%------------------------------------------------------------------------------
% File : LEO-II---2.3.1
% Problem : SEU647^1 : TPTP v9.3.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Oct 7 10:45:51 AM UTC 2026
% Result : Theorem 36.38s 6.36s
% Output : CNFRefutation 36.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 170
% Syntax : Number of formulae : 2852 (1127 unt; 0 typ; 169 def)
% Number of atoms : 22190 (9056 equ; 0 cnn)
% Maximal formula atoms : 165 ( 7 avg)
% Number of connectives : 53253 (8372 ~;8562 |; 379 &;34682 @)
% ( 42 <=>;1216 =>; 0 <=; 0 <~>)
% Maximal formula depth : 169 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 1634 (1634 >; 0 *; 0 +; 0 <<)
% Number of symbols : 280 ( 277 usr; 171 con; 0-4 aty)
% Number of variables : 10442 ( 878 ^;9402 !; 162 ?;10442 :)
% Comments :
%------------------------------------------------------------------------------
thf(tp_atleast2p,type,
atleast2p: $i > $o ).
thf(tp_atmost1p,type,
atmost1p: $i > $o ).
thf(tp_atmost2p,type,
atmost2p: $i > $o ).
thf(tp_binintersect,type,
binintersect: $i > $i > $i ).
thf(tp_binintersectEL,type,
binintersectEL: $o ).
thf(tp_binintersectER,type,
binintersectER: $o ).
thf(tp_binintersectI,type,
binintersectI: $o ).
thf(tp_binintersectLsub,type,
binintersectLsub: $o ).
thf(tp_binintersectRsub,type,
binintersectRsub: $o ).
thf(tp_binintersectSubset1,type,
binintersectSubset1: $o ).
thf(tp_binintersectSubset2,type,
binintersectSubset2: $o ).
thf(tp_binintersectSubset3,type,
binintersectSubset3: $o ).
thf(tp_binintersectSubset4,type,
binintersectSubset4: $o ).
thf(tp_binintersectSubset5,type,
binintersectSubset5: $o ).
thf(tp_binunion,type,
binunion: $i > $i > $i ).
thf(tp_binunionE,type,
binunionE: $o ).
thf(tp_binunionEcases,type,
binunionEcases: $o ).
thf(tp_binunionIL,type,
binunionIL: $o ).
thf(tp_binunionIR,type,
binunionIR: $o ).
thf(tp_binunionLsub,type,
binunionLsub: $o ).
thf(tp_binunionRsub,type,
binunionRsub: $o ).
thf(tp_bs114d,type,
bs114d: $o ).
thf(tp_cartprod,type,
cartprod: $i > $i > $i ).
thf(tp_cartprodfstin,type,
cartprodfstin: $o ).
thf(tp_cartprodmempair,type,
cartprodmempair: $o ).
thf(tp_cartprodmempair1,type,
cartprodmempair1: $o ).
thf(tp_cartprodpairin,type,
cartprodpairin: $o ).
thf(tp_descr,type,
descr: ( $i > $o ) > $i ).
thf(tp_descr__Cong,type,
descr__Cong: $o ).
thf(tp_descrp,type,
descrp: $o ).
thf(tp_disjoint,type,
disjoint: $i > $i > $o ).
thf(tp_disjointsetsI1,type,
disjointsetsI1: $o ).
thf(tp_dsetconstr,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(tp_dsetconstrEL,type,
dsetconstrEL: $o ).
thf(tp_dsetconstrER,type,
dsetconstrER: $o ).
thf(tp_dsetconstrI,type,
dsetconstrI: $o ).
thf(tp_dsetconstr__Cong,type,
dsetconstr__Cong: $o ).
thf(tp_emptyE1,type,
emptyE1: $o ).
thf(tp_emptyI,type,
emptyI: $o ).
thf(tp_emptyInPowerset,type,
emptyInPowerset: $o ).
thf(tp_emptyinPowerset,type,
emptyinPowerset: $o ).
thf(tp_emptyinunitempty,type,
emptyinunitempty: $o ).
thf(tp_emptyset,type,
emptyset: $i ).
thf(tp_emptysetAx,type,
emptysetAx: $o ).
thf(tp_emptysetE,type,
emptysetE: $o ).
thf(tp_emptyset__Cong,type,
emptyset__Cong: $o ).
thf(tp_emptysetimpfalse,type,
emptysetimpfalse: $o ).
thf(tp_emptysetsubset,type,
emptysetsubset: $o ).
thf(tp_eqimpsubset1,type,
eqimpsubset1: $o ).
thf(tp_eqimpsubset2,type,
eqimpsubset2: $o ).
thf(tp_eqinunit,type,
eqinunit: $o ).
thf(tp_ex1,type,
ex1: $i > ( $i > $o ) > $o ).
thf(tp_ex1E1,type,
ex1E1: $o ).
thf(tp_ex1I,type,
ex1I: $o ).
thf(tp_ex1I2,type,
ex1I2: $o ).
thf(tp_exu,type,
exu: ( $i > $o ) > $o ).
thf(tp_exuE1,type,
exuE1: $o ).
thf(tp_exuE2,type,
exuE2: $o ).
thf(tp_exuE3e,type,
exuE3e: $o ).
thf(tp_exuE3u,type,
exuE3u: $o ).
thf(tp_exuEu,type,
exuEu: $o ).
thf(tp_exuI1,type,
exuI1: $o ).
thf(tp_exuI2,type,
exuI2: $o ).
thf(tp_exuI3,type,
exuI3: $o ).
thf(tp_exu__Cong,type,
exu__Cong: $o ).
thf(tp_foundationAx,type,
foundationAx: $o ).
thf(tp_in,type,
in: $i > $i > $o ).
thf(tp_inCongP,type,
inCongP: $o ).
thf(tp_inPowerset,type,
inPowerset: $o ).
thf(tp_in__Cong,type,
in__Cong: $o ).
thf(tp_iskpair,type,
iskpair: $i > $o ).
thf(tp_kfst,type,
kfst: $i > $i ).
thf(tp_kfstpairEq,type,
kfstpairEq: $o ).
thf(tp_kfstsingleton,type,
kfstsingleton: $o ).
thf(tp_kpair,type,
kpair: $i > $i > $i ).
thf(tp_kpairiskpair,type,
kpairiskpair: $o ).
thf(tp_kpairp,type,
kpairp: $o ).
thf(tp_noeltsimpempty,type,
noeltsimpempty: $o ).
thf(tp_nonempty,type,
nonempty: $i > $o ).
thf(tp_nonemptyE1,type,
nonemptyE1: $o ).
thf(tp_nonemptyI,type,
nonemptyI: $o ).
thf(tp_nonemptyI1,type,
nonemptyI1: $o ).
thf(tp_nonemptyImpWitness,type,
nonemptyImpWitness: $o ).
thf(tp_notdallE,type,
notdallE: $o ).
thf(tp_notdexE,type,
notdexE: $o ).
thf(tp_notequalI1,type,
notequalI1: $o ).
thf(tp_notequalI2,type,
notequalI2: $o ).
thf(tp_notinemptyset,type,
notinemptyset: $o ).
thf(tp_notinsingleton,type,
notinsingleton: $o ).
thf(tp_notsubsetI,type,
notsubsetI: $o ).
thf(tp_omega,type,
omega: $i ).
thf(tp_omega0Ax,type,
omega0Ax: $o ).
thf(tp_omegaIndAx,type,
omegaIndAx: $o ).
thf(tp_omegaSAx,type,
omegaSAx: $o ).
thf(tp_omega__Cong,type,
omega__Cong: $o ).
thf(tp_powerset,type,
powerset: $i > $i ).
thf(tp_powersetAx,type,
powersetAx: $o ).
thf(tp_powersetE,type,
powersetE: $o ).
thf(tp_powersetE1,type,
powersetE1: $o ).
thf(tp_powersetI,type,
powersetI: $o ).
thf(tp_powersetI1,type,
powersetI1: $o ).
thf(tp_powerset__Cong,type,
powerset__Cong: $o ).
thf(tp_powersetsubset,type,
powersetsubset: $o ).
thf(tp_prop2set,type,
prop2set: $o > $i ).
thf(tp_prop2set2propI,type,
prop2set2propI: $o ).
thf(tp_prop2setE,type,
prop2setE: $o ).
thf(tp_prop2setI,type,
prop2setI: $o ).
thf(tp_quantDeMorgan1,type,
quantDeMorgan1: $o ).
thf(tp_quantDeMorgan2,type,
quantDeMorgan2: $o ).
thf(tp_quantDeMorgan3,type,
quantDeMorgan3: $o ).
thf(tp_quantDeMorgan4,type,
quantDeMorgan4: $o ).
thf(tp_regular,type,
regular: $i > $o ).
thf(tp_replAx,type,
replAx: $o ).
thf(tp_sK10_Xy,type,
sK10_Xy: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK11_SY23,type,
sK11_SY23: $i > ( $i > $i > $o ) > $i ).
thf(tp_sK12_SY1066,type,
sK12_SY1066: $i > $i > ( $i > $i > $o ) > $i ).
thf(tp_sK13_B,type,
sK13_B: $i > $i ).
thf(tp_sK14_B,type,
sK14_B: $i > $i ).
thf(tp_sK15_SY1084,type,
sK15_SY1084: $i > $i > $i > $i ).
thf(tp_sK16_SY1071,type,
sK16_SY1071: $i > $i > $i ).
thf(tp_sK17_SY1085,type,
sK17_SY1085: $i > $i > $i ).
thf(tp_sK18_Xx,type,
sK18_Xx: $i > $i > $i ).
thf(tp_sK19_SY56,type,
sK19_SY56: $i > ( $i > $o ) > $i ).
thf(tp_sK1_Xx,type,
sK1_Xx: $i ).
thf(tp_sK20_Xx,type,
sK20_Xx: ( $i > $o ) > $i ).
thf(tp_sK21_SY73,type,
sK21_SY73: $i > ( $i > $o ) > $i ).
thf(tp_sK22_Xx,type,
sK22_Xx: ( $i > $o ) > $i ).
thf(tp_sK23_SY85,type,
sK23_SY85: $i > ( $i > $o ) > $i ).
thf(tp_sK24_Xx,type,
sK24_Xx: $i > $i > $i ).
thf(tp_sK25_Xx,type,
sK25_Xx: $i > $i > $i ).
thf(tp_sK26_Xx,type,
sK26_Xx: $i > $i ).
thf(tp_sK27_Xx,type,
sK27_Xx: $i > $i ).
thf(tp_sK28_Xx,type,
sK28_Xx: $i > $i ).
thf(tp_sK29_Xx,type,
sK29_Xx: $i > $i > $i ).
thf(tp_sK2_SY1055,type,
sK2_SY1055: $i ).
thf(tp_sK30_B,type,
sK30_B: $o > $i > $i > $i ).
thf(tp_sK31_Xx,type,
sK31_Xx: ( $i > $o ) > $i ).
thf(tp_sK32_SY141,type,
sK32_SY141: $i > ( $i > $o ) > $i ).
thf(tp_sK33_Xx,type,
sK33_Xx: $i > $i ).
thf(tp_sK34_Xx,type,
sK34_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK35_Xx,type,
sK35_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK36_Xx,type,
sK36_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK37_Xx,type,
sK37_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK38_Xx,type,
sK38_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK39_Xx,type,
sK39_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK3_SY1058,type,
sK3_SY1058: $i ).
thf(tp_sK40_SY197,type,
sK40_SY197: ( $i > $o ) > $i ).
thf(tp_sK41_Xy,type,
sK41_Xy: $i > ( $i > $o ) > $i ).
thf(tp_sK42_SY204,type,
sK42_SY204: ( $i > $o ) > $i ).
thf(tp_sK43_Xx,type,
sK43_Xx: ( $i > $o ) > $i ).
thf(tp_sK44_SY1097,type,
sK44_SY1097: ( $i > $o ) > $i ).
thf(tp_sK45_SY210,type,
sK45_SY210: ( $i > $o ) > $i ).
thf(tp_sK46_Xy,type,
sK46_Xy: $i > ( $i > $o ) > $i ).
thf(tp_sK47_SY223,type,
sK47_SY223: $i > ( $i > $o ) > $i ).
thf(tp_sK48_SY231,type,
sK48_SY231: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK49_SY235,type,
sK49_SY235: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK4_SY1060,type,
sK4_SY1060: $i ).
thf(tp_sK50_Xx,type,
sK50_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK51_SY1100,type,
sK51_SY1100: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK52_SY234,type,
sK52_SY234: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK53_SY232,type,
sK53_SY232: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK54_Xx,type,
sK54_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK55_SY1102,type,
sK55_SY1102: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK56_SY247,type,
sK56_SY247: $i > ( $i > $o ) > $i ).
thf(tp_sK57_SY259,type,
sK57_SY259: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK58_SY256,type,
sK58_SY256: $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK59_Xx,type,
sK59_Xx: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK5_Xx,type,
sK5_Xx: $i > $i > $i ).
thf(tp_sK60_SY1103,type,
sK60_SY1103: ( $i > $o ) > ( $i > $o ) > $i ).
thf(tp_sK61_Xx,type,
sK61_Xx: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK62_SY1104,type,
sK62_SY1104: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(tp_sK63_Xx,type,
sK63_Xx: $i > $i > $i ).
thf(tp_sK64_Xx,type,
sK64_Xx: $i > $i > $i ).
thf(tp_sK65_Xx,type,
sK65_Xx: $i > $i > $i ).
thf(tp_sK66_SY422,type,
sK66_SY422: $i > $i > $i ).
thf(tp_sK67_SY1105,type,
sK67_SY1105: $i > $i > $i ).
thf(tp_sK68_SY427,type,
sK68_SY427: $i > $i > $i ).
thf(tp_sK69_SY1106,type,
sK69_SY1106: $i > $i > $i ).
thf(tp_sK6_Xx,type,
sK6_Xx: $i > $i > $i ).
thf(tp_sK70_SY468,type,
sK70_SY468: $i > $i > $i > $i ).
thf(tp_sK71_SY1107,type,
sK71_SY1107: $i > $i > $i > $i ).
thf(tp_sK72_SY474,type,
sK72_SY474: $i > $i > $i > $i ).
thf(tp_sK73_SY1108,type,
sK73_SY1108: $i > $i > $i > $i ).
thf(tp_sK74_X,type,
sK74_X: $i > $i > $i ).
thf(tp_sK75_SY488,type,
sK75_SY488: ( $i > $o ) > $i > $i ).
thf(tp_sK76_Xx,type,
sK76_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK77_SY1111,type,
sK77_SY1111: ( $i > $o ) > $i > $i ).
thf(tp_sK78_Xx,type,
sK78_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK79_SY507,type,
sK79_SY507: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK7_B,type,
sK7_B: $i > $i > $i ).
thf(tp_sK80_Xy,type,
sK80_Xy: $i > ( $i > $o ) > $i > $i ).
thf(tp_sK81_SY519,type,
sK81_SY519: ( $i > $o ) > $i > $i ).
thf(tp_sK82_Xx,type,
sK82_Xx: ( $i > $o ) > $i > $i ).
thf(tp_sK83_SY1116,type,
sK83_SY1116: ( $i > $o ) > $i > $i ).
thf(tp_sK84_SY531,type,
sK84_SY531: $i > $i ).
thf(tp_sK8_Xx,type,
sK8_Xx: $i > $i ).
thf(tp_sK9_B,type,
sK9_B: $i > ( $i > $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_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_setukpairinjL1,type,
setukpairinjL1: $o ).
thf(tp_setunion,type,
setunion: $i > $i ).
thf(tp_setunionAx,type,
setunionAx: $o ).
thf(tp_setunionE,type,
setunionE: $o ).
thf(tp_setunionE2,type,
setunionE2: $o ).
thf(tp_setunionI,type,
setunionI: $o ).
thf(tp_setunion__Cong,type,
setunion__Cong: $o ).
thf(tp_setunionsingleton,type,
setunionsingleton: $o ).
thf(tp_setunionsingleton1,type,
setunionsingleton1: $o ).
thf(tp_setunionsingleton2,type,
setunionsingleton2: $o ).
thf(tp_singleton,type,
singleton: $i > $o ).
thf(tp_singletoninpowerset,type,
singletoninpowerset: $o ).
thf(tp_singletoninpowunion,type,
singletoninpowunion: $o ).
thf(tp_singletonprop,type,
singletonprop: $o ).
thf(tp_singletonsswitch,type,
singletonsswitch: $o ).
thf(tp_singletonsubset,type,
singletonsubset: $o ).
thf(tp_singletonsuniq,type,
singletonsuniq: $o ).
thf(tp_subPowSU,type,
subPowSU: $o ).
thf(tp_subset,type,
subset: $i > $i > $o ).
thf(tp_subset2powerset,type,
subset2powerset: $o ).
thf(tp_subsetE,type,
subsetE: $o ).
thf(tp_subsetE2,type,
subsetE2: $o ).
thf(tp_subsetI1,type,
subsetI1: $o ).
thf(tp_subsetI2,type,
subsetI2: $o ).
thf(tp_subsetRefl,type,
subsetRefl: $o ).
thf(tp_subsetTrans,type,
subsetTrans: $o ).
thf(tp_subsetemptysetimpeq,type,
subsetemptysetimpeq: $o ).
thf(tp_symdiff,type,
symdiff: $i > $i > $i ).
thf(tp_symdiffE,type,
symdiffE: $o ).
thf(tp_symdiffI1,type,
symdiffI1: $o ).
thf(tp_symdiffI2,type,
symdiffI2: $o ).
thf(tp_symdiffIneg1,type,
symdiffIneg1: $o ).
thf(tp_symdiffIneg2,type,
symdiffIneg2: $o ).
thf(tp_theprop,type,
theprop: $o ).
thf(tp_ubforcartprodlem1,type,
ubforcartprodlem1: $o ).
thf(tp_ubforcartprodlem2,type,
ubforcartprodlem2: $o ).
thf(tp_ubforcartprodlem3,type,
ubforcartprodlem3: $o ).
thf(tp_uniqinunit,type,
uniqinunit: $o ).
thf(tp_upairinpowunion,type,
upairinpowunion: $o ).
thf(tp_upairset2E,type,
upairset2E: $o ).
thf(tp_upairset2IR,type,
upairset2IR: $o ).
thf(tp_upairsetE,type,
upairsetE: $o ).
thf(tp_upairsetIL,type,
upairsetIL: $o ).
thf(tp_upairsetIR,type,
upairsetIR: $o ).
thf(tp_upairsetp,type,
upairsetp: $i > $o ).
thf(tp_upairsubunion,type,
upairsubunion: $o ).
thf(tp_vacuousDall,type,
vacuousDall: $o ).
thf(tp_wellorderingAx,type,
wellorderingAx: $o ).
thf(binintersectEL,definition,
( binintersectEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectEL) ).
thf(binintersectER,definition,
( binintersectER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectER) ).
thf(binintersectI,definition,
( binintersectI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectI) ).
thf(binintersectLsub,definition,
( binintersectLsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectLsub) ).
thf(binintersectRsub,definition,
( binintersectRsub
= ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectRsub) ).
thf(binintersectSubset1,definition,
( binintersectSubset1
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset1) ).
thf(binintersectSubset2,definition,
( binintersectSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset2) ).
thf(binintersectSubset3,definition,
( binintersectSubset3
= ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset3) ).
thf(binintersectSubset4,definition,
( binintersectSubset4
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset4) ).
thf(binintersectSubset5,definition,
( binintersectSubset5
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binintersectSubset5) ).
thf(binunionE,definition,
( binunionE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionE) ).
thf(binunionEcases,definition,
( binunionEcases
= ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionEcases) ).
thf(binunionIL,definition,
( binunionIL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIL) ).
thf(binunionIR,definition,
( binunionIR
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionIR) ).
thf(binunionLsub,definition,
( binunionLsub
= ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionLsub) ).
thf(binunionRsub,definition,
( binunionRsub
= ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',binunionRsub) ).
thf(bs114d,definition,
( bs114d
= ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',bs114d) ).
thf(cartprodfstin,definition,
( cartprodfstin
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodfstin) ).
thf(cartprodmempair,definition,
( cartprodmempair
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( iskpair @ Xu ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair) ).
thf(cartprodmempair1,definition,
( cartprodmempair1
= ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ? [Xy: $i] :
( ( in @ Xy @ B )
& ( Xu
= ( kpair @ Xx @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodmempair1) ).
thf(cartprodpairin,definition,
( cartprodpairin
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( cartprod @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cartprodpairin) ).
thf(descr__Cong,definition,
( descr__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) )
=> ( ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descr__Cong) ).
thf(descrp,definition,
( descrp
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ( Xphi
@ ( descr
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',descrp) ).
thf(disjointsetsI1,definition,
( disjointsetsI1
= ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',disjointsetsI1) ).
thf(dsetconstrEL,definition,
( dsetconstrEL
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrEL) ).
thf(dsetconstrER,definition,
( dsetconstrER
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrER) ).
thf(dsetconstrI,definition,
( dsetconstrI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstrI) ).
thf(dsetconstr__Cong,definition,
( dsetconstr__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dsetconstr__Cong) ).
thf(emptyE1,definition,
( emptyE1
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyE1) ).
thf(emptyI,definition,
( emptyI
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyI) ).
thf(emptyInPowerset,definition,
( emptyInPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyInPowerset) ).
thf(emptyinPowerset,definition,
( emptyinPowerset
= ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinPowerset) ).
thf(emptyinunitempty,definition,
( emptyinunitempty
= ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyinunitempty) ).
thf(emptysetAx,definition,
( emptysetAx
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetAx) ).
thf(emptysetE,definition,
( emptysetE
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetE) ).
thf(emptyset__Cong,definition,
( emptyset__Cong
= ( emptyset = emptyset ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptyset__Cong) ).
thf(emptysetimpfalse,definition,
( emptysetimpfalse
= ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetimpfalse) ).
thf(emptysetsubset,definition,
( emptysetsubset
= ( ! [A: $i] : ( subset @ emptyset @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',emptysetsubset) ).
thf(eqimpsubset1,definition,
( eqimpsubset1
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset1) ).
thf(eqimpsubset2,definition,
( eqimpsubset2
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqimpsubset2) ).
thf(eqinunit,definition,
( eqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eqinunit) ).
thf(ex1,definition,
( ex1
= ( ^ [A: $i,Xphi: $i > $o] :
( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1) ).
thf(ex1E1,definition,
( ex1E1
= ( ! [A: $i,Xphi: $i > $o] :
( ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1E1) ).
thf(ex1I,definition,
( ex1I
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xy )
=> ( Xy = Xx ) ) )
=> ( ex1 @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I) ).
thf(ex1I2,definition,
( ex1I2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ex1 @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ex1I2) ).
thf(exu,definition,
( exu
= ( ^ [Xphi: $i > $o] :
? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu) ).
thf(exuE1,definition,
( exuE1
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE1) ).
thf(exuE2,definition,
( exuE2
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE2) ).
thf(exuE3e,definition,
( exuE3e
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ? [Xx: $i] : ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3e) ).
thf(exuE3u,definition,
( exuE3u
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuE3u) ).
thf(exuEu,definition,
( exuEu
= ( ! [Xphi: $i > $o] :
( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
=> ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuEu) ).
thf(exuI1,definition,
( exuI1
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
( ( Xphi @ Xx )
& ! [Xy: $i] :
( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI1) ).
thf(exuI2,definition,
( exuI2
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( Xphi @ Xy )
<=> ( Xy = Xx ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI2) ).
thf(exuI3,definition,
( exuI3
= ( ! [Xphi: $i > $o] :
( ? [Xx: $i] : ( Xphi @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) )
=> ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exuI3) ).
thf(exu__Cong,definition,
( exu__Cong
= ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) )
=> ( ( exu
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
<=> ( exu
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',exu__Cong) ).
thf(foundationAx,definition,
( foundationAx
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',foundationAx) ).
thf(inCongP,definition,
( inCongP
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inCongP) ).
thf(inPowerset,definition,
( inPowerset
= ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',inPowerset) ).
thf(in__Cong,definition,
( in__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',in__Cong) ).
thf(iskpair,definition,
( iskpair
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
& ? [Xy: $i] :
( ( in @ Xy @ ( setunion @ A ) )
& ( A
= ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',iskpair) ).
thf(kfstpairEq,definition,
( kfstpairEq
= ( ! [Xx: $i,Xy: $i] :
( ( kfst @ ( kpair @ Xx @ Xy ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstpairEq) ).
thf(kfstsingleton,definition,
( kfstsingleton
= ( ! [Xu: $i] :
( ( iskpair @ Xu )
=> ( singleton
@ ( dsetconstr @ ( setunion @ Xu )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kfstsingleton) ).
thf(kpair,definition,
( kpair
= ( ^ [Xx: $i,Xy: $i] : ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpair) ).
thf(kpairiskpair,definition,
( kpairiskpair
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairiskpair) ).
thf(kpairp,definition,
( kpairp
= ( ! [Xx: $i,Xy: $i] : ( iskpair @ ( kpair @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',kpairp) ).
thf(noeltsimpempty,definition,
( noeltsimpempty
= ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',noeltsimpempty) ).
thf(nonempty,definition,
( nonempty
= ( ^ [Xx: $i] : ( Xx != emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonempty) ).
thf(nonemptyE1,definition,
( nonemptyE1
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] : ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyE1) ).
thf(nonemptyI,definition,
( nonemptyI
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( nonempty
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI) ).
thf(nonemptyI1,definition,
( nonemptyI1
= ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ( nonempty @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyI1) ).
thf(nonemptyImpWitness,definition,
( nonemptyImpWitness
= ( ! [A: $i] :
( ( nonempty @ A )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& $true ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonemptyImpWitness) ).
thf(notdallE,definition,
( notdallE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdallE) ).
thf(notdexE,definition,
( notdexE
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notdexE) ).
thf(notequalI1,definition,
( notequalI1
= ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI1) ).
thf(notequalI2,definition,
( notequalI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notequalI2) ).
thf(notinemptyset,definition,
( notinemptyset
= ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinemptyset) ).
thf(notinsingleton,definition,
( notinsingleton
= ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notinsingleton) ).
thf(notsubsetI,definition,
( notsubsetI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',notsubsetI) ).
thf(omega0Ax,definition,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega0Ax) ).
thf(omegaIndAx,definition,
( omegaIndAx
= ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaIndAx) ).
thf(omegaSAx,definition,
( omegaSAx
= ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omegaSAx) ).
thf(omega__Cong,definition,
( omega__Cong
= ( omega = omega ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',omega__Cong) ).
thf(powersetAx,definition,
( powersetAx
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetAx) ).
thf(powersetE,definition,
( powersetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE) ).
thf(powersetE1,definition,
( powersetE1
= ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetE1) ).
thf(powersetI,definition,
( powersetI
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI) ).
thf(powersetI1,definition,
( powersetI1
= ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetI1) ).
thf(powerset__Cong,definition,
( powerset__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powerset__Cong) ).
thf(powersetsubset,definition,
( powersetsubset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',powersetsubset) ).
thf(prop2set2propI,definition,
( prop2set2propI
= ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2set2propI) ).
thf(prop2setE,definition,
( prop2setE
= ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setE) ).
thf(prop2setI,definition,
( prop2setI
= ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prop2setI) ).
thf(quantDeMorgan1,definition,
( quantDeMorgan1
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan1) ).
thf(quantDeMorgan2,definition,
( quantDeMorgan2
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan2) ).
thf(quantDeMorgan3,definition,
( quantDeMorgan3
= ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan3) ).
thf(quantDeMorgan4,definition,
( quantDeMorgan4
= ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',quantDeMorgan4) ).
thf(replAx,definition,
( replAx
= ( ! [Xphi: $i > $i > $o,A: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( exu
@ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ A )
& ( Xphi @ Xy @ Xx ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',replAx) ).
thf(secondinupair,definition,
( secondinupair
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',secondinupair) ).
thf(sepInPowerset,definition,
( sepInPowerset
= ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepInPowerset) ).
thf(sepSubset,definition,
( sepSubset
= ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sepSubset) ).
thf(setadjoinAx,definition,
( setadjoinAx
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinAx) ).
thf(setadjoinE,definition,
( setadjoinE
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinE) ).
thf(setadjoinIL,definition,
( setadjoinIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIL) ).
thf(setadjoinIR,definition,
( setadjoinIR
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinIR) ).
thf(setadjoinOr,definition,
( setadjoinOr
= ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinOr) ).
thf(setadjoinSub,definition,
( setadjoinSub
= ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub) ).
thf(setadjoinSub2,definition,
( setadjoinSub2
= ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoinSub2) ).
thf(setadjoin__Cong,definition,
( setadjoin__Cong
= ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setadjoin__Cong) ).
thf(setbeta,definition,
( setbeta
= ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setbeta) ).
thf(setext,definition,
( setext
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setext) ).
thf(setextAx,definition,
( setextAx
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextAx) ).
thf(setextsub,definition,
( setextsub
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setextsub) ).
thf(setminusEL,definition,
( setminusEL
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusEL) ).
thf(setminusELneg,definition,
( setminusELneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusELneg) ).
thf(setminusER,definition,
( setminusER
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusER) ).
thf(setminusERneg,definition,
( setminusERneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusERneg) ).
thf(setminusI,definition,
( setminusI
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusI) ).
thf(setminusILneg,definition,
( setminusILneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusILneg) ).
thf(setminusIRneg,definition,
( setminusIRneg
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusIRneg) ).
thf(setminusLsub,definition,
( setminusLsub
= ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusLsub) ).
thf(setminusSubset1,definition,
( setminusSubset1
= ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset1) ).
thf(setminusSubset2,definition,
( setminusSubset2
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setminusSubset2) ).
thf(setoftrueEq,definition,
( setoftrueEq
= ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setoftrueEq) ).
thf(setukpairIL,definition,
( setukpairIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIL) ).
thf(setukpairIR,definition,
( setukpairIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairIR) ).
thf(setukpairinjL1,definition,
( setukpairinjL1
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL1) ).
thf(setunionAx,definition,
( setunionAx
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionAx) ).
thf(setunionE,definition,
( setunionE
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE) ).
thf(setunionE2,definition,
( setunionE2
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionE2) ).
thf(setunionI,definition,
( setunionI
= ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionI) ).
thf(setunion__Cong,definition,
( setunion__Cong
= ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunion__Cong) ).
thf(setunionsingleton,definition,
( setunionsingleton
= ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton) ).
thf(setunionsingleton1,definition,
( setunionsingleton1
= ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton1) ).
thf(setunionsingleton2,definition,
( setunionsingleton2
= ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setunionsingleton2) ).
thf(singleton,definition,
( singleton
= ( ^ [A: $i] :
? [Xx: $i] :
( ( in @ Xx @ A )
& ( A
= ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singleton) ).
thf(singletoninpowerset,definition,
( singletoninpowerset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowerset) ).
thf(singletoninpowunion,definition,
( singletoninpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletoninpowunion) ).
thf(singletonprop,definition,
( singletonprop
= ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ A )
=> ( ( Xphi @ Xx )
=> ( ( Xphi @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( singleton
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonprop) ).
thf(singletonsswitch,definition,
( singletonsswitch
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsswitch) ).
thf(singletonsubset,definition,
( singletonsubset
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsubset) ).
thf(singletonsuniq,definition,
( singletonsuniq
= ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',singletonsuniq) ).
thf(subPowSU,definition,
( subPowSU
= ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subPowSU) ).
thf(subset2powerset,definition,
( subset2powerset
= ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subset2powerset) ).
thf(subsetE,definition,
( subsetE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE) ).
thf(subsetE2,definition,
( subsetE2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetE2) ).
thf(subsetI1,definition,
( subsetI1
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI1) ).
thf(subsetI2,definition,
( subsetI2
= ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetI2) ).
thf(subsetRefl,definition,
( subsetRefl
= ( ! [A: $i] : ( subset @ A @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetRefl) ).
thf(subsetTrans,definition,
( subsetTrans
= ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetTrans) ).
thf(subsetemptysetimpeq,definition,
( subsetemptysetimpeq
= ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',subsetemptysetimpeq) ).
thf(symdiffE,definition,
( symdiffE
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffE) ).
thf(symdiffI1,definition,
( symdiffI1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI1) ).
thf(symdiffI2,definition,
( symdiffI2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffI2) ).
thf(symdiffIneg1,definition,
( symdiffIneg1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg1) ).
thf(symdiffIneg2,definition,
( symdiffIneg2
= ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',symdiffIneg2) ).
thf(theprop,definition,
( theprop
= ( ! [X: $i] :
( ( singleton @ X )
=> ( in @ ( setunion @ X ) @ X ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',theprop) ).
thf(ubforcartprodlem1,definition,
( ubforcartprodlem1
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem1) ).
thf(ubforcartprodlem2,definition,
( ubforcartprodlem2
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem2) ).
thf(ubforcartprodlem3,definition,
( ubforcartprodlem3
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( kpair @ Xx @ Xy ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ubforcartprodlem3) ).
thf(uniqinunit,definition,
( uniqinunit
= ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',uniqinunit) ).
thf(upairinpowunion,definition,
( upairinpowunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairinpowunion) ).
thf(upairset2E,definition,
( upairset2E
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2E) ).
thf(upairset2IR,definition,
( upairset2IR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairset2IR) ).
thf(upairsetE,definition,
( upairsetE
= ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetE) ).
thf(upairsetIL,definition,
( upairsetIL
= ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIL) ).
thf(upairsetIR,definition,
( upairsetIR
= ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsetIR) ).
thf(upairsubunion,definition,
( upairsubunion
= ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',upairsubunion) ).
thf(vacuousDall,definition,
( vacuousDall
= ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',vacuousDall) ).
thf(wellorderingAx,definition,
( wellorderingAx
= ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',wellorderingAx) ).
thf(1,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ( setminusER
=> ( setminusSubset2
=> ( setminusERneg
=> ( setminusELneg
=> ( setminusILneg
=> ( setminusIRneg
=> ( setminusLsub
=> ( setminusSubset1
=> ( symdiffE
=> ( symdiffI1
=> ( symdiffI2
=> ( symdiffIneg1
=> ( symdiffIneg2
=> ( secondinupair
=> ( setukpairIL
=> ( setukpairIR
=> ( kpairiskpair
=> ( kpairp
=> ( singletonsubset
=> ( singletoninpowerset
=> ( singletoninpowunion
=> ( upairset2E
=> ( upairsubunion
=> ( upairinpowunion
=> ( ubforcartprodlem1
=> ( ubforcartprodlem2
=> ( ubforcartprodlem3
=> ( cartprodpairin
=> ( cartprodmempair1
=> ( cartprodmempair
=> ( setunionE2
=> ( setunionsingleton1
=> ( setunionsingleton2
=> ( setunionsingleton
=> ( singletonprop
=> ( ex1E1
=> ( ex1I
=> ( ex1I2
=> ( singletonsuniq
=> ( setukpairinjL1
=> ( kfstsingleton
=> ( theprop
=> ( kfstpairEq
=> ( cartprodfstin
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',setukpairinjL2) ).
thf(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
=> ! [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 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(negate_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) )
=> ( ( in @ emptyset @ omega )
=> ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) )
=> ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) )
=> ( ! [SY21: $i > $i > $o,SY22: $i] :
( ! [SY23: $i] :
( ( in @ SY23 @ SY22 )
=> ? [SY25: $i] :
( ( SY21 @ SY23 @ SY25 )
& ! [SY26: $i] :
( ( SY21 @ SY23 @ SY26 )
=> ( SY25 = SY26 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY22 )
& ( SY21 @ Xy @ Xx ) ) ) )
=> ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) )
=> ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) )
=> ( ! [SY53: $i > $o] :
( ? [SY55: $i] :
( ( SY53 @ SY55 )
& ! [SY56: $i] :
( ( SY53 @ SY56 )
=> ( SY55 = SY56 ) ) )
=> ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) )
=> ( ! [SY70: $i > $o] :
( ? [SY72: $i] :
( ( SY70 @ SY72 )
& ! [SY73: $i] :
( ( SY70 @ SY73 )
=> ( SY72 = SY73 ) ) )
=> ? [Xx: $i] :
( ( SY70 @ Xx )
& ! [Xy: $i] :
( ( SY70 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi )
=> ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false )
=> ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
=> ( ! [SY82: $i > $o] :
( ? [SY84: $i] :
( ( SY82 @ SY84 )
& ! [SY85: $i] :
( ( SY82 @ SY85 )
=> ( SY84 = SY85 ) ) )
=> ? [Xx: $i] : ( SY82 @ Xx ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) )
=> ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) )
=> ( ! [SY99: $i] :
( ( SY99 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY99 ) )
=> ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ( in @ SY103 @ SY101 )
=> ( ( SY102 @ SY103 )
=> ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) )
=> ( ! [SY105: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY105 )
=> ( SY105 != emptyset ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) )
=> ( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) )
=> ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) )
=> ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) )
=> ( ! [SY138: $i > $o] :
( ? [SY140: $i] :
( ( SY138 @ SY140 )
& ! [SY141: $i] :
( ( SY138 @ SY141 )
=> ( SY140 = SY141 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY138 @ Xy )
<=> ( Xy = Xx ) ) )
=> ( ! [SY144: $i] :
( ( SY144 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY144 )
& $true ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) )
=> ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) )
=> ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) )
=> ( ! [SY193: $i > $o] :
( ? [Xx: $i] :
( ( SY193 @ Xx )
& ! [Xy: $i] :
( ( SY193 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY197: $i] :
( ( SY193 @ SY197 )
& ! [SY198: $i] :
( ( SY193 @ SY198 )
=> ( SY197 = SY198 ) ) ) )
=> ( ! [SY199: $i > $o] :
( ? [Xx: $i] : ( SY199 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY199 @ Xx )
=> ( ( SY199 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY204: $i] :
( ( SY199 @ SY204 )
& ! [SY205: $i] :
( ( SY199 @ SY205 )
=> ( SY204 = SY205 ) ) ) ) )
=> ( ! [SY206: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY206 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY210: $i] :
( ( SY206 @ SY210 )
& ! [SY211: $i] :
( ( SY206 @ SY211 )
=> ( SY210 = SY211 ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) )
=> ( ! [SY220: $i > $o] :
( ? [SY222: $i] :
( ( SY220 @ SY222 )
& ! [SY223: $i] :
( ( SY220 @ SY223 )
=> ( SY222 = SY223 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY220 @ Xx )
=> ( ( SY220 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY226: $i > $o,SY227: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY226 @ Xx )
<=> ( SY227 @ Xy ) ) )
=> ( ? [SY231: $i] :
( ( SY226 @ SY231 )
& ! [SY232: $i] :
( ( SY226 @ SY232 )
=> ( SY231 = SY232 ) ) )
<=> ? [SY234: $i] :
( ( SY227 @ SY234 )
& ! [SY235: $i] :
( ( SY227 @ SY235 )
=> ( SY234 = SY235 ) ) ) ) )
=> ( ( emptyset = emptyset )
=> ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) )
=> ( ( omega = omega )
=> ( ! [SY244: $i > $o] :
( ? [SY246: $i] :
( ( SY244 @ SY246 )
& ! [SY247: $i] :
( ( SY244 @ SY247 )
=> ( SY246 = SY247 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY244 @ Xx )
=> ( ( SY244 @ Xy )
=> ( Xx = Xy ) ) ) )
=> ( ! [SY250: $i > $o,SY251: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY250 @ Xx )
<=> ( SY251 @ Xy ) ) )
=> ( ? [SY255: $i] :
( ( SY250 @ SY255 )
& ! [SY256: $i] :
( ( SY250 @ SY256 )
=> ( SY255 = SY256 ) ) )
=> ( ? [SY258: $i] :
( ( SY251 @ SY258 )
& ! [SY259: $i] :
( ( SY251 @ SY259 )
=> ( SY258 = SY259 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) )
=> ( ! [A: $i] : ( subset @ emptyset @ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) )
=> ( ! [A: $i] : ( subset @ A @ A )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) )
=> ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) )
=> ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) )
=> ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) )
=> ( ! [A: $i] : ( in @ A @ ( powerset @ A ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) )
=> ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B )
=> ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) )
=> ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) )
=> ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) )
=> ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A )
=> ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) )
=> ( ! [SY420: $i,SY421: $i] :
? [SY422: $i] :
( ( in @ SY422 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY423: $i] :
( ( in @ SY423 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [SY424: $i,SY425: $i] :
? [SY427: $i] :
( ( in @ SY427 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY428: $i] :
( ( in @ SY428 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY427 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY427 @ ( setadjoin @ SY428 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
=> ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
=> ( ! [SY455: $i,SY456: $i,SY457: $i] :
( ( in @ SY457 @ SY455 )
=> ! [SY458: $i] :
( ( in @ SY458 @ SY456 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY457 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY457 @ ( setadjoin @ SY458 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SY455 @ SY456 ) ) ) ) ) )
=> ( ! [SY460: $i,SY461: $i,SY462: $i] :
( ( in @ SY462 @ SY460 )
=> ! [SY463: $i] :
( ( in @ SY463 @ SY461 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY462 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY462 @ ( setadjoin @ SY463 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SY460 @ SY461 ) ) ) )
=> ( ! [SY465: $i,SY466: $i,SY467: $i] :
( ( in @ SY467 @ ( cartprod @ SY465 @ SY466 ) )
=> ? [SY468: $i] :
( ( in @ SY468 @ SY465 )
& ? [SY469: $i] :
( ( in @ SY469 @ SY466 )
& ( SY467
= ( setadjoin @ ( setadjoin @ SY468 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY468 @ ( setadjoin @ SY469 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [SY471: $i,SY472: $i,SY473: $i] :
( ( in @ SY473 @ ( cartprod @ SY471 @ SY472 ) )
=> ? [SY474: $i] :
( ( in @ SY474 @ ( setunion @ SY473 ) )
& ? [SY475: $i] :
( ( in @ SY475 @ ( setunion @ SY473 ) )
& ( SY473
= ( setadjoin @ ( setadjoin @ SY474 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY474 @ ( setadjoin @ SY475 @ emptyset ) ) @ emptyset ) ) ) ) ) )
=> ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) )
=> ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A )
=> ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) )
=> ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx )
=> ( ! [SY482: $i,SY483: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY482 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY482 )
=> ( ( SY483 @ Xx )
=> ( ( SY483 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY482 )
& ( SY483 @ Xx ) )
=> ? [SY488: $i] :
( ( in @ SY488
@ ( dsetconstr @ SY482
@ ^ [Xx: $i] : ( SY483 @ Xx ) ) )
& ( ( dsetconstr @ SY482
@ ^ [Xx: $i] : ( SY483 @ Xx ) )
= ( setadjoin @ SY488 @ emptyset ) ) ) ) )
=> ( ! [SY489: $i,SY490: $i > $o] :
( ? [SY495: $i] :
( ( in @ SY495
@ ( dsetconstr @ SY489
@ ^ [SY496: $i] : ( SY490 @ SY496 ) ) )
& ( ( dsetconstr @ SY489
@ ^ [SY497: $i] : ( SY490 @ SY497 ) )
= ( setadjoin @ SY495 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY489 )
& ( SY490 @ Xx ) ) )
=> ( ! [SY499: $i,SY500: $i > $o,SY501: $i] :
( ( in @ SY501 @ SY499 )
=> ( ( SY500 @ SY501 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY499 )
=> ( ( SY500 @ Xy )
=> ( Xy = SY501 ) ) )
=> ? [SY507: $i] :
( ( in @ SY507
@ ( dsetconstr @ SY499
@ ^ [SY508: $i] : ( SY500 @ SY508 ) ) )
& ( ( dsetconstr @ SY499
@ ^ [SY509: $i] : ( SY500 @ SY509 ) )
= ( setadjoin @ SY507 @ emptyset ) ) ) ) ) )
=> ( ! [SY510: $i,SY511: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY510 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY510 )
=> ( ( SY511 @ Xx )
=> ( ( SY511 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY510 )
& ( SY511 @ Xx ) )
=> ? [SY519: $i] :
( ( in @ SY519
@ ( dsetconstr @ SY510
@ ^ [SY520: $i] : ( SY511 @ SY520 ) ) )
& ( ( dsetconstr @ SY510
@ ^ [SY521: $i] : ( SY511 @ SY521 ) )
= ( setadjoin @ SY519 @ emptyset ) ) ) ) )
=> ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) )
=> ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) )
=> ( ! [SY527: $i] :
( ? [SY528: $i] :
( ( in @ SY528 @ ( setunion @ SY527 ) )
& ? [SY529: $i] :
( ( in @ SY529 @ ( setunion @ SY527 ) )
& ( SY527
= ( setadjoin @ ( setadjoin @ SY528 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY528 @ ( setadjoin @ SY529 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [SY531: $i] :
( ( in @ SY531
@ ( dsetconstr @ ( setunion @ SY527 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY527 ) ) )
& ( ( dsetconstr @ ( setunion @ SY527 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY527 ) )
= ( setadjoin @ SY531 @ emptyset ) ) ) )
=> ( ! [SY532: $i] :
( ? [SY533: $i] :
( ( in @ SY533 @ SY532 )
& ( SY532
= ( setadjoin @ SY533 @ emptyset ) ) )
=> ( in @ ( setunion @ SY532 ) @ SY532 ) )
=> ( ! [SY534: $i,SY535: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ SY534 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY534 @ ( setadjoin @ SY535 @ emptyset ) ) @ emptyset ) ) )
= SY534 )
=> ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) )
=> ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
= $false ),
inference(unfold_def,[status(thm)],[2,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(4,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
<=> ( in @ Xx @ B ) )
=> ( A = B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(5,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(6,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
<=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(7,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
<=> ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(8,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
<=> ? [B: $i] :
( ( in @ Xx @ B )
& ( in @ B @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(9,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(10,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(11,plain,
( ( ! [A: $i] :
( ( ( in @ emptyset @ A )
& ! [Xx: $i] :
( ( ( in @ Xx @ omega )
& ( in @ Xx @ A ) )
=> ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
=> ! [Xx: $i] :
( ( in @ Xx @ omega )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(12,plain,
( ( ! [SY21: $i > $i > $o,SY22: $i] :
( ! [SY23: $i] :
( ( in @ SY23 @ SY22 )
=> ? [SY25: $i] :
( ( SY21 @ SY23 @ SY25 )
& ! [SY26: $i] :
( ( SY21 @ SY23 @ SY26 )
=> ( SY25 = SY26 ) ) ) )
=> ? [B: $i] :
! [Xx: $i] :
( ( in @ Xx @ B )
<=> ? [Xy: $i] :
( ( in @ Xy @ SY22 )
& ( SY21 @ Xy @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(13,plain,
( ( ! [A: $i] :
( ? [Xx: $i] : ( in @ Xx @ A )
=> ? [B: $i] :
( ( in @ B @ A )
& ~ ? [Xx: $i] :
( ( in @ Xx @ B )
& ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(14,plain,
( ( ! [A: $i] :
? [B: $i] :
( ! [C: $i] :
( ( in @ C @ B )
=> ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) ) )
& ! [Xx: $i,Xy: $i] :
( ( ( in @ Xx @ A )
& ( in @ Xy @ A ) )
=> ( ! [C: $i] :
( ( in @ C @ B )
=> ( ( in @ Xx @ C )
<=> ( in @ Xy @ C ) ) )
=> ( Xx = Xy ) ) )
& ! [C: $i,D: $i] :
( ( ( in @ C @ B )
& ( in @ D @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ D ) )
| ! [Xx: $i] :
( ( in @ Xx @ D )
=> ( in @ Xx @ C ) ) ) )
& ! [C: $i] :
( ( ! [Xx: $i] :
( ( in @ Xx @ C )
=> ( in @ Xx @ A ) )
& ? [Xx: $i] : ( in @ Xx @ C ) )
=> ? [D: $i,Xx: $i] :
( ( in @ D @ B )
& ( in @ Xx @ C )
& ~ ? [Xy: $i] :
( ( in @ Xy @ D )
& ( in @ Xy @ C ) )
& ! [E: $i] :
( ( in @ E @ B )
=> ( ! [Xy: $i] :
( ( in @ Xy @ E )
=> ( in @ Xy @ D ) )
| ( in @ Xx @ E ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(15,plain,
( ( ! [SY53: $i > $o] :
( ? [SY55: $i] :
( ( SY53 @ SY55 )
& ! [SY56: $i] :
( ( SY53 @ SY56 )
=> ( SY55 = SY56 ) ) )
=> ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(16,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( Xphi @ Xx )
=> ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(17,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(18,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(19,plain,
( ( ! [SY70: $i > $o] :
( ? [SY72: $i] :
( ( SY70 @ SY72 )
& ! [SY73: $i] :
( ( SY70 @ SY73 )
=> ( SY72 = SY73 ) ) )
=> ? [Xx: $i] :
( ( SY70 @ Xx )
& ! [Xy: $i] :
( ( SY70 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(20,plain,
( ( ! [Xphi: $o,Xx: $i] :
( ( in @ Xx @ ( prop2set @ Xphi ) )
=> Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(21,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> ! [Xphi: $o] : Xphi ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(22,plain,
( ( ! [Xx: $i] :
( ( in @ Xx @ emptyset )
=> $false ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(23,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(24,plain,
( ( ! [SY82: $i > $o] :
( ? [SY84: $i] :
( ( SY82 @ SY84 )
& ! [SY85: $i] :
( ( SY82 @ SY85 )
=> ( SY84 = SY85 ) ) )
=> ? [Xx: $i] : ( SY82 @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(25,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(26,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(27,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(28,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
<=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(29,plain,
( ( ! [SY99: $i] :
( ( SY99 != emptyset )
=> ? [Xx: $i] : ( in @ Xx @ SY99 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(30,plain,
( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ( in @ SY103 @ SY101 )
=> ( ( SY102 @ SY103 )
=> ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(31,plain,
( ( ! [SY105: $i] :
( ? [Xx: $i] : ( in @ Xx @ SY105 )
=> ( SY105 != emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(32,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(33,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(34,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ A )
=> ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(35,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ! [Xphi: $o] :
( ( ( Xy = Xx )
=> Xphi )
=> ( ( ( in @ Xy @ A )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(36,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
=> ( ( Xy = Xx )
| ( in @ Xy @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(37,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(38,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ A ) )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(39,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(40,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(41,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(42,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> ( in @ Xx @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(43,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ! [Xphi: $o] :
( ! [B: $i] :
( ( in @ Xx @ B )
=> ( ( in @ B @ A )
=> Xphi ) )
=> Xphi ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(44,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(45,plain,
( ( ! [SY138: $i > $o] :
( ? [SY140: $i] :
( ( SY138 @ SY140 )
& ! [SY141: $i] :
( ( SY138 @ SY141 )
=> ( SY140 = SY141 ) ) )
=> ? [Xx: $i] :
! [Xy: $i] :
( ( SY138 @ Xy )
<=> ( Xy = Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(46,plain,
( ( ! [SY144: $i] :
( ( SY144 != emptyset )
=> ? [Xx: $i] :
( ( in @ Xx @ SY144 )
& $true ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(47,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(48,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
=> ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(49,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(50,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
=> ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(51,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(52,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(53,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(54,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ( ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= emptyset )
=> $false ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(55,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ( in @ Xx @ emptyset )
=> ( Xphi @ Xx ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(56,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(57,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) )
=> ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(58,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(59,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) )
=> ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(60,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(61,plain,
( ( ! [Xphi: $o] :
( Xphi
=> ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(62,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( Xphi @ Xx ) )
=> ! [Xx: $i] :
( ( in @ Xx @ A )
=> ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(63,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ~ ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( Xphi @ Xx ) )
=> ? [Xx: $i] :
( ( in @ Xx @ A )
& ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(64,plain,
( ( ! [SY193: $i > $o] :
( ? [Xx: $i] :
( ( SY193 @ Xx )
& ! [Xy: $i] :
( ( SY193 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY197: $i] :
( ( SY193 @ SY197 )
& ! [SY198: $i] :
( ( SY193 @ SY198 )
=> ( SY197 = SY198 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(65,plain,
( ( ! [SY199: $i > $o] :
( ? [Xx: $i] : ( SY199 @ Xx )
=> ( ! [Xx: $i,Xy: $i] :
( ( SY199 @ Xx )
=> ( ( SY199 @ Xy )
=> ( Xx = Xy ) ) )
=> ? [SY204: $i] :
( ( SY199 @ SY204 )
& ! [SY205: $i] :
( ( SY199 @ SY205 )
=> ( SY204 = SY205 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(66,plain,
( ( ! [SY206: $i > $o] :
( ? [Xx: $i] :
! [Xy: $i] :
( ( SY206 @ Xy )
<=> ( Xy = Xx ) )
=> ? [SY210: $i] :
( ( SY206 @ SY210 )
& ! [SY211: $i] :
( ( SY206 @ SY211 )
=> ( SY210 = SY211 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(67,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(68,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( in @ Xx @ A )
<=> ( in @ Xy @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(69,plain,
( ( ! [SY220: $i > $o] :
( ? [SY222: $i] :
( ( SY220 @ SY222 )
& ! [SY223: $i] :
( ( SY220 @ SY223 )
=> ( SY222 = SY223 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY220 @ Xx )
=> ( ( SY220 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(70,plain,
( ( ! [SY226: $i > $o,SY227: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY226 @ Xx )
<=> ( SY227 @ Xy ) ) )
=> ( ? [SY231: $i] :
( ( SY226 @ SY231 )
& ! [SY232: $i] :
( ( SY226 @ SY232 )
=> ( SY231 = SY232 ) ) )
<=> ? [SY234: $i] :
( ( SY227 @ SY234 )
& ! [SY235: $i] :
( ( SY227 @ SY235 )
=> ( SY234 = SY235 ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(71,plain,
( ( emptyset = emptyset )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(72,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ! [Xz: $i,Xu: $i] :
( ( Xz = Xu )
=> ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(73,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(74,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(75,plain,
( ( omega = omega )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(76,plain,
( ( ! [SY244: $i > $o] :
( ? [SY246: $i] :
( ( SY244 @ SY246 )
& ! [SY247: $i] :
( ( SY244 @ SY247 )
=> ( SY246 = SY247 ) ) )
=> ! [Xx: $i,Xy: $i] :
( ( SY244 @ Xx )
=> ( ( SY244 @ Xy )
=> ( Xx = Xy ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(77,plain,
( ( ! [SY250: $i > $o,SY251: $i > $o] :
( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
=> ( ( SY250 @ Xx )
<=> ( SY251 @ Xy ) ) )
=> ( ? [SY255: $i] :
( ( SY250 @ SY255 )
& ! [SY256: $i] :
( ( SY250 @ SY256 )
=> ( SY255 = SY256 ) ) )
=> ( ? [SY258: $i] :
( ( SY251 @ SY258 )
& ! [SY259: $i] :
( ( SY251 @ SY259 )
=> ( SY258 = SY259 ) ) )
=> ( ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(78,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( ( Xx = Xy )
=> ( ( Xphi @ Xx )
<=> ( Xpsi @ Xy ) ) ) ) )
=> ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(79,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(80,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(81,plain,
( ( ! [A: $i,B: $i] :
( ( A = B )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(82,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ B ) )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(83,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(84,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(85,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( subset @ A @ B )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(86,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( subset @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(87,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
=> ( A != B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(88,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( A != B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(89,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(90,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ C )
=> ( subset @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(91,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(92,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(93,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(94,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( subset @ B @ A )
=> ( A = B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(95,plain,
( ( ! [A: $i] :
( ( subset @ A @ emptyset )
=> ( A = emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(96,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(97,plain,
( ( ! [A: $i,B: $i] :
( ( in @ B @ ( powerset @ A ) )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(98,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(99,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(100,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(101,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(102,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(103,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(104,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(105,plain,
( ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( ( in @ Xx @ A )
=> Xphi )
=> ( ( ( in @ Xx @ B )
=> Xphi )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(106,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binunion @ A @ B ) )
=> ( ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(107,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(108,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(109,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(110,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( subset @ C @ A )
=> ( ( subset @ C @ B )
=> ( subset @ C @ ( binintersect @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(111,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(112,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(113,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(114,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= B )
=> ( subset @ B @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(115,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( binintersect @ A @ B ) )
=> ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(116,plain,
( ( ! [A: $i,B: $i] :
( ~ ? [Xx: $i] :
( ( in @ Xx @ A )
& ( in @ Xx @ B ) )
=> ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(117,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(118,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ B @ A )
=> ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(119,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
= A )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(120,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(121,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( setminus @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(122,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ( in @ Xx @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(123,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
=> ~ ( in @ Xx @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(124,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
=> ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(125,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ( in @ Xx @ A )
=> ( in @ Xx @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(126,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(127,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(128,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(129,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(130,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
= emptyset )
=> ( subset @ A @ B ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(131,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( symdiff @ A @ B ) )
=> ! [Xphi: $o] :
( ( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> Xphi ) )
=> ( ( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> Xphi ) )
=> Xphi ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(132,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(133,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(134,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(135,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
=> ( ~ ( in @ Xx @ B )
=> ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(136,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(137,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(138,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(139,plain,
( ( ! [SY420: $i,SY421: $i] :
? [SY422: $i] :
( ( in @ SY422 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY423: $i] :
( ( in @ SY423 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY422 @ ( setadjoin @ SY423 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(140,plain,
( ( ! [SY424: $i,SY425: $i] :
? [SY427: $i] :
( ( in @ SY427 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) ) ) )
& ? [SY428: $i] :
( ( in @ SY428 @ ( setunion @ ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) ) ) )
& ( ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ SY427 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY427 @ ( setadjoin @ SY428 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(141,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(142,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(143,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(144,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
=> ( ( Xz = Xx )
| ( Xz = Xy ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(145,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(146,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(147,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(148,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
=> ! [Xy: $i] :
( ( in @ Xy @ B )
=> ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(149,plain,
( ( ! [SY455: $i,SY456: $i,SY457: $i] :
( ( in @ SY457 @ SY455 )
=> ! [SY458: $i] :
( ( in @ SY458 @ SY456 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY457 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY457 @ ( setadjoin @ SY458 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SY455 @ SY456 ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(150,plain,
( ( ! [SY460: $i,SY461: $i,SY462: $i] :
( ( in @ SY462 @ SY460 )
=> ! [SY463: $i] :
( ( in @ SY463 @ SY461 )
=> ( in @ ( setadjoin @ ( setadjoin @ SY462 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY462 @ ( setadjoin @ SY463 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SY460 @ SY461 ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(151,plain,
( ( ! [SY465: $i,SY466: $i,SY467: $i] :
( ( in @ SY467 @ ( cartprod @ SY465 @ SY466 ) )
=> ? [SY468: $i] :
( ( in @ SY468 @ SY465 )
& ? [SY469: $i] :
( ( in @ SY469 @ SY466 )
& ( SY467
= ( setadjoin @ ( setadjoin @ SY468 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY468 @ ( setadjoin @ SY469 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(152,plain,
( ( ! [SY471: $i,SY472: $i,SY473: $i] :
( ( in @ SY473 @ ( cartprod @ SY471 @ SY472 ) )
=> ? [SY474: $i] :
( ( in @ SY474 @ ( setunion @ SY473 ) )
& ? [SY475: $i] :
( ( in @ SY475 @ ( setunion @ SY473 ) )
& ( SY473
= ( setadjoin @ ( setadjoin @ SY474 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY474 @ ( setadjoin @ SY475 @ emptyset ) ) @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(153,plain,
( ( ! [A: $i,Xx: $i] :
( ( in @ Xx @ ( setunion @ A ) )
=> ? [X: $i] :
( ( in @ X @ A )
& ( in @ Xx @ X ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(154,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(155,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(156,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(157,plain,
( ( ! [SY482: $i,SY483: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY482 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY482 )
=> ( ( SY483 @ Xx )
=> ( ( SY483 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY482 )
& ( SY483 @ Xx ) )
=> ? [SY488: $i] :
( ( in @ SY488
@ ( dsetconstr @ SY482
@ ^ [Xx: $i] : ( SY483 @ Xx ) ) )
& ( ( dsetconstr @ SY482
@ ^ [Xx: $i] : ( SY483 @ Xx ) )
= ( setadjoin @ SY488 @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(158,plain,
( ( ! [SY489: $i,SY490: $i > $o] :
( ? [SY495: $i] :
( ( in @ SY495
@ ( dsetconstr @ SY489
@ ^ [SY496: $i] : ( SY490 @ SY496 ) ) )
& ( ( dsetconstr @ SY489
@ ^ [SY497: $i] : ( SY490 @ SY497 ) )
= ( setadjoin @ SY495 @ emptyset ) ) )
=> ? [Xx: $i] :
( ( in @ Xx @ SY489 )
& ( SY490 @ Xx ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(159,plain,
( ( ! [SY499: $i,SY500: $i > $o,SY501: $i] :
( ( in @ SY501 @ SY499 )
=> ( ( SY500 @ SY501 )
=> ( ! [Xy: $i] :
( ( in @ Xy @ SY499 )
=> ( ( SY500 @ Xy )
=> ( Xy = SY501 ) ) )
=> ? [SY507: $i] :
( ( in @ SY507
@ ( dsetconstr @ SY499
@ ^ [SY508: $i] : ( SY500 @ SY508 ) ) )
& ( ( dsetconstr @ SY499
@ ^ [SY509: $i] : ( SY500 @ SY509 ) )
= ( setadjoin @ SY507 @ emptyset ) ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(160,plain,
( ( ! [SY510: $i,SY511: $i > $o] :
( ! [Xx: $i] :
( ( in @ Xx @ SY510 )
=> ! [Xy: $i] :
( ( in @ Xy @ SY510 )
=> ( ( SY511 @ Xx )
=> ( ( SY511 @ Xy )
=> ( Xx = Xy ) ) ) ) )
=> ( ? [Xx: $i] :
( ( in @ Xx @ SY510 )
& ( SY511 @ Xx ) )
=> ? [SY519: $i] :
( ( in @ SY519
@ ( dsetconstr @ SY510
@ ^ [SY520: $i] : ( SY511 @ SY520 ) ) )
& ( ( dsetconstr @ SY510
@ ^ [SY521: $i] : ( SY511 @ SY521 ) )
= ( setadjoin @ SY519 @ emptyset ) ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(161,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
= ( setadjoin @ Xy @ emptyset ) )
=> ( Xx = Xy ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(162,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(163,plain,
( ( ! [SY527: $i] :
( ? [SY528: $i] :
( ( in @ SY528 @ ( setunion @ SY527 ) )
& ? [SY529: $i] :
( ( in @ SY529 @ ( setunion @ SY527 ) )
& ( SY527
= ( setadjoin @ ( setadjoin @ SY528 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY528 @ ( setadjoin @ SY529 @ emptyset ) ) @ emptyset ) ) ) ) )
=> ? [SY531: $i] :
( ( in @ SY531
@ ( dsetconstr @ ( setunion @ SY527 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY527 ) ) )
& ( ( dsetconstr @ ( setunion @ SY527 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY527 ) )
= ( setadjoin @ SY531 @ emptyset ) ) ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(164,plain,
( ( ! [SY532: $i] :
( ? [SY533: $i] :
( ( in @ SY533 @ SY532 )
& ( SY532
= ( setadjoin @ SY533 @ emptyset ) ) )
=> ( in @ ( setunion @ SY532 ) @ SY532 ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(165,plain,
( ( ! [SY534: $i,SY535: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ SY534 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY534 @ ( setadjoin @ SY535 @ emptyset ) ) @ emptyset ) ) )
= SY534 ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(166,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ( in @ Xu @ ( cartprod @ A @ B ) )
=> ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(167,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $false ),
inference(standard_cnf,[status(thm)],[3]) ).
thf(168,plain,
( ( ~ ! [Xx: $i,Xy: $i,Xz: $i,Xu: $i] :
( ( ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xz @ ( setadjoin @ Xu @ emptyset ) ) @ emptyset ) ) )
=> ( Xx = Xz ) ) )
= $true ),
inference(polarity_switch,[status(thm)],[167]) ).
thf(169,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY1055 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY1058 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY1058 @ ( setadjoin @ sK4_SY1060 @ emptyset ) ) @ emptyset ) ) )
& ( sK1_Xx != sK3_SY1058 ) )
= $true ),
inference(extcnf_combined,[status(esa)],[168]) ).
thf(170,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK5_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK5_Xx @ B @ A ) @ A )
| ( in @ ( sK5_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[4]) ).
thf(171,plain,
( ( ! [Xx: $i] :
( ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) )
& ! [A: $i,Xy: $i] :
( ( Xy != Xx )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
& ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[6]) ).
thf(172,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK6_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK6_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[7]) ).
thf(173,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK7_B @ Xx @ A ) )
& ( in @ ( sK7_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[8]) ).
thf(174,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[10]) ).
thf(175,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK8_Xx @ A ) @ omega )
& ( in @ ( sK8_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK8_Xx @ A ) @ ( sK8_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[11]) ).
thf(176,plain,
( ( ! [SY21: $i > $i > $o,SY22: $i] :
( ( ( in @ ( sK11_SY23 @ SY22 @ SY21 ) @ SY22 )
& ! [SY1065: $i] :
( ( ( SY21 @ ( sK11_SY23 @ SY22 @ SY21 ) @ ( sK12_SY1066 @ SY1065 @ SY22 @ SY21 ) )
& ( SY1065
!= ( sK12_SY1066 @ SY1065 @ SY22 @ SY21 ) ) )
| ~ ( SY21 @ ( sK11_SY23 @ SY22 @ SY21 ) @ SY1065 ) ) )
| ( ! [SY1061: $i] :
( ! [Xy: $i] :
( ~ ( SY21 @ Xy @ SY1061 )
| ~ ( in @ Xy @ SY22 ) )
| ( in @ SY1061 @ ( sK9_B @ SY22 @ SY21 ) ) )
& ! [SY1063: $i] :
( ~ ( in @ SY1063 @ ( sK9_B @ SY22 @ SY21 ) )
| ( ( SY21 @ ( sK10_Xy @ SY1063 @ SY22 @ SY21 ) @ SY1063 )
& ( in @ ( sK10_Xy @ SY1063 @ SY22 @ SY21 ) @ SY22 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[12]) ).
thf(177,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK13_B @ A ) @ A )
& ! [SY1067: $i] :
( ~ ( in @ SY1067 @ ( sK13_B @ A ) )
| ~ ( in @ SY1067 @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[13]) ).
thf(178,plain,
( ( ! [A: $i] :
( ! [SY1068: $i] :
( ( ( in @ ( sK18_Xx @ SY1068 @ A ) @ SY1068 )
& ~ ( in @ ( sK18_Xx @ SY1068 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY1068 )
| ( ! [SY1089: $i] :
( ~ ( in @ SY1089 @ ( sK14_B @ A ) )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SY1089 )
| ( in @ SY1087 @ ( sK16_SY1071 @ SY1068 @ A ) ) )
| ( in @ ( sK17_SY1085 @ SY1068 @ A ) @ SY1089 ) )
& ( in @ ( sK16_SY1071 @ SY1068 @ A ) @ ( sK14_B @ A ) )
& ( in @ ( sK17_SY1085 @ SY1068 @ A ) @ SY1068 )
& ! [SY1088: $i] :
( ~ ( in @ SY1088 @ ( sK16_SY1071 @ SY1068 @ A ) )
| ~ ( in @ SY1088 @ SY1068 ) ) ) )
& ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ SY1076 @ ( sK14_B @ A ) )
| ~ ( in @ SY1077 @ ( sK14_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1076 )
| ( in @ Xx @ SY1077 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1077 )
| ( in @ Xx @ SY1076 ) ) )
& ! [SY1080: $i] :
( ~ ( in @ SY1080 @ ( sK14_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1080 )
| ( in @ Xx @ A ) ) )
& ! [SY1082: $i,SY1083: $i] :
( ~ ( in @ SY1082 @ A )
| ~ ( in @ SY1083 @ A )
| ( ( in @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) @ ( sK14_B @ A ) )
& ( ~ ( in @ SY1082 @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) )
| ~ ( in @ SY1083 @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) ) )
& ( ( in @ SY1082 @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) )
| ( in @ SY1083 @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) ) ) )
| ( SY1082 = SY1083 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[14]) ).
thf(179,plain,
( ( ! [SY53: $i > $o] :
( ! [SY55: $i] :
( ( ( SY53 @ ( sK19_SY56 @ SY55 @ SY53 ) )
& ( SY55
!= ( sK19_SY56 @ SY55 @ SY53 ) ) )
| ~ ( SY53 @ SY55 ) )
| ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[15]) ).
thf(180,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[16]) ).
thf(181,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[17]) ).
thf(182,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[18]) ).
thf(183,plain,
( ( ! [SY70: $i > $o] :
( ! [SY72: $i] :
( ( ( SY70 @ ( sK21_SY73 @ SY72 @ SY70 ) )
& ( SY72
!= ( sK21_SY73 @ SY72 @ SY70 ) ) )
| ~ ( SY70 @ SY72 ) )
| ( ! [SY1092: $i] :
( ~ ( SY70 @ SY1092 )
| ( ( sK20_Xx @ SY70 )
= SY1092 ) )
& ( SY70 @ ( sK20_Xx @ SY70 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[19]) ).
thf(184,plain,
( ( ! [Xphi: $o] :
( ! [Xx: $i] :
~ ( in @ Xx @ ( prop2set @ Xphi ) )
| Xphi ) )
= $true ),
inference(extcnf_combined,[status(esa)],[20]) ).
thf(185,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(extcnf_combined,[status(esa)],[21]) ).
thf(186,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(extcnf_combined,[status(esa)],[22]) ).
thf(187,plain,
( ( ! [SY82: $i > $o] :
( ! [SY84: $i] :
( ( ( SY82 @ ( sK23_SY85 @ SY84 @ SY82 ) )
& ( SY84
!= ( sK23_SY85 @ SY84 @ SY82 ) ) )
| ~ ( SY82 @ SY84 ) )
| ( SY82 @ ( sK22_Xx @ SY82 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[24]) ).
thf(188,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK25_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK25_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK24_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK24_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[25]) ).
thf(189,plain,
( ( ! [A: $i] :
( ( in @ ( sK26_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[26]) ).
thf(190,plain,
( ( ! [A: $i] :
( ( in @ ( sK27_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[27]) ).
thf(191,plain,
( ( ! [A: $i] :
( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
& ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[28]) ).
thf(192,plain,
( ( ! [SY99: $i] :
( ( SY99 = emptyset )
| ( in @ ( sK28_Xx @ SY99 ) @ SY99 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[29]) ).
thf(193,plain,
( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ~ ( in @ SY103 @ SY101 )
| ~ ( SY102 @ SY103 )
| ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[30]) ).
thf(194,plain,
( ( ! [SY105: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ SY105 )
| ( SY105 != emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[31]) ).
thf(195,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[34]) ).
thf(196,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( ( ( Xy = Xx )
| ( in @ Xy @ A )
| ! [Xphi: $o] : Xphi )
& ( ( Xy = Xx )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xy @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[35]) ).
thf(197,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[36]) ).
thf(198,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK29_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK29_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[38]) ).
thf(199,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[41]) ).
thf(200,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A )
| ( in @ Xx @ ( setunion @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[42]) ).
thf(201,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ! [Xphi: $o] :
( ( ( in @ Xx @ ( sK30_B @ Xphi @ Xx @ A ) )
& ( in @ ( sK30_B @ Xphi @ Xx @ A ) @ A )
& ~ Xphi )
| Xphi ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[43]) ).
thf(202,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[44]) ).
thf(203,plain,
( ( ! [SY138: $i > $o] :
( ! [SY140: $i] :
( ( ( SY138 @ ( sK32_SY141 @ SY140 @ SY138 ) )
& ( SY140
!= ( sK32_SY141 @ SY140 @ SY138 ) ) )
| ~ ( SY138 @ SY140 ) )
| ( ! [SY1093: $i] :
( ( SY1093
!= ( sK31_Xx @ SY138 ) )
| ( SY138 @ SY1093 ) )
& ! [SY1094: $i] :
( ~ ( SY138 @ SY1094 )
| ( SY1094
= ( sK31_Xx @ SY138 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[45]) ).
thf(204,plain,
( ( ! [SY144: $i] :
( ( SY144 = emptyset )
| ( in @ ( sK33_Xx @ SY144 ) @ SY144 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[46]) ).
thf(205,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[47]) ).
thf(206,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
| ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[48]) ).
thf(207,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[49]) ).
thf(208,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[50]) ).
thf(209,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[51]) ).
thf(210,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[54]) ).
thf(211,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[55]) ).
thf(212,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK34_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK34_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[56]) ).
thf(213,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( in @ ( sK35_Xx @ Xphi @ A ) @ A )
& ( Xphi @ ( sK35_Xx @ Xphi @ A ) ) )
| ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[57]) ).
thf(214,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK36_Xx @ Xphi @ A ) )
& ( in @ ( sK36_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[58]) ).
thf(215,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK37_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK37_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[59]) ).
thf(216,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[60]) ).
thf(217,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[61]) ).
thf(218,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK38_Xx @ Xphi @ A ) )
& ( in @ ( sK38_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[62]) ).
thf(219,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK39_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK39_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[63]) ).
thf(220,plain,
( ( ! [SY193: $i > $o] :
( ! [Xx: $i] :
( ( ( SY193 @ ( sK41_Xy @ Xx @ SY193 ) )
& ( Xx
!= ( sK41_Xy @ Xx @ SY193 ) ) )
| ~ ( SY193 @ Xx ) )
| ( ! [SY1095: $i] :
( ~ ( SY193 @ SY1095 )
| ( ( sK40_SY197 @ SY193 )
= SY1095 ) )
& ( SY193 @ ( sK40_SY197 @ SY193 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[64]) ).
thf(221,plain,
( ( ! [SY199: $i > $o] :
( ! [Xx: $i] :
~ ( SY199 @ Xx )
| ( ( SY199 @ ( sK43_Xx @ SY199 ) )
& ( SY199 @ ( sK44_SY1097 @ SY199 ) )
& ( ( sK43_Xx @ SY199 )
!= ( sK44_SY1097 @ SY199 ) ) )
| ( ! [SY1096: $i] :
( ~ ( SY199 @ SY1096 )
| ( ( sK42_SY204 @ SY199 )
= SY1096 ) )
& ( SY199 @ ( sK42_SY204 @ SY199 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[65]) ).
thf(222,plain,
( ( ! [SY206: $i > $o] :
( ! [Xx: $i] :
( ( ( ( sK46_Xy @ Xx @ SY206 )
!= Xx )
| ~ ( SY206 @ ( sK46_Xy @ Xx @ SY206 ) ) )
& ( ( ( sK46_Xy @ Xx @ SY206 )
= Xx )
| ( SY206 @ ( sK46_Xy @ Xx @ SY206 ) ) ) )
| ( ! [SY1098: $i] :
( ~ ( SY206 @ SY1098 )
| ( ( sK45_SY210 @ SY206 )
= SY1098 ) )
& ( SY206 @ ( sK45_SY210 @ SY206 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[66]) ).
thf(223,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[67]) ).
thf(224,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) )
& ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xy @ B )
| ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[68]) ).
thf(225,plain,
( ( ! [SY220: $i > $o] :
( ! [SY222: $i] :
( ( ( SY220 @ ( sK47_SY223 @ SY222 @ SY220 ) )
& ( SY222
!= ( sK47_SY223 @ SY222 @ SY220 ) ) )
| ~ ( SY220 @ SY222 ) )
| ! [Xx: $i] :
( ~ ( SY220 @ Xx )
| ! [Xy: $i] :
( ~ ( SY220 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[69]) ).
thf(226,plain,
( ( ! [SY226: $i > $o,SY227: $i > $o] :
( ( ( ( sK54_Xx @ SY227 @ SY226 )
= ( sK55_SY1102 @ SY227 @ SY226 ) )
& ( ~ ( SY226 @ ( sK54_Xx @ SY227 @ SY226 ) )
| ~ ( SY227 @ ( sK55_SY1102 @ SY227 @ SY226 ) ) )
& ( ( SY226 @ ( sK54_Xx @ SY227 @ SY226 ) )
| ( SY227 @ ( sK55_SY1102 @ SY227 @ SY226 ) ) ) )
| ! [SY231: $i] :
( ( ( SY226 @ ( sK53_SY232 @ SY231 @ SY227 @ SY226 ) )
& ( SY231
!= ( sK53_SY232 @ SY231 @ SY227 @ SY226 ) ) )
| ~ ( SY226 @ SY231 ) )
| ( ! [SY1101: $i] :
( ~ ( SY227 @ SY1101 )
| ( ( sK52_SY234 @ SY227 @ SY226 )
= SY1101 ) )
& ( SY227 @ ( sK52_SY234 @ SY227 @ SY226 ) ) ) )
& ! [SY226: $i > $o,SY227: $i > $o] :
( ( ( ( sK50_Xx @ SY227 @ SY226 )
= ( sK51_SY1100 @ SY227 @ SY226 ) )
& ( ~ ( SY226 @ ( sK50_Xx @ SY227 @ SY226 ) )
| ~ ( SY227 @ ( sK51_SY1100 @ SY227 @ SY226 ) ) )
& ( ( SY226 @ ( sK50_Xx @ SY227 @ SY226 ) )
| ( SY227 @ ( sK51_SY1100 @ SY227 @ SY226 ) ) ) )
| ! [SY234: $i] :
( ( ( SY227 @ ( sK49_SY235 @ SY234 @ SY227 @ SY226 ) )
& ( SY234
!= ( sK49_SY235 @ SY234 @ SY227 @ SY226 ) ) )
| ~ ( SY227 @ SY234 ) )
| ( ! [SY1099: $i] :
( ~ ( SY226 @ SY1099 )
| ( ( sK48_SY231 @ SY227 @ SY226 )
= SY1099 ) )
& ( SY226 @ ( sK48_SY231 @ SY227 @ SY226 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[70]) ).
thf(227,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[71]) ).
thf(228,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ! [Xz: $i,Xu: $i] :
( ( Xz != Xu )
| ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[72]) ).
thf(229,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[73]) ).
thf(230,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[74]) ).
thf(231,plain,
$true = $true,
inference(extcnf_combined,[status(esa)],[75]) ).
thf(232,plain,
( ( ! [SY244: $i > $o] :
( ! [SY246: $i] :
( ( ( SY244 @ ( sK56_SY247 @ SY246 @ SY244 ) )
& ( SY246
!= ( sK56_SY247 @ SY246 @ SY244 ) ) )
| ~ ( SY244 @ SY246 ) )
| ! [Xx: $i] :
( ~ ( SY244 @ Xx )
| ! [Xy: $i] :
( ~ ( SY244 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[76]) ).
thf(233,plain,
( ( ! [SY250: $i > $o,SY251: $i > $o] :
( ( ( ( sK59_Xx @ SY251 @ SY250 )
= ( sK60_SY1103 @ SY251 @ SY250 ) )
& ( ~ ( SY250 @ ( sK59_Xx @ SY251 @ SY250 ) )
| ~ ( SY251 @ ( sK60_SY1103 @ SY251 @ SY250 ) ) )
& ( ( SY250 @ ( sK59_Xx @ SY251 @ SY250 ) )
| ( SY251 @ ( sK60_SY1103 @ SY251 @ SY250 ) ) ) )
| ! [SY255: $i] :
( ( ( SY250 @ ( sK58_SY256 @ SY255 @ SY251 @ SY250 ) )
& ( SY255
!= ( sK58_SY256 @ SY255 @ SY251 @ SY250 ) ) )
| ~ ( SY250 @ SY255 ) )
| ! [SY258: $i] :
( ( ( SY251 @ ( sK57_SY259 @ SY258 @ SY251 @ SY250 ) )
& ( SY258
!= ( sK57_SY259 @ SY258 @ SY251 @ SY250 ) ) )
| ~ ( SY251 @ SY258 ) )
| ( ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[77]) ).
thf(234,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ( ( in @ ( sK61_Xx @ Xpsi @ Xphi @ B @ A ) @ A )
& ( in @ ( sK62_SY1104 @ Xpsi @ Xphi @ B @ A ) @ B )
& ( ( sK61_Xx @ Xpsi @ Xphi @ B @ A )
= ( sK62_SY1104 @ Xpsi @ Xphi @ B @ A ) )
& ( ~ ( Xphi @ ( sK61_Xx @ Xpsi @ Xphi @ B @ A ) )
| ~ ( Xpsi @ ( sK62_SY1104 @ Xpsi @ Xphi @ B @ A ) ) )
& ( ( Xphi @ ( sK61_Xx @ Xpsi @ Xphi @ B @ A ) )
| ( Xpsi @ ( sK62_SY1104 @ Xpsi @ Xphi @ B @ A ) ) ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[78]) ).
thf(235,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK63_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK63_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[79]) ).
thf(236,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[80]) ).
thf(237,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[81]) ).
thf(238,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK64_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK64_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[82]) ).
thf(239,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[84]) ).
thf(240,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[85]) ).
thf(241,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[86]) ).
thf(242,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
| ( A != B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[87]) ).
thf(243,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( A != B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[88]) ).
thf(244,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[90]) ).
thf(245,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[92]) ).
thf(246,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[93]) ).
thf(247,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[94]) ).
thf(248,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[95]) ).
thf(249,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[96]) ).
thf(250,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[97]) ).
thf(251,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[99]) ).
thf(252,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[102]) ).
thf(253,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[104]) ).
thf(254,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi ) )
& ( ! [Xx: $i] :
~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[105]) ).
thf(255,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[106]) ).
thf(256,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[109]) ).
thf(257,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ C @ A )
| ~ ( subset @ C @ B )
| ( subset @ C @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[110]) ).
thf(258,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[111]) ).
thf(259,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[113]) ).
thf(260,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= B )
| ( subset @ B @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[114]) ).
thf(261,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[115]) ).
thf(262,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK65_Xx @ B @ A ) @ A )
& ( in @ ( sK65_Xx @ B @ A ) @ B ) )
| ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[116]) ).
thf(263,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[118]) ).
thf(264,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= A )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[119]) ).
thf(265,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[121]) ).
thf(266,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[122]) ).
thf(267,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[123]) ).
thf(268,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[124]) ).
thf(269,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[125]) ).
thf(270,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[126]) ).
thf(271,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[127]) ).
thf(272,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[128]) ).
thf(273,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
!= emptyset )
| ( subset @ A @ B ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[130]) ).
thf(274,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( symdiff @ A @ B ) )
| ( ( ( in @ Xx @ A )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ~ ( in @ Xx @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[131]) ).
thf(275,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[132]) ).
thf(276,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[133]) ).
thf(277,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[134]) ).
thf(278,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[135]) ).
thf(279,plain,
( ( ! [SY420: $i,SY421: $i] :
( ( ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SY421 @ SY420 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SY421 @ SY420 ) @ ( setadjoin @ ( sK67_SY1105 @ SY421 @ SY420 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK67_SY1105 @ SY421 @ SY420 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( sK66_SY422 @ SY421 @ SY420 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[139]) ).
thf(280,plain,
( ( ! [SY424: $i,SY425: $i] :
( ( ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SY425 @ SY424 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SY425 @ SY424 ) @ ( setadjoin @ ( sK69_SY1106 @ SY425 @ SY424 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK69_SY1106 @ SY425 @ SY424 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( sK68_SY427 @ SY425 @ SY424 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[140]) ).
thf(281,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[141]) ).
thf(282,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[142]) ).
thf(283,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[143]) ).
thf(284,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[144]) ).
thf(285,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[145]) ).
thf(286,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[146]) ).
thf(287,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[147]) ).
thf(288,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[148]) ).
thf(289,plain,
( ( ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ( in @ SY457 @ SY455 )
| ! [SY458: $i] :
( ~ ( in @ SY458 @ SY456 )
| ( in @ ( setadjoin @ ( setadjoin @ SY457 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY457 @ ( setadjoin @ SY458 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SY455 @ SY456 ) ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[149]) ).
thf(290,plain,
( ( ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ( in @ SY462 @ SY460 )
| ! [SY463: $i] :
( ~ ( in @ SY463 @ SY461 )
| ( in @ ( setadjoin @ ( setadjoin @ SY462 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY462 @ ( setadjoin @ SY463 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SY460 @ SY461 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[150]) ).
thf(291,plain,
( ( ! [SY465: $i,SY466: $i,SY467: $i] :
( ~ ( in @ SY467 @ ( cartprod @ SY465 @ SY466 ) )
| ( ( SY467
= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SY467 @ SY466 @ SY465 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SY467 @ SY466 @ SY465 ) @ ( setadjoin @ ( sK71_SY1107 @ SY467 @ SY466 @ SY465 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK71_SY1107 @ SY467 @ SY466 @ SY465 ) @ SY466 )
& ( in @ ( sK70_SY468 @ SY467 @ SY466 @ SY465 ) @ SY465 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[151]) ).
thf(292,plain,
( ( ! [SY471: $i,SY472: $i,SY473: $i] :
( ~ ( in @ SY473 @ ( cartprod @ SY471 @ SY472 ) )
| ( ( SY473
= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SY473 @ SY472 @ SY471 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SY473 @ SY472 @ SY471 ) @ ( setadjoin @ ( sK73_SY1108 @ SY473 @ SY472 @ SY471 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK73_SY1108 @ SY473 @ SY472 @ SY471 ) @ ( setunion @ SY473 ) )
& ( in @ ( sK72_SY474 @ SY473 @ SY472 @ SY471 ) @ ( setunion @ SY473 ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[152]) ).
thf(293,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ ( sK74_X @ Xx @ A ) @ A )
& ( in @ Xx @ ( sK74_X @ Xx @ A ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[153]) ).
thf(294,plain,
( ( ! [SY482: $i,SY483: $i > $o] :
( ( ( in @ ( sK76_Xx @ SY483 @ SY482 ) @ SY482 )
& ( in @ ( sK77_SY1111 @ SY483 @ SY482 ) @ SY482 )
& ( SY483 @ ( sK76_Xx @ SY483 @ SY482 ) )
& ( SY483 @ ( sK77_SY1111 @ SY483 @ SY482 ) )
& ( ( sK76_Xx @ SY483 @ SY482 )
!= ( sK77_SY1111 @ SY483 @ SY482 ) ) )
| ! [Xx: $i] :
( ~ ( SY483 @ Xx )
| ~ ( in @ Xx @ SY482 ) )
| ( ( ( dsetconstr @ SY482
@ ^ [Xx: $i] : ( SY483 @ Xx ) )
= ( setadjoin @ ( sK75_SY488 @ SY483 @ SY482 ) @ emptyset ) )
& ( in @ ( sK75_SY488 @ SY483 @ SY482 )
@ ( dsetconstr @ SY482
@ ^ [Xx: $i] : ( SY483 @ Xx ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[157]) ).
thf(295,plain,
( ( ! [SY489: $i,SY490: $i > $o] :
( ! [SY495: $i] :
( ( ( dsetconstr @ SY489
@ ^ [SY497: $i] : ( SY490 @ SY497 ) )
!= ( setadjoin @ SY495 @ emptyset ) )
| ~ ( in @ SY495
@ ( dsetconstr @ SY489
@ ^ [SY496: $i] : ( SY490 @ SY496 ) ) ) )
| ( ( SY490 @ ( sK78_Xx @ SY490 @ SY489 ) )
& ( in @ ( sK78_Xx @ SY490 @ SY489 ) @ SY489 ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[158]) ).
thf(296,plain,
( ( ! [SY499: $i,SY500: $i > $o,SY501: $i] :
( ~ ( in @ SY501 @ SY499 )
| ~ ( SY500 @ SY501 )
| ( ( in @ ( sK80_Xy @ SY501 @ SY500 @ SY499 ) @ SY499 )
& ( SY500 @ ( sK80_Xy @ SY501 @ SY500 @ SY499 ) )
& ( ( sK80_Xy @ SY501 @ SY500 @ SY499 )
!= SY501 ) )
| ( ( ( dsetconstr @ SY499
@ ^ [SY509: $i] : ( SY500 @ SY509 ) )
= ( setadjoin @ ( sK79_SY507 @ SY501 @ SY500 @ SY499 ) @ emptyset ) )
& ( in @ ( sK79_SY507 @ SY501 @ SY500 @ SY499 )
@ ( dsetconstr @ SY499
@ ^ [SY508: $i] : ( SY500 @ SY508 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[159]) ).
thf(297,plain,
( ( ! [SY510: $i,SY511: $i > $o] :
( ( ( in @ ( sK82_Xx @ SY511 @ SY510 ) @ SY510 )
& ( in @ ( sK83_SY1116 @ SY511 @ SY510 ) @ SY510 )
& ( SY511 @ ( sK82_Xx @ SY511 @ SY510 ) )
& ( SY511 @ ( sK83_SY1116 @ SY511 @ SY510 ) )
& ( ( sK82_Xx @ SY511 @ SY510 )
!= ( sK83_SY1116 @ SY511 @ SY510 ) ) )
| ! [Xx: $i] :
( ~ ( SY511 @ Xx )
| ~ ( in @ Xx @ SY510 ) )
| ( ( ( dsetconstr @ SY510
@ ^ [SY521: $i] : ( SY511 @ SY521 ) )
= ( setadjoin @ ( sK81_SY519 @ SY511 @ SY510 ) @ emptyset ) )
& ( in @ ( sK81_SY519 @ SY511 @ SY510 )
@ ( dsetconstr @ SY510
@ ^ [SY520: $i] : ( SY511 @ SY520 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[160]) ).
thf(298,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
!= ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[161]) ).
thf(299,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[162]) ).
thf(300,plain,
( ( ! [SY527: $i] :
( ! [SY528: $i] :
( ! [SY529: $i] :
( ( SY527
!= ( setadjoin @ ( setadjoin @ SY528 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY528 @ ( setadjoin @ SY529 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY529 @ ( setunion @ SY527 ) ) )
| ~ ( in @ SY528 @ ( setunion @ SY527 ) ) )
| ( ( ( dsetconstr @ ( setunion @ SY527 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY527 ) )
= ( setadjoin @ ( sK84_SY531 @ SY527 ) @ emptyset ) )
& ( in @ ( sK84_SY531 @ SY527 )
@ ( dsetconstr @ ( setunion @ SY527 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY527 ) ) ) ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[163]) ).
thf(301,plain,
( ( ! [SY532: $i] :
( ! [SY533: $i] :
( ( SY532
!= ( setadjoin @ SY533 @ emptyset ) )
| ~ ( in @ SY533 @ SY532 ) )
| ( in @ ( setunion @ SY532 ) @ SY532 ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[164]) ).
thf(302,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(extcnf_combined,[status(esa)],[166]) ).
thf(303,plain,
( ( ! [A: $i,B: $i,Xu: $i] :
( ~ ( in @ Xu @ ( cartprod @ A @ B ) )
| ( in @ ( kfst @ Xu ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[302]) ).
thf(304,plain,
( ( ! [SY534: $i,SY535: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ SY534 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY534 @ ( setadjoin @ SY535 @ emptyset ) ) @ emptyset ) ) )
= SY534 ) )
= $true ),
inference(copy,[status(thm)],[165]) ).
thf(305,plain,
( ( ! [SY532: $i] :
( ! [SY533: $i] :
( ( SY532
!= ( setadjoin @ SY533 @ emptyset ) )
| ~ ( in @ SY533 @ SY532 ) )
| ( in @ ( setunion @ SY532 ) @ SY532 ) ) )
= $true ),
inference(copy,[status(thm)],[301]) ).
thf(306,plain,
( ( ! [SY527: $i] :
( ! [SY528: $i] :
( ! [SY529: $i] :
( ( SY527
!= ( setadjoin @ ( setadjoin @ SY528 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY528 @ ( setadjoin @ SY529 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY529 @ ( setunion @ SY527 ) ) )
| ~ ( in @ SY528 @ ( setunion @ SY527 ) ) )
| ( ( ( dsetconstr @ ( setunion @ SY527 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY527 ) )
= ( setadjoin @ ( sK84_SY531 @ SY527 ) @ emptyset ) )
& ( in @ ( sK84_SY531 @ SY527 )
@ ( dsetconstr @ ( setunion @ SY527 )
@ ^ [Xx: $i] : ( in @ ( setadjoin @ Xx @ emptyset ) @ SY527 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[300]) ).
thf(307,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ ( setadjoin @ Xz @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) )
| ( Xx = Xz ) ) )
= $true ),
inference(copy,[status(thm)],[299]) ).
thf(308,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( ( setadjoin @ Xx @ emptyset )
!= ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[298]) ).
thf(309,plain,
( ( ! [SY510: $i,SY511: $i > $o] :
( ( ( in @ ( sK82_Xx @ SY511 @ SY510 ) @ SY510 )
& ( in @ ( sK83_SY1116 @ SY511 @ SY510 ) @ SY510 )
& ( SY511 @ ( sK82_Xx @ SY511 @ SY510 ) )
& ( SY511 @ ( sK83_SY1116 @ SY511 @ SY510 ) )
& ( ( sK82_Xx @ SY511 @ SY510 )
!= ( sK83_SY1116 @ SY511 @ SY510 ) ) )
| ! [Xx: $i] :
( ~ ( SY511 @ Xx )
| ~ ( in @ Xx @ SY510 ) )
| ( ( ( dsetconstr @ SY510
@ ^ [SY521: $i] : ( SY511 @ SY521 ) )
= ( setadjoin @ ( sK81_SY519 @ SY511 @ SY510 ) @ emptyset ) )
& ( in @ ( sK81_SY519 @ SY511 @ SY510 )
@ ( dsetconstr @ SY510
@ ^ [SY520: $i] : ( SY511 @ SY520 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[297]) ).
thf(310,plain,
( ( ! [SY499: $i,SY500: $i > $o,SY501: $i] :
( ~ ( in @ SY501 @ SY499 )
| ~ ( SY500 @ SY501 )
| ( ( in @ ( sK80_Xy @ SY501 @ SY500 @ SY499 ) @ SY499 )
& ( SY500 @ ( sK80_Xy @ SY501 @ SY500 @ SY499 ) )
& ( ( sK80_Xy @ SY501 @ SY500 @ SY499 )
!= SY501 ) )
| ( ( ( dsetconstr @ SY499
@ ^ [SY509: $i] : ( SY500 @ SY509 ) )
= ( setadjoin @ ( sK79_SY507 @ SY501 @ SY500 @ SY499 ) @ emptyset ) )
& ( in @ ( sK79_SY507 @ SY501 @ SY500 @ SY499 )
@ ( dsetconstr @ SY499
@ ^ [SY508: $i] : ( SY500 @ SY508 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[296]) ).
thf(311,plain,
( ( ! [SY489: $i,SY490: $i > $o] :
( ! [SY495: $i] :
( ( ( dsetconstr @ SY489
@ ^ [SY497: $i] : ( SY490 @ SY497 ) )
!= ( setadjoin @ SY495 @ emptyset ) )
| ~ ( in @ SY495
@ ( dsetconstr @ SY489
@ ^ [SY496: $i] : ( SY490 @ SY496 ) ) ) )
| ( ( SY490 @ ( sK78_Xx @ SY490 @ SY489 ) )
& ( in @ ( sK78_Xx @ SY490 @ SY489 ) @ SY489 ) ) ) )
= $true ),
inference(copy,[status(thm)],[295]) ).
thf(312,plain,
( ( ! [SY482: $i,SY483: $i > $o] :
( ( ( in @ ( sK76_Xx @ SY483 @ SY482 ) @ SY482 )
& ( in @ ( sK77_SY1111 @ SY483 @ SY482 ) @ SY482 )
& ( SY483 @ ( sK76_Xx @ SY483 @ SY482 ) )
& ( SY483 @ ( sK77_SY1111 @ SY483 @ SY482 ) )
& ( ( sK76_Xx @ SY483 @ SY482 )
!= ( sK77_SY1111 @ SY483 @ SY482 ) ) )
| ! [Xx: $i] :
( ~ ( SY483 @ Xx )
| ~ ( in @ Xx @ SY482 ) )
| ( ( ( dsetconstr @ SY482
@ ^ [Xx: $i] : ( SY483 @ Xx ) )
= ( setadjoin @ ( sK75_SY488 @ SY483 @ SY482 ) @ emptyset ) )
& ( in @ ( sK75_SY488 @ SY483 @ SY482 )
@ ( dsetconstr @ SY482
@ ^ [Xx: $i] : ( SY483 @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[294]) ).
thf(313,plain,
( ( ! [Xx: $i] :
( ( setunion @ ( setadjoin @ Xx @ emptyset ) )
= Xx ) )
= $true ),
inference(copy,[status(thm)],[156]) ).
thf(314,plain,
( ( ! [A: $i] : ( subset @ A @ ( setunion @ ( setadjoin @ A @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[155]) ).
thf(315,plain,
( ( ! [A: $i] : ( subset @ ( setunion @ ( setadjoin @ A @ emptyset ) ) @ A ) )
= $true ),
inference(copy,[status(thm)],[154]) ).
thf(316,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ ( sK74_X @ Xx @ A ) @ A )
& ( in @ Xx @ ( sK74_X @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[293]) ).
thf(317,plain,
( ( ! [SY471: $i,SY472: $i,SY473: $i] :
( ~ ( in @ SY473 @ ( cartprod @ SY471 @ SY472 ) )
| ( ( SY473
= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SY473 @ SY472 @ SY471 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SY473 @ SY472 @ SY471 ) @ ( setadjoin @ ( sK73_SY1108 @ SY473 @ SY472 @ SY471 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK73_SY1108 @ SY473 @ SY472 @ SY471 ) @ ( setunion @ SY473 ) )
& ( in @ ( sK72_SY474 @ SY473 @ SY472 @ SY471 ) @ ( setunion @ SY473 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[292]) ).
thf(318,plain,
( ( ! [SY465: $i,SY466: $i,SY467: $i] :
( ~ ( in @ SY467 @ ( cartprod @ SY465 @ SY466 ) )
| ( ( SY467
= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SY467 @ SY466 @ SY465 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SY467 @ SY466 @ SY465 ) @ ( setadjoin @ ( sK71_SY1107 @ SY467 @ SY466 @ SY465 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK71_SY1107 @ SY467 @ SY466 @ SY465 ) @ SY466 )
& ( in @ ( sK70_SY468 @ SY467 @ SY466 @ SY465 ) @ SY465 ) ) ) )
= $true ),
inference(copy,[status(thm)],[291]) ).
thf(319,plain,
( ( ! [SY460: $i,SY461: $i,SY462: $i] :
( ~ ( in @ SY462 @ SY460 )
| ! [SY463: $i] :
( ~ ( in @ SY463 @ SY461 )
| ( in @ ( setadjoin @ ( setadjoin @ SY462 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY462 @ ( setadjoin @ SY463 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SY460 @ SY461 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[290]) ).
thf(320,plain,
( ( ! [SY455: $i,SY456: $i,SY457: $i] :
( ~ ( in @ SY457 @ SY455 )
| ! [SY458: $i] :
( ~ ( in @ SY458 @ SY456 )
| ( in @ ( setadjoin @ ( setadjoin @ SY457 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY457 @ ( setadjoin @ SY458 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SY455 @ SY456 ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[289]) ).
thf(321,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[288]) ).
thf(322,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( subset @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[287]) ).
thf(323,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( in @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[286]) ).
thf(324,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ! [Xy: $i] :
( ~ ( in @ Xy @ B )
| ( subset @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[285]) ).
thf(325,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[284]) ).
thf(326,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ ( binunion @ A @ B ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[283]) ).
thf(327,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ ( setadjoin @ Xx @ emptyset ) @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[282]) ).
thf(328,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( subset @ ( setadjoin @ Xx @ emptyset ) @ A ) ) )
= $true ),
inference(copy,[status(thm)],[281]) ).
thf(329,plain,
( ( ! [SY424: $i,SY425: $i] :
( ( ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SY425 @ SY424 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SY425 @ SY424 ) @ ( setadjoin @ ( sK69_SY1106 @ SY425 @ SY424 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK69_SY1106 @ SY425 @ SY424 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( sK68_SY427 @ SY425 @ SY424 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY424 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY424 @ ( setadjoin @ SY425 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[280]) ).
thf(330,plain,
( ( ! [SY420: $i,SY421: $i] :
( ( ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SY421 @ SY420 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SY421 @ SY420 ) @ ( setadjoin @ ( sK67_SY1105 @ SY421 @ SY420 ) @ emptyset ) ) @ emptyset ) ) )
& ( in @ ( sK67_SY1105 @ SY421 @ SY420 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) )
& ( in @ ( sK66_SY422 @ SY421 @ SY420 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SY420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY420 @ ( setadjoin @ SY421 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[279]) ).
thf(331,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[138]) ).
thf(332,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setunion @ ( setadjoin @ ( setadjoin @ Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[137]) ).
thf(333,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[136]) ).
thf(334,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[278]) ).
thf(335,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[277]) ).
thf(336,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[276]) ).
thf(337,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( symdiff @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[275]) ).
thf(338,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( symdiff @ A @ B ) )
| ( ( ( in @ Xx @ A )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ A )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ( ~ ( in @ Xx @ B )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ~ ( in @ Xx @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[274]) ).
thf(339,plain,
( ( ! [A: $i,B: $i] :
( ( ( setminus @ A @ B )
!= emptyset )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[273]) ).
thf(340,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( setminus @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[129]) ).
thf(341,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[272]) ).
thf(342,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ A )
| ~ ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[271]) ).
thf(343,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[270]) ).
thf(344,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[269]) ).
thf(345,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( setminus @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[268]) ).
thf(346,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ~ ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[267]) ).
thf(347,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setminus @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[266]) ).
thf(348,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( in @ Xx @ ( setminus @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[265]) ).
thf(349,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ( binintersect @ A @ ( binunion @ B @ C ) )
= ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[120]) ).
thf(350,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= A )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[264]) ).
thf(351,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( ( binintersect @ A @ B )
= B ) ) )
= $true ),
inference(copy,[status(thm)],[263]) ).
thf(352,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) )
= $true ),
inference(copy,[status(thm)],[117]) ).
thf(353,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK65_Xx @ B @ A ) @ A )
& ( in @ ( sK65_Xx @ B @ A ) @ B ) )
| ( ( binintersect @ A @ B )
= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[262]) ).
thf(354,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[261]) ).
thf(355,plain,
( ( ! [A: $i,B: $i] :
( ( ( binintersect @ A @ B )
!= B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[260]) ).
thf(356,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( ( binintersect @ A @ B )
= A ) ) )
= $true ),
inference(copy,[status(thm)],[259]) ).
thf(357,plain,
( ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) )
= $true ),
inference(copy,[status(thm)],[112]) ).
thf(358,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binintersect @ A @ B ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[258]) ).
thf(359,plain,
( ( ! [A: $i,B: $i,C: $i] :
( ~ ( subset @ C @ A )
| ~ ( subset @ C @ B )
| ( subset @ C @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[257]) ).
thf(360,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binintersect @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[256]) ).
thf(361,plain,
( ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[108]) ).
thf(362,plain,
( ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[107]) ).
thf(363,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B ) ) )
= $true ),
inference(copy,[status(thm)],[255]) ).
thf(364,plain,
( ( ! [A: $i,B: $i] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ( in @ Xx @ B )
| ! [Xphi: $o] : Xphi )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ( in @ Xx @ A )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xx: $i] :
( ~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xx @ B )
| Xphi ) )
& ( ! [Xx: $i] :
~ ( in @ Xx @ ( binunion @ A @ B ) )
| ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[254]) ).
thf(365,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[253]) ).
thf(366,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[103]) ).
thf(367,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( binunion @ A @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[252]) ).
thf(368,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( subset
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ A ) )
= $true ),
inference(copy,[status(thm)],[101]) ).
thf(369,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( in
@ ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
@ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[100]) ).
thf(370,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[251]) ).
thf(371,plain,
( ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[98]) ).
thf(372,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[250]) ).
thf(373,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ B @ A )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[249]) ).
thf(374,plain,
( ( ! [A: $i] :
( ~ ( subset @ A @ emptyset )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[248]) ).
thf(375,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ~ ( subset @ B @ A )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[247]) ).
thf(376,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( in @ A @ ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[246]) ).
thf(377,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( subset @ A @ B )
| ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[245]) ).
thf(378,plain,
( ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[91]) ).
thf(379,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [C: $i] :
( ~ ( subset @ B @ C )
| ( subset @ A @ C ) ) ) )
= $true ),
inference(copy,[status(thm)],[244]) ).
thf(380,plain,
( ( ! [A: $i] : ( subset @ A @ A ) )
= $true ),
inference(copy,[status(thm)],[89]) ).
thf(381,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[243]) ).
thf(382,plain,
( ( ! [A: $i,B: $i] :
( ( subset @ A @ B )
| ( A != B ) ) )
= $true ),
inference(copy,[status(thm)],[242]) ).
thf(383,plain,
( ( ! [A: $i,B: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B )
| ~ ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[241]) ).
thf(384,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ( in @ Xx @ B )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[240]) ).
thf(385,plain,
( ( ! [A: $i,B: $i] :
( ~ ( subset @ A @ B )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[239]) ).
thf(386,plain,
( ( ! [A: $i] : ( subset @ emptyset @ A ) )
= $true ),
inference(copy,[status(thm)],[83]) ).
thf(387,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK64_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK64_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[238]) ).
thf(388,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[237]) ).
thf(389,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( subset @ B @ A ) ) )
= $true ),
inference(copy,[status(thm)],[236]) ).
thf(390,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK63_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK63_Xx @ B @ A ) @ B ) )
| ( subset @ A @ B ) ) )
= $true ),
inference(copy,[status(thm)],[235]) ).
thf(391,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xphi: $i > $o,Xpsi: $i > $o] :
( ( ( in @ ( sK61_Xx @ Xpsi @ Xphi @ B @ A ) @ A )
& ( in @ ( sK62_SY1104 @ Xpsi @ Xphi @ B @ A ) @ B )
& ( ( sK61_Xx @ Xpsi @ Xphi @ B @ A )
= ( sK62_SY1104 @ Xpsi @ Xphi @ B @ A ) )
& ( ~ ( Xphi @ ( sK61_Xx @ Xpsi @ Xphi @ B @ A ) )
| ~ ( Xpsi @ ( sK62_SY1104 @ Xpsi @ Xphi @ B @ A ) ) )
& ( ( Xphi @ ( sK61_Xx @ Xpsi @ Xphi @ B @ A ) )
| ( Xpsi @ ( sK62_SY1104 @ Xpsi @ Xphi @ B @ A ) ) ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
= ( dsetconstr @ B
@ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[234]) ).
thf(392,plain,
( ( ! [SY250: $i > $o,SY251: $i > $o] :
( ( ( ( sK59_Xx @ SY251 @ SY250 )
= ( sK60_SY1103 @ SY251 @ SY250 ) )
& ( ~ ( SY250 @ ( sK59_Xx @ SY251 @ SY250 ) )
| ~ ( SY251 @ ( sK60_SY1103 @ SY251 @ SY250 ) ) )
& ( ( SY250 @ ( sK59_Xx @ SY251 @ SY250 ) )
| ( SY251 @ ( sK60_SY1103 @ SY251 @ SY250 ) ) ) )
| ! [SY255: $i] :
( ( ( SY250 @ ( sK58_SY256 @ SY255 @ SY251 @ SY250 ) )
& ( SY255
!= ( sK58_SY256 @ SY255 @ SY251 @ SY250 ) ) )
| ~ ( SY250 @ SY255 ) )
| ! [SY258: $i] :
( ( ( SY251 @ ( sK57_SY259 @ SY258 @ SY251 @ SY250 ) )
& ( SY258
!= ( sK57_SY259 @ SY258 @ SY251 @ SY250 ) ) )
| ~ ( SY251 @ SY258 ) )
| ( ( descr
@ ^ [Xx: $i] : ( SY250 @ Xx ) )
= ( descr
@ ^ [Xx: $i] : ( SY251 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[233]) ).
thf(393,plain,
( ( ! [SY244: $i > $o] :
( ! [SY246: $i] :
( ( ( SY244 @ ( sK56_SY247 @ SY246 @ SY244 ) )
& ( SY246
!= ( sK56_SY247 @ SY246 @ SY244 ) ) )
| ~ ( SY244 @ SY246 ) )
| ! [Xx: $i] :
( ~ ( SY244 @ Xx )
| ! [Xy: $i] :
( ~ ( SY244 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[232]) ).
thf(394,plain,
$true = $true,
inference(copy,[status(thm)],[231]) ).
thf(395,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( setunion @ A )
= ( setunion @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[230]) ).
thf(396,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ( powerset @ A )
= ( powerset @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[229]) ).
thf(397,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ! [Xz: $i,Xu: $i] :
( ( Xz != Xu )
| ( ( setadjoin @ Xx @ Xz )
= ( setadjoin @ Xy @ Xu ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[228]) ).
thf(398,plain,
$true = $true,
inference(copy,[status(thm)],[227]) ).
thf(399,plain,
( ( ! [SY226: $i > $o,SY227: $i > $o] :
( ( ( ( sK54_Xx @ SY227 @ SY226 )
= ( sK55_SY1102 @ SY227 @ SY226 ) )
& ( ~ ( SY226 @ ( sK54_Xx @ SY227 @ SY226 ) )
| ~ ( SY227 @ ( sK55_SY1102 @ SY227 @ SY226 ) ) )
& ( ( SY226 @ ( sK54_Xx @ SY227 @ SY226 ) )
| ( SY227 @ ( sK55_SY1102 @ SY227 @ SY226 ) ) ) )
| ! [SY231: $i] :
( ( ( SY226 @ ( sK53_SY232 @ SY231 @ SY227 @ SY226 ) )
& ( SY231
!= ( sK53_SY232 @ SY231 @ SY227 @ SY226 ) ) )
| ~ ( SY226 @ SY231 ) )
| ( ! [SY1101: $i] :
( ~ ( SY227 @ SY1101 )
| ( ( sK52_SY234 @ SY227 @ SY226 )
= SY1101 ) )
& ( SY227 @ ( sK52_SY234 @ SY227 @ SY226 ) ) ) )
& ! [SY226: $i > $o,SY227: $i > $o] :
( ( ( ( sK50_Xx @ SY227 @ SY226 )
= ( sK51_SY1100 @ SY227 @ SY226 ) )
& ( ~ ( SY226 @ ( sK50_Xx @ SY227 @ SY226 ) )
| ~ ( SY227 @ ( sK51_SY1100 @ SY227 @ SY226 ) ) )
& ( ( SY226 @ ( sK50_Xx @ SY227 @ SY226 ) )
| ( SY227 @ ( sK51_SY1100 @ SY227 @ SY226 ) ) ) )
| ! [SY234: $i] :
( ( ( SY227 @ ( sK49_SY235 @ SY234 @ SY227 @ SY226 ) )
& ( SY234
!= ( sK49_SY235 @ SY234 @ SY227 @ SY226 ) ) )
| ~ ( SY227 @ SY234 ) )
| ( ! [SY1099: $i] :
( ~ ( SY226 @ SY1099 )
| ( ( sK48_SY231 @ SY227 @ SY226 )
= SY1099 ) )
& ( SY226 @ ( sK48_SY231 @ SY227 @ SY226 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[226]) ).
thf(400,plain,
( ( ! [SY220: $i > $o] :
( ! [SY222: $i] :
( ( ( SY220 @ ( sK47_SY223 @ SY222 @ SY220 ) )
& ( SY222
!= ( sK47_SY223 @ SY222 @ SY220 ) ) )
| ~ ( SY220 @ SY222 ) )
| ! [Xx: $i] :
( ~ ( SY220 @ Xx )
| ! [Xy: $i] :
( ~ ( SY220 @ Xy )
| ( Xx = Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[225]) ).
thf(401,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) )
& ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xy @ B )
| ( in @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[224]) ).
thf(402,plain,
( ( ! [A: $i,B: $i] :
( ( A != B )
| ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ~ ( in @ Xx @ A )
| ( in @ Xy @ B ) ) ) )
= $true ),
inference(copy,[status(thm)],[223]) ).
thf(403,plain,
( ( ! [SY206: $i > $o] :
( ! [Xx: $i] :
( ( ( ( sK46_Xy @ Xx @ SY206 )
!= Xx )
| ~ ( SY206 @ ( sK46_Xy @ Xx @ SY206 ) ) )
& ( ( ( sK46_Xy @ Xx @ SY206 )
= Xx )
| ( SY206 @ ( sK46_Xy @ Xx @ SY206 ) ) ) )
| ( ! [SY1098: $i] :
( ~ ( SY206 @ SY1098 )
| ( ( sK45_SY210 @ SY206 )
= SY1098 ) )
& ( SY206 @ ( sK45_SY210 @ SY206 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[222]) ).
thf(404,plain,
( ( ! [SY199: $i > $o] :
( ! [Xx: $i] :
~ ( SY199 @ Xx )
| ( ( SY199 @ ( sK43_Xx @ SY199 ) )
& ( SY199 @ ( sK44_SY1097 @ SY199 ) )
& ( ( sK43_Xx @ SY199 )
!= ( sK44_SY1097 @ SY199 ) ) )
| ( ! [SY1096: $i] :
( ~ ( SY199 @ SY1096 )
| ( ( sK42_SY204 @ SY199 )
= SY1096 ) )
& ( SY199 @ ( sK42_SY204 @ SY199 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[221]) ).
thf(405,plain,
( ( ! [SY193: $i > $o] :
( ! [Xx: $i] :
( ( ( SY193 @ ( sK41_Xy @ Xx @ SY193 ) )
& ( Xx
!= ( sK41_Xy @ Xx @ SY193 ) ) )
| ~ ( SY193 @ Xx ) )
| ( ! [SY1095: $i] :
( ~ ( SY193 @ SY1095 )
| ( ( sK40_SY197 @ SY193 )
= SY1095 ) )
& ( SY193 @ ( sK40_SY197 @ SY193 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[220]) ).
thf(406,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK39_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK39_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[219]) ).
thf(407,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK38_Xx @ Xphi @ A ) )
& ( in @ ( sK38_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[218]) ).
thf(408,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( set2prop @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[217]) ).
thf(409,plain,
( ( ! [Xphi: $o] :
( ~ Xphi
| ( in @ emptyset @ ( prop2set @ Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[216]) ).
thf(410,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK37_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK37_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[215]) ).
thf(411,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( Xphi @ ( sK36_Xx @ Xphi @ A ) )
& ( in @ ( sK36_Xx @ Xphi @ A ) @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[214]) ).
thf(412,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ( ( in @ ( sK35_Xx @ Xphi @ A ) @ A )
& ( Xphi @ ( sK35_Xx @ Xphi @ A ) ) )
| ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[213]) ).
thf(413,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( in @ Xx @ A )
| ( Xphi @ Xx ) )
| ( ( in @ ( sK34_Xx @ Xphi @ A ) @ A )
& ~ ( Xphi @ ( sK34_Xx @ Xphi @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[212]) ).
thf(414,plain,
( ( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ emptyset )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[211]) ).
thf(415,plain,
( ( ! [A: $i,Xphi: $i > $o] :
( ! [Xx: $i] :
( ~ ( Xphi @ Xx )
| ~ ( in @ Xx @ A ) )
| ( ( dsetconstr @ A
@ ^ [Xx: $i] : ( Xphi @ Xx ) )
!= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[210]) ).
thf(416,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[53]) ).
thf(417,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[52]) ).
thf(418,plain,
( ( ! [Xx: $i,Xy: $i,Xz: $i] :
( ~ ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
| ( Xz = Xx )
| ( Xz = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[209]) ).
thf(419,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[208]) ).
thf(420,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx != Xy )
| ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[207]) ).
thf(421,plain,
( ( ! [Xx: $i,Xy: $i] :
( ( Xx = Xy )
| ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) )
= $true ),
inference(copy,[status(thm)],[206]) ).
thf(422,plain,
( ( ! [Xx: $i,Xy: $i] :
( ~ ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
| ( Xx = Xy ) ) )
= $true ),
inference(copy,[status(thm)],[205]) ).
thf(423,plain,
( ( ! [SY144: $i] :
( ( SY144 = emptyset )
| ( in @ ( sK33_Xx @ SY144 ) @ SY144 ) ) )
= $true ),
inference(copy,[status(thm)],[204]) ).
thf(424,plain,
( ( ! [SY138: $i > $o] :
( ! [SY140: $i] :
( ( ( SY138 @ ( sK32_SY141 @ SY140 @ SY138 ) )
& ( SY140
!= ( sK32_SY141 @ SY140 @ SY138 ) ) )
| ~ ( SY138 @ SY140 ) )
| ( ! [SY1093: $i] :
( ( SY1093
!= ( sK31_Xx @ SY138 ) )
| ( SY138 @ SY1093 ) )
& ! [SY1094: $i] :
( ~ ( SY138 @ SY1094 )
| ( SY1094
= ( sK31_Xx @ SY138 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[203]) ).
thf(425,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ A )
| ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[202]) ).
thf(426,plain,
( ( ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ! [Xphi: $o] :
( ( ( in @ Xx @ ( sK30_B @ Xphi @ Xx @ A ) )
& ( in @ ( sK30_B @ Xphi @ Xx @ A ) @ A )
& ~ Xphi )
| Xphi ) ) )
= $true ),
inference(copy,[status(thm)],[201]) ).
thf(427,plain,
( ( ! [A: $i,Xx: $i,B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A )
| ( in @ Xx @ ( setunion @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[200]) ).
thf(428,plain,
( ( ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[199]) ).
thf(429,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[40]) ).
thf(430,plain,
( ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) )
= $true ),
inference(copy,[status(thm)],[39]) ).
thf(431,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK29_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK29_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[198]) ).
thf(432,plain,
( ( ! [A: $i] :
( ( dsetconstr @ A
@ ^ [Xx: $i] : $true )
= A ) )
= $true ),
inference(copy,[status(thm)],[37]) ).
thf(433,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) ) )
= $true ),
inference(copy,[status(thm)],[197]) ).
thf(434,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( ( ( Xy = Xx )
| ( in @ Xy @ A )
| ! [Xphi: $o] : Xphi )
& ( ( Xy = Xx )
| ! [Xphi: $o] :
( ~ Xphi
| Xphi ) )
& ! [Xphi: $o] :
( ~ Xphi
| ( in @ Xy @ A )
| Xphi )
& ! [Xphi: $o] :
( ~ Xphi
| ~ Xphi
| Xphi ) ) ) )
= $true ),
inference(copy,[status(thm)],[196]) ).
thf(435,plain,
( ( ! [Xx: $i,A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[195]) ).
thf(436,plain,
( ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[33]) ).
thf(437,plain,
( ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) )
= $true ),
inference(copy,[status(thm)],[32]) ).
thf(438,plain,
( ( ! [SY105: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ SY105 )
| ( SY105 != emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[194]) ).
thf(439,plain,
( ( ! [SY101: $i,SY102: $i > $o,SY103: $i] :
( ~ ( in @ SY103 @ SY101 )
| ~ ( SY102 @ SY103 )
| ( ( dsetconstr @ SY101
@ ^ [Xy: $i] : ( SY102 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[193]) ).
thf(440,plain,
( ( ! [SY99: $i] :
( ( SY99 = emptyset )
| ( in @ ( sK28_Xx @ SY99 ) @ SY99 ) ) )
= $true ),
inference(copy,[status(thm)],[192]) ).
thf(441,plain,
( ( ! [A: $i] :
( ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) )
& ! [Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) ) )
= $true ),
inference(copy,[status(thm)],[191]) ).
thf(442,plain,
( ( ! [A: $i] :
( ( in @ ( sK27_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[190]) ).
thf(443,plain,
( ( ! [A: $i] :
( ( in @ ( sK26_Xx @ A ) @ A )
| ( A = emptyset ) ) )
= $true ),
inference(copy,[status(thm)],[189]) ).
thf(444,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK25_Xx @ B @ A ) @ A )
& ~ ( in @ ( sK25_Xx @ B @ A ) @ B ) )
| ( ( in @ ( sK24_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK24_Xx @ B @ A ) @ A ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[188]) ).
thf(445,plain,
( ( ! [SY82: $i > $o] :
( ! [SY84: $i] :
( ( ( SY82 @ ( sK23_SY85 @ SY84 @ SY82 ) )
& ( SY84
!= ( sK23_SY85 @ SY84 @ SY82 ) ) )
| ~ ( SY82 @ SY84 ) )
| ( SY82 @ ( sK22_Xx @ SY82 ) ) ) )
= $true ),
inference(copy,[status(thm)],[187]) ).
thf(446,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[23]) ).
thf(447,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[186]) ).
thf(448,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset )
| ! [Xphi: $o] : Xphi )
= $true ),
inference(copy,[status(thm)],[185]) ).
thf(449,plain,
( ( ! [Xphi: $o] :
( ! [Xx: $i] :
~ ( in @ Xx @ ( prop2set @ Xphi ) )
| Xphi ) )
= $true ),
inference(copy,[status(thm)],[184]) ).
thf(450,plain,
( ( ! [SY70: $i > $o] :
( ! [SY72: $i] :
( ( ( SY70 @ ( sK21_SY73 @ SY72 @ SY70 ) )
& ( SY72
!= ( sK21_SY73 @ SY72 @ SY70 ) ) )
| ~ ( SY70 @ SY72 ) )
| ( ! [SY1092: $i] :
( ~ ( SY70 @ SY1092 )
| ( ( sK20_Xx @ SY70 )
= SY1092 ) )
& ( SY70 @ ( sK20_Xx @ SY70 ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[183]) ).
thf(451,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( Xphi @ Xx ) ) )
= $true ),
inference(copy,[status(thm)],[182]) ).
thf(452,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
| ( in @ Xx @ A ) ) )
= $true ),
inference(copy,[status(thm)],[181]) ).
thf(453,plain,
( ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
( ~ ( in @ Xx @ A )
| ~ ( Xphi @ Xx )
| ( in @ Xx
@ ( dsetconstr @ A
@ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[180]) ).
thf(454,plain,
( ( ! [SY53: $i > $o] :
( ! [SY55: $i] :
( ( ( SY53 @ ( sK19_SY56 @ SY55 @ SY53 ) )
& ( SY55
!= ( sK19_SY56 @ SY55 @ SY53 ) ) )
| ~ ( SY53 @ SY55 ) )
| ( SY53
@ ( descr
@ ^ [Xx: $i] : ( SY53 @ Xx ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[179]) ).
thf(455,plain,
( ( ! [A: $i] :
( ! [SY1068: $i] :
( ( ( in @ ( sK18_Xx @ SY1068 @ A ) @ SY1068 )
& ~ ( in @ ( sK18_Xx @ SY1068 @ A ) @ A ) )
| ! [Xx: $i] :
~ ( in @ Xx @ SY1068 )
| ( ! [SY1089: $i] :
( ~ ( in @ SY1089 @ ( sK14_B @ A ) )
| ! [SY1087: $i] :
( ~ ( in @ SY1087 @ SY1089 )
| ( in @ SY1087 @ ( sK16_SY1071 @ SY1068 @ A ) ) )
| ( in @ ( sK17_SY1085 @ SY1068 @ A ) @ SY1089 ) )
& ( in @ ( sK16_SY1071 @ SY1068 @ A ) @ ( sK14_B @ A ) )
& ( in @ ( sK17_SY1085 @ SY1068 @ A ) @ SY1068 )
& ! [SY1088: $i] :
( ~ ( in @ SY1088 @ ( sK16_SY1071 @ SY1068 @ A ) )
| ~ ( in @ SY1088 @ SY1068 ) ) ) )
& ! [SY1076: $i,SY1077: $i] :
( ~ ( in @ SY1076 @ ( sK14_B @ A ) )
| ~ ( in @ SY1077 @ ( sK14_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1076 )
| ( in @ Xx @ SY1077 ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1077 )
| ( in @ Xx @ SY1076 ) ) )
& ! [SY1080: $i] :
( ~ ( in @ SY1080 @ ( sK14_B @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ SY1080 )
| ( in @ Xx @ A ) ) )
& ! [SY1082: $i,SY1083: $i] :
( ~ ( in @ SY1082 @ A )
| ~ ( in @ SY1083 @ A )
| ( ( in @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) @ ( sK14_B @ A ) )
& ( ~ ( in @ SY1082 @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) )
| ~ ( in @ SY1083 @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) ) )
& ( ( in @ SY1082 @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) )
| ( in @ SY1083 @ ( sK15_SY1084 @ SY1083 @ SY1082 @ A ) ) ) )
| ( SY1082 = SY1083 ) ) ) )
= $true ),
inference(copy,[status(thm)],[178]) ).
thf(456,plain,
( ( ! [A: $i] :
( ! [Xx: $i] :
~ ( in @ Xx @ A )
| ( ( in @ ( sK13_B @ A ) @ A )
& ! [SY1067: $i] :
( ~ ( in @ SY1067 @ ( sK13_B @ A ) )
| ~ ( in @ SY1067 @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[177]) ).
thf(457,plain,
( ( ! [SY21: $i > $i > $o,SY22: $i] :
( ( ( in @ ( sK11_SY23 @ SY22 @ SY21 ) @ SY22 )
& ! [SY1065: $i] :
( ( ( SY21 @ ( sK11_SY23 @ SY22 @ SY21 ) @ ( sK12_SY1066 @ SY1065 @ SY22 @ SY21 ) )
& ( SY1065
!= ( sK12_SY1066 @ SY1065 @ SY22 @ SY21 ) ) )
| ~ ( SY21 @ ( sK11_SY23 @ SY22 @ SY21 ) @ SY1065 ) ) )
| ( ! [SY1061: $i] :
( ! [Xy: $i] :
( ~ ( SY21 @ Xy @ SY1061 )
| ~ ( in @ Xy @ SY22 ) )
| ( in @ SY1061 @ ( sK9_B @ SY22 @ SY21 ) ) )
& ! [SY1063: $i] :
( ~ ( in @ SY1063 @ ( sK9_B @ SY22 @ SY21 ) )
| ( ( SY21 @ ( sK10_Xy @ SY1063 @ SY22 @ SY21 ) @ SY1063 )
& ( in @ ( sK10_Xy @ SY1063 @ SY22 @ SY21 ) @ SY22 ) ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[176]) ).
thf(458,plain,
( ( ! [A: $i] :
( ( ( in @ ( sK8_Xx @ A ) @ omega )
& ( in @ ( sK8_Xx @ A ) @ A )
& ~ ( in @ ( setadjoin @ ( sK8_Xx @ A ) @ ( sK8_Xx @ A ) ) @ A ) )
| ~ ( in @ emptyset @ A )
| ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[175]) ).
thf(459,plain,
( ( ! [Xx: $i] :
( ~ ( in @ Xx @ omega )
| ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) )
= $true ),
inference(copy,[status(thm)],[174]) ).
thf(460,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(copy,[status(thm)],[9]) ).
thf(461,plain,
( ( ! [A: $i,Xx: $i] :
( ! [B: $i] :
( ~ ( in @ Xx @ B )
| ~ ( in @ B @ A ) )
| ( in @ Xx @ ( setunion @ A ) ) )
& ! [A: $i,Xx: $i] :
( ~ ( in @ Xx @ ( setunion @ A ) )
| ( ( in @ Xx @ ( sK7_B @ Xx @ A ) )
& ( in @ ( sK7_B @ Xx @ A ) @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[173]) ).
thf(462,plain,
( ( ! [A: $i,B: $i] :
( ( ( in @ ( sK6_Xx @ B @ A ) @ B )
& ~ ( in @ ( sK6_Xx @ B @ A ) @ A ) )
| ( in @ B @ ( powerset @ A ) ) )
& ! [A: $i,B: $i] :
( ~ ( in @ B @ ( powerset @ A ) )
| ! [Xx: $i] :
( ~ ( in @ Xx @ B )
| ( in @ Xx @ A ) ) ) )
= $true ),
inference(copy,[status(thm)],[172]) ).
thf(463,plain,
( ( ! [Xx: $i] :
( ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ ( setadjoin @ Xx @ A ) )
| ( Xy = Xx )
| ( in @ Xy @ A ) )
& ! [A: $i,Xy: $i] :
( ( Xy != Xx )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) )
& ! [A: $i,Xy: $i] :
( ~ ( in @ Xy @ A )
| ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) )
= $true ),
inference(copy,[status(thm)],[171]) ).
thf(464,plain,
( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true ),
inference(copy,[status(thm)],[5]) ).
thf(465,plain,
( ( ! [A: $i,B: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ B @ A ) @ A )
| ~ ( in @ ( sK5_Xx @ B @ A ) @ B ) )
& ( ( in @ ( sK5_Xx @ B @ A ) @ A )
| ( in @ ( sK5_Xx @ B @ A ) @ B ) ) )
| ( A = B ) ) )
= $true ),
inference(copy,[status(thm)],[170]) ).
thf(466,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY1055 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY1058 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY1058 @ ( setadjoin @ sK4_SY1060 @ emptyset ) ) @ emptyset ) ) )
& ( sK1_Xx != sK3_SY1058 ) )
= $true ),
inference(copy,[status(thm)],[169]) ).
thf(467,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ SX2 @ emptyset ) )
| ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
| ~ ( ~ ( SX1 @ ( sK78_Xx @ SX1 @ SX0 ) )
| ~ ( in @ ( sK78_Xx @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[311,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(468,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i] :
( ~ ( ~ ( in @ ( sK18_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK18_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SX1 )
| ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK14_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ ( sK16_SY1071 @ SX1 @ SX0 ) ) )
| ( in @ ( sK17_SY1085 @ SX1 @ SX0 ) @ SX2 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SX1 @ SX0 ) @ ( sK14_B @ SX0 ) )
| ~ ( in @ ( sK17_SY1085 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK16_SY1071 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ SX1 ) ) ) ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ ( sK14_B @ SX0 ) )
| ~ ( in @ SX2 @ ( sK14_B @ SX0 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX1 )
| ( in @ SX3 @ SX2 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SX2 )
| ( in @ SX3 @ SX1 ) ) )
| ~ ~ ( ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK14_B @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX1 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SX2 @ SX1 @ SX0 ) @ ( sK14_B @ SX0 ) )
| ~ ~ ( ~ ( ~ ( in @ SX1 @ ( sK15_SY1084 @ SX2 @ SX1 @ SX0 ) )
| ~ ( in @ SX2 @ ( sK15_SY1084 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( in @ SX1 @ ( sK15_SY1084 @ SX2 @ SX1 @ SX0 ) )
| ( in @ SX2 @ ( sK15_SY1084 @ SX2 @ SX1 @ SX0 ) ) ) ) )
| ( SX1 = SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[455,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(469,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[462,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(470,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( in @ ( sK39_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( SX1 @ ( sK39_Xx @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[406,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(471,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( in @ ( sK37_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( SX1 @ ( sK37_Xx @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[410,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(472,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ~ ( ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX2 @ SX0 )
| ( in @ SX3 @ SX1 ) )
| ~ ! [SX2: $i,SX3: $i] :
( ( SX2 != SX3 )
| ~ ( in @ SX3 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[401,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(473,plain,
( ( ~ ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY1055 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY1058 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY1058 @ ( setadjoin @ sK4_SY1060 @ emptyset ) ) @ emptyset ) ) )
| ~ ( ( sK1_Xx != sK3_SY1058 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[466,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(474,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK23_SY85 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK23_SY85 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0 @ ( sK22_Xx @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[445,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(475,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ ( sK74_X @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ SX1 @ ( sK74_X @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[316,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(476,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( in @ ( sK76_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK77_SY1111 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK76_Xx @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( SX1 @ ( sK77_SY1111 @ SX1 @ SX0 ) )
| ~ ( ( ( sK76_Xx @ SX1 @ SX0 )
!= ( sK77_SY1111 @ SX1 @ SX0 ) ) ) ) ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= ( setadjoin @ ( sK75_SY488 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SX1 @ SX0 )
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[312,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(477,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK21_SY73 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK21_SY73 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK20_Xx @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK20_Xx @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[450,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(478,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK56_SY247 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK56_SY247 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[393,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(479,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK36_Xx @ SX1 @ SX0 ) )
| ~ ( in @ ( sK36_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[411,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(480,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SX1 @ SX0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SX1 @ SX0 ) @ ( setadjoin @ ( sK69_SY1106 @ SX1 @ SX0 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK69_SY1106 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK68_SY427 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[329,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(481,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
~ ( in @ SX1 @ SX0 )
| ~ ( ~ ( in @ ( sK13_B @ SX0 ) @ SX0 )
| ~ ! [SX1: $i] :
( ~ ( in @ SX1 @ ( sK13_B @ SX0 ) )
| ~ ( in @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[456,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(482,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( in @ ( sK82_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK83_SY1116 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK82_Xx @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( SX1 @ ( sK83_SY1116 @ SX1 @ SX0 ) )
| ~ ( ( ( sK82_Xx @ SX1 @ SX0 )
!= ( sK83_SY1116 @ SX1 @ SX0 ) ) ) ) ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ~ ( ( ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) )
!= ( setadjoin @ ( sK81_SY519 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SX1 @ SX0 )
@ ( dsetconstr @ SX0
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[309,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(483,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( symdiff @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SX2 @ SX0 )
| ~ ( in @ SX2 @ SX0 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SX2 @ SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ~ ( in @ SX2 @ SX0 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SX2 @ SX1 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ~ ( in @ SX2 @ SX0 )
| SX3 )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[338,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(484,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK32_SY141 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK32_SY141 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ( SX1
!= ( sK31_Xx @ SX0 ) )
| ( SX0 @ SX1 ) )
| ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( SX1
= ( sK31_Xx @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[424,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(485,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ( SX1 @ SX2 ) )
| ~ ( ~ ( in @ ( sK34_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( SX1 @ ( sK34_Xx @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[413,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(486,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK41_Xy @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK41_Xy @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK40_SY197 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK40_SY197 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[405,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(487,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK19_SY56 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK19_SY56 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ( SX0
@ ( descr
@ ^ [SX1: $i] : ( SX0 @ SX1 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[454,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(488,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ( SX2 = SX0 )
| ( in @ SX2 @ SX1 ) )
| ~ ~ ( ~ ! [SX1: $i,SX2: $i] :
( ( SX2 != SX0 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) )
| ~ ! [SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[463,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(489,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( in @ ( sK35_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( SX1 @ ( sK35_Xx @ SX1 @ SX0 ) ) )
| ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[412,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(490,plain,
( ( ! [SX0: $i] :
( ! [SX1: $i] :
( ! [SX2: $i] :
( ( SX0
!= ( setadjoin @ ( setadjoin @ SX1 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX1 @ ( setadjoin @ SX2 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SX2 @ ( setunion @ SX0 ) ) )
| ~ ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ( ( ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) )
!= ( setadjoin @ ( sK84_SY531 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SX0 )
@ ( dsetconstr @ ( setunion @ SX0 )
@ ^ [SX1: $i] : ( in @ ( setadjoin @ SX1 @ emptyset ) @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[306,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(491,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK29_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK29_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[431,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(492,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ! [SX2: $o] :
( ~ ( ~ ( in @ SX1 @ ( sK30_B @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ SX2 ) )
| SX2 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[426,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(493,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
( ~ ( ~ ( SX0 @ ( sK47_SY223 @ SX1 @ SX0 ) )
| ~ ( ( SX1
!= ( sK47_SY223 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX1 ) )
| ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( SX1 = SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[400,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(494,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK25_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK25_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ~ ( in @ ( sK24_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK24_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[444,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(495,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ( SX2
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SX2 @ SX1 @ SX0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SX2 @ SX1 @ SX0 ) @ ( setadjoin @ ( sK71_SY1107 @ SX2 @ SX1 @ SX0 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SX2 @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( in @ ( sK70_SY468 @ SX2 @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[318,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(496,plain,
( ( ~ ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK7_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK7_B @ SX1 @ SX0 ) @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[461,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(497,plain,
( ( ! [SX0: $i > $i > $o,SX1: $i] :
( ~ ( ~ ( in @ ( sK11_SY23 @ SX1 @ SX0 ) @ SX1 )
| ~ ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK11_SY23 @ SX1 @ SX0 ) @ ( sK12_SY1066 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK12_SY1066 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ ( sK11_SY23 @ SX1 @ SX0 ) @ SX2 ) ) )
| ~ ( ~ ! [SX2: $i] :
( ! [SX3: $i] :
( ~ ( SX0 @ SX3 @ SX2 )
| ~ ( in @ SX3 @ SX1 ) )
| ( in @ SX2 @ ( sK9_B @ SX1 @ SX0 ) ) )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( sK9_B @ SX1 @ SX0 ) )
| ~ ( ~ ( SX0 @ ( sK10_Xy @ SX2 @ SX1 @ SX0 ) @ SX2 )
| ~ ( in @ ( sK10_Xy @ SX2 @ SX1 @ SX0 ) @ SX1 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[457,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(498,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK63_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK63_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[390,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(499,plain,
( ( ! [SX0: $i,SX1: $i > $o] :
( ~ ( ~ ( SX1 @ ( sK38_Xx @ SX1 @ SX0 ) )
| ~ ( in @ ( sK38_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[407,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(500,plain,
( ( ~ ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK54_Xx @ SX1 @ SX0 )
!= ( sK55_SY1102 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK54_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK55_SY1102 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK54_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK55_SY1102 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK53_SY232 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK53_SY232 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK52_SY234 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK52_SY234 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK50_Xx @ SX1 @ SX0 )
!= ( sK51_SY1100 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK50_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK51_SY1100 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK50_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK51_SY1100 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK49_SY235 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK49_SY235 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK48_SY231 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK48_SY231 @ SX1 @ SX0 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[399,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(501,plain,
( ( ! [SX0: $i,SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ~ ( ~ ( in @ ( sK80_Xy @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( SX1 @ ( sK80_Xy @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( ( sK80_Xy @ SX2 @ SX1 @ SX0 )
!= SX2 ) ) ) )
| ~ ( ( ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) )
!= ( setadjoin @ ( sK79_SY507 @ SX2 @ SX1 @ SX0 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SX2 @ SX1 @ SX0 )
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[310,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(502,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK64_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( in @ ( sK64_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( subset @ SX0 @ SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[387,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(503,plain,
( ( ! [SX0: $i] :
~ ( ~ ! [SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( SX1 @ SX2 )
| ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) ) )
| ~ ! [SX1: $i > $o,SX2: $i] :
( ~ ( in @ SX2 @ SX0 )
| ~ ( in @ SX2
@ ( dsetconstr @ SX0
@ ^ [SX3: $i] : ( SX1 @ SX3 ) ) )
| ( SX1 @ SX2 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[441,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(504,plain,
( ( ! [SX0: $i] :
( ~ ( ~ ~ ( ~ ( in @ ( sK8_Xx @ SX0 ) @ omega )
| ~ ( in @ ( sK8_Xx @ SX0 ) @ SX0 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK8_Xx @ SX0 ) @ ( sK8_Xx @ SX0 ) ) @ SX0 ) )
| ~ ( in @ emptyset @ SX0 )
| ! [SX1: $i] :
( ~ ( in @ SX1 @ omega )
| ( in @ SX1 @ SX0 ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[458,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(505,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( cartprod @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ( SX2
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SX2 @ SX1 @ SX0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SX2 @ SX1 @ SX0 ) @ ( setadjoin @ ( sK73_SY1108 @ SX2 @ SX1 @ SX0 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SX2 @ SX1 @ SX0 ) @ ( setunion @ SX2 ) ) )
| ~ ( in @ ( sK72_SY474 @ SX2 @ SX1 @ SX0 ) @ ( setunion @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[317,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(506,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SX1 @ SX0 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SX1 @ SX0 ) @ ( setadjoin @ ( sK67_SY1105 @ SX1 @ SX0 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK67_SY1105 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK66_SY422 @ SX1 @ SX0 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SX0 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SX0 @ ( setadjoin @ SX1 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[330,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(507,plain,
( ( ! [SX0: $i,SX1: $i] :
~ ( ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ( in @ SX2 @ SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX2: $i] :
( ~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 ) )
| ~ ( ! [SX2: $i] :
~ ( in @ SX2 @ ( binunion @ SX0 @ SX1 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[364,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(508,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
~ ( SX0 @ SX1 )
| ~ ( ~ ( SX0 @ ( sK43_Xx @ SX0 ) )
| ~ ~ ( ~ ( SX0 @ ( sK44_SY1097 @ SX0 ) )
| ~ ( ( ( sK43_Xx @ SX0 )
!= ( sK44_SY1097 @ SX0 ) ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK42_SY204 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK42_SY204 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[404,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(509,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK65_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK65_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ( ( binintersect @ SX0 @ SX1 )
= emptyset ) ) )
= $true ),
inference(unfold_def,[status(thm)],[353,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(510,plain,
( ( ! [SX0: $i,SX1: $i,SX2: $i] :
( ~ ( in @ SX2 @ ( setadjoin @ SX0 @ SX1 ) )
| ~ ( ~ ~ ( ~ ( ( SX2 = SX0 )
| ( in @ SX2 @ SX1 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SX2 = SX0 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SX2 @ SX1 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[434,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(511,plain,
( ( ! [SX0: $i,SX1: $i] :
( ( SX0 != SX1 )
| ! [SX2: $i > $o,SX3: $i > $o] :
( ~ ( ~ ( in @ ( sK61_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX0 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SX3 @ SX2 @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( ( ( sK61_Xx @ SX3 @ SX2 @ SX1 @ SX0 )
!= ( sK62_SY1104 @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX2 @ ( sK61_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ~ ( SX3 @ ( sK62_SY1104 @ SX3 @ SX2 @ SX1 @ SX0 ) ) )
| ~ ( ( SX2 @ ( sK61_Xx @ SX3 @ SX2 @ SX1 @ SX0 ) )
| ( SX3 @ ( sK62_SY1104 @ SX3 @ SX2 @ SX1 @ SX0 ) ) ) ) ) ) )
| ( ( dsetconstr @ SX0
@ ^ [SX4: $i] : ( SX2 @ SX4 ) )
= ( dsetconstr @ SX1
@ ^ [SX4: $i] : ( SX3 @ SX4 ) ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[391,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(512,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK59_Xx @ SX1 @ SX0 )
!= ( sK60_SY1103 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK59_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK60_SY1103 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK59_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK60_SY1103 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK58_SY256 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK58_SY256 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK57_SY259 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK57_SY259 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ( ( descr
@ ^ [SX2: $i] : ( SX0 @ SX2 ) )
= ( descr
@ ^ [SX2: $i] : ( SX1 @ SX2 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[392,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(513,plain,
( ( ! [SX0: $i > $o] :
( ! [SX1: $i] :
~ ( ~ ( ( ( sK46_Xy @ SX1 @ SX0 )
!= SX1 )
| ~ ( SX0 @ ( sK46_Xy @ SX1 @ SX0 ) ) )
| ~ ( ( ( sK46_Xy @ SX1 @ SX0 )
= SX1 )
| ( SX0 @ ( sK46_Xy @ SX1 @ SX0 ) ) ) )
| ~ ( ~ ! [SX1: $i] :
( ~ ( SX0 @ SX1 )
| ( ( sK45_SY210 @ SX0 )
= SX1 ) )
| ~ ( SX0 @ ( sK45_SY210 @ SX0 ) ) ) ) )
= $true ),
inference(unfold_def,[status(thm)],[403,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(514,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX0 )
| ~ ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX1 ) )
| ~ ( ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX0 )
| ( in @ ( sK5_Xx @ SX1 @ SX0 ) @ SX1 ) ) )
| ( SX0 = SX1 ) ) )
= $true ),
inference(unfold_def,[status(thm)],[465,binintersectEL,binintersectER,binintersectI,binintersectLsub,binintersectRsub,binintersectSubset1,binintersectSubset2,binintersectSubset3,binintersectSubset4,binintersectSubset5,binunionE,binunionEcases,binunionIL,binunionIR,binunionLsub,binunionRsub,bs114d,cartprodfstin,cartprodmempair,cartprodmempair1,cartprodpairin,descr__Cong,descrp,disjointsetsI1,dsetconstrEL,dsetconstrER,dsetconstrI,dsetconstr__Cong,emptyE1,emptyI,emptyInPowerset,emptyinPowerset,emptyinunitempty,emptysetAx,emptysetE,emptyset__Cong,emptysetimpfalse,emptysetsubset,eqimpsubset1,eqimpsubset2,eqinunit,ex1,ex1E1,ex1I,ex1I2,exu,exuE1,exuE2,exuE3e,exuE3u,exuEu,exuI1,exuI2,exuI3,exu__Cong,foundationAx,inCongP,inPowerset,in__Cong,iskpair,kfstpairEq,kfstsingleton,kpair,kpairiskpair,kpairp,noeltsimpempty,nonempty,nonemptyE1,nonemptyI,nonemptyI1,nonemptyImpWitness,notdallE,notdexE,notequalI1,notequalI2,notinemptyset,notinsingleton,notsubsetI,omega0Ax,omegaIndAx,omegaSAx,omega__Cong,powersetAx,powersetE,powersetE1,powersetI,powersetI1,powerset__Cong,powersetsubset,prop2set2propI,prop2setE,prop2setI,quantDeMorgan1,quantDeMorgan2,quantDeMorgan3,quantDeMorgan4,replAx,secondinupair,sepInPowerset,sepSubset,setadjoinAx,setadjoinE,setadjoinIL,setadjoinIR,setadjoinOr,setadjoinSub,setadjoinSub2,setadjoin__Cong,setbeta,setext,setextAx,setextsub,setminusEL,setminusELneg,setminusER,setminusERneg,setminusI,setminusILneg,setminusIRneg,setminusLsub,setminusSubset1,setminusSubset2,setoftrueEq,setukpairIL,setukpairIR,setukpairinjL1,setunionAx,setunionE,setunionE2,setunionI,setunion__Cong,setunionsingleton,setunionsingleton1,setunionsingleton2,singleton,singletoninpowerset,singletoninpowunion,singletonprop,singletonsswitch,singletonsubset,singletonsuniq,subPowSU,subset2powerset,subsetE,subsetE2,subsetI1,subsetI2,subsetRefl,subsetTrans,subsetemptysetimpeq,symdiffE,symdiffI1,symdiffI2,symdiffIneg1,symdiffIneg2,theprop,ubforcartprodlem1,ubforcartprodlem2,ubforcartprodlem3,uniqinunit,upairinpowunion,upairset2E,upairset2IR,upairsetE,upairsetIL,upairsetIR,upairsubunion,vacuousDall,wellorderingAx]) ).
thf(515,plain,
! [SV1: $i] :
( ( ! [SY1119: $i,SY1120: $i] :
( ~ ( in @ SY1120 @ ( cartprod @ SV1 @ SY1119 ) )
| ( in @ ( kfst @ SY1120 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[303]) ).
thf(516,plain,
! [SV2: $i] :
( ( ! [SY1121: $i] :
( ( kfst @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SY1121 @ emptyset ) ) @ emptyset ) ) )
= SV2 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[304]) ).
thf(517,plain,
! [SV3: $i] :
( ( ! [SY1122: $i] :
( ( SV3
!= ( setadjoin @ SY1122 @ emptyset ) )
| ~ ( in @ SY1122 @ SV3 ) )
| ( in @ ( setunion @ SV3 ) @ SV3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[305]) ).
thf(518,plain,
! [SV4: $i] :
( ( ! [SY1123: $i,SY1124: $i] :
( ~ ( in @ ( setadjoin @ SY1124 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SY1123 @ emptyset ) ) @ emptyset ) ) )
| ( SV4 = SY1124 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[307]) ).
thf(519,plain,
! [SV5: $i] :
( ( ! [SY1125: $i] :
( ( ( setadjoin @ SV5 @ emptyset )
!= ( setadjoin @ SY1125 @ emptyset ) )
| ( SV5 = SY1125 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[308]) ).
thf(520,plain,
! [SV6: $i] :
( ( ( setunion @ ( setadjoin @ SV6 @ emptyset ) )
= SV6 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[313]) ).
thf(521,plain,
! [SV7: $i] :
( ( subset @ SV7 @ ( setunion @ ( setadjoin @ SV7 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[314]) ).
thf(522,plain,
! [SV8: $i] :
( ( subset @ ( setunion @ ( setadjoin @ SV8 @ emptyset ) ) @ SV8 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[315]) ).
thf(523,plain,
! [SV9: $i] :
( ( ! [SY1126: $i,SY1127: $i] :
( ~ ( in @ SY1127 @ SV9 )
| ! [SY1128: $i] :
( ~ ( in @ SY1128 @ SY1126 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1127 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1127 @ ( setadjoin @ SY1128 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV9 @ SY1126 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[319]) ).
thf(524,plain,
! [SV10: $i] :
( ( ! [SY1129: $i,SY1130: $i] :
( ~ ( in @ SY1130 @ SV10 )
| ! [SY1131: $i] :
( ~ ( in @ SY1131 @ SY1129 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1130 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1130 @ ( setadjoin @ SY1131 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV10 @ SY1129 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[320]) ).
thf(525,plain,
! [SV11: $i] :
( ( ! [SY1132: $i,SY1133: $i] :
( ~ ( in @ SY1133 @ SV11 )
| ! [SY1134: $i] :
( ~ ( in @ SY1134 @ SY1132 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1133 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1133 @ ( setadjoin @ SY1134 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV11 @ SY1132 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[321]) ).
thf(526,plain,
! [SV12: $i] :
( ( ! [SY1135: $i,SY1136: $i] :
( ~ ( in @ SY1136 @ SV12 )
| ! [SY1137: $i] :
( ~ ( in @ SY1137 @ SY1135 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1136 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1136 @ ( setadjoin @ SY1137 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV12 @ SY1135 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[322]) ).
thf(527,plain,
! [SV13: $i] :
( ( ! [SY1138: $i,SY1139: $i] :
( ~ ( in @ SY1139 @ SV13 )
| ! [SY1140: $i] :
( ~ ( in @ SY1140 @ SY1138 )
| ( in @ ( setadjoin @ SY1139 @ ( setadjoin @ SY1140 @ emptyset ) ) @ ( powerset @ ( binunion @ SV13 @ SY1138 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[323]) ).
thf(528,plain,
! [SV14: $i] :
( ( ! [SY1141: $i,SY1142: $i] :
( ~ ( in @ SY1142 @ SV14 )
| ! [SY1143: $i] :
( ~ ( in @ SY1143 @ SY1141 )
| ( subset @ ( setadjoin @ SY1142 @ ( setadjoin @ SY1143 @ emptyset ) ) @ ( binunion @ SV14 @ SY1141 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[324]) ).
thf(529,plain,
! [SV15: $i] :
( ( ! [SY1144: $i,SY1145: $i] :
( ~ ( in @ SY1145 @ ( setadjoin @ SV15 @ ( setadjoin @ SY1144 @ emptyset ) ) )
| ( SY1145 = SV15 )
| ( SY1145 = SY1144 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[325]) ).
thf(530,plain,
! [SV16: $i] :
( ( ! [SY1146: $i,SY1147: $i] :
( ~ ( in @ SY1147 @ SV16 )
| ( in @ ( setadjoin @ SY1147 @ emptyset ) @ ( powerset @ ( binunion @ SV16 @ SY1146 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[326]) ).
thf(531,plain,
! [SV17: $i] :
( ( ! [SY1148: $i] :
( ~ ( in @ SY1148 @ SV17 )
| ( in @ ( setadjoin @ SY1148 @ emptyset ) @ ( powerset @ SV17 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[327]) ).
thf(532,plain,
! [SV18: $i] :
( ( ! [SY1149: $i] :
( ~ ( in @ SY1149 @ SV18 )
| ( subset @ ( setadjoin @ SY1149 @ emptyset ) @ SV18 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[328]) ).
thf(533,plain,
! [SV19: $i] :
( ( ! [SY1150: $i] : ( in @ SY1150 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV19 @ ( setadjoin @ SY1150 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[331]) ).
thf(534,plain,
! [SV20: $i] :
( ( ! [SY1151: $i] : ( in @ SV20 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV20 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV20 @ ( setadjoin @ SY1151 @ emptyset ) ) @ emptyset ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[332]) ).
thf(535,plain,
! [SV21: $i] :
( ( ! [SY1152: $i] : ( in @ SY1152 @ ( setadjoin @ SV21 @ ( setadjoin @ SY1152 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[333]) ).
thf(536,plain,
! [SV22: $i] :
( ( ! [SY1153: $i,SY1154: $i] :
( ( in @ SY1154 @ SV22 )
| ( in @ SY1154 @ SY1153 )
| ~ ( in @ SY1154 @ ( symdiff @ SV22 @ SY1153 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[334]) ).
thf(537,plain,
! [SV23: $i] :
( ( ! [SY1155: $i,SY1156: $i] :
( ~ ( in @ SY1156 @ SV23 )
| ~ ( in @ SY1156 @ SY1155 )
| ~ ( in @ SY1156 @ ( symdiff @ SV23 @ SY1155 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[335]) ).
thf(538,plain,
! [SV24: $i] :
( ( ! [SY1157: $i,SY1158: $i] :
( ( in @ SY1158 @ SV24 )
| ~ ( in @ SY1158 @ SY1157 )
| ( in @ SY1158 @ ( symdiff @ SV24 @ SY1157 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[336]) ).
thf(539,plain,
! [SV25: $i] :
( ( ! [SY1159: $i,SY1160: $i] :
( ~ ( in @ SY1160 @ SV25 )
| ( in @ SY1160 @ SY1159 )
| ( in @ SY1160 @ ( symdiff @ SV25 @ SY1159 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[337]) ).
thf(540,plain,
! [SV26: $i] :
( ( ! [SY1161: $i] :
( ( ( setminus @ SV26 @ SY1161 )
!= emptyset )
| ( subset @ SV26 @ SY1161 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[339]) ).
thf(541,plain,
! [SV27: $i] :
( ( ! [SY1162: $i] : ( subset @ ( setminus @ SV27 @ SY1162 ) @ SV27 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[340]) ).
thf(542,plain,
! [SV28: $i] :
( ( ! [SY1163: $i,SY1164: $i] :
( ~ ( in @ SY1164 @ SY1163 )
| ~ ( in @ SY1164 @ ( setminus @ SV28 @ SY1163 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[341]) ).
thf(543,plain,
! [SV29: $i] :
( ( ! [SY1165: $i,SY1166: $i] :
( ( in @ SY1166 @ SV29 )
| ~ ( in @ SY1166 @ ( setminus @ SV29 @ SY1165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[342]) ).
thf(544,plain,
! [SV30: $i] :
( ( ! [SY1167: $i,SY1168: $i] :
( ( in @ SY1168 @ ( setminus @ SV30 @ SY1167 ) )
| ( in @ SY1168 @ SY1167 )
| ~ ( in @ SY1168 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[343]) ).
thf(545,plain,
! [SV31: $i] :
( ( ! [SY1169: $i,SY1170: $i] :
( ( in @ SY1170 @ ( setminus @ SV31 @ SY1169 ) )
| ~ ( in @ SY1170 @ SV31 )
| ( in @ SY1170 @ SY1169 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[344]) ).
thf(546,plain,
! [SV32: $i] :
( ( ! [SY1171: $i] :
( ~ ( subset @ SV32 @ SY1171 )
| ( ( setminus @ SV32 @ SY1171 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[345]) ).
thf(547,plain,
! [SV33: $i] :
( ( ! [SY1172: $i,SY1173: $i] :
( ~ ( in @ SY1173 @ ( setminus @ SV33 @ SY1172 ) )
| ~ ( in @ SY1173 @ SY1172 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[346]) ).
thf(548,plain,
! [SV34: $i] :
( ( ! [SY1174: $i,SY1175: $i] :
( ~ ( in @ SY1175 @ ( setminus @ SV34 @ SY1174 ) )
| ( in @ SY1175 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[347]) ).
thf(549,plain,
! [SV35: $i] :
( ( ! [SY1176: $i,SY1177: $i] :
( ~ ( in @ SY1177 @ SV35 )
| ( in @ SY1177 @ SY1176 )
| ( in @ SY1177 @ ( setminus @ SV35 @ SY1176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[348]) ).
thf(550,plain,
! [SV36: $i] :
( ( ! [SY1178: $i,SY1179: $i] :
( ( binintersect @ SV36 @ ( binunion @ SY1178 @ SY1179 ) )
= ( binunion @ ( binintersect @ SV36 @ SY1178 ) @ ( binintersect @ SV36 @ SY1179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[349]) ).
thf(551,plain,
! [SV37: $i] :
( ( ! [SY1180: $i] :
( ( ( binintersect @ SV37 @ SY1180 )
!= SV37 )
| ( subset @ SV37 @ SY1180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[350]) ).
thf(552,plain,
! [SV38: $i] :
( ( ! [SY1181: $i] :
( ~ ( subset @ SY1181 @ SV38 )
| ( ( binintersect @ SV38 @ SY1181 )
= SY1181 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[351]) ).
thf(553,plain,
! [SV39: $i] :
( ( ! [SY1182: $i] : ( subset @ ( binintersect @ SV39 @ SY1182 ) @ SY1182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[352]) ).
thf(554,plain,
! [SV40: $i] :
( ( ! [SY1183: $i,SY1184: $i] :
( ~ ( in @ SY1184 @ ( binintersect @ SV40 @ SY1183 ) )
| ( in @ SY1184 @ SY1183 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[354]) ).
thf(555,plain,
! [SV41: $i] :
( ( ! [SY1185: $i] :
( ( ( binintersect @ SV41 @ SY1185 )
!= SY1185 )
| ( subset @ SY1185 @ SV41 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[355]) ).
thf(556,plain,
! [SV42: $i] :
( ( ! [SY1186: $i] :
( ~ ( subset @ SV42 @ SY1186 )
| ( ( binintersect @ SV42 @ SY1186 )
= SV42 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[356]) ).
thf(557,plain,
! [SV43: $i] :
( ( ! [SY1187: $i] : ( subset @ ( binintersect @ SV43 @ SY1187 ) @ SV43 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[357]) ).
thf(558,plain,
! [SV44: $i] :
( ( ! [SY1188: $i,SY1189: $i] :
( ~ ( in @ SY1189 @ ( binintersect @ SV44 @ SY1188 ) )
| ( in @ SY1189 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[358]) ).
thf(559,plain,
! [SV45: $i] :
( ( ! [SY1190: $i,SY1191: $i] :
( ~ ( subset @ SY1191 @ SV45 )
| ~ ( subset @ SY1191 @ SY1190 )
| ( subset @ SY1191 @ ( binintersect @ SV45 @ SY1190 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[359]) ).
thf(560,plain,
! [SV46: $i] :
( ( ! [SY1192: $i,SY1193: $i] :
( ~ ( in @ SY1193 @ SV46 )
| ~ ( in @ SY1193 @ SY1192 )
| ( in @ SY1193 @ ( binintersect @ SV46 @ SY1192 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[360]) ).
thf(561,plain,
! [SV47: $i] :
( ( ! [SY1194: $i] : ( subset @ SY1194 @ ( binunion @ SV47 @ SY1194 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[361]) ).
thf(562,plain,
! [SV48: $i] :
( ( ! [SY1195: $i] : ( subset @ SV48 @ ( binunion @ SV48 @ SY1195 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[362]) ).
thf(563,plain,
! [SV49: $i] :
( ( ! [SY1196: $i,SY1197: $i] :
( ~ ( in @ SY1197 @ ( binunion @ SV49 @ SY1196 ) )
| ( in @ SY1197 @ SV49 )
| ( in @ SY1197 @ SY1196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[363]) ).
thf(564,plain,
! [SV50: $i] :
( ( ! [SY1198: $i,SY1199: $i] :
( ~ ( in @ SY1199 @ SY1198 )
| ( in @ SY1199 @ ( binunion @ SV50 @ SY1198 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[365]) ).
thf(565,plain,
! [SV51: $i] :
( ( ! [SY1200: $i] : ( in @ SY1200 @ ( setadjoin @ SV51 @ ( setadjoin @ SY1200 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[366]) ).
thf(566,plain,
! [SV52: $i] :
( ( ! [SY1201: $i,SY1202: $i] :
( ~ ( in @ SY1202 @ SV52 )
| ( in @ SY1202 @ ( binunion @ SV52 @ SY1201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[367]) ).
thf(567,plain,
! [SV53: $i] :
( ( ! [SY1203: $i > $o] :
( subset
@ ( dsetconstr @ SV53
@ ^ [Xx: $i] : ( SY1203 @ Xx ) )
@ SV53 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[368]) ).
thf(568,plain,
! [SV54: $i] :
( ( ! [SY1205: $i > $o] :
( in
@ ( dsetconstr @ SV54
@ ^ [Xx: $i] : ( SY1205 @ Xx ) )
@ ( powerset @ SV54 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[369]) ).
thf(569,plain,
! [SV55: $i] :
( ( ! [SY1207: $i] :
( ~ ( subset @ SV55 @ SY1207 )
| ( subset @ ( powerset @ SV55 ) @ ( powerset @ SY1207 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[370]) ).
thf(570,plain,
! [SV56: $i] :
( ( in @ SV56 @ ( powerset @ SV56 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[371]) ).
thf(571,plain,
! [SV57: $i] :
( ( ! [SY1208: $i] :
( ~ ( in @ SY1208 @ ( powerset @ SV57 ) )
| ( subset @ SY1208 @ SV57 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[372]) ).
thf(572,plain,
! [SV58: $i] :
( ( ! [SY1209: $i] :
( ~ ( subset @ SY1209 @ SV58 )
| ( in @ SY1209 @ ( powerset @ SV58 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[373]) ).
thf(573,plain,
! [SV59: $i] :
( ( ~ ( subset @ SV59 @ emptyset )
| ( SV59 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[374]) ).
thf(574,plain,
! [SV60: $i] :
( ( ! [SY1210: $i] :
( ~ ( subset @ SV60 @ SY1210 )
| ~ ( subset @ SY1210 @ SV60 )
| ( SV60 = SY1210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[375]) ).
thf(575,plain,
! [SV61: $i] :
( ( ! [SY1211: $i] :
( ~ ( subset @ SV61 @ SY1211 )
| ( in @ SV61 @ ( powerset @ SY1211 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[376]) ).
thf(576,plain,
! [SV62: $i] :
( ( ! [SY1212: $i,SY1213: $i] :
( ~ ( subset @ SV62 @ SY1213 )
| ( subset @ SV62 @ ( setadjoin @ SY1212 @ SY1213 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[377]) ).
thf(577,plain,
! [SV63: $i] :
( ( ! [SY1214: $i] : ( subset @ SY1214 @ ( setadjoin @ SV63 @ SY1214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[378]) ).
thf(578,plain,
! [SV64: $i] :
( ( ! [SY1215: $i] :
( ~ ( subset @ SV64 @ SY1215 )
| ! [SY1216: $i] :
( ~ ( subset @ SY1215 @ SY1216 )
| ( subset @ SV64 @ SY1216 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[379]) ).
thf(579,plain,
! [SV65: $i] :
( ( subset @ SV65 @ SV65 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[380]) ).
thf(580,plain,
! [SV66: $i] :
( ( ! [SY1217: $i,SY1218: $i] :
( ~ ( in @ SY1218 @ SV66 )
| ( in @ SY1218 @ SY1217 )
| ( SV66 != SY1217 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[381]) ).
thf(581,plain,
! [SV67: $i] :
( ( ! [SY1219: $i] :
( ( subset @ SV67 @ SY1219 )
| ( SV67 != SY1219 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[382]) ).
thf(582,plain,
! [SV68: $i] :
( ( ! [SY1220: $i,SY1221: $i] :
( ~ ( in @ SY1221 @ SV68 )
| ( in @ SY1221 @ SY1220 )
| ~ ( subset @ SV68 @ SY1220 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[383]) ).
thf(583,plain,
! [SV69: $i] :
( ( ! [SY1222: $i] :
( ~ ( subset @ SV69 @ SY1222 )
| ! [SY1223: $i] :
( ( in @ SY1223 @ SY1222 )
| ~ ( in @ SY1223 @ SV69 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[384]) ).
thf(584,plain,
! [SV70: $i] :
( ( ! [SY1224: $i] :
( ~ ( subset @ SV70 @ SY1224 )
| ! [SY1225: $i] :
( ~ ( in @ SY1225 @ SV70 )
| ( in @ SY1225 @ SY1224 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[385]) ).
thf(585,plain,
! [SV71: $i] :
( ( subset @ emptyset @ SV71 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[386]) ).
thf(586,plain,
! [SV72: $i] :
( ( ! [SY1226: $i] :
( ( SV72 != SY1226 )
| ( subset @ SV72 @ SY1226 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[388]) ).
thf(587,plain,
! [SV73: $i] :
( ( ! [SY1227: $i] :
( ( SV73 != SY1227 )
| ( subset @ SY1227 @ SV73 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[389]) ).
thf(588,plain,
! [SV74: $i] :
( ( ! [SY1228: $i] :
( ( SV74 != SY1228 )
| ( ( setunion @ SV74 )
= ( setunion @ SY1228 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[395]) ).
thf(589,plain,
! [SV75: $i] :
( ( ! [SY1229: $i] :
( ( SV75 != SY1229 )
| ( ( powerset @ SV75 )
= ( powerset @ SY1229 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[396]) ).
thf(590,plain,
! [SV76: $i] :
( ( ! [SY1230: $i] :
( ( SV76 != SY1230 )
| ! [SY1231: $i,SY1232: $i] :
( ( SY1231 != SY1232 )
| ( ( setadjoin @ SV76 @ SY1231 )
= ( setadjoin @ SY1230 @ SY1232 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[397]) ).
thf(591,plain,
! [SV77: $i] :
( ( ! [SY1233: $i] :
( ( SV77 != SY1233 )
| ! [SY1234: $i,SY1235: $i] :
( ( SY1234 != SY1235 )
| ~ ( in @ SY1234 @ SV77 )
| ( in @ SY1235 @ SY1233 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[402]) ).
thf(592,plain,
! [SV78: $o] :
( ( ~ SV78
| ( set2prop @ ( prop2set @ SV78 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[408]) ).
thf(593,plain,
( ( ~ $true
| ( set2prop @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[408]) ).
thf(594,plain,
( ( ~ $false
| ( set2prop @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[408]) ).
thf(595,plain,
! [SV79: $o] :
( ( ~ SV79
| ( in @ emptyset @ ( prop2set @ SV79 ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[409]) ).
thf(596,plain,
( ( ~ $true
| ( in @ emptyset @ ( prop2set @ $true ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[409]) ).
thf(597,plain,
( ( ~ $false
| ( in @ emptyset @ ( prop2set @ $false ) ) )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[409]) ).
thf(598,plain,
! [SV80: $i > $o] :
( ( ! [SY1236: $i] :
( ~ ( in @ SY1236 @ emptyset )
| ( SV80 @ SY1236 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[414]) ).
thf(599,plain,
! [SV81: $i] :
( ( ! [SY1237: $i > $o] :
( ! [SY1238: $i] :
( ~ ( SY1237 @ SY1238 )
| ~ ( in @ SY1238 @ SV81 ) )
| ( ( dsetconstr @ SV81
@ ^ [Xx: $i] : ( SY1237 @ Xx ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[415]) ).
thf(600,plain,
! [SV82: $i] :
( ( ! [SY1240: $i] : ( in @ SY1240 @ ( setadjoin @ SV82 @ ( setadjoin @ SY1240 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[416]) ).
thf(601,plain,
! [SV83: $i] :
( ( ! [SY1241: $i] : ( in @ SV83 @ ( setadjoin @ SV83 @ ( setadjoin @ SY1241 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[417]) ).
thf(602,plain,
! [SV84: $i] :
( ( ! [SY1242: $i,SY1243: $i] :
( ~ ( in @ SY1243 @ ( setadjoin @ SV84 @ ( setadjoin @ SY1242 @ emptyset ) ) )
| ( SY1243 = SV84 )
| ( SY1243 = SY1242 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[418]) ).
thf(603,plain,
! [SV85: $i] :
( ( ! [SY1244: $i] :
( ~ ( in @ SV85 @ ( setadjoin @ SY1244 @ emptyset ) )
| ( in @ SY1244 @ ( setadjoin @ SV85 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[419]) ).
thf(604,plain,
! [SV86: $i] :
( ( ! [SY1245: $i] :
( ( SV86 != SY1245 )
| ( in @ SV86 @ ( setadjoin @ SY1245 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[420]) ).
thf(605,plain,
! [SV87: $i] :
( ( ! [SY1246: $i] :
( ( SV87 = SY1246 )
| ~ ( in @ SY1246 @ ( setadjoin @ SV87 @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[421]) ).
thf(606,plain,
! [SV88: $i] :
( ( ! [SY1247: $i] :
( ~ ( in @ SV88 @ ( setadjoin @ SY1247 @ emptyset ) )
| ( SV88 = SY1247 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[422]) ).
thf(607,plain,
! [SV89: $i] :
( ( ( SV89 = emptyset )
| ( in @ ( sK33_Xx @ SV89 ) @ SV89 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[423]) ).
thf(608,plain,
! [SV90: $i] :
( ( ! [SY1248: $i] :
( ~ ( in @ SY1248 @ SV90 )
| ( in @ SY1248 @ ( powerset @ ( setunion @ SV90 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[425]) ).
thf(609,plain,
! [SV91: $i] :
( ( ! [SY1249: $i,SY1250: $i] :
( ~ ( in @ SY1249 @ SY1250 )
| ~ ( in @ SY1250 @ SV91 )
| ( in @ SY1249 @ ( setunion @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[427]) ).
thf(610,plain,
! [SV92: $i] :
( ( ! [SY1251: $i] :
( ~ ( in @ SY1251 @ ( powerset @ SV92 ) )
| ! [SY1252: $i] :
( ~ ( in @ SY1252 @ SY1251 )
| ( in @ SY1252 @ SV92 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[428]) ).
thf(611,plain,
! [SV93: $i] :
( ( in @ emptyset @ ( powerset @ SV93 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[429]) ).
thf(612,plain,
! [SV94: $i] :
( ( in @ emptyset @ ( powerset @ SV94 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[430]) ).
thf(613,plain,
! [SV95: $i] :
( ( ( dsetconstr @ SV95
@ ^ [Xx: $i] : $true )
= SV95 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[432]) ).
thf(614,plain,
! [SV96: $i] :
( ( ! [SY1254: $i,SY1255: $i] :
( ~ ( in @ SY1255 @ ( setadjoin @ SV96 @ SY1254 ) )
| ( SY1255 = SV96 )
| ( in @ SY1255 @ SY1254 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[433]) ).
thf(615,plain,
! [SV97: $i] :
( ( ! [SY1256: $i,SY1257: $i] :
( ~ ( in @ SY1257 @ SY1256 )
| ( in @ SY1257 @ ( setadjoin @ SV97 @ SY1256 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[435]) ).
thf(616,plain,
! [SV98: $i] :
( ( ! [SY1258: $i] : ( in @ SV98 @ ( setadjoin @ SV98 @ SY1258 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[437]) ).
thf(617,plain,
! [SV99: $i] :
( ( ! [SY1259: $i] :
~ ( in @ SY1259 @ SV99 )
| ( SV99 != emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[438]) ).
thf(618,plain,
! [SV100: $i] :
( ( ! [SY1260: $i > $o,SY1261: $i] :
( ~ ( in @ SY1261 @ SV100 )
| ~ ( SY1260 @ SY1261 )
| ( ( dsetconstr @ SV100
@ ^ [Xy: $i] : ( SY1260 @ Xy ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[439]) ).
thf(619,plain,
! [SV101: $i] :
( ( ( SV101 = emptyset )
| ( in @ ( sK28_Xx @ SV101 ) @ SV101 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[440]) ).
thf(620,plain,
! [SV102: $i] :
( ( ( in @ ( sK27_Xx @ SV102 ) @ SV102 )
| ( SV102 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[442]) ).
thf(621,plain,
! [SV103: $i] :
( ( ( in @ ( sK26_Xx @ SV103 ) @ SV103 )
| ( SV103 = emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[443]) ).
thf(622,plain,
! [SV104: $i] :
( ( ~ ( in @ SV104 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[446]) ).
thf(623,plain,
! [SV105: $i] :
( ( ~ ( in @ SV105 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[447]) ).
thf(624,plain,
( ( ( ! [Xx: $i] :
~ ( in @ Xx @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[448]) ).
thf(625,plain,
! [SV106: $o] :
( ( ! [SY1263: $i] :
~ ( in @ SY1263 @ ( prop2set @ SV106 ) )
| SV106 )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[449]) ).
thf(626,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $true ) )
| $true )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[449]) ).
thf(627,plain,
( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $false ) )
| $false )
= $true ),
inference(extcnf_forall_special_pos,[status(thm)],[449]) ).
thf(628,plain,
! [SV107: $i] :
( ( ! [SY1264: $i > $o,SY1265: $i] :
( ~ ( in @ SY1265
@ ( dsetconstr @ SV107
@ ^ [Xy: $i] : ( SY1264 @ Xy ) ) )
| ( SY1264 @ SY1265 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[451]) ).
thf(629,plain,
! [SV108: $i] :
( ( ! [SY1267: $i > $o,SY1268: $i] :
( ~ ( in @ SY1268
@ ( dsetconstr @ SV108
@ ^ [Xy: $i] : ( SY1267 @ Xy ) ) )
| ( in @ SY1268 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[452]) ).
thf(630,plain,
! [SV109: $i] :
( ( ! [SY1270: $i > $o,SY1271: $i] :
( ~ ( in @ SY1271 @ SV109 )
| ~ ( SY1270 @ SY1271 )
| ( in @ SY1271
@ ( dsetconstr @ SV109
@ ^ [Xy: $i] : ( SY1270 @ Xy ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[453]) ).
thf(631,plain,
! [SV110: $i] :
( ( ~ ( in @ SV110 @ omega )
| ( in @ ( setadjoin @ SV110 @ SV110 ) @ omega ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[459]) ).
thf(632,plain,
! [SV111: $i] :
( ( ~ ( in @ SV111 @ emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[464]) ).
thf(633,plain,
! [SV112: $i] :
( ( ! [SY1273: $i > $o] :
( ! [SY1274: $i] :
( ( ( dsetconstr @ SV112
@ ^ [SX3: $i] : ( SY1273 @ SX3 ) )
!= ( setadjoin @ SY1274 @ emptyset ) )
| ~ ( in @ SY1274
@ ( dsetconstr @ SV112
@ ^ [SX3: $i] : ( SY1273 @ SX3 ) ) ) )
| ~ ( ~ ( SY1273 @ ( sK78_Xx @ SY1273 @ SV112 ) )
| ~ ( in @ ( sK78_Xx @ SY1273 @ SV112 ) @ SV112 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[467]) ).
thf(634,plain,
! [SV113: $i] :
( ( ~ ( ~ ! [SY1277: $i] :
( ~ ( ~ ( in @ ( sK18_Xx @ SY1277 @ SV113 ) @ SY1277 )
| ~ ~ ( in @ ( sK18_Xx @ SY1277 @ SV113 ) @ SV113 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY1277 )
| ~ ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ ( sK14_B @ SV113 ) )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SY1279 )
| ( in @ SY1280 @ ( sK16_SY1071 @ SY1277 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SY1277 @ SV113 ) @ SY1279 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SY1277 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SY1277 @ SV113 ) @ SY1277 ) )
| ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ ( sK16_SY1071 @ SY1277 @ SV113 ) )
| ~ ( in @ SY1281 @ SY1277 ) ) ) ) )
| ~ ~ ( ~ ! [SY1282: $i,SY1283: $i] :
( ~ ( in @ SY1282 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY1283 @ ( sK14_B @ SV113 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1282 )
| ( in @ SX3 @ SY1283 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1283 )
| ( in @ SX3 @ SY1282 ) ) )
| ~ ~ ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) )
| ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[468]) ).
thf(635,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[469]) ).
thf(636,plain,
! [SV114: $i] :
( ( ! [SY1290: $i > $o] :
( ! [SY1291: $i] :
( ~ ( in @ SY1291 @ SV114 )
| ( SY1290 @ SY1291 ) )
| ~ ( ~ ( in @ ( sK39_Xx @ SY1290 @ SV114 ) @ SV114 )
| ~ ~ ( SY1290 @ ( sK39_Xx @ SY1290 @ SV114 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[470]) ).
thf(637,plain,
! [SV115: $i] :
( ( ! [SY1292: $i > $o] :
( ! [SY1293: $i] :
( ~ ( in @ SY1293 @ SV115 )
| ( SY1292 @ SY1293 ) )
| ~ ( ~ ( in @ ( sK37_Xx @ SY1292 @ SV115 ) @ SV115 )
| ~ ~ ( SY1292 @ ( sK37_Xx @ SY1292 @ SV115 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[471]) ).
thf(638,plain,
! [SV116: $i] :
( ( ! [SY1294: $i] :
( ( SV116 != SY1294 )
| ~ ( ~ ! [SY1295: $i,SY1296: $i] :
( ( SY1295 != SY1296 )
| ~ ( in @ SY1295 @ SV116 )
| ( in @ SY1296 @ SY1294 ) )
| ~ ! [SY1297: $i,SY1298: $i] :
( ( SY1297 != SY1298 )
| ~ ( in @ SY1298 @ SY1294 )
| ( in @ SY1297 @ SV116 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[472]) ).
thf(639,plain,
( ( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY1055 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY1058 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY1058 @ ( setadjoin @ sK4_SY1060 @ emptyset ) ) @ emptyset ) ) )
| ~ ( ( sK1_Xx != sK3_SY1058 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[473]) ).
thf(640,plain,
! [SV117: $i > $o] :
( ( ! [SY1299: $i] :
( ~ ( ~ ( SV117 @ ( sK23_SY85 @ SY1299 @ SV117 ) )
| ~ ( ( SY1299
!= ( sK23_SY85 @ SY1299 @ SV117 ) ) ) )
| ~ ( SV117 @ SY1299 ) )
| ( SV117 @ ( sK22_Xx @ SV117 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[474]) ).
thf(641,plain,
! [SV118: $i] :
( ( ! [SY1300: $i] :
( ~ ( in @ SY1300 @ ( setunion @ SV118 ) )
| ~ ( ~ ( in @ ( sK74_X @ SY1300 @ SV118 ) @ SV118 )
| ~ ( in @ SY1300 @ ( sK74_X @ SY1300 @ SV118 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[475]) ).
thf(642,plain,
! [SV119: $i] :
( ( ! [SY1301: $i > $o] :
( ~ ( ~ ( in @ ( sK76_Xx @ SY1301 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( in @ ( sK77_SY1111 @ SY1301 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( SY1301 @ ( sK76_Xx @ SY1301 @ SV119 ) )
| ~ ~ ( ~ ( SY1301 @ ( sK77_SY1111 @ SY1301 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SY1301 @ SV119 )
!= ( sK77_SY1111 @ SY1301 @ SV119 ) ) ) ) ) ) )
| ! [SY1302: $i] :
( ~ ( SY1301 @ SY1302 )
| ~ ( in @ SY1302 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SX2: $i] : ( SY1301 @ SX2 ) )
!= ( setadjoin @ ( sK75_SY488 @ SY1301 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SY1301 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SX2: $i] : ( SY1301 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[476]) ).
thf(643,plain,
! [SV120: $i > $o] :
( ( ! [SY1305: $i] :
( ~ ( ~ ( SV120 @ ( sK21_SY73 @ SY1305 @ SV120 ) )
| ~ ( ( SY1305
!= ( sK21_SY73 @ SY1305 @ SV120 ) ) ) )
| ~ ( SV120 @ SY1305 ) )
| ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[477]) ).
thf(644,plain,
! [SV121: $i > $o] :
( ( ! [SY1307: $i] :
( ~ ( ~ ( SV121 @ ( sK56_SY247 @ SY1307 @ SV121 ) )
| ~ ( ( SY1307
!= ( sK56_SY247 @ SY1307 @ SV121 ) ) ) )
| ~ ( SV121 @ SY1307 ) )
| ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[478]) ).
thf(645,plain,
! [SV122: $i] :
( ( ! [SY1310: $i > $o] :
( ~ ( ~ ( SY1310 @ ( sK36_Xx @ SY1310 @ SV122 ) )
| ~ ( in @ ( sK36_Xx @ SY1310 @ SV122 ) @ SV122 ) )
| ! [SY1311: $i] :
( ~ ( in @ SY1311 @ SV122 )
| ~ ( SY1310 @ SY1311 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[479]) ).
thf(646,plain,
! [SV123: $i] :
( ( ! [SY1312: $i] :
~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SY1312 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SY1312 @ SV123 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SY1312 @ SV123 ) @ ( setadjoin @ ( sK69_SY1106 @ SY1312 @ SV123 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK69_SY1106 @ SY1312 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SY1312 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK68_SY427 @ SY1312 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SY1312 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[480]) ).
thf(647,plain,
! [SV124: $i] :
( ( ! [SY1313: $i] :
~ ( in @ SY1313 @ SV124 )
| ~ ( ~ ( in @ ( sK13_B @ SV124 ) @ SV124 )
| ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK13_B @ SV124 ) )
| ~ ( in @ SY1314 @ SV124 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[481]) ).
thf(648,plain,
! [SV125: $i] :
( ( ! [SY1315: $i > $o] :
( ~ ( ~ ( in @ ( sK82_Xx @ SY1315 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( in @ ( sK83_SY1116 @ SY1315 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( SY1315 @ ( sK82_Xx @ SY1315 @ SV125 ) )
| ~ ~ ( ~ ( SY1315 @ ( sK83_SY1116 @ SY1315 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SY1315 @ SV125 )
!= ( sK83_SY1116 @ SY1315 @ SV125 ) ) ) ) ) ) )
| ! [SY1316: $i] :
( ~ ( SY1315 @ SY1316 )
| ~ ( in @ SY1316 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SX2: $i] : ( SY1315 @ SX2 ) )
!= ( setadjoin @ ( sK81_SY519 @ SY1315 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SY1315 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SX2: $i] : ( SY1315 @ SX2 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[482]) ).
thf(649,plain,
! [SV126: $i] :
( ( ! [SY1319: $i,SY1320: $i] :
( ~ ( in @ SY1320 @ ( symdiff @ SV126 @ SY1319 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SY1320 @ SV126 )
| ~ ( in @ SY1320 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SY1320 @ SV126 )
| ( in @ SY1320 @ SY1319 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SY1320 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY1320 @ SY1319 )
| ~ ( in @ SY1320 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SY1320 @ SY1319 )
| ( in @ SY1320 @ SY1319 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SY1320 @ SY1319 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1327: $o] :
( ~ SY1327
| ~ ( in @ SY1320 @ SV126 )
| SY1327 )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY1320 @ SY1319 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[483]) ).
thf(650,plain,
! [SV127: $i > $o] :
( ( ! [SY1330: $i] :
( ~ ( ~ ( SV127 @ ( sK32_SY141 @ SY1330 @ SV127 ) )
| ~ ( ( SY1330
!= ( sK32_SY141 @ SY1330 @ SV127 ) ) ) )
| ~ ( SV127 @ SY1330 ) )
| ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[484]) ).
thf(651,plain,
! [SV128: $i] :
( ( ! [SY1333: $i > $o] :
( ! [SY1334: $i] :
( ~ ( in @ SY1334 @ SV128 )
| ( SY1333 @ SY1334 ) )
| ~ ( ~ ( in @ ( sK34_Xx @ SY1333 @ SV128 ) @ SV128 )
| ~ ~ ( SY1333 @ ( sK34_Xx @ SY1333 @ SV128 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[485]) ).
thf(652,plain,
! [SV129: $i > $o] :
( ( ! [SY1335: $i] :
( ~ ( ~ ( SV129 @ ( sK41_Xy @ SY1335 @ SV129 ) )
| ~ ( ( SY1335
!= ( sK41_Xy @ SY1335 @ SV129 ) ) ) )
| ~ ( SV129 @ SY1335 ) )
| ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[486]) ).
thf(653,plain,
! [SV130: $i > $o] :
( ( ! [SY1337: $i] :
( ~ ( ~ ( SV130 @ ( sK19_SY56 @ SY1337 @ SV130 ) )
| ~ ( ( SY1337
!= ( sK19_SY56 @ SY1337 @ SV130 ) ) ) )
| ~ ( SV130 @ SY1337 ) )
| ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[487]) ).
thf(654,plain,
! [SV131: $i] :
( ( ~ ( ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ SY1340 @ ( setadjoin @ SV131 @ SY1339 ) )
| ( SY1340 = SV131 )
| ( in @ SY1340 @ SY1339 ) )
| ~ ~ ( ~ ! [SY1341: $i,SY1342: $i] :
( ( SY1342 != SV131 )
| ( in @ SY1342 @ ( setadjoin @ SV131 @ SY1341 ) ) )
| ~ ! [SY1343: $i,SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( setadjoin @ SV131 @ SY1343 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[488]) ).
thf(655,plain,
! [SV132: $i] :
( ( ! [SY1345: $i > $o] :
( ~ ( ~ ( in @ ( sK35_Xx @ SY1345 @ SV132 ) @ SV132 )
| ~ ( SY1345 @ ( sK35_Xx @ SY1345 @ SV132 ) ) )
| ! [SY1346: $i] :
( ~ ( SY1345 @ SY1346 )
| ~ ( in @ SY1346 @ SV132 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[489]) ).
thf(656,plain,
! [SV133: $i] :
( ( ! [SY1347: $i] :
( ! [SY1348: $i] :
( ( SV133
!= ( setadjoin @ ( setadjoin @ SY1347 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1347 @ ( setadjoin @ SY1348 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY1348 @ ( setunion @ SV133 ) ) )
| ~ ( in @ SY1347 @ ( setunion @ SV133 ) ) )
| ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[490]) ).
thf(657,plain,
! [SV134: $i] :
( ( ! [SY1351: $i] :
( ~ ( ~ ( in @ ( sK29_Xx @ SY1351 @ SV134 ) @ SY1351 )
| ~ ~ ( in @ ( sK29_Xx @ SY1351 @ SV134 ) @ SV134 ) )
| ( in @ SY1351 @ ( powerset @ SV134 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[491]) ).
thf(658,plain,
! [SV135: $i] :
( ( ! [SY1352: $i] :
( ~ ( in @ SY1352 @ ( setunion @ SV135 ) )
| ! [SY1353: $o] :
( ~ ( ~ ( in @ SY1352 @ ( sK30_B @ SY1353 @ SY1352 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ SY1353 @ SY1352 @ SV135 ) @ SV135 )
| ~ ~ SY1353 ) )
| SY1353 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[492]) ).
thf(659,plain,
! [SV136: $i > $o] :
( ( ! [SY1354: $i] :
( ~ ( ~ ( SV136 @ ( sK47_SY223 @ SY1354 @ SV136 ) )
| ~ ( ( SY1354
!= ( sK47_SY223 @ SY1354 @ SV136 ) ) ) )
| ~ ( SV136 @ SY1354 ) )
| ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[493]) ).
thf(660,plain,
! [SV137: $i] :
( ( ! [SY1357: $i] :
( ~ ( ~ ( in @ ( sK25_Xx @ SY1357 @ SV137 ) @ SV137 )
| ~ ~ ( in @ ( sK25_Xx @ SY1357 @ SV137 ) @ SY1357 ) )
| ~ ( ~ ( in @ ( sK24_Xx @ SY1357 @ SV137 ) @ SY1357 )
| ~ ~ ( in @ ( sK24_Xx @ SY1357 @ SV137 ) @ SV137 ) )
| ( SV137 = SY1357 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[494]) ).
thf(661,plain,
! [SV138: $i] :
( ( ! [SY1358: $i,SY1359: $i] :
( ~ ( in @ SY1359 @ ( cartprod @ SV138 @ SY1358 ) )
| ~ ( ~ ~ ( ( SY1359
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SY1359 @ SY1358 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SY1359 @ SY1358 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SY1359 @ SY1358 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SY1359 @ SY1358 @ SV138 ) @ SY1358 ) )
| ~ ( in @ ( sK70_SY468 @ SY1359 @ SY1358 @ SV138 ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[495]) ).
thf(662,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) )
| ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK7_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK7_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[496]) ).
thf(663,plain,
! [SV139: $i > $i > $o] :
( ( ! [SY1360: $i] :
( ~ ( ~ ( in @ ( sK11_SY23 @ SY1360 @ SV139 ) @ SY1360 )
| ~ ! [SY1361: $i] :
( ~ ( ~ ( SV139 @ ( sK11_SY23 @ SY1360 @ SV139 ) @ ( sK12_SY1066 @ SY1361 @ SY1360 @ SV139 ) )
| ~ ( ( SY1361
!= ( sK12_SY1066 @ SY1361 @ SY1360 @ SV139 ) ) ) )
| ~ ( SV139 @ ( sK11_SY23 @ SY1360 @ SV139 ) @ SY1361 ) ) )
| ~ ( ~ ! [SY1362: $i] :
( ! [SY1363: $i] :
( ~ ( SV139 @ SY1363 @ SY1362 )
| ~ ( in @ SY1363 @ SY1360 ) )
| ( in @ SY1362 @ ( sK9_B @ SY1360 @ SV139 ) ) )
| ~ ! [SY1364: $i] :
( ~ ( in @ SY1364 @ ( sK9_B @ SY1360 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1364 @ SY1360 @ SV139 ) @ SY1364 )
| ~ ( in @ ( sK10_Xy @ SY1364 @ SY1360 @ SV139 ) @ SY1360 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[497]) ).
thf(664,plain,
! [SV140: $i] :
( ( ! [SY1365: $i] :
( ~ ( ~ ( in @ ( sK63_Xx @ SY1365 @ SV140 ) @ SV140 )
| ~ ~ ( in @ ( sK63_Xx @ SY1365 @ SV140 ) @ SY1365 ) )
| ( subset @ SV140 @ SY1365 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[498]) ).
thf(665,plain,
! [SV141: $i] :
( ( ! [SY1366: $i > $o] :
( ~ ( ~ ( SY1366 @ ( sK38_Xx @ SY1366 @ SV141 ) )
| ~ ( in @ ( sK38_Xx @ SY1366 @ SV141 ) @ SV141 ) )
| ! [SY1367: $i] :
( ~ ( in @ SY1367 @ SV141 )
| ~ ( SY1366 @ SY1367 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[499]) ).
thf(666,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK54_Xx @ SX1 @ SX0 )
!= ( sK55_SY1102 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK54_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK55_SY1102 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK54_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK55_SY1102 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK53_SY232 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK53_SY232 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK52_SY234 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK52_SY234 @ SX1 @ SX0 ) ) ) )
| ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK50_Xx @ SX1 @ SX0 )
!= ( sK51_SY1100 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK50_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK51_SY1100 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK50_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK51_SY1100 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK49_SY235 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK49_SY235 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK48_SY231 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK48_SY231 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[500]) ).
thf(667,plain,
! [SV142: $i] :
( ( ! [SY1368: $i > $o,SY1369: $i] :
( ~ ( in @ SY1369 @ SV142 )
| ~ ( SY1368 @ SY1369 )
| ~ ( ~ ( in @ ( sK80_Xy @ SY1369 @ SY1368 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SY1368 @ ( sK80_Xy @ SY1369 @ SY1368 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SY1369 @ SY1368 @ SV142 )
!= SY1369 ) ) ) )
| ~ ( ( ( dsetconstr @ SV142
@ ^ [SX3: $i] : ( SY1368 @ SX3 ) )
!= ( setadjoin @ ( sK79_SY507 @ SY1369 @ SY1368 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SY1369 @ SY1368 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SX3: $i] : ( SY1368 @ SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[501]) ).
thf(668,plain,
! [SV143: $i] :
( ( ! [SY1372: $i] :
( ~ ( ~ ( in @ ( sK64_Xx @ SY1372 @ SV143 ) @ SV143 )
| ~ ~ ( in @ ( sK64_Xx @ SY1372 @ SV143 ) @ SY1372 ) )
| ( subset @ SV143 @ SY1372 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[502]) ).
thf(669,plain,
! [SV144: $i] :
( ( ~ ( ~ ! [SY1373: $i > $o,SY1374: $i] :
( ~ ( in @ SY1374 @ SV144 )
| ~ ( SY1373 @ SY1374 )
| ( in @ SY1374
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1373 @ SX3 ) ) ) )
| ~ ! [SY1376: $i > $o,SY1377: $i] :
( ~ ( in @ SY1377 @ SV144 )
| ~ ( in @ SY1377
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1376 @ SX3 ) ) )
| ( SY1376 @ SY1377 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[503]) ).
thf(670,plain,
! [SV145: $i] :
( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_Xx @ SV145 ) @ omega )
| ~ ( in @ ( sK8_Xx @ SV145 ) @ SV145 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 ) )
| ~ ( in @ emptyset @ SV145 )
| ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[504]) ).
thf(671,plain,
! [SV146: $i] :
( ( ! [SY1380: $i,SY1381: $i] :
( ~ ( in @ SY1381 @ ( cartprod @ SV146 @ SY1380 ) )
| ~ ( ~ ~ ( ( SY1381
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SY1381 @ SY1380 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SY1381 @ SY1380 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SY1381 @ SY1380 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SY1381 @ SY1380 @ SV146 ) @ ( setunion @ SY1381 ) ) )
| ~ ( in @ ( sK72_SY474 @ SY1381 @ SY1380 @ SV146 ) @ ( setunion @ SY1381 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[505]) ).
thf(672,plain,
! [SV147: $i] :
( ( ! [SY1382: $i] :
~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SY1382 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SY1382 @ SV147 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SY1382 @ SV147 ) @ ( setadjoin @ ( sK67_SY1105 @ SY1382 @ SV147 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK67_SY1105 @ SY1382 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SY1382 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK66_SY422 @ SY1382 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SY1382 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[506]) ).
thf(673,plain,
! [SV148: $i] :
( ( ! [SY1383: $i] :
~ ( ~ ~ ( ~ ! [SY1384: $i] :
( ~ ( in @ SY1384 @ ( binunion @ SV148 @ SY1383 ) )
| ( in @ SY1384 @ SV148 )
| ( in @ SY1384 @ SY1383 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY1386: $i] :
( ~ ( in @ SY1386 @ ( binunion @ SV148 @ SY1383 ) )
| ( in @ SY1386 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1388: $i] :
( ~ ( in @ SY1388 @ ( binunion @ SV148 @ SY1383 ) )
| ! [SX3: $o] :
( ~ SX3
| ( in @ SY1388 @ SY1383 )
| SX3 ) )
| ~ ( ! [SY1390: $i] :
~ ( in @ SY1390 @ ( binunion @ SV148 @ SY1383 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[507]) ).
thf(674,plain,
! [SV149: $i > $o] :
( ( ! [SY1392: $i] :
~ ( SV149 @ SY1392 )
| ~ ( ~ ( SV149 @ ( sK43_Xx @ SV149 ) )
| ~ ~ ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) ) )
| ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[508]) ).
thf(675,plain,
! [SV150: $i] :
( ( ! [SY1394: $i] :
( ~ ( ~ ( in @ ( sK65_Xx @ SY1394 @ SV150 ) @ SV150 )
| ~ ( in @ ( sK65_Xx @ SY1394 @ SV150 ) @ SY1394 ) )
| ( ( binintersect @ SV150 @ SY1394 )
= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[509]) ).
thf(676,plain,
! [SV151: $i] :
( ( ! [SY1395: $i,SY1396: $i] :
( ~ ( in @ SY1396 @ ( setadjoin @ SV151 @ SY1395 ) )
| ~ ( ~ ~ ( ~ ( ( SY1396 = SV151 )
| ( in @ SY1396 @ SY1395 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY1396 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SX3: $o] :
( ~ SX3
| ( in @ SY1396 @ SY1395 )
| SX3 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[510]) ).
thf(677,plain,
! [SV152: $i] :
( ( ! [SY1401: $i] :
( ( SV152 != SY1401 )
| ! [SY1402: $i > $o,SY1403: $i > $o] :
( ~ ( ~ ( in @ ( sK61_Xx @ SY1403 @ SY1402 @ SY1401 @ SV152 ) @ SV152 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SY1403 @ SY1402 @ SY1401 @ SV152 ) @ SY1401 )
| ~ ~ ( ( ( sK61_Xx @ SY1403 @ SY1402 @ SY1401 @ SV152 )
!= ( sK62_SY1104 @ SY1403 @ SY1402 @ SY1401 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SY1402 @ ( sK61_Xx @ SY1403 @ SY1402 @ SY1401 @ SV152 ) )
| ~ ( SY1403 @ ( sK62_SY1104 @ SY1403 @ SY1402 @ SY1401 @ SV152 ) ) )
| ~ ( ( SY1402 @ ( sK61_Xx @ SY1403 @ SY1402 @ SY1401 @ SV152 ) )
| ( SY1403 @ ( sK62_SY1104 @ SY1403 @ SY1402 @ SY1401 @ SV152 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV152
@ ^ [SX4: $i] : ( SY1402 @ SX4 ) )
= ( dsetconstr @ SY1401
@ ^ [SX4: $i] : ( SY1403 @ SX4 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[511]) ).
thf(678,plain,
! [SV153: $i > $o] :
( ( ! [SY1406: $i > $o] :
( ~ ( ( ( sK59_Xx @ SY1406 @ SV153 )
!= ( sK60_SY1103 @ SY1406 @ SV153 ) )
| ~ ~ ( ~ ( ~ ( SV153 @ ( sK59_Xx @ SY1406 @ SV153 ) )
| ~ ( SY1406 @ ( sK60_SY1103 @ SY1406 @ SV153 ) ) )
| ~ ( ( SV153 @ ( sK59_Xx @ SY1406 @ SV153 ) )
| ( SY1406 @ ( sK60_SY1103 @ SY1406 @ SV153 ) ) ) ) )
| ! [SY1407: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1407 @ SY1406 @ SV153 ) )
| ~ ( ( SY1407
!= ( sK58_SY256 @ SY1407 @ SY1406 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1407 ) )
| ! [SY1408: $i] :
( ~ ( ~ ( SY1406 @ ( sK57_SY259 @ SY1408 @ SY1406 @ SV153 ) )
| ~ ( ( SY1408
!= ( sK57_SY259 @ SY1408 @ SY1406 @ SV153 ) ) ) )
| ~ ( SY1406 @ SY1408 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SX2: $i] : ( SY1406 @ SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[512]) ).
thf(679,plain,
! [SV154: $i > $o] :
( ( ! [SY1411: $i] :
~ ( ~ ( ( ( sK46_Xy @ SY1411 @ SV154 )
!= SY1411 )
| ~ ( SV154 @ ( sK46_Xy @ SY1411 @ SV154 ) ) )
| ~ ( ( ( sK46_Xy @ SY1411 @ SV154 )
= SY1411 )
| ( SV154 @ ( sK46_Xy @ SY1411 @ SV154 ) ) ) )
| ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[513]) ).
thf(680,plain,
! [SV155: $i] :
( ( ! [SY1413: $i] :
( ~ ( ~ ( ~ ( in @ ( sK5_Xx @ SY1413 @ SV155 ) @ SV155 )
| ~ ( in @ ( sK5_Xx @ SY1413 @ SV155 ) @ SY1413 ) )
| ~ ( ( in @ ( sK5_Xx @ SY1413 @ SV155 ) @ SV155 )
| ( in @ ( sK5_Xx @ SY1413 @ SV155 ) @ SY1413 ) ) )
| ( SV155 = SY1413 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[514]) ).
thf(681,plain,
! [SV156: $i,SV1: $i] :
( ( ! [SY1414: $i] :
( ~ ( in @ SY1414 @ ( cartprod @ SV1 @ SV156 ) )
| ( in @ ( kfst @ SY1414 ) @ SV1 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[515]) ).
thf(682,plain,
! [SV157: $i,SV2: $i] :
( ( ( kfst @ ( setadjoin @ ( setadjoin @ SV2 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV2 @ ( setadjoin @ SV157 @ emptyset ) ) @ emptyset ) ) )
= SV2 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[516]) ).
thf(683,plain,
! [SV3: $i] :
( ( ( ! [SY1122: $i] :
( ( SV3
!= ( setadjoin @ SY1122 @ emptyset ) )
| ~ ( in @ SY1122 @ SV3 ) ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[517]) ).
thf(684,plain,
! [SV158: $i,SV4: $i] :
( ( ! [SY1415: $i] :
( ~ ( in @ ( setadjoin @ SY1415 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV158 @ emptyset ) ) @ emptyset ) ) )
| ( SV4 = SY1415 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[518]) ).
thf(685,plain,
! [SV159: $i,SV5: $i] :
( ( ( ( setadjoin @ SV5 @ emptyset )
!= ( setadjoin @ SV159 @ emptyset ) )
| ( SV5 = SV159 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[519]) ).
thf(686,plain,
! [SV160: $i,SV9: $i] :
( ( ! [SY1416: $i] :
( ~ ( in @ SY1416 @ SV9 )
| ! [SY1417: $i] :
( ~ ( in @ SY1417 @ SV160 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1416 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1416 @ ( setadjoin @ SY1417 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV9 @ SV160 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[523]) ).
thf(687,plain,
! [SV161: $i,SV10: $i] :
( ( ! [SY1418: $i] :
( ~ ( in @ SY1418 @ SV10 )
| ! [SY1419: $i] :
( ~ ( in @ SY1419 @ SV161 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1418 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1418 @ ( setadjoin @ SY1419 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV10 @ SV161 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[524]) ).
thf(688,plain,
! [SV162: $i,SV11: $i] :
( ( ! [SY1420: $i] :
( ~ ( in @ SY1420 @ SV11 )
| ! [SY1421: $i] :
( ~ ( in @ SY1421 @ SV162 )
| ( in @ ( setadjoin @ ( setadjoin @ SY1420 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1420 @ ( setadjoin @ SY1421 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV11 @ SV162 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[525]) ).
thf(689,plain,
! [SV163: $i,SV12: $i] :
( ( ! [SY1422: $i] :
( ~ ( in @ SY1422 @ SV12 )
| ! [SY1423: $i] :
( ~ ( in @ SY1423 @ SV163 )
| ( subset @ ( setadjoin @ ( setadjoin @ SY1422 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1422 @ ( setadjoin @ SY1423 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV12 @ SV163 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[526]) ).
thf(690,plain,
! [SV164: $i,SV13: $i] :
( ( ! [SY1424: $i] :
( ~ ( in @ SY1424 @ SV13 )
| ! [SY1425: $i] :
( ~ ( in @ SY1425 @ SV164 )
| ( in @ ( setadjoin @ SY1424 @ ( setadjoin @ SY1425 @ emptyset ) ) @ ( powerset @ ( binunion @ SV13 @ SV164 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[527]) ).
thf(691,plain,
! [SV165: $i,SV14: $i] :
( ( ! [SY1426: $i] :
( ~ ( in @ SY1426 @ SV14 )
| ! [SY1427: $i] :
( ~ ( in @ SY1427 @ SV165 )
| ( subset @ ( setadjoin @ SY1426 @ ( setadjoin @ SY1427 @ emptyset ) ) @ ( binunion @ SV14 @ SV165 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[528]) ).
thf(692,plain,
! [SV166: $i,SV15: $i] :
( ( ! [SY1428: $i] :
( ~ ( in @ SY1428 @ ( setadjoin @ SV15 @ ( setadjoin @ SV166 @ emptyset ) ) )
| ( SY1428 = SV15 )
| ( SY1428 = SV166 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[529]) ).
thf(693,plain,
! [SV167: $i,SV16: $i] :
( ( ! [SY1429: $i] :
( ~ ( in @ SY1429 @ SV16 )
| ( in @ ( setadjoin @ SY1429 @ emptyset ) @ ( powerset @ ( binunion @ SV16 @ SV167 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[530]) ).
thf(694,plain,
! [SV17: $i,SV168: $i] :
( ( ~ ( in @ SV168 @ SV17 )
| ( in @ ( setadjoin @ SV168 @ emptyset ) @ ( powerset @ SV17 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[531]) ).
thf(695,plain,
! [SV18: $i,SV169: $i] :
( ( ~ ( in @ SV169 @ SV18 )
| ( subset @ ( setadjoin @ SV169 @ emptyset ) @ SV18 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[532]) ).
thf(696,plain,
! [SV19: $i,SV170: $i] :
( ( in @ SV170 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV19 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV19 @ ( setadjoin @ SV170 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[533]) ).
thf(697,plain,
! [SV171: $i,SV20: $i] :
( ( in @ SV20 @ ( setunion @ ( setadjoin @ ( setadjoin @ SV20 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV20 @ ( setadjoin @ SV171 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[534]) ).
thf(698,plain,
! [SV21: $i,SV172: $i] :
( ( in @ SV172 @ ( setadjoin @ SV21 @ ( setadjoin @ SV172 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[535]) ).
thf(699,plain,
! [SV173: $i,SV22: $i] :
( ( ! [SY1430: $i] :
( ( in @ SY1430 @ SV22 )
| ( in @ SY1430 @ SV173 )
| ~ ( in @ SY1430 @ ( symdiff @ SV22 @ SV173 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[536]) ).
thf(700,plain,
! [SV174: $i,SV23: $i] :
( ( ! [SY1431: $i] :
( ~ ( in @ SY1431 @ SV23 )
| ~ ( in @ SY1431 @ SV174 )
| ~ ( in @ SY1431 @ ( symdiff @ SV23 @ SV174 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[537]) ).
thf(701,plain,
! [SV175: $i,SV24: $i] :
( ( ! [SY1432: $i] :
( ( in @ SY1432 @ SV24 )
| ~ ( in @ SY1432 @ SV175 )
| ( in @ SY1432 @ ( symdiff @ SV24 @ SV175 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[538]) ).
thf(702,plain,
! [SV176: $i,SV25: $i] :
( ( ! [SY1433: $i] :
( ~ ( in @ SY1433 @ SV25 )
| ( in @ SY1433 @ SV176 )
| ( in @ SY1433 @ ( symdiff @ SV25 @ SV176 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[539]) ).
thf(703,plain,
! [SV177: $i,SV26: $i] :
( ( ( ( setminus @ SV26 @ SV177 )
!= emptyset )
| ( subset @ SV26 @ SV177 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[540]) ).
thf(704,plain,
! [SV178: $i,SV27: $i] :
( ( subset @ ( setminus @ SV27 @ SV178 ) @ SV27 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[541]) ).
thf(705,plain,
! [SV28: $i,SV179: $i] :
( ( ! [SY1434: $i] :
( ~ ( in @ SY1434 @ SV179 )
| ~ ( in @ SY1434 @ ( setminus @ SV28 @ SV179 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[542]) ).
thf(706,plain,
! [SV180: $i,SV29: $i] :
( ( ! [SY1435: $i] :
( ( in @ SY1435 @ SV29 )
| ~ ( in @ SY1435 @ ( setminus @ SV29 @ SV180 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[543]) ).
thf(707,plain,
! [SV181: $i,SV30: $i] :
( ( ! [SY1436: $i] :
( ( in @ SY1436 @ ( setminus @ SV30 @ SV181 ) )
| ( in @ SY1436 @ SV181 )
| ~ ( in @ SY1436 @ SV30 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[544]) ).
thf(708,plain,
! [SV182: $i,SV31: $i] :
( ( ! [SY1437: $i] :
( ( in @ SY1437 @ ( setminus @ SV31 @ SV182 ) )
| ~ ( in @ SY1437 @ SV31 )
| ( in @ SY1437 @ SV182 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[545]) ).
thf(709,plain,
! [SV183: $i,SV32: $i] :
( ( ~ ( subset @ SV32 @ SV183 )
| ( ( setminus @ SV32 @ SV183 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[546]) ).
thf(710,plain,
! [SV184: $i,SV33: $i] :
( ( ! [SY1438: $i] :
( ~ ( in @ SY1438 @ ( setminus @ SV33 @ SV184 ) )
| ~ ( in @ SY1438 @ SV184 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[547]) ).
thf(711,plain,
! [SV185: $i,SV34: $i] :
( ( ! [SY1439: $i] :
( ~ ( in @ SY1439 @ ( setminus @ SV34 @ SV185 ) )
| ( in @ SY1439 @ SV34 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[548]) ).
thf(712,plain,
! [SV186: $i,SV35: $i] :
( ( ! [SY1440: $i] :
( ~ ( in @ SY1440 @ SV35 )
| ( in @ SY1440 @ SV186 )
| ( in @ SY1440 @ ( setminus @ SV35 @ SV186 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[549]) ).
thf(713,plain,
! [SV187: $i,SV36: $i] :
( ( ! [SY1441: $i] :
( ( binintersect @ SV36 @ ( binunion @ SV187 @ SY1441 ) )
= ( binunion @ ( binintersect @ SV36 @ SV187 ) @ ( binintersect @ SV36 @ SY1441 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[550]) ).
thf(714,plain,
! [SV188: $i,SV37: $i] :
( ( ( ( binintersect @ SV37 @ SV188 )
!= SV37 )
| ( subset @ SV37 @ SV188 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[551]) ).
thf(715,plain,
! [SV38: $i,SV189: $i] :
( ( ~ ( subset @ SV189 @ SV38 )
| ( ( binintersect @ SV38 @ SV189 )
= SV189 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[552]) ).
thf(716,plain,
! [SV190: $i,SV39: $i] :
( ( subset @ ( binintersect @ SV39 @ SV190 ) @ SV190 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[553]) ).
thf(717,plain,
! [SV191: $i,SV40: $i] :
( ( ! [SY1442: $i] :
( ~ ( in @ SY1442 @ ( binintersect @ SV40 @ SV191 ) )
| ( in @ SY1442 @ SV191 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[554]) ).
thf(718,plain,
! [SV192: $i,SV41: $i] :
( ( ( ( binintersect @ SV41 @ SV192 )
!= SV192 )
| ( subset @ SV192 @ SV41 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[555]) ).
thf(719,plain,
! [SV193: $i,SV42: $i] :
( ( ~ ( subset @ SV42 @ SV193 )
| ( ( binintersect @ SV42 @ SV193 )
= SV42 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[556]) ).
thf(720,plain,
! [SV194: $i,SV43: $i] :
( ( subset @ ( binintersect @ SV43 @ SV194 ) @ SV43 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[557]) ).
thf(721,plain,
! [SV195: $i,SV44: $i] :
( ( ! [SY1443: $i] :
( ~ ( in @ SY1443 @ ( binintersect @ SV44 @ SV195 ) )
| ( in @ SY1443 @ SV44 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[558]) ).
thf(722,plain,
! [SV196: $i,SV45: $i] :
( ( ! [SY1444: $i] :
( ~ ( subset @ SY1444 @ SV45 )
| ~ ( subset @ SY1444 @ SV196 )
| ( subset @ SY1444 @ ( binintersect @ SV45 @ SV196 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[559]) ).
thf(723,plain,
! [SV197: $i,SV46: $i] :
( ( ! [SY1445: $i] :
( ~ ( in @ SY1445 @ SV46 )
| ~ ( in @ SY1445 @ SV197 )
| ( in @ SY1445 @ ( binintersect @ SV46 @ SV197 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[560]) ).
thf(724,plain,
! [SV47: $i,SV198: $i] :
( ( subset @ SV198 @ ( binunion @ SV47 @ SV198 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[561]) ).
thf(725,plain,
! [SV199: $i,SV48: $i] :
( ( subset @ SV48 @ ( binunion @ SV48 @ SV199 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[562]) ).
thf(726,plain,
! [SV200: $i,SV49: $i] :
( ( ! [SY1446: $i] :
( ~ ( in @ SY1446 @ ( binunion @ SV49 @ SV200 ) )
| ( in @ SY1446 @ SV49 )
| ( in @ SY1446 @ SV200 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[563]) ).
thf(727,plain,
! [SV50: $i,SV201: $i] :
( ( ! [SY1447: $i] :
( ~ ( in @ SY1447 @ SV201 )
| ( in @ SY1447 @ ( binunion @ SV50 @ SV201 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[564]) ).
thf(728,plain,
! [SV51: $i,SV202: $i] :
( ( in @ SV202 @ ( setadjoin @ SV51 @ ( setadjoin @ SV202 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[565]) ).
thf(729,plain,
! [SV203: $i,SV52: $i] :
( ( ! [SY1448: $i] :
( ~ ( in @ SY1448 @ SV52 )
| ( in @ SY1448 @ ( binunion @ SV52 @ SV203 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[566]) ).
thf(730,plain,
! [SV204: $i > $o,SV53: $i] :
( ( subset
@ ( dsetconstr @ SV53
@ ^ [SY1449: $i] : ( SV204 @ SY1449 ) )
@ SV53 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[567]) ).
thf(731,plain,
! [SV205: $i > $o,SV54: $i] :
( ( in
@ ( dsetconstr @ SV54
@ ^ [SY1450: $i] : ( SV205 @ SY1450 ) )
@ ( powerset @ SV54 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[568]) ).
thf(732,plain,
! [SV206: $i,SV55: $i] :
( ( ~ ( subset @ SV55 @ SV206 )
| ( subset @ ( powerset @ SV55 ) @ ( powerset @ SV206 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[569]) ).
thf(733,plain,
! [SV57: $i,SV207: $i] :
( ( ~ ( in @ SV207 @ ( powerset @ SV57 ) )
| ( subset @ SV207 @ SV57 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[571]) ).
thf(734,plain,
! [SV58: $i,SV208: $i] :
( ( ~ ( subset @ SV208 @ SV58 )
| ( in @ SV208 @ ( powerset @ SV58 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[572]) ).
thf(735,plain,
! [SV59: $i] :
( ( ( ~ ( subset @ SV59 @ emptyset ) )
= $true )
| ( ( SV59 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[573]) ).
thf(736,plain,
! [SV209: $i,SV60: $i] :
( ( ~ ( subset @ SV60 @ SV209 )
| ~ ( subset @ SV209 @ SV60 )
| ( SV60 = SV209 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[574]) ).
thf(737,plain,
! [SV210: $i,SV61: $i] :
( ( ~ ( subset @ SV61 @ SV210 )
| ( in @ SV61 @ ( powerset @ SV210 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[575]) ).
thf(738,plain,
! [SV211: $i,SV62: $i] :
( ( ! [SY1451: $i] :
( ~ ( subset @ SV62 @ SY1451 )
| ( subset @ SV62 @ ( setadjoin @ SV211 @ SY1451 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[576]) ).
thf(739,plain,
! [SV63: $i,SV212: $i] :
( ( subset @ SV212 @ ( setadjoin @ SV63 @ SV212 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[577]) ).
thf(740,plain,
! [SV213: $i,SV64: $i] :
( ( ~ ( subset @ SV64 @ SV213 )
| ! [SY1452: $i] :
( ~ ( subset @ SV213 @ SY1452 )
| ( subset @ SV64 @ SY1452 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[578]) ).
thf(741,plain,
! [SV214: $i,SV66: $i] :
( ( ! [SY1453: $i] :
( ~ ( in @ SY1453 @ SV66 )
| ( in @ SY1453 @ SV214 )
| ( SV66 != SV214 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[580]) ).
thf(742,plain,
! [SV215: $i,SV67: $i] :
( ( ( subset @ SV67 @ SV215 )
| ( SV67 != SV215 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[581]) ).
thf(743,plain,
! [SV216: $i,SV68: $i] :
( ( ! [SY1454: $i] :
( ~ ( in @ SY1454 @ SV68 )
| ( in @ SY1454 @ SV216 )
| ~ ( subset @ SV68 @ SV216 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[582]) ).
thf(744,plain,
! [SV217: $i,SV69: $i] :
( ( ~ ( subset @ SV69 @ SV217 )
| ! [SY1455: $i] :
( ( in @ SY1455 @ SV217 )
| ~ ( in @ SY1455 @ SV69 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[583]) ).
thf(745,plain,
! [SV218: $i,SV70: $i] :
( ( ~ ( subset @ SV70 @ SV218 )
| ! [SY1456: $i] :
( ~ ( in @ SY1456 @ SV70 )
| ( in @ SY1456 @ SV218 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[584]) ).
thf(746,plain,
! [SV219: $i,SV72: $i] :
( ( ( SV72 != SV219 )
| ( subset @ SV72 @ SV219 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[586]) ).
thf(747,plain,
! [SV220: $i,SV73: $i] :
( ( ( SV73 != SV220 )
| ( subset @ SV220 @ SV73 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[587]) ).
thf(748,plain,
! [SV221: $i,SV74: $i] :
( ( ( SV74 != SV221 )
| ( ( setunion @ SV74 )
= ( setunion @ SV221 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[588]) ).
thf(749,plain,
! [SV222: $i,SV75: $i] :
( ( ( SV75 != SV222 )
| ( ( powerset @ SV75 )
= ( powerset @ SV222 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[589]) ).
thf(750,plain,
! [SV223: $i,SV76: $i] :
( ( ( SV76 != SV223 )
| ! [SY1457: $i,SY1458: $i] :
( ( SY1457 != SY1458 )
| ( ( setadjoin @ SV76 @ SY1457 )
= ( setadjoin @ SV223 @ SY1458 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[590]) ).
thf(751,plain,
! [SV224: $i,SV77: $i] :
( ( ( SV77 != SV224 )
| ! [SY1459: $i,SY1460: $i] :
( ( SY1459 != SY1460 )
| ~ ( in @ SY1459 @ SV77 )
| ( in @ SY1460 @ SV224 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[591]) ).
thf(752,plain,
! [SV78: $o] :
( ( ( ~ SV78 ) = $true )
| ( ( set2prop @ ( prop2set @ SV78 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[592]) ).
thf(753,plain,
( ( ( ~ $true ) = $true )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[593]) ).
thf(754,plain,
( ( ( ~ $false ) = $true )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[594]) ).
thf(755,plain,
! [SV79: $o] :
( ( ( ~ SV79 ) = $true )
| ( ( in @ emptyset @ ( prop2set @ SV79 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[595]) ).
thf(756,plain,
( ( ( ~ $true ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[596]) ).
thf(757,plain,
( ( ( ~ $false ) = $true )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[597]) ).
thf(758,plain,
! [SV80: $i > $o,SV225: $i] :
( ( ~ ( in @ SV225 @ emptyset )
| ( SV80 @ SV225 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[598]) ).
thf(759,plain,
! [SV81: $i,SV226: $i > $o] :
( ( ! [SY1461: $i] :
( ~ ( SV226 @ SY1461 )
| ~ ( in @ SY1461 @ SV81 ) )
| ( ( dsetconstr @ SV81
@ ^ [SY1462: $i] : ( SV226 @ SY1462 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[599]) ).
thf(760,plain,
! [SV82: $i,SV227: $i] :
( ( in @ SV227 @ ( setadjoin @ SV82 @ ( setadjoin @ SV227 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[600]) ).
thf(761,plain,
! [SV228: $i,SV83: $i] :
( ( in @ SV83 @ ( setadjoin @ SV83 @ ( setadjoin @ SV228 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[601]) ).
thf(762,plain,
! [SV229: $i,SV84: $i] :
( ( ! [SY1463: $i] :
( ~ ( in @ SY1463 @ ( setadjoin @ SV84 @ ( setadjoin @ SV229 @ emptyset ) ) )
| ( SY1463 = SV84 )
| ( SY1463 = SV229 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[602]) ).
thf(763,plain,
! [SV230: $i,SV85: $i] :
( ( ~ ( in @ SV85 @ ( setadjoin @ SV230 @ emptyset ) )
| ( in @ SV230 @ ( setadjoin @ SV85 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[603]) ).
thf(764,plain,
! [SV231: $i,SV86: $i] :
( ( ( SV86 != SV231 )
| ( in @ SV86 @ ( setadjoin @ SV231 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[604]) ).
thf(765,plain,
! [SV232: $i,SV87: $i] :
( ( ( SV87 = SV232 )
| ~ ( in @ SV232 @ ( setadjoin @ SV87 @ emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[605]) ).
thf(766,plain,
! [SV233: $i,SV88: $i] :
( ( ~ ( in @ SV88 @ ( setadjoin @ SV233 @ emptyset ) )
| ( SV88 = SV233 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[606]) ).
thf(767,plain,
! [SV89: $i] :
( ( ( SV89 = emptyset )
= $true )
| ( ( in @ ( sK33_Xx @ SV89 ) @ SV89 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[607]) ).
thf(768,plain,
! [SV90: $i,SV234: $i] :
( ( ~ ( in @ SV234 @ SV90 )
| ( in @ SV234 @ ( powerset @ ( setunion @ SV90 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[608]) ).
thf(769,plain,
! [SV91: $i,SV235: $i] :
( ( ! [SY1464: $i] :
( ~ ( in @ SV235 @ SY1464 )
| ~ ( in @ SY1464 @ SV91 )
| ( in @ SV235 @ ( setunion @ SV91 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[609]) ).
thf(770,plain,
! [SV92: $i,SV236: $i] :
( ( ~ ( in @ SV236 @ ( powerset @ SV92 ) )
| ! [SY1465: $i] :
( ~ ( in @ SY1465 @ SV236 )
| ( in @ SY1465 @ SV92 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[610]) ).
thf(771,plain,
! [SV237: $i,SV96: $i] :
( ( ! [SY1466: $i] :
( ~ ( in @ SY1466 @ ( setadjoin @ SV96 @ SV237 ) )
| ( SY1466 = SV96 )
| ( in @ SY1466 @ SV237 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[614]) ).
thf(772,plain,
! [SV97: $i,SV238: $i] :
( ( ! [SY1467: $i] :
( ~ ( in @ SY1467 @ SV238 )
| ( in @ SY1467 @ ( setadjoin @ SV97 @ SV238 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[615]) ).
thf(773,plain,
! [SV239: $i,SV98: $i] :
( ( in @ SV98 @ ( setadjoin @ SV98 @ SV239 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[616]) ).
thf(774,plain,
! [SV99: $i] :
( ( ( ! [SY1259: $i] :
~ ( in @ SY1259 @ SV99 ) )
= $true )
| ( ( SV99 != emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[617]) ).
thf(775,plain,
! [SV240: $i > $o,SV100: $i] :
( ( ! [SY1468: $i] :
( ~ ( in @ SY1468 @ SV100 )
| ~ ( SV240 @ SY1468 )
| ( ( dsetconstr @ SV100
@ ^ [SY1469: $i] : ( SV240 @ SY1469 ) )
!= emptyset ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[618]) ).
thf(776,plain,
! [SV101: $i] :
( ( ( SV101 = emptyset )
= $true )
| ( ( in @ ( sK28_Xx @ SV101 ) @ SV101 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[619]) ).
thf(777,plain,
! [SV102: $i] :
( ( ( in @ ( sK27_Xx @ SV102 ) @ SV102 )
= $true )
| ( ( SV102 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[620]) ).
thf(778,plain,
! [SV103: $i] :
( ( ( in @ ( sK26_Xx @ SV103 ) @ SV103 )
= $true )
| ( ( SV103 = emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[621]) ).
thf(779,plain,
! [SV104: $i] :
( ( in @ SV104 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[622]) ).
thf(780,plain,
! [SV105: $i] :
( ( in @ SV105 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[623]) ).
thf(781,plain,
! [SV241: $i] :
( ( ( ~ ( in @ SV241 @ emptyset ) )
= $true )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[624]) ).
thf(782,plain,
! [SV106: $o] :
( ( ( ! [SY1263: $i] :
~ ( in @ SY1263 @ ( prop2set @ SV106 ) ) )
= $true )
| ( SV106 = $true ) ),
inference(extcnf_or_pos,[status(thm)],[625]) ).
thf(783,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_or_pos,[status(thm)],[626]) ).
thf(784,plain,
( ( ( ! [SX0: $i] :
~ ( in @ SX0 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_or_pos,[status(thm)],[627]) ).
thf(785,plain,
! [SV242: $i > $o,SV107: $i] :
( ( ! [SY1470: $i] :
( ~ ( in @ SY1470
@ ( dsetconstr @ SV107
@ ^ [SY1471: $i] : ( SV242 @ SY1471 ) ) )
| ( SV242 @ SY1470 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[628]) ).
thf(786,plain,
! [SV243: $i > $o,SV108: $i] :
( ( ! [SY1472: $i] :
( ~ ( in @ SY1472
@ ( dsetconstr @ SV108
@ ^ [SY1473: $i] : ( SV243 @ SY1473 ) ) )
| ( in @ SY1472 @ SV108 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[629]) ).
thf(787,plain,
! [SV244: $i > $o,SV109: $i] :
( ( ! [SY1474: $i] :
( ~ ( in @ SY1474 @ SV109 )
| ~ ( SV244 @ SY1474 )
| ( in @ SY1474
@ ( dsetconstr @ SV109
@ ^ [SY1475: $i] : ( SV244 @ SY1475 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[630]) ).
thf(788,plain,
! [SV110: $i] :
( ( ( ~ ( in @ SV110 @ omega ) )
= $true )
| ( ( in @ ( setadjoin @ SV110 @ SV110 ) @ omega )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[631]) ).
thf(789,plain,
! [SV111: $i] :
( ( in @ SV111 @ emptyset )
= $false ),
inference(extcnf_not_pos,[status(thm)],[632]) ).
thf(790,plain,
! [SV245: $i > $o,SV112: $i] :
( ( ! [SY1476: $i] :
( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
!= ( setadjoin @ SY1476 @ emptyset ) )
| ~ ( in @ SY1476
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) ) )
| ~ ( ~ ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) )
| ~ ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[633]) ).
thf(791,plain,
! [SV113: $i] :
( ( ~ ! [SY1277: $i] :
( ~ ( ~ ( in @ ( sK18_Xx @ SY1277 @ SV113 ) @ SY1277 )
| ~ ~ ( in @ ( sK18_Xx @ SY1277 @ SV113 ) @ SV113 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY1277 )
| ~ ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ ( sK14_B @ SV113 ) )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SY1279 )
| ( in @ SY1280 @ ( sK16_SY1071 @ SY1277 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SY1277 @ SV113 ) @ SY1279 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SY1277 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SY1277 @ SV113 ) @ SY1277 ) )
| ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ ( sK16_SY1071 @ SY1277 @ SV113 ) )
| ~ ( in @ SY1281 @ SY1277 ) ) ) ) )
| ~ ~ ( ~ ! [SY1282: $i,SY1283: $i] :
( ~ ( in @ SY1282 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY1283 @ ( sK14_B @ SV113 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1282 )
| ( in @ SX3 @ SY1283 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1283 )
| ( in @ SX3 @ SY1282 ) ) )
| ~ ~ ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) )
| ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[634]) ).
thf(792,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(793,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[635]) ).
thf(794,plain,
! [SV246: $i > $o,SV114: $i] :
( ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV114 )
| ( SV246 @ SY1479 ) )
| ~ ( ~ ( in @ ( sK39_Xx @ SV246 @ SV114 ) @ SV114 )
| ~ ~ ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[636]) ).
thf(795,plain,
! [SV247: $i > $o,SV115: $i] :
( ( ! [SY1480: $i] :
( ~ ( in @ SY1480 @ SV115 )
| ( SV247 @ SY1480 ) )
| ~ ( ~ ( in @ ( sK37_Xx @ SV247 @ SV115 ) @ SV115 )
| ~ ~ ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[637]) ).
thf(796,plain,
! [SV248: $i,SV116: $i] :
( ( ( SV116 != SV248 )
| ~ ( ~ ! [SY1481: $i,SY1482: $i] :
( ( SY1481 != SY1482 )
| ~ ( in @ SY1481 @ SV116 )
| ( in @ SY1482 @ SV248 ) )
| ~ ! [SY1483: $i,SY1484: $i] :
( ( SY1483 != SY1484 )
| ~ ( in @ SY1484 @ SV248 )
| ( in @ SY1483 @ SV116 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[638]) ).
thf(797,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY1055 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ sK3_SY1058 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY1058 @ ( setadjoin @ sK4_SY1060 @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(798,plain,
( ( ~ ( ( sK1_Xx != sK3_SY1058 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[639]) ).
thf(799,plain,
! [SV117: $i > $o] :
( ( ( ! [SY1299: $i] :
( ~ ( ~ ( SV117 @ ( sK23_SY85 @ SY1299 @ SV117 ) )
| ~ ( ( SY1299
!= ( sK23_SY85 @ SY1299 @ SV117 ) ) ) )
| ~ ( SV117 @ SY1299 ) ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[640]) ).
thf(800,plain,
! [SV118: $i,SV249: $i] :
( ( ~ ( in @ SV249 @ ( setunion @ SV118 ) )
| ~ ( ~ ( in @ ( sK74_X @ SV249 @ SV118 ) @ SV118 )
| ~ ( in @ SV249 @ ( sK74_X @ SV249 @ SV118 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[641]) ).
thf(801,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ~ ( ~ ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) ) ) )
| ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[642]) ).
thf(802,plain,
! [SV120: $i > $o] :
( ( ( ! [SY1305: $i] :
( ~ ( ~ ( SV120 @ ( sK21_SY73 @ SY1305 @ SV120 ) )
| ~ ( ( SY1305
!= ( sK21_SY73 @ SY1305 @ SV120 ) ) ) )
| ~ ( SV120 @ SY1305 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[643]) ).
thf(803,plain,
! [SV121: $i > $o] :
( ( ( ! [SY1307: $i] :
( ~ ( ~ ( SV121 @ ( sK56_SY247 @ SY1307 @ SV121 ) )
| ~ ( ( SY1307
!= ( sK56_SY247 @ SY1307 @ SV121 ) ) ) )
| ~ ( SV121 @ SY1307 ) ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[644]) ).
thf(804,plain,
! [SV122: $i,SV251: $i > $o] :
( ( ~ ( ~ ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) )
| ~ ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 ) )
| ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV122 )
| ~ ( SV251 @ SY1488 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[645]) ).
thf(805,plain,
! [SV252: $i,SV123: $i] :
( ( ~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setadjoin @ ( sK69_SY1106 @ SV252 @ SV123 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK69_SY1106 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[646]) ).
thf(806,plain,
! [SV124: $i] :
( ( ( ! [SY1313: $i] :
~ ( in @ SY1313 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_B @ SV124 ) @ SV124 )
| ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK13_B @ SV124 ) )
| ~ ( in @ SY1314 @ SV124 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[647]) ).
thf(807,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ~ ( ~ ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) ) ) )
| ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[648]) ).
thf(808,plain,
! [SV254: $i,SV126: $i] :
( ( ! [SY1492: $i] :
( ~ ( in @ SY1492 @ ( symdiff @ SV126 @ SV254 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SY1492 @ SV126 )
| ~ ( in @ SY1492 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SY1492 @ SV126 )
| ( in @ SY1492 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SY1492 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SY1492 @ SV254 )
| ~ ( in @ SY1492 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SY1492 @ SV254 )
| ( in @ SY1492 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SY1492 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1327: $o] :
( ~ SY1327
| ~ ( in @ SY1492 @ SV126 )
| SY1327 )
| ~ ~ ( ~ ! [SY1500: $o] :
( ~ SY1500
| ( in @ SY1492 @ SV254 )
| SY1500 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[649]) ).
thf(809,plain,
! [SV127: $i > $o] :
( ( ( ! [SY1330: $i] :
( ~ ( ~ ( SV127 @ ( sK32_SY141 @ SY1330 @ SV127 ) )
| ~ ( ( SY1330
!= ( sK32_SY141 @ SY1330 @ SV127 ) ) ) )
| ~ ( SV127 @ SY1330 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[650]) ).
thf(810,plain,
! [SV255: $i > $o,SV128: $i] :
( ( ! [SY1502: $i] :
( ~ ( in @ SY1502 @ SV128 )
| ( SV255 @ SY1502 ) )
| ~ ( ~ ( in @ ( sK34_Xx @ SV255 @ SV128 ) @ SV128 )
| ~ ~ ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[651]) ).
thf(811,plain,
! [SV129: $i > $o] :
( ( ( ! [SY1335: $i] :
( ~ ( ~ ( SV129 @ ( sK41_Xy @ SY1335 @ SV129 ) )
| ~ ( ( SY1335
!= ( sK41_Xy @ SY1335 @ SV129 ) ) ) )
| ~ ( SV129 @ SY1335 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[652]) ).
thf(812,plain,
! [SV130: $i > $o] :
( ( ( ! [SY1337: $i] :
( ~ ( ~ ( SV130 @ ( sK19_SY56 @ SY1337 @ SV130 ) )
| ~ ( ( SY1337
!= ( sK19_SY56 @ SY1337 @ SV130 ) ) ) )
| ~ ( SV130 @ SY1337 ) ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[653]) ).
thf(813,plain,
! [SV131: $i] :
( ( ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ SY1340 @ ( setadjoin @ SV131 @ SY1339 ) )
| ( SY1340 = SV131 )
| ( in @ SY1340 @ SY1339 ) )
| ~ ~ ( ~ ! [SY1341: $i,SY1342: $i] :
( ( SY1342 != SV131 )
| ( in @ SY1342 @ ( setadjoin @ SV131 @ SY1341 ) ) )
| ~ ! [SY1343: $i,SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( setadjoin @ SV131 @ SY1343 ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[654]) ).
thf(814,plain,
! [SV132: $i,SV256: $i > $o] :
( ( ~ ( ~ ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 )
| ~ ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) ) )
| ! [SY1503: $i] :
( ~ ( SV256 @ SY1503 )
| ~ ( in @ SY1503 @ SV132 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[655]) ).
thf(815,plain,
! [SV133: $i] :
( ( ( ! [SY1347: $i] :
( ! [SY1348: $i] :
( ( SV133
!= ( setadjoin @ ( setadjoin @ SY1347 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SY1347 @ ( setadjoin @ SY1348 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY1348 @ ( setunion @ SV133 ) ) )
| ~ ( in @ SY1347 @ ( setunion @ SV133 ) ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[656]) ).
thf(816,plain,
! [SV134: $i,SV257: $i] :
( ( ~ ( ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV257 )
| ~ ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV134 ) )
| ( in @ SV257 @ ( powerset @ SV134 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[657]) ).
thf(817,plain,
! [SV135: $i,SV258: $i] :
( ( ~ ( in @ SV258 @ ( setunion @ SV135 ) )
| ! [SY1504: $o] :
( ~ ( ~ ( in @ SV258 @ ( sK30_B @ SY1504 @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ SY1504 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SY1504 ) )
| SY1504 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[658]) ).
thf(818,plain,
! [SV136: $i > $o] :
( ( ( ! [SY1354: $i] :
( ~ ( ~ ( SV136 @ ( sK47_SY223 @ SY1354 @ SV136 ) )
| ~ ( ( SY1354
!= ( sK47_SY223 @ SY1354 @ SV136 ) ) ) )
| ~ ( SV136 @ SY1354 ) ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[659]) ).
thf(819,plain,
! [SV137: $i,SV259: $i] :
( ( ~ ( ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
| ~ ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 ) )
| ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
| ( SV137 = SV259 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[660]) ).
thf(820,plain,
! [SV260: $i,SV138: $i] :
( ( ! [SY1505: $i] :
( ~ ( in @ SY1505 @ ( cartprod @ SV138 @ SV260 ) )
| ~ ( ~ ~ ( ( SY1505
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SY1505 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SY1505 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SY1505 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SY1505 @ SV260 @ SV138 ) @ SV260 ) )
| ~ ( in @ ( sK70_SY468 @ SY1505 @ SV260 @ SV138 ) @ SV138 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[661]) ).
thf(821,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(822,plain,
( ( ~ ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK7_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK7_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[662]) ).
thf(823,plain,
! [SV139: $i > $i > $o,SV261: $i] :
( ( ~ ( ~ ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
| ~ ! [SY1506: $i] :
( ~ ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) )
| ~ ( ( SY1506
!= ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) ) ) )
| ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SY1506 ) ) )
| ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[663]) ).
thf(824,plain,
! [SV140: $i,SV262: $i] :
( ( ~ ( ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV140 )
| ~ ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV262 ) )
| ( subset @ SV140 @ SV262 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[664]) ).
thf(825,plain,
! [SV141: $i,SV263: $i > $o] :
( ( ~ ( ~ ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) )
| ~ ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 ) )
| ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV141 )
| ~ ( SV263 @ SY1510 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[665]) ).
thf(826,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK54_Xx @ SX1 @ SX0 )
!= ( sK55_SY1102 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK54_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK55_SY1102 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK54_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK55_SY1102 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK53_SY232 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK53_SY232 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK52_SY234 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK52_SY234 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(827,plain,
( ( ~ ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK50_Xx @ SX1 @ SX0 )
!= ( sK51_SY1100 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK50_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK51_SY1100 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK50_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK51_SY1100 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK49_SY235 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK49_SY235 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK48_SY231 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK48_SY231 @ SX1 @ SX0 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[666]) ).
thf(828,plain,
! [SV264: $i > $o,SV142: $i] :
( ( ! [SY1511: $i] :
( ~ ( in @ SY1511 @ SV142 )
| ~ ( SV264 @ SY1511 )
| ~ ( ~ ( in @ ( sK80_Xy @ SY1511 @ SV264 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SY1511 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SY1511 @ SV264 @ SV142 )
!= SY1511 ) ) ) )
| ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SY1511 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SY1511 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[667]) ).
thf(829,plain,
! [SV143: $i,SV265: $i] :
( ( ~ ( ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV143 )
| ~ ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV265 ) )
| ( subset @ SV143 @ SV265 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[668]) ).
thf(830,plain,
! [SV144: $i] :
( ( ~ ! [SY1373: $i > $o,SY1374: $i] :
( ~ ( in @ SY1374 @ SV144 )
| ~ ( SY1373 @ SY1374 )
| ( in @ SY1374
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1373 @ SX3 ) ) ) )
| ~ ! [SY1376: $i > $o,SY1377: $i] :
( ~ ( in @ SY1377 @ SV144 )
| ~ ( in @ SY1377
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1376 @ SX3 ) ) )
| ( SY1376 @ SY1377 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[669]) ).
thf(831,plain,
! [SV145: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_Xx @ SV145 ) @ omega )
| ~ ( in @ ( sK8_Xx @ SV145 ) @ SV145 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 ) )
| ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[670]) ).
thf(832,plain,
! [SV266: $i,SV146: $i] :
( ( ! [SY1514: $i] :
( ~ ( in @ SY1514 @ ( cartprod @ SV146 @ SV266 ) )
| ~ ( ~ ~ ( ( SY1514
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SY1514 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SY1514 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SY1514 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SY1514 @ SV266 @ SV146 ) @ ( setunion @ SY1514 ) ) )
| ~ ( in @ ( sK72_SY474 @ SY1514 @ SV266 @ SV146 ) @ ( setunion @ SY1514 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[671]) ).
thf(833,plain,
! [SV267: $i,SV147: $i] :
( ( ~ ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setadjoin @ ( sK67_SY1105 @ SV267 @ SV147 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK67_SY1105 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[672]) ).
thf(834,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ( ~ ~ ( ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1515 @ SV148 )
| ( in @ SY1515 @ SV268 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1517 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ ( binunion @ SV148 @ SV268 ) )
| ! [SY1520: $o] :
( ~ SY1520
| ( in @ SY1519 @ SV268 )
| SY1520 ) )
| ~ ( ! [SY1521: $i] :
~ ( in @ SY1521 @ ( binunion @ SV148 @ SV268 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[673]) ).
thf(835,plain,
! [SV149: $i > $o] :
( ( ( ! [SY1392: $i] :
~ ( SV149 @ SY1392 ) )
= $true )
| ( ( ~ ( ~ ( SV149 @ ( sK43_Xx @ SV149 ) )
| ~ ~ ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) ) )
| ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[674]) ).
thf(836,plain,
! [SV150: $i,SV269: $i] :
( ( ~ ( ~ ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV150 )
| ~ ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV269 ) )
| ( ( binintersect @ SV150 @ SV269 )
= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[675]) ).
thf(837,plain,
! [SV270: $i,SV151: $i] :
( ( ! [SY1523: $i] :
( ~ ( in @ SY1523 @ ( setadjoin @ SV151 @ SV270 ) )
| ~ ( ~ ~ ( ~ ( ( SY1523 = SV151 )
| ( in @ SY1523 @ SV270 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SY1523 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1526: $o] :
( ~ SY1526
| ( in @ SY1523 @ SV270 )
| SY1526 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[676]) ).
thf(838,plain,
! [SV271: $i,SV152: $i] :
( ( ( SV152 != SV271 )
| ! [SY1528: $i > $o,SY1529: $i > $o] :
( ~ ( ~ ( in @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) @ SV152 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SY1528 @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ~ ( SY1529 @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) ) )
| ~ ( ( SY1528 @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ( SY1529 @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV152
@ ^ [SX4: $i] : ( SY1528 @ SX4 ) )
= ( dsetconstr @ SV271
@ ^ [SX4: $i] : ( SY1529 @ SX4 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[677]) ).
thf(839,plain,
! [SV153: $i > $o,SV272: $i > $o] :
( ( ~ ( ( ( sK59_Xx @ SV272 @ SV153 )
!= ( sK60_SY1103 @ SV272 @ SV153 ) )
| ~ ~ ( ~ ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
| ~ ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) ) ) )
| ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[678]) ).
thf(840,plain,
! [SV154: $i > $o] :
( ( ( ! [SY1411: $i] :
~ ( ~ ( ( ( sK46_Xy @ SY1411 @ SV154 )
!= SY1411 )
| ~ ( SV154 @ ( sK46_Xy @ SY1411 @ SV154 ) ) )
| ~ ( ( ( sK46_Xy @ SY1411 @ SV154 )
= SY1411 )
| ( SV154 @ ( sK46_Xy @ SY1411 @ SV154 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[679]) ).
thf(841,plain,
! [SV155: $i,SV273: $i] :
( ( ~ ( ~ ( ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) )
| ~ ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) ) )
| ( SV155 = SV273 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[680]) ).
thf(842,plain,
! [SV156: $i,SV1: $i,SV274: $i] :
( ( ~ ( in @ SV274 @ ( cartprod @ SV1 @ SV156 ) )
| ( in @ ( kfst @ SV274 ) @ SV1 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[681]) ).
thf(843,plain,
! [SV275: $i,SV3: $i] :
( ( ( ( SV3
!= ( setadjoin @ SV275 @ emptyset ) )
| ~ ( in @ SV275 @ SV3 ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[683]) ).
thf(844,plain,
! [SV158: $i,SV4: $i,SV276: $i] :
( ( ~ ( in @ ( setadjoin @ SV276 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV158 @ emptyset ) ) @ emptyset ) ) )
| ( SV4 = SV276 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[684]) ).
thf(845,plain,
! [SV159: $i,SV5: $i] :
( ( ( ( setadjoin @ SV5 @ emptyset )
!= ( setadjoin @ SV159 @ emptyset ) )
= $true )
| ( ( SV5 = SV159 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[685]) ).
thf(846,plain,
! [SV160: $i,SV9: $i,SV277: $i] :
( ( ~ ( in @ SV277 @ SV9 )
| ! [SY1536: $i] :
( ~ ( in @ SY1536 @ SV160 )
| ( in @ ( setadjoin @ ( setadjoin @ SV277 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV277 @ ( setadjoin @ SY1536 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV9 @ SV160 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[686]) ).
thf(847,plain,
! [SV161: $i,SV10: $i,SV278: $i] :
( ( ~ ( in @ SV278 @ SV10 )
| ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV161 )
| ( in @ ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1537 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV10 @ SV161 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[687]) ).
thf(848,plain,
! [SV162: $i,SV11: $i,SV279: $i] :
( ( ~ ( in @ SV279 @ SV11 )
| ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV162 )
| ( in @ ( setadjoin @ ( setadjoin @ SV279 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV279 @ ( setadjoin @ SY1538 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV11 @ SV162 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[688]) ).
thf(849,plain,
! [SV163: $i,SV12: $i,SV280: $i] :
( ( ~ ( in @ SV280 @ SV12 )
| ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV163 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV280 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV280 @ ( setadjoin @ SY1539 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV12 @ SV163 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[689]) ).
thf(850,plain,
! [SV164: $i,SV13: $i,SV281: $i] :
( ( ~ ( in @ SV281 @ SV13 )
| ! [SY1540: $i] :
( ~ ( in @ SY1540 @ SV164 )
| ( in @ ( setadjoin @ SV281 @ ( setadjoin @ SY1540 @ emptyset ) ) @ ( powerset @ ( binunion @ SV13 @ SV164 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[690]) ).
thf(851,plain,
! [SV165: $i,SV14: $i,SV282: $i] :
( ( ~ ( in @ SV282 @ SV14 )
| ! [SY1541: $i] :
( ~ ( in @ SY1541 @ SV165 )
| ( subset @ ( setadjoin @ SV282 @ ( setadjoin @ SY1541 @ emptyset ) ) @ ( binunion @ SV14 @ SV165 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[691]) ).
thf(852,plain,
! [SV166: $i,SV15: $i,SV283: $i] :
( ( ~ ( in @ SV283 @ ( setadjoin @ SV15 @ ( setadjoin @ SV166 @ emptyset ) ) )
| ( SV283 = SV15 )
| ( SV283 = SV166 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[692]) ).
thf(853,plain,
! [SV167: $i,SV16: $i,SV284: $i] :
( ( ~ ( in @ SV284 @ SV16 )
| ( in @ ( setadjoin @ SV284 @ emptyset ) @ ( powerset @ ( binunion @ SV16 @ SV167 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[693]) ).
thf(854,plain,
! [SV17: $i,SV168: $i] :
( ( ( ~ ( in @ SV168 @ SV17 ) )
= $true )
| ( ( in @ ( setadjoin @ SV168 @ emptyset ) @ ( powerset @ SV17 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[694]) ).
thf(855,plain,
! [SV18: $i,SV169: $i] :
( ( ( ~ ( in @ SV169 @ SV18 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV169 @ emptyset ) @ SV18 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[695]) ).
thf(856,plain,
! [SV173: $i,SV22: $i,SV285: $i] :
( ( ( in @ SV285 @ SV22 )
| ( in @ SV285 @ SV173 )
| ~ ( in @ SV285 @ ( symdiff @ SV22 @ SV173 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[699]) ).
thf(857,plain,
! [SV174: $i,SV23: $i,SV286: $i] :
( ( ~ ( in @ SV286 @ SV23 )
| ~ ( in @ SV286 @ SV174 )
| ~ ( in @ SV286 @ ( symdiff @ SV23 @ SV174 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[700]) ).
thf(858,plain,
! [SV175: $i,SV24: $i,SV287: $i] :
( ( ( in @ SV287 @ SV24 )
| ~ ( in @ SV287 @ SV175 )
| ( in @ SV287 @ ( symdiff @ SV24 @ SV175 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[701]) ).
thf(859,plain,
! [SV176: $i,SV25: $i,SV288: $i] :
( ( ~ ( in @ SV288 @ SV25 )
| ( in @ SV288 @ SV176 )
| ( in @ SV288 @ ( symdiff @ SV25 @ SV176 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[702]) ).
thf(860,plain,
! [SV177: $i,SV26: $i] :
( ( ( ( setminus @ SV26 @ SV177 )
!= emptyset )
= $true )
| ( ( subset @ SV26 @ SV177 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[703]) ).
thf(861,plain,
! [SV28: $i,SV179: $i,SV289: $i] :
( ( ~ ( in @ SV289 @ SV179 )
| ~ ( in @ SV289 @ ( setminus @ SV28 @ SV179 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[705]) ).
thf(862,plain,
! [SV180: $i,SV29: $i,SV290: $i] :
( ( ( in @ SV290 @ SV29 )
| ~ ( in @ SV290 @ ( setminus @ SV29 @ SV180 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[706]) ).
thf(863,plain,
! [SV181: $i,SV30: $i,SV291: $i] :
( ( ( in @ SV291 @ ( setminus @ SV30 @ SV181 ) )
| ( in @ SV291 @ SV181 )
| ~ ( in @ SV291 @ SV30 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[707]) ).
thf(864,plain,
! [SV182: $i,SV31: $i,SV292: $i] :
( ( ( in @ SV292 @ ( setminus @ SV31 @ SV182 ) )
| ~ ( in @ SV292 @ SV31 )
| ( in @ SV292 @ SV182 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[708]) ).
thf(865,plain,
! [SV183: $i,SV32: $i] :
( ( ( ~ ( subset @ SV32 @ SV183 ) )
= $true )
| ( ( ( setminus @ SV32 @ SV183 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[709]) ).
thf(866,plain,
! [SV184: $i,SV33: $i,SV293: $i] :
( ( ~ ( in @ SV293 @ ( setminus @ SV33 @ SV184 ) )
| ~ ( in @ SV293 @ SV184 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[710]) ).
thf(867,plain,
! [SV185: $i,SV34: $i,SV294: $i] :
( ( ~ ( in @ SV294 @ ( setminus @ SV34 @ SV185 ) )
| ( in @ SV294 @ SV34 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[711]) ).
thf(868,plain,
! [SV186: $i,SV35: $i,SV295: $i] :
( ( ~ ( in @ SV295 @ SV35 )
| ( in @ SV295 @ SV186 )
| ( in @ SV295 @ ( setminus @ SV35 @ SV186 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[712]) ).
thf(869,plain,
! [SV296: $i,SV187: $i,SV36: $i] :
( ( ( binintersect @ SV36 @ ( binunion @ SV187 @ SV296 ) )
= ( binunion @ ( binintersect @ SV36 @ SV187 ) @ ( binintersect @ SV36 @ SV296 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[713]) ).
thf(870,plain,
! [SV188: $i,SV37: $i] :
( ( ( ( binintersect @ SV37 @ SV188 )
!= SV37 )
= $true )
| ( ( subset @ SV37 @ SV188 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[714]) ).
thf(871,plain,
! [SV38: $i,SV189: $i] :
( ( ( ~ ( subset @ SV189 @ SV38 ) )
= $true )
| ( ( ( binintersect @ SV38 @ SV189 )
= SV189 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[715]) ).
thf(872,plain,
! [SV191: $i,SV40: $i,SV297: $i] :
( ( ~ ( in @ SV297 @ ( binintersect @ SV40 @ SV191 ) )
| ( in @ SV297 @ SV191 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[717]) ).
thf(873,plain,
! [SV192: $i,SV41: $i] :
( ( ( ( binintersect @ SV41 @ SV192 )
!= SV192 )
= $true )
| ( ( subset @ SV192 @ SV41 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[718]) ).
thf(874,plain,
! [SV193: $i,SV42: $i] :
( ( ( ~ ( subset @ SV42 @ SV193 ) )
= $true )
| ( ( ( binintersect @ SV42 @ SV193 )
= SV42 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[719]) ).
thf(875,plain,
! [SV195: $i,SV44: $i,SV298: $i] :
( ( ~ ( in @ SV298 @ ( binintersect @ SV44 @ SV195 ) )
| ( in @ SV298 @ SV44 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[721]) ).
thf(876,plain,
! [SV196: $i,SV45: $i,SV299: $i] :
( ( ~ ( subset @ SV299 @ SV45 )
| ~ ( subset @ SV299 @ SV196 )
| ( subset @ SV299 @ ( binintersect @ SV45 @ SV196 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[722]) ).
thf(877,plain,
! [SV197: $i,SV46: $i,SV300: $i] :
( ( ~ ( in @ SV300 @ SV46 )
| ~ ( in @ SV300 @ SV197 )
| ( in @ SV300 @ ( binintersect @ SV46 @ SV197 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[723]) ).
thf(878,plain,
! [SV200: $i,SV49: $i,SV301: $i] :
( ( ~ ( in @ SV301 @ ( binunion @ SV49 @ SV200 ) )
| ( in @ SV301 @ SV49 )
| ( in @ SV301 @ SV200 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[726]) ).
thf(879,plain,
! [SV50: $i,SV201: $i,SV302: $i] :
( ( ~ ( in @ SV302 @ SV201 )
| ( in @ SV302 @ ( binunion @ SV50 @ SV201 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[727]) ).
thf(880,plain,
! [SV203: $i,SV52: $i,SV303: $i] :
( ( ~ ( in @ SV303 @ SV52 )
| ( in @ SV303 @ ( binunion @ SV52 @ SV203 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[729]) ).
thf(881,plain,
! [SV206: $i,SV55: $i] :
( ( ( ~ ( subset @ SV55 @ SV206 ) )
= $true )
| ( ( subset @ ( powerset @ SV55 ) @ ( powerset @ SV206 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[732]) ).
thf(882,plain,
! [SV57: $i,SV207: $i] :
( ( ( ~ ( in @ SV207 @ ( powerset @ SV57 ) ) )
= $true )
| ( ( subset @ SV207 @ SV57 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[733]) ).
thf(883,plain,
! [SV58: $i,SV208: $i] :
( ( ( ~ ( subset @ SV208 @ SV58 ) )
= $true )
| ( ( in @ SV208 @ ( powerset @ SV58 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[734]) ).
thf(884,plain,
! [SV59: $i] :
( ( ( subset @ SV59 @ emptyset )
= $false )
| ( ( SV59 = emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[735]) ).
thf(885,plain,
! [SV209: $i,SV60: $i] :
( ( ( ~ ( subset @ SV60 @ SV209 ) )
= $true )
| ( ( ~ ( subset @ SV209 @ SV60 )
| ( SV60 = SV209 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[736]) ).
thf(886,plain,
! [SV210: $i,SV61: $i] :
( ( ( ~ ( subset @ SV61 @ SV210 ) )
= $true )
| ( ( in @ SV61 @ ( powerset @ SV210 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[737]) ).
thf(887,plain,
! [SV211: $i,SV304: $i,SV62: $i] :
( ( ~ ( subset @ SV62 @ SV304 )
| ( subset @ SV62 @ ( setadjoin @ SV211 @ SV304 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[738]) ).
thf(888,plain,
! [SV213: $i,SV64: $i] :
( ( ( ~ ( subset @ SV64 @ SV213 ) )
= $true )
| ( ( ! [SY1452: $i] :
( ~ ( subset @ SV213 @ SY1452 )
| ( subset @ SV64 @ SY1452 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[740]) ).
thf(889,plain,
! [SV214: $i,SV66: $i,SV305: $i] :
( ( ~ ( in @ SV305 @ SV66 )
| ( in @ SV305 @ SV214 )
| ( SV66 != SV214 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[741]) ).
thf(890,plain,
! [SV215: $i,SV67: $i] :
( ( ( subset @ SV67 @ SV215 )
= $true )
| ( ( SV67 != SV215 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[742]) ).
thf(891,plain,
! [SV216: $i,SV68: $i,SV306: $i] :
( ( ~ ( in @ SV306 @ SV68 )
| ( in @ SV306 @ SV216 )
| ~ ( subset @ SV68 @ SV216 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[743]) ).
thf(892,plain,
! [SV217: $i,SV69: $i] :
( ( ( ~ ( subset @ SV69 @ SV217 ) )
= $true )
| ( ( ! [SY1455: $i] :
( ( in @ SY1455 @ SV217 )
| ~ ( in @ SY1455 @ SV69 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[744]) ).
thf(893,plain,
! [SV218: $i,SV70: $i] :
( ( ( ~ ( subset @ SV70 @ SV218 ) )
= $true )
| ( ( ! [SY1456: $i] :
( ~ ( in @ SY1456 @ SV70 )
| ( in @ SY1456 @ SV218 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[745]) ).
thf(894,plain,
! [SV219: $i,SV72: $i] :
( ( ( SV72 != SV219 )
= $true )
| ( ( subset @ SV72 @ SV219 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[746]) ).
thf(895,plain,
! [SV220: $i,SV73: $i] :
( ( ( SV73 != SV220 )
= $true )
| ( ( subset @ SV220 @ SV73 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[747]) ).
thf(896,plain,
! [SV221: $i,SV74: $i] :
( ( ( SV74 != SV221 )
= $true )
| ( ( ( setunion @ SV74 )
= ( setunion @ SV221 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[748]) ).
thf(897,plain,
! [SV222: $i,SV75: $i] :
( ( ( SV75 != SV222 )
= $true )
| ( ( ( powerset @ SV75 )
= ( powerset @ SV222 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[749]) ).
thf(898,plain,
! [SV223: $i,SV76: $i] :
( ( ( SV76 != SV223 )
= $true )
| ( ( ! [SY1457: $i,SY1458: $i] :
( ( SY1457 != SY1458 )
| ( ( setadjoin @ SV76 @ SY1457 )
= ( setadjoin @ SV223 @ SY1458 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[750]) ).
thf(899,plain,
! [SV224: $i,SV77: $i] :
( ( ( SV77 != SV224 )
= $true )
| ( ( ! [SY1459: $i,SY1460: $i] :
( ( SY1459 != SY1460 )
| ~ ( in @ SY1459 @ SV77 )
| ( in @ SY1460 @ SV224 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[751]) ).
thf(900,plain,
! [SV78: $o] :
( ( SV78 = $false )
| ( ( set2prop @ ( prop2set @ SV78 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[752]) ).
thf(901,plain,
( ( $true = $false )
| ( ( set2prop @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[753]) ).
thf(902,plain,
( ( $false = $false )
| ( ( set2prop @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[754]) ).
thf(903,plain,
! [SV79: $o] :
( ( SV79 = $false )
| ( ( in @ emptyset @ ( prop2set @ SV79 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[755]) ).
thf(904,plain,
( ( $true = $false )
| ( ( in @ emptyset @ ( prop2set @ $true ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[756]) ).
thf(905,plain,
( ( $false = $false )
| ( ( in @ emptyset @ ( prop2set @ $false ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[757]) ).
thf(906,plain,
! [SV80: $i > $o,SV225: $i] :
( ( ( ~ ( in @ SV225 @ emptyset ) )
= $true )
| ( ( SV80 @ SV225 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[758]) ).
thf(907,plain,
! [SV81: $i,SV226: $i > $o] :
( ( ( ! [SY1461: $i] :
( ~ ( SV226 @ SY1461 )
| ~ ( in @ SY1461 @ SV81 ) ) )
= $true )
| ( ( ( dsetconstr @ SV81
@ ^ [SY1462: $i] : ( SV226 @ SY1462 ) )
!= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[759]) ).
thf(908,plain,
! [SV229: $i,SV84: $i,SV307: $i] :
( ( ~ ( in @ SV307 @ ( setadjoin @ SV84 @ ( setadjoin @ SV229 @ emptyset ) ) )
| ( SV307 = SV84 )
| ( SV307 = SV229 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[762]) ).
thf(909,plain,
! [SV230: $i,SV85: $i] :
( ( ( ~ ( in @ SV85 @ ( setadjoin @ SV230 @ emptyset ) ) )
= $true )
| ( ( in @ SV230 @ ( setadjoin @ SV85 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[763]) ).
thf(910,plain,
! [SV231: $i,SV86: $i] :
( ( ( SV86 != SV231 )
= $true )
| ( ( in @ SV86 @ ( setadjoin @ SV231 @ emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[764]) ).
thf(911,plain,
! [SV232: $i,SV87: $i] :
( ( ( SV87 = SV232 )
= $true )
| ( ( ~ ( in @ SV232 @ ( setadjoin @ SV87 @ emptyset ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[765]) ).
thf(912,plain,
! [SV233: $i,SV88: $i] :
( ( ( ~ ( in @ SV88 @ ( setadjoin @ SV233 @ emptyset ) ) )
= $true )
| ( ( SV88 = SV233 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[766]) ).
thf(913,plain,
! [SV90: $i,SV234: $i] :
( ( ( ~ ( in @ SV234 @ SV90 ) )
= $true )
| ( ( in @ SV234 @ ( powerset @ ( setunion @ SV90 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[768]) ).
thf(914,plain,
! [SV91: $i,SV308: $i,SV235: $i] :
( ( ~ ( in @ SV235 @ SV308 )
| ~ ( in @ SV308 @ SV91 )
| ( in @ SV235 @ ( setunion @ SV91 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[769]) ).
thf(915,plain,
! [SV92: $i,SV236: $i] :
( ( ( ~ ( in @ SV236 @ ( powerset @ SV92 ) ) )
= $true )
| ( ( ! [SY1465: $i] :
( ~ ( in @ SY1465 @ SV236 )
| ( in @ SY1465 @ SV92 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[770]) ).
thf(916,plain,
! [SV237: $i,SV96: $i,SV309: $i] :
( ( ~ ( in @ SV309 @ ( setadjoin @ SV96 @ SV237 ) )
| ( SV309 = SV96 )
| ( in @ SV309 @ SV237 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[771]) ).
thf(917,plain,
! [SV97: $i,SV238: $i,SV310: $i] :
( ( ~ ( in @ SV310 @ SV238 )
| ( in @ SV310 @ ( setadjoin @ SV97 @ SV238 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[772]) ).
thf(918,plain,
! [SV99: $i,SV311: $i] :
( ( ( ~ ( in @ SV311 @ SV99 ) )
= $true )
| ( ( SV99 != emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[774]) ).
thf(919,plain,
! [SV240: $i > $o,SV100: $i,SV312: $i] :
( ( ~ ( in @ SV312 @ SV100 )
| ~ ( SV240 @ SV312 )
| ( ( dsetconstr @ SV100
@ ^ [SY1469: $i] : ( SV240 @ SY1469 ) )
!= emptyset ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[775]) ).
thf(920,plain,
! [SV241: $i] :
( ( ( in @ SV241 @ emptyset )
= $false )
| ( ( ! [Xphi: $o] : Xphi )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[781]) ).
thf(921,plain,
! [SV106: $o,SV313: $i] :
( ( ( ~ ( in @ SV313 @ ( prop2set @ SV106 ) ) )
= $true )
| ( SV106 = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[782]) ).
thf(922,plain,
! [SV314: $i] :
( ( ( ~ ( in @ SV314 @ ( prop2set @ $true ) ) )
= $true )
| ( $true = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[783]) ).
thf(923,plain,
! [SV315: $i] :
( ( ( ~ ( in @ SV315 @ ( prop2set @ $false ) ) )
= $true )
| ( $false = $true ) ),
inference(extcnf_forall_pos,[status(thm)],[784]) ).
thf(924,plain,
! [SV242: $i > $o,SV107: $i,SV316: $i] :
( ( ~ ( in @ SV316
@ ( dsetconstr @ SV107
@ ^ [SY1471: $i] : ( SV242 @ SY1471 ) ) )
| ( SV242 @ SV316 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[785]) ).
thf(925,plain,
! [SV243: $i > $o,SV108: $i,SV317: $i] :
( ( ~ ( in @ SV317
@ ( dsetconstr @ SV108
@ ^ [SY1473: $i] : ( SV243 @ SY1473 ) ) )
| ( in @ SV317 @ SV108 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[786]) ).
thf(926,plain,
! [SV244: $i > $o,SV109: $i,SV318: $i] :
( ( ~ ( in @ SV318 @ SV109 )
| ~ ( SV244 @ SV318 )
| ( in @ SV318
@ ( dsetconstr @ SV109
@ ^ [SY1475: $i] : ( SV244 @ SY1475 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[787]) ).
thf(927,plain,
! [SV110: $i] :
( ( ( in @ SV110 @ omega )
= $false )
| ( ( in @ ( setadjoin @ SV110 @ SV110 ) @ omega )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[788]) ).
thf(928,plain,
! [SV245: $i > $o,SV112: $i] :
( ( ( ! [SY1476: $i] :
( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
!= ( setadjoin @ SY1476 @ emptyset ) )
| ~ ( in @ SY1476
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) )
| ~ ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[790]) ).
thf(929,plain,
! [SV113: $i] :
( ( ~ ! [SY1277: $i] :
( ~ ( ~ ( in @ ( sK18_Xx @ SY1277 @ SV113 ) @ SY1277 )
| ~ ~ ( in @ ( sK18_Xx @ SY1277 @ SV113 ) @ SV113 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY1277 )
| ~ ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ ( sK14_B @ SV113 ) )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SY1279 )
| ( in @ SY1280 @ ( sK16_SY1071 @ SY1277 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SY1277 @ SV113 ) @ SY1279 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SY1277 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SY1277 @ SV113 ) @ SY1277 ) )
| ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ ( sK16_SY1071 @ SY1277 @ SV113 ) )
| ~ ( in @ SY1281 @ SY1277 ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(930,plain,
! [SV113: $i] :
( ( ~ ~ ( ~ ! [SY1282: $i,SY1283: $i] :
( ~ ( in @ SY1282 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY1283 @ ( sK14_B @ SV113 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1282 )
| ( in @ SX3 @ SY1283 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1283 )
| ( in @ SX3 @ SY1282 ) ) )
| ~ ~ ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) )
| ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[791]) ).
thf(931,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX1 )
| ~ ~ ( in @ ( sK6_Xx @ SX1 @ SX0 ) @ SX0 ) )
| ( in @ SX1 @ ( powerset @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[792]) ).
thf(932,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( powerset @ SX0 ) )
| ! [SX2: $i] :
( ~ ( in @ SX2 @ SX1 )
| ( in @ SX2 @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[793]) ).
thf(933,plain,
! [SV246: $i > $o,SV114: $i] :
( ( ( ! [SY1479: $i] :
( ~ ( in @ SY1479 @ SV114 )
| ( SV246 @ SY1479 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK39_Xx @ SV246 @ SV114 ) @ SV114 )
| ~ ~ ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[794]) ).
thf(934,plain,
! [SV247: $i > $o,SV115: $i] :
( ( ( ! [SY1480: $i] :
( ~ ( in @ SY1480 @ SV115 )
| ( SV247 @ SY1480 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK37_Xx @ SV247 @ SV115 ) @ SV115 )
| ~ ~ ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[795]) ).
thf(935,plain,
! [SV248: $i,SV116: $i] :
( ( ( SV116 != SV248 )
= $true )
| ( ( ~ ( ~ ! [SY1481: $i,SY1482: $i] :
( ( SY1481 != SY1482 )
| ~ ( in @ SY1481 @ SV116 )
| ( in @ SY1482 @ SV248 ) )
| ~ ! [SY1483: $i,SY1484: $i] :
( ( SY1483 != SY1484 )
| ~ ( in @ SY1484 @ SV248 )
| ( in @ SY1483 @ SV116 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[796]) ).
thf(936,plain,
( ( ( setadjoin @ ( setadjoin @ sK1_Xx @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK1_Xx @ ( setadjoin @ sK2_SY1055 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ sK3_SY1058 @ emptyset ) @ ( setadjoin @ ( setadjoin @ sK3_SY1058 @ ( setadjoin @ sK4_SY1060 @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[797]) ).
thf(937,plain,
( ( sK1_Xx != sK3_SY1058 )
= $true ),
inference(extcnf_not_neg,[status(thm)],[798]) ).
thf(938,plain,
! [SV319: $i,SV117: $i > $o] :
( ( ( ~ ( ~ ( SV117 @ ( sK23_SY85 @ SV319 @ SV117 ) )
| ~ ( ( SV319
!= ( sK23_SY85 @ SV319 @ SV117 ) ) ) )
| ~ ( SV117 @ SV319 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[799]) ).
thf(939,plain,
! [SV118: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ ( setunion @ SV118 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK74_X @ SV249 @ SV118 ) @ SV118 )
| ~ ( in @ SV249 @ ( sK74_X @ SV249 @ SV118 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[800]) ).
thf(940,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) ) ) ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[801]) ).
thf(941,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ( ~ ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
| ~ ( ( SV320
!= ( sK21_SY73 @ SV320 @ SV120 ) ) ) )
| ~ ( SV120 @ SV320 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[802]) ).
thf(942,plain,
! [SV321: $i,SV121: $i > $o] :
( ( ( ~ ( ~ ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
| ~ ( ( SV321
!= ( sK56_SY247 @ SV321 @ SV121 ) ) ) )
| ~ ( SV121 @ SV321 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[803]) ).
thf(943,plain,
! [SV122: $i,SV251: $i > $o] :
( ( ( ~ ( ~ ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) )
| ~ ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 ) ) )
= $true )
| ( ( ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV122 )
| ~ ( SV251 @ SY1488 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[804]) ).
thf(944,plain,
! [SV252: $i,SV123: $i] :
( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setadjoin @ ( sK69_SY1106 @ SV252 @ SV123 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK69_SY1106 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[805]) ).
thf(945,plain,
! [SV124: $i,SV322: $i] :
( ( ( ~ ( in @ SV322 @ SV124 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK13_B @ SV124 ) @ SV124 )
| ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK13_B @ SV124 ) )
| ~ ( in @ SY1314 @ SV124 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[806]) ).
thf(946,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) ) ) ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[807]) ).
thf(947,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ~ ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
| ~ ( ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[808]) ).
thf(948,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ( ~ ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
| ~ ( ( SV324
!= ( sK32_SY141 @ SV324 @ SV127 ) ) ) )
| ~ ( SV127 @ SV324 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[809]) ).
thf(949,plain,
! [SV255: $i > $o,SV128: $i] :
( ( ( ! [SY1502: $i] :
( ~ ( in @ SY1502 @ SV128 )
| ( SV255 @ SY1502 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK34_Xx @ SV255 @ SV128 ) @ SV128 )
| ~ ~ ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[810]) ).
thf(950,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ( ~ ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
| ~ ( ( SV325
!= ( sK41_Xy @ SV325 @ SV129 ) ) ) )
| ~ ( SV129 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[811]) ).
thf(951,plain,
! [SV326: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK19_SY56 @ SV326 @ SV130 ) )
| ~ ( ( SV326
!= ( sK19_SY56 @ SV326 @ SV130 ) ) ) )
| ~ ( SV130 @ SV326 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[812]) ).
thf(952,plain,
! [SV131: $i] :
( ( ~ ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ SY1340 @ ( setadjoin @ SV131 @ SY1339 ) )
| ( SY1340 = SV131 )
| ( in @ SY1340 @ SY1339 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[813]) ).
thf(953,plain,
! [SV131: $i] :
( ( ~ ~ ( ~ ! [SY1341: $i,SY1342: $i] :
( ( SY1342 != SV131 )
| ( in @ SY1342 @ ( setadjoin @ SV131 @ SY1341 ) ) )
| ~ ! [SY1343: $i,SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( setadjoin @ SV131 @ SY1343 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[813]) ).
thf(954,plain,
! [SV132: $i,SV256: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 )
| ~ ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) ) ) )
= $true )
| ( ( ! [SY1503: $i] :
( ~ ( SV256 @ SY1503 )
| ~ ( in @ SY1503 @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[814]) ).
thf(955,plain,
! [SV327: $i,SV133: $i] :
( ( ( ! [SY1555: $i] :
( ( SV133
!= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SY1555 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY1555 @ ( setunion @ SV133 ) ) )
| ~ ( in @ SV327 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[815]) ).
thf(956,plain,
! [SV134: $i,SV257: $i] :
( ( ( ~ ( ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV257 )
| ~ ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV134 ) ) )
= $true )
| ( ( in @ SV257 @ ( powerset @ SV134 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[816]) ).
thf(957,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ ( setunion @ SV135 ) ) )
= $true )
| ( ( ! [SY1504: $o] :
( ~ ( ~ ( in @ SV258 @ ( sK30_B @ SY1504 @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ SY1504 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SY1504 ) )
| SY1504 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[817]) ).
thf(958,plain,
! [SV328: $i,SV136: $i > $o] :
( ( ( ~ ( ~ ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
| ~ ( ( SV328
!= ( sK47_SY223 @ SV328 @ SV136 ) ) ) )
| ~ ( SV136 @ SV328 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[818]) ).
thf(959,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
| ~ ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
| ( SV137 = SV259 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[819]) ).
thf(960,plain,
! [SV260: $i,SV138: $i,SV329: $i] :
( ( ~ ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
| ~ ( ~ ~ ( ( SV329
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 ) )
| ~ ( in @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ SV138 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[820]) ).
thf(961,plain,
( ( ! [SX0: $i,SX1: $i] :
( ! [SX2: $i] :
( ~ ( in @ SX1 @ SX2 )
| ~ ( in @ SX2 @ SX0 ) )
| ( in @ SX1 @ ( setunion @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[821]) ).
thf(962,plain,
( ( ! [SX0: $i,SX1: $i] :
( ~ ( in @ SX1 @ ( setunion @ SX0 ) )
| ~ ( ~ ( in @ SX1 @ ( sK7_B @ SX1 @ SX0 ) )
| ~ ( in @ ( sK7_B @ SX1 @ SX0 ) @ SX0 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[822]) ).
thf(963,plain,
! [SV139: $i > $i > $o,SV261: $i] :
( ( ( ~ ( ~ ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
| ~ ! [SY1506: $i] :
( ~ ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) )
| ~ ( ( SY1506
!= ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) ) ) )
| ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SY1506 ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[823]) ).
thf(964,plain,
! [SV140: $i,SV262: $i] :
( ( ( ~ ( ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV140 )
| ~ ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV262 ) ) )
= $true )
| ( ( subset @ SV140 @ SV262 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[824]) ).
thf(965,plain,
! [SV141: $i,SV263: $i > $o] :
( ( ( ~ ( ~ ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) )
| ~ ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 ) ) )
= $true )
| ( ( ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV141 )
| ~ ( SV263 @ SY1510 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[825]) ).
thf(966,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK54_Xx @ SX1 @ SX0 )
!= ( sK55_SY1102 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK54_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK55_SY1102 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK54_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK55_SY1102 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX0 @ ( sK53_SY232 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK53_SY232 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX0 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX1 @ SX2 )
| ( ( sK52_SY234 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX1 @ ( sK52_SY234 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[826]) ).
thf(967,plain,
( ( ! [SX0: $i > $o,SX1: $i > $o] :
( ~ ( ( ( sK50_Xx @ SX1 @ SX0 )
!= ( sK51_SY1100 @ SX1 @ SX0 ) )
| ~ ~ ( ~ ( ~ ( SX0 @ ( sK50_Xx @ SX1 @ SX0 ) )
| ~ ( SX1 @ ( sK51_SY1100 @ SX1 @ SX0 ) ) )
| ~ ( ( SX0 @ ( sK50_Xx @ SX1 @ SX0 ) )
| ( SX1 @ ( sK51_SY1100 @ SX1 @ SX0 ) ) ) ) )
| ! [SX2: $i] :
( ~ ( ~ ( SX1 @ ( sK49_SY235 @ SX2 @ SX1 @ SX0 ) )
| ~ ( ( SX2
!= ( sK49_SY235 @ SX2 @ SX1 @ SX0 ) ) ) )
| ~ ( SX1 @ SX2 ) )
| ~ ( ~ ! [SX2: $i] :
( ~ ( SX0 @ SX2 )
| ( ( sK48_SY231 @ SX1 @ SX0 )
= SX2 ) )
| ~ ( SX0 @ ( sK48_SY231 @ SX1 @ SX0 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[827]) ).
thf(968,plain,
! [SV264: $i > $o,SV142: $i,SV330: $i] :
( ( ~ ( in @ SV330 @ SV142 )
| ~ ( SV264 @ SV330 )
| ~ ( ~ ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) )
| ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[828]) ).
thf(969,plain,
! [SV143: $i,SV265: $i] :
( ( ( ~ ( ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV143 )
| ~ ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV265 ) ) )
= $true )
| ( ( subset @ SV143 @ SV265 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[829]) ).
thf(970,plain,
! [SV144: $i] :
( ( ~ ! [SY1373: $i > $o,SY1374: $i] :
( ~ ( in @ SY1374 @ SV144 )
| ~ ( SY1373 @ SY1374 )
| ( in @ SY1374
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1373 @ SX3 ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(971,plain,
! [SV144: $i] :
( ( ~ ! [SY1376: $i > $o,SY1377: $i] :
( ~ ( in @ SY1377 @ SV144 )
| ~ ( in @ SY1377
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1376 @ SX3 ) ) )
| ( SY1376 @ SY1377 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[830]) ).
thf(972,plain,
! [SV145: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK8_Xx @ SV145 ) @ omega )
| ~ ( in @ ( sK8_Xx @ SV145 ) @ SV145 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[831]) ).
thf(973,plain,
! [SV266: $i,SV146: $i,SV331: $i] :
( ( ~ ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
| ~ ( ~ ~ ( ( SV331
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) )
| ~ ( in @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[832]) ).
thf(974,plain,
! [SV267: $i,SV147: $i] :
( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setadjoin @ ( sK67_SY1105 @ SV267 @ SV147 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK67_SY1105 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) )
| ~ ( in @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[833]) ).
thf(975,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ~ ( ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1515 @ SV148 )
| ( in @ SY1515 @ SV268 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1517 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ ( binunion @ SV148 @ SV268 ) )
| ! [SY1520: $o] :
( ~ SY1520
| ( in @ SY1519 @ SV268 )
| SY1520 ) )
| ~ ( ! [SY1521: $i] :
~ ( in @ SY1521 @ ( binunion @ SV148 @ SV268 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[834]) ).
thf(976,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ SV332 ) )
= $true )
| ( ( ~ ( ~ ( SV149 @ ( sK43_Xx @ SV149 ) )
| ~ ~ ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) ) )
| ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[835]) ).
thf(977,plain,
! [SV150: $i,SV269: $i] :
( ( ( ~ ( ~ ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV150 )
| ~ ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV269 ) ) )
= $true )
| ( ( ( binintersect @ SV150 @ SV269 )
= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[836]) ).
thf(978,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ~ ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
| ~ ( ~ ~ ( ~ ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[837]) ).
thf(979,plain,
! [SV271: $i,SV152: $i] :
( ( ( SV152 != SV271 )
= $true )
| ( ( ! [SY1528: $i > $o,SY1529: $i > $o] :
( ~ ( ~ ( in @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) @ SV152 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SY1528 @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ~ ( SY1529 @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) ) )
| ~ ( ( SY1528 @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ( SY1529 @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV152
@ ^ [SX4: $i] : ( SY1528 @ SX4 ) )
= ( dsetconstr @ SV271
@ ^ [SX4: $i] : ( SY1529 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[838]) ).
thf(980,plain,
! [SV153: $i > $o,SV272: $i > $o] :
( ( ( ~ ( ( ( sK59_Xx @ SV272 @ SV153 )
!= ( sK60_SY1103 @ SV272 @ SV153 ) )
| ~ ~ ( ~ ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
| ~ ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) ) ) ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[839]) ).
thf(981,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ~ ( ~ ( ( ( sK46_Xy @ SV334 @ SV154 )
!= SV334 )
| ~ ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) )
| ~ ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
| ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[840]) ).
thf(982,plain,
! [SV155: $i,SV273: $i] :
( ( ( ~ ( ~ ( ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) )
| ~ ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) ) ) )
= $true )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[841]) ).
thf(983,plain,
! [SV156: $i,SV1: $i,SV274: $i] :
( ( ( ~ ( in @ SV274 @ ( cartprod @ SV1 @ SV156 ) ) )
= $true )
| ( ( in @ ( kfst @ SV274 ) @ SV1 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[842]) ).
thf(984,plain,
! [SV275: $i,SV3: $i] :
( ( ( SV3
!= ( setadjoin @ SV275 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV275 @ SV3 ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[843]) ).
thf(985,plain,
! [SV158: $i,SV4: $i,SV276: $i] :
( ( ( ~ ( in @ ( setadjoin @ SV276 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV158 @ emptyset ) ) @ emptyset ) ) ) )
= $true )
| ( ( SV4 = SV276 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[844]) ).
thf(986,plain,
! [SV159: $i,SV5: $i] :
( ( ( ( setadjoin @ SV5 @ emptyset )
= ( setadjoin @ SV159 @ emptyset ) )
= $false )
| ( ( SV5 = SV159 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[845]) ).
thf(987,plain,
! [SV160: $i,SV9: $i,SV277: $i] :
( ( ( ~ ( in @ SV277 @ SV9 ) )
= $true )
| ( ( ! [SY1536: $i] :
( ~ ( in @ SY1536 @ SV160 )
| ( in @ ( setadjoin @ ( setadjoin @ SV277 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV277 @ ( setadjoin @ SY1536 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV9 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[846]) ).
thf(988,plain,
! [SV161: $i,SV10: $i,SV278: $i] :
( ( ( ~ ( in @ SV278 @ SV10 ) )
= $true )
| ( ( ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV161 )
| ( in @ ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1537 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV10 @ SV161 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[847]) ).
thf(989,plain,
! [SV162: $i,SV11: $i,SV279: $i] :
( ( ( ~ ( in @ SV279 @ SV11 ) )
= $true )
| ( ( ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV162 )
| ( in @ ( setadjoin @ ( setadjoin @ SV279 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV279 @ ( setadjoin @ SY1538 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV11 @ SV162 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[848]) ).
thf(990,plain,
! [SV163: $i,SV12: $i,SV280: $i] :
( ( ( ~ ( in @ SV280 @ SV12 ) )
= $true )
| ( ( ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV163 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV280 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV280 @ ( setadjoin @ SY1539 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV12 @ SV163 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[849]) ).
thf(991,plain,
! [SV164: $i,SV13: $i,SV281: $i] :
( ( ( ~ ( in @ SV281 @ SV13 ) )
= $true )
| ( ( ! [SY1540: $i] :
( ~ ( in @ SY1540 @ SV164 )
| ( in @ ( setadjoin @ SV281 @ ( setadjoin @ SY1540 @ emptyset ) ) @ ( powerset @ ( binunion @ SV13 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[850]) ).
thf(992,plain,
! [SV165: $i,SV14: $i,SV282: $i] :
( ( ( ~ ( in @ SV282 @ SV14 ) )
= $true )
| ( ( ! [SY1541: $i] :
( ~ ( in @ SY1541 @ SV165 )
| ( subset @ ( setadjoin @ SV282 @ ( setadjoin @ SY1541 @ emptyset ) ) @ ( binunion @ SV14 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[851]) ).
thf(993,plain,
! [SV166: $i,SV15: $i,SV283: $i] :
( ( ( ~ ( in @ SV283 @ ( setadjoin @ SV15 @ ( setadjoin @ SV166 @ emptyset ) ) ) )
= $true )
| ( ( ( SV283 = SV15 )
| ( SV283 = SV166 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[852]) ).
thf(994,plain,
! [SV167: $i,SV16: $i,SV284: $i] :
( ( ( ~ ( in @ SV284 @ SV16 ) )
= $true )
| ( ( in @ ( setadjoin @ SV284 @ emptyset ) @ ( powerset @ ( binunion @ SV16 @ SV167 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[853]) ).
thf(995,plain,
! [SV17: $i,SV168: $i] :
( ( ( in @ SV168 @ SV17 )
= $false )
| ( ( in @ ( setadjoin @ SV168 @ emptyset ) @ ( powerset @ SV17 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[854]) ).
thf(996,plain,
! [SV18: $i,SV169: $i] :
( ( ( in @ SV169 @ SV18 )
= $false )
| ( ( subset @ ( setadjoin @ SV169 @ emptyset ) @ SV18 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[855]) ).
thf(997,plain,
! [SV173: $i,SV22: $i,SV285: $i] :
( ( ( in @ SV285 @ SV22 )
= $true )
| ( ( ( in @ SV285 @ SV173 )
| ~ ( in @ SV285 @ ( symdiff @ SV22 @ SV173 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[856]) ).
thf(998,plain,
! [SV174: $i,SV23: $i,SV286: $i] :
( ( ( ~ ( in @ SV286 @ SV23 ) )
= $true )
| ( ( ~ ( in @ SV286 @ SV174 )
| ~ ( in @ SV286 @ ( symdiff @ SV23 @ SV174 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[857]) ).
thf(999,plain,
! [SV175: $i,SV24: $i,SV287: $i] :
( ( ( in @ SV287 @ SV24 )
= $true )
| ( ( ~ ( in @ SV287 @ SV175 )
| ( in @ SV287 @ ( symdiff @ SV24 @ SV175 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[858]) ).
thf(1000,plain,
! [SV176: $i,SV25: $i,SV288: $i] :
( ( ( ~ ( in @ SV288 @ SV25 ) )
= $true )
| ( ( ( in @ SV288 @ SV176 )
| ( in @ SV288 @ ( symdiff @ SV25 @ SV176 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[859]) ).
thf(1001,plain,
! [SV177: $i,SV26: $i] :
( ( ( ( setminus @ SV26 @ SV177 )
= emptyset )
= $false )
| ( ( subset @ SV26 @ SV177 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[860]) ).
thf(1002,plain,
! [SV28: $i,SV179: $i,SV289: $i] :
( ( ( ~ ( in @ SV289 @ SV179 ) )
= $true )
| ( ( ~ ( in @ SV289 @ ( setminus @ SV28 @ SV179 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[861]) ).
thf(1003,plain,
! [SV180: $i,SV29: $i,SV290: $i] :
( ( ( in @ SV290 @ SV29 )
= $true )
| ( ( ~ ( in @ SV290 @ ( setminus @ SV29 @ SV180 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[862]) ).
thf(1004,plain,
! [SV181: $i,SV30: $i,SV291: $i] :
( ( ( in @ SV291 @ ( setminus @ SV30 @ SV181 ) )
= $true )
| ( ( ( in @ SV291 @ SV181 )
| ~ ( in @ SV291 @ SV30 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[863]) ).
thf(1005,plain,
! [SV182: $i,SV31: $i,SV292: $i] :
( ( ( in @ SV292 @ ( setminus @ SV31 @ SV182 ) )
= $true )
| ( ( ~ ( in @ SV292 @ SV31 )
| ( in @ SV292 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[864]) ).
thf(1006,plain,
! [SV183: $i,SV32: $i] :
( ( ( subset @ SV32 @ SV183 )
= $false )
| ( ( ( setminus @ SV32 @ SV183 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[865]) ).
thf(1007,plain,
! [SV184: $i,SV33: $i,SV293: $i] :
( ( ( ~ ( in @ SV293 @ ( setminus @ SV33 @ SV184 ) ) )
= $true )
| ( ( ~ ( in @ SV293 @ SV184 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[866]) ).
thf(1008,plain,
! [SV185: $i,SV34: $i,SV294: $i] :
( ( ( ~ ( in @ SV294 @ ( setminus @ SV34 @ SV185 ) ) )
= $true )
| ( ( in @ SV294 @ SV34 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[867]) ).
thf(1009,plain,
! [SV186: $i,SV35: $i,SV295: $i] :
( ( ( ~ ( in @ SV295 @ SV35 ) )
= $true )
| ( ( ( in @ SV295 @ SV186 )
| ( in @ SV295 @ ( setminus @ SV35 @ SV186 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[868]) ).
thf(1010,plain,
! [SV188: $i,SV37: $i] :
( ( ( ( binintersect @ SV37 @ SV188 )
= SV37 )
= $false )
| ( ( subset @ SV37 @ SV188 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[870]) ).
thf(1011,plain,
! [SV38: $i,SV189: $i] :
( ( ( subset @ SV189 @ SV38 )
= $false )
| ( ( ( binintersect @ SV38 @ SV189 )
= SV189 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[871]) ).
thf(1012,plain,
! [SV191: $i,SV40: $i,SV297: $i] :
( ( ( ~ ( in @ SV297 @ ( binintersect @ SV40 @ SV191 ) ) )
= $true )
| ( ( in @ SV297 @ SV191 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[872]) ).
thf(1013,plain,
! [SV192: $i,SV41: $i] :
( ( ( ( binintersect @ SV41 @ SV192 )
= SV192 )
= $false )
| ( ( subset @ SV192 @ SV41 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[873]) ).
thf(1014,plain,
! [SV193: $i,SV42: $i] :
( ( ( subset @ SV42 @ SV193 )
= $false )
| ( ( ( binintersect @ SV42 @ SV193 )
= SV42 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[874]) ).
thf(1015,plain,
! [SV195: $i,SV44: $i,SV298: $i] :
( ( ( ~ ( in @ SV298 @ ( binintersect @ SV44 @ SV195 ) ) )
= $true )
| ( ( in @ SV298 @ SV44 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[875]) ).
thf(1016,plain,
! [SV196: $i,SV45: $i,SV299: $i] :
( ( ( ~ ( subset @ SV299 @ SV45 ) )
= $true )
| ( ( ~ ( subset @ SV299 @ SV196 )
| ( subset @ SV299 @ ( binintersect @ SV45 @ SV196 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[876]) ).
thf(1017,plain,
! [SV197: $i,SV46: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV46 ) )
= $true )
| ( ( ~ ( in @ SV300 @ SV197 )
| ( in @ SV300 @ ( binintersect @ SV46 @ SV197 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[877]) ).
thf(1018,plain,
! [SV200: $i,SV49: $i,SV301: $i] :
( ( ( ~ ( in @ SV301 @ ( binunion @ SV49 @ SV200 ) ) )
= $true )
| ( ( ( in @ SV301 @ SV49 )
| ( in @ SV301 @ SV200 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[878]) ).
thf(1019,plain,
! [SV50: $i,SV201: $i,SV302: $i] :
( ( ( ~ ( in @ SV302 @ SV201 ) )
= $true )
| ( ( in @ SV302 @ ( binunion @ SV50 @ SV201 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[879]) ).
thf(1020,plain,
! [SV203: $i,SV52: $i,SV303: $i] :
( ( ( ~ ( in @ SV303 @ SV52 ) )
= $true )
| ( ( in @ SV303 @ ( binunion @ SV52 @ SV203 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[880]) ).
thf(1021,plain,
! [SV206: $i,SV55: $i] :
( ( ( subset @ SV55 @ SV206 )
= $false )
| ( ( subset @ ( powerset @ SV55 ) @ ( powerset @ SV206 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[881]) ).
thf(1022,plain,
! [SV57: $i,SV207: $i] :
( ( ( in @ SV207 @ ( powerset @ SV57 ) )
= $false )
| ( ( subset @ SV207 @ SV57 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[882]) ).
thf(1023,plain,
! [SV58: $i,SV208: $i] :
( ( ( subset @ SV208 @ SV58 )
= $false )
| ( ( in @ SV208 @ ( powerset @ SV58 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[883]) ).
thf(1024,plain,
! [SV209: $i,SV60: $i] :
( ( ( subset @ SV60 @ SV209 )
= $false )
| ( ( ~ ( subset @ SV209 @ SV60 )
| ( SV60 = SV209 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[885]) ).
thf(1025,plain,
! [SV210: $i,SV61: $i] :
( ( ( subset @ SV61 @ SV210 )
= $false )
| ( ( in @ SV61 @ ( powerset @ SV210 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[886]) ).
thf(1026,plain,
! [SV211: $i,SV304: $i,SV62: $i] :
( ( ( ~ ( subset @ SV62 @ SV304 ) )
= $true )
| ( ( subset @ SV62 @ ( setadjoin @ SV211 @ SV304 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[887]) ).
thf(1027,plain,
! [SV213: $i,SV64: $i] :
( ( ( subset @ SV64 @ SV213 )
= $false )
| ( ( ! [SY1452: $i] :
( ~ ( subset @ SV213 @ SY1452 )
| ( subset @ SV64 @ SY1452 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[888]) ).
thf(1028,plain,
! [SV214: $i,SV66: $i,SV305: $i] :
( ( ( ~ ( in @ SV305 @ SV66 ) )
= $true )
| ( ( ( in @ SV305 @ SV214 )
| ( SV66 != SV214 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[889]) ).
thf(1029,plain,
! [SV215: $i,SV67: $i] :
( ( ( SV67 = SV215 )
= $false )
| ( ( subset @ SV67 @ SV215 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[890]) ).
thf(1030,plain,
! [SV216: $i,SV68: $i,SV306: $i] :
( ( ( ~ ( in @ SV306 @ SV68 ) )
= $true )
| ( ( ( in @ SV306 @ SV216 )
| ~ ( subset @ SV68 @ SV216 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[891]) ).
thf(1031,plain,
! [SV217: $i,SV69: $i] :
( ( ( subset @ SV69 @ SV217 )
= $false )
| ( ( ! [SY1455: $i] :
( ( in @ SY1455 @ SV217 )
| ~ ( in @ SY1455 @ SV69 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[892]) ).
thf(1032,plain,
! [SV218: $i,SV70: $i] :
( ( ( subset @ SV70 @ SV218 )
= $false )
| ( ( ! [SY1456: $i] :
( ~ ( in @ SY1456 @ SV70 )
| ( in @ SY1456 @ SV218 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[893]) ).
thf(1033,plain,
! [SV219: $i,SV72: $i] :
( ( ( SV72 = SV219 )
= $false )
| ( ( subset @ SV72 @ SV219 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[894]) ).
thf(1034,plain,
! [SV220: $i,SV73: $i] :
( ( ( SV73 = SV220 )
= $false )
| ( ( subset @ SV220 @ SV73 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[895]) ).
thf(1035,plain,
! [SV221: $i,SV74: $i] :
( ( ( SV74 = SV221 )
= $false )
| ( ( ( setunion @ SV74 )
= ( setunion @ SV221 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[896]) ).
thf(1036,plain,
! [SV222: $i,SV75: $i] :
( ( ( SV75 = SV222 )
= $false )
| ( ( ( powerset @ SV75 )
= ( powerset @ SV222 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[897]) ).
thf(1037,plain,
! [SV223: $i,SV76: $i] :
( ( ( SV76 = SV223 )
= $false )
| ( ( ! [SY1457: $i,SY1458: $i] :
( ( SY1457 != SY1458 )
| ( ( setadjoin @ SV76 @ SY1457 )
= ( setadjoin @ SV223 @ SY1458 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[898]) ).
thf(1038,plain,
! [SV224: $i,SV77: $i] :
( ( ( SV77 = SV224 )
= $false )
| ( ( ! [SY1459: $i,SY1460: $i] :
( ( SY1459 != SY1460 )
| ~ ( in @ SY1459 @ SV77 )
| ( in @ SY1460 @ SV224 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[899]) ).
thf(1039,plain,
! [SV80: $i > $o,SV225: $i] :
( ( ( in @ SV225 @ emptyset )
= $false )
| ( ( SV80 @ SV225 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[906]) ).
thf(1040,plain,
! [SV81: $i,SV335: $i,SV226: $i > $o] :
( ( ( ~ ( SV226 @ SV335 )
| ~ ( in @ SV335 @ SV81 ) )
= $true )
| ( ( ( dsetconstr @ SV81
@ ^ [SY1462: $i] : ( SV226 @ SY1462 ) )
!= emptyset )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[907]) ).
thf(1041,plain,
! [SV229: $i,SV84: $i,SV307: $i] :
( ( ( ~ ( in @ SV307 @ ( setadjoin @ SV84 @ ( setadjoin @ SV229 @ emptyset ) ) ) )
= $true )
| ( ( ( SV307 = SV84 )
| ( SV307 = SV229 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[908]) ).
thf(1042,plain,
! [SV230: $i,SV85: $i] :
( ( ( in @ SV85 @ ( setadjoin @ SV230 @ emptyset ) )
= $false )
| ( ( in @ SV230 @ ( setadjoin @ SV85 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[909]) ).
thf(1043,plain,
! [SV231: $i,SV86: $i] :
( ( ( SV86 = SV231 )
= $false )
| ( ( in @ SV86 @ ( setadjoin @ SV231 @ emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[910]) ).
thf(1044,plain,
! [SV87: $i,SV232: $i] :
( ( ( in @ SV232 @ ( setadjoin @ SV87 @ emptyset ) )
= $false )
| ( ( SV87 = SV232 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[911]) ).
thf(1045,plain,
! [SV233: $i,SV88: $i] :
( ( ( in @ SV88 @ ( setadjoin @ SV233 @ emptyset ) )
= $false )
| ( ( SV88 = SV233 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[912]) ).
thf(1046,plain,
! [SV90: $i,SV234: $i] :
( ( ( in @ SV234 @ SV90 )
= $false )
| ( ( in @ SV234 @ ( powerset @ ( setunion @ SV90 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[913]) ).
thf(1047,plain,
! [SV91: $i,SV308: $i,SV235: $i] :
( ( ( ~ ( in @ SV235 @ SV308 ) )
= $true )
| ( ( ~ ( in @ SV308 @ SV91 )
| ( in @ SV235 @ ( setunion @ SV91 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[914]) ).
thf(1048,plain,
! [SV92: $i,SV236: $i] :
( ( ( in @ SV236 @ ( powerset @ SV92 ) )
= $false )
| ( ( ! [SY1465: $i] :
( ~ ( in @ SY1465 @ SV236 )
| ( in @ SY1465 @ SV92 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[915]) ).
thf(1049,plain,
! [SV237: $i,SV96: $i,SV309: $i] :
( ( ( ~ ( in @ SV309 @ ( setadjoin @ SV96 @ SV237 ) ) )
= $true )
| ( ( ( SV309 = SV96 )
| ( in @ SV309 @ SV237 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[916]) ).
thf(1050,plain,
! [SV97: $i,SV238: $i,SV310: $i] :
( ( ( ~ ( in @ SV310 @ SV238 ) )
= $true )
| ( ( in @ SV310 @ ( setadjoin @ SV97 @ SV238 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[917]) ).
thf(1051,plain,
! [SV99: $i,SV311: $i] :
( ( ( in @ SV311 @ SV99 )
= $false )
| ( ( SV99 != emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[918]) ).
thf(1052,plain,
! [SV240: $i > $o,SV100: $i,SV312: $i] :
( ( ( ~ ( in @ SV312 @ SV100 ) )
= $true )
| ( ( ~ ( SV240 @ SV312 )
| ( ( dsetconstr @ SV100
@ ^ [SY1469: $i] : ( SV240 @ SY1469 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[919]) ).
thf(1053,plain,
! [SV241: $i,SV336: $o] :
( ( SV336 = $true )
| ( ( in @ SV241 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[920]) ).
thf(1054,plain,
! [SV241: $i] :
( ( $true = $true )
| ( ( in @ SV241 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[920]) ).
thf(1055,plain,
! [SV241: $i] :
( ( $false = $true )
| ( ( in @ SV241 @ emptyset )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[920]) ).
thf(1056,plain,
! [SV106: $o,SV313: $i] :
( ( ( in @ SV313 @ ( prop2set @ SV106 ) )
= $false )
| ( SV106 = $true ) ),
inference(extcnf_not_pos,[status(thm)],[921]) ).
thf(1057,plain,
! [SV314: $i] :
( ( ( in @ SV314 @ ( prop2set @ $true ) )
= $false )
| ( $true = $true ) ),
inference(extcnf_not_pos,[status(thm)],[922]) ).
thf(1058,plain,
! [SV315: $i] :
( ( ( in @ SV315 @ ( prop2set @ $false ) )
= $false )
| ( $false = $true ) ),
inference(extcnf_not_pos,[status(thm)],[923]) ).
thf(1059,plain,
! [SV242: $i > $o,SV107: $i,SV316: $i] :
( ( ( ~ ( in @ SV316
@ ( dsetconstr @ SV107
@ ^ [SY1471: $i] : ( SV242 @ SY1471 ) ) ) )
= $true )
| ( ( SV242 @ SV316 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[924]) ).
thf(1060,plain,
! [SV243: $i > $o,SV108: $i,SV317: $i] :
( ( ( ~ ( in @ SV317
@ ( dsetconstr @ SV108
@ ^ [SY1473: $i] : ( SV243 @ SY1473 ) ) ) )
= $true )
| ( ( in @ SV317 @ SV108 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[925]) ).
thf(1061,plain,
! [SV244: $i > $o,SV109: $i,SV318: $i] :
( ( ( ~ ( in @ SV318 @ SV109 ) )
= $true )
| ( ( ~ ( SV244 @ SV318 )
| ( in @ SV318
@ ( dsetconstr @ SV109
@ ^ [SY1475: $i] : ( SV244 @ SY1475 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[926]) ).
thf(1062,plain,
! [SV337: $i,SV245: $i > $o,SV112: $i] :
( ( ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
!= ( setadjoin @ SV337 @ emptyset ) )
| ~ ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) )
| ~ ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[928]) ).
thf(1063,plain,
! [SV113: $i] :
( ( ! [SY1277: $i] :
( ~ ( ~ ( in @ ( sK18_Xx @ SY1277 @ SV113 ) @ SY1277 )
| ~ ~ ( in @ ( sK18_Xx @ SY1277 @ SV113 ) @ SV113 ) )
| ! [SX2: $i] :
~ ( in @ SX2 @ SY1277 )
| ~ ( ~ ! [SY1279: $i] :
( ~ ( in @ SY1279 @ ( sK14_B @ SV113 ) )
| ! [SY1280: $i] :
( ~ ( in @ SY1280 @ SY1279 )
| ( in @ SY1280 @ ( sK16_SY1071 @ SY1277 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SY1277 @ SV113 ) @ SY1279 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SY1277 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SY1277 @ SV113 ) @ SY1277 ) )
| ~ ! [SY1281: $i] :
( ~ ( in @ SY1281 @ ( sK16_SY1071 @ SY1277 @ SV113 ) )
| ~ ( in @ SY1281 @ SY1277 ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[929]) ).
thf(1064,plain,
! [SV113: $i] :
( ( ~ ( ~ ! [SY1282: $i,SY1283: $i] :
( ~ ( in @ SY1282 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY1283 @ ( sK14_B @ SV113 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1282 )
| ( in @ SX3 @ SY1283 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1283 )
| ( in @ SX3 @ SY1282 ) ) )
| ~ ~ ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) )
| ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[930]) ).
thf(1065,plain,
! [SV338: $i] :
( ( ! [SY1564: $i] :
( ~ ( ~ ( in @ ( sK6_Xx @ SY1564 @ SV338 ) @ SY1564 )
| ~ ~ ( in @ ( sK6_Xx @ SY1564 @ SV338 ) @ SV338 ) )
| ( in @ SY1564 @ ( powerset @ SV338 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[931]) ).
thf(1066,plain,
! [SV339: $i] :
( ( ! [SY1565: $i] :
( ~ ( in @ SY1565 @ ( powerset @ SV339 ) )
| ! [SY1566: $i] :
( ~ ( in @ SY1566 @ SY1565 )
| ( in @ SY1566 @ SV339 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[932]) ).
thf(1067,plain,
! [SV246: $i > $o,SV114: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ SV114 )
| ( SV246 @ SV340 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK39_Xx @ SV246 @ SV114 ) @ SV114 )
| ~ ~ ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[933]) ).
thf(1068,plain,
! [SV247: $i > $o,SV115: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV115 )
| ( SV247 @ SV341 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK37_Xx @ SV247 @ SV115 ) @ SV115 )
| ~ ~ ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[934]) ).
thf(1069,plain,
! [SV248: $i,SV116: $i] :
( ( ( SV116 = SV248 )
= $false )
| ( ( ~ ( ~ ! [SY1481: $i,SY1482: $i] :
( ( SY1481 != SY1482 )
| ~ ( in @ SY1481 @ SV116 )
| ( in @ SY1482 @ SV248 ) )
| ~ ! [SY1483: $i,SY1484: $i] :
( ( SY1483 != SY1484 )
| ~ ( in @ SY1484 @ SV248 )
| ( in @ SY1483 @ SV116 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[935]) ).
thf(1070,plain,
( ( sK1_Xx = sK3_SY1058 )
= $false ),
inference(extcnf_not_pos,[status(thm)],[937]) ).
thf(1071,plain,
! [SV319: $i,SV117: $i > $o] :
( ( ( ~ ( ~ ( SV117 @ ( sK23_SY85 @ SV319 @ SV117 ) )
| ~ ( ( SV319
!= ( sK23_SY85 @ SV319 @ SV117 ) ) ) ) )
= $true )
| ( ( ~ ( SV117 @ SV319 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[938]) ).
thf(1072,plain,
! [SV118: $i,SV249: $i] :
( ( ( in @ SV249 @ ( setunion @ SV118 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK74_X @ SV249 @ SV118 ) @ SV118 )
| ~ ( in @ SV249 @ ( sK74_X @ SV249 @ SV118 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[939]) ).
thf(1073,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[940]) ).
thf(1074,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ( ~ ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
| ~ ( ( SV320
!= ( sK21_SY73 @ SV320 @ SV120 ) ) ) ) )
= $true )
| ( ( ~ ( SV120 @ SV320 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[941]) ).
thf(1075,plain,
! [SV321: $i,SV121: $i > $o] :
( ( ( ~ ( ~ ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
| ~ ( ( SV321
!= ( sK56_SY247 @ SV321 @ SV121 ) ) ) ) )
= $true )
| ( ( ~ ( SV121 @ SV321 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[942]) ).
thf(1076,plain,
! [SV122: $i,SV251: $i > $o] :
( ( ( ~ ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) )
| ~ ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 ) )
= $false )
| ( ( ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV122 )
| ~ ( SV251 @ SY1488 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[943]) ).
thf(1077,plain,
! [SV252: $i,SV123: $i] :
( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setadjoin @ ( sK69_SY1106 @ SV252 @ SV123 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK69_SY1106 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1078,plain,
! [SV123: $i,SV252: $i] :
( ( ~ ( in @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[944]) ).
thf(1079,plain,
! [SV124: $i,SV322: $i] :
( ( ( in @ SV322 @ SV124 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK13_B @ SV124 ) @ SV124 )
| ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK13_B @ SV124 ) )
| ~ ( in @ SY1314 @ SV124 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[945]) ).
thf(1080,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[946]) ).
thf(1081,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[947]) ).
thf(1082,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ( ~ ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
| ~ ( ( SV324
!= ( sK32_SY141 @ SV324 @ SV127 ) ) ) ) )
= $true )
| ( ( ~ ( SV127 @ SV324 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[948]) ).
thf(1083,plain,
! [SV255: $i > $o,SV128: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ SV128 )
| ( SV255 @ SV342 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK34_Xx @ SV255 @ SV128 ) @ SV128 )
| ~ ~ ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[949]) ).
thf(1084,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ( ~ ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
| ~ ( ( SV325
!= ( sK41_Xy @ SV325 @ SV129 ) ) ) ) )
= $true )
| ( ( ~ ( SV129 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[950]) ).
thf(1085,plain,
! [SV326: $i,SV130: $i > $o] :
( ( ( ~ ( ~ ( SV130 @ ( sK19_SY56 @ SV326 @ SV130 ) )
| ~ ( ( SV326
!= ( sK19_SY56 @ SV326 @ SV130 ) ) ) ) )
= $true )
| ( ( ~ ( SV130 @ SV326 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[951]) ).
thf(1086,plain,
! [SV131: $i] :
( ( ! [SY1339: $i,SY1340: $i] :
( ~ ( in @ SY1340 @ ( setadjoin @ SV131 @ SY1339 ) )
| ( SY1340 = SV131 )
| ( in @ SY1340 @ SY1339 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[952]) ).
thf(1087,plain,
! [SV131: $i] :
( ( ~ ( ~ ! [SY1341: $i,SY1342: $i] :
( ( SY1342 != SV131 )
| ( in @ SY1342 @ ( setadjoin @ SV131 @ SY1341 ) ) )
| ~ ! [SY1343: $i,SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( setadjoin @ SV131 @ SY1343 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[953]) ).
thf(1088,plain,
! [SV132: $i,SV256: $i > $o] :
( ( ( ~ ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 )
| ~ ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) ) )
= $false )
| ( ( ! [SY1503: $i] :
( ~ ( SV256 @ SY1503 )
| ~ ( in @ SY1503 @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[954]) ).
thf(1089,plain,
! [SV327: $i,SV133: $i] :
( ( ( ! [SY1555: $i] :
( ( SV133
!= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SY1555 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SY1555 @ ( setunion @ SV133 ) ) ) )
= $true )
| ( ( ~ ( in @ SV327 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[955]) ).
thf(1090,plain,
! [SV134: $i,SV257: $i] :
( ( ( ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV257 )
| ~ ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV134 ) )
= $false )
| ( ( in @ SV257 @ ( powerset @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[956]) ).
thf(1091,plain,
! [SV135: $i,SV258: $i] :
( ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false )
| ( ( ! [SY1504: $o] :
( ~ ( ~ ( in @ SV258 @ ( sK30_B @ SY1504 @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ SY1504 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SY1504 ) )
| SY1504 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[957]) ).
thf(1092,plain,
! [SV328: $i,SV136: $i > $o] :
( ( ( ~ ( ~ ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
| ~ ( ( SV328
!= ( sK47_SY223 @ SV328 @ SV136 ) ) ) ) )
= $true )
| ( ( ~ ( SV136 @ SV328 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[958]) ).
thf(1093,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
| ~ ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
| ( SV137 = SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[959]) ).
thf(1094,plain,
! [SV260: $i,SV138: $i,SV329: $i] :
( ( ( ~ ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV329
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 ) )
| ~ ( in @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ SV138 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[960]) ).
thf(1095,plain,
! [SV343: $i] :
( ( ! [SY1567: $i] :
( ! [SY1568: $i] :
( ~ ( in @ SY1567 @ SY1568 )
| ~ ( in @ SY1568 @ SV343 ) )
| ( in @ SY1567 @ ( setunion @ SV343 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[961]) ).
thf(1096,plain,
! [SV344: $i] :
( ( ! [SY1569: $i] :
( ~ ( in @ SY1569 @ ( setunion @ SV344 ) )
| ~ ( ~ ( in @ SY1569 @ ( sK7_B @ SY1569 @ SV344 ) )
| ~ ( in @ ( sK7_B @ SY1569 @ SV344 ) @ SV344 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[962]) ).
thf(1097,plain,
! [SV139: $i > $i > $o,SV261: $i] :
( ( ( ~ ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
| ~ ! [SY1506: $i] :
( ~ ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) )
| ~ ( ( SY1506
!= ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) ) ) )
| ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SY1506 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[963]) ).
thf(1098,plain,
! [SV140: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV140 )
| ~ ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV262 ) )
= $false )
| ( ( subset @ SV140 @ SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[964]) ).
thf(1099,plain,
! [SV141: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) )
| ~ ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 ) )
= $false )
| ( ( ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV141 )
| ~ ( SV263 @ SY1510 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[965]) ).
thf(1100,plain,
! [SV345: $i > $o] :
( ( ! [SY1570: $i > $o] :
( ~ ( ( ( sK54_Xx @ SY1570 @ SV345 )
!= ( sK55_SY1102 @ SY1570 @ SV345 ) )
| ~ ~ ( ~ ( ~ ( SV345 @ ( sK54_Xx @ SY1570 @ SV345 ) )
| ~ ( SY1570 @ ( sK55_SY1102 @ SY1570 @ SV345 ) ) )
| ~ ( ( SV345 @ ( sK54_Xx @ SY1570 @ SV345 ) )
| ( SY1570 @ ( sK55_SY1102 @ SY1570 @ SV345 ) ) ) ) )
| ! [SY1571: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1571 @ SY1570 @ SV345 ) )
| ~ ( ( SY1571
!= ( sK53_SY232 @ SY1571 @ SY1570 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1571 ) )
| ~ ( ~ ! [SY1572: $i] :
( ~ ( SY1570 @ SY1572 )
| ( ( sK52_SY234 @ SY1570 @ SV345 )
= SY1572 ) )
| ~ ( SY1570 @ ( sK52_SY234 @ SY1570 @ SV345 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[966]) ).
thf(1101,plain,
! [SV346: $i > $o] :
( ( ! [SY1573: $i > $o] :
( ~ ( ( ( sK50_Xx @ SY1573 @ SV346 )
!= ( sK51_SY1100 @ SY1573 @ SV346 ) )
| ~ ~ ( ~ ( ~ ( SV346 @ ( sK50_Xx @ SY1573 @ SV346 ) )
| ~ ( SY1573 @ ( sK51_SY1100 @ SY1573 @ SV346 ) ) )
| ~ ( ( SV346 @ ( sK50_Xx @ SY1573 @ SV346 ) )
| ( SY1573 @ ( sK51_SY1100 @ SY1573 @ SV346 ) ) ) ) )
| ! [SY1574: $i] :
( ~ ( ~ ( SY1573 @ ( sK49_SY235 @ SY1574 @ SY1573 @ SV346 ) )
| ~ ( ( SY1574
!= ( sK49_SY235 @ SY1574 @ SY1573 @ SV346 ) ) ) )
| ~ ( SY1573 @ SY1574 ) )
| ~ ( ~ ! [SY1575: $i] :
( ~ ( SV346 @ SY1575 )
| ( ( sK48_SY231 @ SY1573 @ SV346 )
= SY1575 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SY1573 @ SV346 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[967]) ).
thf(1102,plain,
! [SV264: $i > $o,SV142: $i,SV330: $i] :
( ( ( ~ ( in @ SV330 @ SV142 ) )
= $true )
| ( ( ~ ( SV264 @ SV330 )
| ~ ( ~ ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) )
| ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[968]) ).
thf(1103,plain,
! [SV143: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV143 )
| ~ ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV265 ) )
= $false )
| ( ( subset @ SV143 @ SV265 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[969]) ).
thf(1104,plain,
! [SV144: $i] :
( ( ! [SY1373: $i > $o,SY1374: $i] :
( ~ ( in @ SY1374 @ SV144 )
| ~ ( SY1373 @ SY1374 )
| ( in @ SY1374
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1373 @ SX3 ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[970]) ).
thf(1105,plain,
! [SV144: $i] :
( ( ! [SY1376: $i > $o,SY1377: $i] :
( ~ ( in @ SY1377 @ SV144 )
| ~ ( in @ SY1377
@ ( dsetconstr @ SV144
@ ^ [SX3: $i] : ( SY1376 @ SX3 ) ) )
| ( SY1376 @ SY1377 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[971]) ).
thf(1106,plain,
! [SV145: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_Xx @ SV145 ) @ omega )
| ~ ( in @ ( sK8_Xx @ SV145 ) @ SV145 ) )
| ~ ~ ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[972]) ).
thf(1107,plain,
! [SV266: $i,SV146: $i,SV331: $i] :
( ( ( ~ ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ( SV331
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) )
| ~ ( in @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[973]) ).
thf(1108,plain,
! [SV267: $i,SV147: $i] :
( ( ~ ~ ( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setadjoin @ ( sK67_SY1105 @ SV267 @ SV147 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK67_SY1105 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1109,plain,
! [SV147: $i,SV267: $i] :
( ( ~ ( in @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[974]) ).
thf(1110,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ~ ( ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1515 @ SV148 )
| ( in @ SY1515 @ SV268 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1517 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1111,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ~ ( ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ ( binunion @ SV148 @ SV268 ) )
| ! [SY1520: $o] :
( ~ SY1520
| ( in @ SY1519 @ SV268 )
| SY1520 ) )
| ~ ( ! [SY1521: $i] :
~ ( in @ SY1521 @ ( binunion @ SV148 @ SV268 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[975]) ).
thf(1112,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( SV149 @ SV332 )
= $false )
| ( ( ~ ( ~ ( SV149 @ ( sK43_Xx @ SV149 ) )
| ~ ~ ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) ) )
| ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[976]) ).
thf(1113,plain,
! [SV150: $i,SV269: $i] :
( ( ( ~ ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV150 )
| ~ ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV269 ) )
= $false )
| ( ( ( binintersect @ SV150 @ SV269 )
= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[977]) ).
thf(1114,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) ) )
= $true )
| ( ( ~ ( ~ ~ ( ~ ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[978]) ).
thf(1115,plain,
! [SV271: $i,SV152: $i] :
( ( ( SV152 = SV271 )
= $false )
| ( ( ! [SY1528: $i > $o,SY1529: $i > $o] :
( ~ ( ~ ( in @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) @ SV152 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SY1528 @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ~ ( SY1529 @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) ) )
| ~ ( ( SY1528 @ ( sK61_Xx @ SY1529 @ SY1528 @ SV271 @ SV152 ) )
| ( SY1529 @ ( sK62_SY1104 @ SY1529 @ SY1528 @ SV271 @ SV152 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV152
@ ^ [SX4: $i] : ( SY1528 @ SX4 ) )
= ( dsetconstr @ SV271
@ ^ [SX4: $i] : ( SY1529 @ SX4 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[979]) ).
thf(1116,plain,
! [SV153: $i > $o,SV272: $i > $o] :
( ( ( ( ( sK59_Xx @ SV272 @ SV153 )
!= ( sK60_SY1103 @ SV272 @ SV153 ) )
| ~ ~ ( ~ ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
| ~ ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) ) ) )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[980]) ).
thf(1117,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ~ ( ( ( sK46_Xy @ SV334 @ SV154 )
!= SV334 )
| ~ ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) )
| ~ ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
| ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[981]) ).
thf(1118,plain,
! [SV155: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) )
| ~ ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) ) )
= $false )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[982]) ).
thf(1119,plain,
! [SV156: $i,SV1: $i,SV274: $i] :
( ( ( in @ SV274 @ ( cartprod @ SV1 @ SV156 ) )
= $false )
| ( ( in @ ( kfst @ SV274 ) @ SV1 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[983]) ).
thf(1120,plain,
! [SV275: $i,SV3: $i] :
( ( ( SV3
= ( setadjoin @ SV275 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV275 @ SV3 ) )
= $true )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[984]) ).
thf(1121,plain,
! [SV158: $i,SV4: $i,SV276: $i] :
( ( ( in @ ( setadjoin @ SV276 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV4 @ ( setadjoin @ SV158 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( SV4 = SV276 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[985]) ).
thf(1122,plain,
! [SV160: $i,SV9: $i,SV277: $i] :
( ( ( in @ SV277 @ SV9 )
= $false )
| ( ( ! [SY1536: $i] :
( ~ ( in @ SY1536 @ SV160 )
| ( in @ ( setadjoin @ ( setadjoin @ SV277 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV277 @ ( setadjoin @ SY1536 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV9 @ SV160 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[987]) ).
thf(1123,plain,
! [SV161: $i,SV10: $i,SV278: $i] :
( ( ( in @ SV278 @ SV10 )
= $false )
| ( ( ! [SY1537: $i] :
( ~ ( in @ SY1537 @ SV161 )
| ( in @ ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SY1537 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV10 @ SV161 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[988]) ).
thf(1124,plain,
! [SV162: $i,SV11: $i,SV279: $i] :
( ( ( in @ SV279 @ SV11 )
= $false )
| ( ( ! [SY1538: $i] :
( ~ ( in @ SY1538 @ SV162 )
| ( in @ ( setadjoin @ ( setadjoin @ SV279 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV279 @ ( setadjoin @ SY1538 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV11 @ SV162 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[989]) ).
thf(1125,plain,
! [SV163: $i,SV12: $i,SV280: $i] :
( ( ( in @ SV280 @ SV12 )
= $false )
| ( ( ! [SY1539: $i] :
( ~ ( in @ SY1539 @ SV163 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV280 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV280 @ ( setadjoin @ SY1539 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV12 @ SV163 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[990]) ).
thf(1126,plain,
! [SV164: $i,SV13: $i,SV281: $i] :
( ( ( in @ SV281 @ SV13 )
= $false )
| ( ( ! [SY1540: $i] :
( ~ ( in @ SY1540 @ SV164 )
| ( in @ ( setadjoin @ SV281 @ ( setadjoin @ SY1540 @ emptyset ) ) @ ( powerset @ ( binunion @ SV13 @ SV164 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[991]) ).
thf(1127,plain,
! [SV165: $i,SV14: $i,SV282: $i] :
( ( ( in @ SV282 @ SV14 )
= $false )
| ( ( ! [SY1541: $i] :
( ~ ( in @ SY1541 @ SV165 )
| ( subset @ ( setadjoin @ SV282 @ ( setadjoin @ SY1541 @ emptyset ) ) @ ( binunion @ SV14 @ SV165 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[992]) ).
thf(1128,plain,
! [SV166: $i,SV15: $i,SV283: $i] :
( ( ( in @ SV283 @ ( setadjoin @ SV15 @ ( setadjoin @ SV166 @ emptyset ) ) )
= $false )
| ( ( ( SV283 = SV15 )
| ( SV283 = SV166 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[993]) ).
thf(1129,plain,
! [SV167: $i,SV16: $i,SV284: $i] :
( ( ( in @ SV284 @ SV16 )
= $false )
| ( ( in @ ( setadjoin @ SV284 @ emptyset ) @ ( powerset @ ( binunion @ SV16 @ SV167 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[994]) ).
thf(1130,plain,
! [SV22: $i,SV173: $i,SV285: $i] :
( ( ( in @ SV285 @ SV173 )
= $true )
| ( ( ~ ( in @ SV285 @ ( symdiff @ SV22 @ SV173 ) ) )
= $true )
| ( ( in @ SV285 @ SV22 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[997]) ).
thf(1131,plain,
! [SV174: $i,SV23: $i,SV286: $i] :
( ( ( in @ SV286 @ SV23 )
= $false )
| ( ( ~ ( in @ SV286 @ SV174 )
| ~ ( in @ SV286 @ ( symdiff @ SV23 @ SV174 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[998]) ).
thf(1132,plain,
! [SV24: $i,SV175: $i,SV287: $i] :
( ( ( ~ ( in @ SV287 @ SV175 ) )
= $true )
| ( ( in @ SV287 @ ( symdiff @ SV24 @ SV175 ) )
= $true )
| ( ( in @ SV287 @ SV24 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[999]) ).
thf(1133,plain,
! [SV176: $i,SV25: $i,SV288: $i] :
( ( ( in @ SV288 @ SV25 )
= $false )
| ( ( ( in @ SV288 @ SV176 )
| ( in @ SV288 @ ( symdiff @ SV25 @ SV176 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1000]) ).
thf(1134,plain,
! [SV28: $i,SV179: $i,SV289: $i] :
( ( ( in @ SV289 @ SV179 )
= $false )
| ( ( ~ ( in @ SV289 @ ( setminus @ SV28 @ SV179 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1002]) ).
thf(1135,plain,
! [SV180: $i,SV29: $i,SV290: $i] :
( ( ( in @ SV290 @ ( setminus @ SV29 @ SV180 ) )
= $false )
| ( ( in @ SV290 @ SV29 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1003]) ).
thf(1136,plain,
! [SV30: $i,SV181: $i,SV291: $i] :
( ( ( in @ SV291 @ SV181 )
= $true )
| ( ( ~ ( in @ SV291 @ SV30 ) )
= $true )
| ( ( in @ SV291 @ ( setminus @ SV30 @ SV181 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1004]) ).
thf(1137,plain,
! [SV182: $i,SV31: $i,SV292: $i] :
( ( ( ~ ( in @ SV292 @ SV31 ) )
= $true )
| ( ( in @ SV292 @ SV182 )
= $true )
| ( ( in @ SV292 @ ( setminus @ SV31 @ SV182 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1005]) ).
thf(1138,plain,
! [SV184: $i,SV33: $i,SV293: $i] :
( ( ( in @ SV293 @ ( setminus @ SV33 @ SV184 ) )
= $false )
| ( ( ~ ( in @ SV293 @ SV184 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1007]) ).
thf(1139,plain,
! [SV185: $i,SV34: $i,SV294: $i] :
( ( ( in @ SV294 @ ( setminus @ SV34 @ SV185 ) )
= $false )
| ( ( in @ SV294 @ SV34 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1008]) ).
thf(1140,plain,
! [SV186: $i,SV35: $i,SV295: $i] :
( ( ( in @ SV295 @ SV35 )
= $false )
| ( ( ( in @ SV295 @ SV186 )
| ( in @ SV295 @ ( setminus @ SV35 @ SV186 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1009]) ).
thf(1141,plain,
! [SV191: $i,SV40: $i,SV297: $i] :
( ( ( in @ SV297 @ ( binintersect @ SV40 @ SV191 ) )
= $false )
| ( ( in @ SV297 @ SV191 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1012]) ).
thf(1142,plain,
! [SV195: $i,SV44: $i,SV298: $i] :
( ( ( in @ SV298 @ ( binintersect @ SV44 @ SV195 ) )
= $false )
| ( ( in @ SV298 @ SV44 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1015]) ).
thf(1143,plain,
! [SV196: $i,SV45: $i,SV299: $i] :
( ( ( subset @ SV299 @ SV45 )
= $false )
| ( ( ~ ( subset @ SV299 @ SV196 )
| ( subset @ SV299 @ ( binintersect @ SV45 @ SV196 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1016]) ).
thf(1144,plain,
! [SV197: $i,SV46: $i,SV300: $i] :
( ( ( in @ SV300 @ SV46 )
= $false )
| ( ( ~ ( in @ SV300 @ SV197 )
| ( in @ SV300 @ ( binintersect @ SV46 @ SV197 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1017]) ).
thf(1145,plain,
! [SV200: $i,SV49: $i,SV301: $i] :
( ( ( in @ SV301 @ ( binunion @ SV49 @ SV200 ) )
= $false )
| ( ( ( in @ SV301 @ SV49 )
| ( in @ SV301 @ SV200 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1018]) ).
thf(1146,plain,
! [SV50: $i,SV201: $i,SV302: $i] :
( ( ( in @ SV302 @ SV201 )
= $false )
| ( ( in @ SV302 @ ( binunion @ SV50 @ SV201 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1019]) ).
thf(1147,plain,
! [SV203: $i,SV52: $i,SV303: $i] :
( ( ( in @ SV303 @ SV52 )
= $false )
| ( ( in @ SV303 @ ( binunion @ SV52 @ SV203 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1020]) ).
thf(1148,plain,
! [SV60: $i,SV209: $i] :
( ( ( ~ ( subset @ SV209 @ SV60 ) )
= $true )
| ( ( SV60 = SV209 )
= $true )
| ( ( subset @ SV60 @ SV209 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1024]) ).
thf(1149,plain,
! [SV211: $i,SV304: $i,SV62: $i] :
( ( ( subset @ SV62 @ SV304 )
= $false )
| ( ( subset @ SV62 @ ( setadjoin @ SV211 @ SV304 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1026]) ).
thf(1150,plain,
! [SV64: $i,SV347: $i,SV213: $i] :
( ( ( ~ ( subset @ SV213 @ SV347 )
| ( subset @ SV64 @ SV347 ) )
= $true )
| ( ( subset @ SV64 @ SV213 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1027]) ).
thf(1151,plain,
! [SV214: $i,SV66: $i,SV305: $i] :
( ( ( in @ SV305 @ SV66 )
= $false )
| ( ( ( in @ SV305 @ SV214 )
| ( SV66 != SV214 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1028]) ).
thf(1152,plain,
! [SV216: $i,SV68: $i,SV306: $i] :
( ( ( in @ SV306 @ SV68 )
= $false )
| ( ( ( in @ SV306 @ SV216 )
| ~ ( subset @ SV68 @ SV216 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1030]) ).
thf(1153,plain,
! [SV69: $i,SV217: $i,SV348: $i] :
( ( ( ( in @ SV348 @ SV217 )
| ~ ( in @ SV348 @ SV69 ) )
= $true )
| ( ( subset @ SV69 @ SV217 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1031]) ).
thf(1154,plain,
! [SV218: $i,SV70: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ SV70 )
| ( in @ SV349 @ SV218 ) )
= $true )
| ( ( subset @ SV70 @ SV218 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1032]) ).
thf(1155,plain,
! [SV223: $i,SV76: $i,SV350: $i] :
( ( ( ! [SY1576: $i] :
( ( SV350 != SY1576 )
| ( ( setadjoin @ SV76 @ SV350 )
= ( setadjoin @ SV223 @ SY1576 ) ) ) )
= $true )
| ( ( SV76 = SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1037]) ).
thf(1156,plain,
! [SV224: $i,SV77: $i,SV351: $i] :
( ( ( ! [SY1577: $i] :
( ( SV351 != SY1577 )
| ~ ( in @ SV351 @ SV77 )
| ( in @ SY1577 @ SV224 ) ) )
= $true )
| ( ( SV77 = SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1038]) ).
thf(1157,plain,
! [SV81: $i,SV335: $i,SV226: $i > $o] :
( ( ( ~ ( SV226 @ SV335 ) )
= $true )
| ( ( ~ ( in @ SV335 @ SV81 ) )
= $true )
| ( ( ( dsetconstr @ SV81
@ ^ [SY1462: $i] : ( SV226 @ SY1462 ) )
!= emptyset )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1040]) ).
thf(1158,plain,
! [SV229: $i,SV84: $i,SV307: $i] :
( ( ( in @ SV307 @ ( setadjoin @ SV84 @ ( setadjoin @ SV229 @ emptyset ) ) )
= $false )
| ( ( ( SV307 = SV84 )
| ( SV307 = SV229 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1041]) ).
thf(1159,plain,
! [SV91: $i,SV308: $i,SV235: $i] :
( ( ( in @ SV235 @ SV308 )
= $false )
| ( ( ~ ( in @ SV308 @ SV91 )
| ( in @ SV235 @ ( setunion @ SV91 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1047]) ).
thf(1160,plain,
! [SV92: $i,SV236: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ SV236 )
| ( in @ SV352 @ SV92 ) )
= $true )
| ( ( in @ SV236 @ ( powerset @ SV92 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1048]) ).
thf(1161,plain,
! [SV237: $i,SV96: $i,SV309: $i] :
( ( ( in @ SV309 @ ( setadjoin @ SV96 @ SV237 ) )
= $false )
| ( ( ( SV309 = SV96 )
| ( in @ SV309 @ SV237 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1049]) ).
thf(1162,plain,
! [SV97: $i,SV238: $i,SV310: $i] :
( ( ( in @ SV310 @ SV238 )
= $false )
| ( ( in @ SV310 @ ( setadjoin @ SV97 @ SV238 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1050]) ).
thf(1163,plain,
! [SV311: $i,SV99: $i] :
( ( ( SV99 = emptyset )
= $false )
| ( ( in @ SV311 @ SV99 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1051]) ).
thf(1164,plain,
! [SV240: $i > $o,SV100: $i,SV312: $i] :
( ( ( in @ SV312 @ SV100 )
= $false )
| ( ( ~ ( SV240 @ SV312 )
| ( ( dsetconstr @ SV100
@ ^ [SY1469: $i] : ( SV240 @ SY1469 ) )
!= emptyset ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1052]) ).
thf(1165,plain,
! [SV242: $i > $o,SV107: $i,SV316: $i] :
( ( ( in @ SV316
@ ( dsetconstr @ SV107
@ ^ [SY1471: $i] : ( SV242 @ SY1471 ) ) )
= $false )
| ( ( SV242 @ SV316 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1059]) ).
thf(1166,plain,
! [SV243: $i > $o,SV108: $i,SV317: $i] :
( ( ( in @ SV317
@ ( dsetconstr @ SV108
@ ^ [SY1473: $i] : ( SV243 @ SY1473 ) ) )
= $false )
| ( ( in @ SV317 @ SV108 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1060]) ).
thf(1167,plain,
! [SV244: $i > $o,SV109: $i,SV318: $i] :
( ( ( in @ SV318 @ SV109 )
= $false )
| ( ( ~ ( SV244 @ SV318 )
| ( in @ SV318
@ ( dsetconstr @ SV109
@ ^ [SY1475: $i] : ( SV244 @ SY1475 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1061]) ).
thf(1168,plain,
! [SV337: $i,SV245: $i > $o,SV112: $i] :
( ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
!= ( setadjoin @ SV337 @ emptyset ) )
= $true )
| ( ( ~ ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) )
| ~ ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1062]) ).
thf(1169,plain,
! [SV113: $i,SV353: $i] :
( ( ~ ( ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
| ~ ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 ) )
| ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 )
| ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1063]) ).
thf(1170,plain,
! [SV113: $i] :
( ( ~ ! [SY1282: $i,SY1283: $i] :
( ~ ( in @ SY1282 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY1283 @ ( sK14_B @ SV113 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1282 )
| ( in @ SX3 @ SY1283 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1283 )
| ( in @ SX3 @ SY1282 ) ) )
| ~ ~ ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) )
| ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1064]) ).
thf(1171,plain,
! [SV338: $i,SV354: $i] :
( ( ~ ( ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV354 )
| ~ ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV338 ) )
| ( in @ SV354 @ ( powerset @ SV338 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1065]) ).
thf(1172,plain,
! [SV339: $i,SV355: $i] :
( ( ~ ( in @ SV355 @ ( powerset @ SV339 ) )
| ! [SY1582: $i] :
( ~ ( in @ SY1582 @ SV355 )
| ( in @ SY1582 @ SV339 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1066]) ).
thf(1173,plain,
! [SV246: $i > $o,SV114: $i,SV340: $i] :
( ( ( ~ ( in @ SV340 @ SV114 ) )
= $true )
| ( ( SV246 @ SV340 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK39_Xx @ SV246 @ SV114 ) @ SV114 )
| ~ ~ ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1067]) ).
thf(1174,plain,
! [SV247: $i > $o,SV115: $i,SV341: $i] :
( ( ( ~ ( in @ SV341 @ SV115 ) )
= $true )
| ( ( SV247 @ SV341 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK37_Xx @ SV247 @ SV115 ) @ SV115 )
| ~ ~ ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1068]) ).
thf(1175,plain,
! [SV248: $i,SV116: $i] :
( ( ( ~ ! [SY1481: $i,SY1482: $i] :
( ( SY1481 != SY1482 )
| ~ ( in @ SY1481 @ SV116 )
| ( in @ SY1482 @ SV248 ) )
| ~ ! [SY1483: $i,SY1484: $i] :
( ( SY1483 != SY1484 )
| ~ ( in @ SY1484 @ SV248 )
| ( in @ SY1483 @ SV116 ) ) )
= $false )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1069]) ).
thf(1176,plain,
! [SV319: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ ( sK23_SY85 @ SV319 @ SV117 ) )
| ~ ( ( SV319
!= ( sK23_SY85 @ SV319 @ SV117 ) ) ) )
= $false )
| ( ( ~ ( SV117 @ SV319 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1071]) ).
thf(1177,plain,
! [SV118: $i,SV249: $i] :
( ( ( ~ ( in @ ( sK74_X @ SV249 @ SV118 ) @ SV118 )
| ~ ( in @ SV249 @ ( sK74_X @ SV249 @ SV118 ) ) )
= $false )
| ( ( in @ SV249 @ ( setunion @ SV118 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1072]) ).
thf(1178,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1179,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1073]) ).
thf(1180,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
| ~ ( ( SV320
!= ( sK21_SY73 @ SV320 @ SV120 ) ) ) )
= $false )
| ( ( ~ ( SV120 @ SV320 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1074]) ).
thf(1181,plain,
! [SV321: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
| ~ ( ( SV321
!= ( sK56_SY247 @ SV321 @ SV121 ) ) ) )
= $false )
| ( ( ~ ( SV121 @ SV321 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1075]) ).
thf(1182,plain,
! [SV122: $i,SV251: $i > $o] :
( ( ( ~ ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) ) )
= $false )
| ( ( ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV122 )
| ~ ( SV251 @ SY1488 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1183,plain,
! [SV122: $i,SV251: $i > $o] :
( ( ( ~ ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 ) )
= $false )
| ( ( ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV122 )
| ~ ( SV251 @ SY1488 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1076]) ).
thf(1184,plain,
! [SV252: $i,SV123: $i] :
( ( ~ ( ( ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setadjoin @ ( sK69_SY1106 @ SV252 @ SV123 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK69_SY1106 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1077]) ).
thf(1185,plain,
! [SV123: $i,SV252: $i] :
( ( in @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1078]) ).
thf(1186,plain,
! [SV322: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK13_B @ SV124 ) @ SV124 )
| ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK13_B @ SV124 ) )
| ~ ( in @ SY1314 @ SV124 ) ) )
= $false )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1079]) ).
thf(1187,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1080]) ).
thf(1188,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1080]) ).
thf(1189,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1081]) ).
thf(1190,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
| ~ ( ( SV324
!= ( sK32_SY141 @ SV324 @ SV127 ) ) ) )
= $false )
| ( ( ~ ( SV127 @ SV324 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1082]) ).
thf(1191,plain,
! [SV255: $i > $o,SV128: $i,SV342: $i] :
( ( ( ~ ( in @ SV342 @ SV128 ) )
= $true )
| ( ( SV255 @ SV342 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK34_Xx @ SV255 @ SV128 ) @ SV128 )
| ~ ~ ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1083]) ).
thf(1192,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
| ~ ( ( SV325
!= ( sK41_Xy @ SV325 @ SV129 ) ) ) )
= $false )
| ( ( ~ ( SV129 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1084]) ).
thf(1193,plain,
! [SV326: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK19_SY56 @ SV326 @ SV130 ) )
| ~ ( ( SV326
!= ( sK19_SY56 @ SV326 @ SV130 ) ) ) )
= $false )
| ( ( ~ ( SV130 @ SV326 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1085]) ).
thf(1194,plain,
! [SV356: $i,SV131: $i] :
( ( ! [SY1583: $i] :
( ~ ( in @ SY1583 @ ( setadjoin @ SV131 @ SV356 ) )
| ( SY1583 = SV131 )
| ( in @ SY1583 @ SV356 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1086]) ).
thf(1195,plain,
! [SV131: $i] :
( ( ~ ! [SY1341: $i,SY1342: $i] :
( ( SY1342 != SV131 )
| ( in @ SY1342 @ ( setadjoin @ SV131 @ SY1341 ) ) )
| ~ ! [SY1343: $i,SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( setadjoin @ SV131 @ SY1343 ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1087]) ).
thf(1196,plain,
! [SV132: $i,SV256: $i > $o] :
( ( ( ~ ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 ) )
= $false )
| ( ( ! [SY1503: $i] :
( ~ ( SV256 @ SY1503 )
| ~ ( in @ SY1503 @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1088]) ).
thf(1197,plain,
! [SV132: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) ) )
= $false )
| ( ( ! [SY1503: $i] :
( ~ ( SV256 @ SY1503 )
| ~ ( in @ SY1503 @ SV132 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1088]) ).
thf(1198,plain,
! [SV357: $i,SV327: $i,SV133: $i] :
( ( ( ( SV133
!= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ SV357 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( in @ SV327 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1089]) ).
thf(1199,plain,
! [SV134: $i,SV257: $i] :
( ( ( ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV257 ) )
= $false )
| ( ( in @ SV257 @ ( powerset @ SV134 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1200,plain,
! [SV134: $i,SV257: $i] :
( ( ( ~ ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV134 ) )
= $false )
| ( ( in @ SV257 @ ( powerset @ SV134 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1090]) ).
thf(1201,plain,
! [SV135: $i,SV358: $o,SV258: $i] :
( ( ( ~ ( ~ ( in @ SV258 @ ( sK30_B @ SV358 @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ SV358 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SV358 ) )
| SV358 )
= $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1091]) ).
thf(1202,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( ~ ( in @ SV258 @ ( sK30_B @ $true @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ $true @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $true ) )
| $true )
= $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1091]) ).
thf(1203,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( ~ ( in @ SV258 @ ( sK30_B @ $false @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ $false @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $false ) )
| $false )
= $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1091]) ).
thf(1204,plain,
! [SV328: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
| ~ ( ( SV328
!= ( sK47_SY223 @ SV328 @ SV136 ) ) ) )
= $false )
| ( ( ~ ( SV136 @ SV328 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1092]) ).
thf(1205,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
| ( SV137 = SV259 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1206,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 ) )
= $false )
| ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
| ( SV137 = SV259 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1093]) ).
thf(1207,plain,
! [SV260: $i,SV138: $i,SV329: $i] :
( ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV329
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 ) )
| ~ ( in @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ SV138 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1094]) ).
thf(1208,plain,
! [SV343: $i,SV359: $i] :
( ( ! [SY1584: $i] :
( ~ ( in @ SV359 @ SY1584 )
| ~ ( in @ SY1584 @ SV343 ) )
| ( in @ SV359 @ ( setunion @ SV343 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1095]) ).
thf(1209,plain,
! [SV344: $i,SV360: $i] :
( ( ~ ( in @ SV360 @ ( setunion @ SV344 ) )
| ~ ( ~ ( in @ SV360 @ ( sK7_B @ SV360 @ SV344 ) )
| ~ ( in @ ( sK7_B @ SV360 @ SV344 ) @ SV344 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1096]) ).
thf(1210,plain,
! [SV139: $i > $i > $o,SV261: $i] :
( ( ( ~ ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 ) )
= $false )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1211,plain,
! [SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ! [SY1506: $i] :
( ~ ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) )
| ~ ( ( SY1506
!= ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) ) ) )
| ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SY1506 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1097]) ).
thf(1212,plain,
! [SV140: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV140 ) )
= $false )
| ( ( subset @ SV140 @ SV262 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1213,plain,
! [SV140: $i,SV262: $i] :
( ( ( ~ ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV262 ) )
= $false )
| ( ( subset @ SV140 @ SV262 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1098]) ).
thf(1214,plain,
! [SV141: $i,SV263: $i > $o] :
( ( ( ~ ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) ) )
= $false )
| ( ( ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV141 )
| ~ ( SV263 @ SY1510 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1215,plain,
! [SV141: $i,SV263: $i > $o] :
( ( ( ~ ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 ) )
= $false )
| ( ( ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV141 )
| ~ ( SV263 @ SY1510 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1099]) ).
thf(1216,plain,
! [SV345: $i > $o,SV361: $i > $o] :
( ( ~ ( ( ( sK54_Xx @ SV361 @ SV345 )
!= ( sK55_SY1102 @ SV361 @ SV345 ) )
| ~ ~ ( ~ ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
| ~ ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) ) ) )
| ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1100]) ).
thf(1217,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ~ ( ( ( sK50_Xx @ SV362 @ SV346 )
!= ( sK51_SY1100 @ SV362 @ SV346 ) )
| ~ ~ ( ~ ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
| ~ ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) ) ) )
| ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1101]) ).
thf(1218,plain,
! [SV264: $i > $o,SV142: $i,SV330: $i] :
( ( ( in @ SV330 @ SV142 )
= $false )
| ( ( ~ ( SV264 @ SV330 )
| ~ ( ~ ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) )
| ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1102]) ).
thf(1219,plain,
! [SV143: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV143 ) )
= $false )
| ( ( subset @ SV143 @ SV265 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1220,plain,
! [SV143: $i,SV265: $i] :
( ( ( ~ ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV265 ) )
= $false )
| ( ( subset @ SV143 @ SV265 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1103]) ).
thf(1221,plain,
! [SV363: $i > $o,SV144: $i] :
( ( ! [SY1589: $i] :
( ~ ( in @ SY1589 @ SV144 )
| ~ ( SV363 @ SY1589 )
| ( in @ SY1589
@ ( dsetconstr @ SV144
@ ^ [SY1590: $i] : ( SV363 @ SY1590 ) ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1104]) ).
thf(1222,plain,
! [SV364: $i > $o,SV144: $i] :
( ( ! [SY1591: $i] :
( ~ ( in @ SY1591 @ SV144 )
| ~ ( in @ SY1591
@ ( dsetconstr @ SV144
@ ^ [SY1592: $i] : ( SV364 @ SY1592 ) ) )
| ( SV364 @ SY1591 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1105]) ).
thf(1223,plain,
! [SV145: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK8_Xx @ SV145 ) @ omega )
| ~ ( in @ ( sK8_Xx @ SV145 ) @ SV145 ) ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1224,plain,
! [SV145: $i] :
( ( ( ~ ~ ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1106]) ).
thf(1225,plain,
! [SV266: $i,SV146: $i,SV331: $i] :
( ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false )
| ( ( ~ ( ~ ~ ( ( SV331
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) )
| ~ ( in @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1107]) ).
thf(1226,plain,
! [SV267: $i,SV147: $i] :
( ( ~ ( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setadjoin @ ( sK67_SY1105 @ SV267 @ SV147 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK67_SY1105 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1108]) ).
thf(1227,plain,
! [SV147: $i,SV267: $i] :
( ( in @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1109]) ).
thf(1228,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ( ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1515 @ SV148 )
| ( in @ SY1515 @ SV268 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1517 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1110]) ).
thf(1229,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ( ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ ( binunion @ SV148 @ SV268 ) )
| ! [SY1520: $o] :
( ~ SY1520
| ( in @ SY1519 @ SV268 )
| SY1520 ) )
| ~ ( ! [SY1521: $i] :
~ ( in @ SY1521 @ ( binunion @ SV148 @ SV268 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1111]) ).
thf(1230,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( ~ ( SV149 @ ( sK43_Xx @ SV149 ) )
| ~ ~ ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1112]) ).
thf(1231,plain,
! [SV150: $i,SV269: $i] :
( ( ( ~ ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV150 ) )
= $false )
| ( ( ( binintersect @ SV150 @ SV269 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1232,plain,
! [SV150: $i,SV269: $i] :
( ( ( ~ ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV269 ) )
= $false )
| ( ( ( binintersect @ SV150 @ SV269 )
= emptyset )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1113]) ).
thf(1233,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false )
| ( ( ~ ( ~ ~ ( ~ ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1114]) ).
thf(1234,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o] :
( ( ( ! [SY1593: $i > $o] :
( ~ ( ~ ( in @ ( sK61_Xx @ SY1593 @ SV365 @ SV271 @ SV152 ) @ SV152 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SY1593 @ SV365 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SY1593 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SY1593 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SY1593 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SY1593 @ ( sK62_SY1104 @ SY1593 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SY1593 @ SV365 @ SV271 @ SV152 ) )
| ( SY1593 @ ( sK62_SY1104 @ SY1593 @ SV365 @ SV271 @ SV152 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SX4: $i] : ( SY1593 @ SX4 ) ) ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1115]) ).
thf(1235,plain,
! [SV153: $i > $o,SV272: $i > $o] :
( ( ( ( sK59_Xx @ SV272 @ SV153 )
!= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1116]) ).
thf(1236,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
| ~ ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) ) ) )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1116]) ).
thf(1237,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ~ ( ( ( sK46_Xy @ SV334 @ SV154 )
!= SV334 )
| ~ ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1238,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ~ ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
| ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1117]) ).
thf(1239,plain,
! [SV155: $i,SV273: $i] :
( ( ( ~ ( ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) ) )
= $false )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1240,plain,
! [SV155: $i,SV273: $i] :
( ( ( ~ ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) ) )
= $false )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1118]) ).
thf(1241,plain,
! [SV3: $i,SV275: $i] :
( ( ( in @ SV275 @ SV3 )
= $false )
| ( ( SV3
= ( setadjoin @ SV275 @ emptyset ) )
= $false )
| ( ( in @ ( setunion @ SV3 ) @ SV3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1120]) ).
thf(1242,plain,
! [SV9: $i,SV277: $i,SV160: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV160 )
| ( in @ ( setadjoin @ ( setadjoin @ SV277 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV277 @ ( setadjoin @ SV366 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV9 @ SV160 ) ) )
= $true )
| ( ( in @ SV277 @ SV9 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1122]) ).
thf(1243,plain,
! [SV10: $i,SV278: $i,SV161: $i,SV367: $i] :
( ( ( ~ ( in @ SV367 @ SV161 )
| ( in @ ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV367 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV10 @ SV161 ) ) ) ) )
= $true )
| ( ( in @ SV278 @ SV10 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1123]) ).
thf(1244,plain,
! [SV11: $i,SV279: $i,SV162: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV162 )
| ( in @ ( setadjoin @ ( setadjoin @ SV279 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV279 @ ( setadjoin @ SV368 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV11 @ SV162 ) ) ) ) )
= $true )
| ( ( in @ SV279 @ SV11 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1124]) ).
thf(1245,plain,
! [SV12: $i,SV280: $i,SV163: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV163 )
| ( subset @ ( setadjoin @ ( setadjoin @ SV280 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV280 @ ( setadjoin @ SV369 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV12 @ SV163 ) ) ) )
= $true )
| ( ( in @ SV280 @ SV12 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1125]) ).
thf(1246,plain,
! [SV13: $i,SV281: $i,SV164: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV164 )
| ( in @ ( setadjoin @ SV281 @ ( setadjoin @ SV370 @ emptyset ) ) @ ( powerset @ ( binunion @ SV13 @ SV164 ) ) ) )
= $true )
| ( ( in @ SV281 @ SV13 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1126]) ).
thf(1247,plain,
! [SV14: $i,SV282: $i,SV165: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV165 )
| ( subset @ ( setadjoin @ SV282 @ ( setadjoin @ SV371 @ emptyset ) ) @ ( binunion @ SV14 @ SV165 ) ) )
= $true )
| ( ( in @ SV282 @ SV14 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1127]) ).
thf(1248,plain,
! [SV166: $i,SV15: $i,SV283: $i] :
( ( ( SV283 = SV15 )
= $true )
| ( ( SV283 = SV166 )
= $true )
| ( ( in @ SV283 @ ( setadjoin @ SV15 @ ( setadjoin @ SV166 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1128]) ).
thf(1249,plain,
! [SV173: $i,SV22: $i,SV285: $i] :
( ( ( in @ SV285 @ ( symdiff @ SV22 @ SV173 ) )
= $false )
| ( ( in @ SV285 @ SV173 )
= $true )
| ( ( in @ SV285 @ SV22 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1130]) ).
thf(1250,plain,
! [SV23: $i,SV174: $i,SV286: $i] :
( ( ( ~ ( in @ SV286 @ SV174 ) )
= $true )
| ( ( ~ ( in @ SV286 @ ( symdiff @ SV23 @ SV174 ) ) )
= $true )
| ( ( in @ SV286 @ SV23 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1131]) ).
thf(1251,plain,
! [SV24: $i,SV175: $i,SV287: $i] :
( ( ( in @ SV287 @ SV175 )
= $false )
| ( ( in @ SV287 @ ( symdiff @ SV24 @ SV175 ) )
= $true )
| ( ( in @ SV287 @ SV24 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1132]) ).
thf(1252,plain,
! [SV25: $i,SV176: $i,SV288: $i] :
( ( ( in @ SV288 @ SV176 )
= $true )
| ( ( in @ SV288 @ ( symdiff @ SV25 @ SV176 ) )
= $true )
| ( ( in @ SV288 @ SV25 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1133]) ).
thf(1253,plain,
! [SV179: $i,SV28: $i,SV289: $i] :
( ( ( in @ SV289 @ ( setminus @ SV28 @ SV179 ) )
= $false )
| ( ( in @ SV289 @ SV179 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1134]) ).
thf(1254,plain,
! [SV181: $i,SV30: $i,SV291: $i] :
( ( ( in @ SV291 @ SV30 )
= $false )
| ( ( in @ SV291 @ SV181 )
= $true )
| ( ( in @ SV291 @ ( setminus @ SV30 @ SV181 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1136]) ).
thf(1255,plain,
! [SV182: $i,SV31: $i,SV292: $i] :
( ( ( in @ SV292 @ SV31 )
= $false )
| ( ( in @ SV292 @ SV182 )
= $true )
| ( ( in @ SV292 @ ( setminus @ SV31 @ SV182 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1137]) ).
thf(1256,plain,
! [SV33: $i,SV184: $i,SV293: $i] :
( ( ( in @ SV293 @ SV184 )
= $false )
| ( ( in @ SV293 @ ( setminus @ SV33 @ SV184 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1138]) ).
thf(1257,plain,
! [SV35: $i,SV186: $i,SV295: $i] :
( ( ( in @ SV295 @ SV186 )
= $true )
| ( ( in @ SV295 @ ( setminus @ SV35 @ SV186 ) )
= $true )
| ( ( in @ SV295 @ SV35 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1140]) ).
thf(1258,plain,
! [SV45: $i,SV196: $i,SV299: $i] :
( ( ( ~ ( subset @ SV299 @ SV196 ) )
= $true )
| ( ( subset @ SV299 @ ( binintersect @ SV45 @ SV196 ) )
= $true )
| ( ( subset @ SV299 @ SV45 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1143]) ).
thf(1259,plain,
! [SV46: $i,SV197: $i,SV300: $i] :
( ( ( ~ ( in @ SV300 @ SV197 ) )
= $true )
| ( ( in @ SV300 @ ( binintersect @ SV46 @ SV197 ) )
= $true )
| ( ( in @ SV300 @ SV46 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1144]) ).
thf(1260,plain,
! [SV200: $i,SV49: $i,SV301: $i] :
( ( ( in @ SV301 @ SV49 )
= $true )
| ( ( in @ SV301 @ SV200 )
= $true )
| ( ( in @ SV301 @ ( binunion @ SV49 @ SV200 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1145]) ).
thf(1261,plain,
! [SV60: $i,SV209: $i] :
( ( ( subset @ SV209 @ SV60 )
= $false )
| ( ( SV60 = SV209 )
= $true )
| ( ( subset @ SV60 @ SV209 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1148]) ).
thf(1262,plain,
! [SV64: $i,SV347: $i,SV213: $i] :
( ( ( ~ ( subset @ SV213 @ SV347 ) )
= $true )
| ( ( subset @ SV64 @ SV347 )
= $true )
| ( ( subset @ SV64 @ SV213 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1150]) ).
thf(1263,plain,
! [SV66: $i,SV214: $i,SV305: $i] :
( ( ( in @ SV305 @ SV214 )
= $true )
| ( ( SV66 != SV214 )
= $true )
| ( ( in @ SV305 @ SV66 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1151]) ).
thf(1264,plain,
! [SV68: $i,SV216: $i,SV306: $i] :
( ( ( in @ SV306 @ SV216 )
= $true )
| ( ( ~ ( subset @ SV68 @ SV216 ) )
= $true )
| ( ( in @ SV306 @ SV68 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1152]) ).
thf(1265,plain,
! [SV69: $i,SV217: $i,SV348: $i] :
( ( ( in @ SV348 @ SV217 )
= $true )
| ( ( ~ ( in @ SV348 @ SV69 ) )
= $true )
| ( ( subset @ SV69 @ SV217 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1153]) ).
thf(1266,plain,
! [SV218: $i,SV70: $i,SV349: $i] :
( ( ( ~ ( in @ SV349 @ SV70 ) )
= $true )
| ( ( in @ SV349 @ SV218 )
= $true )
| ( ( subset @ SV70 @ SV218 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1154]) ).
thf(1267,plain,
! [SV223: $i,SV76: $i,SV372: $i,SV350: $i] :
( ( ( ( SV350 != SV372 )
| ( ( setadjoin @ SV76 @ SV350 )
= ( setadjoin @ SV223 @ SV372 ) ) )
= $true )
| ( ( SV76 = SV223 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1155]) ).
thf(1268,plain,
! [SV224: $i,SV77: $i,SV373: $i,SV351: $i] :
( ( ( ( SV351 != SV373 )
| ~ ( in @ SV351 @ SV77 )
| ( in @ SV373 @ SV224 ) )
= $true )
| ( ( SV77 = SV224 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1156]) ).
thf(1269,plain,
! [SV81: $i,SV335: $i,SV226: $i > $o] :
( ( ( SV226 @ SV335 )
= $false )
| ( ( ~ ( in @ SV335 @ SV81 ) )
= $true )
| ( ( ( dsetconstr @ SV81
@ ^ [SY1462: $i] : ( SV226 @ SY1462 ) )
!= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1157]) ).
thf(1270,plain,
! [SV229: $i,SV84: $i,SV307: $i] :
( ( ( SV307 = SV84 )
= $true )
| ( ( SV307 = SV229 )
= $true )
| ( ( in @ SV307 @ ( setadjoin @ SV84 @ ( setadjoin @ SV229 @ emptyset ) ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1158]) ).
thf(1271,plain,
! [SV235: $i,SV91: $i,SV308: $i] :
( ( ( ~ ( in @ SV308 @ SV91 ) )
= $true )
| ( ( in @ SV235 @ ( setunion @ SV91 ) )
= $true )
| ( ( in @ SV235 @ SV308 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1159]) ).
thf(1272,plain,
! [SV92: $i,SV236: $i,SV352: $i] :
( ( ( ~ ( in @ SV352 @ SV236 ) )
= $true )
| ( ( in @ SV352 @ SV92 )
= $true )
| ( ( in @ SV236 @ ( powerset @ SV92 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1160]) ).
thf(1273,plain,
! [SV237: $i,SV96: $i,SV309: $i] :
( ( ( SV309 = SV96 )
= $true )
| ( ( in @ SV309 @ SV237 )
= $true )
| ( ( in @ SV309 @ ( setadjoin @ SV96 @ SV237 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1161]) ).
thf(1274,plain,
! [SV100: $i,SV312: $i,SV240: $i > $o] :
( ( ( ~ ( SV240 @ SV312 ) )
= $true )
| ( ( ( dsetconstr @ SV100
@ ^ [SY1469: $i] : ( SV240 @ SY1469 ) )
!= emptyset )
= $true )
| ( ( in @ SV312 @ SV100 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1164]) ).
thf(1275,plain,
! [SV109: $i,SV318: $i,SV244: $i > $o] :
( ( ( ~ ( SV244 @ SV318 ) )
= $true )
| ( ( in @ SV318
@ ( dsetconstr @ SV109
@ ^ [SY1475: $i] : ( SV244 @ SY1475 ) ) )
= $true )
| ( ( in @ SV318 @ SV109 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1167]) ).
thf(1276,plain,
! [SV337: $i,SV245: $i > $o,SV112: $i] :
( ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
= ( setadjoin @ SV337 @ emptyset ) )
= $false )
| ( ( ~ ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) ) )
= $true )
| ( ( ~ ( ~ ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) )
| ~ ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1168]) ).
thf(1277,plain,
! [SV113: $i,SV353: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
| ~ ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 ) )
| ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1169]) ).
thf(1278,plain,
! [SV113: $i] :
( ( ~ ! [SY1282: $i,SY1283: $i] :
( ~ ( in @ SY1282 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY1283 @ ( sK14_B @ SV113 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1282 )
| ( in @ SX3 @ SY1283 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1283 )
| ( in @ SX3 @ SY1282 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1279,plain,
! [SV113: $i] :
( ( ~ ~ ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) )
| ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1170]) ).
thf(1280,plain,
! [SV338: $i,SV354: $i] :
( ( ( ~ ( ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV354 )
| ~ ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV338 ) ) )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV338 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1171]) ).
thf(1281,plain,
! [SV339: $i,SV355: $i] :
( ( ( ~ ( in @ SV355 @ ( powerset @ SV339 ) ) )
= $true )
| ( ( ! [SY1582: $i] :
( ~ ( in @ SY1582 @ SV355 )
| ( in @ SY1582 @ SV339 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1172]) ).
thf(1282,plain,
! [SV246: $i > $o,SV114: $i,SV340: $i] :
( ( ( in @ SV340 @ SV114 )
= $false )
| ( ( SV246 @ SV340 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK39_Xx @ SV246 @ SV114 ) @ SV114 )
| ~ ~ ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1173]) ).
thf(1283,plain,
! [SV247: $i > $o,SV115: $i,SV341: $i] :
( ( ( in @ SV341 @ SV115 )
= $false )
| ( ( SV247 @ SV341 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK37_Xx @ SV247 @ SV115 ) @ SV115 )
| ~ ~ ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1174]) ).
thf(1284,plain,
! [SV248: $i,SV116: $i] :
( ( ( ~ ! [SY1481: $i,SY1482: $i] :
( ( SY1481 != SY1482 )
| ~ ( in @ SY1481 @ SV116 )
| ( in @ SY1482 @ SV248 ) ) )
= $false )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1285,plain,
! [SV116: $i,SV248: $i] :
( ( ( ~ ! [SY1483: $i,SY1484: $i] :
( ( SY1483 != SY1484 )
| ~ ( in @ SY1484 @ SV248 )
| ( in @ SY1483 @ SV116 ) ) )
= $false )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1175]) ).
thf(1286,plain,
! [SV319: $i,SV117: $i > $o] :
( ( ( ~ ( SV117 @ ( sK23_SY85 @ SV319 @ SV117 ) ) )
= $false )
| ( ( ~ ( SV117 @ SV319 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1176]) ).
thf(1287,plain,
! [SV117: $i > $o,SV319: $i] :
( ( ( ~ ( ( SV319
!= ( sK23_SY85 @ SV319 @ SV117 ) ) ) )
= $false )
| ( ( ~ ( SV117 @ SV319 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1176]) ).
thf(1288,plain,
! [SV118: $i,SV249: $i] :
( ( ( ~ ( in @ ( sK74_X @ SV249 @ SV118 ) @ SV118 ) )
= $false )
| ( ( in @ SV249 @ ( setunion @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1289,plain,
! [SV118: $i,SV249: $i] :
( ( ( ~ ( in @ SV249 @ ( sK74_X @ SV249 @ SV118 ) ) )
= $false )
| ( ( in @ SV249 @ ( setunion @ SV118 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1177]) ).
thf(1290,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1178]) ).
thf(1291,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1179]) ).
thf(1292,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) ) )
= $false )
| ( ( ~ ( SV120 @ SV320 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1293,plain,
! [SV120: $i > $o,SV320: $i] :
( ( ( ~ ( ( SV320
!= ( sK21_SY73 @ SV320 @ SV120 ) ) ) )
= $false )
| ( ( ~ ( SV120 @ SV320 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1180]) ).
thf(1294,plain,
! [SV321: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) ) )
= $false )
| ( ( ~ ( SV121 @ SV321 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1295,plain,
! [SV121: $i > $o,SV321: $i] :
( ( ( ~ ( ( SV321
!= ( sK56_SY247 @ SV321 @ SV121 ) ) ) )
= $false )
| ( ( ~ ( SV121 @ SV321 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1181]) ).
thf(1296,plain,
! [SV122: $i,SV251: $i > $o] :
( ( ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) )
= $true )
| ( ( ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV122 )
| ~ ( SV251 @ SY1488 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1182]) ).
thf(1297,plain,
! [SV122: $i,SV251: $i > $o] :
( ( ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 )
= $true )
| ( ( ! [SY1488: $i] :
( ~ ( in @ SY1488 @ SV122 )
| ~ ( SV251 @ SY1488 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1183]) ).
thf(1298,plain,
! [SV252: $i,SV123: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setadjoin @ ( sK69_SY1106 @ SV252 @ SV123 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK69_SY1106 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1184]) ).
thf(1299,plain,
! [SV322: $i,SV124: $i] :
( ( ( ~ ( in @ ( sK13_B @ SV124 ) @ SV124 ) )
= $false )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1300,plain,
! [SV322: $i,SV124: $i] :
( ( ( ~ ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK13_B @ SV124 ) )
| ~ ( in @ SY1314 @ SV124 ) ) )
= $false )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1186]) ).
thf(1301,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1187]) ).
thf(1302,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) ) ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1188]) ).
thf(1303,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1189]) ).
thf(1304,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) ) )
= $false )
| ( ( ~ ( SV127 @ SV324 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1190]) ).
thf(1305,plain,
! [SV127: $i > $o,SV324: $i] :
( ( ( ~ ( ( SV324
!= ( sK32_SY141 @ SV324 @ SV127 ) ) ) )
= $false )
| ( ( ~ ( SV127 @ SV324 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1190]) ).
thf(1306,plain,
! [SV255: $i > $o,SV128: $i,SV342: $i] :
( ( ( in @ SV342 @ SV128 )
= $false )
| ( ( SV255 @ SV342 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK34_Xx @ SV255 @ SV128 ) @ SV128 )
| ~ ~ ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1191]) ).
thf(1307,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) ) )
= $false )
| ( ( ~ ( SV129 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1192]) ).
thf(1308,plain,
! [SV129: $i > $o,SV325: $i] :
( ( ( ~ ( ( SV325
!= ( sK41_Xy @ SV325 @ SV129 ) ) ) )
= $false )
| ( ( ~ ( SV129 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1192]) ).
thf(1309,plain,
! [SV326: $i,SV130: $i > $o] :
( ( ( ~ ( SV130 @ ( sK19_SY56 @ SV326 @ SV130 ) ) )
= $false )
| ( ( ~ ( SV130 @ SV326 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1310,plain,
! [SV130: $i > $o,SV326: $i] :
( ( ( ~ ( ( SV326
!= ( sK19_SY56 @ SV326 @ SV130 ) ) ) )
= $false )
| ( ( ~ ( SV130 @ SV326 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1193]) ).
thf(1311,plain,
! [SV356: $i,SV131: $i,SV374: $i] :
( ( ~ ( in @ SV374 @ ( setadjoin @ SV131 @ SV356 ) )
| ( SV374 = SV131 )
| ( in @ SV374 @ SV356 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1194]) ).
thf(1312,plain,
! [SV131: $i] :
( ( ~ ! [SY1341: $i,SY1342: $i] :
( ( SY1342 != SV131 )
| ( in @ SY1342 @ ( setadjoin @ SV131 @ SY1341 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1313,plain,
! [SV131: $i] :
( ( ~ ! [SY1343: $i,SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( setadjoin @ SV131 @ SY1343 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1195]) ).
thf(1314,plain,
! [SV132: $i,SV256: $i > $o] :
( ( ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 )
= $true )
| ( ( ! [SY1503: $i] :
( ~ ( SV256 @ SY1503 )
| ~ ( in @ SY1503 @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1196]) ).
thf(1315,plain,
! [SV132: $i,SV256: $i > $o] :
( ( ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) )
= $true )
| ( ( ! [SY1503: $i] :
( ~ ( SV256 @ SY1503 )
| ~ ( in @ SY1503 @ SV132 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1197]) ).
thf(1316,plain,
! [SV357: $i,SV327: $i,SV133: $i] :
( ( ( SV133
!= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( ~ ( in @ SV357 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( in @ SV327 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1198]) ).
thf(1317,plain,
! [SV134: $i,SV257: $i] :
( ( ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV257 )
= $true )
| ( ( in @ SV257 @ ( powerset @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1199]) ).
thf(1318,plain,
! [SV134: $i,SV257: $i] :
( ( ( ~ ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV134 ) )
= $true )
| ( ( in @ SV257 @ ( powerset @ SV134 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1200]) ).
thf(1319,plain,
! [SV135: $i,SV358: $o,SV258: $i] :
( ( ( ~ ( ~ ( in @ SV258 @ ( sK30_B @ SV358 @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ SV358 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SV358 ) ) )
= $true )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1201]) ).
thf(1320,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( ~ ( in @ SV258 @ ( sK30_B @ $true @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ $true @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $true ) ) )
= $true )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1202]) ).
thf(1321,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( ~ ( in @ SV258 @ ( sK30_B @ $false @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ $false @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $false ) ) )
= $true )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1203]) ).
thf(1322,plain,
! [SV328: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) ) )
= $false )
| ( ( ~ ( SV136 @ SV328 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1323,plain,
! [SV136: $i > $o,SV328: $i] :
( ( ( ~ ( ( SV328
!= ( sK47_SY223 @ SV328 @ SV136 ) ) ) )
= $false )
| ( ( ~ ( SV136 @ SV328 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1204]) ).
thf(1324,plain,
! [SV137: $i,SV259: $i] :
( ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
= $true )
| ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
| ( SV137 = SV259 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1205]) ).
thf(1325,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
| ( SV137 = SV259 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1206]) ).
thf(1326,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( ~ ~ ( ( SV329
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 ) )
| ~ ( in @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ SV138 ) )
= $false )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1207]) ).
thf(1327,plain,
! [SV343: $i,SV359: $i] :
( ( ( ! [SY1584: $i] :
( ~ ( in @ SV359 @ SY1584 )
| ~ ( in @ SY1584 @ SV343 ) ) )
= $true )
| ( ( in @ SV359 @ ( setunion @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1208]) ).
thf(1328,plain,
! [SV344: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ ( setunion @ SV344 ) ) )
= $true )
| ( ( ~ ( ~ ( in @ SV360 @ ( sK7_B @ SV360 @ SV344 ) )
| ~ ( in @ ( sK7_B @ SV360 @ SV344 ) @ SV344 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1209]) ).
thf(1329,plain,
! [SV139: $i > $i > $o,SV261: $i] :
( ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1210]) ).
thf(1330,plain,
! [SV261: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1506: $i] :
( ~ ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) )
| ~ ( ( SY1506
!= ( sK12_SY1066 @ SY1506 @ SV261 @ SV139 ) ) ) )
| ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SY1506 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1211]) ).
thf(1331,plain,
! [SV140: $i,SV262: $i] :
( ( ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV140 )
= $true )
| ( ( subset @ SV140 @ SV262 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1212]) ).
thf(1332,plain,
! [SV140: $i,SV262: $i] :
( ( ( ~ ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV262 ) )
= $true )
| ( ( subset @ SV140 @ SV262 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1213]) ).
thf(1333,plain,
! [SV141: $i,SV263: $i > $o] :
( ( ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) )
= $true )
| ( ( ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV141 )
| ~ ( SV263 @ SY1510 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1214]) ).
thf(1334,plain,
! [SV141: $i,SV263: $i > $o] :
( ( ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 )
= $true )
| ( ( ! [SY1510: $i] :
( ~ ( in @ SY1510 @ SV141 )
| ~ ( SV263 @ SY1510 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1215]) ).
thf(1335,plain,
! [SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ( ( ( sK54_Xx @ SV361 @ SV345 )
!= ( sK55_SY1102 @ SV361 @ SV345 ) )
| ~ ~ ( ~ ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
| ~ ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) ) ) ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1216]) ).
thf(1336,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ( ~ ( ( ( sK50_Xx @ SV362 @ SV346 )
!= ( sK51_SY1100 @ SV362 @ SV346 ) )
| ~ ~ ( ~ ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
| ~ ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) ) ) ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1217]) ).
thf(1337,plain,
! [SV142: $i,SV330: $i,SV264: $i > $o] :
( ( ( ~ ( SV264 @ SV330 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) )
| ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1218]) ).
thf(1338,plain,
! [SV143: $i,SV265: $i] :
( ( ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV143 )
= $true )
| ( ( subset @ SV143 @ SV265 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1219]) ).
thf(1339,plain,
! [SV143: $i,SV265: $i] :
( ( ( ~ ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV265 ) )
= $true )
| ( ( subset @ SV143 @ SV265 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1220]) ).
thf(1340,plain,
! [SV363: $i > $o,SV144: $i,SV375: $i] :
( ( ~ ( in @ SV375 @ SV144 )
| ~ ( SV363 @ SV375 )
| ( in @ SV375
@ ( dsetconstr @ SV144
@ ^ [SY1590: $i] : ( SV363 @ SY1590 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1221]) ).
thf(1341,plain,
! [SV364: $i > $o,SV144: $i,SV376: $i] :
( ( ~ ( in @ SV376 @ SV144 )
| ~ ( in @ SV376
@ ( dsetconstr @ SV144
@ ^ [SY1592: $i] : ( SV364 @ SY1592 ) ) )
| ( SV364 @ SV376 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1222]) ).
thf(1342,plain,
! [SV145: $i] :
( ( ( ~ ( ~ ( in @ ( sK8_Xx @ SV145 ) @ omega )
| ~ ( in @ ( sK8_Xx @ SV145 ) @ SV145 ) ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1223]) ).
thf(1343,plain,
! [SV145: $i] :
( ( ( ~ ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 ) )
= $true )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1224]) ).
thf(1344,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( ~ ~ ( ( SV331
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) )
| ~ ( in @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) )
= $false )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1225]) ).
thf(1345,plain,
! [SV267: $i,SV147: $i] :
( ( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setadjoin @ ( sK67_SY1105 @ SV267 @ SV147 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK67_SY1105 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1226]) ).
thf(1346,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1515 @ SV148 )
| ( in @ SY1515 @ SV268 )
| ! [SX3: $o] : SX3 )
| ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1517 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1228]) ).
thf(1347,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ ( binunion @ SV148 @ SV268 ) )
| ! [SY1520: $o] :
( ~ SY1520
| ( in @ SY1519 @ SV268 )
| SY1520 ) )
| ~ ( ! [SY1521: $i] :
~ ( in @ SY1521 @ ( binunion @ SV148 @ SV268 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1229]) ).
thf(1348,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ ( sK43_Xx @ SV149 ) )
| ~ ~ ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1230]) ).
thf(1349,plain,
! [SV150: $i,SV269: $i] :
( ( ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV150 )
= $true )
| ( ( ( binintersect @ SV150 @ SV269 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1231]) ).
thf(1350,plain,
! [SV150: $i,SV269: $i] :
( ( ( in @ ( sK65_Xx @ SV269 @ SV150 ) @ SV269 )
= $true )
| ( ( ( binintersect @ SV150 @ SV269 )
= emptyset )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1232]) ).
thf(1351,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ ~ ( ~ ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
| ~ ~ ( ~ ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1233]) ).
thf(1352,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV152 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) ) ) )
| ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1234]) ).
thf(1353,plain,
! [SV153: $i > $o,SV272: $i > $o] :
( ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1235]) ).
thf(1354,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
| ~ ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1236]) ).
thf(1355,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ( ( sK46_Xy @ SV334 @ SV154 )
!= SV334 )
| ~ ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1237]) ).
thf(1356,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
| ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1238]) ).
thf(1357,plain,
! [SV155: $i,SV273: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) )
= $true )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1239]) ).
thf(1358,plain,
! [SV155: $i,SV273: $i] :
( ( ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
| ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) )
= $true )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1240]) ).
thf(1359,plain,
! [SV9: $i,SV277: $i,SV160: $i,SV366: $i] :
( ( ( ~ ( in @ SV366 @ SV160 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV277 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV277 @ ( setadjoin @ SV366 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV9 @ SV160 ) )
= $true )
| ( ( in @ SV277 @ SV9 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1242]) ).
thf(1360,plain,
! [SV10: $i,SV278: $i,SV161: $i,SV367: $i] :
( ( ( ~ ( in @ SV367 @ SV161 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV367 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV10 @ SV161 ) ) ) )
= $true )
| ( ( in @ SV278 @ SV10 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1243]) ).
thf(1361,plain,
! [SV11: $i,SV279: $i,SV162: $i,SV368: $i] :
( ( ( ~ ( in @ SV368 @ SV162 ) )
= $true )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV279 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV279 @ ( setadjoin @ SV368 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV11 @ SV162 ) ) ) )
= $true )
| ( ( in @ SV279 @ SV11 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1244]) ).
thf(1362,plain,
! [SV12: $i,SV280: $i,SV163: $i,SV369: $i] :
( ( ( ~ ( in @ SV369 @ SV163 ) )
= $true )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV280 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV280 @ ( setadjoin @ SV369 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV12 @ SV163 ) ) )
= $true )
| ( ( in @ SV280 @ SV12 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1245]) ).
thf(1363,plain,
! [SV13: $i,SV281: $i,SV164: $i,SV370: $i] :
( ( ( ~ ( in @ SV370 @ SV164 ) )
= $true )
| ( ( in @ ( setadjoin @ SV281 @ ( setadjoin @ SV370 @ emptyset ) ) @ ( powerset @ ( binunion @ SV13 @ SV164 ) ) )
= $true )
| ( ( in @ SV281 @ SV13 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1246]) ).
thf(1364,plain,
! [SV14: $i,SV282: $i,SV165: $i,SV371: $i] :
( ( ( ~ ( in @ SV371 @ SV165 ) )
= $true )
| ( ( subset @ ( setadjoin @ SV282 @ ( setadjoin @ SV371 @ emptyset ) ) @ ( binunion @ SV14 @ SV165 ) )
= $true )
| ( ( in @ SV282 @ SV14 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1247]) ).
thf(1365,plain,
! [SV23: $i,SV174: $i,SV286: $i] :
( ( ( in @ SV286 @ SV174 )
= $false )
| ( ( ~ ( in @ SV286 @ ( symdiff @ SV23 @ SV174 ) ) )
= $true )
| ( ( in @ SV286 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1250]) ).
thf(1366,plain,
! [SV45: $i,SV196: $i,SV299: $i] :
( ( ( subset @ SV299 @ SV196 )
= $false )
| ( ( subset @ SV299 @ ( binintersect @ SV45 @ SV196 ) )
= $true )
| ( ( subset @ SV299 @ SV45 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1258]) ).
thf(1367,plain,
! [SV46: $i,SV197: $i,SV300: $i] :
( ( ( in @ SV300 @ SV197 )
= $false )
| ( ( in @ SV300 @ ( binintersect @ SV46 @ SV197 ) )
= $true )
| ( ( in @ SV300 @ SV46 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1259]) ).
thf(1368,plain,
! [SV64: $i,SV347: $i,SV213: $i] :
( ( ( subset @ SV213 @ SV347 )
= $false )
| ( ( subset @ SV64 @ SV347 )
= $true )
| ( ( subset @ SV64 @ SV213 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1262]) ).
thf(1369,plain,
! [SV305: $i,SV214: $i,SV66: $i] :
( ( ( SV66 = SV214 )
= $false )
| ( ( in @ SV305 @ SV214 )
= $true )
| ( ( in @ SV305 @ SV66 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1263]) ).
thf(1370,plain,
! [SV306: $i,SV216: $i,SV68: $i] :
( ( ( subset @ SV68 @ SV216 )
= $false )
| ( ( in @ SV306 @ SV216 )
= $true )
| ( ( in @ SV306 @ SV68 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1264]) ).
thf(1371,plain,
! [SV217: $i,SV69: $i,SV348: $i] :
( ( ( in @ SV348 @ SV69 )
= $false )
| ( ( in @ SV348 @ SV217 )
= $true )
| ( ( subset @ SV69 @ SV217 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1265]) ).
thf(1372,plain,
! [SV218: $i,SV70: $i,SV349: $i] :
( ( ( in @ SV349 @ SV70 )
= $false )
| ( ( in @ SV349 @ SV218 )
= $true )
| ( ( subset @ SV70 @ SV218 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1266]) ).
thf(1373,plain,
! [SV223: $i,SV76: $i,SV372: $i,SV350: $i] :
( ( ( SV350 != SV372 )
= $true )
| ( ( ( setadjoin @ SV76 @ SV350 )
= ( setadjoin @ SV223 @ SV372 ) )
= $true )
| ( ( SV76 = SV223 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1267]) ).
thf(1374,plain,
! [SV224: $i,SV77: $i,SV373: $i,SV351: $i] :
( ( ( SV351 != SV373 )
= $true )
| ( ( ~ ( in @ SV351 @ SV77 )
| ( in @ SV373 @ SV224 ) )
= $true )
| ( ( SV77 = SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1268]) ).
thf(1375,plain,
! [SV226: $i > $o,SV81: $i,SV335: $i] :
( ( ( in @ SV335 @ SV81 )
= $false )
| ( ( SV226 @ SV335 )
= $false )
| ( ( ( dsetconstr @ SV81
@ ^ [SY1462: $i] : ( SV226 @ SY1462 ) )
!= emptyset )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1269]) ).
thf(1376,plain,
! [SV235: $i,SV91: $i,SV308: $i] :
( ( ( in @ SV308 @ SV91 )
= $false )
| ( ( in @ SV235 @ ( setunion @ SV91 ) )
= $true )
| ( ( in @ SV235 @ SV308 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1271]) ).
thf(1377,plain,
! [SV92: $i,SV236: $i,SV352: $i] :
( ( ( in @ SV352 @ SV236 )
= $false )
| ( ( in @ SV352 @ SV92 )
= $true )
| ( ( in @ SV236 @ ( powerset @ SV92 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1272]) ).
thf(1378,plain,
! [SV100: $i,SV312: $i,SV240: $i > $o] :
( ( ( SV240 @ SV312 )
= $false )
| ( ( ( dsetconstr @ SV100
@ ^ [SY1469: $i] : ( SV240 @ SY1469 ) )
!= emptyset )
= $true )
| ( ( in @ SV312 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1274]) ).
thf(1379,plain,
! [SV109: $i,SV318: $i,SV244: $i > $o] :
( ( ( SV244 @ SV318 )
= $false )
| ( ( in @ SV318
@ ( dsetconstr @ SV109
@ ^ [SY1475: $i] : ( SV244 @ SY1475 ) ) )
= $true )
| ( ( in @ SV318 @ SV109 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1275]) ).
thf(1380,plain,
! [SV245: $i > $o,SV112: $i,SV337: $i] :
( ( ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) )
= $false )
| ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
= ( setadjoin @ SV337 @ emptyset ) )
= $false )
| ( ( ~ ( ~ ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) )
| ~ ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1276]) ).
thf(1381,plain,
! [SV113: $i,SV353: $i] :
( ( ( ~ ( ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
| ~ ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 ) ) )
= $true )
| ( ( ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1277]) ).
thf(1382,plain,
! [SV113: $i] :
( ( ! [SY1282: $i,SY1283: $i] :
( ~ ( in @ SY1282 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY1283 @ ( sK14_B @ SV113 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1282 )
| ( in @ SX3 @ SY1283 ) )
| ! [SX3: $i] :
( ~ ( in @ SX3 @ SY1283 )
| ( in @ SX3 @ SY1282 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1278]) ).
thf(1383,plain,
! [SV113: $i] :
( ( ~ ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) )
| ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1279]) ).
thf(1384,plain,
! [SV338: $i,SV354: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV354 )
| ~ ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV338 ) )
= $false )
| ( ( in @ SV354 @ ( powerset @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1280]) ).
thf(1385,plain,
! [SV339: $i,SV355: $i] :
( ( ( in @ SV355 @ ( powerset @ SV339 ) )
= $false )
| ( ( ! [SY1582: $i] :
( ~ ( in @ SY1582 @ SV355 )
| ( in @ SY1582 @ SV339 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1281]) ).
thf(1386,plain,
! [SV340: $i,SV114: $i,SV246: $i > $o] :
( ( ( ~ ( in @ ( sK39_Xx @ SV246 @ SV114 ) @ SV114 )
| ~ ~ ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) ) )
= $false )
| ( ( SV246 @ SV340 )
= $true )
| ( ( in @ SV340 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1282]) ).
thf(1387,plain,
! [SV341: $i,SV115: $i,SV247: $i > $o] :
( ( ( ~ ( in @ ( sK37_Xx @ SV247 @ SV115 ) @ SV115 )
| ~ ~ ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) ) )
= $false )
| ( ( SV247 @ SV341 )
= $true )
| ( ( in @ SV341 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1283]) ).
thf(1388,plain,
! [SV248: $i,SV116: $i] :
( ( ( ! [SY1481: $i,SY1482: $i] :
( ( SY1481 != SY1482 )
| ~ ( in @ SY1481 @ SV116 )
| ( in @ SY1482 @ SV248 ) ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1284]) ).
thf(1389,plain,
! [SV116: $i,SV248: $i] :
( ( ( ! [SY1483: $i,SY1484: $i] :
( ( SY1483 != SY1484 )
| ~ ( in @ SY1484 @ SV248 )
| ( in @ SY1483 @ SV116 ) ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1285]) ).
thf(1390,plain,
! [SV319: $i,SV117: $i > $o] :
( ( ( SV117 @ ( sK23_SY85 @ SV319 @ SV117 ) )
= $true )
| ( ( ~ ( SV117 @ SV319 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1286]) ).
thf(1391,plain,
! [SV117: $i > $o,SV319: $i] :
( ( ( SV319
!= ( sK23_SY85 @ SV319 @ SV117 ) )
= $true )
| ( ( ~ ( SV117 @ SV319 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1287]) ).
thf(1392,plain,
! [SV118: $i,SV249: $i] :
( ( ( in @ ( sK74_X @ SV249 @ SV118 ) @ SV118 )
= $true )
| ( ( in @ SV249 @ ( setunion @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1288]) ).
thf(1393,plain,
! [SV118: $i,SV249: $i] :
( ( ( in @ SV249 @ ( sK74_X @ SV249 @ SV118 ) )
= $true )
| ( ( in @ SV249 @ ( setunion @ SV118 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1289]) ).
thf(1394,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1290]) ).
thf(1395,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
| ~ ~ ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1291]) ).
thf(1396,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( ~ ( SV120 @ SV320 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1292]) ).
thf(1397,plain,
! [SV120: $i > $o,SV320: $i] :
( ( ( SV320
!= ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( ~ ( SV120 @ SV320 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1293]) ).
thf(1398,plain,
! [SV321: $i,SV121: $i > $o] :
( ( ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( ~ ( SV121 @ SV321 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1294]) ).
thf(1399,plain,
! [SV121: $i > $o,SV321: $i] :
( ( ( SV321
!= ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( ~ ( SV121 @ SV321 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1295]) ).
thf(1400,plain,
! [SV251: $i > $o,SV122: $i,SV378: $i] :
( ( ( ~ ( in @ SV378 @ SV122 )
| ~ ( SV251 @ SV378 ) )
= $true )
| ( ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1296]) ).
thf(1401,plain,
! [SV251: $i > $o,SV122: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV122 )
| ~ ( SV251 @ SV379 ) )
= $true )
| ( ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1297]) ).
thf(1402,plain,
! [SV252: $i,SV123: $i] :
( ( ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setadjoin @ ( sK69_SY1106 @ SV252 @ SV123 ) @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1403,plain,
! [SV123: $i,SV252: $i] :
( ( ~ ( in @ ( sK69_SY1106 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1298]) ).
thf(1404,plain,
! [SV322: $i,SV124: $i] :
( ( ( in @ ( sK13_B @ SV124 ) @ SV124 )
= $true )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1299]) ).
thf(1405,plain,
! [SV322: $i,SV124: $i] :
( ( ( ! [SY1314: $i] :
( ~ ( in @ SY1314 @ ( sK13_B @ SV124 ) )
| ~ ( in @ SY1314 @ SV124 ) ) )
= $true )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1300]) ).
thf(1406,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1301]) ).
thf(1407,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
| ~ ~ ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1302]) ).
thf(1408,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1409,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1303]) ).
thf(1410,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( ~ ( SV127 @ SV324 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1304]) ).
thf(1411,plain,
! [SV127: $i > $o,SV324: $i] :
( ( ( SV324
!= ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( ~ ( SV127 @ SV324 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1305]) ).
thf(1412,plain,
! [SV342: $i,SV128: $i,SV255: $i > $o] :
( ( ( ~ ( in @ ( sK34_Xx @ SV255 @ SV128 ) @ SV128 )
| ~ ~ ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) ) )
= $false )
| ( ( SV255 @ SV342 )
= $true )
| ( ( in @ SV342 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1306]) ).
thf(1413,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( ~ ( SV129 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1307]) ).
thf(1414,plain,
! [SV129: $i > $o,SV325: $i] :
( ( ( SV325
!= ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( ~ ( SV129 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1308]) ).
thf(1415,plain,
! [SV326: $i,SV130: $i > $o] :
( ( ( SV130 @ ( sK19_SY56 @ SV326 @ SV130 ) )
= $true )
| ( ( ~ ( SV130 @ SV326 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1309]) ).
thf(1416,plain,
! [SV130: $i > $o,SV326: $i] :
( ( ( SV326
!= ( sK19_SY56 @ SV326 @ SV130 ) )
= $true )
| ( ( ~ ( SV130 @ SV326 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1310]) ).
thf(1417,plain,
! [SV356: $i,SV131: $i,SV374: $i] :
( ( ( ~ ( in @ SV374 @ ( setadjoin @ SV131 @ SV356 ) ) )
= $true )
| ( ( ( SV374 = SV131 )
| ( in @ SV374 @ SV356 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1311]) ).
thf(1418,plain,
! [SV131: $i] :
( ( ! [SY1341: $i,SY1342: $i] :
( ( SY1342 != SV131 )
| ( in @ SY1342 @ ( setadjoin @ SV131 @ SY1341 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1312]) ).
thf(1419,plain,
! [SV131: $i] :
( ( ! [SY1343: $i,SY1344: $i] :
( ~ ( in @ SY1344 @ SY1343 )
| ( in @ SY1344 @ ( setadjoin @ SV131 @ SY1343 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1313]) ).
thf(1420,plain,
! [SV132: $i,SV380: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV380 )
| ~ ( in @ SV380 @ SV132 ) )
= $true )
| ( ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1314]) ).
thf(1421,plain,
! [SV132: $i,SV381: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV381 )
| ~ ( in @ SV381 @ SV132 ) )
= $true )
| ( ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1315]) ).
thf(1422,plain,
! [SV357: $i,SV327: $i,SV133: $i] :
( ( ( SV133
= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ~ ( in @ SV357 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( in @ SV327 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1316]) ).
thf(1423,plain,
! [SV134: $i,SV257: $i] :
( ( ( in @ ( sK29_Xx @ SV257 @ SV134 ) @ SV134 )
= $false )
| ( ( in @ SV257 @ ( powerset @ SV134 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1318]) ).
thf(1424,plain,
! [SV135: $i,SV358: $o,SV258: $i] :
( ( ( ~ ( in @ SV258 @ ( sK30_B @ SV358 @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ SV358 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SV358 ) )
= $false )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1319]) ).
thf(1425,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ ( sK30_B @ $true @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ $true @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1320]) ).
thf(1426,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ ( sK30_B @ $false @ SV258 @ SV135 ) )
| ~ ~ ( ~ ( in @ ( sK30_B @ $false @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1321]) ).
thf(1427,plain,
! [SV328: $i,SV136: $i > $o] :
( ( ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( ~ ( SV136 @ SV328 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1322]) ).
thf(1428,plain,
! [SV136: $i > $o,SV328: $i] :
( ( ( SV328
!= ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( ~ ( SV136 @ SV328 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1323]) ).
thf(1429,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) ) )
= $true )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1324]) ).
thf(1430,plain,
! [SV137: $i,SV259: $i] :
( ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
| ( SV137 = SV259 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1325]) ).
thf(1431,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( ~ ~ ( ( SV329
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 ) ) )
= $false )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1432,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( ~ ( in @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ SV138 ) )
= $false )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1326]) ).
thf(1433,plain,
! [SV343: $i,SV382: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV382 )
| ~ ( in @ SV382 @ SV343 ) )
= $true )
| ( ( in @ SV359 @ ( setunion @ SV343 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1327]) ).
thf(1434,plain,
! [SV344: $i,SV360: $i] :
( ( ( in @ SV360 @ ( setunion @ SV344 ) )
= $false )
| ( ( ~ ( ~ ( in @ SV360 @ ( sK7_B @ SV360 @ SV344 ) )
| ~ ( in @ ( sK7_B @ SV360 @ SV344 ) @ SV344 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1328]) ).
thf(1435,plain,
! [SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $false )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1329]) ).
thf(1436,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
| ~ ( ( SV383
!= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) ) ) )
| ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1330]) ).
thf(1437,plain,
! [SV140: $i,SV262: $i] :
( ( ( in @ ( sK63_Xx @ SV262 @ SV140 ) @ SV262 )
= $false )
| ( ( subset @ SV140 @ SV262 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1332]) ).
thf(1438,plain,
! [SV263: $i > $o,SV141: $i,SV384: $i] :
( ( ( ~ ( in @ SV384 @ SV141 )
| ~ ( SV263 @ SV384 ) )
= $true )
| ( ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1333]) ).
thf(1439,plain,
! [SV263: $i > $o,SV141: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV141 )
| ~ ( SV263 @ SV385 ) )
= $true )
| ( ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1334]) ).
thf(1440,plain,
! [SV345: $i > $o,SV361: $i > $o] :
( ( ( ( ( sK54_Xx @ SV361 @ SV345 )
!= ( sK55_SY1102 @ SV361 @ SV345 ) )
| ~ ~ ( ~ ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
| ~ ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) ) ) )
= $false )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1335]) ).
thf(1441,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ( ( ( sK50_Xx @ SV362 @ SV346 )
!= ( sK51_SY1100 @ SV362 @ SV346 ) )
| ~ ~ ( ~ ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
| ~ ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) ) ) )
= $false )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1336]) ).
thf(1442,plain,
! [SV142: $i,SV330: $i,SV264: $i > $o] :
( ( ( SV264 @ SV330 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) )
| ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1337]) ).
thf(1443,plain,
! [SV143: $i,SV265: $i] :
( ( ( in @ ( sK64_Xx @ SV265 @ SV143 ) @ SV265 )
= $false )
| ( ( subset @ SV143 @ SV265 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1339]) ).
thf(1444,plain,
! [SV363: $i > $o,SV144: $i,SV375: $i] :
( ( ( ~ ( in @ SV375 @ SV144 ) )
= $true )
| ( ( ~ ( SV363 @ SV375 )
| ( in @ SV375
@ ( dsetconstr @ SV144
@ ^ [SY1590: $i] : ( SV363 @ SY1590 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1340]) ).
thf(1445,plain,
! [SV364: $i > $o,SV144: $i,SV376: $i] :
( ( ( ~ ( in @ SV376 @ SV144 ) )
= $true )
| ( ( ~ ( in @ SV376
@ ( dsetconstr @ SV144
@ ^ [SY1592: $i] : ( SV364 @ SY1592 ) ) )
| ( SV364 @ SV376 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1341]) ).
thf(1446,plain,
! [SV145: $i] :
( ( ( ~ ( in @ ( sK8_Xx @ SV145 ) @ omega )
| ~ ( in @ ( sK8_Xx @ SV145 ) @ SV145 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1342]) ).
thf(1447,plain,
! [SV145: $i] :
( ( ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 )
= $false )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1343]) ).
thf(1448,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( ~ ~ ( ( SV331
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) ) )
= $false )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1449,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( ~ ( in @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) )
= $false )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1344]) ).
thf(1450,plain,
! [SV267: $i,SV147: $i] :
( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) )
!= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setadjoin @ ( sK67_SY1105 @ SV267 @ SV147 ) @ emptyset ) ) @ emptyset ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1451,plain,
! [SV147: $i,SV267: $i] :
( ( ~ ( in @ ( sK67_SY1105 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1345]) ).
thf(1452,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ! [SY1515: $i] :
( ~ ( in @ SY1515 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1515 @ SV148 )
| ( in @ SY1515 @ SV268 )
| ! [SX3: $o] : SX3 ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1453,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ! [SY1517: $i] :
( ~ ( in @ SY1517 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1517 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1346]) ).
thf(1454,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ! [SY1519: $i] :
( ~ ( in @ SY1519 @ ( binunion @ SV148 @ SV268 ) )
| ! [SY1520: $o] :
( ~ SY1520
| ( in @ SY1519 @ SV268 )
| SY1520 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1455,plain,
! [SV268: $i,SV148: $i] :
( ( ~ ( ! [SY1521: $i] :
~ ( in @ SY1521 @ ( binunion @ SV148 @ SV268 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1347]) ).
thf(1456,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ ( sK43_Xx @ SV149 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1457,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ~ ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1348]) ).
thf(1458,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ ~ ( ~ ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1459,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ~ ~ ( ~ ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1351]) ).
thf(1460,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV152 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1352]) ).
thf(1461,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1353]) ).
thf(1462,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
| ~ ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1354]) ).
thf(1463,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ( sK46_Xy @ SV334 @ SV154 )
!= SV334 )
= $true )
| ( ( ~ ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1355]) ).
thf(1464,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1356]) ).
thf(1465,plain,
! [SV155: $i,SV273: $i] :
( ( ( ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 ) )
= $true )
| ( ( ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) )
= $true )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1357]) ).
thf(1466,plain,
! [SV155: $i,SV273: $i] :
( ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
= $true )
| ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 )
= $true )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1358]) ).
thf(1467,plain,
! [SV9: $i,SV277: $i,SV160: $i,SV366: $i] :
( ( ( in @ SV366 @ SV160 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV277 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV277 @ ( setadjoin @ SV366 @ emptyset ) ) @ emptyset ) ) @ ( cartprod @ SV9 @ SV160 ) )
= $true )
| ( ( in @ SV277 @ SV9 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1359]) ).
thf(1468,plain,
! [SV10: $i,SV278: $i,SV161: $i,SV367: $i] :
( ( ( in @ SV367 @ SV161 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV278 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV278 @ ( setadjoin @ SV367 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV10 @ SV161 ) ) ) )
= $true )
| ( ( in @ SV278 @ SV10 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1360]) ).
thf(1469,plain,
! [SV11: $i,SV279: $i,SV162: $i,SV368: $i] :
( ( ( in @ SV368 @ SV162 )
= $false )
| ( ( in @ ( setadjoin @ ( setadjoin @ SV279 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV279 @ ( setadjoin @ SV368 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( powerset @ ( binunion @ SV11 @ SV162 ) ) ) )
= $true )
| ( ( in @ SV279 @ SV11 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1361]) ).
thf(1470,plain,
! [SV12: $i,SV280: $i,SV163: $i,SV369: $i] :
( ( ( in @ SV369 @ SV163 )
= $false )
| ( ( subset @ ( setadjoin @ ( setadjoin @ SV280 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV280 @ ( setadjoin @ SV369 @ emptyset ) ) @ emptyset ) ) @ ( powerset @ ( binunion @ SV12 @ SV163 ) ) )
= $true )
| ( ( in @ SV280 @ SV12 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1362]) ).
thf(1471,plain,
! [SV13: $i,SV281: $i,SV164: $i,SV370: $i] :
( ( ( in @ SV370 @ SV164 )
= $false )
| ( ( in @ ( setadjoin @ SV281 @ ( setadjoin @ SV370 @ emptyset ) ) @ ( powerset @ ( binunion @ SV13 @ SV164 ) ) )
= $true )
| ( ( in @ SV281 @ SV13 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1363]) ).
thf(1472,plain,
! [SV14: $i,SV282: $i,SV165: $i,SV371: $i] :
( ( ( in @ SV371 @ SV165 )
= $false )
| ( ( subset @ ( setadjoin @ SV282 @ ( setadjoin @ SV371 @ emptyset ) ) @ ( binunion @ SV14 @ SV165 ) )
= $true )
| ( ( in @ SV282 @ SV14 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1364]) ).
thf(1473,plain,
! [SV174: $i,SV23: $i,SV286: $i] :
( ( ( in @ SV286 @ ( symdiff @ SV23 @ SV174 ) )
= $false )
| ( ( in @ SV286 @ SV174 )
= $false )
| ( ( in @ SV286 @ SV23 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1365]) ).
thf(1474,plain,
! [SV223: $i,SV76: $i,SV372: $i,SV350: $i] :
( ( ( SV350 = SV372 )
= $false )
| ( ( ( setadjoin @ SV76 @ SV350 )
= ( setadjoin @ SV223 @ SV372 ) )
= $true )
| ( ( SV76 = SV223 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1373]) ).
thf(1475,plain,
! [SV224: $i,SV77: $i,SV373: $i,SV351: $i] :
( ( ( SV351 = SV373 )
= $false )
| ( ( ~ ( in @ SV351 @ SV77 )
| ( in @ SV373 @ SV224 ) )
= $true )
| ( ( SV77 = SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1374]) ).
thf(1476,plain,
! [SV335: $i,SV226: $i > $o,SV81: $i] :
( ( ( ( dsetconstr @ SV81
@ ^ [SY1462: $i] : ( SV226 @ SY1462 ) )
= emptyset )
= $false )
| ( ( SV226 @ SV335 )
= $false )
| ( ( in @ SV335 @ SV81 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1375]) ).
thf(1477,plain,
! [SV312: $i,SV240: $i > $o,SV100: $i] :
( ( ( ( dsetconstr @ SV100
@ ^ [SY1469: $i] : ( SV240 @ SY1469 ) )
= emptyset )
= $false )
| ( ( SV240 @ SV312 )
= $false )
| ( ( in @ SV312 @ SV100 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1378]) ).
thf(1478,plain,
! [SV337: $i,SV112: $i,SV245: $i > $o] :
( ( ( ~ ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) )
| ~ ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 ) )
= $false )
| ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
= ( setadjoin @ SV337 @ emptyset ) )
= $false )
| ( ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1380]) ).
thf(1479,plain,
! [SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
| ~ ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 ) )
= $false )
| ( ( ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1381]) ).
thf(1480,plain,
! [SV113: $i,SV386: $i] :
( ( ! [SY1600: $i] :
( ~ ( in @ SV386 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SY1600 @ ( sK14_B @ SV113 ) )
| ! [SY1601: $i] :
( ~ ( in @ SY1601 @ SV386 )
| ( in @ SY1601 @ SY1600 ) )
| ! [SY1602: $i] :
( ~ ( in @ SY1602 @ SY1600 )
| ( in @ SY1602 @ SV386 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1382]) ).
thf(1481,plain,
! [SV113: $i] :
( ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) )
| ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) )
= $false ),
inference(extcnf_not_pos,[status(thm)],[1383]) ).
thf(1482,plain,
! [SV338: $i,SV354: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV354 ) )
= $false )
| ( ( in @ SV354 @ ( powerset @ SV338 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1483,plain,
! [SV338: $i,SV354: $i] :
( ( ( ~ ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV338 ) )
= $false )
| ( ( in @ SV354 @ ( powerset @ SV338 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1384]) ).
thf(1484,plain,
! [SV339: $i,SV355: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV355 )
| ( in @ SV387 @ SV339 ) )
= $true )
| ( ( in @ SV355 @ ( powerset @ SV339 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1385]) ).
thf(1485,plain,
! [SV340: $i,SV114: $i,SV246: $i > $o] :
( ( ( ~ ( in @ ( sK39_Xx @ SV246 @ SV114 ) @ SV114 ) )
= $false )
| ( ( SV246 @ SV340 )
= $true )
| ( ( in @ SV340 @ SV114 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1486,plain,
! [SV340: $i,SV114: $i,SV246: $i > $o] :
( ( ( ~ ~ ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) ) )
= $false )
| ( ( SV246 @ SV340 )
= $true )
| ( ( in @ SV340 @ SV114 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1386]) ).
thf(1487,plain,
! [SV341: $i,SV115: $i,SV247: $i > $o] :
( ( ( ~ ( in @ ( sK37_Xx @ SV247 @ SV115 ) @ SV115 ) )
= $false )
| ( ( SV247 @ SV341 )
= $true )
| ( ( in @ SV341 @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1488,plain,
! [SV341: $i,SV115: $i,SV247: $i > $o] :
( ( ( ~ ~ ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) ) )
= $false )
| ( ( SV247 @ SV341 )
= $true )
| ( ( in @ SV341 @ SV115 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1387]) ).
thf(1489,plain,
! [SV248: $i,SV116: $i,SV388: $i] :
( ( ( ! [SY1603: $i] :
( ( SV388 != SY1603 )
| ~ ( in @ SV388 @ SV116 )
| ( in @ SY1603 @ SV248 ) ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1388]) ).
thf(1490,plain,
! [SV116: $i,SV248: $i,SV389: $i] :
( ( ( ! [SY1604: $i] :
( ( SV389 != SY1604 )
| ~ ( in @ SY1604 @ SV248 )
| ( in @ SV389 @ SV116 ) ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1389]) ).
thf(1491,plain,
! [SV319: $i,SV117: $i > $o] :
( ( ( SV117 @ SV319 )
= $false )
| ( ( SV117 @ ( sK23_SY85 @ SV319 @ SV117 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1390]) ).
thf(1492,plain,
! [SV117: $i > $o,SV319: $i] :
( ( ( SV319
= ( sK23_SY85 @ SV319 @ SV117 ) )
= $false )
| ( ( ~ ( SV117 @ SV319 ) )
= $true )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1391]) ).
thf(1493,plain,
! [SV119: $i,SV390: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV390 )
| ~ ( in @ SV390 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1394]) ).
thf(1494,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1395]) ).
thf(1495,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ~ ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1395]) ).
thf(1496,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( SV120 @ SV320 )
= $false )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1396]) ).
thf(1497,plain,
! [SV120: $i > $o,SV320: $i] :
( ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( ~ ( SV120 @ SV320 ) )
= $true )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1397]) ).
thf(1498,plain,
! [SV321: $i,SV121: $i > $o] :
( ( ( SV121 @ SV321 )
= $false )
| ( ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1398]) ).
thf(1499,plain,
! [SV121: $i > $o,SV321: $i] :
( ( ( SV321
= ( sK56_SY247 @ SV321 @ SV121 ) )
= $false )
| ( ( ~ ( SV121 @ SV321 ) )
= $true )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1399]) ).
thf(1500,plain,
! [SV251: $i > $o,SV122: $i,SV378: $i] :
( ( ( ~ ( in @ SV378 @ SV122 ) )
= $true )
| ( ( ~ ( SV251 @ SV378 ) )
= $true )
| ( ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1400]) ).
thf(1501,plain,
! [SV251: $i > $o,SV122: $i,SV379: $i] :
( ( ( ~ ( in @ SV379 @ SV122 ) )
= $true )
| ( ( ~ ( SV251 @ SV379 ) )
= $true )
| ( ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1401]) ).
thf(1502,plain,
! [SV252: $i,SV123: $i] :
( ( ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK68_SY427 @ SV252 @ SV123 ) @ ( setadjoin @ ( sK69_SY1106 @ SV252 @ SV123 ) @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1402]) ).
thf(1503,plain,
! [SV123: $i,SV252: $i] :
( ( in @ ( sK69_SY1106 @ SV252 @ SV123 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV123 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV123 @ ( setadjoin @ SV252 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1403]) ).
thf(1504,plain,
! [SV322: $i,SV124: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ ( sK13_B @ SV124 ) )
| ~ ( in @ SV391 @ SV124 ) )
= $true )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1405]) ).
thf(1505,plain,
! [SV125: $i,SV392: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV392 )
| ~ ( in @ SV392 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1406]) ).
thf(1506,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1507,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ~ ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1407]) ).
thf(1508,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( ~ ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1408]) ).
thf(1509,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1409]) ).
thf(1510,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( SV127 @ SV324 )
= $false )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1410]) ).
thf(1511,plain,
! [SV127: $i > $o,SV324: $i] :
( ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( ~ ( SV127 @ SV324 ) )
= $true )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1411]) ).
thf(1512,plain,
! [SV342: $i,SV128: $i,SV255: $i > $o] :
( ( ( ~ ( in @ ( sK34_Xx @ SV255 @ SV128 ) @ SV128 ) )
= $false )
| ( ( SV255 @ SV342 )
= $true )
| ( ( in @ SV342 @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1513,plain,
! [SV342: $i,SV128: $i,SV255: $i > $o] :
( ( ( ~ ~ ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) ) )
= $false )
| ( ( SV255 @ SV342 )
= $true )
| ( ( in @ SV342 @ SV128 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1412]) ).
thf(1514,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( SV129 @ SV325 )
= $false )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1413]) ).
thf(1515,plain,
! [SV129: $i > $o,SV325: $i] :
( ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( ~ ( SV129 @ SV325 ) )
= $true )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1414]) ).
thf(1516,plain,
! [SV326: $i,SV130: $i > $o] :
( ( ( SV130 @ SV326 )
= $false )
| ( ( SV130 @ ( sK19_SY56 @ SV326 @ SV130 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1415]) ).
thf(1517,plain,
! [SV130: $i > $o,SV326: $i] :
( ( ( SV326
= ( sK19_SY56 @ SV326 @ SV130 ) )
= $false )
| ( ( ~ ( SV130 @ SV326 ) )
= $true )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1416]) ).
thf(1518,plain,
! [SV356: $i,SV131: $i,SV374: $i] :
( ( ( in @ SV374 @ ( setadjoin @ SV131 @ SV356 ) )
= $false )
| ( ( ( SV374 = SV131 )
| ( in @ SV374 @ SV356 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1417]) ).
thf(1519,plain,
! [SV393: $i,SV131: $i] :
( ( ! [SY1605: $i] :
( ( SY1605 != SV131 )
| ( in @ SY1605 @ ( setadjoin @ SV131 @ SV393 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1418]) ).
thf(1520,plain,
! [SV131: $i,SV394: $i] :
( ( ! [SY1606: $i] :
( ~ ( in @ SY1606 @ SV394 )
| ( in @ SY1606 @ ( setadjoin @ SV131 @ SV394 ) ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1419]) ).
thf(1521,plain,
! [SV132: $i,SV380: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV380 ) )
= $true )
| ( ( ~ ( in @ SV380 @ SV132 ) )
= $true )
| ( ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1420]) ).
thf(1522,plain,
! [SV132: $i,SV381: $i,SV256: $i > $o] :
( ( ( ~ ( SV256 @ SV381 ) )
= $true )
| ( ( ~ ( in @ SV381 @ SV132 ) )
= $true )
| ( ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1421]) ).
thf(1523,plain,
! [SV327: $i,SV133: $i,SV357: $i] :
( ( ( in @ SV357 @ ( setunion @ SV133 ) )
= $false )
| ( ( SV133
= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( ~ ( in @ SV327 @ ( setunion @ SV133 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1422]) ).
thf(1524,plain,
! [SV135: $i,SV358: $o,SV258: $i] :
( ( ( ~ ( in @ SV258 @ ( sK30_B @ SV358 @ SV258 @ SV135 ) ) )
= $false )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1424]) ).
thf(1525,plain,
! [SV135: $i,SV258: $i,SV358: $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_B @ SV358 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SV358 ) )
= $false )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1424]) ).
thf(1526,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ ( sK30_B @ $true @ SV258 @ SV135 ) ) )
= $false )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1527,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_B @ $true @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $true ) )
= $false )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1425]) ).
thf(1528,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ SV258 @ ( sK30_B @ $false @ SV258 @ SV135 ) ) )
= $false )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1529,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK30_B @ $false @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $false ) )
= $false )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1426]) ).
thf(1530,plain,
! [SV328: $i,SV136: $i > $o] :
( ( ( SV136 @ SV328 )
= $false )
| ( ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1427]) ).
thf(1531,plain,
! [SV136: $i > $o,SV328: $i] :
( ( ( SV328
= ( sK47_SY223 @ SV328 @ SV136 ) )
= $false )
| ( ( ~ ( SV136 @ SV328 ) )
= $true )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1428]) ).
thf(1532,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
= $false )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1429]) ).
thf(1533,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) ) )
= $true )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1430]) ).
thf(1534,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( ~ ( ( SV329
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 ) ) )
= $true )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1431]) ).
thf(1535,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( in @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ SV138 )
= $true )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1432]) ).
thf(1536,plain,
! [SV343: $i,SV382: $i,SV359: $i] :
( ( ( ~ ( in @ SV359 @ SV382 ) )
= $true )
| ( ( ~ ( in @ SV382 @ SV343 ) )
= $true )
| ( ( in @ SV359 @ ( setunion @ SV343 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1433]) ).
thf(1537,plain,
! [SV344: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ ( sK7_B @ SV360 @ SV344 ) )
| ~ ( in @ ( sK7_B @ SV360 @ SV344 ) @ SV344 ) )
= $false )
| ( ( in @ SV360 @ ( setunion @ SV344 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1434]) ).
thf(1538,plain,
! [SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) ) )
= $false )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1539,plain,
! [SV139: $i > $i > $o,SV261: $i] :
( ( ( ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $false )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1435]) ).
thf(1540,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
| ~ ( ( SV383
!= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) ) ) ) )
= $true )
| ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1436]) ).
thf(1541,plain,
! [SV263: $i > $o,SV141: $i,SV384: $i] :
( ( ( ~ ( in @ SV384 @ SV141 ) )
= $true )
| ( ( ~ ( SV263 @ SV384 ) )
= $true )
| ( ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1438]) ).
thf(1542,plain,
! [SV263: $i > $o,SV141: $i,SV385: $i] :
( ( ( ~ ( in @ SV385 @ SV141 ) )
= $true )
| ( ( ~ ( SV263 @ SV385 ) )
= $true )
| ( ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1439]) ).
thf(1543,plain,
! [SV345: $i > $o,SV361: $i > $o] :
( ( ( ( sK54_Xx @ SV361 @ SV345 )
!= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1544,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
| ~ ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) ) ) )
= $false )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1440]) ).
thf(1545,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ( ( sK50_Xx @ SV362 @ SV346 )
!= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1546,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
| ~ ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) ) ) )
= $false )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1441]) ).
thf(1547,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ~ ( ~ ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1442]) ).
thf(1548,plain,
! [SV363: $i > $o,SV144: $i,SV375: $i] :
( ( ( in @ SV375 @ SV144 )
= $false )
| ( ( ~ ( SV363 @ SV375 )
| ( in @ SV375
@ ( dsetconstr @ SV144
@ ^ [SY1590: $i] : ( SV363 @ SY1590 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1444]) ).
thf(1549,plain,
! [SV364: $i > $o,SV144: $i,SV376: $i] :
( ( ( in @ SV376 @ SV144 )
= $false )
| ( ( ~ ( in @ SV376
@ ( dsetconstr @ SV144
@ ^ [SY1592: $i] : ( SV364 @ SY1592 ) ) )
| ( SV364 @ SV376 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1445]) ).
thf(1550,plain,
! [SV145: $i] :
( ( ( ~ ( in @ ( sK8_Xx @ SV145 ) @ omega ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1551,plain,
! [SV145: $i] :
( ( ( ~ ( in @ ( sK8_Xx @ SV145 ) @ SV145 ) )
= $false )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1446]) ).
thf(1552,plain,
! [SV145: $i] :
( ( ( in @ emptyset @ SV145 )
= $false )
| ( ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 )
= $false )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1447]) ).
thf(1553,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( ~ ( ( SV331
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) ) )
= $true )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1448]) ).
thf(1554,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( in @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) )
= $true )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1449]) ).
thf(1555,plain,
! [SV267: $i,SV147: $i] :
( ( ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) )
= ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK66_SY422 @ SV267 @ SV147 ) @ ( setadjoin @ ( sK67_SY1105 @ SV267 @ SV147 ) @ emptyset ) ) @ emptyset ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1450]) ).
thf(1556,plain,
! [SV147: $i,SV267: $i] :
( ( in @ ( sK67_SY1105 @ SV267 @ SV147 ) @ ( setunion @ ( setadjoin @ ( setadjoin @ SV147 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV147 @ ( setadjoin @ SV267 @ emptyset ) ) @ emptyset ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1451]) ).
thf(1557,plain,
! [SV268: $i,SV148: $i] :
( ( ! [SY1515: $i] :
( ~ ( in @ SY1515 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1515 @ SV148 )
| ( in @ SY1515 @ SV268 )
| ! [SX3: $o] : SX3 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1452]) ).
thf(1558,plain,
! [SV268: $i,SV148: $i] :
( ( ! [SY1517: $i] :
( ~ ( in @ SY1517 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SY1517 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1453]) ).
thf(1559,plain,
! [SV268: $i,SV148: $i] :
( ( ! [SY1519: $i] :
( ~ ( in @ SY1519 @ ( binunion @ SV148 @ SV268 ) )
| ! [SY1520: $o] :
( ~ SY1520
| ( in @ SY1519 @ SV268 )
| SY1520 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1454]) ).
thf(1560,plain,
! [SV268: $i,SV148: $i] :
( ( ! [SY1521: $i] :
~ ( in @ SY1521 @ ( binunion @ SV148 @ SV268 ) )
| ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1455]) ).
thf(1561,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1456]) ).
thf(1562,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1457]) ).
thf(1563,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ ( ~ ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1458]) ).
thf(1564,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ~ ( ~ ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1459]) ).
thf(1565,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ( in @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV152 )
| ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1460]) ).
thf(1566,plain,
! [SV272: $i > $o,SV395: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
| ~ ( ( SV395
!= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SV395 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1461]) ).
thf(1567,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1568,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ~ ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1462]) ).
thf(1569,plain,
! [SV154: $i > $o,SV334: $i] :
( ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( ~ ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1463]) ).
thf(1570,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1464]) ).
thf(1571,plain,
! [SV155: $i,SV273: $i] :
( ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
= $false )
| ( ( ~ ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 ) )
= $true )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1465]) ).
thf(1572,plain,
! [SV224: $i,SV373: $i,SV77: $i,SV351: $i] :
( ( ( ~ ( in @ SV351 @ SV77 ) )
= $true )
| ( ( in @ SV373 @ SV224 )
= $true )
| ( ( SV351 = SV373 )
= $false )
| ( ( SV77 = SV224 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1475]) ).
thf(1573,plain,
! [SV337: $i,SV112: $i,SV245: $i > $o] :
( ( ( ~ ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) ) )
= $false )
| ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
= ( setadjoin @ SV337 @ emptyset ) )
= $false )
| ( ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1574,plain,
! [SV337: $i,SV112: $i,SV245: $i > $o] :
( ( ( ~ ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 ) )
= $false )
| ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
= ( setadjoin @ SV337 @ emptyset ) )
= $false )
| ( ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1478]) ).
thf(1575,plain,
! [SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 ) )
= $false )
| ( ( ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1576,plain,
! [SV113: $i,SV353: $i] :
( ( ( ~ ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 ) )
= $false )
| ( ( ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1479]) ).
thf(1577,plain,
! [SV396: $i,SV113: $i,SV386: $i] :
( ( ~ ( in @ SV386 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SV396 @ ( sK14_B @ SV113 ) )
| ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV386 )
| ( in @ SY1607 @ SV396 ) )
| ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1480]) ).
thf(1578,plain,
! [SV113: $i] :
( ( ~ ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1579,plain,
! [SV113: $i] :
( ( ~ ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) )
= $false ),
inference(extcnf_or_neg,[status(thm)],[1481]) ).
thf(1580,plain,
! [SV338: $i,SV354: $i] :
( ( ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV354 )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV338 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1482]) ).
thf(1581,plain,
! [SV338: $i,SV354: $i] :
( ( ( ~ ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV338 ) )
= $true )
| ( ( in @ SV354 @ ( powerset @ SV338 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1483]) ).
thf(1582,plain,
! [SV339: $i,SV355: $i,SV387: $i] :
( ( ( ~ ( in @ SV387 @ SV355 ) )
= $true )
| ( ( in @ SV387 @ SV339 )
= $true )
| ( ( in @ SV355 @ ( powerset @ SV339 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1484]) ).
thf(1583,plain,
! [SV340: $i,SV114: $i,SV246: $i > $o] :
( ( ( in @ ( sK39_Xx @ SV246 @ SV114 ) @ SV114 )
= $true )
| ( ( SV246 @ SV340 )
= $true )
| ( ( in @ SV340 @ SV114 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1485]) ).
thf(1584,plain,
! [SV340: $i,SV114: $i,SV246: $i > $o] :
( ( ( ~ ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) ) )
= $true )
| ( ( SV246 @ SV340 )
= $true )
| ( ( in @ SV340 @ SV114 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1486]) ).
thf(1585,plain,
! [SV341: $i,SV115: $i,SV247: $i > $o] :
( ( ( in @ ( sK37_Xx @ SV247 @ SV115 ) @ SV115 )
= $true )
| ( ( SV247 @ SV341 )
= $true )
| ( ( in @ SV341 @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1487]) ).
thf(1586,plain,
! [SV341: $i,SV115: $i,SV247: $i > $o] :
( ( ( ~ ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) ) )
= $true )
| ( ( SV247 @ SV341 )
= $true )
| ( ( in @ SV341 @ SV115 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1488]) ).
thf(1587,plain,
! [SV248: $i,SV116: $i,SV397: $i,SV388: $i] :
( ( ( ( SV388 != SV397 )
| ~ ( in @ SV388 @ SV116 )
| ( in @ SV397 @ SV248 ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1489]) ).
thf(1588,plain,
! [SV116: $i,SV248: $i,SV398: $i,SV389: $i] :
( ( ( ( SV389 != SV398 )
| ~ ( in @ SV398 @ SV248 )
| ( in @ SV389 @ SV116 ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1490]) ).
thf(1589,plain,
! [SV319: $i,SV117: $i > $o] :
( ( ( SV117 @ SV319 )
= $false )
| ( ( SV319
= ( sK23_SY85 @ SV319 @ SV117 ) )
= $false )
| ( ( SV117 @ ( sK22_Xx @ SV117 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1492]) ).
thf(1590,plain,
! [SV119: $i,SV390: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV390 ) )
= $true )
| ( ( ~ ( in @ SV390 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1493]) ).
thf(1591,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1494]) ).
thf(1592,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1495]) ).
thf(1593,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) )
= $false )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1496]) ).
thf(1594,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( SV120 @ SV320 )
= $false )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( ~ ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1497]) ).
thf(1595,plain,
! [SV321: $i,SV399: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ SV399 )
| ! [SY1609: $i] :
( ~ ( SV121 @ SY1609 )
| ( SV399 = SY1609 ) ) )
= $true )
| ( ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1498]) ).
thf(1596,plain,
! [SV321: $i,SV121: $i > $o] :
( ( ( SV121 @ SV321 )
= $false )
| ( ( SV321
= ( sK56_SY247 @ SV321 @ SV121 ) )
= $false )
| ( ( ! [SY1308: $i] :
( ~ ( SV121 @ SY1308 )
| ! [SY1309: $i] :
( ~ ( SV121 @ SY1309 )
| ( SY1308 = SY1309 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1499]) ).
thf(1597,plain,
! [SV251: $i > $o,SV122: $i,SV378: $i] :
( ( ( in @ SV378 @ SV122 )
= $false )
| ( ( ~ ( SV251 @ SV378 ) )
= $true )
| ( ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1500]) ).
thf(1598,plain,
! [SV251: $i > $o,SV122: $i,SV379: $i] :
( ( ( in @ SV379 @ SV122 )
= $false )
| ( ( ~ ( SV251 @ SV379 ) )
= $true )
| ( ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1501]) ).
thf(1599,plain,
! [SV322: $i,SV124: $i,SV391: $i] :
( ( ( ~ ( in @ SV391 @ ( sK13_B @ SV124 ) ) )
= $true )
| ( ( ~ ( in @ SV391 @ SV124 ) )
= $true )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1504]) ).
thf(1600,plain,
! [SV125: $i,SV392: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV392 ) )
= $true )
| ( ( ~ ( in @ SV392 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1505]) ).
thf(1601,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1506]) ).
thf(1602,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1507]) ).
thf(1603,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1508]) ).
thf(1604,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
| ~ ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1509]) ).
thf(1605,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) )
= $false )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1510]) ).
thf(1606,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( SV127 @ SV324 )
= $false )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( ~ ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1511]) ).
thf(1607,plain,
! [SV342: $i,SV128: $i,SV255: $i > $o] :
( ( ( in @ ( sK34_Xx @ SV255 @ SV128 ) @ SV128 )
= $true )
| ( ( SV255 @ SV342 )
= $true )
| ( ( in @ SV342 @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1512]) ).
thf(1608,plain,
! [SV342: $i,SV128: $i,SV255: $i > $o] :
( ( ( ~ ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) ) )
= $true )
| ( ( SV255 @ SV342 )
= $true )
| ( ( in @ SV342 @ SV128 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1513]) ).
thf(1609,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1514]) ).
thf(1610,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( SV129 @ SV325 )
= $false )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( ~ ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1515]) ).
thf(1611,plain,
! [SV326: $i,SV130: $i > $o] :
( ( ( SV130 @ SV326 )
= $false )
| ( ( SV326
= ( sK19_SY56 @ SV326 @ SV130 ) )
= $false )
| ( ( SV130
@ ( descr
@ ^ [SY1338: $i] : ( SV130 @ SY1338 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1517]) ).
thf(1612,plain,
! [SV356: $i,SV131: $i,SV374: $i] :
( ( ( SV374 = SV131 )
= $true )
| ( ( in @ SV374 @ SV356 )
= $true )
| ( ( in @ SV374 @ ( setadjoin @ SV131 @ SV356 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1518]) ).
thf(1613,plain,
! [SV393: $i,SV131: $i,SV400: $i] :
( ( ( SV400 != SV131 )
| ( in @ SV400 @ ( setadjoin @ SV131 @ SV393 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1519]) ).
thf(1614,plain,
! [SV131: $i,SV394: $i,SV401: $i] :
( ( ~ ( in @ SV401 @ SV394 )
| ( in @ SV401 @ ( setadjoin @ SV131 @ SV394 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1520]) ).
thf(1615,plain,
! [SV132: $i,SV380: $i,SV256: $i > $o] :
( ( ( SV256 @ SV380 )
= $false )
| ( ( ~ ( in @ SV380 @ SV132 ) )
= $true )
| ( ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1521]) ).
thf(1616,plain,
! [SV132: $i,SV381: $i,SV256: $i > $o] :
( ( ( SV256 @ SV381 )
= $false )
| ( ( ~ ( in @ SV381 @ SV132 ) )
= $true )
| ( ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1522]) ).
thf(1617,plain,
! [SV357: $i,SV133: $i,SV327: $i] :
( ( ( in @ SV327 @ ( setunion @ SV133 ) )
= $false )
| ( ( SV133
= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV357 @ ( setunion @ SV133 ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1523]) ).
thf(1618,plain,
! [SV135: $i,SV358: $o,SV258: $i] :
( ( ( in @ SV258 @ ( sK30_B @ SV358 @ SV258 @ SV135 ) )
= $true )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1524]) ).
thf(1619,plain,
! [SV135: $i,SV258: $i,SV358: $o] :
( ( ( ~ ( ~ ( in @ ( sK30_B @ SV358 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SV358 ) )
= $true )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1525]) ).
thf(1620,plain,
! [SV135: $i,SV258: $i] :
( ( ( in @ SV258 @ ( sK30_B @ $true @ SV258 @ SV135 ) )
= $true )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1526]) ).
thf(1621,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_B @ $true @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $true ) )
= $true )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1527]) ).
thf(1622,plain,
! [SV135: $i,SV258: $i] :
( ( ( in @ SV258 @ ( sK30_B @ $false @ SV258 @ SV135 ) )
= $true )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1528]) ).
thf(1623,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( ~ ( in @ ( sK30_B @ $false @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $false ) )
= $true )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1529]) ).
thf(1624,plain,
! [SV328: $i,SV402: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV402 )
| ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV402 = SY1610 ) ) )
= $true )
| ( ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1530]) ).
thf(1625,plain,
! [SV328: $i,SV136: $i > $o] :
( ( ( SV136 @ SV328 )
= $false )
| ( ( SV328
= ( sK47_SY223 @ SV328 @ SV136 ) )
= $false )
| ( ( ! [SY1355: $i] :
( ~ ( SV136 @ SY1355 )
| ! [SY1356: $i] :
( ~ ( SV136 @ SY1356 )
| ( SY1355 = SY1356 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1531]) ).
thf(1626,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 ) )
= $false )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1627,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
= $false )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1532]) ).
thf(1628,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
| ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
= $false )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1533]) ).
thf(1629,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( ( SV329
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 ) )
= $false )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1534]) ).
thf(1630,plain,
! [SV343: $i,SV382: $i,SV359: $i] :
( ( ( in @ SV359 @ SV382 )
= $false )
| ( ( ~ ( in @ SV382 @ SV343 ) )
= $true )
| ( ( in @ SV359 @ ( setunion @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1536]) ).
thf(1631,plain,
! [SV344: $i,SV360: $i] :
( ( ( ~ ( in @ SV360 @ ( sK7_B @ SV360 @ SV344 ) ) )
= $false )
| ( ( in @ SV360 @ ( setunion @ SV344 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1537]) ).
thf(1632,plain,
! [SV344: $i,SV360: $i] :
( ( ( ~ ( in @ ( sK7_B @ SV360 @ SV344 ) @ SV344 ) )
= $false )
| ( ( in @ SV360 @ ( setunion @ SV344 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1537]) ).
thf(1633,plain,
! [SV261: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1538]) ).
thf(1634,plain,
! [SV139: $i > $i > $o,SV261: $i] :
( ( ( ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1539]) ).
thf(1635,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
| ~ ( ( SV383
!= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) ) ) )
= $false )
| ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1540]) ).
thf(1636,plain,
! [SV263: $i > $o,SV141: $i,SV384: $i] :
( ( ( in @ SV384 @ SV141 )
= $false )
| ( ( ~ ( SV263 @ SV384 ) )
= $true )
| ( ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1541]) ).
thf(1637,plain,
! [SV263: $i > $o,SV141: $i,SV385: $i] :
( ( ( in @ SV385 @ SV141 )
= $false )
| ( ( ~ ( SV263 @ SV385 ) )
= $true )
| ( ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1542]) ).
thf(1638,plain,
! [SV345: $i > $o,SV361: $i > $o] :
( ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1543]) ).
thf(1639,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
| ~ ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) ) ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1544]) ).
thf(1640,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1545]) ).
thf(1641,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
| ~ ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) ) ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1546]) ).
thf(1642,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ~ ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
| ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1547]) ).
thf(1643,plain,
! [SV144: $i,SV375: $i,SV363: $i > $o] :
( ( ( ~ ( SV363 @ SV375 ) )
= $true )
| ( ( in @ SV375
@ ( dsetconstr @ SV144
@ ^ [SY1590: $i] : ( SV363 @ SY1590 ) ) )
= $true )
| ( ( in @ SV375 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1548]) ).
thf(1644,plain,
! [SV364: $i > $o,SV144: $i,SV376: $i] :
( ( ( ~ ( in @ SV376
@ ( dsetconstr @ SV144
@ ^ [SY1592: $i] : ( SV364 @ SY1592 ) ) ) )
= $true )
| ( ( SV364 @ SV376 )
= $true )
| ( ( in @ SV376 @ SV144 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1549]) ).
thf(1645,plain,
! [SV145: $i] :
( ( ( in @ ( sK8_Xx @ SV145 ) @ omega )
= $true )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1550]) ).
thf(1646,plain,
! [SV145: $i] :
( ( ( in @ ( sK8_Xx @ SV145 ) @ SV145 )
= $true )
| ( ( ~ ( in @ emptyset @ SV145 ) )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1551]) ).
thf(1647,plain,
! [SV145: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ omega )
| ( in @ SV403 @ SV145 ) )
= $true )
| ( ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 )
= $false )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1552]) ).
thf(1648,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( ( SV331
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
| ~ ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) )
= $false )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1553]) ).
thf(1649,plain,
! [SV268: $i,SV148: $i,SV404: $i] :
( ( ~ ( in @ SV404 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SV404 @ SV148 )
| ( in @ SV404 @ SV268 )
| ! [SX3: $o] : SX3 )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1557]) ).
thf(1650,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( ~ ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
| ( in @ SV405 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1558]) ).
thf(1651,plain,
! [SV268: $i,SV148: $i,SV406: $i] :
( ( ~ ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
| ! [SY1613: $o] :
( ~ SY1613
| ( in @ SV406 @ SV268 )
| SY1613 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1559]) ).
thf(1652,plain,
! [SV268: $i,SV148: $i] :
( ( ( ! [SY1521: $i] :
~ ( in @ SY1521 @ ( binunion @ SV148 @ SV268 ) ) )
= $true )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1560]) ).
thf(1653,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) )
= $false )
| ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1561]) ).
thf(1654,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) )
| ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1562]) ).
thf(1655,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
| ~ ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1563]) ).
thf(1656,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ~ ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1564]) ).
thf(1657,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ( in @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV152 ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1658,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ~ ( ~ ( in @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1565]) ).
thf(1659,plain,
! [SV272: $i > $o,SV395: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
| ~ ( ( SV395
!= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV153 @ SV395 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1566]) ).
thf(1660,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1567]) ).
thf(1661,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
| ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1568]) ).
thf(1662,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( ~ ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1569]) ).
thf(1663,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) ) )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1570]) ).
thf(1664,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1570]) ).
thf(1665,plain,
! [SV155: $i,SV273: $i] :
( ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV273 )
= $false )
| ( ( in @ ( sK5_Xx @ SV273 @ SV155 ) @ SV155 )
= $false )
| ( ( SV155 = SV273 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1571]) ).
thf(1666,plain,
! [SV224: $i,SV373: $i,SV77: $i,SV351: $i] :
( ( ( in @ SV351 @ SV77 )
= $false )
| ( ( in @ SV373 @ SV224 )
= $true )
| ( ( SV351 = SV373 )
= $false )
| ( ( SV77 = SV224 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1572]) ).
thf(1667,plain,
! [SV337: $i,SV112: $i,SV245: $i > $o] :
( ( ( SV245 @ ( sK78_Xx @ SV245 @ SV112 ) )
= $true )
| ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
= ( setadjoin @ SV337 @ emptyset ) )
= $false )
| ( ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1573]) ).
thf(1668,plain,
! [SV337: $i,SV112: $i,SV245: $i > $o] :
( ( ( in @ ( sK78_Xx @ SV245 @ SV112 ) @ SV112 )
= $true )
| ( ( ( dsetconstr @ SV112
@ ^ [SY1477: $i] : ( SV245 @ SY1477 ) )
= ( setadjoin @ SV337 @ emptyset ) )
= $false )
| ( ( in @ SV337
@ ( dsetconstr @ SV112
@ ^ [SY1478: $i] : ( SV245 @ SY1478 ) ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1574]) ).
thf(1669,plain,
! [SV113: $i,SV353: $i] :
( ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1575]) ).
thf(1670,plain,
! [SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 ) )
= $true )
| ( ( ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1576]) ).
thf(1671,plain,
! [SV396: $i,SV113: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ ( sK14_B @ SV113 ) )
| ~ ( in @ SV396 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV386 )
| ( in @ SY1607 @ SV396 ) )
| ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1577]) ).
thf(1672,plain,
! [SV113: $i] :
( ( ! [SY1286: $i] :
( ~ ( in @ SY1286 @ ( sK14_B @ SV113 ) )
| ! [SY1287: $i] :
( ~ ( in @ SY1287 @ SY1286 )
| ( in @ SY1287 @ SV113 ) ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1578]) ).
thf(1673,plain,
! [SV113: $i] :
( ( ! [SY1288: $i,SY1289: $i] :
( ~ ( in @ SY1288 @ SV113 )
| ~ ( in @ SY1289 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ~ ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) )
| ~ ( ( in @ SY1288 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) )
| ( in @ SY1289 @ ( sK15_SY1084 @ SY1289 @ SY1288 @ SV113 ) ) ) ) )
| ( SY1288 = SY1289 ) ) )
= $true ),
inference(extcnf_not_neg,[status(thm)],[1579]) ).
thf(1674,plain,
! [SV338: $i,SV354: $i] :
( ( ( in @ ( sK6_Xx @ SV354 @ SV338 ) @ SV338 )
= $false )
| ( ( in @ SV354 @ ( powerset @ SV338 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1581]) ).
thf(1675,plain,
! [SV339: $i,SV355: $i,SV387: $i] :
( ( ( in @ SV387 @ SV355 )
= $false )
| ( ( in @ SV387 @ SV339 )
= $true )
| ( ( in @ SV355 @ ( powerset @ SV339 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1582]) ).
thf(1676,plain,
! [SV340: $i,SV114: $i,SV246: $i > $o] :
( ( ( SV246 @ ( sK39_Xx @ SV246 @ SV114 ) )
= $false )
| ( ( SV246 @ SV340 )
= $true )
| ( ( in @ SV340 @ SV114 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1584]) ).
thf(1677,plain,
! [SV341: $i,SV115: $i,SV247: $i > $o] :
( ( ( SV247 @ ( sK37_Xx @ SV247 @ SV115 ) )
= $false )
| ( ( SV247 @ SV341 )
= $true )
| ( ( in @ SV341 @ SV115 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1586]) ).
thf(1678,plain,
! [SV248: $i,SV116: $i,SV397: $i,SV388: $i] :
( ( ( SV388 != SV397 )
= $true )
| ( ( ~ ( in @ SV388 @ SV116 )
| ( in @ SV397 @ SV248 ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1587]) ).
thf(1679,plain,
! [SV116: $i,SV248: $i,SV398: $i,SV389: $i] :
( ( ( SV389 != SV398 )
= $true )
| ( ( ~ ( in @ SV398 @ SV248 )
| ( in @ SV389 @ SV116 ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1588]) ).
thf(1680,plain,
! [SV119: $i,SV390: $i,SV250: $i > $o] :
( ( ( SV250 @ SV390 )
= $false )
| ( ( ~ ( in @ SV390 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1590]) ).
thf(1681,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1591]) ).
thf(1682,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
| ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1592]) ).
thf(1683,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) ) )
= $false )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1684,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) )
= $false )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1593]) ).
thf(1685,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) )
| ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) )
= $false )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1594]) ).
thf(1686,plain,
! [SV321: $i,SV399: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ SV399 ) )
= $true )
| ( ( ! [SY1609: $i] :
( ~ ( SV121 @ SY1609 )
| ( SV399 = SY1609 ) ) )
= $true )
| ( ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1595]) ).
thf(1687,plain,
! [SV321: $i,SV407: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ SV407 )
| ! [SY1614: $i] :
( ~ ( SV121 @ SY1614 )
| ( SV407 = SY1614 ) ) )
= $true )
| ( ( SV321
= ( sK56_SY247 @ SV321 @ SV121 ) )
= $false )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1596]) ).
thf(1688,plain,
! [SV122: $i,SV378: $i,SV251: $i > $o] :
( ( ( SV251 @ SV378 )
= $false )
| ( ( in @ SV378 @ SV122 )
= $false )
| ( ( SV251 @ ( sK36_Xx @ SV251 @ SV122 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1597]) ).
thf(1689,plain,
! [SV122: $i,SV379: $i,SV251: $i > $o] :
( ( ( SV251 @ SV379 )
= $false )
| ( ( in @ SV379 @ SV122 )
= $false )
| ( ( in @ ( sK36_Xx @ SV251 @ SV122 ) @ SV122 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1598]) ).
thf(1690,plain,
! [SV322: $i,SV124: $i,SV391: $i] :
( ( ( in @ SV391 @ ( sK13_B @ SV124 ) )
= $false )
| ( ( ~ ( in @ SV391 @ SV124 ) )
= $true )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1599]) ).
thf(1691,plain,
! [SV125: $i,SV392: $i,SV253: $i > $o] :
( ( ( SV253 @ SV392 )
= $false )
| ( ( ~ ( in @ SV392 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1600]) ).
thf(1692,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1601]) ).
thf(1693,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
| ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1602]) ).
thf(1694,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1695,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1603]) ).
thf(1696,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1697,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1604]) ).
thf(1698,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) ) )
= $false )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1699,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) )
= $false )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1605]) ).
thf(1700,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) )
| ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) )
= $false )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1606]) ).
thf(1701,plain,
! [SV342: $i,SV128: $i,SV255: $i > $o] :
( ( ( SV255 @ ( sK34_Xx @ SV255 @ SV128 ) )
= $false )
| ( ( SV255 @ SV342 )
= $true )
| ( ( in @ SV342 @ SV128 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1608]) ).
thf(1702,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) ) )
= $false )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1703,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) )
= $false )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1609]) ).
thf(1704,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) )
| ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) )
= $false )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1610]) ).
thf(1705,plain,
! [SV393: $i,SV131: $i,SV400: $i] :
( ( ( SV400 != SV131 )
= $true )
| ( ( in @ SV400 @ ( setadjoin @ SV131 @ SV393 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1613]) ).
thf(1706,plain,
! [SV131: $i,SV394: $i,SV401: $i] :
( ( ( ~ ( in @ SV401 @ SV394 ) )
= $true )
| ( ( in @ SV401 @ ( setadjoin @ SV131 @ SV394 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1614]) ).
thf(1707,plain,
! [SV256: $i > $o,SV132: $i,SV380: $i] :
( ( ( in @ SV380 @ SV132 )
= $false )
| ( ( SV256 @ SV380 )
= $false )
| ( ( in @ ( sK35_Xx @ SV256 @ SV132 ) @ SV132 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1615]) ).
thf(1708,plain,
! [SV256: $i > $o,SV132: $i,SV381: $i] :
( ( ( in @ SV381 @ SV132 )
= $false )
| ( ( SV256 @ SV381 )
= $false )
| ( ( SV256 @ ( sK35_Xx @ SV256 @ SV132 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1616]) ).
thf(1709,plain,
! [SV327: $i,SV357: $i,SV133: $i] :
( ( ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
| ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) )
= $false )
| ( ( in @ SV357 @ ( setunion @ SV133 ) )
= $false )
| ( ( SV133
= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV327 @ ( setunion @ SV133 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1617]) ).
thf(1710,plain,
! [SV135: $i,SV258: $i,SV358: $o] :
( ( ( ~ ( in @ ( sK30_B @ SV358 @ SV258 @ SV135 ) @ SV135 )
| ~ ~ SV358 )
= $false )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1619]) ).
thf(1711,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ ( sK30_B @ $true @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $true )
= $false )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1621]) ).
thf(1712,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ ( sK30_B @ $false @ SV258 @ SV135 ) @ SV135 )
| ~ ~ $false )
= $false )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1623]) ).
thf(1713,plain,
! [SV328: $i,SV402: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV402 ) )
= $true )
| ( ( ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV402 = SY1610 ) ) )
= $true )
| ( ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1624]) ).
thf(1714,plain,
! [SV328: $i,SV408: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV408 )
| ! [SY1615: $i] :
( ~ ( SV136 @ SY1615 )
| ( SV408 = SY1615 ) ) )
= $true )
| ( ( SV328
= ( sK47_SY223 @ SV328 @ SV136 ) )
= $false )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1625]) ).
thf(1715,plain,
! [SV137: $i,SV259: $i] :
( ( ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
= $true )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1626]) ).
thf(1716,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
= $true )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1627]) ).
thf(1717,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 ) )
= $false )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1718,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
= $false )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1628]) ).
thf(1719,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( SV329
!= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1720,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( ~ ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 ) )
= $false )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1629]) ).
thf(1721,plain,
! [SV359: $i,SV343: $i,SV382: $i] :
( ( ( in @ SV382 @ SV343 )
= $false )
| ( ( in @ SV359 @ SV382 )
= $false )
| ( ( in @ SV359 @ ( setunion @ SV343 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1630]) ).
thf(1722,plain,
! [SV344: $i,SV360: $i] :
( ( ( in @ SV360 @ ( sK7_B @ SV360 @ SV344 ) )
= $true )
| ( ( in @ SV360 @ ( setunion @ SV344 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1631]) ).
thf(1723,plain,
! [SV344: $i,SV360: $i] :
( ( ( in @ ( sK7_B @ SV360 @ SV344 ) @ SV344 )
= $true )
| ( ( in @ SV360 @ ( setunion @ SV344 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1632]) ).
thf(1724,plain,
! [SV261: $i,SV409: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1616: $i] :
( ~ ( SV139 @ SY1616 @ SV409 )
| ~ ( in @ SY1616 @ SV261 ) )
| ( in @ SV409 @ ( sK9_B @ SV261 @ SV139 ) ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1633]) ).
thf(1725,plain,
! [SV139: $i > $i > $o,SV261: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV410 )
| ~ ( in @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1634]) ).
thf(1726,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) ) )
= $false )
| ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1727,plain,
! [SV139: $i > $i > $o,SV261: $i,SV383: $i] :
( ( ( ~ ( ( SV383
!= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) ) ) )
= $false )
| ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1635]) ).
thf(1728,plain,
! [SV141: $i,SV384: $i,SV263: $i > $o] :
( ( ( SV263 @ SV384 )
= $false )
| ( ( in @ SV384 @ SV141 )
= $false )
| ( ( SV263 @ ( sK38_Xx @ SV263 @ SV141 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1636]) ).
thf(1729,plain,
! [SV141: $i,SV385: $i,SV263: $i > $o] :
( ( ( SV263 @ SV385 )
= $false )
| ( ( in @ SV385 @ SV141 )
= $false )
| ( ( in @ ( sK38_Xx @ SV263 @ SV141 ) @ SV141 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1637]) ).
thf(1730,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1638]) ).
thf(1731,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ~ ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
| ~ ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1639]) ).
thf(1732,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1640]) ).
thf(1733,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
| ~ ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1641]) ).
thf(1734,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ~ ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1735,plain,
! [SV142: $i,SV330: $i,SV264: $i > $o] :
( ( ( ~ ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1642]) ).
thf(1736,plain,
! [SV144: $i,SV375: $i,SV363: $i > $o] :
( ( ( SV363 @ SV375 )
= $false )
| ( ( in @ SV375
@ ( dsetconstr @ SV144
@ ^ [SY1590: $i] : ( SV363 @ SY1590 ) ) )
= $true )
| ( ( in @ SV375 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1643]) ).
thf(1737,plain,
! [SV364: $i > $o,SV144: $i,SV376: $i] :
( ( ( in @ SV376
@ ( dsetconstr @ SV144
@ ^ [SY1592: $i] : ( SV364 @ SY1592 ) ) )
= $false )
| ( ( SV364 @ SV376 )
= $true )
| ( ( in @ SV376 @ SV144 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1644]) ).
thf(1738,plain,
! [SV145: $i] :
( ( ( in @ emptyset @ SV145 )
= $false )
| ( ( in @ ( sK8_Xx @ SV145 ) @ omega )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1645]) ).
thf(1739,plain,
! [SV145: $i] :
( ( ( in @ emptyset @ SV145 )
= $false )
| ( ( in @ ( sK8_Xx @ SV145 ) @ SV145 )
= $true )
| ( ( ! [SY1379: $i] :
( ~ ( in @ SY1379 @ omega )
| ( in @ SY1379 @ SV145 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1646]) ).
thf(1740,plain,
! [SV145: $i,SV403: $i] :
( ( ( ~ ( in @ SV403 @ omega ) )
= $true )
| ( ( in @ SV403 @ SV145 )
= $true )
| ( ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 )
= $false )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1647]) ).
thf(1741,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( SV331
!= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1648]) ).
thf(1742,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( ~ ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) ) )
= $false )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1648]) ).
thf(1743,plain,
! [SV268: $i,SV148: $i,SV404: $i] :
( ( ( ~ ( in @ SV404 @ ( binunion @ SV148 @ SV268 ) ) )
= $true )
| ( ( ( in @ SV404 @ SV148 )
| ( in @ SV404 @ SV268 )
| ! [SX3: $o] : SX3 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1649]) ).
thf(1744,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( ( ~ ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) ) )
= $true )
| ( ( ( in @ SV405 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1650]) ).
thf(1745,plain,
! [SV268: $i,SV148: $i,SV406: $i] :
( ( ( ~ ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) ) )
= $true )
| ( ( ! [SY1613: $o] :
( ~ SY1613
| ( in @ SV406 @ SV268 )
| SY1613 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1651]) ).
thf(1746,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( ( ~ ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) ) )
= $true )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1652]) ).
thf(1747,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) ) )
= $false )
| ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1748,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) )
= $false )
| ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1653]) ).
thf(1749,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ ( sK44_SY1097 @ SV149 ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1750,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) ) ) )
= $false )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1654]) ).
thf(1751,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1655]) ).
thf(1752,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1655]) ).
thf(1753,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ~ ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1754,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1656]) ).
thf(1755,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( in @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV152 )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1657]) ).
thf(1756,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ( ~ ( in @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1658]) ).
thf(1757,plain,
! [SV272: $i > $o,SV395: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
| ~ ( ( SV395
!= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV153 @ SV395 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1659]) ).
thf(1758,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) ) )
= $true )
| ( ( ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1660]) ).
thf(1759,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1661]) ).
thf(1760,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) )
| ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) )
= $false )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1662]) ).
thf(1761,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) ) )
= $true )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1663]) ).
thf(1762,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( SV154 @ ( sK45_SY210 @ SV154 ) )
= $true )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1664]) ).
thf(1763,plain,
! [SV113: $i,SV353: $i,SV412: $i] :
( ( ( ~ ( in @ SV412 @ SV353 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1669]) ).
thf(1764,plain,
! [SV113: $i,SV353: $i] :
( ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( ! [SY1578: $i] :
~ ( in @ SY1578 @ SV353 ) )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1670]) ).
thf(1765,plain,
! [SV396: $i,SV113: $i,SV386: $i] :
( ( ( ~ ( in @ SV386 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( ~ ( in @ SV396 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV386 )
| ( in @ SY1607 @ SV396 ) )
| ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1671]) ).
thf(1766,plain,
! [SV113: $i,SV413: $i] :
( ( ~ ( in @ SV413 @ ( sK14_B @ SV113 ) )
| ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV413 )
| ( in @ SY1617 @ SV113 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1672]) ).
thf(1767,plain,
! [SV113: $i,SV414: $i] :
( ( ! [SY1618: $i] :
( ~ ( in @ SV414 @ SV113 )
| ~ ( in @ SY1618 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SY1618 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SY1618 @ SV414 @ SV113 ) )
| ~ ( in @ SY1618 @ ( sK15_SY1084 @ SY1618 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SY1618 @ SV414 @ SV113 ) )
| ( in @ SY1618 @ ( sK15_SY1084 @ SY1618 @ SV414 @ SV113 ) ) ) ) )
| ( SV414 = SY1618 ) ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1673]) ).
thf(1768,plain,
! [SV248: $i,SV116: $i,SV397: $i,SV388: $i] :
( ( ( SV388 = SV397 )
= $false )
| ( ( ~ ( in @ SV388 @ SV116 )
| ( in @ SV397 @ SV248 ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1678]) ).
thf(1769,plain,
! [SV116: $i,SV248: $i,SV398: $i,SV389: $i] :
( ( ( SV389 = SV398 )
= $false )
| ( ( ~ ( in @ SV398 @ SV248 )
| ( in @ SV389 @ SV116 ) )
= $true )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1679]) ).
thf(1770,plain,
! [SV250: $i > $o,SV119: $i,SV390: $i] :
( ( ( in @ SV390 @ SV119 )
= $false )
| ( ( SV250 @ SV390 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1680]) ).
thf(1771,plain,
! [SV119: $i,SV415: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV415 )
| ~ ( in @ SV415 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1681]) ).
thf(1772,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1773,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1682]) ).
thf(1774,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) ) )
= $true )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1683]) ).
thf(1775,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( SV120 @ ( sK20_Xx @ SV120 ) )
= $true )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1684]) ).
thf(1776,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) ) )
= $false )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1685]) ).
thf(1777,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ~ ( SV120 @ ( sK20_Xx @ SV120 ) ) )
= $false )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1685]) ).
thf(1778,plain,
! [SV321: $i,SV399: $i,SV121: $i > $o] :
( ( ( SV121 @ SV399 )
= $false )
| ( ( ! [SY1609: $i] :
( ~ ( SV121 @ SY1609 )
| ( SV399 = SY1609 ) ) )
= $true )
| ( ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1686]) ).
thf(1779,plain,
! [SV321: $i,SV407: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ SV407 ) )
= $true )
| ( ( ! [SY1614: $i] :
( ~ ( SV121 @ SY1614 )
| ( SV407 = SY1614 ) ) )
= $true )
| ( ( SV321
= ( sK56_SY247 @ SV321 @ SV121 ) )
= $false )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1687]) ).
thf(1780,plain,
! [SV322: $i,SV124: $i,SV391: $i] :
( ( ( in @ SV391 @ SV124 )
= $false )
| ( ( in @ SV391 @ ( sK13_B @ SV124 ) )
= $false )
| ( ( in @ SV322 @ SV124 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1690]) ).
thf(1781,plain,
! [SV253: $i > $o,SV125: $i,SV392: $i] :
( ( ( in @ SV392 @ SV125 )
= $false )
| ( ( SV253 @ SV392 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1691]) ).
thf(1782,plain,
! [SV125: $i,SV416: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV416 )
| ~ ( in @ SV416 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1692]) ).
thf(1783,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1784,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1693]) ).
thf(1785,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ( in @ SV323 @ SV126 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1694]) ).
thf(1786,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1695]) ).
thf(1787,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1696]) ).
thf(1788,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1697]) ).
thf(1789,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) ) )
= $true )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1698]) ).
thf(1790,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) )
= $true )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1699]) ).
thf(1791,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) ) )
= $false )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1792,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ~ ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) )
= $false )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1700]) ).
thf(1793,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) ) )
= $true )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1702]) ).
thf(1794,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( SV129 @ ( sK40_SY197 @ SV129 ) )
= $true )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1703]) ).
thf(1795,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) ) )
= $false )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1796,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ ( sK40_SY197 @ SV129 ) ) )
= $false )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1704]) ).
thf(1797,plain,
! [SV393: $i,SV131: $i,SV400: $i] :
( ( ( SV400 = SV131 )
= $false )
| ( ( in @ SV400 @ ( setadjoin @ SV131 @ SV393 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1705]) ).
thf(1798,plain,
! [SV131: $i,SV394: $i,SV401: $i] :
( ( ( in @ SV401 @ SV394 )
= $false )
| ( ( in @ SV401 @ ( setadjoin @ SV131 @ SV394 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1706]) ).
thf(1799,plain,
! [SV327: $i,SV357: $i,SV133: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
!= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
= $false )
| ( ( in @ SV357 @ ( setunion @ SV133 ) )
= $false )
| ( ( SV133
= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV327 @ ( setunion @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1709]) ).
thf(1800,plain,
! [SV327: $i,SV357: $i,SV133: $i] :
( ( ( ~ ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) ) )
= $false )
| ( ( in @ SV357 @ ( setunion @ SV133 ) )
= $false )
| ( ( SV133
= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV327 @ ( setunion @ SV133 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1709]) ).
thf(1801,plain,
! [SV135: $i,SV258: $i,SV358: $o] :
( ( ( ~ ( in @ ( sK30_B @ SV358 @ SV258 @ SV135 ) @ SV135 ) )
= $false )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1802,plain,
! [SV135: $i,SV258: $i,SV358: $o] :
( ( ( ~ ~ SV358 )
= $false )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1710]) ).
thf(1803,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ ( sK30_B @ $true @ SV258 @ SV135 ) @ SV135 ) )
= $false )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1804,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ~ $true )
= $false )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1711]) ).
thf(1805,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ( in @ ( sK30_B @ $false @ SV258 @ SV135 ) @ SV135 ) )
= $false )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1712]) ).
thf(1806,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ ~ $false )
= $false )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1712]) ).
thf(1807,plain,
! [SV328: $i,SV402: $i,SV136: $i > $o] :
( ( ( SV136 @ SV402 )
= $false )
| ( ( ! [SY1610: $i] :
( ~ ( SV136 @ SY1610 )
| ( SV402 = SY1610 ) ) )
= $true )
| ( ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1713]) ).
thf(1808,plain,
! [SV328: $i,SV408: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV408 ) )
= $true )
| ( ( ! [SY1615: $i] :
( ~ ( SV136 @ SY1615 )
| ( SV408 = SY1615 ) ) )
= $true )
| ( ( SV328
= ( sK47_SY223 @ SV328 @ SV136 ) )
= $false )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1714]) ).
thf(1809,plain,
! [SV137: $i,SV259: $i] :
( ( ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 )
= $false )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV137 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1716]) ).
thf(1810,plain,
! [SV137: $i,SV259: $i] :
( ( ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV259 )
= $true )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1717]) ).
thf(1811,plain,
! [SV137: $i,SV259: $i] :
( ( ( ~ ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 ) )
= $true )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1718]) ).
thf(1812,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( SV329
= ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK70_SY468 @ SV329 @ SV260 @ SV138 ) @ ( setadjoin @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1719]) ).
thf(1813,plain,
! [SV138: $i,SV260: $i,SV329: $i] :
( ( ( in @ ( sK71_SY1107 @ SV329 @ SV260 @ SV138 ) @ SV260 )
= $true )
| ( ( in @ SV329 @ ( cartprod @ SV138 @ SV260 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1720]) ).
thf(1814,plain,
! [SV261: $i,SV409: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1616: $i] :
( ~ ( SV139 @ SY1616 @ SV409 )
| ~ ( in @ SY1616 @ SV261 ) ) )
= $true )
| ( ( in @ SV409 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1724]) ).
thf(1815,plain,
! [SV139: $i > $i > $o,SV261: $i,SV410: $i] :
( ( ( ~ ( in @ SV410 @ ( sK9_B @ SV261 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ( SV139 @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV410 )
| ~ ( in @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1725]) ).
thf(1816,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1726]) ).
thf(1817,plain,
! [SV139: $i > $i > $o,SV261: $i,SV383: $i] :
( ( ( SV383
!= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1727]) ).
thf(1818,plain,
! [SV361: $i > $o,SV417: $i,SV345: $i > $o] :
( ( ( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
| ~ ( ( SV417
!= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SV417 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1730]) ).
thf(1819,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ~ ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1820,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ~ ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1731]) ).
thf(1821,plain,
! [SV346: $i > $o,SV418: $i,SV362: $i > $o] :
( ( ( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
| ~ ( ( SV418
!= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SV418 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1732]) ).
thf(1822,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1823,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1733]) ).
thf(1824,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1734]) ).
thf(1825,plain,
! [SV142: $i,SV330: $i,SV264: $i > $o] :
( ( ( ~ ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1735]) ).
thf(1826,plain,
! [SV145: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ omega )
| ( in @ SV419 @ SV145 ) )
= $true )
| ( ( in @ ( sK8_Xx @ SV145 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1738]) ).
thf(1827,plain,
! [SV145: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ omega )
| ( in @ SV420 @ SV145 ) )
= $true )
| ( ( in @ ( sK8_Xx @ SV145 ) @ SV145 )
= $true )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1739]) ).
thf(1828,plain,
! [SV145: $i,SV403: $i] :
( ( ( in @ SV403 @ omega )
= $false )
| ( ( in @ SV403 @ SV145 )
= $true )
| ( ( in @ ( setadjoin @ ( sK8_Xx @ SV145 ) @ ( sK8_Xx @ SV145 ) ) @ SV145 )
= $false )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1740]) ).
thf(1829,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( SV331
= ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ emptyset ) @ ( setadjoin @ ( setadjoin @ ( sK72_SY474 @ SV331 @ SV266 @ SV146 ) @ ( setadjoin @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ emptyset ) ) @ emptyset ) ) )
= $true )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1741]) ).
thf(1830,plain,
! [SV146: $i,SV266: $i,SV331: $i] :
( ( ( in @ ( sK73_SY1108 @ SV331 @ SV266 @ SV146 ) @ ( setunion @ SV331 ) )
= $true )
| ( ( in @ SV331 @ ( cartprod @ SV146 @ SV266 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1742]) ).
thf(1831,plain,
! [SV268: $i,SV148: $i,SV404: $i] :
( ( ( in @ SV404 @ ( binunion @ SV148 @ SV268 ) )
= $false )
| ( ( ( in @ SV404 @ SV148 )
| ( in @ SV404 @ SV268 )
| ! [SX3: $o] : SX3 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1743]) ).
thf(1832,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false )
| ( ( ( in @ SV405 @ SV148 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1744]) ).
thf(1833,plain,
! [SV268: $i,SV148: $i,SV406: $i] :
( ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false )
| ( ( ! [SY1613: $o] :
( ~ SY1613
| ( in @ SV406 @ SV268 )
| SY1613 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1745]) ).
thf(1834,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false )
| ( ( ! [SX2: $o] :
( ~ SX2
| ~ SX2
| SX2 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1746]) ).
thf(1835,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) ) )
= $true )
| ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1747]) ).
thf(1836,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( SV149 @ ( sK42_SY204 @ SV149 ) )
= $true )
| ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1748]) ).
thf(1837,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1749]) ).
thf(1838,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ( sK43_Xx @ SV149 )
!= ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1750]) ).
thf(1839,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ( SV333 = SV151 )
| ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1751]) ).
thf(1840,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ( SV333 = SV151 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1752]) ).
thf(1841,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ! [SY1560: $o] :
( ~ SY1560
| ( in @ SV333 @ SV270 )
| SY1560 ) )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1753]) ).
thf(1842,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1754]) ).
thf(1843,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ( in @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV271 )
| ~ ~ ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1756]) ).
thf(1844,plain,
! [SV272: $i > $o,SV395: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV153 @ SV395 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1757]) ).
thf(1845,plain,
! [SV153: $i > $o,SV272: $i > $o,SV395: $i] :
( ( ( ~ ( ( SV395
!= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV153 @ SV395 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1757]) ).
thf(1846,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) ) )
= $true )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1758]) ).
thf(1847,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1759]) ).
thf(1848,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( ~ ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) ) )
= $false )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1849,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( ~ ( SV154 @ ( sK45_SY210 @ SV154 ) ) )
= $false )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1760]) ).
thf(1850,plain,
! [SV334: $i,SV421: $i,SV154: $i > $o] :
( ( ( ~ ( SV154 @ SV421 )
| ( ( sK45_SY210 @ SV154 )
= SV421 ) )
= $true )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1761]) ).
thf(1851,plain,
! [SV113: $i,SV353: $i,SV412: $i] :
( ( ( in @ SV412 @ SV353 )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1763]) ).
thf(1852,plain,
! [SV113: $i,SV353: $i,SV422: $i] :
( ( ( ~ ( in @ SV422 @ SV353 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1764]) ).
thf(1853,plain,
! [SV396: $i,SV113: $i,SV386: $i] :
( ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( ~ ( in @ SV396 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV386 )
| ( in @ SY1607 @ SV396 ) )
| ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1765]) ).
thf(1854,plain,
! [SV113: $i,SV413: $i] :
( ( ( ~ ( in @ SV413 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV413 )
| ( in @ SY1617 @ SV113 ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1766]) ).
thf(1855,plain,
! [SV423: $i,SV113: $i,SV414: $i] :
( ( ~ ( in @ SV414 @ SV113 )
| ~ ( in @ SV423 @ SV113 )
| ~ ( ~ ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) )
| ( SV414 = SV423 ) )
= $true ),
inference(extcnf_forall_pos,[status(thm)],[1767]) ).
thf(1856,plain,
! [SV248: $i,SV397: $i,SV116: $i,SV388: $i] :
( ( ( ~ ( in @ SV388 @ SV116 ) )
= $true )
| ( ( in @ SV397 @ SV248 )
= $true )
| ( ( SV388 = SV397 )
= $false )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1768]) ).
thf(1857,plain,
! [SV116: $i,SV389: $i,SV248: $i,SV398: $i] :
( ( ( ~ ( in @ SV398 @ SV248 ) )
= $true )
| ( ( in @ SV389 @ SV116 )
= $true )
| ( ( SV389 = SV398 )
= $false )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1769]) ).
thf(1858,plain,
! [SV390: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV390 )
= $false )
| ( ( in @ SV390 @ SV119 )
= $false )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1770]) ).
thf(1859,plain,
! [SV119: $i,SV415: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV415 ) )
= $true )
| ( ( ~ ( in @ SV415 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1771]) ).
thf(1860,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1772]) ).
thf(1861,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1773]) ).
thf(1862,plain,
! [SV320: $i,SV424: $i,SV120: $i > $o] :
( ( ( ~ ( SV120 @ SV424 )
| ( ( sK20_Xx @ SV120 )
= SV424 ) )
= $true )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1774]) ).
thf(1863,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( ! [SY1306: $i] :
( ~ ( SV120 @ SY1306 )
| ( ( sK20_Xx @ SV120 )
= SY1306 ) ) )
= $true )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1776]) ).
thf(1864,plain,
! [SV320: $i,SV120: $i > $o] :
( ( ( SV120 @ ( sK20_Xx @ SV120 ) )
= $true )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1777]) ).
thf(1865,plain,
! [SV321: $i,SV399: $i,SV425: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ SV425 )
| ( SV399 = SV425 ) )
= $true )
| ( ( SV121 @ SV399 )
= $false )
| ( ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1778]) ).
thf(1866,plain,
! [SV321: $i,SV407: $i,SV121: $i > $o] :
( ( ( SV121 @ SV407 )
= $false )
| ( ( ! [SY1614: $i] :
( ~ ( SV121 @ SY1614 )
| ( SV407 = SY1614 ) ) )
= $true )
| ( ( SV321
= ( sK56_SY247 @ SV321 @ SV121 ) )
= $false )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1779]) ).
thf(1867,plain,
! [SV392: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV392 )
= $false )
| ( ( in @ SV392 @ SV125 )
= $false )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1781]) ).
thf(1868,plain,
! [SV125: $i,SV416: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV416 ) )
= $true )
| ( ( ~ ( in @ SV416 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1782]) ).
thf(1869,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1783]) ).
thf(1870,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1784]) ).
thf(1871,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ SV126 )
= $true )
| ( ( ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1785]) ).
thf(1872,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1786]) ).
thf(1873,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
| ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1787]) ).
thf(1874,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 )
| ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1788]) ).
thf(1875,plain,
! [SV324: $i,SV127: $i > $o,SV426: $i] :
( ( ( ( SV426
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SV426 ) )
= $true )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1789]) ).
thf(1876,plain,
! [SV324: $i,SV427: $i,SV127: $i > $o] :
( ( ( ~ ( SV127 @ SV427 )
| ( SV427
= ( sK31_Xx @ SV127 ) ) )
= $true )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1790]) ).
thf(1877,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ! [SY1331: $i] :
( ( SY1331
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SY1331 ) ) )
= $true )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1791]) ).
thf(1878,plain,
! [SV324: $i,SV127: $i > $o] :
( ( ( ! [SY1332: $i] :
( ~ ( SV127 @ SY1332 )
| ( SY1332
= ( sK31_Xx @ SV127 ) ) ) )
= $true )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1792]) ).
thf(1879,plain,
! [SV325: $i,SV428: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV428 )
| ( ( sK40_SY197 @ SV129 )
= SV428 ) )
= $true )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1793]) ).
thf(1880,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( ! [SY1336: $i] :
( ~ ( SV129 @ SY1336 )
| ( ( sK40_SY197 @ SV129 )
= SY1336 ) ) )
= $true )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1795]) ).
thf(1881,plain,
! [SV325: $i,SV129: $i > $o] :
( ( ( SV129 @ ( sK40_SY197 @ SV129 ) )
= $true )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1796]) ).
thf(1882,plain,
! [SV327: $i,SV357: $i,SV133: $i] :
( ( ( ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1349: $i] : ( in @ ( setadjoin @ SY1349 @ emptyset ) @ SV133 ) )
= ( setadjoin @ ( sK84_SY531 @ SV133 ) @ emptyset ) )
= $true )
| ( ( in @ SV357 @ ( setunion @ SV133 ) )
= $false )
| ( ( SV133
= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV327 @ ( setunion @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1799]) ).
thf(1883,plain,
! [SV327: $i,SV357: $i,SV133: $i] :
( ( ( in @ ( sK84_SY531 @ SV133 )
@ ( dsetconstr @ ( setunion @ SV133 )
@ ^ [SY1350: $i] : ( in @ ( setadjoin @ SY1350 @ emptyset ) @ SV133 ) ) )
= $true )
| ( ( in @ SV357 @ ( setunion @ SV133 ) )
= $false )
| ( ( SV133
= ( setadjoin @ ( setadjoin @ SV327 @ emptyset ) @ ( setadjoin @ ( setadjoin @ SV327 @ ( setadjoin @ SV357 @ emptyset ) ) @ emptyset ) ) )
= $false )
| ( ( in @ SV327 @ ( setunion @ SV133 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1800]) ).
thf(1884,plain,
! [SV135: $i,SV258: $i,SV358: $o] :
( ( ( in @ ( sK30_B @ SV358 @ SV258 @ SV135 ) @ SV135 )
= $true )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1801]) ).
thf(1885,plain,
! [SV135: $i,SV258: $i,SV358: $o] :
( ( ( ~ SV358 ) = $true )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1802]) ).
thf(1886,plain,
! [SV135: $i,SV258: $i] :
( ( ( in @ ( sK30_B @ $true @ SV258 @ SV135 ) @ SV135 )
= $true )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1803]) ).
thf(1887,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1804]) ).
thf(1888,plain,
! [SV135: $i,SV258: $i] :
( ( ( in @ ( sK30_B @ $false @ SV258 @ SV135 ) @ SV135 )
= $true )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1805]) ).
thf(1889,plain,
! [SV135: $i,SV258: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1806]) ).
thf(1890,plain,
! [SV328: $i,SV402: $i,SV429: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV429 )
| ( SV402 = SV429 ) )
= $true )
| ( ( SV136 @ SV402 )
= $false )
| ( ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1807]) ).
thf(1891,plain,
! [SV328: $i,SV408: $i,SV136: $i > $o] :
( ( ( SV136 @ SV408 )
= $false )
| ( ( ! [SY1615: $i] :
( ~ ( SV136 @ SY1615 )
| ( SV408 = SY1615 ) ) )
= $true )
| ( ( SV328
= ( sK47_SY223 @ SV328 @ SV136 ) )
= $false )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1808]) ).
thf(1892,plain,
! [SV137: $i,SV259: $i] :
( ( ( in @ ( sK24_Xx @ SV259 @ SV137 ) @ SV137 )
= $false )
| ( ( SV137 = SV259 )
= $true )
| ( ( in @ ( sK25_Xx @ SV259 @ SV137 ) @ SV259 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1811]) ).
thf(1893,plain,
! [SV261: $i,SV409: $i,SV430: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ SV430 @ SV409 )
| ~ ( in @ SV430 @ SV261 ) )
= $true )
| ( ( in @ SV409 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1814]) ).
thf(1894,plain,
! [SV139: $i > $i > $o,SV261: $i,SV410: $i] :
( ( ( in @ SV410 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ( SV139 @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV410 )
| ~ ( in @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1815]) ).
thf(1895,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1816]) ).
thf(1896,plain,
! [SV139: $i > $i > $o,SV261: $i,SV383: $i] :
( ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( ~ ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 ) )
= $true )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1817]) ).
thf(1897,plain,
! [SV361: $i > $o,SV417: $i,SV345: $i > $o] :
( ( ( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
| ~ ( ( SV417
!= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) ) ) ) )
= $true )
| ( ( ~ ( SV345 @ SV417 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1818]) ).
thf(1898,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1819]) ).
thf(1899,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
| ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1820]) ).
thf(1900,plain,
! [SV346: $i > $o,SV418: $i,SV362: $i > $o] :
( ( ( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
| ~ ( ( SV418
!= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) ) ) ) )
= $true )
| ( ( ~ ( SV362 @ SV418 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1821]) ).
thf(1901,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1822]) ).
thf(1902,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
| ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1823]) ).
thf(1903,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) )
= $false )
| ( ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1824]) ).
thf(1904,plain,
! [SV142: $i,SV330: $i,SV264: $i > $o] :
( ( ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
| ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1825]) ).
thf(1905,plain,
! [SV145: $i,SV419: $i] :
( ( ( ~ ( in @ SV419 @ omega ) )
= $true )
| ( ( in @ SV419 @ SV145 )
= $true )
| ( ( in @ ( sK8_Xx @ SV145 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1826]) ).
thf(1906,plain,
! [SV145: $i,SV420: $i] :
( ( ( ~ ( in @ SV420 @ omega ) )
= $true )
| ( ( in @ SV420 @ SV145 )
= $true )
| ( ( in @ ( sK8_Xx @ SV145 ) @ SV145 )
= $true )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1827]) ).
thf(1907,plain,
! [SV268: $i,SV148: $i,SV404: $i] :
( ( ( in @ SV404 @ SV148 )
= $true )
| ( ( ( in @ SV404 @ SV268 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV404 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1831]) ).
thf(1908,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( ( in @ SV405 @ SV148 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1832]) ).
thf(1909,plain,
! [SV148: $i,SV268: $i,SV406: $i,SV431: $o] :
( ( ( ~ SV431
| ( in @ SV406 @ SV268 )
| SV431 )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1833]) ).
thf(1910,plain,
! [SV148: $i,SV268: $i,SV406: $i] :
( ( ( ~ $true
| ( in @ SV406 @ SV268 )
| $true )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1833]) ).
thf(1911,plain,
! [SV148: $i,SV268: $i,SV406: $i] :
( ( ( ~ $false
| ( in @ SV406 @ SV268 )
| $false )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1833]) ).
thf(1912,plain,
! [SV268: $i,SV148: $i,SV411: $i,SV432: $o] :
( ( ( ~ SV432
| ~ SV432
| SV432 )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1834]) ).
thf(1913,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1834]) ).
thf(1914,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1834]) ).
thf(1915,plain,
! [SV332: $i,SV433: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ SV433 )
| ( ( sK42_SY204 @ SV149 )
= SV433 ) )
= $true )
| ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1835]) ).
thf(1916,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) )
= $false )
| ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1837]) ).
thf(1917,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( ~ ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1838]) ).
thf(1918,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( SV333 = SV151 )
= $true )
| ( ( ( in @ SV333 @ SV270 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1839]) ).
thf(1919,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( SV333 = SV151 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1840]) ).
thf(1920,plain,
! [SV151: $i,SV270: $i,SV333: $i,SV434: $o] :
( ( ( ~ SV434
| ( in @ SV333 @ SV270 )
| SV434 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1841]) ).
thf(1921,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ~ $true
| ( in @ SV333 @ SV270 )
| $true )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1841]) ).
thf(1922,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ~ $false
| ( in @ SV333 @ SV270 )
| $false )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1841]) ).
thf(1923,plain,
! [SV270: $i,SV151: $i,SV333: $i,SV435: $o] :
( ( ( ~ SV435
| ~ SV435
| SV435 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1842]) ).
thf(1924,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1842]) ).
thf(1925,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1842]) ).
thf(1926,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ( in @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV271 ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1927,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ~ ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1843]) ).
thf(1928,plain,
! [SV272: $i > $o,SV395: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV153 @ SV395 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1844]) ).
thf(1929,plain,
! [SV153: $i > $o,SV272: $i > $o,SV395: $i] :
( ( ( SV395
!= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV153 @ SV395 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1845]) ).
thf(1930,plain,
! [SV153: $i > $o,SV272: $i > $o] :
( ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) )
| ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1846]) ).
thf(1931,plain,
! [SV272: $i > $o,SV436: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
| ~ ( ( SV436
!= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SV436 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1847]) ).
thf(1932,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( ! [SY1412: $i] :
( ~ ( SV154 @ SY1412 )
| ( ( sK45_SY210 @ SV154 )
= SY1412 ) ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1848]) ).
thf(1933,plain,
! [SV334: $i,SV154: $i > $o] :
( ( ( SV154 @ ( sK45_SY210 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1849]) ).
thf(1934,plain,
! [SV334: $i,SV421: $i,SV154: $i > $o] :
( ( ( ~ ( SV154 @ SV421 ) )
= $true )
| ( ( ( sK45_SY210 @ SV154 )
= SV421 )
= $true )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1850]) ).
thf(1935,plain,
! [SV412: $i,SV353: $i,SV113: $i] :
( ( ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1851]) ).
thf(1936,plain,
! [SV113: $i,SV353: $i,SV422: $i] :
( ( ( in @ SV422 @ SV353 )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( ~ ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1852]) ).
thf(1937,plain,
! [SV386: $i,SV113: $i,SV396: $i] :
( ( ( in @ SV396 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV386 )
| ( in @ SY1607 @ SV396 ) )
| ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1853]) ).
thf(1938,plain,
! [SV113: $i,SV413: $i] :
( ( ( in @ SV413 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( ! [SY1617: $i] :
( ~ ( in @ SY1617 @ SV413 )
| ( in @ SY1617 @ SV113 ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1854]) ).
thf(1939,plain,
! [SV423: $i,SV113: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV113 )
| ~ ( in @ SV423 @ SV113 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) )
| ( SV414 = SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1855]) ).
thf(1940,plain,
! [SV248: $i,SV397: $i,SV116: $i,SV388: $i] :
( ( ( in @ SV388 @ SV116 )
= $false )
| ( ( in @ SV397 @ SV248 )
= $true )
| ( ( SV388 = SV397 )
= $false )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1856]) ).
thf(1941,plain,
! [SV116: $i,SV389: $i,SV248: $i,SV398: $i] :
( ( ( in @ SV398 @ SV248 )
= $false )
| ( ( in @ SV389 @ SV116 )
= $true )
| ( ( SV389 = SV398 )
= $false )
| ( ( SV116 = SV248 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1857]) ).
thf(1942,plain,
! [SV390: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $false )
| ( ( SV250 @ SV390 )
= $false )
| ( ( in @ SV390 @ SV119 )
= $false )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1943,plain,
! [SV390: $i,SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV390 )
= $false )
| ( ( in @ SV390 @ SV119 )
= $false )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1858]) ).
thf(1944,plain,
! [SV119: $i,SV415: $i,SV250: $i > $o] :
( ( ( SV250 @ SV415 )
= $false )
| ( ( ~ ( in @ SV415 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1859]) ).
thf(1945,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1860]) ).
thf(1946,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
| ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1861]) ).
thf(1947,plain,
! [SV320: $i,SV424: $i,SV120: $i > $o] :
( ( ( ~ ( SV120 @ SV424 ) )
= $true )
| ( ( ( sK20_Xx @ SV120 )
= SV424 )
= $true )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1862]) ).
thf(1948,plain,
! [SV320: $i,SV437: $i,SV120: $i > $o] :
( ( ( ~ ( SV120 @ SV437 )
| ( ( sK20_Xx @ SV120 )
= SV437 ) )
= $true )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1863]) ).
thf(1949,plain,
! [SV321: $i,SV399: $i,SV425: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ SV425 ) )
= $true )
| ( ( SV399 = SV425 )
= $true )
| ( ( SV121 @ SV399 )
= $false )
| ( ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1865]) ).
thf(1950,plain,
! [SV321: $i,SV407: $i,SV438: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ SV438 )
| ( SV407 = SV438 ) )
= $true )
| ( ( SV121 @ SV407 )
= $false )
| ( ( SV321
= ( sK56_SY247 @ SV321 @ SV121 ) )
= $false )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1866]) ).
thf(1951,plain,
! [SV392: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $false )
| ( ( SV253 @ SV392 )
= $false )
| ( ( in @ SV392 @ SV125 )
= $false )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1952,plain,
! [SV392: $i,SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV392 )
= $false )
| ( ( in @ SV392 @ SV125 )
= $false )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1867]) ).
thf(1953,plain,
! [SV125: $i,SV416: $i,SV253: $i > $o] :
( ( ( SV253 @ SV416 )
= $false )
| ( ( ~ ( in @ SV416 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1868]) ).
thf(1954,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1869]) ).
thf(1955,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
| ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1870]) ).
thf(1956,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV126 ) )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1871]) ).
thf(1957,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1958,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1872]) ).
thf(1959,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1960,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1873]) ).
thf(1961,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1962,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1874]) ).
thf(1963,plain,
! [SV324: $i,SV127: $i > $o,SV426: $i] :
( ( ( SV426
!= ( sK31_Xx @ SV127 ) )
= $true )
| ( ( SV127 @ SV426 )
= $true )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1875]) ).
thf(1964,plain,
! [SV324: $i,SV427: $i,SV127: $i > $o] :
( ( ( ~ ( SV127 @ SV427 ) )
= $true )
| ( ( SV427
= ( sK31_Xx @ SV127 ) )
= $true )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1876]) ).
thf(1965,plain,
! [SV324: $i,SV127: $i > $o,SV439: $i] :
( ( ( ( SV439
!= ( sK31_Xx @ SV127 ) )
| ( SV127 @ SV439 ) )
= $true )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1877]) ).
thf(1966,plain,
! [SV324: $i,SV440: $i,SV127: $i > $o] :
( ( ( ~ ( SV127 @ SV440 )
| ( SV440
= ( sK31_Xx @ SV127 ) ) )
= $true )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1878]) ).
thf(1967,plain,
! [SV325: $i,SV428: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV428 ) )
= $true )
| ( ( ( sK40_SY197 @ SV129 )
= SV428 )
= $true )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1879]) ).
thf(1968,plain,
! [SV325: $i,SV441: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV441 )
| ( ( sK40_SY197 @ SV129 )
= SV441 ) )
= $true )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1880]) ).
thf(1969,plain,
! [SV135: $i,SV258: $i,SV358: $o] :
( ( SV358 = $false )
| ( SV358 = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1885]) ).
thf(1970,plain,
! [SV135: $i,SV258: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1887]) ).
thf(1971,plain,
! [SV135: $i,SV258: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV258 @ ( setunion @ SV135 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1889]) ).
thf(1972,plain,
! [SV328: $i,SV402: $i,SV429: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV429 ) )
= $true )
| ( ( SV402 = SV429 )
= $true )
| ( ( SV136 @ SV402 )
= $false )
| ( ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1890]) ).
thf(1973,plain,
! [SV328: $i,SV408: $i,SV442: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV442 )
| ( SV408 = SV442 ) )
= $true )
| ( ( SV136 @ SV408 )
= $false )
| ( ( SV328
= ( sK47_SY223 @ SV328 @ SV136 ) )
= $false )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1891]) ).
thf(1974,plain,
! [SV261: $i,SV409: $i,SV430: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ SV430 @ SV409 ) )
= $true )
| ( ( ~ ( in @ SV430 @ SV261 ) )
= $true )
| ( ( in @ SV409 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1893]) ).
thf(1975,plain,
! [SV261: $i,SV410: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV410 )
| ~ ( in @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV261 ) )
= $false )
| ( ( in @ SV410 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1894]) ).
thf(1976,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1895]) ).
thf(1977,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1896]) ).
thf(1978,plain,
! [SV361: $i > $o,SV417: $i,SV345: $i > $o] :
( ( ( ~ ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
| ~ ( ( SV417
!= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ~ ( SV345 @ SV417 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1897]) ).
thf(1979,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ~ ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) ) )
= $true )
| ( ( ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1898]) ).
thf(1980,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1899]) ).
thf(1981,plain,
! [SV346: $i > $o,SV418: $i,SV362: $i > $o] :
( ( ( ~ ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
| ~ ( ( SV418
!= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ~ ( SV362 @ SV418 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1900]) ).
thf(1982,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) ) )
= $true )
| ( ( ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1901]) ).
thf(1983,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1902]) ).
thf(1984,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
= $false )
| ( ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1903]) ).
thf(1985,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) )
= $false )
| ( ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1903]) ).
thf(1986,plain,
! [SV142: $i,SV330: $i,SV264: $i > $o] :
( ( ( ~ ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1904]) ).
thf(1987,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ~ ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 ) ) )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1904]) ).
thf(1988,plain,
! [SV145: $i,SV419: $i] :
( ( ( in @ SV419 @ omega )
= $false )
| ( ( in @ SV419 @ SV145 )
= $true )
| ( ( in @ ( sK8_Xx @ SV145 ) @ omega )
= $true )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1905]) ).
thf(1989,plain,
! [SV145: $i,SV420: $i] :
( ( ( in @ SV420 @ omega )
= $false )
| ( ( in @ SV420 @ SV145 )
= $true )
| ( ( in @ ( sK8_Xx @ SV145 ) @ SV145 )
= $true )
| ( ( in @ emptyset @ SV145 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1906]) ).
thf(1990,plain,
! [SV148: $i,SV268: $i,SV404: $i] :
( ( ( in @ SV404 @ SV268 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV404 @ SV148 )
= $true )
| ( ( in @ SV404 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1907]) ).
thf(1991,plain,
! [SV268: $i,SV148: $i,SV405: $i,SV443: $o] :
( ( ( ~ SV443
| SV443 )
= $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1908]) ).
thf(1992,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1908]) ).
thf(1993,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1908]) ).
thf(1994,plain,
! [SV148: $i,SV268: $i,SV406: $i,SV431: $o] :
( ( ( ~ SV431 ) = $true )
| ( ( ( in @ SV406 @ SV268 )
| SV431 )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1909]) ).
thf(1995,plain,
! [SV148: $i,SV268: $i,SV406: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV406 @ SV268 )
| $true )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1910]) ).
thf(1996,plain,
! [SV148: $i,SV268: $i,SV406: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV406 @ SV268 )
| $false )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1911]) ).
thf(1997,plain,
! [SV268: $i,SV148: $i,SV411: $i,SV432: $o] :
( ( ( ~ SV432 ) = $true )
| ( ( ~ SV432
| SV432 )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1912]) ).
thf(1998,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1913]) ).
thf(1999,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1914]) ).
thf(2000,plain,
! [SV332: $i,SV433: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ SV433 ) )
= $true )
| ( ( ( sK42_SY204 @ SV149 )
= SV433 )
= $true )
| ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1915]) ).
thf(2001,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) ) )
= $false )
| ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1916]) ).
thf(2002,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) )
= $false )
| ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1916]) ).
thf(2003,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) )
| ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) )
= $false )
| ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1917]) ).
thf(2004,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( in @ SV333 @ SV270 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1918]) ).
thf(2005,plain,
! [SV270: $i,SV151: $i,SV333: $i,SV444: $o] :
( ( ( ~ SV444
| SV444 )
= $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1919]) ).
thf(2006,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1919]) ).
thf(2007,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1919]) ).
thf(2008,plain,
! [SV151: $i,SV270: $i,SV333: $i,SV434: $o] :
( ( ( ~ SV434 ) = $true )
| ( ( ( in @ SV333 @ SV270 )
| SV434 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1920]) ).
thf(2009,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV333 @ SV270 )
| $true )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1921]) ).
thf(2010,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV333 @ SV270 )
| $false )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1922]) ).
thf(2011,plain,
! [SV270: $i,SV151: $i,SV333: $i,SV435: $o] :
( ( ( ~ SV435 ) = $true )
| ( ( ~ SV435
| SV435 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1923]) ).
thf(2012,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1924]) ).
thf(2013,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1925]) ).
thf(2014,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( in @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) @ SV271 )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1926]) ).
thf(2015,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ~ ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1927]) ).
thf(2016,plain,
! [SV272: $i > $o,SV395: $i,SV153: $i > $o] :
( ( ( SV153 @ SV395 )
= $false )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1928]) ).
thf(2017,plain,
! [SV153: $i > $o,SV272: $i > $o,SV395: $i] :
( ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV153 @ SV395 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1929]) ).
thf(2018,plain,
! [SV272: $i > $o,SV153: $i > $o] :
( ( ( ! [SY1532: $i] :
( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) )
| ~ ( ( SY1532
!= ( sK58_SY256 @ SY1532 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SY1532 ) ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1930]) ).
thf(2019,plain,
! [SV272: $i > $o,SV436: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
| ~ ( ( SV436
!= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV153 @ SV436 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1931]) ).
thf(2020,plain,
! [SV334: $i,SV445: $i,SV154: $i > $o] :
( ( ( ~ ( SV154 @ SV445 )
| ( ( sK45_SY210 @ SV154 )
= SV445 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1932]) ).
thf(2021,plain,
! [SV334: $i,SV421: $i,SV154: $i > $o] :
( ( ( SV154 @ SV421 )
= $false )
| ( ( ( sK45_SY210 @ SV154 )
= SV421 )
= $true )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1934]) ).
thf(2022,plain,
! [SV412: $i,SV353: $i,SV113: $i] :
( ( ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1935]) ).
thf(2023,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1935]) ).
thf(2024,plain,
! [SV422: $i,SV353: $i,SV113: $i] :
( ( ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) )
| ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1936]) ).
thf(2025,plain,
! [SV113: $i,SV396: $i,SV386: $i] :
( ( ( ! [SY1607: $i] :
( ~ ( in @ SY1607 @ SV386 )
| ( in @ SY1607 @ SV396 ) ) )
= $true )
| ( ( ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true )
| ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ SV396 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1937]) ).
thf(2026,plain,
! [SV113: $i,SV413: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ SV413 )
| ( in @ SV446 @ SV113 ) )
= $true )
| ( ( in @ SV413 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[1938]) ).
thf(2027,plain,
! [SV423: $i,SV113: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ SV113 ) )
= $true )
| ( ( ~ ( in @ SV423 @ SV113 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) )
| ( SV414 = SV423 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1939]) ).
thf(2028,plain,
! [SV390: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $true )
| ( ( SV250 @ SV390 )
= $false )
| ( ( in @ SV390 @ SV119 )
= $false )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1942]) ).
thf(2029,plain,
! [SV390: $i,SV119: $i,SV250: $i > $o] :
( ( ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) )
= $true )
| ( ( SV250 @ SV390 )
= $false )
| ( ( in @ SV390 @ SV119 )
= $false )
| ( ( in @ ( sK76_Xx @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1943]) ).
thf(2030,plain,
! [SV250: $i > $o,SV119: $i,SV415: $i] :
( ( ( in @ SV415 @ SV119 )
= $false )
| ( ( SV250 @ SV415 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1944]) ).
thf(2031,plain,
! [SV119: $i,SV447: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV447 )
| ~ ( in @ SV447 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1945]) ).
thf(2032,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2033,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ~ ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) ) ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1946]) ).
thf(2034,plain,
! [SV320: $i,SV424: $i,SV120: $i > $o] :
( ( ( SV120 @ SV424 )
= $false )
| ( ( ( sK20_Xx @ SV120 )
= SV424 )
= $true )
| ( ( SV120 @ ( sK21_SY73 @ SV320 @ SV120 ) )
= $true )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1947]) ).
thf(2035,plain,
! [SV320: $i,SV437: $i,SV120: $i > $o] :
( ( ( ~ ( SV120 @ SV437 ) )
= $true )
| ( ( ( sK20_Xx @ SV120 )
= SV437 )
= $true )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1948]) ).
thf(2036,plain,
! [SV321: $i,SV399: $i,SV425: $i,SV121: $i > $o] :
( ( ( SV121 @ SV425 )
= $false )
| ( ( SV399 = SV425 )
= $true )
| ( ( SV121 @ SV399 )
= $false )
| ( ( SV121 @ ( sK56_SY247 @ SV321 @ SV121 ) )
= $true )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1949]) ).
thf(2037,plain,
! [SV321: $i,SV407: $i,SV438: $i,SV121: $i > $o] :
( ( ( ~ ( SV121 @ SV438 ) )
= $true )
| ( ( SV407 = SV438 )
= $true )
| ( ( SV121 @ SV407 )
= $false )
| ( ( SV321
= ( sK56_SY247 @ SV321 @ SV121 ) )
= $false )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1950]) ).
thf(2038,plain,
! [SV392: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $true )
| ( ( SV253 @ SV392 )
= $false )
| ( ( in @ SV392 @ SV125 )
= $false )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1951]) ).
thf(2039,plain,
! [SV392: $i,SV125: $i,SV253: $i > $o] :
( ( ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) )
= $true )
| ( ( SV253 @ SV392 )
= $false )
| ( ( in @ SV392 @ SV125 )
= $false )
| ( ( in @ ( sK82_Xx @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[1952]) ).
thf(2040,plain,
! [SV253: $i > $o,SV125: $i,SV416: $i] :
( ( ( in @ SV416 @ SV125 )
= $false )
| ( ( SV253 @ SV416 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1953]) ).
thf(2041,plain,
! [SV125: $i,SV448: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV448 )
| ~ ( in @ SV448 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[1954]) ).
thf(2042,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2043,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ~ ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) ) ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1955]) ).
thf(2044,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ SV126 )
= $false )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1956]) ).
thf(2045,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ( in @ SV323 @ SV126 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1957]) ).
thf(2046,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ( in @ SV323 @ SV126 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1958]) ).
thf(2047,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV254 )
| ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1959]) ).
thf(2048,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1960]) ).
thf(2049,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ! [SY1552: $o] :
( ~ SY1552
| ~ ( in @ SV323 @ SV126 )
| SY1552 ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1961]) ).
thf(2050,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1962]) ).
thf(2051,plain,
! [SV324: $i,SV127: $i > $o,SV426: $i] :
( ( ( SV426
= ( sK31_Xx @ SV127 ) )
= $false )
| ( ( SV127 @ SV426 )
= $true )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1963]) ).
thf(2052,plain,
! [SV324: $i,SV427: $i,SV127: $i > $o] :
( ( ( SV127 @ SV427 )
= $false )
| ( ( SV427
= ( sK31_Xx @ SV127 ) )
= $true )
| ( ( SV127 @ ( sK32_SY141 @ SV324 @ SV127 ) )
= $true )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1964]) ).
thf(2053,plain,
! [SV324: $i,SV127: $i > $o,SV439: $i] :
( ( ( SV439
!= ( sK31_Xx @ SV127 ) )
= $true )
| ( ( SV127 @ SV439 )
= $true )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1965]) ).
thf(2054,plain,
! [SV324: $i,SV440: $i,SV127: $i > $o] :
( ( ( ~ ( SV127 @ SV440 ) )
= $true )
| ( ( SV440
= ( sK31_Xx @ SV127 ) )
= $true )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1966]) ).
thf(2055,plain,
! [SV325: $i,SV428: $i,SV129: $i > $o] :
( ( ( SV129 @ SV428 )
= $false )
| ( ( ( sK40_SY197 @ SV129 )
= SV428 )
= $true )
| ( ( SV129 @ ( sK41_Xy @ SV325 @ SV129 ) )
= $true )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1967]) ).
thf(2056,plain,
! [SV325: $i,SV441: $i,SV129: $i > $o] :
( ( ( ~ ( SV129 @ SV441 ) )
= $true )
| ( ( ( sK40_SY197 @ SV129 )
= SV441 )
= $true )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1968]) ).
thf(2057,plain,
! [SV328: $i,SV402: $i,SV429: $i,SV136: $i > $o] :
( ( ( SV136 @ SV429 )
= $false )
| ( ( SV402 = SV429 )
= $true )
| ( ( SV136 @ SV402 )
= $false )
| ( ( SV136 @ ( sK47_SY223 @ SV328 @ SV136 ) )
= $true )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1972]) ).
thf(2058,plain,
! [SV328: $i,SV408: $i,SV442: $i,SV136: $i > $o] :
( ( ( ~ ( SV136 @ SV442 ) )
= $true )
| ( ( SV408 = SV442 )
= $true )
| ( ( SV136 @ SV408 )
= $false )
| ( ( SV328
= ( sK47_SY223 @ SV328 @ SV136 ) )
= $false )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1973]) ).
thf(2059,plain,
! [SV261: $i,SV409: $i,SV430: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ SV430 @ SV409 )
= $false )
| ( ( ~ ( in @ SV430 @ SV261 ) )
= $true )
| ( ( in @ SV409 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1974]) ).
thf(2060,plain,
! [SV261: $i,SV410: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV410 ) )
= $false )
| ( ( in @ SV410 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2061,plain,
! [SV139: $i > $i > $o,SV261: $i,SV410: $i] :
( ( ( ~ ( in @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV261 ) )
= $false )
| ( ( in @ SV410 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1975]) ).
thf(2062,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2063,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i] :
( ( ( ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[1976]) ).
thf(2064,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) )
| ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1977]) ).
thf(2065,plain,
! [SV361: $i > $o,SV417: $i,SV345: $i > $o] :
( ( ( ~ ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) ) )
= $false )
| ( ( ~ ( SV345 @ SV417 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1978]) ).
thf(2066,plain,
! [SV345: $i > $o,SV361: $i > $o,SV417: $i] :
( ( ( ~ ( ( SV417
!= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ~ ( SV345 @ SV417 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1978]) ).
thf(2067,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( ~ ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) ) )
= $true )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1979]) ).
thf(2068,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1980]) ).
thf(2069,plain,
! [SV346: $i > $o,SV418: $i,SV362: $i > $o] :
( ( ( ~ ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) ) )
= $false )
| ( ( ~ ( SV362 @ SV418 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1981]) ).
thf(2070,plain,
! [SV346: $i > $o,SV362: $i > $o,SV418: $i] :
( ( ( ~ ( ( SV418
!= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ~ ( SV362 @ SV418 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[1981]) ).
thf(2071,plain,
! [SV362: $i > $o,SV346: $i > $o] :
( ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( ~ ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) ) )
= $true )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[1982]) ).
thf(2072,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[1983]) ).
thf(2073,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
= $true )
| ( ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1984]) ).
thf(2074,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) )
= $true )
| ( ( in @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) @ SV142 )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1985]) ).
thf(2075,plain,
! [SV142: $i,SV330: $i,SV264: $i > $o] :
( ( ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1986]) ).
thf(2076,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
!= SV330 )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[1987]) ).
thf(2077,plain,
! [SV148: $i,SV268: $i,SV404: $i,SV449: $o] :
( ( SV449 = $true )
| ( ( in @ SV404 @ SV268 )
= $true )
| ( ( in @ SV404 @ SV148 )
= $true )
| ( ( in @ SV404 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1990]) ).
thf(2078,plain,
! [SV148: $i,SV268: $i,SV404: $i] :
( ( $true = $true )
| ( ( in @ SV404 @ SV268 )
= $true )
| ( ( in @ SV404 @ SV148 )
= $true )
| ( ( in @ SV404 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1990]) ).
thf(2079,plain,
! [SV148: $i,SV268: $i,SV404: $i] :
( ( $false = $true )
| ( ( in @ SV404 @ SV268 )
= $true )
| ( ( in @ SV404 @ SV148 )
= $true )
| ( ( in @ SV404 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[1990]) ).
thf(2080,plain,
! [SV268: $i,SV148: $i,SV405: $i,SV443: $o] :
( ( ( ~ SV443 ) = $true )
| ( SV443 = $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1991]) ).
thf(2081,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1992]) ).
thf(2082,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[1993]) ).
thf(2083,plain,
! [SV148: $i,SV268: $i,SV406: $i,SV431: $o] :
( ( SV431 = $false )
| ( ( ( in @ SV406 @ SV268 )
| SV431 )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1994]) ).
thf(2084,plain,
! [SV148: $i,SV268: $i,SV406: $i] :
( ( $true = $false )
| ( ( ( in @ SV406 @ SV268 )
| $true )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1995]) ).
thf(2085,plain,
! [SV148: $i,SV268: $i,SV406: $i] :
( ( $false = $false )
| ( ( ( in @ SV406 @ SV268 )
| $false )
= $true )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1996]) ).
thf(2086,plain,
! [SV268: $i,SV148: $i,SV411: $i,SV432: $o] :
( ( SV432 = $false )
| ( ( ~ SV432
| SV432 )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1997]) ).
thf(2087,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1998]) ).
thf(2088,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[1999]) ).
thf(2089,plain,
! [SV332: $i,SV433: $i,SV149: $i > $o] :
( ( ( SV149 @ SV433 )
= $false )
| ( ( ( sK42_SY204 @ SV149 )
= SV433 )
= $true )
| ( ( SV149 @ ( sK43_Xx @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2000]) ).
thf(2090,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) ) )
= $true )
| ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2001]) ).
thf(2091,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( SV149 @ ( sK42_SY204 @ SV149 ) )
= $true )
| ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2002]) ).
thf(2092,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) ) )
= $false )
| ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2003]) ).
thf(2093,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ ( sK42_SY204 @ SV149 ) ) )
= $false )
| ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2003]) ).
thf(2094,plain,
! [SV151: $i,SV270: $i,SV333: $i,SV450: $o] :
( ( SV450 = $true )
| ( ( in @ SV333 @ SV270 )
= $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2004]) ).
thf(2095,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( $true = $true )
| ( ( in @ SV333 @ SV270 )
= $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2004]) ).
thf(2096,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( $false = $true )
| ( ( in @ SV333 @ SV270 )
= $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2004]) ).
thf(2097,plain,
! [SV270: $i,SV151: $i,SV333: $i,SV444: $o] :
( ( ( ~ SV444 ) = $true )
| ( SV444 = $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2005]) ).
thf(2098,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2006]) ).
thf(2099,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2007]) ).
thf(2100,plain,
! [SV151: $i,SV270: $i,SV333: $i,SV434: $o] :
( ( SV434 = $false )
| ( ( ( in @ SV333 @ SV270 )
| SV434 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2008]) ).
thf(2101,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( $true = $false )
| ( ( ( in @ SV333 @ SV270 )
| $true )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2009]) ).
thf(2102,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( $false = $false )
| ( ( ( in @ SV333 @ SV270 )
| $false )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2010]) ).
thf(2103,plain,
! [SV270: $i,SV151: $i,SV333: $i,SV435: $o] :
( ( SV435 = $false )
| ( ( ~ SV435
| SV435 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2011]) ).
thf(2104,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2012]) ).
thf(2105,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2013]) ).
thf(2106,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2015]) ).
thf(2107,plain,
! [SV395: $i,SV153: $i > $o,SV272: $i > $o] :
( ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2016]) ).
thf(2108,plain,
! [SV272: $i > $o,SV395: $i,SV153: $i > $o] :
( ( ( SV153 @ SV395 )
= $false )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2017]) ).
thf(2109,plain,
! [SV272: $i > $o,SV451: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
| ~ ( ( SV451
!= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) ) ) )
| ~ ( SV153 @ SV451 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2018]) ).
thf(2110,plain,
! [SV272: $i > $o,SV436: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
| ~ ( ( SV436
!= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV153 @ SV436 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2019]) ).
thf(2111,plain,
! [SV334: $i,SV445: $i,SV154: $i > $o] :
( ( ( ~ ( SV154 @ SV445 ) )
= $true )
| ( ( ( sK45_SY210 @ SV154 )
= SV445 )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2020]) ).
thf(2112,plain,
! [SV412: $i,SV353: $i,SV113: $i] :
( ( ( ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2022]) ).
thf(2113,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2023]) ).
thf(2114,plain,
! [SV422: $i,SV353: $i,SV113: $i] :
( ( ( ~ ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2024]) ).
thf(2115,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2024]) ).
thf(2116,plain,
! [SV113: $i,SV396: $i,SV386: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ SV386 )
| ( in @ SV452 @ SV396 ) )
= $true )
| ( ( ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true )
| ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ SV396 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2025]) ).
thf(2117,plain,
! [SV113: $i,SV413: $i,SV446: $i] :
( ( ( ~ ( in @ SV446 @ SV413 ) )
= $true )
| ( ( in @ SV446 @ SV113 )
= $true )
| ( ( in @ SV413 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2026]) ).
thf(2118,plain,
! [SV423: $i,SV113: $i,SV414: $i] :
( ( ( in @ SV414 @ SV113 )
= $false )
| ( ( ~ ( in @ SV423 @ SV113 ) )
= $true )
| ( ( ~ ( ~ ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) )
| ( SV414 = SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2027]) ).
thf(2119,plain,
! [SV415: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV415 )
= $false )
| ( ( in @ SV415 @ SV119 )
= $false )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2030]) ).
thf(2120,plain,
! [SV119: $i,SV447: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV447 ) )
= $true )
| ( ( ~ ( in @ SV447 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2031]) ).
thf(2121,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2032]) ).
thf(2122,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ( sK76_Xx @ SV250 @ SV119 )
!= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2033]) ).
thf(2123,plain,
! [SV320: $i,SV437: $i,SV120: $i > $o] :
( ( ( SV120 @ SV437 )
= $false )
| ( ( ( sK20_Xx @ SV120 )
= SV437 )
= $true )
| ( ( SV320
= ( sK21_SY73 @ SV320 @ SV120 ) )
= $false )
| ( ( SV120 @ SV320 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2035]) ).
thf(2124,plain,
! [SV321: $i,SV407: $i,SV438: $i,SV121: $i > $o] :
( ( ( SV121 @ SV438 )
= $false )
| ( ( SV407 = SV438 )
= $true )
| ( ( SV121 @ SV407 )
= $false )
| ( ( SV321
= ( sK56_SY247 @ SV321 @ SV121 ) )
= $false )
| ( ( SV121 @ SV321 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2037]) ).
thf(2125,plain,
! [SV416: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV416 )
= $false )
| ( ( in @ SV416 @ SV125 )
= $false )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2040]) ).
thf(2126,plain,
! [SV125: $i,SV448: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV448 ) )
= $true )
| ( ( ~ ( in @ SV448 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2041]) ).
thf(2127,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2042]) ).
thf(2128,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ( sK82_Xx @ SV253 @ SV125 )
!= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2043]) ).
thf(2129,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV453: $o] :
( ( SV453 = $true )
| ( ( in @ SV323 @ SV126 )
= $false )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2044]) ).
thf(2130,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $true = $true )
| ( ( in @ SV323 @ SV126 )
= $false )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2044]) ).
thf(2131,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $false = $true )
| ( ( in @ SV323 @ SV126 )
= $false )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2044]) ).
thf(2132,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ SV126 )
= $true )
| ( ( ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2045]) ).
thf(2133,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ SV126 )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2046]) ).
thf(2134,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV254 ) )
= $true )
| ( ( ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2047]) ).
thf(2135,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
| ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2048]) ).
thf(2136,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV454: $o] :
( ( ( ~ SV454
| ~ ( in @ SV323 @ SV126 )
| SV454 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2049]) ).
thf(2137,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $true
| ~ ( in @ SV323 @ SV126 )
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2049]) ).
thf(2138,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $false
| ~ ( in @ SV323 @ SV126 )
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2049]) ).
thf(2139,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 )
| ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2050]) ).
thf(2140,plain,
! [SV324: $i,SV127: $i > $o,SV439: $i] :
( ( ( SV439
= ( sK31_Xx @ SV127 ) )
= $false )
| ( ( SV127 @ SV439 )
= $true )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2053]) ).
thf(2141,plain,
! [SV324: $i,SV440: $i,SV127: $i > $o] :
( ( ( SV127 @ SV440 )
= $false )
| ( ( SV440
= ( sK31_Xx @ SV127 ) )
= $true )
| ( ( SV324
= ( sK32_SY141 @ SV324 @ SV127 ) )
= $false )
| ( ( SV127 @ SV324 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2054]) ).
thf(2142,plain,
! [SV325: $i,SV441: $i,SV129: $i > $o] :
( ( ( SV129 @ SV441 )
= $false )
| ( ( ( sK40_SY197 @ SV129 )
= SV441 )
= $true )
| ( ( SV325
= ( sK41_Xy @ SV325 @ SV129 ) )
= $false )
| ( ( SV129 @ SV325 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2056]) ).
thf(2143,plain,
! [SV328: $i,SV408: $i,SV442: $i,SV136: $i > $o] :
( ( ( SV136 @ SV442 )
= $false )
| ( ( SV408 = SV442 )
= $true )
| ( ( SV136 @ SV408 )
= $false )
| ( ( SV328
= ( sK47_SY223 @ SV328 @ SV136 ) )
= $false )
| ( ( SV136 @ SV328 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2058]) ).
thf(2144,plain,
! [SV409: $i,SV139: $i > $i > $o,SV261: $i,SV430: $i] :
( ( ( in @ SV430 @ SV261 )
= $false )
| ( ( SV139 @ SV430 @ SV409 )
= $false )
| ( ( in @ SV409 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2059]) ).
thf(2145,plain,
! [SV261: $i,SV410: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV410 )
= $true )
| ( ( in @ SV410 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2060]) ).
thf(2146,plain,
! [SV139: $i > $i > $o,SV261: $i,SV410: $i] :
( ( ( in @ ( sK10_Xy @ SV410 @ SV261 @ SV139 ) @ SV261 )
= $true )
| ( ( in @ SV410 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( in @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV261 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2061]) ).
thf(2147,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2062]) ).
thf(2148,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i] :
( ( ( ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2063]) ).
thf(2149,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ~ ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) ) )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2064]) ).
thf(2150,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i] :
( ( ( ~ ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2064]) ).
thf(2151,plain,
! [SV361: $i > $o,SV417: $i,SV345: $i > $o] :
( ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( SV345 @ SV417 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2065]) ).
thf(2152,plain,
! [SV345: $i > $o,SV361: $i > $o,SV417: $i] :
( ( ( SV417
!= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( SV345 @ SV417 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2066]) ).
thf(2153,plain,
! [SV345: $i > $o,SV361: $i > $o] :
( ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) )
| ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2067]) ).
thf(2154,plain,
! [SV361: $i > $o,SV455: $i,SV345: $i > $o] :
( ( ( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
| ~ ( ( SV455
!= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2068]) ).
thf(2155,plain,
! [SV346: $i > $o,SV418: $i,SV362: $i > $o] :
( ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( SV362 @ SV418 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2069]) ).
thf(2156,plain,
! [SV346: $i > $o,SV362: $i > $o,SV418: $i] :
( ( ( SV418
!= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( SV362 @ SV418 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2070]) ).
thf(2157,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) )
| ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2071]) ).
thf(2158,plain,
! [SV346: $i > $o,SV456: $i,SV362: $i > $o] :
( ( ( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
| ~ ( ( SV456
!= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SV456 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2072]) ).
thf(2159,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) )
= $false )
| ( ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2075]) ).
thf(2160,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
= SV330 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2076]) ).
thf(2161,plain,
! [SV268: $i,SV148: $i,SV405: $i,SV443: $o] :
( ( SV443 = $false )
| ( SV443 = $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2080]) ).
thf(2162,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2081]) ).
thf(2163,plain,
! [SV268: $i,SV148: $i,SV405: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV405 @ SV148 )
= $true )
| ( ( in @ SV405 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2082]) ).
thf(2164,plain,
! [SV148: $i,SV431: $o,SV268: $i,SV406: $i] :
( ( ( in @ SV406 @ SV268 )
= $true )
| ( SV431 = $true )
| ( SV431 = $false )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2083]) ).
thf(2165,plain,
! [SV148: $i,SV268: $i,SV406: $i] :
( ( ( in @ SV406 @ SV268 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2084]) ).
thf(2166,plain,
! [SV148: $i,SV268: $i,SV406: $i] :
( ( ( in @ SV406 @ SV268 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV406 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2085]) ).
thf(2167,plain,
! [SV268: $i,SV148: $i,SV411: $i,SV432: $o] :
( ( ( ~ SV432 ) = $true )
| ( SV432 = $true )
| ( SV432 = $false )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2086]) ).
thf(2168,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2087]) ).
thf(2169,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2088]) ).
thf(2170,plain,
! [SV332: $i,SV457: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ SV457 )
| ( ( sK42_SY204 @ SV149 )
= SV457 ) )
= $true )
| ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2090]) ).
thf(2171,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( ! [SY1393: $i] :
( ~ ( SV149 @ SY1393 )
| ( ( sK42_SY204 @ SV149 )
= SY1393 ) ) )
= $true )
| ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2092]) ).
thf(2172,plain,
! [SV332: $i,SV149: $i > $o] :
( ( ( SV149 @ ( sK42_SY204 @ SV149 ) )
= $true )
| ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2093]) ).
thf(2173,plain,
! [SV270: $i,SV151: $i,SV333: $i,SV444: $o] :
( ( SV444 = $false )
| ( SV444 = $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2097]) ).
thf(2174,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2098]) ).
thf(2175,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( SV333 = SV151 )
= $true )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2099]) ).
thf(2176,plain,
! [SV151: $i,SV434: $o,SV270: $i,SV333: $i] :
( ( ( in @ SV333 @ SV270 )
= $true )
| ( SV434 = $true )
| ( SV434 = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2100]) ).
thf(2177,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( in @ SV333 @ SV270 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2101]) ).
thf(2178,plain,
! [SV151: $i,SV270: $i,SV333: $i] :
( ( ( in @ SV333 @ SV270 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2102]) ).
thf(2179,plain,
! [SV270: $i,SV151: $i,SV333: $i,SV435: $o] :
( ( ( ~ SV435 ) = $true )
| ( SV435 = $true )
| ( SV435 = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2103]) ).
thf(2180,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2104]) ).
thf(2181,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2105]) ).
thf(2182,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
!= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2106]) ).
thf(2183,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( ~ ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2106]) ).
thf(2184,plain,
! [SV395: $i,SV153: $i > $o,SV458: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) )
| ~ ( ( SV458
!= ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SV458 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2107]) ).
thf(2185,plain,
! [SV395: $i,SV153: $i > $o,SV272: $i > $o] :
( ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2108]) ).
thf(2186,plain,
! [SV272: $i > $o,SV451: $i,SV153: $i > $o] :
( ( ( ~ ( ~ ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
| ~ ( ( SV451
!= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV153 @ SV451 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2109]) ).
thf(2187,plain,
! [SV272: $i > $o,SV436: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV153 @ SV436 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2110]) ).
thf(2188,plain,
! [SV153: $i > $o,SV272: $i > $o,SV436: $i] :
( ( ( ~ ( ( SV436
!= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV153 @ SV436 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2110]) ).
thf(2189,plain,
! [SV334: $i,SV445: $i,SV154: $i > $o] :
( ( ( SV154 @ SV445 )
= $false )
| ( ( ( sK45_SY210 @ SV154 )
= SV445 )
= $true )
| ( ( ( sK46_Xy @ SV334 @ SV154 )
= SV334 )
= $false )
| ( ( SV154 @ ( sK46_Xy @ SV334 @ SV154 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2111]) ).
thf(2190,plain,
! [SV412: $i,SV353: $i,SV113: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( sK14_B @ SV113 ) )
| ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV459 )
| ( in @ SY1619 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV459 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2112]) ).
thf(2191,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2113]) ).
thf(2192,plain,
! [SV422: $i,SV353: $i,SV113: $i] :
( ( ( ! [SY1579: $i] :
( ~ ( in @ SY1579 @ ( sK14_B @ SV113 ) )
| ! [SY1580: $i] :
( ~ ( in @ SY1580 @ SY1579 )
| ( in @ SY1580 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SY1579 ) ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2114]) ).
thf(2193,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2115]) ).
thf(2194,plain,
! [SV113: $i,SV396: $i,SV386: $i,SV452: $i] :
( ( ( ~ ( in @ SV452 @ SV386 ) )
= $true )
| ( ( in @ SV452 @ SV396 )
= $true )
| ( ( ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true )
| ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ SV396 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2116]) ).
thf(2195,plain,
! [SV113: $i,SV413: $i,SV446: $i] :
( ( ( in @ SV446 @ SV413 )
= $false )
| ( ( in @ SV446 @ SV113 )
= $true )
| ( ( in @ SV413 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2117]) ).
thf(2196,plain,
! [SV414: $i,SV113: $i,SV423: $i] :
( ( ( in @ SV423 @ SV113 )
= $false )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( ~ ( ~ ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) )
| ( SV414 = SV423 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2118]) ).
thf(2197,plain,
! [SV415: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $false )
| ( ( SV250 @ SV415 )
= $false )
| ( ( in @ SV415 @ SV119 )
= $false )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2198,plain,
! [SV415: $i,SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV415 )
= $false )
| ( ( in @ SV415 @ SV119 )
= $false )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2119]) ).
thf(2199,plain,
! [SV119: $i,SV447: $i,SV250: $i > $o] :
( ( ( SV250 @ SV447 )
= $false )
| ( ( ~ ( in @ SV447 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2120]) ).
thf(2200,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2121]) ).
thf(2201,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false )
| ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) )
| ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2122]) ).
thf(2202,plain,
! [SV416: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $false )
| ( ( SV253 @ SV416 )
= $false )
| ( ( in @ SV416 @ SV125 )
= $false )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2125]) ).
thf(2203,plain,
! [SV416: $i,SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV416 )
= $false )
| ( ( in @ SV416 @ SV125 )
= $false )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2125]) ).
thf(2204,plain,
! [SV125: $i,SV448: $i,SV253: $i > $o] :
( ( ( SV253 @ SV448 )
= $false )
| ( ( ~ ( in @ SV448 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2126]) ).
thf(2205,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2127]) ).
thf(2206,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false )
| ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) )
| ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2128]) ).
thf(2207,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( in @ SV323 @ SV254 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2132]) ).
thf(2208,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV460: $o] :
( ( ( ~ SV460
| SV460 )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2133]) ).
thf(2209,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2133]) ).
thf(2210,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2133]) ).
thf(2211,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( in @ SV323 @ SV254 )
= $false )
| ( ( ~ ( in @ SV323 @ SV126 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2134]) ).
thf(2212,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2213,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2135]) ).
thf(2214,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV454: $o] :
( ( ( ~ SV454 ) = $true )
| ( ( ~ ( in @ SV323 @ SV126 )
| SV454 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2136]) ).
thf(2215,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ ( in @ SV323 @ SV126 )
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2137]) ).
thf(2216,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ ( in @ SV323 @ SV126 )
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2138]) ).
thf(2217,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2218,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2139]) ).
thf(2219,plain,
! [SV383: $i,SV261: $i,SV461: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1620: $i] :
( ~ ( SV139 @ SY1620 @ SV461 )
| ~ ( in @ SY1620 @ SV261 ) )
| ( in @ SV461 @ ( sK9_B @ SV261 @ SV139 ) ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2147]) ).
thf(2220,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV462 )
| ~ ( in @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2148]) ).
thf(2221,plain,
! [SV383: $i,SV261: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1507: $i] :
( ! [SY1508: $i] :
( ~ ( SV139 @ SY1508 @ SY1507 )
| ~ ( in @ SY1508 @ SV261 ) )
| ( in @ SY1507 @ ( sK9_B @ SV261 @ SV139 ) ) ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2149]) ).
thf(2222,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i] :
( ( ( ! [SY1509: $i] :
( ~ ( in @ SY1509 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SY1509 )
| ~ ( in @ ( sK10_Xy @ SY1509 @ SV261 @ SV139 ) @ SV261 ) ) ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2150]) ).
thf(2223,plain,
! [SV361: $i > $o,SV417: $i,SV345: $i > $o] :
( ( ( SV345 @ SV417 )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2151]) ).
thf(2224,plain,
! [SV345: $i > $o,SV361: $i > $o,SV417: $i] :
( ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( ~ ( SV345 @ SV417 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2152]) ).
thf(2225,plain,
! [SV361: $i > $o,SV345: $i > $o] :
( ( ( ! [SY1585: $i] :
( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) )
| ~ ( ( SY1585
!= ( sK53_SY232 @ SY1585 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SY1585 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2153]) ).
thf(2226,plain,
! [SV361: $i > $o,SV455: $i,SV345: $i > $o] :
( ( ( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
| ~ ( ( SV455
!= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) ) ) ) )
= $true )
| ( ( ~ ( SV345 @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2154]) ).
thf(2227,plain,
! [SV346: $i > $o,SV418: $i,SV362: $i > $o] :
( ( ( SV362 @ SV418 )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2155]) ).
thf(2228,plain,
! [SV346: $i > $o,SV362: $i > $o,SV418: $i] :
( ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( ~ ( SV362 @ SV418 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2156]) ).
thf(2229,plain,
! [SV346: $i > $o,SV362: $i > $o] :
( ( ( ! [SY1587: $i] :
( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) )
| ~ ( ( SY1587
!= ( sK49_SY235 @ SY1587 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SY1587 ) ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2157]) ).
thf(2230,plain,
! [SV346: $i > $o,SV456: $i,SV362: $i > $o] :
( ( ( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
| ~ ( ( SV456
!= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) ) ) ) )
= $true )
| ( ( ~ ( SV362 @ SV456 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2158]) ).
thf(2231,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
= $false )
| ( ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2159]) ).
thf(2232,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) )
= $false )
| ( ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2159]) ).
thf(2233,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
| ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) )
= $false )
| ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
= SV330 )
= $false )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2160]) ).
thf(2234,plain,
! [SV268: $i,SV148: $i,SV411: $i,SV432: $o] :
( ( SV432 = $false )
| ( SV432 = $true )
| ( SV432 = $false )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2167]) ).
thf(2235,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2168]) ).
thf(2236,plain,
! [SV268: $i,SV148: $i,SV411: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV411 @ ( binunion @ SV148 @ SV268 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2169]) ).
thf(2237,plain,
! [SV332: $i,SV457: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ SV457 ) )
= $true )
| ( ( ( sK42_SY204 @ SV149 )
= SV457 )
= $true )
| ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2170]) ).
thf(2238,plain,
! [SV332: $i,SV463: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ SV463 )
| ( ( sK42_SY204 @ SV149 )
= SV463 ) )
= $true )
| ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2171]) ).
thf(2239,plain,
! [SV270: $i,SV151: $i,SV333: $i,SV435: $o] :
( ( SV435 = $false )
| ( SV435 = $true )
| ( SV435 = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2179]) ).
thf(2240,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2180]) ).
thf(2241,plain,
! [SV270: $i,SV151: $i,SV333: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV333 @ ( setadjoin @ SV151 @ SV270 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2181]) ).
thf(2242,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 )
= ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2182]) ).
thf(2243,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( ~ ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2183]) ).
thf(2244,plain,
! [SV395: $i,SV153: $i > $o,SV458: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) )
| ~ ( ( SV458
!= ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV272 @ SV458 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2184]) ).
thf(2245,plain,
! [SV395: $i,SV153: $i > $o,SV464: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) )
| ~ ( ( SV464
!= ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SV464 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2185]) ).
thf(2246,plain,
! [SV272: $i > $o,SV451: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
| ~ ( ( SV451
!= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV153 @ SV451 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2186]) ).
thf(2247,plain,
! [SV272: $i > $o,SV436: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV153 @ SV436 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2187]) ).
thf(2248,plain,
! [SV153: $i > $o,SV272: $i > $o,SV436: $i] :
( ( ( SV436
!= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV153 @ SV436 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2188]) ).
thf(2249,plain,
! [SV412: $i,SV353: $i,SV113: $i,SV459: $i] :
( ( ( ~ ( in @ SV459 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV459 )
| ( in @ SY1619 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV459 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2190]) ).
thf(2250,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2191]) ).
thf(2251,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2191]) ).
thf(2252,plain,
! [SV422: $i,SV353: $i,SV113: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ ( sK14_B @ SV113 ) )
| ! [SY1621: $i] :
( ~ ( in @ SY1621 @ SV465 )
| ( in @ SY1621 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV465 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2192]) ).
thf(2253,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
| ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2193]) ).
thf(2254,plain,
! [SV113: $i,SV396: $i,SV386: $i,SV452: $i] :
( ( ( in @ SV452 @ SV386 )
= $false )
| ( ( in @ SV452 @ SV396 )
= $true )
| ( ( ! [SY1608: $i] :
( ~ ( in @ SY1608 @ SV396 )
| ( in @ SY1608 @ SV386 ) ) )
= $true )
| ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ SV396 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2194]) ).
thf(2255,plain,
! [SV113: $i,SV414: $i,SV423: $i] :
( ( ( ~ ( ~ ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) ) )
= $true )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2196]) ).
thf(2256,plain,
! [SV415: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $true )
| ( ( SV250 @ SV415 )
= $false )
| ( ( in @ SV415 @ SV119 )
= $false )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2197]) ).
thf(2257,plain,
! [SV415: $i,SV119: $i,SV250: $i > $o] :
( ( ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) )
= $true )
| ( ( SV250 @ SV415 )
= $false )
| ( ( in @ SV415 @ SV119 )
= $false )
| ( ( in @ ( sK77_SY1111 @ SV250 @ SV119 ) @ SV119 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2198]) ).
thf(2258,plain,
! [SV250: $i > $o,SV119: $i,SV447: $i] :
( ( ( in @ SV447 @ SV119 )
= $false )
| ( ( SV250 @ SV447 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2199]) ).
thf(2259,plain,
! [SV119: $i,SV466: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV466 )
| ~ ( in @ SV466 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2200]) ).
thf(2260,plain,
! [SV119: $i,SV250: $i > $o] :
( ( ( ! [SY1485: $i] :
( ~ ( SV250 @ SY1485 )
| ~ ( in @ SY1485 @ SV119 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2201]) ).
thf(2261,plain,
! [SV416: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $true )
| ( ( SV253 @ SV416 )
= $false )
| ( ( in @ SV416 @ SV125 )
= $false )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2202]) ).
thf(2262,plain,
! [SV416: $i,SV125: $i,SV253: $i > $o] :
( ( ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) )
= $true )
| ( ( SV253 @ SV416 )
= $false )
| ( ( in @ SV416 @ SV125 )
= $false )
| ( ( in @ ( sK83_SY1116 @ SV253 @ SV125 ) @ SV125 )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2203]) ).
thf(2263,plain,
! [SV253: $i > $o,SV125: $i,SV448: $i] :
( ( ( in @ SV448 @ SV125 )
= $false )
| ( ( SV253 @ SV448 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2204]) ).
thf(2264,plain,
! [SV125: $i,SV467: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV467 )
| ~ ( in @ SV467 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2205]) ).
thf(2265,plain,
! [SV125: $i,SV253: $i > $o] :
( ( ( ! [SY1489: $i] :
( ~ ( SV253 @ SY1489 )
| ~ ( in @ SY1489 @ SV125 ) ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2206]) ).
thf(2266,plain,
! [SV126: $i,SV254: $i,SV323: $i,SV468: $o] :
( ( SV468 = $true )
| ( ( in @ SV323 @ SV254 )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2207]) ).
thf(2267,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( $true = $true )
| ( ( in @ SV323 @ SV254 )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2207]) ).
thf(2268,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( $false = $true )
| ( ( in @ SV323 @ SV254 )
= $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2207]) ).
thf(2269,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV460: $o] :
( ( ( ~ SV460 ) = $true )
| ( SV460 = $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2208]) ).
thf(2270,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2209]) ).
thf(2271,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2210]) ).
thf(2272,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV126 ) )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2211]) ).
thf(2273,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV254 )
| ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2212]) ).
thf(2274,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV254 )
| ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2213]) ).
thf(2275,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV454: $o] :
( ( SV454 = $false )
| ( ( ~ ( in @ SV323 @ SV126 )
| SV454 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2214]) ).
thf(2276,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $true = $false )
| ( ( ~ ( in @ SV323 @ SV126 )
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2215]) ).
thf(2277,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $false = $false )
| ( ( ~ ( in @ SV323 @ SV126 )
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2216]) ).
thf(2278,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ! [SY1553: $o] :
( ~ SY1553
| ( in @ SV323 @ SV254 )
| SY1553 ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2217]) ).
thf(2279,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ! [SX3: $o] :
( ~ SX3
| ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2218]) ).
thf(2280,plain,
! [SV383: $i,SV261: $i,SV461: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1620: $i] :
( ~ ( SV139 @ SY1620 @ SV461 )
| ~ ( in @ SY1620 @ SV261 ) ) )
= $true )
| ( ( in @ SV461 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2219]) ).
thf(2281,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV462: $i] :
( ( ( ~ ( in @ SV462 @ ( sK9_B @ SV261 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ( SV139 @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV462 )
| ~ ( in @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2220]) ).
thf(2282,plain,
! [SV383: $i,SV261: $i,SV469: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1622: $i] :
( ~ ( SV139 @ SY1622 @ SV469 )
| ~ ( in @ SY1622 @ SV261 ) )
| ( in @ SV469 @ ( sK9_B @ SV261 @ SV139 ) ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2221]) ).
thf(2283,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ ( sK9_B @ SV261 @ SV139 ) )
| ~ ( ~ ( SV139 @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV470 )
| ~ ( in @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2222]) ).
thf(2284,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2223]) ).
thf(2285,plain,
! [SV361: $i > $o,SV417: $i,SV345: $i > $o] :
( ( ( SV345 @ SV417 )
= $false )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2224]) ).
thf(2286,plain,
! [SV361: $i > $o,SV471: $i,SV345: $i > $o] :
( ( ( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
| ~ ( ( SV471
!= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) ) ) )
| ~ ( SV345 @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2225]) ).
thf(2287,plain,
! [SV361: $i > $o,SV455: $i,SV345: $i > $o] :
( ( ( ~ ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
| ~ ( ( SV455
!= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ~ ( SV345 @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2226]) ).
thf(2288,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2227]) ).
thf(2289,plain,
! [SV346: $i > $o,SV418: $i,SV362: $i > $o] :
( ( ( SV362 @ SV418 )
= $false )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2228]) ).
thf(2290,plain,
! [SV346: $i > $o,SV472: $i,SV362: $i > $o] :
( ( ( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
| ~ ( ( SV472
!= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) ) ) )
| ~ ( SV362 @ SV472 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2229]) ).
thf(2291,plain,
! [SV346: $i > $o,SV456: $i,SV362: $i > $o] :
( ( ( ~ ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
| ~ ( ( SV456
!= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ~ ( SV362 @ SV456 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2230]) ).
thf(2292,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
= $true )
| ( ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2231]) ).
thf(2293,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) )
= $true )
| ( ( SV264 @ ( sK80_Xy @ SV330 @ SV264 @ SV142 ) )
= $true )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2232]) ).
thf(2294,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
!= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
= $false )
| ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
= SV330 )
= $false )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2233]) ).
thf(2295,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( ~ ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) ) )
= $false )
| ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
= SV330 )
= $false )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2233]) ).
thf(2296,plain,
! [SV332: $i,SV457: $i,SV149: $i > $o] :
( ( ( SV149 @ SV457 )
= $false )
| ( ( ( sK42_SY204 @ SV149 )
= SV457 )
= $true )
| ( ( SV149 @ ( sK44_SY1097 @ SV149 ) )
= $true )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2237]) ).
thf(2297,plain,
! [SV332: $i,SV463: $i,SV149: $i > $o] :
( ( ( ~ ( SV149 @ SV463 ) )
= $true )
| ( ( ( sK42_SY204 @ SV149 )
= SV463 )
= $true )
| ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2238]) ).
thf(2298,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
| ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2243]) ).
thf(2299,plain,
! [SV395: $i,SV153: $i > $o,SV458: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) )
| ~ ( ( SV458
!= ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV458 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2244]) ).
thf(2300,plain,
! [SV395: $i,SV153: $i > $o,SV464: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) )
| ~ ( ( SV464
!= ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV272 @ SV464 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2245]) ).
thf(2301,plain,
! [SV272: $i > $o,SV451: $i,SV153: $i > $o] :
( ( ( ~ ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV153 @ SV451 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2246]) ).
thf(2302,plain,
! [SV153: $i > $o,SV272: $i > $o,SV451: $i] :
( ( ( ~ ( ( SV451
!= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV153 @ SV451 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2246]) ).
thf(2303,plain,
! [SV272: $i > $o,SV436: $i,SV153: $i > $o] :
( ( ( SV153 @ SV436 )
= $false )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2247]) ).
thf(2304,plain,
! [SV153: $i > $o,SV272: $i > $o,SV436: $i] :
( ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV153 @ SV436 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2248]) ).
thf(2305,plain,
! [SV412: $i,SV353: $i,SV113: $i,SV459: $i] :
( ( ( in @ SV459 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV459 )
| ( in @ SY1619 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV459 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2249]) ).
thf(2306,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2250]) ).
thf(2307,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2251]) ).
thf(2308,plain,
! [SV422: $i,SV353: $i,SV113: $i,SV465: $i] :
( ( ( ~ ( in @ SV465 @ ( sK14_B @ SV113 ) ) )
= $true )
| ( ( ! [SY1621: $i] :
( ~ ( in @ SY1621 @ SV465 )
| ( in @ SY1621 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV465 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2252]) ).
thf(2309,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2253]) ).
thf(2310,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2253]) ).
thf(2311,plain,
! [SV113: $i,SV452: $i,SV386: $i,SV396: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ SV396 )
| ( in @ SV473 @ SV386 ) )
= $true )
| ( ( in @ SV452 @ SV396 )
= $true )
| ( ( in @ SV452 @ SV386 )
= $false )
| ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ SV396 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2254]) ).
thf(2312,plain,
! [SV113: $i,SV414: $i,SV423: $i] :
( ( ( ~ ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) )
= $false )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2255]) ).
thf(2313,plain,
! [SV447: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV447 )
= $false )
| ( ( in @ SV447 @ SV119 )
= $false )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2258]) ).
thf(2314,plain,
! [SV119: $i,SV466: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV466 ) )
= $true )
| ( ( ~ ( in @ SV466 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2259]) ).
thf(2315,plain,
! [SV119: $i,SV474: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV474 )
| ~ ( in @ SV474 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2260]) ).
thf(2316,plain,
! [SV448: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV448 )
= $false )
| ( ( in @ SV448 @ SV125 )
= $false )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2263]) ).
thf(2317,plain,
! [SV125: $i,SV467: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV467 ) )
= $true )
| ( ( ~ ( in @ SV467 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2264]) ).
thf(2318,plain,
! [SV125: $i,SV475: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV475 )
| ~ ( in @ SV475 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2265]) ).
thf(2319,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV460: $o] :
( ( SV460 = $false )
| ( SV460 = $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2269]) ).
thf(2320,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2270]) ).
thf(2321,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV323 @ SV126 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2271]) ).
thf(2322,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ SV126 )
= $false )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2272]) ).
thf(2323,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV254 ) )
= $true )
| ( ( ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2273]) ).
thf(2324,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV254 ) )
= $true )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2274]) ).
thf(2325,plain,
! [SV254: $i,SV454: $o,SV126: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV126 ) )
= $true )
| ( SV454 = $true )
| ( SV454 = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2275]) ).
thf(2326,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV126 ) )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2276]) ).
thf(2327,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ ( in @ SV323 @ SV126 ) )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2277]) ).
thf(2328,plain,
! [SV126: $i,SV254: $i,SV323: $i,SV476: $o] :
( ( ( ~ SV476
| ( in @ SV323 @ SV254 )
| SV476 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2278]) ).
thf(2329,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ $true
| ( in @ SV323 @ SV254 )
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2278]) ).
thf(2330,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ $false
| ( in @ SV323 @ SV254 )
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2278]) ).
thf(2331,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV477: $o] :
( ( ( ~ SV477
| ~ SV477
| SV477 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2279]) ).
thf(2332,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $true
| ~ $true
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2279]) ).
thf(2333,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $false
| ~ $false
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2279]) ).
thf(2334,plain,
! [SV383: $i,SV261: $i,SV461: $i,SV478: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ SV478 @ SV461 )
| ~ ( in @ SV478 @ SV261 ) )
= $true )
| ( ( in @ SV461 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2280]) ).
thf(2335,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV462: $i] :
( ( ( in @ SV462 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ( SV139 @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV462 )
| ~ ( in @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2281]) ).
thf(2336,plain,
! [SV383: $i,SV261: $i,SV469: $i,SV139: $i > $i > $o] :
( ( ( ! [SY1622: $i] :
( ~ ( SV139 @ SY1622 @ SV469 )
| ~ ( in @ SY1622 @ SV261 ) ) )
= $true )
| ( ( in @ SV469 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2282]) ).
thf(2337,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV470: $i] :
( ( ( ~ ( in @ SV470 @ ( sK9_B @ SV261 @ SV139 ) ) )
= $true )
| ( ( ~ ( ~ ( SV139 @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV470 )
| ~ ( in @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2283]) ).
thf(2338,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2339,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2284]) ).
thf(2340,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2285]) ).
thf(2341,plain,
! [SV361: $i > $o,SV471: $i,SV345: $i > $o] :
( ( ( ~ ( ~ ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
| ~ ( ( SV471
!= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) ) ) ) )
= $true )
| ( ( ~ ( SV345 @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2286]) ).
thf(2342,plain,
! [SV361: $i > $o,SV455: $i,SV345: $i > $o] :
( ( ( ~ ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) ) )
= $false )
| ( ( ~ ( SV345 @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2287]) ).
thf(2343,plain,
! [SV345: $i > $o,SV361: $i > $o,SV455: $i] :
( ( ( ~ ( ( SV455
!= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ~ ( SV345 @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2287]) ).
thf(2344,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2288]) ).
thf(2345,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2288]) ).
thf(2346,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2289]) ).
thf(2347,plain,
! [SV346: $i > $o,SV472: $i,SV362: $i > $o] :
( ( ( ~ ( ~ ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
| ~ ( ( SV472
!= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) ) ) ) )
= $true )
| ( ( ~ ( SV362 @ SV472 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2290]) ).
thf(2348,plain,
! [SV346: $i > $o,SV456: $i,SV362: $i > $o] :
( ( ( ~ ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) ) )
= $false )
| ( ( ~ ( SV362 @ SV456 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2291]) ).
thf(2349,plain,
! [SV346: $i > $o,SV362: $i > $o,SV456: $i] :
( ( ( ~ ( ( SV456
!= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ~ ( SV362 @ SV456 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2291]) ).
thf(2350,plain,
! [SV330: $i,SV264: $i > $o,SV142: $i] :
( ( ( ( dsetconstr @ SV142
@ ^ [SY1512: $i] : ( SV264 @ SY1512 ) )
= ( setadjoin @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 ) @ emptyset ) )
= $true )
| ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
= SV330 )
= $false )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2294]) ).
thf(2351,plain,
! [SV142: $i,SV264: $i > $o,SV330: $i] :
( ( ( in @ ( sK79_SY507 @ SV330 @ SV264 @ SV142 )
@ ( dsetconstr @ SV142
@ ^ [SY1513: $i] : ( SV264 @ SY1513 ) ) )
= $true )
| ( ( ( sK80_Xy @ SV330 @ SV264 @ SV142 )
= SV330 )
= $false )
| ( ( SV264 @ SV330 )
= $false )
| ( ( in @ SV330 @ SV142 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2295]) ).
thf(2352,plain,
! [SV332: $i,SV463: $i,SV149: $i > $o] :
( ( ( SV149 @ SV463 )
= $false )
| ( ( ( sK42_SY204 @ SV149 )
= SV463 )
= $true )
| ( ( ( sK43_Xx @ SV149 )
= ( sK44_SY1097 @ SV149 ) )
= $false )
| ( ( SV149 @ SV332 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2297]) ).
thf(2353,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( ~ ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2354,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( ~ ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2298]) ).
thf(2355,plain,
! [SV395: $i,SV153: $i > $o,SV458: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV272 @ SV458 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2299]) ).
thf(2356,plain,
! [SV395: $i,SV153: $i > $o,SV272: $i > $o,SV458: $i] :
( ( ( ~ ( ( SV458
!= ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV458 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2299]) ).
thf(2357,plain,
! [SV395: $i,SV153: $i > $o,SV464: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) )
| ~ ( ( SV464
!= ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV464 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2300]) ).
thf(2358,plain,
! [SV272: $i > $o,SV451: $i,SV153: $i > $o] :
( ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV153 @ SV451 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2301]) ).
thf(2359,plain,
! [SV153: $i > $o,SV272: $i > $o,SV451: $i] :
( ( ( SV451
!= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV153 @ SV451 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2302]) ).
thf(2360,plain,
! [SV436: $i,SV153: $i > $o,SV272: $i > $o] :
( ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2303]) ).
thf(2361,plain,
! [SV272: $i > $o,SV436: $i,SV153: $i > $o] :
( ( ( SV153 @ SV436 )
= $false )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2304]) ).
thf(2362,plain,
! [SV412: $i,SV113: $i,SV353: $i,SV459: $i] :
( ( ( ! [SY1619: $i] :
( ~ ( in @ SY1619 @ SV459 )
| ( in @ SY1619 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) ) )
= $true )
| ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV459 )
= $true )
| ( ( in @ SV459 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2305]) ).
thf(2363,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2306]) ).
thf(2364,plain,
! [SV412: $i,SV113: $i,SV353: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SV479 @ SV353 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2307]) ).
thf(2365,plain,
! [SV422: $i,SV353: $i,SV113: $i,SV465: $i] :
( ( ( in @ SV465 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( ! [SY1621: $i] :
( ~ ( in @ SY1621 @ SV465 )
| ( in @ SY1621 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
| ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV465 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2308]) ).
thf(2366,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2309]) ).
thf(2367,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ! [SY1581: $i] :
( ~ ( in @ SY1581 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SY1581 @ SV353 ) ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2310]) ).
thf(2368,plain,
! [SV113: $i,SV452: $i,SV386: $i,SV396: $i,SV473: $i] :
( ( ( ~ ( in @ SV473 @ SV396 ) )
= $true )
| ( ( in @ SV473 @ SV386 )
= $true )
| ( ( in @ SV452 @ SV396 )
= $true )
| ( ( in @ SV452 @ SV386 )
= $false )
| ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ SV396 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2311]) ).
thf(2369,plain,
! [SV113: $i,SV414: $i,SV423: $i] :
( ( ( ~ ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) ) )
= $false )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2312]) ).
thf(2370,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( ~ ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) )
= $false )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2312]) ).
thf(2371,plain,
! [SV447: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $false )
| ( ( SV250 @ SV447 )
= $false )
| ( ( in @ SV447 @ SV119 )
= $false )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2313]) ).
thf(2372,plain,
! [SV447: $i,SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV447 )
= $false )
| ( ( in @ SV447 @ SV119 )
= $false )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2313]) ).
thf(2373,plain,
! [SV119: $i,SV466: $i,SV250: $i > $o] :
( ( ( SV250 @ SV466 )
= $false )
| ( ( ~ ( in @ SV466 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2314]) ).
thf(2374,plain,
! [SV119: $i,SV474: $i,SV250: $i > $o] :
( ( ( ~ ( SV250 @ SV474 ) )
= $true )
| ( ( ~ ( in @ SV474 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2315]) ).
thf(2375,plain,
! [SV448: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $false )
| ( ( SV253 @ SV448 )
= $false )
| ( ( in @ SV448 @ SV125 )
= $false )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2376,plain,
! [SV448: $i,SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV448 )
= $false )
| ( ( in @ SV448 @ SV125 )
= $false )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2316]) ).
thf(2377,plain,
! [SV125: $i,SV467: $i,SV253: $i > $o] :
( ( ( SV253 @ SV467 )
= $false )
| ( ( ~ ( in @ SV467 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2317]) ).
thf(2378,plain,
! [SV125: $i,SV475: $i,SV253: $i > $o] :
( ( ( ~ ( SV253 @ SV475 ) )
= $true )
| ( ( ~ ( in @ SV475 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2318]) ).
thf(2379,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV480: $o] :
( ( SV480 = $true )
| ( ( in @ SV323 @ SV126 )
= $false )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2322]) ).
thf(2380,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $true = $true )
| ( ( in @ SV323 @ SV126 )
= $false )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2322]) ).
thf(2381,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $false = $true )
| ( ( in @ SV323 @ SV126 )
= $false )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2322]) ).
thf(2382,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( in @ SV323 @ SV254 )
= $false )
| ( ( ( in @ SV323 @ SV254 )
| ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2323]) ).
thf(2383,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( in @ SV323 @ SV254 )
= $false )
| ( ( ! [SX3: $o] :
( ~ SX3
| SX3 ) )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2324]) ).
thf(2384,plain,
! [SV254: $i,SV454: $o,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ SV126 )
= $false )
| ( SV454 = $true )
| ( SV454 = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2325]) ).
thf(2385,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ SV126 )
= $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2326]) ).
thf(2386,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( in @ SV323 @ SV126 )
= $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2327]) ).
thf(2387,plain,
! [SV126: $i,SV254: $i,SV323: $i,SV476: $o] :
( ( ( ~ SV476 ) = $true )
| ( ( ( in @ SV323 @ SV254 )
| SV476 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2328]) ).
thf(2388,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ $true ) = $true )
| ( ( ( in @ SV323 @ SV254 )
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2329]) ).
thf(2389,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ $false ) = $true )
| ( ( ( in @ SV323 @ SV254 )
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2330]) ).
thf(2390,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV477: $o] :
( ( ( ~ SV477 ) = $true )
| ( ( ~ SV477
| SV477 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2331]) ).
thf(2391,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $true ) = $true )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2332]) ).
thf(2392,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $false ) = $true )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2333]) ).
thf(2393,plain,
! [SV383: $i,SV261: $i,SV461: $i,SV478: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ SV478 @ SV461 ) )
= $true )
| ( ( ~ ( in @ SV478 @ SV261 ) )
= $true )
| ( ( in @ SV461 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2334]) ).
thf(2394,plain,
! [SV383: $i,SV261: $i,SV462: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV462 )
| ~ ( in @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV261 ) )
= $false )
| ( ( in @ SV462 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2335]) ).
thf(2395,plain,
! [SV383: $i,SV261: $i,SV469: $i,SV481: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ SV481 @ SV469 )
| ~ ( in @ SV481 @ SV261 ) )
= $true )
| ( ( in @ SV469 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2336]) ).
thf(2396,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV470: $i] :
( ( ( in @ SV470 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( ~ ( ~ ( SV139 @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV470 )
| ~ ( in @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV261 ) ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2337]) ).
thf(2397,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2338]) ).
thf(2398,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2339]) ).
thf(2399,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $false )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2340]) ).
thf(2400,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2340]) ).
thf(2401,plain,
! [SV361: $i > $o,SV471: $i,SV345: $i > $o] :
( ( ( ~ ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
| ~ ( ( SV471
!= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ~ ( SV345 @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2341]) ).
thf(2402,plain,
! [SV361: $i > $o,SV455: $i,SV345: $i > $o] :
( ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( SV345 @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2342]) ).
thf(2403,plain,
! [SV345: $i > $o,SV361: $i > $o,SV455: $i] :
( ( ( SV455
!= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( SV345 @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2343]) ).
thf(2404,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2344]) ).
thf(2405,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2345]) ).
thf(2406,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $false )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2346]) ).
thf(2407,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2346]) ).
thf(2408,plain,
! [SV346: $i > $o,SV472: $i,SV362: $i > $o] :
( ( ( ~ ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
| ~ ( ( SV472
!= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ~ ( SV362 @ SV472 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2347]) ).
thf(2409,plain,
! [SV346: $i > $o,SV456: $i,SV362: $i > $o] :
( ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( SV362 @ SV456 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2348]) ).
thf(2410,plain,
! [SV346: $i > $o,SV362: $i > $o,SV456: $i] :
( ( ( SV456
!= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( SV362 @ SV456 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2349]) ).
thf(2411,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2353]) ).
thf(2412,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
| ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2354]) ).
thf(2413,plain,
! [SV395: $i,SV153: $i > $o,SV458: $i,SV272: $i > $o] :
( ( ( SV272 @ ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV458 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2355]) ).
thf(2414,plain,
! [SV395: $i,SV153: $i > $o,SV272: $i > $o,SV458: $i] :
( ( ( SV458
!= ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV458 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2356]) ).
thf(2415,plain,
! [SV395: $i,SV153: $i > $o,SV464: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV272 @ SV464 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2357]) ).
thf(2416,plain,
! [SV395: $i,SV153: $i > $o,SV272: $i > $o,SV464: $i] :
( ( ( ~ ( ( SV464
!= ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV464 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2357]) ).
thf(2417,plain,
! [SV272: $i > $o,SV451: $i,SV153: $i > $o] :
( ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2358]) ).
thf(2418,plain,
! [SV153: $i > $o,SV272: $i > $o,SV451: $i] :
( ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV153 @ SV451 ) )
= $true )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2359]) ).
thf(2419,plain,
! [SV436: $i,SV153: $i > $o,SV482: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) )
| ~ ( ( SV482
!= ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SV482 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2360]) ).
thf(2420,plain,
! [SV436: $i,SV153: $i > $o,SV272: $i > $o] :
( ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2361]) ).
thf(2421,plain,
! [SV412: $i,SV113: $i,SV353: $i,SV459: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ SV459 )
| ( in @ SV483 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
= $true )
| ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV459 )
= $true )
| ( ( in @ SV459 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2362]) ).
thf(2422,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2423,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2363]) ).
thf(2424,plain,
! [SV412: $i,SV113: $i,SV353: $i,SV479: $i] :
( ( ( ~ ( in @ SV479 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
= $true )
| ( ( ~ ( in @ SV479 @ SV353 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2364]) ).
thf(2425,plain,
! [SV422: $i,SV113: $i,SV353: $i,SV465: $i] :
( ( ( ! [SY1621: $i] :
( ~ ( in @ SY1621 @ SV465 )
| ( in @ SY1621 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) ) )
= $true )
| ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV465 )
= $true )
| ( ( in @ SV465 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2365]) ).
thf(2426,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
| ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2366]) ).
thf(2427,plain,
! [SV422: $i,SV113: $i,SV353: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
| ~ ( in @ SV484 @ SV353 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2367]) ).
thf(2428,plain,
! [SV113: $i,SV452: $i,SV386: $i,SV396: $i,SV473: $i] :
( ( ( in @ SV473 @ SV396 )
= $false )
| ( ( in @ SV473 @ SV386 )
= $true )
| ( ( in @ SV452 @ SV396 )
= $true )
| ( ( in @ SV452 @ SV386 )
= $false )
| ( ( in @ SV386 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ SV396 @ ( sK14_B @ SV113 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2368]) ).
thf(2429,plain,
! [SV113: $i,SV414: $i,SV423: $i] :
( ( ( in @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) @ ( sK14_B @ SV113 ) )
= $true )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2369]) ).
thf(2430,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( ~ ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) ) )
= $true )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2370]) ).
thf(2431,plain,
! [SV447: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $true )
| ( ( SV250 @ SV447 )
= $false )
| ( ( in @ SV447 @ SV119 )
= $false )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2371]) ).
thf(2432,plain,
! [SV447: $i,SV119: $i,SV250: $i > $o] :
( ( ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) )
= $true )
| ( ( SV250 @ SV447 )
= $false )
| ( ( in @ SV447 @ SV119 )
= $false )
| ( ( SV250 @ ( sK76_Xx @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2372]) ).
thf(2433,plain,
! [SV250: $i > $o,SV119: $i,SV466: $i] :
( ( ( in @ SV466 @ SV119 )
= $false )
| ( ( SV250 @ SV466 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2373]) ).
thf(2434,plain,
! [SV119: $i,SV474: $i,SV250: $i > $o] :
( ( ( SV250 @ SV474 )
= $false )
| ( ( ~ ( in @ SV474 @ SV119 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2374]) ).
thf(2435,plain,
! [SV448: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $true )
| ( ( SV253 @ SV448 )
= $false )
| ( ( in @ SV448 @ SV125 )
= $false )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2375]) ).
thf(2436,plain,
! [SV448: $i,SV125: $i,SV253: $i > $o] :
( ( ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) )
= $true )
| ( ( SV253 @ SV448 )
= $false )
| ( ( in @ SV448 @ SV125 )
= $false )
| ( ( SV253 @ ( sK82_Xx @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2376]) ).
thf(2437,plain,
! [SV253: $i > $o,SV125: $i,SV467: $i] :
( ( ( in @ SV467 @ SV125 )
= $false )
| ( ( SV253 @ SV467 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2377]) ).
thf(2438,plain,
! [SV125: $i,SV475: $i,SV253: $i > $o] :
( ( ( SV253 @ SV475 )
= $false )
| ( ( ~ ( in @ SV475 @ SV125 ) )
= $true )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2378]) ).
thf(2439,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( in @ SV323 @ SV254 )
= $true )
| ( ( ! [SX3: $o] : SX3 )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2382]) ).
thf(2440,plain,
! [SV126: $i,SV254: $i,SV323: $i,SV485: $o] :
( ( ( ~ SV485
| SV485 )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2383]) ).
thf(2441,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2383]) ).
thf(2442,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2383]) ).
thf(2443,plain,
! [SV126: $i,SV254: $i,SV323: $i,SV476: $o] :
( ( SV476 = $false )
| ( ( ( in @ SV323 @ SV254 )
| SV476 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2387]) ).
thf(2444,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( $true = $false )
| ( ( ( in @ SV323 @ SV254 )
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2388]) ).
thf(2445,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( $false = $false )
| ( ( ( in @ SV323 @ SV254 )
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2389]) ).
thf(2446,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV477: $o] :
( ( SV477 = $false )
| ( ( ~ SV477
| SV477 )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2390]) ).
thf(2447,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $true = $false )
| ( ( ~ $true
| $true )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2391]) ).
thf(2448,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $false = $false )
| ( ( ~ $false
| $false )
= $true )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2392]) ).
thf(2449,plain,
! [SV383: $i,SV261: $i,SV461: $i,SV478: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ SV478 @ SV461 )
= $false )
| ( ( ~ ( in @ SV478 @ SV261 ) )
= $true )
| ( ( in @ SV461 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2393]) ).
thf(2450,plain,
! [SV383: $i,SV261: $i,SV462: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV462 ) )
= $false )
| ( ( in @ SV462 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2394]) ).
thf(2451,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV462: $i] :
( ( ( ~ ( in @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV261 ) )
= $false )
| ( ( in @ SV462 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2394]) ).
thf(2452,plain,
! [SV383: $i,SV261: $i,SV469: $i,SV481: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ SV481 @ SV469 ) )
= $true )
| ( ( ~ ( in @ SV481 @ SV261 ) )
= $true )
| ( ( in @ SV469 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2395]) ).
thf(2453,plain,
! [SV383: $i,SV261: $i,SV470: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV470 )
| ~ ( in @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV261 ) )
= $false )
| ( ( in @ SV470 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2396]) ).
thf(2454,plain,
! [SV417: $i,SV345: $i > $o,SV486: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV486 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SV486 ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2397]) ).
thf(2455,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $true )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2399]) ).
thf(2456,plain,
! [SV417: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) )
= $true )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2400]) ).
thf(2457,plain,
! [SV361: $i > $o,SV471: $i,SV345: $i > $o] :
( ( ( ~ ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) ) )
= $false )
| ( ( ~ ( SV345 @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2401]) ).
thf(2458,plain,
! [SV345: $i > $o,SV361: $i > $o,SV471: $i] :
( ( ( ~ ( ( SV471
!= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) ) ) )
= $false )
| ( ( ~ ( SV345 @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2401]) ).
thf(2459,plain,
! [SV361: $i > $o,SV455: $i,SV345: $i > $o] :
( ( ( SV345 @ SV455 )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2402]) ).
thf(2460,plain,
! [SV345: $i > $o,SV361: $i > $o,SV455: $i] :
( ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( ~ ( SV345 @ SV455 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2403]) ).
thf(2461,plain,
! [SV418: $i,SV362: $i > $o,SV487: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV487 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SV487 ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2404]) ).
thf(2462,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $true )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2406]) ).
thf(2463,plain,
! [SV418: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) )
= $true )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2407]) ).
thf(2464,plain,
! [SV346: $i > $o,SV472: $i,SV362: $i > $o] :
( ( ( ~ ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) ) )
= $false )
| ( ( ~ ( SV362 @ SV472 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2465,plain,
! [SV346: $i > $o,SV362: $i > $o,SV472: $i] :
( ( ( ~ ( ( SV472
!= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) ) ) )
= $false )
| ( ( ~ ( SV362 @ SV472 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2408]) ).
thf(2466,plain,
! [SV346: $i > $o,SV456: $i,SV362: $i > $o] :
( ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2409]) ).
thf(2467,plain,
! [SV346: $i > $o,SV362: $i > $o,SV456: $i] :
( ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( ~ ( SV362 @ SV456 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2410]) ).
thf(2468,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( ~ ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
= $true )
| ( ( ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2411]) ).
thf(2469,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
= $true )
| ( ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2412]) ).
thf(2470,plain,
! [SV395: $i,SV153: $i > $o,SV458: $i,SV272: $i > $o] :
( ( ( SV272 @ SV458 )
= $false )
| ( ( SV272 @ ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2413]) ).
thf(2471,plain,
! [SV395: $i,SV153: $i > $o,SV272: $i > $o,SV458: $i] :
( ( ( SV458
= ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV272 @ SV458 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2414]) ).
thf(2472,plain,
! [SV395: $i,SV153: $i > $o,SV464: $i,SV272: $i > $o] :
( ( ( SV272 @ ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV464 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2415]) ).
thf(2473,plain,
! [SV395: $i,SV153: $i > $o,SV272: $i > $o,SV464: $i] :
( ( ( SV464
!= ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV464 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2416]) ).
thf(2474,plain,
! [SV451: $i,SV153: $i > $o,SV272: $i > $o] :
( ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2417]) ).
thf(2475,plain,
! [SV272: $i > $o,SV451: $i,SV153: $i > $o] :
( ( ( SV153 @ SV451 )
= $false )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) )
| ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2418]) ).
thf(2476,plain,
! [SV436: $i,SV153: $i > $o,SV482: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) )
| ~ ( ( SV482
!= ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV272 @ SV482 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2419]) ).
thf(2477,plain,
! [SV436: $i,SV153: $i > $o,SV488: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) )
| ~ ( ( SV488
!= ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SV488 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2420]) ).
thf(2478,plain,
! [SV412: $i,SV113: $i,SV353: $i,SV459: $i,SV483: $i] :
( ( ( ~ ( in @ SV483 @ SV459 ) )
= $true )
| ( ( in @ SV483 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
= $true )
| ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV459 )
= $true )
| ( ( in @ SV459 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2421]) ).
thf(2479,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2422]) ).
thf(2480,plain,
! [SV412: $i,SV113: $i,SV353: $i] :
( ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2423]) ).
thf(2481,plain,
! [SV412: $i,SV113: $i,SV353: $i,SV479: $i] :
( ( ( in @ SV479 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
= $false )
| ( ( ~ ( in @ SV479 @ SV353 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2424]) ).
thf(2482,plain,
! [SV422: $i,SV113: $i,SV353: $i,SV465: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ SV465 )
| ( in @ SV489 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
= $true )
| ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV465 )
= $true )
| ( ( in @ SV465 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2425]) ).
thf(2483,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2426]) ).
thf(2484,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( ~ ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2426]) ).
thf(2485,plain,
! [SV422: $i,SV113: $i,SV353: $i,SV484: $i] :
( ( ( ~ ( in @ SV484 @ ( sK16_SY1071 @ SV353 @ SV113 ) ) )
= $true )
| ( ( ~ ( in @ SV484 @ SV353 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2427]) ).
thf(2486,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
| ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) )
= $false )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2430]) ).
thf(2487,plain,
! [SV466: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV466 )
= $false )
| ( ( in @ SV466 @ SV119 )
= $false )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2433]) ).
thf(2488,plain,
! [SV250: $i > $o,SV119: $i,SV474: $i] :
( ( ( in @ SV474 @ SV119 )
= $false )
| ( ( SV250 @ SV474 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) ) )
= $true )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2434]) ).
thf(2489,plain,
! [SV467: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV467 )
= $false )
| ( ( in @ SV467 @ SV125 )
= $false )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2437]) ).
thf(2490,plain,
! [SV253: $i > $o,SV125: $i,SV475: $i] :
( ( ( in @ SV475 @ SV125 )
= $false )
| ( ( SV253 @ SV475 )
= $false )
| ( ( ~ ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) ) )
= $true )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2438]) ).
thf(2491,plain,
! [SV126: $i,SV254: $i,SV323: $i,SV490: $o] :
( ( SV490 = $true )
| ( ( in @ SV323 @ SV254 )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2439]) ).
thf(2492,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( $true = $true )
| ( ( in @ SV323 @ SV254 )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2439]) ).
thf(2493,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( $false = $true )
| ( ( in @ SV323 @ SV254 )
= $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_forall_special_pos,[status(thm)],[2439]) ).
thf(2494,plain,
! [SV126: $i,SV254: $i,SV323: $i,SV485: $o] :
( ( ( ~ SV485 ) = $true )
| ( SV485 = $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2440]) ).
thf(2495,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2441]) ).
thf(2496,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2442]) ).
thf(2497,plain,
! [SV126: $i,SV476: $o,SV254: $i,SV323: $i] :
( ( ( in @ SV323 @ SV254 )
= $true )
| ( SV476 = $true )
| ( SV476 = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2443]) ).
thf(2498,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( in @ SV323 @ SV254 )
= $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2444]) ).
thf(2499,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( ( in @ SV323 @ SV254 )
= $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2445]) ).
thf(2500,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV477: $o] :
( ( ( ~ SV477 ) = $true )
| ( SV477 = $true )
| ( SV477 = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2446]) ).
thf(2501,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $true ) = $true )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2447]) ).
thf(2502,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( ( ~ $false ) = $true )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2448]) ).
thf(2503,plain,
! [SV383: $i,SV461: $i,SV139: $i > $i > $o,SV261: $i,SV478: $i] :
( ( ( in @ SV478 @ SV261 )
= $false )
| ( ( SV139 @ SV478 @ SV461 )
= $false )
| ( ( in @ SV461 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2449]) ).
thf(2504,plain,
! [SV383: $i,SV261: $i,SV462: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV462 )
= $true )
| ( ( in @ SV462 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2450]) ).
thf(2505,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV462: $i] :
( ( ( in @ ( sK10_Xy @ SV462 @ SV261 @ SV139 ) @ SV261 )
= $true )
| ( ( in @ SV462 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $true )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2451]) ).
thf(2506,plain,
! [SV383: $i,SV261: $i,SV469: $i,SV481: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ SV481 @ SV469 )
= $false )
| ( ( ~ ( in @ SV481 @ SV261 ) )
= $true )
| ( ( in @ SV469 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2452]) ).
thf(2507,plain,
! [SV383: $i,SV261: $i,SV470: $i,SV139: $i > $i > $o] :
( ( ( ~ ( SV139 @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV470 ) )
= $false )
| ( ( in @ SV470 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2508,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV470: $i] :
( ( ( ~ ( in @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV261 ) )
= $false )
| ( ( in @ SV470 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2453]) ).
thf(2509,plain,
! [SV417: $i,SV345: $i > $o,SV486: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV486 ) )
= $true )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV486 )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2454]) ).
thf(2510,plain,
! [SV417: $i,SV345: $i > $o,SV491: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV491 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SV491 ) )
= $true )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2455]) ).
thf(2511,plain,
! [SV361: $i > $o,SV471: $i,SV345: $i > $o] :
( ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( SV345 @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2457]) ).
thf(2512,plain,
! [SV345: $i > $o,SV361: $i > $o,SV471: $i] :
( ( ( SV471
!= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( SV345 @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2458]) ).
thf(2513,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2459]) ).
thf(2514,plain,
! [SV361: $i > $o,SV455: $i,SV345: $i > $o] :
( ( ( SV345 @ SV455 )
= $false )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2460]) ).
thf(2515,plain,
! [SV418: $i,SV362: $i > $o,SV487: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV487 ) )
= $true )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV487 )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2461]) ).
thf(2516,plain,
! [SV418: $i,SV362: $i > $o,SV492: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV492 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SV492 ) )
= $true )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2462]) ).
thf(2517,plain,
! [SV346: $i > $o,SV472: $i,SV362: $i > $o] :
( ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( SV362 @ SV472 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2464]) ).
thf(2518,plain,
! [SV346: $i > $o,SV362: $i > $o,SV472: $i] :
( ( ( SV472
!= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( SV362 @ SV472 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2465]) ).
thf(2519,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2466]) ).
thf(2520,plain,
! [SV346: $i > $o,SV456: $i,SV362: $i > $o] :
( ( ( SV362 @ SV456 )
= $false )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2467]) ).
thf(2521,plain,
! [SV152: $i,SV271: $i,SV377: $i > $o,SV365: $i > $o] :
( ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
= $false )
| ( ( ~ ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) ) )
= $true )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2468]) ).
thf(2522,plain,
! [SV395: $i,SV153: $i > $o,SV458: $i,SV272: $i > $o] :
( ( ( SV272 @ SV458 )
= $false )
| ( ( SV458
= ( sK57_SY259 @ SV458 @ SV272 @ SV153 ) )
= $false )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2471]) ).
thf(2523,plain,
! [SV395: $i,SV153: $i > $o,SV464: $i,SV272: $i > $o] :
( ( ( SV272 @ SV464 )
= $false )
| ( ( SV272 @ ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2472]) ).
thf(2524,plain,
! [SV395: $i,SV153: $i > $o,SV272: $i > $o,SV464: $i] :
( ( ( SV464
= ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV272 @ SV464 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2473]) ).
thf(2525,plain,
! [SV451: $i,SV153: $i > $o,SV493: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) )
| ~ ( ( SV493
!= ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SV493 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2474]) ).
thf(2526,plain,
! [SV451: $i,SV153: $i > $o,SV272: $i > $o] :
( ( ( ! [SY1533: $i] :
( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) )
| ~ ( ( SY1533
!= ( sK57_SY259 @ SY1533 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SY1533 ) ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2475]) ).
thf(2527,plain,
! [SV436: $i,SV153: $i > $o,SV482: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) )
| ~ ( ( SV482
!= ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV482 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2476]) ).
thf(2528,plain,
! [SV436: $i,SV153: $i > $o,SV488: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) )
| ~ ( ( SV488
!= ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV272 @ SV488 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2477]) ).
thf(2529,plain,
! [SV412: $i,SV113: $i,SV353: $i,SV459: $i,SV483: $i] :
( ( ( in @ SV483 @ SV459 )
= $false )
| ( ( in @ SV483 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
= $true )
| ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV459 )
= $true )
| ( ( in @ SV459 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2478]) ).
thf(2530,plain,
! [SV412: $i,SV113: $i,SV353: $i,SV479: $i] :
( ( ( in @ SV479 @ SV353 )
= $false )
| ( ( in @ SV479 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ SV412 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2481]) ).
thf(2531,plain,
! [SV422: $i,SV113: $i,SV353: $i,SV465: $i,SV489: $i] :
( ( ( ~ ( in @ SV489 @ SV465 ) )
= $true )
| ( ( in @ SV489 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
= $true )
| ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV465 )
= $true )
| ( ( in @ SV465 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2482]) ).
thf(2532,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( in @ ( sK16_SY1071 @ SV353 @ SV113 ) @ ( sK14_B @ SV113 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2483]) ).
thf(2533,plain,
! [SV422: $i,SV113: $i,SV353: $i] :
( ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV353 )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2484]) ).
thf(2534,plain,
! [SV422: $i,SV113: $i,SV353: $i,SV484: $i] :
( ( ( in @ SV484 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
= $false )
| ( ( ~ ( in @ SV484 @ SV353 ) )
= $true )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2485]) ).
thf(2535,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( ~ ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) )
= $false )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2486]) ).
thf(2536,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( ~ ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) ) )
= $false )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2486]) ).
thf(2537,plain,
! [SV466: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $false )
| ( ( SV250 @ SV466 )
= $false )
| ( ( in @ SV466 @ SV119 )
= $false )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2487]) ).
thf(2538,plain,
! [SV466: $i,SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV466 )
= $false )
| ( ( in @ SV466 @ SV119 )
= $false )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2487]) ).
thf(2539,plain,
! [SV474: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
| ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV474 )
= $false )
| ( ( in @ SV474 @ SV119 )
= $false )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2488]) ).
thf(2540,plain,
! [SV467: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $false )
| ( ( SV253 @ SV467 )
= $false )
| ( ( in @ SV467 @ SV125 )
= $false )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2541,plain,
! [SV467: $i,SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV467 )
= $false )
| ( ( in @ SV467 @ SV125 )
= $false )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2489]) ).
thf(2542,plain,
! [SV475: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
| ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV475 )
= $false )
| ( ( in @ SV475 @ SV125 )
= $false )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2490]) ).
thf(2543,plain,
! [SV126: $i,SV254: $i,SV323: $i,SV485: $o] :
( ( SV485 = $false )
| ( SV485 = $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2494]) ).
thf(2544,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( $true = $false )
| ( $true = $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2495]) ).
thf(2545,plain,
! [SV126: $i,SV254: $i,SV323: $i] :
( ( $false = $false )
| ( $false = $true )
| ( ( in @ SV323 @ SV254 )
= $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2496]) ).
thf(2546,plain,
! [SV254: $i,SV126: $i,SV323: $i,SV477: $o] :
( ( SV477 = $false )
| ( SV477 = $true )
| ( SV477 = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2500]) ).
thf(2547,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $true = $false )
| ( $true = $true )
| ( $true = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2501]) ).
thf(2548,plain,
! [SV254: $i,SV126: $i,SV323: $i] :
( ( $false = $false )
| ( $false = $true )
| ( $false = $false )
| ( ( in @ SV323 @ ( symdiff @ SV126 @ SV254 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2502]) ).
thf(2549,plain,
! [SV383: $i,SV469: $i,SV139: $i > $i > $o,SV261: $i,SV481: $i] :
( ( ( in @ SV481 @ SV261 )
= $false )
| ( ( SV139 @ SV481 @ SV469 )
= $false )
| ( ( in @ SV469 @ ( sK9_B @ SV261 @ SV139 ) )
= $true )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2506]) ).
thf(2550,plain,
! [SV383: $i,SV261: $i,SV470: $i,SV139: $i > $i > $o] :
( ( ( SV139 @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV470 )
= $true )
| ( ( in @ SV470 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2507]) ).
thf(2551,plain,
! [SV383: $i,SV139: $i > $i > $o,SV261: $i,SV470: $i] :
( ( ( in @ ( sK10_Xy @ SV470 @ SV261 @ SV139 ) @ SV261 )
= $true )
| ( ( in @ SV470 @ ( sK9_B @ SV261 @ SV139 ) )
= $false )
| ( ( SV383
= ( sK12_SY1066 @ SV383 @ SV261 @ SV139 ) )
= $false )
| ( ( SV139 @ ( sK11_SY23 @ SV261 @ SV139 ) @ SV383 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2508]) ).
thf(2552,plain,
! [SV417: $i,SV345: $i > $o,SV486: $i,SV361: $i > $o] :
( ( ( SV361 @ SV486 )
= $false )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV486 )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2509]) ).
thf(2553,plain,
! [SV417: $i,SV345: $i > $o,SV491: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV491 ) )
= $true )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV491 )
= $true )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2510]) ).
thf(2554,plain,
! [SV361: $i > $o,SV471: $i,SV345: $i > $o] :
( ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2511]) ).
thf(2555,plain,
! [SV345: $i > $o,SV361: $i > $o,SV471: $i] :
( ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( ~ ( SV345 @ SV471 ) )
= $true )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2512]) ).
thf(2556,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2513]) ).
thf(2557,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2513]) ).
thf(2558,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2514]) ).
thf(2559,plain,
! [SV418: $i,SV362: $i > $o,SV487: $i,SV346: $i > $o] :
( ( ( SV346 @ SV487 )
= $false )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV487 )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2515]) ).
thf(2560,plain,
! [SV418: $i,SV362: $i > $o,SV492: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV492 ) )
= $true )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV492 )
= $true )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2516]) ).
thf(2561,plain,
! [SV346: $i > $o,SV472: $i,SV362: $i > $o] :
( ( ( SV362 @ SV472 )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2517]) ).
thf(2562,plain,
! [SV346: $i > $o,SV362: $i > $o,SV472: $i] :
( ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( ~ ( SV362 @ SV472 ) )
= $true )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2518]) ).
thf(2563,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2519]) ).
thf(2564,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2519]) ).
thf(2565,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2520]) ).
thf(2566,plain,
! [SV152: $i,SV271: $i,SV365: $i > $o,SV377: $i > $o] :
( ( ( SV377 @ ( sK62_SY1104 @ SV377 @ SV365 @ SV271 @ SV152 ) )
= $false )
| ( ( SV365 @ ( sK61_Xx @ SV377 @ SV365 @ SV271 @ SV152 ) )
= $false )
| ( ( ( dsetconstr @ SV152
@ ^ [SY1594: $i] : ( SV365 @ SY1594 ) )
= ( dsetconstr @ SV271
@ ^ [SY1599: $i] : ( SV377 @ SY1599 ) ) )
= $true )
| ( ( SV152 = SV271 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2521]) ).
thf(2567,plain,
! [SV395: $i,SV153: $i > $o,SV464: $i,SV272: $i > $o] :
( ( ( SV272 @ SV464 )
= $false )
| ( ( SV464
= ( sK57_SY259 @ SV464 @ SV272 @ SV153 ) )
= $false )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV395
= ( sK58_SY256 @ SV395 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV395 )
= $false )
| ( ( ( sK59_Xx @ SV272 @ SV153 )
= ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2524]) ).
thf(2568,plain,
! [SV451: $i,SV153: $i > $o,SV493: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) )
| ~ ( ( SV493
!= ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV272 @ SV493 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2525]) ).
thf(2569,plain,
! [SV451: $i,SV153: $i > $o,SV494: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) )
| ~ ( ( SV494
!= ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) ) ) )
| ~ ( SV272 @ SV494 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2526]) ).
thf(2570,plain,
! [SV436: $i,SV153: $i > $o,SV482: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV272 @ SV482 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2571,plain,
! [SV436: $i,SV153: $i > $o,SV272: $i > $o,SV482: $i] :
( ( ( ~ ( ( SV482
!= ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV482 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2527]) ).
thf(2572,plain,
! [SV436: $i,SV153: $i > $o,SV488: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) )
| ~ ( ( SV488
!= ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV488 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2528]) ).
thf(2573,plain,
! [SV422: $i,SV113: $i,SV353: $i,SV465: $i,SV489: $i] :
( ( ( in @ SV489 @ SV465 )
= $false )
| ( ( in @ SV489 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
= $true )
| ( ( in @ ( sK17_SY1085 @ SV353 @ SV113 ) @ SV465 )
= $true )
| ( ( in @ SV465 @ ( sK14_B @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2531]) ).
thf(2574,plain,
! [SV422: $i,SV113: $i,SV353: $i,SV484: $i] :
( ( ( in @ SV484 @ SV353 )
= $false )
| ( ( in @ SV484 @ ( sK16_SY1071 @ SV353 @ SV113 ) )
= $false )
| ( ( in @ ( sK18_Xx @ SV353 @ SV113 ) @ SV113 )
= $false )
| ( ( in @ SV422 @ SV353 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2534]) ).
thf(2575,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
= $true )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2535]) ).
thf(2576,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
| ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
= $true )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2536]) ).
thf(2577,plain,
! [SV466: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $true )
| ( ( SV250 @ SV466 )
= $false )
| ( ( in @ SV466 @ SV119 )
= $false )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2537]) ).
thf(2578,plain,
! [SV466: $i,SV119: $i,SV250: $i > $o] :
( ( ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) )
= $true )
| ( ( SV250 @ SV466 )
= $false )
| ( ( in @ SV466 @ SV119 )
= $false )
| ( ( SV250 @ ( sK77_SY1111 @ SV250 @ SV119 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2538]) ).
thf(2579,plain,
! [SV474: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
!= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $false )
| ( ( SV250 @ SV474 )
= $false )
| ( ( in @ SV474 @ SV119 )
= $false )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2539]) ).
thf(2580,plain,
! [SV474: $i,SV119: $i,SV250: $i > $o] :
( ( ( ~ ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) ) )
= $false )
| ( ( SV250 @ SV474 )
= $false )
| ( ( in @ SV474 @ SV119 )
= $false )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2539]) ).
thf(2581,plain,
! [SV467: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $true )
| ( ( SV253 @ SV467 )
= $false )
| ( ( in @ SV467 @ SV125 )
= $false )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2540]) ).
thf(2582,plain,
! [SV467: $i,SV125: $i,SV253: $i > $o] :
( ( ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) )
= $true )
| ( ( SV253 @ SV467 )
= $false )
| ( ( in @ SV467 @ SV125 )
= $false )
| ( ( SV253 @ ( sK83_SY1116 @ SV253 @ SV125 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2541]) ).
thf(2583,plain,
! [SV475: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
!= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $false )
| ( ( SV253 @ SV475 )
= $false )
| ( ( in @ SV475 @ SV125 )
= $false )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2542]) ).
thf(2584,plain,
! [SV475: $i,SV125: $i,SV253: $i > $o] :
( ( ( ~ ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) ) )
= $false )
| ( ( SV253 @ SV475 )
= $false )
| ( ( in @ SV475 @ SV125 )
= $false )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2542]) ).
thf(2585,plain,
! [SV417: $i,SV345: $i > $o,SV491: $i,SV361: $i > $o] :
( ( ( SV361 @ SV491 )
= $false )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV491 )
= $true )
| ( ( SV417
= ( sK53_SY232 @ SV417 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV417 )
= $false )
| ( ( ( sK54_Xx @ SV361 @ SV345 )
= ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2553]) ).
thf(2586,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2554]) ).
thf(2587,plain,
! [SV361: $i > $o,SV471: $i,SV345: $i > $o] :
( ( ( SV345 @ SV471 )
= $false )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( ~ ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2555]) ).
thf(2588,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2556]) ).
thf(2589,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2557]) ).
thf(2590,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $false )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2558]) ).
thf(2591,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2558]) ).
thf(2592,plain,
! [SV418: $i,SV362: $i > $o,SV492: $i,SV346: $i > $o] :
( ( ( SV346 @ SV492 )
= $false )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV492 )
= $true )
| ( ( SV418
= ( sK49_SY235 @ SV418 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV418 )
= $false )
| ( ( ( sK50_Xx @ SV362 @ SV346 )
= ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2560]) ).
thf(2593,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2561]) ).
thf(2594,plain,
! [SV346: $i > $o,SV472: $i,SV362: $i > $o] :
( ( ( SV362 @ SV472 )
= $false )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( ~ ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2562]) ).
thf(2595,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2563]) ).
thf(2596,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2564]) ).
thf(2597,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $false )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2598,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2565]) ).
thf(2599,plain,
! [SV451: $i,SV153: $i > $o,SV493: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) )
| ~ ( ( SV493
!= ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV493 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2568]) ).
thf(2600,plain,
! [SV451: $i,SV153: $i > $o,SV494: $i,SV272: $i > $o] :
( ( ( ~ ( ~ ( SV272 @ ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) )
| ~ ( ( SV494
!= ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) ) ) ) )
= $true )
| ( ( ~ ( SV272 @ SV494 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2569]) ).
thf(2601,plain,
! [SV436: $i,SV153: $i > $o,SV482: $i,SV272: $i > $o] :
( ( ( SV272 @ ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV482 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2570]) ).
thf(2602,plain,
! [SV436: $i,SV153: $i > $o,SV272: $i > $o,SV482: $i] :
( ( ( SV482
!= ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV482 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2571]) ).
thf(2603,plain,
! [SV436: $i,SV153: $i > $o,SV488: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV272 @ SV488 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2604,plain,
! [SV436: $i,SV153: $i > $o,SV272: $i > $o,SV488: $i] :
( ( ( ~ ( ( SV488
!= ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV488 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_or_neg,[status(thm)],[2572]) ).
thf(2605,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( ~ ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
= $true )
| ( ( ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
= $true )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2575]) ).
thf(2606,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
= $true )
| ( ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
= $true )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2576]) ).
thf(2607,plain,
! [SV474: $i,SV250: $i > $o,SV119: $i] :
( ( ( ( dsetconstr @ SV119
@ ^ [SY1486: $i] : ( SV250 @ SY1486 ) )
= ( setadjoin @ ( sK75_SY488 @ SV250 @ SV119 ) @ emptyset ) )
= $true )
| ( ( SV250 @ SV474 )
= $false )
| ( ( in @ SV474 @ SV119 )
= $false )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2579]) ).
thf(2608,plain,
! [SV474: $i,SV119: $i,SV250: $i > $o] :
( ( ( in @ ( sK75_SY488 @ SV250 @ SV119 )
@ ( dsetconstr @ SV119
@ ^ [SY1487: $i] : ( SV250 @ SY1487 ) ) )
= $true )
| ( ( SV250 @ SV474 )
= $false )
| ( ( in @ SV474 @ SV119 )
= $false )
| ( ( ( sK76_Xx @ SV250 @ SV119 )
= ( sK77_SY1111 @ SV250 @ SV119 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2580]) ).
thf(2609,plain,
! [SV475: $i,SV253: $i > $o,SV125: $i] :
( ( ( ( dsetconstr @ SV125
@ ^ [SY1490: $i] : ( SV253 @ SY1490 ) )
= ( setadjoin @ ( sK81_SY519 @ SV253 @ SV125 ) @ emptyset ) )
= $true )
| ( ( SV253 @ SV475 )
= $false )
| ( ( in @ SV475 @ SV125 )
= $false )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2583]) ).
thf(2610,plain,
! [SV475: $i,SV125: $i,SV253: $i > $o] :
( ( ( in @ ( sK81_SY519 @ SV253 @ SV125 )
@ ( dsetconstr @ SV125
@ ^ [SY1491: $i] : ( SV253 @ SY1491 ) ) )
= $true )
| ( ( SV253 @ SV475 )
= $false )
| ( ( in @ SV475 @ SV125 )
= $false )
| ( ( ( sK82_Xx @ SV253 @ SV125 )
= ( sK83_SY1116 @ SV253 @ SV125 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2584]) ).
thf(2611,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2586]) ).
thf(2612,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2586]) ).
thf(2613,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) )
| ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2587]) ).
thf(2614,plain,
! [SV455: $i,SV345: $i > $o,SV495: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV495 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SV495 ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2588]) ).
thf(2615,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $true )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2590]) ).
thf(2616,plain,
! [SV455: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) )
= $true )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2591]) ).
thf(2617,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2593]) ).
thf(2618,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2593]) ).
thf(2619,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) )
| ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2594]) ).
thf(2620,plain,
! [SV456: $i,SV362: $i > $o,SV496: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV496 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SV496 ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2595]) ).
thf(2621,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $true )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2597]) ).
thf(2622,plain,
! [SV456: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) )
= $true )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2598]) ).
thf(2623,plain,
! [SV451: $i,SV153: $i > $o,SV493: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV272 @ SV493 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2624,plain,
! [SV451: $i,SV153: $i > $o,SV272: $i > $o,SV493: $i] :
( ( ( ~ ( ( SV493
!= ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV493 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2599]) ).
thf(2625,plain,
! [SV451: $i,SV153: $i > $o,SV494: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) )
| ~ ( ( SV494
!= ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV494 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2600]) ).
thf(2626,plain,
! [SV436: $i,SV153: $i > $o,SV482: $i,SV272: $i > $o] :
( ( ( SV272 @ SV482 )
= $false )
| ( ( SV272 @ ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2601]) ).
thf(2627,plain,
! [SV436: $i,SV153: $i > $o,SV272: $i > $o,SV482: $i] :
( ( ( SV482
= ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV272 @ SV482 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2602]) ).
thf(2628,plain,
! [SV436: $i,SV153: $i > $o,SV488: $i,SV272: $i > $o] :
( ( ( SV272 @ ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV488 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2603]) ).
thf(2629,plain,
! [SV436: $i,SV153: $i > $o,SV272: $i > $o,SV488: $i] :
( ( ( SV488
!= ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV488 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_neg,[status(thm)],[2604]) ).
thf(2630,plain,
! [SV113: $i,SV423: $i,SV414: $i] :
( ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
= $false )
| ( ( ~ ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) ) )
= $true )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2605]) ).
thf(2631,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2611]) ).
thf(2632,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2612]) ).
thf(2633,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $false )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2613]) ).
thf(2634,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ~ ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) ) )
= $false )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2613]) ).
thf(2635,plain,
! [SV455: $i,SV345: $i > $o,SV495: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV495 ) )
= $true )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV495 )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2614]) ).
thf(2636,plain,
! [SV455: $i,SV345: $i > $o,SV497: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV497 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SV497 ) )
= $true )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2615]) ).
thf(2637,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2617]) ).
thf(2638,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2618]) ).
thf(2639,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $false )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2619]) ).
thf(2640,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ~ ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) ) )
= $false )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2619]) ).
thf(2641,plain,
! [SV456: $i,SV362: $i > $o,SV496: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV496 ) )
= $true )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV496 )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2620]) ).
thf(2642,plain,
! [SV456: $i,SV362: $i > $o,SV498: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV498 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SV498 ) )
= $true )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_forall_pos,[status(thm)],[2621]) ).
thf(2643,plain,
! [SV451: $i,SV153: $i > $o,SV493: $i,SV272: $i > $o] :
( ( ( SV272 @ ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV493 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2623]) ).
thf(2644,plain,
! [SV451: $i,SV153: $i > $o,SV272: $i > $o,SV493: $i] :
( ( ( SV493
!= ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV493 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2624]) ).
thf(2645,plain,
! [SV451: $i,SV153: $i > $o,SV494: $i,SV272: $i > $o] :
( ( ( ~ ( SV272 @ ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) ) )
= $false )
| ( ( ~ ( SV272 @ SV494 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2625]) ).
thf(2646,plain,
! [SV451: $i,SV153: $i > $o,SV272: $i > $o,SV494: $i] :
( ( ( ~ ( ( SV494
!= ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) ) ) )
= $false )
| ( ( ~ ( SV272 @ SV494 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_or_neg,[status(thm)],[2625]) ).
thf(2647,plain,
! [SV436: $i,SV153: $i > $o,SV482: $i,SV272: $i > $o] :
( ( ( SV272 @ SV482 )
= $false )
| ( ( SV482
= ( sK57_SY259 @ SV482 @ SV272 @ SV153 ) )
= $false )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2627]) ).
thf(2648,plain,
! [SV436: $i,SV153: $i > $o,SV488: $i,SV272: $i > $o] :
( ( ( SV272 @ SV488 )
= $false )
| ( ( SV272 @ ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2628]) ).
thf(2649,plain,
! [SV436: $i,SV153: $i > $o,SV272: $i > $o,SV488: $i] :
( ( ( SV488
= ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV272 @ SV488 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2629]) ).
thf(2650,plain,
! [SV113: $i,SV414: $i,SV423: $i] :
( ( ( in @ SV423 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
= $false )
| ( ( in @ SV414 @ ( sK15_SY1084 @ SV423 @ SV414 @ SV113 ) )
= $false )
| ( ( SV414 = SV423 )
= $true )
| ( ( in @ SV414 @ SV113 )
= $false )
| ( ( in @ SV423 @ SV113 )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2630]) ).
thf(2651,plain,
! [SV471: $i,SV345: $i > $o,SV499: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV499 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SV499 ) )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2631]) ).
thf(2652,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( ! [SY1586: $i] :
( ~ ( SV361 @ SY1586 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SY1586 ) ) )
= $true )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2633]) ).
thf(2653,plain,
! [SV471: $i,SV345: $i > $o,SV361: $i > $o] :
( ( ( SV361 @ ( sK52_SY234 @ SV361 @ SV345 ) )
= $true )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2634]) ).
thf(2654,plain,
! [SV455: $i,SV345: $i > $o,SV495: $i,SV361: $i > $o] :
( ( ( SV361 @ SV495 )
= $false )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV495 )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2635]) ).
thf(2655,plain,
! [SV455: $i,SV345: $i > $o,SV497: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV497 ) )
= $true )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV497 )
= $true )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2636]) ).
thf(2656,plain,
! [SV472: $i,SV362: $i > $o,SV500: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV500 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SV500 ) )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2637]) ).
thf(2657,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( ! [SY1588: $i] :
( ~ ( SV346 @ SY1588 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SY1588 ) ) )
= $true )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2639]) ).
thf(2658,plain,
! [SV472: $i,SV362: $i > $o,SV346: $i > $o] :
( ( ( SV346 @ ( sK48_SY231 @ SV362 @ SV346 ) )
= $true )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2640]) ).
thf(2659,plain,
! [SV456: $i,SV362: $i > $o,SV496: $i,SV346: $i > $o] :
( ( ( SV346 @ SV496 )
= $false )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV496 )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2641]) ).
thf(2660,plain,
! [SV456: $i,SV362: $i > $o,SV498: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV498 ) )
= $true )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV498 )
= $true )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_or_pos,[status(thm)],[2642]) ).
thf(2661,plain,
! [SV451: $i,SV153: $i > $o,SV493: $i,SV272: $i > $o] :
( ( ( SV272 @ SV493 )
= $false )
| ( ( SV272 @ ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2643]) ).
thf(2662,plain,
! [SV451: $i,SV153: $i > $o,SV272: $i > $o,SV493: $i] :
( ( ( SV493
= ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV272 @ SV493 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2644]) ).
thf(2663,plain,
! [SV451: $i,SV153: $i > $o,SV494: $i,SV272: $i > $o] :
( ( ( SV272 @ ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV494 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2645]) ).
thf(2664,plain,
! [SV451: $i,SV153: $i > $o,SV272: $i > $o,SV494: $i] :
( ( ( SV494
!= ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) )
= $true )
| ( ( ~ ( SV272 @ SV494 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_neg,[status(thm)],[2646]) ).
thf(2665,plain,
! [SV436: $i,SV153: $i > $o,SV488: $i,SV272: $i > $o] :
( ( ( SV272 @ SV488 )
= $false )
| ( ( SV488
= ( sK57_SY259 @ SV488 @ SV272 @ SV153 ) )
= $false )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV436
= ( sK58_SY256 @ SV436 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV436 )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2649]) ).
thf(2666,plain,
! [SV471: $i,SV345: $i > $o,SV499: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV499 ) )
= $true )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV499 )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2651]) ).
thf(2667,plain,
! [SV471: $i,SV345: $i > $o,SV501: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV501 )
| ( ( sK52_SY234 @ SV361 @ SV345 )
= SV501 ) )
= $true )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2652]) ).
thf(2668,plain,
! [SV455: $i,SV345: $i > $o,SV497: $i,SV361: $i > $o] :
( ( ( SV361 @ SV497 )
= $false )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV497 )
= $true )
| ( ( SV455
= ( sK53_SY232 @ SV455 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV455 )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2655]) ).
thf(2669,plain,
! [SV472: $i,SV362: $i > $o,SV500: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV500 ) )
= $true )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV500 )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2656]) ).
thf(2670,plain,
! [SV472: $i,SV362: $i > $o,SV502: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV502 )
| ( ( sK48_SY231 @ SV362 @ SV346 )
= SV502 ) )
= $true )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_forall_pos,[status(thm)],[2657]) ).
thf(2671,plain,
! [SV456: $i,SV362: $i > $o,SV498: $i,SV346: $i > $o] :
( ( ( SV346 @ SV498 )
= $false )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV498 )
= $true )
| ( ( SV456
= ( sK49_SY235 @ SV456 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV456 )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $true )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $true ) ),
inference(extcnf_not_pos,[status(thm)],[2660]) ).
thf(2672,plain,
! [SV451: $i,SV153: $i > $o,SV493: $i,SV272: $i > $o] :
( ( ( SV272 @ SV493 )
= $false )
| ( ( SV493
= ( sK57_SY259 @ SV493 @ SV272 @ SV153 ) )
= $false )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV153 @ ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $true )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2662]) ).
thf(2673,plain,
! [SV451: $i,SV153: $i > $o,SV494: $i,SV272: $i > $o] :
( ( ( SV272 @ SV494 )
= $false )
| ( ( SV272 @ ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2663]) ).
thf(2674,plain,
! [SV451: $i,SV153: $i > $o,SV272: $i > $o,SV494: $i] :
( ( ( SV494
= ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) )
= $false )
| ( ( ~ ( SV272 @ SV494 ) )
= $true )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2664]) ).
thf(2675,plain,
! [SV471: $i,SV345: $i > $o,SV499: $i,SV361: $i > $o] :
( ( ( SV361 @ SV499 )
= $false )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV499 )
= $true )
| ( ( SV345 @ ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $true )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2666]) ).
thf(2676,plain,
! [SV471: $i,SV345: $i > $o,SV501: $i,SV361: $i > $o] :
( ( ( ~ ( SV361 @ SV501 ) )
= $true )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV501 )
= $true )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2667]) ).
thf(2677,plain,
! [SV472: $i,SV362: $i > $o,SV500: $i,SV346: $i > $o] :
( ( ( SV346 @ SV500 )
= $false )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV500 )
= $true )
| ( ( SV362 @ ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $true )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2669]) ).
thf(2678,plain,
! [SV472: $i,SV362: $i > $o,SV502: $i,SV346: $i > $o] :
( ( ( ~ ( SV346 @ SV502 ) )
= $true )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV502 )
= $true )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_or_pos,[status(thm)],[2670]) ).
thf(2679,plain,
! [SV451: $i,SV153: $i > $o,SV494: $i,SV272: $i > $o] :
( ( ( SV272 @ SV494 )
= $false )
| ( ( SV494
= ( sK57_SY259 @ SV494 @ SV272 @ SV153 ) )
= $false )
| ( ( ( descr
@ ^ [SY1409: $i] : ( SV153 @ SY1409 ) )
= ( descr
@ ^ [SY1535: $i] : ( SV272 @ SY1535 ) ) )
= $true )
| ( ( SV451
= ( sK58_SY256 @ SV451 @ SV272 @ SV153 ) )
= $false )
| ( ( SV153 @ SV451 )
= $false )
| ( ( SV153 @ ( sK59_Xx @ SV272 @ SV153 ) )
= $false )
| ( ( SV272 @ ( sK60_SY1103 @ SV272 @ SV153 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2674]) ).
thf(2680,plain,
! [SV471: $i,SV345: $i > $o,SV501: $i,SV361: $i > $o] :
( ( ( SV361 @ SV501 )
= $false )
| ( ( ( sK52_SY234 @ SV361 @ SV345 )
= SV501 )
= $true )
| ( ( SV471
= ( sK53_SY232 @ SV471 @ SV361 @ SV345 ) )
= $false )
| ( ( SV345 @ SV471 )
= $false )
| ( ( SV345 @ ( sK54_Xx @ SV361 @ SV345 ) )
= $false )
| ( ( SV361 @ ( sK55_SY1102 @ SV361 @ SV345 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2676]) ).
thf(2681,plain,
! [SV472: $i,SV362: $i > $o,SV502: $i,SV346: $i > $o] :
( ( ( SV346 @ SV502 )
= $false )
| ( ( ( sK48_SY231 @ SV362 @ SV346 )
= SV502 )
= $true )
| ( ( SV472
= ( sK49_SY235 @ SV472 @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ SV472 )
= $false )
| ( ( SV346 @ ( sK50_Xx @ SV362 @ SV346 ) )
= $false )
| ( ( SV362 @ ( sK51_SY1100 @ SV362 @ SV346 ) )
= $false ) ),
inference(extcnf_not_pos,[status(thm)],[2678]) ).
thf(2682,plain,
$false = $true,
inference(fo_atp_e,[status(thm)],[394,2681,2680,2679,2677,2675,2673,2672,2671,2668,2665,2661,2659,2658,2654,2653,2650,2648,2647,2638,2632,2626,2622,2616,2610,2609,2608,2607,2606,2596,2592,2589,2585,2582,2581,2578,2577,2574,2573,2567,2566,2559,2552,2551,2550,2549,2548,2547,2546,2545,2544,2543,2533,2532,2530,2529,2523,2522,2505,2504,2503,2499,2498,2497,2493,2492,2491,2480,2479,2470,2469,2463,2456,2436,2435,2432,2431,2429,2428,2405,2398,2386,2385,2384,2381,2380,2379,2352,2351,2350,2321,2320,2319,2296,2293,2292,2268,2267,2266,2262,2261,2257,2256,2242,2241,2240,2239,2236,2235,2234,2195,2189,2178,2177,2176,2175,2174,2173,2172,2166,2165,2164,2163,2162,2161,2146,2145,2144,2143,2142,2141,2140,2131,2130,2129,2124,2123,2096,2095,2094,2091,2089,2079,2078,2077,2074,2073,2057,2055,2052,2051,2039,2038,2036,2034,2029,2028,2021,2014,1989,1988,1971,1970,1969,1941,1940,1933,1892,1888,1886,1884,1883,1882,1881,1864,1836,1830,1829,1828,1813,1812,1810,1809,1798,1797,1794,1780,1775,1762,1755,1737,1736,1729,1728,1723,1722,1721,1715,1708,1707,1701,1689,1688,1677,1676,1675,1674,1668,1667,1666,1665,1622,1620,1618,1612,1611,1607,1589,1585,1583,1580,1556,1555,1554,1535,1516,1503,1502,1491,1477,1476,1474,1473,1472,1471,1470,1469,1468,1467,1466,1443,1437,1423,1404,1393,1392,1379,1377,1376,1372,1371,1370,1369,1368,1367,1366,1350,1349,1338,1331,1317,1273,1270,1261,1260,1257,1256,1255,1254,1253,1252,1251,1249,1248,1241,1227,1185,1166,1165,1163,1162,1149,1147,1146,1142,1141,1139,1135,1129,1121,1119,1070,1058,1057,1056,1055,1054,1053,1046,1045,1044,1043,1042,1039,1036,1035,1034,1033,1029,1025,1023,1022,1021,1014,1013,1011,1010,1006,1001,996,995,986,936,927,905,904,903,902,901,900,884,869,789,780,779,778,777,776,773,767,761,760,739,731,730,728,725,724,720,716,704,698,697,696,682,613,612,611,585,579,570,522,521,520,460,436,398]) ).
thf(2683,plain,
$false,
inference(solved_all_splits,[solved_all_splits(join,[])],[2682]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU647^1 : 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/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.19 % Computer : n009.cluster.edu
% 0.07/0.19 % Model : x86_64 x86_64
% 0.07/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.19 % Memory : 8046.5625MB
% 0.07/0.19 % OS : Linux 6.8.0-71-generic
% 0.07/0.19 % CPULimit : 300
% 0.07/0.19 % WCLimit : 300
% 0.07/0.19 % DateTime : Tue Oct 6 15:30:02 UTC 2026
% 0.07/0.20 % CPUTime :
% 0.07/0.20 Running leo --cores 7 --timeout 300 --proofoutput 1 --foatp e --atp e=/export/starexec/sandbox2/solver/bin/eprover /export/starexec/sandbox2/benchmark/theBenchmark.p
% 36.38/6.36
% 36.38/6.36 No.of.Axioms: 0
% 36.38/6.36
% 36.38/6.36 Length.of.Defs: 35198
% 36.38/6.36
% 36.38/6.36 Contains.Choice.Funs: true
% 36.38/6.36 ...........................................................................................................
% 36.38/6.36
% 36.38/6.36 ********************************
% 36.38/6.36 * All subproblems solved! *
% 36.38/6.36 ********************************
% 36.38/6.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:163,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2682,loop_count:0,foatp_calls:1,translation:fof_full)
% 36.38/6.36
% 36.38/6.36 %**** Beginning of derivation protocol ****
% 36.38/6.36 % SZS output start CNFRefutation
% See solution above
% 36.38/6.37
% 36.38/6.37 %**** End of derivation protocol ****
% 36.38/6.37 %**** no. of clauses in derivation: 2683 ****
% 36.38/6.37 %**** clause counter: 2682 ****
% 36.38/6.37
% 36.38/6.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : (rf:0,axioms:163,ps:3,u:6,ude:true,rLeibEQ:true,rAndEQ:true,use_choice:true,use_extuni:true,use_extcnf_combined:true,expand_extuni:false,foatp:e,atp_timeout:25,atp_calls_frequency:5,ordering:none,proof_output:1,protocol_output:false,clause_count:2682,loop_count:0,foatp_calls:1,translation:fof_full)
%------------------------------------------------------------------------------