,
! [SV621: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3437]) ).
thf(3475,plain,
! [SV188: $i > $o,SV359: $i > $o,SV621: $i] :
( ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3437]) ).
thf(3476,plain,
! [SV622: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3438]) ).
thf(3477,plain,
! [SV359: $i > $o,SV188: $i > $o,SV622: $i] :
( ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3438]) ).
thf(3478,plain,
! [SV623: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3439]) ).
thf(3479,plain,
! [SV188: $i > $o,SV359: $i > $o,SV623: $i] :
( ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3439]) ).
thf(3480,plain,
! [SV624: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3440]) ).
thf(3481,plain,
! [SV359: $i > $o,SV188: $i > $o,SV624: $i] :
( ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3440]) ).
thf(3482,plain,
! [SV617: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3441]) ).
thf(3483,plain,
! [SV617: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3442]) ).
thf(3484,plain,
! [SV618: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3443]) ).
thf(3485,plain,
! [SV618: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3444]) ).
thf(3486,plain,
! [SV554: $i,SV49: $i > $o,SV630: $i,SV246: $i > $o] :
( ( ( ! [SY1125: $i] :
( ~ ( SV246 @ SY1125 )
| ( SV630 = SY1125 ) ) )
= $false )
| ( ( SV246 @ SV630 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3445]) ).
thf(3487,plain,
! [SV628: $i,SV49: $i > $o,SV554: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK142_SY1124 @ SV554 @ SV49 @ SV628 @ SV246 ) )
| ( SV628
= ( sK142_SY1124 @ SV554 @ SV49 @ SV628 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV628 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3446]) ).
thf(3488,plain,
! [SV605: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ~ ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3447]) ).
thf(3489,plain,
! [SV605: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3448]) ).
thf(3490,plain,
! [SV600: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3449]) ).
thf(3491,plain,
! [SV600: $i,SV49: $i > $o,SV634: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV634 )
| ~ ! [SY1137: $i] :
( ~ ( SV246 @ SY1137 )
| ( SV634 = SY1137 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3450]) ).
thf(3492,plain,
! [SV601: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3451]) ).
thf(3493,plain,
! [SV601: $i,SV49: $i > $o,SV635: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV635 )
| ~ ! [SY1138: $i] :
( ~ ( SV246 @ SY1138 )
| ( SV635 = SY1138 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3452]) ).
thf(3494,plain,
! [SV597: $i,SV49: $i > $o,SV636: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV636 )
| ~ ! [SY1139: $i] :
( ~ ( SV246 @ SY1139 )
| ( SV636 = SY1139 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3453]) ).
thf(3495,plain,
! [SV597: $i,SV49: $i > $o,SV633: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV633 )
| ~ ! [SY1136: $i] :
( ~ ( SV246 @ SY1136 )
| ( SV633 = SY1136 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3454]) ).
thf(3496,plain,
! [SV62: $i,SV586: $i,SV574: $i] :
( ( ( ~ ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
= $false )
| ( ( ~ ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3455]) ).
thf(3497,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3455]) ).
thf(3498,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3456]) ).
thf(3499,plain,
! [SV539: $i,SV606: $i,SV62: $i] :
( ( ( ! [SY1132: $i] :
( ~ ( in @ SY1132 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1119: $i] :
( ~ ( in @ SY1119 @ SY1132 )
| ( in @ SY1119 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SY1132 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3457]) ).
thf(3500,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) )
| ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3458]) ).
thf(3501,plain,
! [SV539: $i,SV602: $i,SV62: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV637 )
| ( in @ SY1140 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV637 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3459]) ).
thf(3502,plain,
! [SV313: $i,SV134: $i > $i > $o,SV616: $i,SV541: $i] :
( ( ( ~ ( in @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV313 )
| ~ ( SV134 @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV616 ) )
= $false )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3460]) ).
thf(3503,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ SV313 )
| ~ ( SV134 @ SV632 @ SV616 ) )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3461]) ).
thf(3504,plain,
! [SV313: $i,SV134: $i > $i > $o,SV610: $i,SV541: $i] :
( ( ( ~ ( in @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV313 ) )
= $false )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3462]) ).
thf(3505,plain,
! [SV313: $i,SV610: $i,SV541: $i,SV134: $i > $i > $o] :
( ( ( ~ ( SV134 @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV610 ) )
= $false )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3462]) ).
thf(3506,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i,SV631: $i] :
( ( ( ~ ( in @ SV631 @ SV313 ) )
= $true )
| ( ( ~ ( SV134 @ SV631 @ SV610 ) )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3463]) ).
thf(3507,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK130_SY768 @ SV592 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3464]) ).
thf(3508,plain,
! [SV188: $i > $o,SV592: $i,SV359: $i > $o] :
( ( ( ! [SY1134: $i] :
( ~ ( SV359 @ SY1134 )
| ( ( sK130_SY768 @ SV592 @ SV188 @ SV359 )
= SY1134 ) ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3465]) ).
thf(3509,plain,
! [SV188: $i > $o,SV592: $i,SV638: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV638 )
| ( ( sK126_SY768 @ SV592 @ SV188 @ SV359 )
= SV638 ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3467]) ).
thf(3510,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK131_SY472 @ SV593 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3468]) ).
thf(3511,plain,
! [SV359: $i > $o,SV593: $i,SV188: $i > $o] :
( ( ( ! [SY1135: $i] :
( ~ ( SV188 @ SY1135 )
| ( ( sK131_SY472 @ SV593 @ SV359 @ SV188 )
= SY1135 ) ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3469]) ).
thf(3512,plain,
! [SV359: $i > $o,SV593: $i,SV639: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV639 )
| ( ( sK127_SY472 @ SV593 @ SV359 @ SV188 )
= SV639 ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3471]) ).
thf(3513,plain,
! [SV626: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3472]) ).
thf(3514,plain,
! [SV188: $i > $o,SV359: $i > $o,SV626: $i] :
( ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3472]) ).
thf(3515,plain,
! [SV627: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3473]) ).
thf(3516,plain,
! [SV359: $i > $o,SV188: $i > $o,SV627: $i] :
( ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3473]) ).
thf(3517,plain,
! [SV621: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3474]) ).
thf(3518,plain,
! [SV621: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3475]) ).
thf(3519,plain,
! [SV622: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3476]) ).
thf(3520,plain,
! [SV622: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3477]) ).
thf(3521,plain,
! [SV623: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3478]) ).
thf(3522,plain,
! [SV623: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3479]) ).
thf(3523,plain,
! [SV624: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3480]) ).
thf(3524,plain,
! [SV624: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3481]) ).
thf(3525,plain,
! [SV617: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3482]) ).
thf(3526,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK143_SY768 @ SV617 @ SV188 @ SV359 ) )
| ~ ! [SY1141: $i] :
( ~ ( SV359 @ SY1141 )
| ( ( sK143_SY768 @ SV617 @ SV188 @ SV359 )
= SY1141 ) ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3483]) ).
thf(3527,plain,
! [SV618: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3484]) ).
thf(3528,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK144_SY472 @ SV618 @ SV359 @ SV188 ) )
| ~ ! [SY1142: $i] :
( ~ ( SV188 @ SY1142 )
| ( ( sK144_SY472 @ SV618 @ SV359 @ SV188 )
= SY1142 ) ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3485]) ).
thf(3529,plain,
! [SV630: $i,SV49: $i > $o,SV554: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK145_SY1125 @ SV554 @ SV49 @ SV630 @ SV246 ) )
| ( SV630
= ( sK145_SY1125 @ SV554 @ SV49 @ SV630 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV630 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3486]) ).
thf(3530,plain,
! [SV628: $i,SV49: $i > $o,SV554: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK142_SY1124 @ SV554 @ SV49 @ SV628 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV628 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3487]) ).
thf(3531,plain,
! [SV246: $i > $o,SV49: $i > $o,SV554: $i,SV628: $i] :
( ( ( SV628
= ( sK142_SY1124 @ SV554 @ SV49 @ SV628 @ SV246 ) )
= $false )
| ( ( SV246 @ SV628 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3487]) ).
thf(3532,plain,
! [SV605: $i,SV49: $i > $o,SV246: $i > $o] :
( ( ( ! [SY594: $i] :
~ ~ ( ~ ( SV246 @ SY594 )
| ~ ! [SY595: $i] :
( ~ ( SV246 @ SY595 )
| ( SY594 = SY595 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3488]) ).
thf(3533,plain,
! [SV605: $i,SV49: $i > $o,SV640: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV640 )
| ~ ! [SY1143: $i] :
( ~ ( SV246 @ SY1143 )
| ( SV640 = SY1143 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3489]) ).
thf(3534,plain,
! [SV600: $i,SV49: $i > $o,SV641: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV641 )
| ~ ! [SY1144: $i] :
( ~ ( SV246 @ SY1144 )
| ( SV641 = SY1144 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3490]) ).
thf(3535,plain,
! [SV600: $i,SV49: $i > $o,SV634: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV634 )
| ~ ! [SY1137: $i] :
( ~ ( SV246 @ SY1137 )
| ( SV634 = SY1137 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3491]) ).
thf(3536,plain,
! [SV601: $i,SV49: $i > $o,SV642: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV642 )
| ~ ! [SY1145: $i] :
( ~ ( SV246 @ SY1145 )
| ( SV642 = SY1145 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3492]) ).
thf(3537,plain,
! [SV601: $i,SV49: $i > $o,SV635: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV635 )
| ~ ! [SY1138: $i] :
( ~ ( SV246 @ SY1138 )
| ( SV635 = SY1138 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3493]) ).
thf(3538,plain,
! [SV597: $i,SV49: $i > $o,SV636: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV636 )
| ~ ! [SY1139: $i] :
( ~ ( SV246 @ SY1139 )
| ( SV636 = SY1139 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3494]) ).
thf(3539,plain,
! [SV597: $i,SV49: $i > $o,SV633: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV633 )
| ~ ! [SY1136: $i] :
( ~ ( SV246 @ SY1136 )
| ( SV633 = SY1136 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3495]) ).
thf(3540,plain,
! [SV62: $i,SV586: $i,SV574: $i] :
( ( ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $true )
| ( ( ~ ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3496]) ).
thf(3541,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
= $false )
| ( ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $false )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3497]) ).
thf(3542,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) )
| ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3498]) ).
thf(3543,plain,
! [SV539: $i,SV606: $i,SV62: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ ( sK5_SY153 @ SV62 ) )
| ! [SY1146: $i] :
( ~ ( in @ SY1146 @ SV643 )
| ( in @ SY1146 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV643 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3499]) ).
thf(3544,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3500]) ).
thf(3545,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3500]) ).
thf(3546,plain,
! [SV539: $i,SV602: $i,SV62: $i,SV637: $i] :
( ( ( ~ ( in @ SV637 @ ( sK5_SY153 @ SV62 ) ) )
= $true )
| ( ( ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV637 )
| ( in @ SY1140 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV637 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3501]) ).
thf(3547,plain,
! [SV313: $i,SV134: $i > $i > $o,SV616: $i,SV541: $i] :
( ( ( ~ ( in @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV313 ) )
= $false )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3502]) ).
thf(3548,plain,
! [SV313: $i,SV616: $i,SV541: $i,SV134: $i > $i > $o] :
( ( ( ~ ( SV134 @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV616 ) )
= $false )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3502]) ).
thf(3549,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i,SV632: $i] :
( ( ( ~ ( in @ SV632 @ SV313 ) )
= $true )
| ( ( ~ ( SV134 @ SV632 @ SV616 ) )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3503]) ).
thf(3550,plain,
! [SV313: $i,SV134: $i > $i > $o,SV610: $i,SV541: $i] :
( ( ( in @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV313 )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3504]) ).
thf(3551,plain,
! [SV313: $i,SV610: $i,SV541: $i,SV134: $i > $i > $o] :
( ( ( SV134 @ ( sK132_SY1087 @ SV541 @ SV610 @ SV134 @ SV313 ) @ SV610 )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3505]) ).
thf(3552,plain,
! [SV541: $i,SV610: $i,SV134: $i > $i > $o,SV313: $i,SV631: $i] :
( ( ( in @ SV631 @ SV313 )
= $false )
| ( ( ~ ( SV134 @ SV631 @ SV610 ) )
= $true )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3506]) ).
thf(3553,plain,
! [SV188: $i > $o,SV592: $i,SV644: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV644 )
| ( ( sK130_SY768 @ SV592 @ SV188 @ SV359 )
= SV644 ) )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3508]) ).
thf(3554,plain,
! [SV188: $i > $o,SV592: $i,SV638: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV638 ) )
= $true )
| ( ( ( sK126_SY768 @ SV592 @ SV188 @ SV359 )
= SV638 )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3509]) ).
thf(3555,plain,
! [SV359: $i > $o,SV593: $i,SV645: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV645 )
| ( ( sK131_SY472 @ SV593 @ SV359 @ SV188 )
= SV645 ) )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3511]) ).
thf(3556,plain,
! [SV359: $i > $o,SV593: $i,SV639: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV639 ) )
= $true )
| ( ( ( sK127_SY472 @ SV593 @ SV359 @ SV188 )
= SV639 )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3512]) ).
thf(3557,plain,
! [SV626: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( ~ ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3513]) ).
thf(3558,plain,
! [SV626: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3514]) ).
thf(3559,plain,
! [SV627: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( ~ ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3515]) ).
thf(3560,plain,
! [SV627: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3516]) ).
thf(3561,plain,
! [SV621: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3517]) ).
thf(3562,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK146_SY768 @ SV621 @ SV188 @ SV359 ) )
| ~ ! [SY1147: $i] :
( ~ ( SV359 @ SY1147 )
| ( ( sK146_SY768 @ SV621 @ SV188 @ SV359 )
= SY1147 ) ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3518]) ).
thf(3563,plain,
! [SV622: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3519]) ).
thf(3564,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK147_SY472 @ SV622 @ SV359 @ SV188 ) )
| ~ ! [SY1148: $i] :
( ~ ( SV188 @ SY1148 )
| ( ( sK147_SY472 @ SV622 @ SV359 @ SV188 )
= SY1148 ) ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3520]) ).
thf(3565,plain,
! [SV623: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3521]) ).
thf(3566,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK148_SY768 @ SV623 @ SV188 @ SV359 ) )
| ~ ! [SY1149: $i] :
( ~ ( SV359 @ SY1149 )
| ( ( sK148_SY768 @ SV623 @ SV188 @ SV359 )
= SY1149 ) ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3522]) ).
thf(3567,plain,
! [SV624: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3523]) ).
thf(3568,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK149_SY472 @ SV624 @ SV359 @ SV188 ) )
| ~ ! [SY1150: $i] :
( ~ ( SV188 @ SY1150 )
| ( ( sK149_SY472 @ SV624 @ SV359 @ SV188 )
= SY1150 ) ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3524]) ).
thf(3569,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK150_SY768 @ SV617 @ SV188 @ SV359 ) )
| ~ ! [SY1151: $i] :
( ~ ( SV359 @ SY1151 )
| ( ( sK150_SY768 @ SV617 @ SV188 @ SV359 )
= SY1151 ) ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3525]) ).
thf(3570,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK143_SY768 @ SV617 @ SV188 @ SV359 ) )
| ~ ! [SY1141: $i] :
( ~ ( SV359 @ SY1141 )
| ( ( sK143_SY768 @ SV617 @ SV188 @ SV359 )
= SY1141 ) ) ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3526]) ).
thf(3571,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK151_SY472 @ SV618 @ SV359 @ SV188 ) )
| ~ ! [SY1152: $i] :
( ~ ( SV188 @ SY1152 )
| ( ( sK151_SY472 @ SV618 @ SV359 @ SV188 )
= SY1152 ) ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3527]) ).
thf(3572,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK144_SY472 @ SV618 @ SV359 @ SV188 ) )
| ~ ! [SY1142: $i] :
( ~ ( SV188 @ SY1142 )
| ( ( sK144_SY472 @ SV618 @ SV359 @ SV188 )
= SY1142 ) ) ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3528]) ).
thf(3573,plain,
! [SV630: $i,SV49: $i > $o,SV554: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK145_SY1125 @ SV554 @ SV49 @ SV630 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV630 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3529]) ).
thf(3574,plain,
! [SV246: $i > $o,SV49: $i > $o,SV554: $i,SV630: $i] :
( ( ( SV630
= ( sK145_SY1125 @ SV554 @ SV49 @ SV630 @ SV246 ) )
= $false )
| ( ( SV246 @ SV630 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3529]) ).
thf(3575,plain,
! [SV628: $i,SV49: $i > $o,SV554: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK142_SY1124 @ SV554 @ SV49 @ SV628 @ SV246 ) )
= $true )
| ( ( SV246 @ SV628 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV554
= ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $false )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3530]) ).
thf(3576,plain,
! [SV605: $i,SV49: $i > $o,SV646: $i,SV246: $i > $o] :
( ( ( ~ ~ ( ~ ( SV246 @ SV646 )
| ~ ! [SY1153: $i] :
( ~ ( SV246 @ SY1153 )
| ( SV646 = SY1153 ) ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3532]) ).
thf(3577,plain,
! [SV605: $i,SV49: $i > $o,SV640: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV640 )
| ~ ! [SY1143: $i] :
( ~ ( SV246 @ SY1143 )
| ( SV640 = SY1143 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3533]) ).
thf(3578,plain,
! [SV600: $i,SV49: $i > $o,SV641: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV641 )
| ~ ! [SY1144: $i] :
( ~ ( SV246 @ SY1144 )
| ( SV641 = SY1144 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3534]) ).
thf(3579,plain,
! [SV600: $i,SV49: $i > $o,SV634: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV634 )
| ~ ! [SY1137: $i] :
( ~ ( SV246 @ SY1137 )
| ( SV634 = SY1137 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3535]) ).
thf(3580,plain,
! [SV601: $i,SV49: $i > $o,SV642: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV642 )
| ~ ! [SY1145: $i] :
( ~ ( SV246 @ SY1145 )
| ( SV642 = SY1145 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3536]) ).
thf(3581,plain,
! [SV601: $i,SV49: $i > $o,SV635: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV635 )
| ~ ! [SY1138: $i] :
( ~ ( SV246 @ SY1138 )
| ( SV635 = SY1138 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3537]) ).
thf(3582,plain,
! [SV597: $i,SV49: $i > $o,SV636: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV636 )
| ~ ! [SY1139: $i] :
( ~ ( SV246 @ SY1139 )
| ( SV636 = SY1139 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3538]) ).
thf(3583,plain,
! [SV597: $i,SV49: $i > $o,SV633: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV633 ) )
= $true )
| ( ( ~ ! [SY1136: $i] :
( ~ ( SV246 @ SY1136 )
| ( SV633 = SY1136 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3539]) ).
thf(3584,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
| ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
= $false )
| ( ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3540]) ).
thf(3585,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
= $false )
| ( ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $false )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3541]) ).
thf(3586,plain,
! [SV62: $i,SV586: $i,SV574: $i] :
( ( ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $false )
| ( ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $false )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3541]) ).
thf(3587,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3542]) ).
thf(3588,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3542]) ).
thf(3589,plain,
! [SV539: $i,SV606: $i,SV62: $i,SV643: $i] :
( ( ( ~ ( in @ SV643 @ ( sK5_SY153 @ SV62 ) ) )
= $true )
| ( ( ! [SY1146: $i] :
( ~ ( in @ SY1146 @ SV643 )
| ( in @ SY1146 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV643 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3543]) ).
thf(3590,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3544]) ).
thf(3591,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3545]) ).
thf(3592,plain,
! [SV539: $i,SV602: $i,SV62: $i,SV637: $i] :
( ( ( in @ SV637 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV637 )
| ( in @ SY1140 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
| ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV637 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3546]) ).
thf(3593,plain,
! [SV313: $i,SV134: $i > $i > $o,SV616: $i,SV541: $i] :
( ( ( in @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV313 )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3547]) ).
thf(3594,plain,
! [SV313: $i,SV616: $i,SV541: $i,SV134: $i > $i > $o] :
( ( ( SV134 @ ( sK135_SY1092 @ SV541 @ SV616 @ SV134 @ SV313 ) @ SV616 )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3548]) ).
thf(3595,plain,
! [SV541: $i,SV616: $i,SV134: $i > $i > $o,SV313: $i,SV632: $i] :
( ( ( in @ SV632 @ SV313 )
= $false )
| ( ( ~ ( SV134 @ SV632 @ SV616 ) )
= $true )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3549]) ).
thf(3596,plain,
! [SV541: $i,SV313: $i,SV610: $i,SV631: $i,SV134: $i > $i > $o] :
( ( ( SV134 @ SV631 @ SV610 )
= $false )
| ( ( in @ SV631 @ SV313 )
= $false )
| ( ( in @ SV610 @ ( sK96_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV541
= ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3552]) ).
thf(3597,plain,
! [SV188: $i > $o,SV592: $i,SV644: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV644 ) )
= $true )
| ( ( ( sK130_SY768 @ SV592 @ SV188 @ SV359 )
= SV644 )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3553]) ).
thf(3598,plain,
! [SV188: $i > $o,SV592: $i,SV638: $i,SV359: $i > $o] :
( ( ( SV359 @ SV638 )
= $false )
| ( ( ( sK126_SY768 @ SV592 @ SV188 @ SV359 )
= SV638 )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV592
= ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3554]) ).
thf(3599,plain,
! [SV359: $i > $o,SV593: $i,SV645: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV645 ) )
= $true )
| ( ( ( sK131_SY472 @ SV593 @ SV359 @ SV188 )
= SV645 )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3555]) ).
thf(3600,plain,
! [SV359: $i > $o,SV593: $i,SV639: $i,SV188: $i > $o] :
( ( ( SV188 @ SV639 )
= $false )
| ( ( ( sK127_SY472 @ SV593 @ SV359 @ SV188 )
= SV639 )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV593
= ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $false )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3556]) ).
thf(3601,plain,
! [SV626: $i,SV188: $i > $o,SV359: $i > $o] :
( ( ( ! [SY768: $i] :
~ ~ ( ~ ( SV359 @ SY768 )
| ~ ! [SY769: $i] :
( ~ ( SV359 @ SY769 )
| ( SY768 = SY769 ) ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3557]) ).
thf(3602,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK152_SY768 @ SV626 @ SV188 @ SV359 ) )
| ~ ! [SY1154: $i] :
( ~ ( SV359 @ SY1154 )
| ( ( sK152_SY768 @ SV626 @ SV188 @ SV359 )
= SY1154 ) ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3558]) ).
thf(3603,plain,
! [SV627: $i,SV359: $i > $o,SV188: $i > $o] :
( ( ( ! [SY472: $i] :
~ ~ ( ~ ( SV188 @ SY472 )
| ~ ! [SY473: $i] :
( ~ ( SV188 @ SY473 )
| ( SY472 = SY473 ) ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3559]) ).
thf(3604,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK153_SY472 @ SV627 @ SV359 @ SV188 ) )
| ~ ! [SY1155: $i] :
( ~ ( SV188 @ SY1155 )
| ( ( sK153_SY472 @ SV627 @ SV359 @ SV188 )
= SY1155 ) ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3560]) ).
thf(3605,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK154_SY768 @ SV621 @ SV188 @ SV359 ) )
| ~ ! [SY1156: $i] :
( ~ ( SV359 @ SY1156 )
| ( ( sK154_SY768 @ SV621 @ SV188 @ SV359 )
= SY1156 ) ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3561]) ).
thf(3606,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK146_SY768 @ SV621 @ SV188 @ SV359 ) )
| ~ ! [SY1147: $i] :
( ~ ( SV359 @ SY1147 )
| ( ( sK146_SY768 @ SV621 @ SV188 @ SV359 )
= SY1147 ) ) ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3562]) ).
thf(3607,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK155_SY472 @ SV622 @ SV359 @ SV188 ) )
| ~ ! [SY1157: $i] :
( ~ ( SV188 @ SY1157 )
| ( ( sK155_SY472 @ SV622 @ SV359 @ SV188 )
= SY1157 ) ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3563]) ).
thf(3608,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK147_SY472 @ SV622 @ SV359 @ SV188 ) )
| ~ ! [SY1148: $i] :
( ~ ( SV188 @ SY1148 )
| ( ( sK147_SY472 @ SV622 @ SV359 @ SV188 )
= SY1148 ) ) ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3564]) ).
thf(3609,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK156_SY768 @ SV623 @ SV188 @ SV359 ) )
| ~ ! [SY1158: $i] :
( ~ ( SV359 @ SY1158 )
| ( ( sK156_SY768 @ SV623 @ SV188 @ SV359 )
= SY1158 ) ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3565]) ).
thf(3610,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK148_SY768 @ SV623 @ SV188 @ SV359 ) )
| ~ ! [SY1149: $i] :
( ~ ( SV359 @ SY1149 )
| ( ( sK148_SY768 @ SV623 @ SV188 @ SV359 )
= SY1149 ) ) ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3566]) ).
thf(3611,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK157_SY472 @ SV624 @ SV359 @ SV188 ) )
| ~ ! [SY1159: $i] :
( ~ ( SV188 @ SY1159 )
| ( ( sK157_SY472 @ SV624 @ SV359 @ SV188 )
= SY1159 ) ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3567]) ).
thf(3612,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK149_SY472 @ SV624 @ SV359 @ SV188 ) )
| ~ ! [SY1150: $i] :
( ~ ( SV188 @ SY1150 )
| ( ( sK149_SY472 @ SV624 @ SV359 @ SV188 )
= SY1150 ) ) ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3568]) ).
thf(3613,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK150_SY768 @ SV617 @ SV188 @ SV359 ) )
| ~ ! [SY1151: $i] :
( ~ ( SV359 @ SY1151 )
| ( ( sK150_SY768 @ SV617 @ SV188 @ SV359 )
= SY1151 ) ) ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3569]) ).
thf(3614,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK143_SY768 @ SV617 @ SV188 @ SV359 ) )
| ~ ! [SY1141: $i] :
( ~ ( SV359 @ SY1141 )
| ( ( sK143_SY768 @ SV617 @ SV188 @ SV359 )
= SY1141 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3570]) ).
thf(3615,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK151_SY472 @ SV618 @ SV359 @ SV188 ) )
| ~ ! [SY1152: $i] :
( ~ ( SV188 @ SY1152 )
| ( ( sK151_SY472 @ SV618 @ SV359 @ SV188 )
= SY1152 ) ) ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3571]) ).
thf(3616,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK144_SY472 @ SV618 @ SV359 @ SV188 ) )
| ~ ! [SY1142: $i] :
( ~ ( SV188 @ SY1142 )
| ( ( sK144_SY472 @ SV618 @ SV359 @ SV188 )
= SY1142 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3572]) ).
thf(3617,plain,
! [SV630: $i,SV49: $i > $o,SV554: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK145_SY1125 @ SV554 @ SV49 @ SV630 @ SV246 ) )
= $true )
| ( ( SV246 @ SV630 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV554 )
= $false )
| ( ( SV49 @ ( sK98_SY1035 @ SV246 @ SV554 @ SV49 ) )
= $true )
| ( ( ( sK9_SY590 @ SV246 @ SV49 )
= ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3573]) ).
thf(3618,plain,
! [SV605: $i,SV49: $i > $o,SV646: $i,SV246: $i > $o] :
( ( ( ~ ( ~ ( SV246 @ SV646 )
| ~ ! [SY1153: $i] :
( ~ ( SV246 @ SY1153 )
| ( SV646 = SY1153 ) ) ) )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3576]) ).
thf(3619,plain,
! [SV605: $i,SV49: $i > $o,SV640: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV640 )
| ~ ! [SY1143: $i] :
( ~ ( SV246 @ SY1143 )
| ( SV640 = SY1143 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3577]) ).
thf(3620,plain,
! [SV600: $i,SV49: $i > $o,SV641: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV641 )
| ~ ! [SY1144: $i] :
( ~ ( SV246 @ SY1144 )
| ( SV641 = SY1144 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3578]) ).
thf(3621,plain,
! [SV600: $i,SV49: $i > $o,SV634: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV634 ) )
= $true )
| ( ( ~ ! [SY1137: $i] :
( ~ ( SV246 @ SY1137 )
| ( SV634 = SY1137 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3579]) ).
thf(3622,plain,
! [SV601: $i,SV49: $i > $o,SV642: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV642 )
| ~ ! [SY1145: $i] :
( ~ ( SV246 @ SY1145 )
| ( SV642 = SY1145 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3580]) ).
thf(3623,plain,
! [SV601: $i,SV49: $i > $o,SV635: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV635 ) )
= $true )
| ( ( ~ ! [SY1138: $i] :
( ~ ( SV246 @ SY1138 )
| ( SV635 = SY1138 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3581]) ).
thf(3624,plain,
! [SV597: $i,SV49: $i > $o,SV636: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV636 ) )
= $true )
| ( ( ~ ! [SY1139: $i] :
( ~ ( SV246 @ SY1139 )
| ( SV636 = SY1139 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3582]) ).
thf(3625,plain,
! [SV597: $i,SV49: $i > $o,SV633: $i,SV246: $i > $o] :
( ( ( SV246 @ SV633 )
= $false )
| ( ( ~ ! [SY1136: $i] :
( ~ ( SV246 @ SY1136 )
| ( SV633 = SY1136 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3583]) ).
thf(3626,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( ~ ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) ) )
= $false )
| ( ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3627,plain,
! [SV62: $i,SV586: $i,SV574: $i] :
( ( ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $false )
| ( ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3584]) ).
thf(3628,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $true )
| ( ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $false )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3585]) ).
thf(3629,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3587]) ).
thf(3630,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3588]) ).
thf(3631,plain,
! [SV539: $i,SV606: $i,SV62: $i,SV643: $i] :
( ( ( in @ SV643 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( ! [SY1146: $i] :
( ~ ( in @ SY1146 @ SV643 )
| ( in @ SY1146 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
| ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV643 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3589]) ).
thf(3632,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3590]) ).
thf(3633,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3591]) ).
thf(3634,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV637: $i] :
( ( ( ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SV637 )
| ( in @ SY1140 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) ) )
= $true )
| ( ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV637 )
= $true )
| ( ( in @ SV637 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3592]) ).
thf(3635,plain,
! [SV541: $i,SV313: $i,SV616: $i,SV632: $i,SV134: $i > $i > $o] :
( ( ( SV134 @ SV632 @ SV616 )
= $false )
| ( ( in @ SV632 @ SV313 )
= $false )
| ( ( in @ SV616 @ ( sK100_SY695 @ SV541 @ SV134 @ SV313 ) )
= $true )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ SV541 )
= $false )
| ( ( SV134 @ ( sK16_SY692 @ SV134 @ SV313 ) @ ( sK83_SY1018 @ SV541 @ SV313 @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3595]) ).
thf(3636,plain,
! [SV188: $i > $o,SV592: $i,SV644: $i,SV359: $i > $o] :
( ( ( SV359 @ SV644 )
= $false )
| ( ( ( sK130_SY768 @ SV592 @ SV188 @ SV359 )
= SV644 )
= $true )
| ( ( SV188 @ SV592 )
= $false )
| ( ( SV188 @ ( sK116_SY1065 @ SV359 @ SV592 @ SV188 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3597]) ).
thf(3637,plain,
! [SV359: $i > $o,SV593: $i,SV645: $i,SV188: $i > $o] :
( ( ( SV188 @ SV645 )
= $false )
| ( ( ( sK131_SY472 @ SV593 @ SV359 @ SV188 )
= SV645 )
= $true )
| ( ( SV359 @ SV593 )
= $false )
| ( ( SV359 @ ( sK117_SY1066 @ SV188 @ SV593 @ SV359 ) )
= $true )
| ( ( ( sK20_SY764 @ SV359 @ SV188 )
= ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3599]) ).
thf(3638,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ~ ( ~ ( SV359 @ ( sK158_SY768 @ SV626 @ SV188 @ SV359 ) )
| ~ ! [SY1160: $i] :
( ~ ( SV359 @ SY1160 )
| ( ( sK158_SY768 @ SV626 @ SV188 @ SV359 )
= SY1160 ) ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3601]) ).
thf(3639,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK152_SY768 @ SV626 @ SV188 @ SV359 ) )
| ~ ! [SY1154: $i] :
( ~ ( SV359 @ SY1154 )
| ( ( sK152_SY768 @ SV626 @ SV188 @ SV359 )
= SY1154 ) ) ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3602]) ).
thf(3640,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ~ ( ~ ( SV188 @ ( sK159_SY472 @ SV627 @ SV359 @ SV188 ) )
| ~ ! [SY1161: $i] :
( ~ ( SV188 @ SY1161 )
| ( ( sK159_SY472 @ SV627 @ SV359 @ SV188 )
= SY1161 ) ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3603]) ).
thf(3641,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK153_SY472 @ SV627 @ SV359 @ SV188 ) )
| ~ ! [SY1155: $i] :
( ~ ( SV188 @ SY1155 )
| ( ( sK153_SY472 @ SV627 @ SV359 @ SV188 )
= SY1155 ) ) ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3604]) ).
thf(3642,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK154_SY768 @ SV621 @ SV188 @ SV359 ) )
| ~ ! [SY1156: $i] :
( ~ ( SV359 @ SY1156 )
| ( ( sK154_SY768 @ SV621 @ SV188 @ SV359 )
= SY1156 ) ) ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3605]) ).
thf(3643,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK146_SY768 @ SV621 @ SV188 @ SV359 ) )
| ~ ! [SY1147: $i] :
( ~ ( SV359 @ SY1147 )
| ( ( sK146_SY768 @ SV621 @ SV188 @ SV359 )
= SY1147 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3606]) ).
thf(3644,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK155_SY472 @ SV622 @ SV359 @ SV188 ) )
| ~ ! [SY1157: $i] :
( ~ ( SV188 @ SY1157 )
| ( ( sK155_SY472 @ SV622 @ SV359 @ SV188 )
= SY1157 ) ) ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3607]) ).
thf(3645,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK147_SY472 @ SV622 @ SV359 @ SV188 ) )
| ~ ! [SY1148: $i] :
( ~ ( SV188 @ SY1148 )
| ( ( sK147_SY472 @ SV622 @ SV359 @ SV188 )
= SY1148 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3608]) ).
thf(3646,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK156_SY768 @ SV623 @ SV188 @ SV359 ) )
| ~ ! [SY1158: $i] :
( ~ ( SV359 @ SY1158 )
| ( ( sK156_SY768 @ SV623 @ SV188 @ SV359 )
= SY1158 ) ) ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3609]) ).
thf(3647,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK148_SY768 @ SV623 @ SV188 @ SV359 ) )
| ~ ! [SY1149: $i] :
( ~ ( SV359 @ SY1149 )
| ( ( sK148_SY768 @ SV623 @ SV188 @ SV359 )
= SY1149 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3610]) ).
thf(3648,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK157_SY472 @ SV624 @ SV359 @ SV188 ) )
| ~ ! [SY1159: $i] :
( ~ ( SV188 @ SY1159 )
| ( ( sK157_SY472 @ SV624 @ SV359 @ SV188 )
= SY1159 ) ) ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3611]) ).
thf(3649,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK149_SY472 @ SV624 @ SV359 @ SV188 ) )
| ~ ! [SY1150: $i] :
( ~ ( SV188 @ SY1150 )
| ( ( sK149_SY472 @ SV624 @ SV359 @ SV188 )
= SY1150 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3612]) ).
thf(3650,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK150_SY768 @ SV617 @ SV188 @ SV359 ) )
| ~ ! [SY1151: $i] :
( ~ ( SV359 @ SY1151 )
| ( ( sK150_SY768 @ SV617 @ SV188 @ SV359 )
= SY1151 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3613]) ).
thf(3651,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK143_SY768 @ SV617 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3614]) ).
thf(3652,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1141: $i] :
( ~ ( SV359 @ SY1141 )
| ( ( sK143_SY768 @ SV617 @ SV188 @ SV359 )
= SY1141 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3614]) ).
thf(3653,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK151_SY472 @ SV618 @ SV359 @ SV188 ) )
| ~ ! [SY1152: $i] :
( ~ ( SV188 @ SY1152 )
| ( ( sK151_SY472 @ SV618 @ SV359 @ SV188 )
= SY1152 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3615]) ).
thf(3654,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK144_SY472 @ SV618 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3616]) ).
thf(3655,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1142: $i] :
( ~ ( SV188 @ SY1142 )
| ( ( sK144_SY472 @ SV618 @ SV359 @ SV188 )
= SY1142 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3616]) ).
thf(3656,plain,
! [SV605: $i,SV49: $i > $o,SV646: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV646 )
| ~ ! [SY1153: $i] :
( ~ ( SV246 @ SY1153 )
| ( SV646 = SY1153 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3618]) ).
thf(3657,plain,
! [SV605: $i,SV49: $i > $o,SV640: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV640 ) )
= $true )
| ( ( ~ ! [SY1143: $i] :
( ~ ( SV246 @ SY1143 )
| ( SV640 = SY1143 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3619]) ).
thf(3658,plain,
! [SV600: $i,SV49: $i > $o,SV641: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV641 ) )
= $true )
| ( ( ~ ! [SY1144: $i] :
( ~ ( SV246 @ SY1144 )
| ( SV641 = SY1144 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3620]) ).
thf(3659,plain,
! [SV600: $i,SV49: $i > $o,SV634: $i,SV246: $i > $o] :
( ( ( SV246 @ SV634 )
= $false )
| ( ( ~ ! [SY1137: $i] :
( ~ ( SV246 @ SY1137 )
| ( SV634 = SY1137 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3621]) ).
thf(3660,plain,
! [SV601: $i,SV49: $i > $o,SV642: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV642 ) )
= $true )
| ( ( ~ ! [SY1145: $i] :
( ~ ( SV246 @ SY1145 )
| ( SV642 = SY1145 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3622]) ).
thf(3661,plain,
! [SV601: $i,SV49: $i > $o,SV635: $i,SV246: $i > $o] :
( ( ( SV246 @ SV635 )
= $false )
| ( ( ~ ! [SY1138: $i] :
( ~ ( SV246 @ SY1138 )
| ( SV635 = SY1138 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3623]) ).
thf(3662,plain,
! [SV597: $i,SV49: $i > $o,SV636: $i,SV246: $i > $o] :
( ( ( SV246 @ SV636 )
= $false )
| ( ( ~ ! [SY1139: $i] :
( ~ ( SV246 @ SY1139 )
| ( SV636 = SY1139 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3624]) ).
thf(3663,plain,
! [SV597: $i,SV49: $i > $o,SV633: $i,SV246: $i > $o] :
( ( ( ! [SY1136: $i] :
( ~ ( SV246 @ SY1136 )
| ( SV633 = SY1136 ) ) )
= $false )
| ( ( SV246 @ SV633 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3625]) ).
thf(3664,plain,
! [SV62: $i,SV574: $i,SV586: $i] :
( ( ( in @ SV586 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $true )
| ( ( in @ SV574 @ ( sK124_SY1061 @ SV586 @ SV574 @ SV62 ) )
= $true )
| ( ( SV574 = SV586 )
= $true )
| ( ( in @ SV574 @ SV62 )
= $false )
| ( ( in @ SV586 @ SV62 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3626]) ).
thf(3665,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
| ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3629]) ).
thf(3666,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3630]) ).
thf(3667,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV643: $i] :
( ( ( ! [SY1146: $i] :
( ~ ( in @ SY1146 @ SV643 )
| ( in @ SY1146 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) ) )
= $true )
| ( ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV643 )
= $true )
| ( ( in @ SV643 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3631]) ).
thf(3668,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ~ ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3632]) ).
thf(3669,plain,
! [SV602: $i,SV539: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3632]) ).
thf(3670,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( ! [SY1103: $i] :
~ ~ ( ~ ( in @ SY1103 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SY1103 @ SV539 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3633]) ).
thf(3671,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV637: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV637 )
| ( in @ SV647 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
= $true )
| ( ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV637 )
= $true )
| ( ( in @ SV637 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3634]) ).
thf(3672,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ( ~ ( SV359 @ ( sK158_SY768 @ SV626 @ SV188 @ SV359 ) )
| ~ ! [SY1160: $i] :
( ~ ( SV359 @ SY1160 )
| ( ( sK158_SY768 @ SV626 @ SV188 @ SV359 )
= SY1160 ) ) ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3638]) ).
thf(3673,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK152_SY768 @ SV626 @ SV188 @ SV359 ) )
| ~ ! [SY1154: $i] :
( ~ ( SV359 @ SY1154 )
| ( ( sK152_SY768 @ SV626 @ SV188 @ SV359 )
= SY1154 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3639]) ).
thf(3674,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ( ~ ( SV188 @ ( sK159_SY472 @ SV627 @ SV359 @ SV188 ) )
| ~ ! [SY1161: $i] :
( ~ ( SV188 @ SY1161 )
| ( ( sK159_SY472 @ SV627 @ SV359 @ SV188 )
= SY1161 ) ) ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3640]) ).
thf(3675,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK153_SY472 @ SV627 @ SV359 @ SV188 ) )
| ~ ! [SY1155: $i] :
( ~ ( SV188 @ SY1155 )
| ( ( sK153_SY472 @ SV627 @ SV359 @ SV188 )
= SY1155 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3641]) ).
thf(3676,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK154_SY768 @ SV621 @ SV188 @ SV359 ) )
| ~ ! [SY1156: $i] :
( ~ ( SV359 @ SY1156 )
| ( ( sK154_SY768 @ SV621 @ SV188 @ SV359 )
= SY1156 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3642]) ).
thf(3677,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK146_SY768 @ SV621 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3643]) ).
thf(3678,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1147: $i] :
( ~ ( SV359 @ SY1147 )
| ( ( sK146_SY768 @ SV621 @ SV188 @ SV359 )
= SY1147 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3643]) ).
thf(3679,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK155_SY472 @ SV622 @ SV359 @ SV188 ) )
| ~ ! [SY1157: $i] :
( ~ ( SV188 @ SY1157 )
| ( ( sK155_SY472 @ SV622 @ SV359 @ SV188 )
= SY1157 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3644]) ).
thf(3680,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK147_SY472 @ SV622 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3645]) ).
thf(3681,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1148: $i] :
( ~ ( SV188 @ SY1148 )
| ( ( sK147_SY472 @ SV622 @ SV359 @ SV188 )
= SY1148 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3645]) ).
thf(3682,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK156_SY768 @ SV623 @ SV188 @ SV359 ) )
| ~ ! [SY1158: $i] :
( ~ ( SV359 @ SY1158 )
| ( ( sK156_SY768 @ SV623 @ SV188 @ SV359 )
= SY1158 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3646]) ).
thf(3683,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK148_SY768 @ SV623 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3647]) ).
thf(3684,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1149: $i] :
( ~ ( SV359 @ SY1149 )
| ( ( sK148_SY768 @ SV623 @ SV188 @ SV359 )
= SY1149 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3647]) ).
thf(3685,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK157_SY472 @ SV624 @ SV359 @ SV188 ) )
| ~ ! [SY1159: $i] :
( ~ ( SV188 @ SY1159 )
| ( ( sK157_SY472 @ SV624 @ SV359 @ SV188 )
= SY1159 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3648]) ).
thf(3686,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK149_SY472 @ SV624 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3649]) ).
thf(3687,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1150: $i] :
( ~ ( SV188 @ SY1150 )
| ( ( sK149_SY472 @ SV624 @ SV359 @ SV188 )
= SY1150 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3649]) ).
thf(3688,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK150_SY768 @ SV617 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3650]) ).
thf(3689,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1151: $i] :
( ~ ( SV359 @ SY1151 )
| ( ( sK150_SY768 @ SV617 @ SV188 @ SV359 )
= SY1151 ) ) )
= $false )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3650]) ).
thf(3690,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK143_SY768 @ SV617 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3651]) ).
thf(3691,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ! [SY1141: $i] :
( ~ ( SV359 @ SY1141 )
| ( ( sK143_SY768 @ SV617 @ SV188 @ SV359 )
= SY1141 ) ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3652]) ).
thf(3692,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK151_SY472 @ SV618 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3653]) ).
thf(3693,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1152: $i] :
( ~ ( SV188 @ SY1152 )
| ( ( sK151_SY472 @ SV618 @ SV359 @ SV188 )
= SY1152 ) ) )
= $false )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3653]) ).
thf(3694,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK144_SY472 @ SV618 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3654]) ).
thf(3695,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ! [SY1142: $i] :
( ~ ( SV188 @ SY1142 )
| ( ( sK144_SY472 @ SV618 @ SV359 @ SV188 )
= SY1142 ) ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3655]) ).
thf(3696,plain,
! [SV605: $i,SV49: $i > $o,SV646: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ SV646 ) )
= $true )
| ( ( ~ ! [SY1153: $i] :
( ~ ( SV246 @ SY1153 )
| ( SV646 = SY1153 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3656]) ).
thf(3697,plain,
! [SV605: $i,SV49: $i > $o,SV640: $i,SV246: $i > $o] :
( ( ( SV246 @ SV640 )
= $false )
| ( ( ~ ! [SY1143: $i] :
( ~ ( SV246 @ SY1143 )
| ( SV640 = SY1143 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3657]) ).
thf(3698,plain,
! [SV600: $i,SV49: $i > $o,SV641: $i,SV246: $i > $o] :
( ( ( SV246 @ SV641 )
= $false )
| ( ( ~ ! [SY1144: $i] :
( ~ ( SV246 @ SY1144 )
| ( SV641 = SY1144 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3658]) ).
thf(3699,plain,
! [SV600: $i,SV49: $i > $o,SV634: $i,SV246: $i > $o] :
( ( ( ! [SY1137: $i] :
( ~ ( SV246 @ SY1137 )
| ( SV634 = SY1137 ) ) )
= $false )
| ( ( SV246 @ SV634 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3659]) ).
thf(3700,plain,
! [SV601: $i,SV49: $i > $o,SV642: $i,SV246: $i > $o] :
( ( ( SV246 @ SV642 )
= $false )
| ( ( ~ ! [SY1145: $i] :
( ~ ( SV246 @ SY1145 )
| ( SV642 = SY1145 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3660]) ).
thf(3701,plain,
! [SV601: $i,SV49: $i > $o,SV635: $i,SV246: $i > $o] :
( ( ( ! [SY1138: $i] :
( ~ ( SV246 @ SY1138 )
| ( SV635 = SY1138 ) ) )
= $false )
| ( ( SV246 @ SV635 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3661]) ).
thf(3702,plain,
! [SV597: $i,SV49: $i > $o,SV636: $i,SV246: $i > $o] :
( ( ( ! [SY1139: $i] :
( ~ ( SV246 @ SY1139 )
| ( SV636 = SY1139 ) ) )
= $false )
| ( ( SV246 @ SV636 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3662]) ).
thf(3703,plain,
! [SV633: $i,SV49: $i > $o,SV597: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK160_SY1136 @ SV597 @ SV49 @ SV633 @ SV246 ) )
| ( SV633
= ( sK160_SY1136 @ SV597 @ SV49 @ SV633 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV633 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3663]) ).
thf(3704,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ~ ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3665]) ).
thf(3705,plain,
! [SV606: $i,SV539: $i,SV62: $i] :
( ( ( ~ ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3665]) ).
thf(3706,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( ! [SY1117: $i] :
~ ~ ( ~ ( in @ SY1117 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SY1117 @ SV539 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3666]) ).
thf(3707,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV643: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ SV643 )
| ( in @ SV648 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
= $true )
| ( ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV643 )
= $true )
| ( ( in @ SV643 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3667]) ).
thf(3708,plain,
! [SV62: $i,SV539: $i,SV602: $i] :
( ( ( in @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3668]) ).
thf(3709,plain,
! [SV602: $i,SV539: $i,SV62: $i] :
( ( ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV539 )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3669]) ).
thf(3710,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV649: $i] :
( ( ( ~ ~ ( ~ ( in @ SV649 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SV649 @ SV539 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3670]) ).
thf(3711,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV637: $i,SV647: $i] :
( ( ( ~ ( in @ SV647 @ SV637 ) )
= $true )
| ( ( in @ SV647 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
= $true )
| ( ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV637 )
= $true )
| ( ( in @ SV637 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3671]) ).
thf(3712,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK158_SY768 @ SV626 @ SV188 @ SV359 ) )
| ~ ! [SY1160: $i] :
( ~ ( SV359 @ SY1160 )
| ( ( sK158_SY768 @ SV626 @ SV188 @ SV359 )
= SY1160 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3672]) ).
thf(3713,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK152_SY768 @ SV626 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3673]) ).
thf(3714,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1154: $i] :
( ~ ( SV359 @ SY1154 )
| ( ( sK152_SY768 @ SV626 @ SV188 @ SV359 )
= SY1154 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3673]) ).
thf(3715,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK159_SY472 @ SV627 @ SV359 @ SV188 ) )
| ~ ! [SY1161: $i] :
( ~ ( SV188 @ SY1161 )
| ( ( sK159_SY472 @ SV627 @ SV359 @ SV188 )
= SY1161 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3674]) ).
thf(3716,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK153_SY472 @ SV627 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3675]) ).
thf(3717,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1155: $i] :
( ~ ( SV188 @ SY1155 )
| ( ( sK153_SY472 @ SV627 @ SV359 @ SV188 )
= SY1155 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3675]) ).
thf(3718,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK154_SY768 @ SV621 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3676]) ).
thf(3719,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1156: $i] :
( ~ ( SV359 @ SY1156 )
| ( ( sK154_SY768 @ SV621 @ SV188 @ SV359 )
= SY1156 ) ) )
= $false )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3676]) ).
thf(3720,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK146_SY768 @ SV621 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3677]) ).
thf(3721,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ! [SY1147: $i] :
( ~ ( SV359 @ SY1147 )
| ( ( sK146_SY768 @ SV621 @ SV188 @ SV359 )
= SY1147 ) ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3678]) ).
thf(3722,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK155_SY472 @ SV622 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3679]) ).
thf(3723,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1157: $i] :
( ~ ( SV188 @ SY1157 )
| ( ( sK155_SY472 @ SV622 @ SV359 @ SV188 )
= SY1157 ) ) )
= $false )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3679]) ).
thf(3724,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK147_SY472 @ SV622 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3680]) ).
thf(3725,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ! [SY1148: $i] :
( ~ ( SV188 @ SY1148 )
| ( ( sK147_SY472 @ SV622 @ SV359 @ SV188 )
= SY1148 ) ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3681]) ).
thf(3726,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK156_SY768 @ SV623 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3682]) ).
thf(3727,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1158: $i] :
( ~ ( SV359 @ SY1158 )
| ( ( sK156_SY768 @ SV623 @ SV188 @ SV359 )
= SY1158 ) ) )
= $false )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3682]) ).
thf(3728,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK148_SY768 @ SV623 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3683]) ).
thf(3729,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ! [SY1149: $i] :
( ~ ( SV359 @ SY1149 )
| ( ( sK148_SY768 @ SV623 @ SV188 @ SV359 )
= SY1149 ) ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3684]) ).
thf(3730,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK157_SY472 @ SV624 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3685]) ).
thf(3731,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1159: $i] :
( ~ ( SV188 @ SY1159 )
| ( ( sK157_SY472 @ SV624 @ SV359 @ SV188 )
= SY1159 ) ) )
= $false )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3685]) ).
thf(3732,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK149_SY472 @ SV624 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3686]) ).
thf(3733,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ! [SY1150: $i] :
( ~ ( SV188 @ SY1150 )
| ( ( sK149_SY472 @ SV624 @ SV359 @ SV188 )
= SY1150 ) ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3687]) ).
thf(3734,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK150_SY768 @ SV617 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3688]) ).
thf(3735,plain,
! [SV188: $i > $o,SV617: $i,SV359: $i > $o] :
( ( ( ! [SY1151: $i] :
( ~ ( SV359 @ SY1151 )
| ( ( sK150_SY768 @ SV617 @ SV188 @ SV359 )
= SY1151 ) ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3689]) ).
thf(3736,plain,
! [SV188: $i > $o,SV617: $i,SV650: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV650 )
| ( ( sK143_SY768 @ SV617 @ SV188 @ SV359 )
= SV650 ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3691]) ).
thf(3737,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK151_SY472 @ SV618 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3692]) ).
thf(3738,plain,
! [SV359: $i > $o,SV618: $i,SV188: $i > $o] :
( ( ( ! [SY1152: $i] :
( ~ ( SV188 @ SY1152 )
| ( ( sK151_SY472 @ SV618 @ SV359 @ SV188 )
= SY1152 ) ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3693]) ).
thf(3739,plain,
! [SV359: $i > $o,SV618: $i,SV651: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV651 )
| ( ( sK144_SY472 @ SV618 @ SV359 @ SV188 )
= SV651 ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3695]) ).
thf(3740,plain,
! [SV605: $i,SV49: $i > $o,SV646: $i,SV246: $i > $o] :
( ( ( SV246 @ SV646 )
= $false )
| ( ( ~ ! [SY1153: $i] :
( ~ ( SV246 @ SY1153 )
| ( SV646 = SY1153 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3696]) ).
thf(3741,plain,
! [SV605: $i,SV49: $i > $o,SV640: $i,SV246: $i > $o] :
( ( ( ! [SY1143: $i] :
( ~ ( SV246 @ SY1143 )
| ( SV640 = SY1143 ) ) )
= $false )
| ( ( SV246 @ SV640 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3697]) ).
thf(3742,plain,
! [SV600: $i,SV49: $i > $o,SV641: $i,SV246: $i > $o] :
( ( ( ! [SY1144: $i] :
( ~ ( SV246 @ SY1144 )
| ( SV641 = SY1144 ) ) )
= $false )
| ( ( SV246 @ SV641 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3698]) ).
thf(3743,plain,
! [SV634: $i,SV49: $i > $o,SV600: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK161_SY1137 @ SV600 @ SV49 @ SV634 @ SV246 ) )
| ( SV634
= ( sK161_SY1137 @ SV600 @ SV49 @ SV634 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV634 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3699]) ).
thf(3744,plain,
! [SV601: $i,SV49: $i > $o,SV642: $i,SV246: $i > $o] :
( ( ( ! [SY1145: $i] :
( ~ ( SV246 @ SY1145 )
| ( SV642 = SY1145 ) ) )
= $false )
| ( ( SV246 @ SV642 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3700]) ).
thf(3745,plain,
! [SV635: $i,SV49: $i > $o,SV601: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK162_SY1138 @ SV601 @ SV49 @ SV635 @ SV246 ) )
| ( SV635
= ( sK162_SY1138 @ SV601 @ SV49 @ SV635 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV635 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3701]) ).
thf(3746,plain,
! [SV636: $i,SV49: $i > $o,SV597: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK163_SY1139 @ SV597 @ SV49 @ SV636 @ SV246 ) )
| ( SV636
= ( sK163_SY1139 @ SV597 @ SV49 @ SV636 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV636 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3702]) ).
thf(3747,plain,
! [SV633: $i,SV49: $i > $o,SV597: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK160_SY1136 @ SV597 @ SV49 @ SV633 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV633 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3703]) ).
thf(3748,plain,
! [SV246: $i > $o,SV49: $i > $o,SV597: $i,SV633: $i] :
( ( ( SV633
= ( sK160_SY1136 @ SV597 @ SV49 @ SV633 @ SV246 ) )
= $false )
| ( ( SV246 @ SV633 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3703]) ).
thf(3749,plain,
! [SV62: $i,SV539: $i,SV606: $i] :
( ( ( in @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) @ ( sK5_SY153 @ SV62 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3704]) ).
thf(3750,plain,
! [SV606: $i,SV539: $i,SV62: $i] :
( ( ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV539 )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3705]) ).
thf(3751,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV652: $i] :
( ( ( ~ ~ ( ~ ( in @ SV652 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SV652 @ SV539 ) ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3706]) ).
thf(3752,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV643: $i,SV648: $i] :
( ( ( ~ ( in @ SV648 @ SV643 ) )
= $true )
| ( ( in @ SV648 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
= $true )
| ( ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV643 )
= $true )
| ( ( in @ SV643 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3707]) ).
thf(3753,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV649: $i] :
( ( ( ~ ( ~ ( in @ SV649 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SV649 @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3710]) ).
thf(3754,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV637: $i,SV647: $i] :
( ( ( in @ SV647 @ SV637 )
= $false )
| ( ( in @ SV647 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
= $true )
| ( ( in @ ( sK125_SY1102 @ SV62 @ SV539 @ SV602 ) @ SV637 )
= $true )
| ( ( in @ SV637 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3711]) ).
thf(3755,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ ( sK158_SY768 @ SV626 @ SV188 @ SV359 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3712]) ).
thf(3756,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ~ ! [SY1160: $i] :
( ~ ( SV359 @ SY1160 )
| ( ( sK158_SY768 @ SV626 @ SV188 @ SV359 )
= SY1160 ) ) )
= $false )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3712]) ).
thf(3757,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK152_SY768 @ SV626 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3713]) ).
thf(3758,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ! [SY1154: $i] :
( ~ ( SV359 @ SY1154 )
| ( ( sK152_SY768 @ SV626 @ SV188 @ SV359 )
= SY1154 ) ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3714]) ).
thf(3759,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ ( sK159_SY472 @ SV627 @ SV359 @ SV188 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3715]) ).
thf(3760,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ~ ! [SY1161: $i] :
( ~ ( SV188 @ SY1161 )
| ( ( sK159_SY472 @ SV627 @ SV359 @ SV188 )
= SY1161 ) ) )
= $false )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3715]) ).
thf(3761,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK153_SY472 @ SV627 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3716]) ).
thf(3762,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ! [SY1155: $i] :
( ~ ( SV188 @ SY1155 )
| ( ( sK153_SY472 @ SV627 @ SV359 @ SV188 )
= SY1155 ) ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3717]) ).
thf(3763,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK154_SY768 @ SV621 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3718]) ).
thf(3764,plain,
! [SV188: $i > $o,SV621: $i,SV359: $i > $o] :
( ( ( ! [SY1156: $i] :
( ~ ( SV359 @ SY1156 )
| ( ( sK154_SY768 @ SV621 @ SV188 @ SV359 )
= SY1156 ) ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3719]) ).
thf(3765,plain,
! [SV188: $i > $o,SV621: $i,SV653: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV653 )
| ( ( sK146_SY768 @ SV621 @ SV188 @ SV359 )
= SV653 ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3721]) ).
thf(3766,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK155_SY472 @ SV622 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3722]) ).
thf(3767,plain,
! [SV359: $i > $o,SV622: $i,SV188: $i > $o] :
( ( ( ! [SY1157: $i] :
( ~ ( SV188 @ SY1157 )
| ( ( sK155_SY472 @ SV622 @ SV359 @ SV188 )
= SY1157 ) ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3723]) ).
thf(3768,plain,
! [SV359: $i > $o,SV622: $i,SV654: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV654 )
| ( ( sK147_SY472 @ SV622 @ SV359 @ SV188 )
= SV654 ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3725]) ).
thf(3769,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK156_SY768 @ SV623 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3726]) ).
thf(3770,plain,
! [SV188: $i > $o,SV623: $i,SV359: $i > $o] :
( ( ( ! [SY1158: $i] :
( ~ ( SV359 @ SY1158 )
| ( ( sK156_SY768 @ SV623 @ SV188 @ SV359 )
= SY1158 ) ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3727]) ).
thf(3771,plain,
! [SV188: $i > $o,SV623: $i,SV655: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV655 )
| ( ( sK148_SY768 @ SV623 @ SV188 @ SV359 )
= SV655 ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3729]) ).
thf(3772,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK157_SY472 @ SV624 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3730]) ).
thf(3773,plain,
! [SV359: $i > $o,SV624: $i,SV188: $i > $o] :
( ( ( ! [SY1159: $i] :
( ~ ( SV188 @ SY1159 )
| ( ( sK157_SY472 @ SV624 @ SV359 @ SV188 )
= SY1159 ) ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3731]) ).
thf(3774,plain,
! [SV359: $i > $o,SV624: $i,SV656: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV656 )
| ( ( sK149_SY472 @ SV624 @ SV359 @ SV188 )
= SV656 ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3733]) ).
thf(3775,plain,
! [SV188: $i > $o,SV617: $i,SV657: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV657 )
| ( ( sK150_SY768 @ SV617 @ SV188 @ SV359 )
= SV657 ) )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3735]) ).
thf(3776,plain,
! [SV188: $i > $o,SV617: $i,SV650: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV650 ) )
= $true )
| ( ( ( sK143_SY768 @ SV617 @ SV188 @ SV359 )
= SV650 )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3736]) ).
thf(3777,plain,
! [SV359: $i > $o,SV618: $i,SV658: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV658 )
| ( ( sK151_SY472 @ SV618 @ SV359 @ SV188 )
= SV658 ) )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3738]) ).
thf(3778,plain,
! [SV359: $i > $o,SV618: $i,SV651: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV651 ) )
= $true )
| ( ( ( sK144_SY472 @ SV618 @ SV359 @ SV188 )
= SV651 )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3739]) ).
thf(3779,plain,
! [SV605: $i,SV49: $i > $o,SV646: $i,SV246: $i > $o] :
( ( ( ! [SY1153: $i] :
( ~ ( SV246 @ SY1153 )
| ( SV646 = SY1153 ) ) )
= $false )
| ( ( SV246 @ SV646 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3740]) ).
thf(3780,plain,
! [SV640: $i,SV49: $i > $o,SV605: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK164_SY1143 @ SV605 @ SV49 @ SV640 @ SV246 ) )
| ( SV640
= ( sK164_SY1143 @ SV605 @ SV49 @ SV640 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV640 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3741]) ).
thf(3781,plain,
! [SV641: $i,SV49: $i > $o,SV600: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK165_SY1144 @ SV600 @ SV49 @ SV641 @ SV246 ) )
| ( SV641
= ( sK165_SY1144 @ SV600 @ SV49 @ SV641 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV641 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_forall_neg,[status(esa)],[3742]) ).
thf(3782,plain,
! [SV634: $i,SV49: $i > $o,SV600: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK161_SY1137 @ SV600 @ SV49 @ SV634 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV634 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3743]) ).
thf(3783,plain,
! [SV246: $i > $o,SV49: $i > $o,SV600: $i,SV634: $i] :
( ( ( SV634
= ( sK161_SY1137 @ SV600 @ SV49 @ SV634 @ SV246 ) )
= $false )
| ( ( SV246 @ SV634 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3743]) ).
thf(3784,plain,
! [SV642: $i,SV49: $i > $o,SV601: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK166_SY1145 @ SV601 @ SV49 @ SV642 @ SV246 ) )
| ( SV642
= ( sK166_SY1145 @ SV601 @ SV49 @ SV642 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV642 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3744]) ).
thf(3785,plain,
! [SV635: $i,SV49: $i > $o,SV601: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK162_SY1138 @ SV601 @ SV49 @ SV635 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV635 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3745]) ).
thf(3786,plain,
! [SV246: $i > $o,SV49: $i > $o,SV601: $i,SV635: $i] :
( ( ( SV635
= ( sK162_SY1138 @ SV601 @ SV49 @ SV635 @ SV246 ) )
= $false )
| ( ( SV246 @ SV635 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3745]) ).
thf(3787,plain,
! [SV636: $i,SV49: $i > $o,SV597: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK163_SY1139 @ SV597 @ SV49 @ SV636 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV636 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3746]) ).
thf(3788,plain,
! [SV246: $i > $o,SV49: $i > $o,SV597: $i,SV636: $i] :
( ( ( SV636
= ( sK163_SY1139 @ SV597 @ SV49 @ SV636 @ SV246 ) )
= $false )
| ( ( SV246 @ SV636 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3746]) ).
thf(3789,plain,
! [SV633: $i,SV49: $i > $o,SV597: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK160_SY1136 @ SV597 @ SV49 @ SV633 @ SV246 ) )
= $true )
| ( ( SV246 @ SV633 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV597
= ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3747]) ).
thf(3790,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV652: $i] :
( ( ( ~ ( ~ ( in @ SV652 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SV652 @ SV539 ) ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3751]) ).
thf(3791,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV643: $i,SV648: $i] :
( ( ( in @ SV648 @ SV643 )
= $false )
| ( ( in @ SV648 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
= $true )
| ( ( in @ ( sK129_SY1116 @ SV62 @ SV539 @ SV606 ) @ SV643 )
= $true )
| ( ( in @ SV643 @ ( sK5_SY153 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3752]) ).
thf(3792,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
| ~ ( in @ SV649 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3753]) ).
thf(3793,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( SV359 @ ( sK158_SY768 @ SV626 @ SV188 @ SV359 ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3755]) ).
thf(3794,plain,
! [SV188: $i > $o,SV626: $i,SV359: $i > $o] :
( ( ( ! [SY1160: $i] :
( ~ ( SV359 @ SY1160 )
| ( ( sK158_SY768 @ SV626 @ SV188 @ SV359 )
= SY1160 ) ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3756]) ).
thf(3795,plain,
! [SV188: $i > $o,SV626: $i,SV659: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV659 )
| ( ( sK152_SY768 @ SV626 @ SV188 @ SV359 )
= SV659 ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3758]) ).
thf(3796,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( SV188 @ ( sK159_SY472 @ SV627 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3759]) ).
thf(3797,plain,
! [SV359: $i > $o,SV627: $i,SV188: $i > $o] :
( ( ( ! [SY1161: $i] :
( ~ ( SV188 @ SY1161 )
| ( ( sK159_SY472 @ SV627 @ SV359 @ SV188 )
= SY1161 ) ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3760]) ).
thf(3798,plain,
! [SV359: $i > $o,SV627: $i,SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV660 )
| ( ( sK153_SY472 @ SV627 @ SV359 @ SV188 )
= SV660 ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3762]) ).
thf(3799,plain,
! [SV188: $i > $o,SV621: $i,SV661: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV661 )
| ( ( sK154_SY768 @ SV621 @ SV188 @ SV359 )
= SV661 ) )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3764]) ).
thf(3800,plain,
! [SV188: $i > $o,SV621: $i,SV653: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV653 ) )
= $true )
| ( ( ( sK146_SY768 @ SV621 @ SV188 @ SV359 )
= SV653 )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3765]) ).
thf(3801,plain,
! [SV359: $i > $o,SV622: $i,SV662: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV662 )
| ( ( sK155_SY472 @ SV622 @ SV359 @ SV188 )
= SV662 ) )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[3767]) ).
thf(3802,plain,
! [SV359: $i > $o,SV622: $i,SV654: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV654 ) )
= $true )
| ( ( ( sK147_SY472 @ SV622 @ SV359 @ SV188 )
= SV654 )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3768]) ).
thf(3803,plain,
! [SV188: $i > $o,SV623: $i,SV663: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV663 )
| ( ( sK156_SY768 @ SV623 @ SV188 @ SV359 )
= SV663 ) )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3770]) ).
thf(3804,plain,
! [SV188: $i > $o,SV623: $i,SV655: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV655 ) )
= $true )
| ( ( ( sK148_SY768 @ SV623 @ SV188 @ SV359 )
= SV655 )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3771]) ).
thf(3805,plain,
! [SV359: $i > $o,SV624: $i,SV664: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV664 )
| ( ( sK157_SY472 @ SV624 @ SV359 @ SV188 )
= SV664 ) )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3773]) ).
thf(3806,plain,
! [SV359: $i > $o,SV624: $i,SV656: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV656 ) )
= $true )
| ( ( ( sK149_SY472 @ SV624 @ SV359 @ SV188 )
= SV656 )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3774]) ).
thf(3807,plain,
! [SV188: $i > $o,SV617: $i,SV657: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV657 ) )
= $true )
| ( ( ( sK150_SY768 @ SV617 @ SV188 @ SV359 )
= SV657 )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3775]) ).
thf(3808,plain,
! [SV188: $i > $o,SV617: $i,SV650: $i,SV359: $i > $o] :
( ( ( SV359 @ SV650 )
= $false )
| ( ( ( sK143_SY768 @ SV617 @ SV188 @ SV359 )
= SV650 )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV617
= ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3776]) ).
thf(3809,plain,
! [SV359: $i > $o,SV618: $i,SV658: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV658 ) )
= $true )
| ( ( ( sK151_SY472 @ SV618 @ SV359 @ SV188 )
= SV658 )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3777]) ).
thf(3810,plain,
! [SV359: $i > $o,SV618: $i,SV651: $i,SV188: $i > $o] :
( ( ( SV188 @ SV651 )
= $false )
| ( ( ( sK144_SY472 @ SV618 @ SV359 @ SV188 )
= SV651 )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV618
= ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3778]) ).
thf(3811,plain,
! [SV646: $i,SV49: $i > $o,SV605: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK167_SY1153 @ SV605 @ SV49 @ SV646 @ SV246 ) )
| ( SV646
= ( sK167_SY1153 @ SV605 @ SV49 @ SV646 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV646 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_forall_neg,[status(esa)],[3779]) ).
thf(3812,plain,
! [SV640: $i,SV49: $i > $o,SV605: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK164_SY1143 @ SV605 @ SV49 @ SV640 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV640 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3780]) ).
thf(3813,plain,
! [SV246: $i > $o,SV49: $i > $o,SV605: $i,SV640: $i] :
( ( ( SV640
= ( sK164_SY1143 @ SV605 @ SV49 @ SV640 @ SV246 ) )
= $false )
| ( ( SV246 @ SV640 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3780]) ).
thf(3814,plain,
! [SV641: $i,SV49: $i > $o,SV600: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK165_SY1144 @ SV600 @ SV49 @ SV641 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV641 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3781]) ).
thf(3815,plain,
! [SV246: $i > $o,SV49: $i > $o,SV600: $i,SV641: $i] :
( ( ( SV641
= ( sK165_SY1144 @ SV600 @ SV49 @ SV641 @ SV246 ) )
= $false )
| ( ( SV246 @ SV641 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[3781]) ).
thf(3816,plain,
! [SV634: $i,SV49: $i > $o,SV600: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK161_SY1137 @ SV600 @ SV49 @ SV634 @ SV246 ) )
= $true )
| ( ( SV246 @ SV634 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV600
= ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3782]) ).
thf(3817,plain,
! [SV642: $i,SV49: $i > $o,SV601: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK166_SY1145 @ SV601 @ SV49 @ SV642 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV642 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3784]) ).
thf(3818,plain,
! [SV246: $i > $o,SV49: $i > $o,SV601: $i,SV642: $i] :
( ( ( SV642
= ( sK166_SY1145 @ SV601 @ SV49 @ SV642 @ SV246 ) )
= $false )
| ( ( SV246 @ SV642 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3784]) ).
thf(3819,plain,
! [SV635: $i,SV49: $i > $o,SV601: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK162_SY1138 @ SV601 @ SV49 @ SV635 @ SV246 ) )
= $true )
| ( ( SV246 @ SV635 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV601
= ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3785]) ).
thf(3820,plain,
! [SV636: $i,SV49: $i > $o,SV597: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK163_SY1139 @ SV597 @ SV49 @ SV636 @ SV246 ) )
= $true )
| ( ( SV246 @ SV636 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV597 )
= $false )
| ( ( SV49 @ ( sK121_SY1070 @ SV246 @ SV597 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3787]) ).
thf(3821,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
| ~ ( in @ SV652 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3790]) ).
thf(3822,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV649: $i] :
( ( ( ~ ( in @ SV649 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) ) )
= $true )
| ( ( ~ ( in @ SV649 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3792]) ).
thf(3823,plain,
! [SV188: $i > $o,SV626: $i,SV665: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV665 )
| ( ( sK158_SY768 @ SV626 @ SV188 @ SV359 )
= SV665 ) )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3794]) ).
thf(3824,plain,
! [SV188: $i > $o,SV626: $i,SV659: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV659 ) )
= $true )
| ( ( ( sK152_SY768 @ SV626 @ SV188 @ SV359 )
= SV659 )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3795]) ).
thf(3825,plain,
! [SV359: $i > $o,SV627: $i,SV666: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV666 )
| ( ( sK159_SY472 @ SV627 @ SV359 @ SV188 )
= SV666 ) )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[3797]) ).
thf(3826,plain,
! [SV359: $i > $o,SV627: $i,SV660: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV660 ) )
= $true )
| ( ( ( sK153_SY472 @ SV627 @ SV359 @ SV188 )
= SV660 )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3798]) ).
thf(3827,plain,
! [SV188: $i > $o,SV621: $i,SV661: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV661 ) )
= $true )
| ( ( ( sK154_SY768 @ SV621 @ SV188 @ SV359 )
= SV661 )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3799]) ).
thf(3828,plain,
! [SV188: $i > $o,SV621: $i,SV653: $i,SV359: $i > $o] :
( ( ( SV359 @ SV653 )
= $false )
| ( ( ( sK146_SY768 @ SV621 @ SV188 @ SV359 )
= SV653 )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV621
= ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3800]) ).
thf(3829,plain,
! [SV359: $i > $o,SV622: $i,SV662: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV662 ) )
= $true )
| ( ( ( sK155_SY472 @ SV622 @ SV359 @ SV188 )
= SV662 )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3801]) ).
thf(3830,plain,
! [SV359: $i > $o,SV622: $i,SV654: $i,SV188: $i > $o] :
( ( ( SV188 @ SV654 )
= $false )
| ( ( ( sK147_SY472 @ SV622 @ SV359 @ SV188 )
= SV654 )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV622
= ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3802]) ).
thf(3831,plain,
! [SV188: $i > $o,SV623: $i,SV663: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV663 ) )
= $true )
| ( ( ( sK156_SY768 @ SV623 @ SV188 @ SV359 )
= SV663 )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3803]) ).
thf(3832,plain,
! [SV188: $i > $o,SV623: $i,SV655: $i,SV359: $i > $o] :
( ( ( SV359 @ SV655 )
= $false )
| ( ( ( sK148_SY768 @ SV623 @ SV188 @ SV359 )
= SV655 )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV623
= ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3804]) ).
thf(3833,plain,
! [SV359: $i > $o,SV624: $i,SV664: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV664 ) )
= $true )
| ( ( ( sK157_SY472 @ SV624 @ SV359 @ SV188 )
= SV664 )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3805]) ).
thf(3834,plain,
! [SV359: $i > $o,SV624: $i,SV656: $i,SV188: $i > $o] :
( ( ( SV188 @ SV656 )
= $false )
| ( ( ( sK149_SY472 @ SV624 @ SV359 @ SV188 )
= SV656 )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV624
= ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3806]) ).
thf(3835,plain,
! [SV188: $i > $o,SV617: $i,SV657: $i,SV359: $i > $o] :
( ( ( SV359 @ SV657 )
= $false )
| ( ( ( sK150_SY768 @ SV617 @ SV188 @ SV359 )
= SV657 )
= $true )
| ( ( SV188 @ SV617 )
= $false )
| ( ( SV188 @ ( sK133_SY1096 @ SV359 @ SV617 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3807]) ).
thf(3836,plain,
! [SV359: $i > $o,SV618: $i,SV658: $i,SV188: $i > $o] :
( ( ( SV188 @ SV658 )
= $false )
| ( ( ( sK151_SY472 @ SV618 @ SV359 @ SV188 )
= SV658 )
= $true )
| ( ( SV359 @ SV618 )
= $false )
| ( ( SV359 @ ( sK134_SY1097 @ SV188 @ SV618 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3809]) ).
thf(3837,plain,
! [SV646: $i,SV49: $i > $o,SV605: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK167_SY1153 @ SV605 @ SV49 @ SV646 @ SV246 ) ) )
= $false )
| ( ( SV246 @ SV646 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3811]) ).
thf(3838,plain,
! [SV246: $i > $o,SV49: $i > $o,SV605: $i,SV646: $i] :
( ( ( SV646
= ( sK167_SY1153 @ SV605 @ SV49 @ SV646 @ SV246 ) )
= $false )
| ( ( SV246 @ SV646 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[3811]) ).
thf(3839,plain,
! [SV640: $i,SV49: $i > $o,SV605: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK164_SY1143 @ SV605 @ SV49 @ SV640 @ SV246 ) )
= $true )
| ( ( SV246 @ SV640 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV605
= ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $false )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3812]) ).
thf(3840,plain,
! [SV641: $i,SV49: $i > $o,SV600: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK165_SY1144 @ SV600 @ SV49 @ SV641 @ SV246 ) )
= $true )
| ( ( SV246 @ SV641 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV600 )
= $false )
| ( ( SV49 @ ( sK122_SY1077 @ SV246 @ SV600 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[3814]) ).
thf(3841,plain,
! [SV642: $i,SV49: $i > $o,SV601: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK166_SY1145 @ SV601 @ SV49 @ SV642 @ SV246 ) )
= $true )
| ( ( SV246 @ SV642 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV601 )
= $false )
| ( ( SV49 @ ( sK123_SY1078 @ SV246 @ SV601 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $false )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3817]) ).
thf(3842,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV652: $i] :
( ( ( ~ ( in @ SV652 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) ) )
= $true )
| ( ( ~ ( in @ SV652 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[3821]) ).
thf(3843,plain,
! [SV62: $i,SV539: $i,SV602: $i,SV649: $i] :
( ( ( in @ SV649 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
= $false )
| ( ( ~ ( in @ SV649 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3822]) ).
thf(3844,plain,
! [SV188: $i > $o,SV626: $i,SV665: $i,SV359: $i > $o] :
( ( ( ~ ( SV359 @ SV665 ) )
= $true )
| ( ( ( sK158_SY768 @ SV626 @ SV188 @ SV359 )
= SV665 )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3823]) ).
thf(3845,plain,
! [SV188: $i > $o,SV626: $i,SV659: $i,SV359: $i > $o] :
( ( ( SV359 @ SV659 )
= $false )
| ( ( ( sK152_SY768 @ SV626 @ SV188 @ SV359 )
= SV659 )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV626
= ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3824]) ).
thf(3846,plain,
! [SV359: $i > $o,SV627: $i,SV666: $i,SV188: $i > $o] :
( ( ( ~ ( SV188 @ SV666 ) )
= $true )
| ( ( ( sK159_SY472 @ SV627 @ SV359 @ SV188 )
= SV666 )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[3825]) ).
thf(3847,plain,
! [SV359: $i > $o,SV627: $i,SV660: $i,SV188: $i > $o] :
( ( ( SV188 @ SV660 )
= $false )
| ( ( ( sK153_SY472 @ SV627 @ SV359 @ SV188 )
= SV660 )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV627
= ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $false )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3826]) ).
thf(3848,plain,
! [SV188: $i > $o,SV621: $i,SV661: $i,SV359: $i > $o] :
( ( ( SV359 @ SV661 )
= $false )
| ( ( ( sK154_SY768 @ SV621 @ SV188 @ SV359 )
= SV661 )
= $true )
| ( ( SV188 @ SV621 )
= $false )
| ( ( SV188 @ ( sK136_SY1110 @ SV359 @ SV621 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3827]) ).
thf(3849,plain,
! [SV359: $i > $o,SV622: $i,SV662: $i,SV188: $i > $o] :
( ( ( SV188 @ SV662 )
= $false )
| ( ( ( sK155_SY472 @ SV622 @ SV359 @ SV188 )
= SV662 )
= $true )
| ( ( SV359 @ SV622 )
= $false )
| ( ( SV359 @ ( sK137_SY1111 @ SV188 @ SV622 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3829]) ).
thf(3850,plain,
! [SV188: $i > $o,SV623: $i,SV663: $i,SV359: $i > $o] :
( ( ( SV359 @ SV663 )
= $false )
| ( ( ( sK156_SY768 @ SV623 @ SV188 @ SV359 )
= SV663 )
= $true )
| ( ( SV188 @ SV623 )
= $false )
| ( ( SV188 @ ( sK138_SY1112 @ SV359 @ SV623 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3831]) ).
thf(3851,plain,
! [SV359: $i > $o,SV624: $i,SV664: $i,SV188: $i > $o] :
( ( ( SV188 @ SV664 )
= $false )
| ( ( ( sK157_SY472 @ SV624 @ SV359 @ SV188 )
= SV664 )
= $true )
| ( ( SV359 @ SV624 )
= $false )
| ( ( SV359 @ ( sK139_SY1113 @ SV188 @ SV624 @ SV359 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $false )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3833]) ).
thf(3852,plain,
! [SV646: $i,SV49: $i > $o,SV605: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK167_SY1153 @ SV605 @ SV49 @ SV646 @ SV246 ) )
= $true )
| ( ( SV246 @ SV646 )
= $false )
| ( ( ( descr
@ ^ [SY132: $i] : ( SV49 @ SY132 ) )
= ( descr
@ ^ [SY597: $i] : ( SV246 @ SY597 ) ) )
= $true )
| ( ( SV49 @ SV605 )
= $false )
| ( ( SV49 @ ( sK128_SY1086 @ SV246 @ SV605 @ SV49 ) )
= $true )
| ( ( SV49 @ ( sK9_SY590 @ SV246 @ SV49 ) )
= $true )
| ( ( SV246 @ ( sK21_SY950 @ SV49 @ SV246 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[3837]) ).
thf(3853,plain,
! [SV62: $i,SV539: $i,SV606: $i,SV652: $i] :
( ( ( in @ SV652 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
= $false )
| ( ( ~ ( in @ SV652 @ SV539 ) )
= $true )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3842]) ).
thf(3854,plain,
! [SV62: $i,SV602: $i,SV539: $i,SV649: $i] :
( ( ( in @ SV649 @ SV539 )
= $false )
| ( ( in @ SV649 @ ( sK112_SY1012 @ SV602 @ SV539 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV62 )
= $false )
| ( ( in @ SV602 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3843]) ).
thf(3855,plain,
! [SV188: $i > $o,SV626: $i,SV665: $i,SV359: $i > $o] :
( ( ( SV359 @ SV665 )
= $false )
| ( ( ( sK158_SY768 @ SV626 @ SV188 @ SV359 )
= SV665 )
= $true )
| ( ( SV188 @ SV626 )
= $false )
| ( ( SV188 @ ( sK140_SY1122 @ SV359 @ SV626 @ SV188 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3844]) ).
thf(3856,plain,
! [SV359: $i > $o,SV627: $i,SV666: $i,SV188: $i > $o] :
( ( ( SV188 @ SV666 )
= $false )
| ( ( ( sK159_SY472 @ SV627 @ SV359 @ SV188 )
= SV666 )
= $true )
| ( ( SV359 @ SV627 )
= $false )
| ( ( SV359 @ ( sK141_SY1123 @ SV188 @ SV627 @ SV359 ) )
= $true )
| ( ( SV188 @ ( sK20_SY764 @ SV359 @ SV188 ) )
= $true )
| ( ( SV359 @ ( sK28_SY970 @ SV188 @ SV359 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[3846]) ).
thf(3857,plain,
! [SV62: $i,SV606: $i,SV539: $i,SV652: $i] :
( ( ( in @ SV652 @ SV539 )
= $false )
| ( ( in @ SV652 @ ( sK119_SY1012 @ SV606 @ SV539 @ SV62 ) )
= $false )
| ( ( in @ ( sK77_SY1010 @ SV62 @ SV539 ) @ SV539 )
= $true )
| ( ( in @ SV606 @ SV539 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[3853]) ).
thf(3858,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[473,3857,3856,3855,3854,3852,3851,3850,3849,3848,3847,3845,3841,3840,3839,3838,3836,3835,3834,3832,3830,3828,3820,3819,3818,3816,3815,3813,3810,3808,3796,3793,3791,3789,3788,3786,3783,3772,3769,3766,3763,3761,3757,3754,3750,3749,3748,3737,3734,3732,3728,3724,3720,3709,3708,3694,3690,3664,3637,3636,3635,3628,3627,3617,3600,3598,3596,3594,3593,3586,3575,3574,3551,3550,3531,3510,3507,3470,3466,3398,3397,3389,3378,3377,3364,3363,3360,3359,3352,3340,3339,3336,3335,3322,3316,3315,3306,3293,3292,3279,3278,3276,3275,3265,3260,3259,3234,3232,3229,3227,3222,3221,3215,3214,3213,3212,3211,3210,3205,3191,3190,3189,3178,3177,3173,3170,3157,3155,3154,3152,3151,3140,3133,3126,3114,3113,3109,3105,3104,3102,3087,3076,3074,3065,3046,3024,3020,3010,3008,2996,2995,2992,2991,2983,2965,2954,2950,2948,2926,2924,2920,2919,2916,2915,2908,2893,2892,2891,2864,2863,2862,2861,2860,2859,2858,2857,2856,2822,2811,2809,2808,2807,2787,2786,2780,2777,2774,2771,2769,2736,2721,2720,2719,2716,2699,2697,2696,2691,2690,2687,2686,2683,2682,2681,2680,2677,2676,2675,2674,2671,2670,2649,2648,2633,2632,2623,2622,2621,2619,2615,2611,2605,2582,2579,2575,2572,2568,2565,2561,2555,2532,2531,2530,2519,2518,2508,2507,2505,2504,2502,2501,2497,2488,2487,2486,2465,2464,2460,2455,2454,2451,2426,2410,2409,2407,2406,2404,2403,2382,2379,2376,2368,2362,2337,2334,2326,2325,2306,2305,2290,2287,2284,2267,2255,2243,2232,2231,2230,2223,2214,2213,2195,2169,2168,2148,2147,2138,2127,2126,2123,2122,2121,2119,2118,2116,2115,2113,2106,2098,2082,2081,2068,2051,2035,2034,2012,2011,2010,2009,2006,2005,1994,1993,1959,1941,1937,1934,1933,1923,1917,1916,1915,1910,1908,1899,1889,1887,1886,1880,1870,1861,1860,1858,1856,1852,1848,1837,1836,1831,1828,1824,1818,1805,1802,1793,1776,1774,1762,1758,1752,1740,1738,1729,1720,1719,1718,1717,1708,1700,1688,1682,1675,1659,1645,1643,1641,1628,1627,1624,1604,1595,1592,1589,1585,1576,1574,1564,1560,1550,1508,1493,1482,1481,1478,1473,1461,1457,1452,1447,1442,1435,1431,1430,1423,1422,1419,1413,1411,1406,1394,1391,1386,1383,1382,1378,1376,1371,1357,1356,1354,1353,1352,1348,1344,1340,1339,1331,1330,1316,1315,1283,1273,1271,1260,1251,1248,1247,1246,1201,1188,1183,1179,1178,1177,1151,1127,1117,1111,1102,1096,1095,1094,1032,1021,1019,1017,1015,1012,997,995,990,973,961,947,920,913,909,887,884,853,851,850,848,842,793,776,766,764,761,710,692,684,567,491,482]) ).
thf(3859,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[3858]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU693^1 : TPTP v9.3.1. Released v3.7.0.
% 0.00/0.04 % Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.18 % Computer : n017.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Oct 6 15:27:15 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox/solver/bin/eprover /export/starexec/sandbox/benchmark/theBenchmark.p
% 70.39/12.17 .
% 70.39/12.17
% 70.39/12.17 No.of.Axioms: 0
% 70.39/12.17
% 70.39/12.17 Length.of.Defs: 46940
% 70.39/12.17
% 70.39/12.17 Contains.Choice.Funs: true
% 70.39/12.17 ......................................................................................................................................
% 70.39/12.17
% 70.39/12.17 ********************************
% 70.39/12.17 * All subproblems solved! *
% 70.39/12.17 ********************************
% 70.39/12.17 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:209,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3858,loop_count:0,foatp_calls:1,translation:fof_full)
% 70.39/12.17
% 70.39/12.17 %**** Beginning of derivation protocol ****
% 70.39/12.17 % SZS output start CNFRefutation
% See solution above
% 12.10/12.19
% 12.10/12.19 %**** End of derivation protocol ****
% 12.10/12.19 %**** no. of clauses in derivation: 3859 ****
% 12.10/12.19 %**** clause counter: 3858 ****
% 12.10/12.19
% 12.10/12.19 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : (rf:0,axioms:209,ps:3,u:1,ude:false,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:15,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:3858,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------