%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU591^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:28 AM UTC 2026
% Result : Theorem 2.18s 1.74s
% Output : Refutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 7
% Syntax : Number of formulae : 63 ( 43 unt; 0 typ; 1 def)
% Number of atoms : 1906 ( 501 equ; 0 cnn)
% Maximal formula atoms : 109 ( 30 avg)
% Number of connectives : 1147 ( 16 ~; 15 |; 326 &; 299 @)
% ( 1 <=>; 461 =>; 0 <=; 0 <~>)
% Maximal formula depth : 116 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 18 ( 18 >; 0 *; 0 +; 0 <<)
% Number of symbols : 177 ( 173 usr; 115 con; 0-4 aty)
% ( 29 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 119 ( 56 ^; 54 !; 9 ?; 119 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
set2prop: $i > $o ).
thf(func_def_88,type,
subset: $i > $i > $o ).
thf(func_def_89,type,
disjoint: $i > $i > $o ).
thf(func_def_90,type,
setsmeet: $i > $i > $o ).
thf(func_def_114,type,
binunion: $i > $i > $i ).
thf(func_def_122,type,
binintersect: $i > $i > $i ).
thf(func_def_146,type,
sK4: ( $i > $o ) > $i > $i ).
thf(func_def_147,type,
sK5: $i > $i > $i ).
thf(func_def_148,type,
sK6: $i > $i > $i ).
thf(func_def_149,type,
sK7: ( $i > $i > $o ) > $i > $i ).
thf(func_def_150,type,
sK8: ( $i > $i > $o ) > $i > $i ).
thf(func_def_151,type,
sK9: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_152,type,
sK10: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_153,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_154,type,
sK12: $i > $i ).
thf(func_def_155,type,
sK13: $i > $i ).
thf(func_def_156,type,
sK14: $i > $i > $i ).
thf(func_def_157,type,
sK15: $i > $i ).
thf(func_def_158,type,
sK16: $i > $i > $i ).
thf(func_def_159,type,
sK17: $i > $i > $i ).
thf(func_def_160,type,
sK18: $i > $i > $i ).
thf(func_def_161,type,
sK19: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_162,type,
sK20: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_163,type,
sK21: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_164,type,
sK22: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_165,type,
sK23: ( $i > $o ) > $i ).
thf(func_def_166,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_167,type,
sK25: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_168,type,
sK26: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_169,type,
sK27: $i > $i ).
thf(func_def_170,type,
sK28: $i > $i > $i > $i ).
thf(func_def_171,type,
sK29: $i > $i > $i ).
thf(func_def_172,type,
sK30: $i > $i > $i ).
thf(func_def_173,type,
sK31: $i > $i > $i ).
thf(func_def_174,type,
sK32: $i > $i ).
thf(func_def_175,type,
sK33: $i > ( $i > $o ) > $i ).
thf(func_def_176,type,
sK34: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_177,type,
sK35: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_178,type,
sK36: $i > $i ).
thf(func_def_179,type,
sK37: $i > ( $i > $o ) > $i ).
thf(func_def_180,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_181,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_182,type,
sK40: ( $i > $o ) > $i ).
thf(func_def_183,type,
sK41: ( $i > $o ) > $i ).
thf(func_def_184,type,
sK42: $i > $i > $i ).
thf(func_def_185,type,
sK43: $i > $i > $i ).
thf(func_def_186,type,
sK44: $i > $o > $i > $i ).
thf(func_def_187,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_188,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_189,type,
sK47: ( $i > $o ) > $i ).
thf(func_def_190,type,
sK48: $i > $i ).
thf(func_def_191,type,
ph49:
!>[X0: $tType] : X0 ).
thf(f3267,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f2795,f3266]) ).
thf(f3266,plain,
spl3_2,
inference(avatar_split_clause,[status(thm)],[f1802,f1682]) ).
thf(f1682,definition,
( spl3_2
<=> ! [X3: $o] :
( ( $true = X3 )
| ( $false = X3 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition]) ).
thf(f1802,plain,
! [X0: $o] :
( ( $false = X0 )
| ( $true = X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f1795]) ).
thf(f1795,plain,
! [X0: $o] :
( ( $true = X0 )
| ( $false = $true )
| ( $false = X0 ) ),
inference(superposition,[status(thm)],[f1258,f1241]) ).
thf(f1241,plain,
! [X1: $o] :
( ( ( in @ emptyset @ ( prop2set @ X1 ) )
= $true )
| ( $false = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f1240]) ).
thf(f1240,plain,
! [X1: $o] :
( ( X1
=> ( in @ emptyset @ ( prop2set @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1239]) ).
thf(f1239,plain,
! [X1: $o] :
( ( ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f612]) ).
thf(f612,plain,
( ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f502,f467]) ).
thf(f467,plain,
prop2setI = $true,
inference(cnf_transformation,[status(thm)],[f333]) ).
thf(f333,plain,
( ( exuE3e = $true )
& ( quantDeMorgan2 = $true )
& ( exuI2 = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( binunionIL = $true )
& ( emptyI = $true )
& ( exuE2 = $true )
& ( upairsetE = $true )
& ( binunionRsub = $true )
& ( dsetconstrEL = $true )
& ( nonemptyImpWitness = $true )
& ( sepSubset = $true )
& ( omega0Ax = $true )
& ( setext = $true )
& ( binunionE = $true )
& ( in__Cong = $true )
& ( prop2setI = $true )
& ( inPowerset = $true )
& ( setbeta = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( binunionIR = $true )
& ( replAx = $true )
& ( prop2setE = $true )
& ( inCongP = $true )
& ( powerset__Cong = $true )
& ( setunionI = $true )
& ( setextsub = $true )
& ( setadjoinAx = $true )
& ( setadjoinOr = $true )
& ( foundationAx = $true )
& ( subsetI2 = $true )
& ( exuE3u = $true )
& ( subsetTrans = $true )
& ( eqimpsubset1 = $true )
& ( emptysetE = $true )
& ( quantDeMorgan4 = $true )
& ( exuE1 = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( dsetconstrER = $true )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( singletonsswitch = $true )
& ( notequalI2 = $true )
& ( notdexE = $true )
& ( dsetconstrI = $true )
& ( emptyinunitempty = $true )
& ( subsetE = $true )
& ( setadjoinE = $true )
& ( emptyinPowerset = $true )
& ( quantDeMorgan3 = $true )
& ( notsubsetI = $true )
& ( setadjoinIL = $true )
& ( notinemptyset = $true )
& ( prop2set2propI = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( omegaIndAx = $true )
& ( setadjoinIR = $true )
& ( emptysetimpfalse = $true )
& ( setunion__Cong = $true )
& ( powersetAx = $true )
& ( ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) )
= $true )
& ( ( in @ sK2 @ sK1 )
!= $true )
& ( binunionLsub = $true )
& ( subset2powerset = $true )
& ( setunionAx = $true )
& ( quantDeMorgan1 = $true )
& ( powersetI = $true )
& ( powersetI1 = $true )
& ( emptysetsubset = $true )
& ( emptyset__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( exu__Cong = $true )
& ( powersetE1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoin__Cong = $true )
& ( upairsetIR = $true )
& ( nonemptyI = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( dsetconstr__Cong = $true )
& ( powersetE = $true )
& ( sepInPowerset = $true )
& ( subPowSU = $true )
& ( notequalI1 = $true )
& ( setadjoinSub = $true )
& ( subsetI1 = $true )
& ( vacuousDall = $true )
& ( eqimpsubset2 = $true )
& ( omegaSAx = $true )
& ( descr__Cong = $true )
& ( uniqinunit = $true )
& ( emptyInPowerset = $true )
& ( notinsingleton = $true )
& ( binunionEcases = $true )
& ( emptysetAx = $true )
& ( upairsetIL = $true )
& ( subsetRefl = $true )
& ( binintersectI = $true )
& ( setextAx = $true )
& ( nonemptyE1 = $true )
& ( powersetsubset = $true )
& ( eqinunit = $true )
& ( upairset2IR = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f331,f332]) ).
thf(f332,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
=> ( ( ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) )
= $true )
& ( ( in @ sK2 @ sK1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f331,plain,
( ( exuE3e = $true )
& ( quantDeMorgan2 = $true )
& ( exuI2 = $true )
& ( noeltsimpempty = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( binunionIL = $true )
& ( emptyI = $true )
& ( exuE2 = $true )
& ( upairsetE = $true )
& ( binunionRsub = $true )
& ( dsetconstrEL = $true )
& ( nonemptyImpWitness = $true )
& ( sepSubset = $true )
& ( omega0Ax = $true )
& ( setext = $true )
& ( binunionE = $true )
& ( in__Cong = $true )
& ( prop2setI = $true )
& ( inPowerset = $true )
& ( setbeta = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( exuI3 = $true )
& ( binunionIR = $true )
& ( replAx = $true )
& ( prop2setE = $true )
& ( inCongP = $true )
& ( powerset__Cong = $true )
& ( setunionI = $true )
& ( setextsub = $true )
& ( setadjoinAx = $true )
& ( setadjoinOr = $true )
& ( foundationAx = $true )
& ( subsetI2 = $true )
& ( exuE3u = $true )
& ( subsetTrans = $true )
& ( eqimpsubset1 = $true )
& ( emptysetE = $true )
& ( quantDeMorgan4 = $true )
& ( exuE1 = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( dsetconstrER = $true )
& ( setadjoinSub2 = $true )
& ( setoftrueEq = $true )
& ( singletonsswitch = $true )
& ( notequalI2 = $true )
& ( notdexE = $true )
& ( dsetconstrI = $true )
& ( emptyinunitempty = $true )
& ( subsetE = $true )
& ( setadjoinE = $true )
& ( emptyinPowerset = $true )
& ( quantDeMorgan3 = $true )
& ( notsubsetI = $true )
& ( setadjoinIL = $true )
& ( notinemptyset = $true )
& ( prop2set2propI = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( omegaIndAx = $true )
& ( setadjoinIR = $true )
& ( emptysetimpfalse = $true )
& ( setunion__Cong = $true )
& ( powersetAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
& ( binunionLsub = $true )
& ( subset2powerset = $true )
& ( setunionAx = $true )
& ( quantDeMorgan1 = $true )
& ( powersetI = $true )
& ( powersetI1 = $true )
& ( emptysetsubset = $true )
& ( emptyset__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( exu__Cong = $true )
& ( powersetE1 = $true )
& ( nonemptyI1 = $true )
& ( setadjoin__Cong = $true )
& ( upairsetIR = $true )
& ( nonemptyI = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( dsetconstr__Cong = $true )
& ( powersetE = $true )
& ( sepInPowerset = $true )
& ( subPowSU = $true )
& ( notequalI1 = $true )
& ( setadjoinSub = $true )
& ( subsetI1 = $true )
& ( vacuousDall = $true )
& ( eqimpsubset2 = $true )
& ( omegaSAx = $true )
& ( descr__Cong = $true )
& ( uniqinunit = $true )
& ( emptyInPowerset = $true )
& ( notinsingleton = $true )
& ( binunionEcases = $true )
& ( emptysetAx = $true )
& ( upairsetIL = $true )
& ( subsetRefl = $true )
& ( binintersectI = $true )
& ( setextAx = $true )
& ( nonemptyE1 = $true )
& ( powersetsubset = $true )
& ( eqinunit = $true )
& ( upairset2IR = $true ) ),
inference(flattening,[status(thm)],[f330]) ).
thf(f330,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
& ( ( in @ X2 @ X1 )
!= $true ) )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f279]) ).
thf(f279,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f278]) ).
thf(f278,plain,
~ ( 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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
=> ( in @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f112]) ).
thf(f112,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
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f111]) ).
thf(f111,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
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',binintersectEL) ).
thf(f502,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f248]) ).
thf(f248,plain,
( prop2setI
= ( !! @ $o
@ ^ [Y0: $o] :
( Y0
=> ( in @ emptyset @ ( prop2set @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f247]) ).
thf(f247,plain,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f59]) ).
thf(f59,axiom,
( prop2setI
= ( ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',prop2setI) ).
thf(f1258,plain,
! [X2: $i,X1: $o] :
( ( $false
= ( in @ X2 @ ( prop2set @ X1 ) ) )
| ( $true = X1 ) ),
inference(binary_proxy_clausification,[status(thm)],[f1257]) ).
thf(f1257,plain,
! [X2: $i,X1: $o] :
( ( ( in @ X2 @ ( prop2set @ X1 ) )
=> X1 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1256]) ).
thf(f1256,plain,
! [X2: $i,X1: $o] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( prop2set @ X1 ) )
=> X1 )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1255]) ).
thf(f1255,plain,
! [X1: $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( prop2set @ X1 ) )
=> X1 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1254]) ).
thf(f1254,plain,
! [X1: $o] :
( ( ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( prop2set @ Y0 ) )
=> Y0 ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f561]) ).
thf(f561,plain,
( ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( prop2set @ Y0 ) )
=> Y0 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f459,f345]) ).
thf(f345,plain,
( prop2setE
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( prop2set @ Y0 ) )
=> Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f297]) ).
thf(f297,plain,
( prop2setE
= ( !! @ $o
@ ^ [Y0: $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( prop2set @ Y0 ) )
=> Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f296]) ).
thf(f296,plain,
( prop2setE
= ( ! [X0: $i,X1: $o] :
( ( in @ X0 @ ( prop2set @ X1 ) )
=> X1 ) ) ),
inference(rectify,[status(thm)],[f18]) ).
thf(f18,axiom,
( prop2setE
= ( ! [X1: $i,X0: $o] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',prop2setE) ).
thf(f459,plain,
prop2setE = $true,
inference(cnf_transformation,[status(thm)],[f333]) ).
thf(f2795,plain,
~ spl3_2,
inference(avatar_contradiction_clause,[status(thm)],[f2794]) ).
thf(f2794,plain,
( $false
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f2793]) ).
thf(f2793,plain,
( ( $false = $true )
| ~ spl3_2 ),
inference(forward_demodulation,[status(thm)],[f2782,f1729]) ).
thf(f1729,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ~ spl3_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1727]) ).
thf(f1727,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ( $true != $true )
| ~ spl3_2 ),
inference(superposition,[status(thm)],[f418,f1683]) ).
thf(f1683,plain,
( ! [X3: $o] :
( ( $true = X3 )
| ( $false = X3 ) )
| ~ spl3_2 ),
inference(avatar_component_clause,[status(thm)],[f1682]) ).
thf(f418,plain,
( ( in @ sK2 @ sK1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f333]) ).
thf(f2782,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(trivial_inequality_removal,[status(thm)],[f2772]) ).
thf(f2772,plain,
( ( ( in @ sK2 @ sK1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f846,f1003]) ).
thf(f1003,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( $false
= ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) ) )
| ( ( in @ X2 @ X3 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1002]) ).
thf(f1002,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ( in @ X2 @ ( dsetconstr @ X3 @ X1 ) )
=> ( in @ X2 @ X3 ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1001]) ).
thf(f1001,plain,
! [X2: $i,X3: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( in @ X2 @ Y0 ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f1000]) ).
thf(f1000,plain,
! [X2: $i,X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ ( dsetconstr @ Y0 @ X1 ) )
=> ( in @ X2 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f999]) ).
thf(f999,plain,
! [X2: $i,X1: $i > $o] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( in @ Y0 @ Y1 ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f998]) ).
thf(f998,plain,
! [X1: $i > $o] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ ( dsetconstr @ Y1 @ X1 ) )
=> ( in @ Y0 @ Y1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f997]) ).
thf(f997,plain,
! [X1: $i > $o] :
( ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( in @ Y1 @ Y2 ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f996]) ).
thf(f996,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ ( dsetconstr @ Y2 @ Y0 ) )
=> ( in @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f609]) ).
thf(f609,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f499,f474]) ).
thf(f474,plain,
dsetconstrEL = $true,
inference(cnf_transformation,[status(thm)],[f333]) ).
thf(f499,plain,
( dsetconstrEL
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f269]) ).
thf(f269,plain,
( dsetconstrEL
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1
@ ( dsetconstr @ Y2
@ ^ [Y3: $i] : ( Y0 @ Y3 ) ) )
=> ( in @ Y1 @ Y2 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f268]) ).
thf(f268,plain,
! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X2 @ X3 ) ) )
=> ( in @ X1 @ X0 ) )
= dsetconstrEL ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,axiom,
! [X3: $i,X1: $i,X0: $i > $o] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( in @ X1 @ X3 ) )
= dsetconstrEL ),
file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',dsetconstrEL) ).
thf(f846,plain,
( ( in @ sK2
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ Y0 @ sK0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f584]) ).
thf(f584,plain,
( ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK1
@ sK0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f419,f550]) ).
thf(f550,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f267]) ).
thf(f267,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f266]) ).
thf(f266,plain,
( ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] : ( in @ X2 @ X1 ) ) )
= binintersect ),
inference(rectify,[status(thm)],[f108]) ).
thf(f108,axiom,
( ( ^ [X3: $i,X4: $i] :
( dsetconstr @ X3
@ ^ [X1: $i] : ( in @ X1 @ X4 ) ) )
= binintersect ),
file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',binintersect) ).
thf(f419,plain,
( ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f333]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU591^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n023.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:28:34 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.47 thf(spec,logic,$$dhol).
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 % File : SEU591^1 : TPTP v9.2.1. Released v3.7.0.
% 0.31/0.47 % Domain : Set Theory
% 0.31/0.47 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.31/0.47 % Version : Especial.
% 0.31/0.47 % English : (! A:i.! B:i.! x:i.in x (binintersect A B) -> in x A)
% 0.31/0.47
% 0.31/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.31/0.47 % Source : [Bro08]
% 0.31/0.47 % Names : ZFC093g [Bro08]
% 0.31/0.47
% 0.31/0.47 % Status : Theorem
% 0.31/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.31/0.47 % Syntax : Number of formulae : 235 ( 110 unt; 124 typ; 110 def)
% 0.31/0.47 % Number of atoms : 588 ( 159 equ; 0 cnn)
% 0.31/0.47 % Maximal formula atoms : 109 ( 5 avg)
% 0.31/0.47 % Number of connectives : 929 ( 29 ~; 6 |; 27 &; 589 @)
% 0.31/0.47 % ( 14 <=>; 264 =>; 0 <=; 0 <~>)
% 0.31/0.47 % Maximal formula depth : 115 ( 2 avg)
% 0.31/0.47 % Number of types : 2 ( 0 usr)
% 0.31/0.47 % Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% 0.31/0.47 % Number of symbols : 127 ( 124 usr; 111 con; 0-2 aty)
% 0.31/0.47 % Number of variables : 325 ( 33 ^; 264 !; 28 ?; 325 :)
% 0.31/0.47 % SPC : TH0_THM_EQU_NAR
% 0.31/0.47
% 0.31/0.47 % Comments : http://mathgate.info/detsetitem.php?id=167
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 thf(in_type,type,
% 0.31/0.47 in: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu_type,type,
% 0.31/0.47 exu: ( $i > $o ) > $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu,definition,
% 0.31/0.47 ( exu
% 0.31/0.47 = ( ^ [Xphi: $i > $o] :
% 0.31/0.47 ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx_type,type,
% 0.31/0.47 setextAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setextAx,definition,
% 0.31/0.47 ( setextAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xx @ B ) )
% 0.31/0.47 => ( A = B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset_type,type,
% 0.31/0.47 emptyset: $i ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx_type,type,
% 0.31/0.47 emptysetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetAx,definition,
% 0.31/0.47 ( emptysetAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin_type,type,
% 0.31/0.47 setadjoin: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx_type,type,
% 0.31/0.47 setadjoinAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinAx,definition,
% 0.31/0.47 ( setadjoinAx
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 <=> ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset_type,type,
% 0.31/0.47 powerset: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx_type,type,
% 0.31/0.47 powersetAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetAx,definition,
% 0.31/0.47 ( powersetAx
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 <=> ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion_type,type,
% 0.31/0.47 setunion: $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx_type,type,
% 0.31/0.47 setunionAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionAx,definition,
% 0.31/0.47 ( setunionAx
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 <=> ? [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega_type,type,
% 0.31/0.47 omega: $i ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax_type,type,
% 0.31/0.47 omega0Ax: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega0Ax,definition,
% 0.31/0.47 ( omega0Ax
% 0.31/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx_type,type,
% 0.31/0.47 omegaSAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaSAx,definition,
% 0.31/0.47 ( omegaSAx
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx_type,type,
% 0.31/0.47 omegaIndAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omegaIndAx,definition,
% 0.31/0.47 ( omegaIndAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( ( in @ emptyset @ A )
% 0.31/0.47 & ! [Xx: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ omega )
% 0.31/0.47 & ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ omega )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(replAx_type,type,
% 0.31/0.47 replAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(replAx,definition,
% 0.31/0.47 ( replAx
% 0.31/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 <=> ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx_type,type,
% 0.31/0.47 foundationAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(foundationAx,definition,
% 0.31/0.47 ( foundationAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ? [B: $i] :
% 0.31/0.47 ( ( in @ B @ A )
% 0.31/0.47 & ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx_type,type,
% 0.31/0.47 wellorderingAx: $o ).
% 0.31/0.47
% 0.31/0.47 thf(wellorderingAx,definition,
% 0.31/0.47 ( wellorderingAx
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ? [B: $i] :
% 0.31/0.47 ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) ) )
% 0.31/0.47 & ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( ( in @ Xx @ A )
% 0.31/0.47 & ( in @ Xy @ A ) )
% 0.31/0.47 => ( ! [C: $i] :
% 0.31/0.47 ( ( in @ C @ B )
% 0.31/0.47 => ( ( in @ Xx @ C )
% 0.31/0.47 <=> ( in @ Xy @ C ) ) )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 & ! [C: $i,D: $i] :
% 0.31/0.47 ( ( ( in @ C @ B )
% 0.31/0.47 & ( in @ D @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ D ) )
% 0.31/0.47 | ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ D )
% 0.31/0.47 => ( in @ Xx @ C ) ) ) )
% 0.31/0.47 & ! [C: $i] :
% 0.31/0.47 ( ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ C )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/0.47 => ? [D: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ D @ B )
% 0.31/0.47 & ( in @ Xx @ C )
% 0.31/0.47 & ~ ? [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ D )
% 0.31/0.47 & ( in @ Xy @ C ) )
% 0.31/0.47 & ! [E: $i] :
% 0.31/0.47 ( ( in @ E @ B )
% 0.31/0.47 => ( ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ E )
% 0.31/0.47 => ( in @ Xy @ D ) )
% 0.31/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr_type,type,
% 0.31/0.47 descr: ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(descrp_type,type,
% 0.31/0.47 descrp: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descrp,definition,
% 0.31/0.47 ( descrp
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( Xphi
% 0.31/0.47 @ ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr_type,type,
% 0.31/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI_type,type,
% 0.31/0.47 dsetconstrI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrI,definition,
% 0.31/0.47 ( dsetconstrI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL_type,type,
% 0.31/0.47 dsetconstrEL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrEL,definition,
% 0.31/0.47 ( dsetconstrEL
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER_type,type,
% 0.31/0.47 dsetconstrER: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstrER,definition,
% 0.31/0.47 ( dsetconstrER
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1_type,type,
% 0.31/0.47 exuE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE1,definition,
% 0.31/0.47 ( exuE1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set_type,type,
% 0.31/0.47 prop2set: $o > $i ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE_type,type,
% 0.31/0.47 prop2setE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setE,definition,
% 0.31/0.47 ( prop2setE
% 0.31/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE_type,type,
% 0.31/0.47 emptysetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetE,definition,
% 0.31/0.47 ( emptysetE
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse_type,type,
% 0.31/0.47 emptysetimpfalse: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetimpfalse,definition,
% 0.31/0.47 ( emptysetimpfalse
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => $false ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset_type,type,
% 0.31/0.47 notinemptyset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinemptyset,definition,
% 0.31/0.47 ( notinemptyset
% 0.31/0.47 = ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e_type,type,
% 0.31/0.47 exuE3e: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3e,definition,
% 0.31/0.47 ( exuE3e
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setext_type,type,
% 0.31/0.47 setext: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setext,definition,
% 0.31/0.47 ( setext
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( A = B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI_type,type,
% 0.31/0.47 emptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyI,definition,
% 0.31/0.47 ( emptyI
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty_type,type,
% 0.31/0.47 noeltsimpempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(noeltsimpempty,definition,
% 0.31/0.47 ( noeltsimpempty
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ~ ( in @ Xx @ A )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta_type,type,
% 0.31/0.47 setbeta: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setbeta,definition,
% 0.31/0.47 ( setbeta
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty_type,type,
% 0.31/0.47 nonempty: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonempty,definition,
% 0.31/0.47 ( nonempty
% 0.31/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1_type,type,
% 0.31/0.47 nonemptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyE1,definition,
% 0.31/0.47 ( nonemptyE1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI_type,type,
% 0.31/0.47 nonemptyI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI,definition,
% 0.31/0.47 ( nonemptyI
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 => ( nonempty
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1_type,type,
% 0.31/0.47 nonemptyI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyI1,definition,
% 0.31/0.47 ( nonemptyI1
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL_type,type,
% 0.31/0.47 setadjoinIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIL,definition,
% 0.31/0.47 ( setadjoinIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty_type,type,
% 0.31/0.47 emptyinunitempty: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinunitempty,definition,
% 0.31/0.47 ( emptyinunitempty
% 0.31/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR_type,type,
% 0.31/0.47 setadjoinIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinIR,definition,
% 0.31/0.47 ( setadjoinIR
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ A )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE_type,type,
% 0.31/0.47 setadjoinE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinE,definition,
% 0.31/0.47 ( setadjoinE
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ( ( Xy = Xx )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xy @ A )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr_type,type,
% 0.31/0.47 setadjoinOr: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinOr,definition,
% 0.31/0.47 ( setadjoinOr
% 0.31/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/0.47 => ( ( Xy = Xx )
% 0.31/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq_type,type,
% 0.31/0.47 setoftrueEq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setoftrueEq,definition,
% 0.31/0.47 ( setoftrueEq
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : $true )
% 0.31/0.47 = A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI_type,type,
% 0.31/0.47 powersetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI,definition,
% 0.31/0.47 ( powersetI
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) )
% 0.31/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset_type,type,
% 0.31/0.47 emptyinPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyinPowerset,definition,
% 0.31/0.47 ( emptyinPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset_type,type,
% 0.31/0.47 emptyInPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyInPowerset,definition,
% 0.31/0.47 ( emptyInPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE_type,type,
% 0.31/0.47 powersetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE,definition,
% 0.31/0.47 ( powersetE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 => ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunionI_type,type,
% 0.31/0.47 setunionI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionI,definition,
% 0.31/0.47 ( setunionI
% 0.31/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( ( in @ B @ A )
% 0.31/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunionE_type,type,
% 0.31/0.47 setunionE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunionE,definition,
% 0.31/0.47 ( setunionE
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/0.47 => ! [Xphi: $o] :
% 0.31/0.47 ( ! [B: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( ( in @ B @ A )
% 0.31/0.47 => Xphi ) )
% 0.31/0.47 => Xphi ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subPowSU_type,type,
% 0.31/0.47 subPowSU: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subPowSU,definition,
% 0.31/0.47 ( subPowSU
% 0.31/0.47 = ( ! [A: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE2_type,type,
% 0.31/0.47 exuE2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE2,definition,
% 0.31/0.47 ( exuE2
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyImpWitness_type,type,
% 0.31/0.47 nonemptyImpWitness: $o ).
% 0.31/0.47
% 0.31/0.47 thf(nonemptyImpWitness,definition,
% 0.31/0.47 ( nonemptyImpWitness
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( nonempty @ A )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & $true ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(uniqinunit_type,type,
% 0.31/0.47 uniqinunit: $o ).
% 0.31/0.47
% 0.31/0.47 thf(uniqinunit,definition,
% 0.31/0.47 ( uniqinunit
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notinsingleton_type,type,
% 0.31/0.47 notinsingleton: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notinsingleton,definition,
% 0.31/0.47 ( notinsingleton
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx != Xy )
% 0.31/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqinunit_type,type,
% 0.31/0.47 eqinunit: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqinunit,definition,
% 0.31/0.47 ( eqinunit
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(singletonsswitch_type,type,
% 0.31/0.47 singletonsswitch: $o ).
% 0.31/0.47
% 0.31/0.47 thf(singletonsswitch,definition,
% 0.31/0.47 ( singletonsswitch
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetE_type,type,
% 0.31/0.47 upairsetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetE,definition,
% 0.31/0.47 ( upairsetE
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.31/0.47 => ( ( Xz = Xx )
% 0.31/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIL_type,type,
% 0.31/0.47 upairsetIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIL,definition,
% 0.31/0.47 ( upairsetIL
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIR_type,type,
% 0.31/0.47 upairsetIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairsetIR,definition,
% 0.31/0.47 ( upairsetIR
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyE1_type,type,
% 0.31/0.47 emptyE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyE1,definition,
% 0.31/0.47 ( emptyE1
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ( ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = emptyset )
% 0.31/0.47 => $false ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(vacuousDall_type,type,
% 0.31/0.47 vacuousDall: $o ).
% 0.31/0.47
% 0.31/0.47 thf(vacuousDall,definition,
% 0.31/0.47 ( vacuousDall
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ emptyset )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan1_type,type,
% 0.31/0.47 quantDeMorgan1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan1,definition,
% 0.31/0.47 ( quantDeMorgan1
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan2_type,type,
% 0.31/0.47 quantDeMorgan2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan2,definition,
% 0.31/0.47 ( quantDeMorgan2
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) )
% 0.31/0.47 => ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan3_type,type,
% 0.31/0.47 quantDeMorgan3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan3,definition,
% 0.31/0.47 ( quantDeMorgan3
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan4_type,type,
% 0.31/0.47 quantDeMorgan4: $o ).
% 0.31/0.47
% 0.31/0.47 thf(quantDeMorgan4,definition,
% 0.31/0.47 ( quantDeMorgan4
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) )
% 0.31/0.47 => ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setI_type,type,
% 0.31/0.47 prop2setI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2setI,definition,
% 0.31/0.47 ( prop2setI
% 0.31/0.47 = ( ! [Xphi: $o] :
% 0.31/0.47 ( Xphi
% 0.31/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(set2prop_type,type,
% 0.31/0.47 set2prop: $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set2propI_type,type,
% 0.31/0.47 prop2set2propI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(prop2set2propI,definition,
% 0.31/0.47 ( prop2set2propI
% 0.31/0.47 = ( ! [Xphi: $o] :
% 0.31/0.47 ( Xphi
% 0.31/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notdexE_type,type,
% 0.31/0.47 notdexE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notdexE,definition,
% 0.31/0.47 ( notdexE
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notdallE_type,type,
% 0.31/0.47 notdallE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notdallE,definition,
% 0.31/0.47 ( notdallE
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( ~ ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( Xphi @ Xx ) )
% 0.31/0.47 => ? [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI1_type,type,
% 0.31/0.47 exuI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI1,definition,
% 0.31/0.47 ( exuI1
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 & ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI3_type,type,
% 0.31/0.47 exuI3: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI3,definition,
% 0.31/0.47 ( exuI3
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.31/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuI2_type,type,
% 0.31/0.47 exuI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuI2,definition,
% 0.31/0.47 ( exuI2
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ? [Xx: $i] :
% 0.31/0.47 ! [Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xy )
% 0.31/0.47 <=> ( Xy = Xx ) )
% 0.31/0.47 => ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inCongP_type,type,
% 0.31/0.47 inCongP: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inCongP,definition,
% 0.31/0.47 ( inCongP
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong_type,type,
% 0.31/0.47 in__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(in__Cong,definition,
% 0.31/0.47 ( in__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3u_type,type,
% 0.31/0.47 exuE3u: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuE3u,definition,
% 0.31/0.47 ( exuE3u
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exu__Cong_type,type,
% 0.31/0.47 exu__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exu__Cong,definition,
% 0.31/0.47 ( exu__Cong
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 <=> ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset__Cong_type,type,
% 0.31/0.47 emptyset__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptyset__Cong,definition,
% 0.31/0.47 ( emptyset__Cong
% 0.31/0.47 = ( emptyset = emptyset ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin__Cong_type,type,
% 0.31/0.47 setadjoin__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoin__Cong,definition,
% 0.31/0.47 ( setadjoin__Cong
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ! [Xz: $i,Xu: $i] :
% 0.31/0.47 ( ( Xz = Xu )
% 0.31/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.31/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powerset__Cong_type,type,
% 0.31/0.47 powerset__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powerset__Cong,definition,
% 0.31/0.47 ( powerset__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( powerset @ A )
% 0.31/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setunion__Cong_type,type,
% 0.31/0.47 setunion__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setunion__Cong,definition,
% 0.31/0.47 ( setunion__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( ( setunion @ A )
% 0.31/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(omega__Cong_type,type,
% 0.31/0.47 omega__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(omega__Cong,definition,
% 0.31/0.47 ( omega__Cong
% 0.31/0.47 = ( omega = omega ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(exuEu_type,type,
% 0.31/0.47 exuEu: $o ).
% 0.31/0.47
% 0.31/0.47 thf(exuEu,definition,
% 0.31/0.47 ( exuEu
% 0.31/0.47 = ( ! [Xphi: $i > $o] :
% 0.31/0.47 ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xphi @ Xx )
% 0.31/0.47 => ( ( Xphi @ Xy )
% 0.31/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(descr__Cong_type,type,
% 0.31/0.47 descr__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(descr__Cong,definition,
% 0.31/0.47 ( descr__Cong
% 0.31/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.31/0.47 ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 => ( ( exu
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.31/0.47 => ( ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = ( descr
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr__Cong_type,type,
% 0.31/0.47 dsetconstr__Cong: $o ).
% 0.31/0.47
% 0.31/0.47 thf(dsetconstr__Cong,definition,
% 0.31/0.47 ( dsetconstr__Cong
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ! [Xy: $i] :
% 0.31/0.47 ( ( in @ Xy @ B )
% 0.31/0.47 => ( ( Xx = Xy )
% 0.31/0.47 => ( ( Xphi @ Xx )
% 0.31/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.31/0.47 => ( ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 = ( dsetconstr @ B
% 0.31/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subset_type,type,
% 0.31/0.47 subset: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(disjoint_type,type,
% 0.31/0.47 disjoint: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(setsmeet_type,type,
% 0.31/0.47 setsmeet: $i > $i > $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI1_type,type,
% 0.31/0.47 subsetI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI1,definition,
% 0.31/0.47 ( subsetI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset2_type,type,
% 0.31/0.47 eqimpsubset2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset2,definition,
% 0.31/0.47 ( eqimpsubset2
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset1_type,type,
% 0.31/0.47 eqimpsubset1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(eqimpsubset1,definition,
% 0.31/0.47 ( eqimpsubset1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( A = B )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI2_type,type,
% 0.31/0.47 subsetI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetI2,definition,
% 0.31/0.47 ( subsetI2
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ! [Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) )
% 0.31/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetsubset_type,type,
% 0.31/0.47 emptysetsubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(emptysetsubset,definition,
% 0.31/0.47 ( emptysetsubset
% 0.31/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE_type,type,
% 0.31/0.47 subsetE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE,definition,
% 0.31/0.47 ( subsetE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE2_type,type,
% 0.31/0.47 subsetE2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetE2,definition,
% 0.31/0.47 ( subsetE2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notsubsetI_type,type,
% 0.31/0.47 notsubsetI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notsubsetI,definition,
% 0.31/0.47 ( notsubsetI
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI1_type,type,
% 0.31/0.47 notequalI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI1,definition,
% 0.31/0.47 ( notequalI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ~ ( subset @ A @ B )
% 0.31/0.47 => ( A != B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI2_type,type,
% 0.31/0.47 notequalI2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(notequalI2,definition,
% 0.31/0.47 ( notequalI2
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ~ ( in @ Xx @ B )
% 0.31/0.47 => ( A != B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetRefl_type,type,
% 0.31/0.47 subsetRefl: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetRefl,definition,
% 0.31/0.47 ( subsetRefl
% 0.31/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetTrans_type,type,
% 0.31/0.47 subsetTrans: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetTrans,definition,
% 0.31/0.47 ( subsetTrans
% 0.31/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( subset @ B @ C )
% 0.31/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub_type,type,
% 0.31/0.47 setadjoinSub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub,definition,
% 0.31/0.47 ( setadjoinSub
% 0.31/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub2_type,type,
% 0.31/0.47 setadjoinSub2: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setadjoinSub2,definition,
% 0.31/0.47 ( setadjoinSub2
% 0.31/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subset2powerset_type,type,
% 0.31/0.47 subset2powerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subset2powerset,definition,
% 0.31/0.47 ( subset2powerset
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(setextsub_type,type,
% 0.31/0.47 setextsub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(setextsub,definition,
% 0.31/0.47 ( setextsub
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( ( subset @ B @ A )
% 0.31/0.47 => ( A = B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(subsetemptysetimpeq_type,type,
% 0.31/0.47 subsetemptysetimpeq: $o ).
% 0.31/0.47
% 0.31/0.47 thf(subsetemptysetimpeq,definition,
% 0.31/0.47 ( subsetemptysetimpeq
% 0.31/0.47 = ( ! [A: $i] :
% 0.31/0.47 ( ( subset @ A @ emptyset )
% 0.31/0.47 => ( A = emptyset ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI1_type,type,
% 0.31/0.47 powersetI1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetI1,definition,
% 0.31/0.47 ( powersetI1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ B @ A )
% 0.31/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE1_type,type,
% 0.31/0.47 powersetE1: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetE1,definition,
% 0.31/0.47 ( powersetE1
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.31/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(inPowerset_type,type,
% 0.31/0.47 inPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(inPowerset,definition,
% 0.31/0.47 ( inPowerset
% 0.31/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(powersetsubset_type,type,
% 0.31/0.47 powersetsubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(powersetsubset,definition,
% 0.31/0.47 ( powersetsubset
% 0.31/0.47 = ( ! [A: $i,B: $i] :
% 0.31/0.47 ( ( subset @ A @ B )
% 0.31/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sepInPowerset_type,type,
% 0.31/0.47 sepInPowerset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(sepInPowerset,definition,
% 0.31/0.47 ( sepInPowerset
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( in
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(sepSubset_type,type,
% 0.31/0.47 sepSubset: $o ).
% 0.31/0.47
% 0.31/0.47 thf(sepSubset,definition,
% 0.31/0.47 ( sepSubset
% 0.31/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/0.47 ( subset
% 0.31/0.47 @ ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/0.47 @ A ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunion_type,type,
% 0.31/0.47 binunion: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(binunionIL_type,type,
% 0.31/0.47 binunionIL: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionIL,definition,
% 0.31/0.47 ( binunionIL
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(upairset2IR_type,type,
% 0.31/0.47 upairset2IR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(upairset2IR,definition,
% 0.31/0.47 ( upairset2IR
% 0.31/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionIR_type,type,
% 0.31/0.47 binunionIR: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionIR,definition,
% 0.31/0.47 ( binunionIR
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionEcases_type,type,
% 0.31/0.47 binunionEcases: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionEcases,definition,
% 0.31/0.47 ( binunionEcases
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.31/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.31/0.47 => ( ( ( in @ Xx @ A )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => ( ( ( in @ Xx @ B )
% 0.31/0.47 => Xphi )
% 0.31/0.47 => Xphi ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionE_type,type,
% 0.31/0.47 binunionE: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionE,definition,
% 0.31/0.47 ( binunionE
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.31/0.47 => ( ( in @ Xx @ A )
% 0.31/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionLsub_type,type,
% 0.31/0.47 binunionLsub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionLsub,definition,
% 0.31/0.47 ( binunionLsub
% 0.31/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binunionRsub_type,type,
% 0.31/0.47 binunionRsub: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binunionRsub,definition,
% 0.31/0.47 ( binunionRsub
% 0.31/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersect_type,type,
% 0.31/0.47 binintersect: $i > $i > $i ).
% 0.31/0.47
% 0.31/0.47 thf(binintersect,definition,
% 0.31/0.47 ( binintersect
% 0.31/0.47 = ( ^ [A: $i,B: $i] :
% 0.31/0.47 ( dsetconstr @ A
% 0.31/0.47 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectI_type,type,
% 0.31/0.47 binintersectI: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectI,definition,
% 0.31/0.47 ( binintersectI
% 0.31/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ A )
% 0.31/0.47 => ( ( in @ Xx @ B )
% 0.31/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectSubset5_type,type,
% 0.31/0.47 binintersectSubset5: $o ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectSubset5,definition,
% 0.31/0.47 ( binintersectSubset5
% 0.31/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/0.47 ( ( subset @ C @ A )
% 0.31/0.47 => ( ( subset @ C @ B )
% 0.31/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 thf(binintersectEL,conjecture,
% 0.31/0.47 ( setextAx
% 0.31/0.47 => ( emptysetAx
% 0.31/0.47 => ( setadjoinAx
% 0.31/0.47 => ( powersetAx
% 0.31/0.47 => ( setunionAx
% 0.31/0.47 => ( omega0Ax
% 0.31/0.47 => ( omegaSAx
% 0.31/0.47 => ( omegaIndAx
% 0.31/0.47 => ( replAx
% 0.31/0.47 => ( foundationAx
% 0.31/0.47 => ( wellorderingAx
% 0.31/0.47 => ( descrp
% 0.31/0.47 => ( dsetconstrI
% 0.31/0.47 => ( dsetconstrEL
% 0.31/0.47 => ( dsetconstrER
% 0.31/0.47 => ( exuE1
% 0.31/0.47 => ( prop2setE
% 0.31/0.47 => ( emptysetE
% 0.31/0.47 => ( emptysetimpfalse
% 0.31/0.47 => ( notinemptyset
% 0.31/0.47 => ( exuE3e
% 0.31/0.47 => ( setext
% 0.31/0.47 => ( emptyI
% 0.31/0.47 => ( noeltsimpempty
% 0.31/0.47 => ( setbeta
% 0.31/0.47 => ( nonemptyE1
% 0.31/0.47 => ( nonemptyI
% 0.31/0.47 => ( nonemptyI1
% 0.31/0.47 => ( setadjoinIL
% 0.31/0.47 => ( emptyinunitempty
% 0.31/0.47 => ( setadjoinIR
% 0.31/0.47 => ( setadjoinE
% 0.31/0.47 => ( setadjoinOr
% 0.31/0.47 => ( setoftrueEq
% 0.31/0.47 => ( powersetI
% 0.31/0.47 => ( emptyinPowerset
% 0.31/0.47 => ( emptyInPowerset
% 0.31/0.47 => ( powersetE
% 0.31/0.47 => ( setunionI
% 0.31/0.47 => ( setunionE
% 0.31/0.47 => ( subPowSU
% 0.31/0.47 => ( exuE2
% 0.31/0.47 => ( nonemptyImpWitness
% 0.31/0.47 => ( uniqinunit
% 0.31/0.47 => ( notinsingleton
% 0.31/0.47 => ( eqinunit
% 0.31/0.47 => ( singletonsswitch
% 0.31/0.47 => ( upairsetE
% 0.31/0.47 => ( upairsetIL
% 0.31/0.47 => ( upairsetIR
% 0.31/0.47 => ( emptyE1
% 0.31/0.47 => ( vacuousDall
% 0.31/0.47 => ( quantDeMorgan1
% 0.31/0.47 => ( quantDeMorgan2
% 0.31/0.47 => ( quantDeMorgan3
% 0.31/0.47 => ( quantDeMorgan4
% 0.31/0.47 => ( prop2setI
% 0.31/0.47 => ( prop2set2propI
% 0.31/0.47 => ( notdexE
% 0.31/0.47 => ( notdallE
% 0.31/0.47 => ( exuI1
% 0.31/0.47 => ( exuI3
% 0.31/0.47 => ( exuI2
% 0.31/0.47 => ( inCongP
% 0.31/0.47 => ( in__Cong
% 0.31/0.47 => ( exuE3u
% 0.31/0.47 => ( exu__Cong
% 0.31/0.47 => ( emptyset__Cong
% 0.31/0.47 => ( setadjoin__Cong
% 0.31/0.47 => ( powerset__Cong
% 0.31/0.47 => ( setunion__Cong
% 0.31/0.47 => ( omega__Cong
% 0.31/0.47 => ( exuEu
% 0.31/0.47 => ( descr__Cong
% 0.31/0.47 => ( dsetconstr__Cong
% 0.31/0.47 => ( subsetI1
% 0.31/0.47 => ( eqimpsubset2
% 0.31/0.47 => ( eqimpsubset1
% 0.31/0.47 => ( subsetI2
% 0.31/0.47 => ( emptysetsubset
% 0.31/0.47 => ( subsetE
% 0.31/0.47 => ( subsetE2
% 0.31/0.47 => ( notsubsetI
% 0.31/0.47 => ( notequalI1
% 0.31/0.47 => ( notequalI2
% 0.31/0.47 => ( subsetRefl
% 0.31/0.47 => ( subsetTrans
% 0.31/0.47 => ( setadjoinSub
% 0.31/0.47 => ( setadjoinSub2
% 0.31/0.47 => ( subset2powerset
% 0.31/0.47 => ( setextsub
% 0.31/0.47 => ( subsetemptysetimpeq
% 0.31/0.47 => ( powersetI1
% 0.31/0.47 => ( powersetE1
% 0.31/0.47 => ( inPowerset
% 0.31/0.47 => ( powersetsubset
% 0.31/0.47 => ( sepInPowerset
% 0.31/0.47 => ( sepSubset
% 0.31/0.47 => ( binunionIL
% 0.31/0.47 => ( upairset2IR
% 0.31/0.47 => ( binunionIR
% 0.31/0.47 => ( binunionEcases
% 0.31/0.47 => ( binunionE
% 0.31/0.47 => ( binunionLsub
% 0.31/0.47 => ( binunionRsub
% 0.31/0.47 => ( binintersectI
% 0.31/0.47 => ( binintersectSubset5
% 0.31/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.31/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.31/0.47 => ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/0.47
% 0.31/0.47 %------------------------------------------------------------------------------
% 0.31/0.47 ------------------------
% 1.89/1.38 ---- Embedded in THF ---
% 1.89/1.38 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.89/1.38 %%% Generated on Tue Feb 24 12:28:35 EST 2026
% 1.89/1.38 %%% using '$$dhol' embedding, version 1.3.0.
% 1.89/1.38 %%% Logic specification used:
% 1.89/1.38 %%% thf(spec, logic, $$dhol).
% 1.89/1.38
% 1.89/1.38 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2DTF25294.p
% See solution above
% 1.89/1.38 ------------------------
% 2.16/1.40 ---- Cleaned THF ---
% 2.16/1.40 thf(in_type,type,
% 2.16/1.40 in: $i > $i > $o ).
% 2.16/1.40
% 2.16/1.40 thf(exu_type,type,
% 2.16/1.40 exu: ( $i > $o ) > $o ).
% 2.16/1.40
% 2.16/1.40 thf(exu,definition,
% 2.16/1.40 ( exu
% 2.16/1.40 = ( ^ [Xphi: $i > $o] :
% 2.16/1.40 ? [Xx: $i] :
% 2.16/1.40 ( ( Xphi @ Xx )
% 2.16/1.40 & ! [Xy: $i] :
% 2.16/1.40 ( ( Xphi @ Xy )
% 2.16/1.40 => ( Xx = Xy ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setextAx_type,type,
% 2.16/1.40 setextAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setextAx,definition,
% 2.16/1.40 ( setextAx
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 <=> ( in @ Xx @ B ) )
% 2.16/1.40 => ( A = B ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptyset_type,type,
% 2.16/1.40 emptyset: $i ).
% 2.16/1.40
% 2.16/1.40 thf(emptysetAx_type,type,
% 2.16/1.40 emptysetAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptysetAx,definition,
% 2.16/1.40 ( emptysetAx
% 2.16/1.40 = ( ! [Xx: $i] :
% 2.16/1.40 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoin_type,type,
% 2.16/1.40 setadjoin: $i > $i > $i ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinAx_type,type,
% 2.16/1.40 setadjoinAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinAx,definition,
% 2.16/1.40 ( setadjoinAx
% 2.16/1.40 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.16/1.40 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.16/1.40 <=> ( ( Xy = Xx )
% 2.16/1.40 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(powerset_type,type,
% 2.16/1.40 powerset: $i > $i ).
% 2.16/1.40
% 2.16/1.40 thf(powersetAx_type,type,
% 2.16/1.40 powersetAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(powersetAx,definition,
% 2.16/1.40 ( powersetAx
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( in @ B @ ( powerset @ A ) )
% 2.16/1.40 <=> ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setunion_type,type,
% 2.16/1.40 setunion: $i > $i ).
% 2.16/1.40
% 2.16/1.40 thf(setunionAx_type,type,
% 2.16/1.40 setunionAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setunionAx,definition,
% 2.16/1.40 ( setunionAx
% 2.16/1.40 = ( ! [A: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ ( setunion @ A ) )
% 2.16/1.40 <=> ? [B: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 & ( in @ B @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(omega_type,type,
% 2.16/1.40 omega: $i ).
% 2.16/1.40
% 2.16/1.40 thf(omega0Ax_type,type,
% 2.16/1.40 omega0Ax: $o ).
% 2.16/1.40
% 2.16/1.40 thf(omega0Ax,definition,
% 2.16/1.40 ( omega0Ax
% 2.16/1.40 = ( in @ emptyset @ omega ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(omegaSAx_type,type,
% 2.16/1.40 omegaSAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(omegaSAx,definition,
% 2.16/1.40 ( omegaSAx
% 2.16/1.40 = ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ omega )
% 2.16/1.40 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(omegaIndAx_type,type,
% 2.16/1.40 omegaIndAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(omegaIndAx,definition,
% 2.16/1.40 ( omegaIndAx
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ( ( in @ emptyset @ A )
% 2.16/1.40 & ! [Xx: $i] :
% 2.16/1.40 ( ( ( in @ Xx @ omega )
% 2.16/1.40 & ( in @ Xx @ A ) )
% 2.16/1.40 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.16/1.40 => ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ omega )
% 2.16/1.40 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(replAx_type,type,
% 2.16/1.40 replAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(replAx,definition,
% 2.16/1.40 ( replAx
% 2.16/1.40 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( exu
% 2.16/1.40 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.16/1.40 => ? [B: $i] :
% 2.16/1.40 ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 <=> ? [Xy: $i] :
% 2.16/1.40 ( ( in @ Xy @ A )
% 2.16/1.40 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(foundationAx_type,type,
% 2.16/1.40 foundationAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(foundationAx,definition,
% 2.16/1.40 ( foundationAx
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.16/1.40 => ? [B: $i] :
% 2.16/1.40 ( ( in @ B @ A )
% 2.16/1.40 & ~ ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(wellorderingAx_type,type,
% 2.16/1.40 wellorderingAx: $o ).
% 2.16/1.40
% 2.16/1.40 thf(wellorderingAx,definition,
% 2.16/1.40 ( wellorderingAx
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ? [B: $i] :
% 2.16/1.40 ( ! [C: $i] :
% 2.16/1.40 ( ( in @ C @ B )
% 2.16/1.40 => ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ C )
% 2.16/1.40 => ( in @ Xx @ A ) ) )
% 2.16/1.40 & ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( ( in @ Xx @ A )
% 2.16/1.40 & ( in @ Xy @ A ) )
% 2.16/1.40 => ( ! [C: $i] :
% 2.16/1.40 ( ( in @ C @ B )
% 2.16/1.40 => ( ( in @ Xx @ C )
% 2.16/1.40 <=> ( in @ Xy @ C ) ) )
% 2.16/1.40 => ( Xx = Xy ) ) )
% 2.16/1.40 & ! [C: $i,D: $i] :
% 2.16/1.40 ( ( ( in @ C @ B )
% 2.16/1.40 & ( in @ D @ B ) )
% 2.16/1.40 => ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ C )
% 2.16/1.40 => ( in @ Xx @ D ) )
% 2.16/1.40 | ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ D )
% 2.16/1.40 => ( in @ Xx @ C ) ) ) )
% 2.16/1.40 & ! [C: $i] :
% 2.16/1.40 ( ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ C )
% 2.16/1.40 => ( in @ Xx @ A ) )
% 2.16/1.40 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.16/1.40 => ? [D: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ D @ B )
% 2.16/1.40 & ( in @ Xx @ C )
% 2.16/1.40 & ~ ? [Xy: $i] :
% 2.16/1.40 ( ( in @ Xy @ D )
% 2.16/1.40 & ( in @ Xy @ C ) )
% 2.16/1.40 & ! [E: $i] :
% 2.16/1.40 ( ( in @ E @ B )
% 2.16/1.40 => ( ! [Xy: $i] :
% 2.16/1.40 ( ( in @ Xy @ E )
% 2.16/1.40 => ( in @ Xy @ D ) )
% 2.16/1.40 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(descr_type,type,
% 2.16/1.40 descr: ( $i > $o ) > $i ).
% 2.16/1.40
% 2.16/1.40 thf(descrp_type,type,
% 2.16/1.40 descrp: $o ).
% 2.16/1.40
% 2.16/1.40 thf(descrp,definition,
% 2.16/1.40 ( descrp
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 => ( Xphi
% 2.16/1.40 @ ( descr
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstr_type,type,
% 2.16/1.40 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstrI_type,type,
% 2.16/1.40 dsetconstrI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstrI,definition,
% 2.16/1.40 ( dsetconstrI
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( ( Xphi @ Xx )
% 2.16/1.40 => ( in @ Xx
% 2.16/1.40 @ ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstrEL_type,type,
% 2.16/1.40 dsetconstrEL: $o ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstrEL,definition,
% 2.16/1.40 ( dsetconstrEL
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx
% 2.16/1.40 @ ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.16/1.40 => ( in @ Xx @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstrER_type,type,
% 2.16/1.40 dsetconstrER: $o ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstrER,definition,
% 2.16/1.40 ( dsetconstrER
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx
% 2.16/1.40 @ ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.16/1.40 => ( Xphi @ Xx ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exuE1_type,type,
% 2.16/1.40 exuE1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exuE1,definition,
% 2.16/1.40 ( exuE1
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 => ? [Xx: $i] :
% 2.16/1.40 ( ( Xphi @ Xx )
% 2.16/1.40 & ! [Xy: $i] :
% 2.16/1.40 ( ( Xphi @ Xy )
% 2.16/1.40 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(prop2set_type,type,
% 2.16/1.40 prop2set: $o > $i ).
% 2.16/1.40
% 2.16/1.40 thf(prop2setE_type,type,
% 2.16/1.40 prop2setE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(prop2setE,definition,
% 2.16/1.40 ( prop2setE
% 2.16/1.40 = ( ! [Xphi: $o,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.16/1.40 => Xphi ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptysetE_type,type,
% 2.16/1.40 emptysetE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptysetE,definition,
% 2.16/1.40 ( emptysetE
% 2.16/1.40 = ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ emptyset )
% 2.16/1.40 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptysetimpfalse_type,type,
% 2.16/1.40 emptysetimpfalse: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptysetimpfalse,definition,
% 2.16/1.40 ( emptysetimpfalse
% 2.16/1.40 = ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ emptyset )
% 2.16/1.40 => $false ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(notinemptyset_type,type,
% 2.16/1.40 notinemptyset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(notinemptyset,definition,
% 2.16/1.40 ( notinemptyset
% 2.16/1.40 = ( ! [Xx: $i] :
% 2.16/1.40 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exuE3e_type,type,
% 2.16/1.40 exuE3e: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exuE3e,definition,
% 2.16/1.40 ( exuE3e
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setext_type,type,
% 2.16/1.40 setext: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setext,definition,
% 2.16/1.40 ( setext
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( in @ Xx @ B ) )
% 2.16/1.40 => ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 => ( in @ Xx @ A ) )
% 2.16/1.40 => ( A = B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptyI_type,type,
% 2.16/1.40 emptyI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptyI,definition,
% 2.16/1.40 ( emptyI
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ~ ( in @ Xx @ A )
% 2.16/1.40 => ( A = emptyset ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(noeltsimpempty_type,type,
% 2.16/1.40 noeltsimpempty: $o ).
% 2.16/1.40
% 2.16/1.40 thf(noeltsimpempty,definition,
% 2.16/1.40 ( noeltsimpempty
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ~ ( in @ Xx @ A )
% 2.16/1.40 => ( A = emptyset ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setbeta_type,type,
% 2.16/1.40 setbeta: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setbeta,definition,
% 2.16/1.40 ( setbeta
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( ( in @ Xx
% 2.16/1.40 @ ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.16/1.40 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(nonempty_type,type,
% 2.16/1.40 nonempty: $i > $o ).
% 2.16/1.40
% 2.16/1.40 thf(nonempty,definition,
% 2.16/1.40 ( nonempty
% 2.16/1.40 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(nonemptyE1_type,type,
% 2.16/1.40 nonemptyE1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(nonemptyE1,definition,
% 2.16/1.40 ( nonemptyE1
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ( nonempty @ A )
% 2.16/1.40 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(nonemptyI_type,type,
% 2.16/1.40 nonemptyI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(nonemptyI,definition,
% 2.16/1.40 ( nonemptyI
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( ( Xphi @ Xx )
% 2.16/1.40 => ( nonempty
% 2.16/1.40 @ ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(nonemptyI1_type,type,
% 2.16/1.40 nonemptyI1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(nonemptyI1,definition,
% 2.16/1.40 ( nonemptyI1
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.16/1.40 => ( nonempty @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinIL_type,type,
% 2.16/1.40 setadjoinIL: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinIL,definition,
% 2.16/1.40 ( setadjoinIL
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptyinunitempty_type,type,
% 2.16/1.40 emptyinunitempty: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptyinunitempty,definition,
% 2.16/1.40 ( emptyinunitempty
% 2.16/1.40 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinIR_type,type,
% 2.16/1.40 setadjoinIR: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinIR,definition,
% 2.16/1.40 ( setadjoinIR
% 2.16/1.40 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.16/1.40 ( ( in @ Xy @ A )
% 2.16/1.40 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinE_type,type,
% 2.16/1.40 setadjoinE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinE,definition,
% 2.16/1.40 ( setadjoinE
% 2.16/1.40 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.16/1.40 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.16/1.40 => ! [Xphi: $o] :
% 2.16/1.40 ( ( ( Xy = Xx )
% 2.16/1.40 => Xphi )
% 2.16/1.40 => ( ( ( in @ Xy @ A )
% 2.16/1.40 => Xphi )
% 2.16/1.40 => Xphi ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinOr_type,type,
% 2.16/1.40 setadjoinOr: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinOr,definition,
% 2.16/1.40 ( setadjoinOr
% 2.16/1.40 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.16/1.40 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.16/1.40 => ( ( Xy = Xx )
% 2.16/1.40 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setoftrueEq_type,type,
% 2.16/1.40 setoftrueEq: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setoftrueEq,definition,
% 2.16/1.40 ( setoftrueEq
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xx: $i] : $true )
% 2.16/1.40 = A ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(powersetI_type,type,
% 2.16/1.40 powersetI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(powersetI,definition,
% 2.16/1.40 ( powersetI
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 => ( in @ Xx @ A ) )
% 2.16/1.40 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptyinPowerset_type,type,
% 2.16/1.40 emptyinPowerset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptyinPowerset,definition,
% 2.16/1.40 ( emptyinPowerset
% 2.16/1.40 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptyInPowerset_type,type,
% 2.16/1.40 emptyInPowerset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptyInPowerset,definition,
% 2.16/1.40 ( emptyInPowerset
% 2.16/1.40 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(powersetE_type,type,
% 2.16/1.40 powersetE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(powersetE,definition,
% 2.16/1.40 ( powersetE
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ B @ ( powerset @ A ) )
% 2.16/1.40 => ( ( in @ Xx @ B )
% 2.16/1.40 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setunionI_type,type,
% 2.16/1.40 setunionI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setunionI,definition,
% 2.16/1.40 ( setunionI
% 2.16/1.40 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 => ( ( in @ B @ A )
% 2.16/1.40 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setunionE_type,type,
% 2.16/1.40 setunionE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setunionE,definition,
% 2.16/1.40 ( setunionE
% 2.16/1.40 = ( ! [A: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ ( setunion @ A ) )
% 2.16/1.40 => ! [Xphi: $o] :
% 2.16/1.40 ( ! [B: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 => ( ( in @ B @ A )
% 2.16/1.40 => Xphi ) )
% 2.16/1.40 => Xphi ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subPowSU_type,type,
% 2.16/1.40 subPowSU: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subPowSU,definition,
% 2.16/1.40 ( subPowSU
% 2.16/1.40 = ( ! [A: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exuE2_type,type,
% 2.16/1.40 exuE2: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exuE2,definition,
% 2.16/1.40 ( exuE2
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 => ? [Xx: $i] :
% 2.16/1.40 ! [Xy: $i] :
% 2.16/1.40 ( ( Xphi @ Xy )
% 2.16/1.40 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(nonemptyImpWitness_type,type,
% 2.16/1.40 nonemptyImpWitness: $o ).
% 2.16/1.40
% 2.16/1.40 thf(nonemptyImpWitness,definition,
% 2.16/1.40 ( nonemptyImpWitness
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ( nonempty @ A )
% 2.16/1.40 => ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 & $true ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(uniqinunit_type,type,
% 2.16/1.40 uniqinunit: $o ).
% 2.16/1.40
% 2.16/1.40 thf(uniqinunit,definition,
% 2.16/1.40 ( uniqinunit
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.16/1.40 => ( Xx = Xy ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(notinsingleton_type,type,
% 2.16/1.40 notinsingleton: $o ).
% 2.16/1.40
% 2.16/1.40 thf(notinsingleton,definition,
% 2.16/1.40 ( notinsingleton
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xx != Xy )
% 2.16/1.40 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(eqinunit_type,type,
% 2.16/1.40 eqinunit: $o ).
% 2.16/1.40
% 2.16/1.40 thf(eqinunit,definition,
% 2.16/1.40 ( eqinunit
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xx = Xy )
% 2.16/1.40 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(singletonsswitch_type,type,
% 2.16/1.40 singletonsswitch: $o ).
% 2.16/1.40
% 2.16/1.40 thf(singletonsswitch,definition,
% 2.16/1.40 ( singletonsswitch
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.16/1.40 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(upairsetE_type,type,
% 2.16/1.40 upairsetE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(upairsetE,definition,
% 2.16/1.40 ( upairsetE
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.16/1.40 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.16/1.40 => ( ( Xz = Xx )
% 2.16/1.40 | ( Xz = Xy ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(upairsetIL_type,type,
% 2.16/1.40 upairsetIL: $o ).
% 2.16/1.40
% 2.16/1.40 thf(upairsetIL,definition,
% 2.16/1.40 ( upairsetIL
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(upairsetIR_type,type,
% 2.16/1.40 upairsetIR: $o ).
% 2.16/1.40
% 2.16/1.40 thf(upairsetIR,definition,
% 2.16/1.40 ( upairsetIR
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptyE1_type,type,
% 2.16/1.40 emptyE1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptyE1,definition,
% 2.16/1.40 ( emptyE1
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 & ( Xphi @ Xx ) )
% 2.16/1.40 => ( ( ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 = emptyset )
% 2.16/1.40 => $false ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(vacuousDall_type,type,
% 2.16/1.40 vacuousDall: $o ).
% 2.16/1.40
% 2.16/1.40 thf(vacuousDall,definition,
% 2.16/1.40 ( vacuousDall
% 2.16/1.40 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ emptyset )
% 2.16/1.40 => ( Xphi @ Xx ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(quantDeMorgan1_type,type,
% 2.16/1.40 quantDeMorgan1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(quantDeMorgan1,definition,
% 2.16/1.40 ( quantDeMorgan1
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( ~ ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( Xphi @ Xx ) )
% 2.16/1.40 => ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(quantDeMorgan2_type,type,
% 2.16/1.40 quantDeMorgan2: $o ).
% 2.16/1.40
% 2.16/1.40 thf(quantDeMorgan2,definition,
% 2.16/1.40 ( quantDeMorgan2
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ~ ( Xphi @ Xx ) )
% 2.16/1.40 => ~ ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(quantDeMorgan3_type,type,
% 2.16/1.40 quantDeMorgan3: $o ).
% 2.16/1.40
% 2.16/1.40 thf(quantDeMorgan3,definition,
% 2.16/1.40 ( quantDeMorgan3
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( ~ ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 & ( Xphi @ Xx ) )
% 2.16/1.40 => ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(quantDeMorgan4_type,type,
% 2.16/1.40 quantDeMorgan4: $o ).
% 2.16/1.40
% 2.16/1.40 thf(quantDeMorgan4,definition,
% 2.16/1.40 ( quantDeMorgan4
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 & ~ ( Xphi @ Xx ) )
% 2.16/1.40 => ~ ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(prop2setI_type,type,
% 2.16/1.40 prop2setI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(prop2setI,definition,
% 2.16/1.40 ( prop2setI
% 2.16/1.40 = ( ! [Xphi: $o] :
% 2.16/1.40 ( Xphi
% 2.16/1.40 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(set2prop_type,type,
% 2.16/1.40 set2prop: $i > $o ).
% 2.16/1.40
% 2.16/1.40 thf(prop2set2propI_type,type,
% 2.16/1.40 prop2set2propI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(prop2set2propI,definition,
% 2.16/1.40 ( prop2set2propI
% 2.16/1.40 = ( ! [Xphi: $o] :
% 2.16/1.40 ( Xphi
% 2.16/1.40 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(notdexE_type,type,
% 2.16/1.40 notdexE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(notdexE,definition,
% 2.16/1.40 ( notdexE
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( ~ ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 & ( Xphi @ Xx ) )
% 2.16/1.40 => ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(notdallE_type,type,
% 2.16/1.40 notdallE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(notdallE,definition,
% 2.16/1.40 ( notdallE
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( ~ ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( Xphi @ Xx ) )
% 2.16/1.40 => ? [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exuI1_type,type,
% 2.16/1.40 exuI1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exuI1,definition,
% 2.16/1.40 ( exuI1
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ? [Xx: $i] :
% 2.16/1.40 ( ( Xphi @ Xx )
% 2.16/1.40 & ! [Xy: $i] :
% 2.16/1.40 ( ( Xphi @ Xy )
% 2.16/1.40 => ( Xx = Xy ) ) )
% 2.16/1.40 => ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exuI3_type,type,
% 2.16/1.40 exuI3: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exuI3,definition,
% 2.16/1.40 ( exuI3
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.16/1.40 => ( ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xphi @ Xx )
% 2.16/1.40 => ( ( Xphi @ Xy )
% 2.16/1.40 => ( Xx = Xy ) ) )
% 2.16/1.40 => ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exuI2_type,type,
% 2.16/1.40 exuI2: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exuI2,definition,
% 2.16/1.40 ( exuI2
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ? [Xx: $i] :
% 2.16/1.40 ! [Xy: $i] :
% 2.16/1.40 ( ( Xphi @ Xy )
% 2.16/1.40 <=> ( Xy = Xx ) )
% 2.16/1.40 => ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(inCongP_type,type,
% 2.16/1.40 inCongP: $o ).
% 2.16/1.40
% 2.16/1.40 thf(inCongP,definition,
% 2.16/1.40 ( inCongP
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( A = B )
% 2.16/1.40 => ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xx = Xy )
% 2.16/1.40 => ( ( in @ Xx @ A )
% 2.16/1.40 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(in__Cong_type,type,
% 2.16/1.40 in__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(in__Cong,definition,
% 2.16/1.40 ( in__Cong
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( A = B )
% 2.16/1.40 => ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xx = Xy )
% 2.16/1.40 => ( ( in @ Xx @ A )
% 2.16/1.40 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exuE3u_type,type,
% 2.16/1.40 exuE3u: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exuE3u,definition,
% 2.16/1.40 ( exuE3u
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 => ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xphi @ Xx )
% 2.16/1.40 => ( ( Xphi @ Xy )
% 2.16/1.40 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exu__Cong_type,type,
% 2.16/1.40 exu__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exu__Cong,definition,
% 2.16/1.40 ( exu__Cong
% 2.16/1.40 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.16/1.40 ( ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xx = Xy )
% 2.16/1.40 => ( ( Xphi @ Xx )
% 2.16/1.40 <=> ( Xpsi @ Xy ) ) )
% 2.16/1.40 => ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 <=> ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptyset__Cong_type,type,
% 2.16/1.40 emptyset__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptyset__Cong,definition,
% 2.16/1.40 ( emptyset__Cong
% 2.16/1.40 = ( emptyset = emptyset ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoin__Cong_type,type,
% 2.16/1.40 setadjoin__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoin__Cong,definition,
% 2.16/1.40 ( setadjoin__Cong
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xx = Xy )
% 2.16/1.40 => ! [Xz: $i,Xu: $i] :
% 2.16/1.40 ( ( Xz = Xu )
% 2.16/1.40 => ( ( setadjoin @ Xx @ Xz )
% 2.16/1.40 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(powerset__Cong_type,type,
% 2.16/1.40 powerset__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(powerset__Cong,definition,
% 2.16/1.40 ( powerset__Cong
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( A = B )
% 2.16/1.40 => ( ( powerset @ A )
% 2.16/1.40 = ( powerset @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setunion__Cong_type,type,
% 2.16/1.40 setunion__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setunion__Cong,definition,
% 2.16/1.40 ( setunion__Cong
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( A = B )
% 2.16/1.40 => ( ( setunion @ A )
% 2.16/1.40 = ( setunion @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(omega__Cong_type,type,
% 2.16/1.40 omega__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(omega__Cong,definition,
% 2.16/1.40 ( omega__Cong
% 2.16/1.40 = ( omega = omega ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(exuEu_type,type,
% 2.16/1.40 exuEu: $o ).
% 2.16/1.40
% 2.16/1.40 thf(exuEu,definition,
% 2.16/1.40 ( exuEu
% 2.16/1.40 = ( ! [Xphi: $i > $o] :
% 2.16/1.40 ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 => ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xphi @ Xx )
% 2.16/1.40 => ( ( Xphi @ Xy )
% 2.16/1.40 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(descr__Cong_type,type,
% 2.16/1.40 descr__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(descr__Cong,definition,
% 2.16/1.40 ( descr__Cong
% 2.16/1.40 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.16/1.40 ( ! [Xx: $i,Xy: $i] :
% 2.16/1.40 ( ( Xx = Xy )
% 2.16/1.40 => ( ( Xphi @ Xx )
% 2.16/1.40 <=> ( Xpsi @ Xy ) ) )
% 2.16/1.40 => ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 => ( ( exu
% 2.16/1.40 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.16/1.40 => ( ( descr
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 = ( descr
% 2.16/1.40 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstr__Cong_type,type,
% 2.16/1.40 dsetconstr__Cong: $o ).
% 2.16/1.40
% 2.16/1.40 thf(dsetconstr__Cong,definition,
% 2.16/1.40 ( dsetconstr__Cong
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( A = B )
% 2.16/1.40 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ! [Xy: $i] :
% 2.16/1.40 ( ( in @ Xy @ B )
% 2.16/1.40 => ( ( Xx = Xy )
% 2.16/1.40 => ( ( Xphi @ Xx )
% 2.16/1.40 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.16/1.40 => ( ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 = ( dsetconstr @ B
% 2.16/1.40 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subset_type,type,
% 2.16/1.40 subset: $i > $i > $o ).
% 2.16/1.40
% 2.16/1.40 thf(disjoint_type,type,
% 2.16/1.40 disjoint: $i > $i > $o ).
% 2.16/1.40
% 2.16/1.40 thf(setsmeet_type,type,
% 2.16/1.40 setsmeet: $i > $i > $o ).
% 2.16/1.40
% 2.16/1.40 thf(subsetI1_type,type,
% 2.16/1.40 subsetI1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subsetI1,definition,
% 2.16/1.40 ( subsetI1
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( in @ Xx @ B ) )
% 2.16/1.40 => ( subset @ A @ B ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(eqimpsubset2_type,type,
% 2.16/1.40 eqimpsubset2: $o ).
% 2.16/1.40
% 2.16/1.40 thf(eqimpsubset2,definition,
% 2.16/1.40 ( eqimpsubset2
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( A = B )
% 2.16/1.40 => ( subset @ B @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(eqimpsubset1_type,type,
% 2.16/1.40 eqimpsubset1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(eqimpsubset1,definition,
% 2.16/1.40 ( eqimpsubset1
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( A = B )
% 2.16/1.40 => ( subset @ A @ B ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subsetI2_type,type,
% 2.16/1.40 subsetI2: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subsetI2,definition,
% 2.16/1.40 ( subsetI2
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ! [Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( in @ Xx @ B ) )
% 2.16/1.40 => ( subset @ A @ B ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(emptysetsubset_type,type,
% 2.16/1.40 emptysetsubset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(emptysetsubset,definition,
% 2.16/1.40 ( emptysetsubset
% 2.16/1.40 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subsetE_type,type,
% 2.16/1.40 subsetE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subsetE,definition,
% 2.16/1.40 ( subsetE
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( subset @ A @ B )
% 2.16/1.40 => ( ( in @ Xx @ A )
% 2.16/1.40 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subsetE2_type,type,
% 2.16/1.40 subsetE2: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subsetE2,definition,
% 2.16/1.40 ( subsetE2
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( subset @ A @ B )
% 2.16/1.40 => ( ~ ( in @ Xx @ B )
% 2.16/1.40 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(notsubsetI_type,type,
% 2.16/1.40 notsubsetI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(notsubsetI,definition,
% 2.16/1.40 ( notsubsetI
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( ~ ( in @ Xx @ B )
% 2.16/1.40 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(notequalI1_type,type,
% 2.16/1.40 notequalI1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(notequalI1,definition,
% 2.16/1.40 ( notequalI1
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ~ ( subset @ A @ B )
% 2.16/1.40 => ( A != B ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(notequalI2_type,type,
% 2.16/1.40 notequalI2: $o ).
% 2.16/1.40
% 2.16/1.40 thf(notequalI2,definition,
% 2.16/1.40 ( notequalI2
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( ~ ( in @ Xx @ B )
% 2.16/1.40 => ( A != B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subsetRefl_type,type,
% 2.16/1.40 subsetRefl: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subsetRefl,definition,
% 2.16/1.40 ( subsetRefl
% 2.16/1.40 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subsetTrans_type,type,
% 2.16/1.40 subsetTrans: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subsetTrans,definition,
% 2.16/1.40 ( subsetTrans
% 2.16/1.40 = ( ! [A: $i,B: $i,C: $i] :
% 2.16/1.40 ( ( subset @ A @ B )
% 2.16/1.40 => ( ( subset @ B @ C )
% 2.16/1.40 => ( subset @ A @ C ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinSub_type,type,
% 2.16/1.40 setadjoinSub: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinSub,definition,
% 2.16/1.40 ( setadjoinSub
% 2.16/1.40 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinSub2_type,type,
% 2.16/1.40 setadjoinSub2: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setadjoinSub2,definition,
% 2.16/1.40 ( setadjoinSub2
% 2.16/1.40 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.16/1.40 ( ( subset @ A @ B )
% 2.16/1.40 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subset2powerset_type,type,
% 2.16/1.40 subset2powerset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subset2powerset,definition,
% 2.16/1.40 ( subset2powerset
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( subset @ A @ B )
% 2.16/1.40 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(setextsub_type,type,
% 2.16/1.40 setextsub: $o ).
% 2.16/1.40
% 2.16/1.40 thf(setextsub,definition,
% 2.16/1.40 ( setextsub
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( subset @ A @ B )
% 2.16/1.40 => ( ( subset @ B @ A )
% 2.16/1.40 => ( A = B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(subsetemptysetimpeq_type,type,
% 2.16/1.40 subsetemptysetimpeq: $o ).
% 2.16/1.40
% 2.16/1.40 thf(subsetemptysetimpeq,definition,
% 2.16/1.40 ( subsetemptysetimpeq
% 2.16/1.40 = ( ! [A: $i] :
% 2.16/1.40 ( ( subset @ A @ emptyset )
% 2.16/1.40 => ( A = emptyset ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(powersetI1_type,type,
% 2.16/1.40 powersetI1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(powersetI1,definition,
% 2.16/1.40 ( powersetI1
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( subset @ B @ A )
% 2.16/1.40 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(powersetE1_type,type,
% 2.16/1.40 powersetE1: $o ).
% 2.16/1.40
% 2.16/1.40 thf(powersetE1,definition,
% 2.16/1.40 ( powersetE1
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( in @ B @ ( powerset @ A ) )
% 2.16/1.40 => ( subset @ B @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(inPowerset_type,type,
% 2.16/1.40 inPowerset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(inPowerset,definition,
% 2.16/1.40 ( inPowerset
% 2.16/1.40 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(powersetsubset_type,type,
% 2.16/1.40 powersetsubset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(powersetsubset,definition,
% 2.16/1.40 ( powersetsubset
% 2.16/1.40 = ( ! [A: $i,B: $i] :
% 2.16/1.40 ( ( subset @ A @ B )
% 2.16/1.40 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(sepInPowerset_type,type,
% 2.16/1.40 sepInPowerset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(sepInPowerset,definition,
% 2.16/1.40 ( sepInPowerset
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( in
% 2.16/1.40 @ ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 @ ( powerset @ A ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(sepSubset_type,type,
% 2.16/1.40 sepSubset: $o ).
% 2.16/1.40
% 2.16/1.40 thf(sepSubset,definition,
% 2.16/1.40 ( sepSubset
% 2.16/1.40 = ( ! [A: $i,Xphi: $i > $o] :
% 2.16/1.40 ( subset
% 2.16/1.40 @ ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.16/1.40 @ A ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binunion_type,type,
% 2.16/1.40 binunion: $i > $i > $i ).
% 2.16/1.40
% 2.16/1.40 thf(binunionIL_type,type,
% 2.16/1.40 binunionIL: $o ).
% 2.16/1.40
% 2.16/1.40 thf(binunionIL,definition,
% 2.16/1.40 ( binunionIL
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(upairset2IR_type,type,
% 2.16/1.40 upairset2IR: $o ).
% 2.16/1.40
% 2.16/1.40 thf(upairset2IR,definition,
% 2.16/1.40 ( upairset2IR
% 2.16/1.40 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binunionIR_type,type,
% 2.16/1.40 binunionIR: $o ).
% 2.16/1.40
% 2.16/1.40 thf(binunionIR,definition,
% 2.16/1.40 ( binunionIR
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ B )
% 2.16/1.40 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binunionEcases_type,type,
% 2.16/1.40 binunionEcases: $o ).
% 2.16/1.40
% 2.16/1.40 thf(binunionEcases,definition,
% 2.16/1.40 ( binunionEcases
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.16/1.40 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.16/1.40 => ( ( ( in @ Xx @ A )
% 2.16/1.40 => Xphi )
% 2.16/1.40 => ( ( ( in @ Xx @ B )
% 2.16/1.40 => Xphi )
% 2.16/1.40 => Xphi ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binunionE_type,type,
% 2.16/1.40 binunionE: $o ).
% 2.16/1.40
% 2.16/1.40 thf(binunionE,definition,
% 2.16/1.40 ( binunionE
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.16/1.40 => ( ( in @ Xx @ A )
% 2.16/1.40 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binunionLsub_type,type,
% 2.16/1.40 binunionLsub: $o ).
% 2.16/1.40
% 2.16/1.40 thf(binunionLsub,definition,
% 2.16/1.40 ( binunionLsub
% 2.16/1.40 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binunionRsub_type,type,
% 2.16/1.40 binunionRsub: $o ).
% 2.16/1.40
% 2.16/1.40 thf(binunionRsub,definition,
% 2.16/1.40 ( binunionRsub
% 2.16/1.40 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binintersect_type,type,
% 2.16/1.40 binintersect: $i > $i > $i ).
% 2.16/1.40
% 2.16/1.40 thf(binintersect,definition,
% 2.16/1.40 ( binintersect
% 2.16/1.40 = ( ^ [A: $i,B: $i] :
% 2.16/1.40 ( dsetconstr @ A
% 2.16/1.40 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binintersectI_type,type,
% 2.16/1.40 binintersectI: $o ).
% 2.16/1.40
% 2.16/1.40 thf(binintersectI,definition,
% 2.16/1.40 ( binintersectI
% 2.16/1.40 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ A )
% 2.16/1.40 => ( ( in @ Xx @ B )
% 2.16/1.40 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binintersectSubset5_type,type,
% 2.16/1.40 binintersectSubset5: $o ).
% 2.16/1.40
% 2.16/1.40 thf(binintersectSubset5,definition,
% 2.16/1.40 ( binintersectSubset5
% 2.16/1.40 = ( ! [A: $i,B: $i,C: $i] :
% 2.16/1.40 ( ( subset @ C @ A )
% 2.16/1.40 => ( ( subset @ C @ B )
% 2.16/1.40 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.16/1.40
% 2.16/1.40 thf(binintersectEL,conjecture,
% 2.16/1.40 ( setextAx
% 2.16/1.40 => ( emptysetAx
% 2.16/1.40 => ( setadjoinAx
% 2.16/1.40 => ( powersetAx
% 2.16/1.40 => ( setunionAx
% 2.16/1.40 => ( omega0Ax
% 2.16/1.40 => ( omegaSAx
% 2.16/1.40 => ( omegaIndAx
% 2.16/1.40 => ( replAx
% 2.16/1.40 => ( foundationAx
% 2.16/1.40 => ( wellorderingAx
% 2.16/1.40 => ( descrp
% 2.16/1.40 => ( dsetconstrI
% 2.16/1.40 => ( dsetconstrEL
% 2.16/1.40 => ( dsetconstrER
% 2.16/1.40 => ( exuE1
% 2.16/1.40 => ( prop2setE
% 2.16/1.40 => ( emptysetE
% 2.16/1.40 => ( emptysetimpfalse
% 2.16/1.40 => ( notinemptyset
% 2.16/1.40 => ( exuE3e
% 2.16/1.40 => ( setext
% 2.16/1.40 => ( emptyI
% 2.16/1.40 => ( noeltsimpempty
% 2.16/1.40 => ( setbeta
% 2.16/1.40 => ( nonemptyE1
% 2.16/1.40 => ( nonemptyI
% 2.16/1.40 => ( nonemptyI1
% 2.16/1.40 => ( setadjoinIL
% 2.16/1.40 => ( emptyinunitempty
% 2.16/1.40 => ( setadjoinIR
% 2.16/1.40 => ( setadjoinE
% 2.16/1.40 => ( setadjoinOr
% 2.16/1.40 => ( setoftrueEq
% 2.16/1.40 => ( powersetI
% 2.16/1.40 => ( emptyinPowerset
% 2.16/1.40 => ( emptyInPowerset
% 2.16/1.40 => ( powersetE
% 2.16/1.40 => ( setunionI
% 2.16/1.40 => ( setunionE
% 2.16/1.40 => ( subPowSU
% 2.16/1.40 => ( exuE2
% 2.16/1.40 => ( nonemptyImpWitness
% 2.16/1.40 => ( uniqinunit
% 2.16/1.40 => ( notinsingleton
% 2.16/1.40 => ( eqinunit
% 2.16/1.40 => ( singletonsswitch
% 2.16/1.40 => ( upairsetE
% 2.16/1.40 => ( upairsetIL
% 2.16/1.40 => ( upairsetIR
% 2.16/1.40 => ( emptyE1
% 2.16/1.40 => ( vacuousDall
% 2.16/1.40 => ( quantDeMorgan1
% 2.16/1.40 => ( quantDeMorgan2
% 2.16/1.40 => ( quantDeMorgan3
% 2.16/1.40 => ( quantDeMorgan4
% 2.16/1.40 => ( prop2setI
% 2.16/1.40 => ( prop2set2propI
% 2.16/1.40 => ( notdexE
% 2.16/1.40 => ( notdallE
% 2.16/1.40 => ( exuI1
% 2.16/1.40 => ( exuI3
% 2.16/1.40 => ( exuI2
% 2.16/1.40 => ( inCongP
% 2.16/1.40 => ( in__Cong
% 2.16/1.40 => ( exuE3u
% 2.16/1.40 => ( exu__Cong
% 2.16/1.40 => ( emptyset__Cong
% 2.16/1.40 => ( setadjoin__Cong
% 2.16/1.40 => ( powerset__Cong
% 2.16/1.40 => ( setunion__Cong
% 2.16/1.40 => ( omega__Cong
% 2.16/1.40 => ( exuEu
% 2.16/1.40 => ( descr__Cong
% 2.16/1.40 => ( dsetconstr__Cong
% 2.16/1.40 => ( subsetI1
% 2.16/1.40 => ( eqimpsubset2
% 2.16/1.40 => ( eqimpsubset1
% 2.16/1.40 => ( subsetI2
% 2.16/1.40 => ( emptysetsubset
% 2.16/1.40 => ( subsetE
% 2.16/1.40 => ( subsetE2
% 2.16/1.40 => ( notsubsetI
% 2.16/1.40 => ( notequalI1
% 2.16/1.40 => ( notequalI2
% 2.16/1.40 => ( subsetRefl
% 2.16/1.40 => ( subsetTrans
% 2.16/1.40 => ( setadjoinSub
% 2.16/1.40 => ( setadjoinSub2
% 2.16/1.40 => ( subset2powerset
% 2.16/1.40 => ( setextsub
% 2.16/1.40 => ( subsetemptysetimpeq
% 2.16/1.40 => ( powersetI1
% 2.16/1.40 => ( powersetE1
% 2.16/1.40 => ( inPowerset
% 2.16/1.40 => ( powersetsubset
% 2.16/1.40 => ( sepInPowerset
% 2.16/1.40 => ( sepSubset
% 2.16/1.40 => ( binunionIL
% 2.16/1.40 => ( upairset2IR
% 2.16/1.40 => ( binunionIR
% 2.16/1.40 => ( binunionEcases
% 2.16/1.40 => ( binunionE
% 2.16/1.40 => ( binunionLsub
% 2.16/1.40 => ( binunionRsub
% 2.16/1.40 => ( binintersectI
% 2.16/1.40 => ( binintersectSubset5
% 2.16/1.40 => ! [A: $i,B: $i,Xx: $i] :
% 2.16/1.40 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.16/1.40 => ( in @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.16/1.40 ------------------------
% 2.16/1.42 % (25487)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/27Mi)
% 2.16/1.42 % (25489)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/2Mi)
% 2.16/1.42 % (25491)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/18Mi)
% 2.16/1.42 % (25489)Instruction limit reached!
% 2.16/1.42 % (25489)------------------------------
% 2.16/1.42 % (25489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.42 % (25489)Termination reason: Unknown
% 2.16/1.42 % (25489)Termination phase: shuffling
% 2.16/1.42
% 2.16/1.42 % (25489)Memory used [KB]: 1151
% 2.16/1.42 % (25489)Time elapsed: 0.002 s
% 2.16/1.42 % (25489)Instructions burned: 3 (million)
% 2.16/1.42 % (25489)------------------------------
% 2.16/1.42 % (25489)------------------------------
% 2.16/1.42 % (25488)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/2Mi)
% 2.16/1.42 % (25487)Instruction limit reached!
% 2.16/1.42 % (25487)------------------------------
% 2.16/1.42 % (25487)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.42 % (25487)Termination reason: Unknown
% 2.16/1.42 % (25487)Termination phase: Property scanning
% 2.16/1.42
% 2.16/1.42 % (25487)Memory used [KB]: 1535
% 2.16/1.42 % (25487)Time elapsed: 0.009 s
% 2.16/1.42 % (25487)Instructions burned: 29 (million)
% 2.16/1.42 % (25488)Instruction limit reached!
% 2.16/1.42 % (25488)------------------------------
% 2.16/1.42 % (25488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.42 % (25488)Termination reason: Unknown
% 2.16/1.42 % (25488)Termination phase: shuffling
% 2.16/1.42
% 2.16/1.42 % (25488)Memory used [KB]: 1151
% 2.16/1.42 % (25488)Time elapsed: 0.003 s
% 2.16/1.42 % (25488)Instructions burned: 2 (million)
% 2.16/1.42 % (25488)------------------------------
% 2.16/1.42 % (25488)------------------------------
% 2.16/1.42 % (25487)------------------------------
% 2.16/1.42 % (25487)------------------------------
% 2.16/1.42 % (25491)Instruction limit reached!
% 2.16/1.42 % (25491)------------------------------
% 2.16/1.42 % (25491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.42 % (25491)Termination reason: Unknown
% 2.16/1.42 % (25491)Termination phase: Preprocessing 3
% 2.16/1.42
% 2.16/1.42 % (25491)Memory used [KB]: 1535
% 2.16/1.42 % (25491)Time elapsed: 0.007 s
% 2.16/1.42 % (25491)Instructions burned: 18 (million)
% 2.16/1.42 % (25491)------------------------------
% 2.16/1.42 % (25491)------------------------------
% 2.16/1.42 % (25486)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/4Mi)
% 2.16/1.42 % (25485)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/183Mi)
% 2.16/1.43 % (25486)Instruction limit reached!
% 2.16/1.43 % (25486)------------------------------
% 2.16/1.43 % (25486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.43 % (25486)Termination reason: Unknown
% 2.16/1.43 % (25486)Termination phase: shuffling
% 2.16/1.43
% 2.16/1.43 % (25486)Memory used [KB]: 1279
% 2.16/1.43 % (25486)Time elapsed: 0.005 s
% 2.16/1.43 % (25486)Instructions burned: 5 (million)
% 2.16/1.43 % (25486)------------------------------
% 2.16/1.43 % (25486)------------------------------
% 2.16/1.43 % (25490)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/275Mi)
% 2.16/1.43 % (25492)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/3Mi)
% 2.16/1.43 % (25492)Instruction limit reached!
% 2.16/1.43 % (25492)------------------------------
% 2.16/1.43 % (25492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.43 % (25492)Termination reason: Unknown
% 2.16/1.43 % (25492)Termination phase: shuffling
% 2.16/1.43
% 2.16/1.43 % (25492)Memory used [KB]: 1151
% 2.16/1.43 % (25492)Time elapsed: 0.002 s
% 2.16/1.43 % (25492)Instructions burned: 4 (million)
% 2.16/1.43 % (25492)------------------------------
% 2.16/1.43 % (25492)------------------------------
% 2.16/1.43 % (25493)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/37Mi)
% 2.16/1.44 % (25494)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/15Mi)
% 2.16/1.44 % (25495)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/3Mi)
% 2.16/1.44 % (25495)Instruction limit reached!
% 2.16/1.44 % (25495)------------------------------
% 2.16/1.44 % (25495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.44 % (25495)Termination reason: Unknown
% 2.16/1.44 % (25495)Termination phase: shuffling
% 2.16/1.44
% 2.16/1.44 % (25495)Memory used [KB]: 1151
% 2.16/1.44 % (25495)Time elapsed: 0.004 s
% 2.16/1.44 % (25495)Instructions burned: 4 (million)
% 2.16/1.44 % (25495)------------------------------
% 2.16/1.44 % (25495)------------------------------
% 2.16/1.45 % (25497)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/7Mi)
% 2.16/1.45 % (25493)Instruction limit reached!
% 2.16/1.45 % (25493)------------------------------
% 2.16/1.45 % (25493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.45 % (25493)Termination reason: Unknown
% 2.16/1.45 % (25493)Termination phase: Function definition elimination
% 2.16/1.45
% 2.16/1.45 % (25493)Memory used [KB]: 1663
% 2.16/1.45 % (25493)Time elapsed: 0.013 s
% 2.16/1.45 % (25493)Instructions burned: 40 (million)
% 2.16/1.45 % (25493)------------------------------
% 2.16/1.45 % (25493)------------------------------
% 2.16/1.45 % (25497)Instruction limit reached!
% 2.16/1.45 % (25497)------------------------------
% 2.16/1.45 % (25497)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.45 % (25497)Termination reason: Unknown
% 2.16/1.45 % (25497)Termination phase: shuffling
% 2.16/1.45
% 2.16/1.45 % (25497)Memory used [KB]: 1279
% 2.16/1.45 % (25497)Time elapsed: 0.003 s
% 2.16/1.45 % (25497)Instructions burned: 7 (million)
% 2.16/1.45 % (25497)------------------------------
% 2.16/1.45 % (25497)------------------------------
% 2.16/1.45 % (25494)Instruction limit reached!
% 2.16/1.45 % (25494)------------------------------
% 2.16/1.45 % (25494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.45 % (25494)Termination reason: Unknown
% 2.16/1.45 % (25494)Termination phase: Naming
% 2.16/1.45
% 2.16/1.45 % (25494)Memory used [KB]: 1535
% 2.16/1.45 % (25494)Time elapsed: 0.010 s
% 2.16/1.45 % (25494)Instructions burned: 16 (million)
% 2.16/1.45 % (25494)------------------------------
% 2.16/1.45 % (25494)------------------------------
% 2.16/1.45 % (25496)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/1041Mi)
% 2.16/1.46 % (25499)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/3Mi)
% 2.16/1.46 % (25500)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/3Mi)
% 2.16/1.46 % (25499)Instruction limit reached!
% 2.16/1.46 % (25499)------------------------------
% 2.16/1.46 % (25499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.46 % (25499)Termination reason: Unknown
% 2.16/1.46 % (25499)Termination phase: shuffling
% 2.16/1.46
% 2.16/1.46 % (25499)Memory used [KB]: 1151
% 2.16/1.46 % (25499)Time elapsed: 0.002 s
% 2.16/1.46 % (25499)Instructions burned: 3 (million)
% 2.16/1.46 % (25499)------------------------------
% 2.16/1.46 % (25499)------------------------------
% 2.16/1.46 % (25500)Instruction limit reached!
% 2.16/1.46 % (25500)------------------------------
% 2.16/1.46 % (25500)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.46 % (25500)Termination reason: Unknown
% 2.16/1.46 % (25500)Termination phase: shuffling
% 2.16/1.46
% 2.16/1.46 % (25500)Memory used [KB]: 1151
% 2.16/1.46 % (25500)Time elapsed: 0.002 s
% 2.16/1.46 % (25500)Instructions burned: 4 (million)
% 2.16/1.46 % (25500)------------------------------
% 2.16/1.46 % (25500)------------------------------
% 2.16/1.46 % (25498)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/16Mi)
% 2.16/1.47 % (25501)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/7Mi)
% 2.16/1.47 % (25503)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/4Mi)
% 2.16/1.47 % (25502)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/3Mi)
% 2.16/1.47 % (25503)Instruction limit reached!
% 2.16/1.47 % (25503)------------------------------
% 2.16/1.47 % (25503)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.47 % (25503)Termination reason: Unknown
% 2.16/1.47 % (25503)Termination phase: shuffling
% 2.16/1.47
% 2.16/1.47 % (25503)Memory used [KB]: 1151
% 2.16/1.47 % (25503)Time elapsed: 0.002 s
% 2.16/1.47 % (25503)Instructions burned: 4 (million)
% 2.16/1.47 % (25503)------------------------------
% 2.16/1.47 % (25503)------------------------------
% 2.16/1.47 % (25502)Instruction limit reached!
% 2.16/1.47 % (25502)------------------------------
% 2.16/1.47 % (25502)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.47 % (25502)Termination reason: Unknown
% 2.16/1.47 % (25502)Termination phase: shuffling
% 2.16/1.47
% 2.16/1.47 % (25502)Memory used [KB]: 1151
% 2.16/1.47 % (25502)Time elapsed: 0.003 s
% 2.16/1.47 % (25502)Instructions burned: 4 (million)
% 2.16/1.47 % (25502)------------------------------
% 2.16/1.47 % (25502)------------------------------
% 2.16/1.47 % (25501)Instruction limit reached!
% 2.16/1.47 % (25501)------------------------------
% 2.16/1.47 % (25501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.47 % (25501)Termination reason: Unknown
% 2.16/1.47 % (25501)Termination phase: shuffling
% 2.16/1.47
% 2.16/1.47 % (25501)Memory used [KB]: 1279
% 2.16/1.47 % (25501)Time elapsed: 0.005 s
% 2.16/1.47 % (25501)Instructions burned: 8 (million)
% 2.16/1.47 % (25501)------------------------------
% 2.16/1.47 % (25501)------------------------------
% 2.16/1.47 % (25498)Instruction limit reached!
% 2.16/1.47 % (25498)------------------------------
% 2.16/1.47 % (25498)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.47 % (25498)Termination reason: Unknown
% 2.16/1.47 % (25498)Termination phase: Property scanning
% 2.16/1.47
% 2.16/1.47 % (25498)Memory used [KB]: 1407
% 2.16/1.47 % (25498)Time elapsed: 0.010 s
% 2.16/1.47 % (25498)Instructions burned: 16 (million)
% 2.16/1.47 % (25498)------------------------------
% 2.16/1.47 % (25498)------------------------------
% 2.16/1.48 % (25504)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/18Mi)
% 2.16/1.48 % (25505)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/710Mi)
% 2.16/1.48 % (25504)Instruction limit reached!
% 2.16/1.48 % (25504)------------------------------
% 2.16/1.48 % (25504)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.16/1.48 % (25504)Termination reason: Unknown
% 2.16/1.48 % (25504)Termination phase: Property scanning
% 2.16/1.48
% 2.16/1.48 % (25504)Memory used [KB]: 1407
% 2.16/1.48 % (25504)Time elapsed: 0.006 s
% 2.16/1.48 % (25504)Instructions burned: 19 (million)
% 2.16/1.48 % (25504)------------------------------
% 2.16/1.48 % (25504)------------------------------
% 2.16/1.49 % (25508)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/21Mi)
% 2.16/1.49 % (25507)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/902Mi)
% 2.16/1.49 % (25506)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/6Mi)
% 2.18/1.50 % (25506)Instruction limit reached!
% 2.18/1.50 % (25506)------------------------------
% 2.18/1.50 % (25506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.50 % (25506)Termination reason: Unknown
% 2.18/1.50 % (25506)Termination phase: shuffling
% 2.18/1.50
% 2.18/1.50 % (25506)Memory used [KB]: 1279
% 2.18/1.50 % (25506)Time elapsed: 0.006 s
% 2.18/1.50 % (25506)Instructions burned: 7 (million)
% 2.18/1.50 % (25506)------------------------------
% 2.18/1.50 % (25506)------------------------------
% 2.18/1.50 % (25508)Instruction limit reached!
% 2.18/1.50 % (25508)------------------------------
% 2.18/1.50 % (25508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.50 % (25508)Termination reason: Unknown
% 2.18/1.50 % (25508)Termination phase: Property scanning
% 2.18/1.50
% 2.18/1.50 % (25508)Memory used [KB]: 1535
% 2.18/1.50 % (25508)Time elapsed: 0.007 s
% 2.18/1.50 % (25508)Instructions burned: 22 (million)
% 2.18/1.50 % (25508)------------------------------
% 2.18/1.50 % (25508)------------------------------
% 2.18/1.51 % (25485)Instruction limit reached!
% 2.18/1.51 % (25485)------------------------------
% 2.18/1.51 % (25485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.51 % (25485)Termination reason: Unknown
% 2.18/1.51 % (25485)Termination phase: Saturation
% 2.18/1.51
% 2.18/1.51 % (25485)Memory used [KB]: 6908
% 2.18/1.51 % (25485)Time elapsed: 0.084 s
% 2.18/1.51 % (25485)Instructions burned: 183 (million)
% 2.18/1.51 % (25485)------------------------------
% 2.18/1.51 % (25485)------------------------------
% 2.18/1.51 % (25510)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/6Mi)
% 2.18/1.51 % (25510)Instruction limit reached!
% 2.18/1.51 % (25510)------------------------------
% 2.18/1.51 % (25510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.51 % (25510)Termination reason: Unknown
% 2.18/1.51 % (25510)Termination phase: shuffling
% 2.18/1.51
% 2.18/1.51 % (25510)Memory used [KB]: 1279
% 2.18/1.51 % (25510)Time elapsed: 0.003 s
% 2.18/1.51 % (25510)Instructions burned: 7 (million)
% 2.18/1.51 % (25510)------------------------------
% 2.18/1.51 % (25510)------------------------------
% 2.18/1.52 % (25512)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/779Mi)
% 2.18/1.52 % (25490)Instruction limit reached!
% 2.18/1.52 % (25490)------------------------------
% 2.18/1.52 % (25490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.52 % (25490)Termination reason: Unknown
% 2.18/1.52 % (25490)Termination phase: Saturation
% 2.18/1.52
% 2.18/1.52 % (25490)Memory used [KB]: 7675
% 2.18/1.52 % (25490)Time elapsed: 0.092 s
% 2.18/1.52 % (25490)Instructions burned: 277 (million)
% 2.18/1.52 % (25490)------------------------------
% 2.18/1.52 % (25490)------------------------------
% 2.18/1.52 % (25511)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/377Mi)
% 2.18/1.52 % (25509)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_25294 for (2999ds/5Mi)
% 2.18/1.53 % (25509)Instruction limit reached!
% 2.18/1.53 % (25509)------------------------------
% 2.18/1.53 % (25509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.53 % (25509)Termination reason: Unknown
% 2.18/1.53 % (25509)Termination phase: shuffling
% 2.18/1.53
% 2.18/1.53 % (25509)Memory used [KB]: 1279
% 2.18/1.53 % (25509)Time elapsed: 0.006 s
% 2.18/1.53 % (25509)Instructions burned: 5 (million)
% 2.18/1.53 % (25509)------------------------------
% 2.18/1.53 % (25509)------------------------------
% 2.18/1.53 % (25513)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_25294 for (2998ds/19Mi)
% 2.18/1.53 % (25513)Instruction limit reached!
% 2.18/1.53 % (25513)------------------------------
% 2.18/1.53 % (25513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.53 % (25513)Termination reason: Unknown
% 2.18/1.53 % (25513)Termination phase: Property scanning
% 2.18/1.53
% 2.18/1.53 % (25513)Memory used [KB]: 1535
% 2.18/1.53 % (25513)Time elapsed: 0.007 s
% 2.18/1.53 % (25513)Instructions burned: 23 (million)
% 2.18/1.53 % (25513)------------------------------
% 2.18/1.53 % (25513)------------------------------
% 2.18/1.54 % (25515)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_25294 for (2998ds/17Mi)
% 2.18/1.54 % (25514)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_25294 for (2998ds/879Mi)
% 2.18/1.55 % (25515)Instruction limit reached!
% 2.18/1.55 % (25515)------------------------------
% 2.18/1.55 % (25515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.55 % (25515)Termination reason: Unknown
% 2.18/1.55 % (25515)Termination phase: Property scanning
% 2.18/1.55
% 2.18/1.55 % (25515)Memory used [KB]: 1407
% 2.18/1.55 % (25515)Time elapsed: 0.006 s
% 2.18/1.55 % (25515)Instructions burned: 17 (million)
% 2.18/1.55 % (25515)------------------------------
% 2.18/1.55 % (25515)------------------------------
% 2.18/1.56 % (25516)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_25294 for (2998ds/3Mi)
% 2.18/1.56 % (25516)Instruction limit reached!
% 2.18/1.56 % (25516)------------------------------
% 2.18/1.56 % (25516)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.56 % (25516)Termination reason: Unknown
% 2.18/1.56 % (25516)Termination phase: shuffling
% 2.18/1.56
% 2.18/1.56 % (25516)Memory used [KB]: 1279
% 2.18/1.56 % (25516)Time elapsed: 0.003 s
% 2.18/1.56 % (25516)Instructions burned: 5 (million)
% 2.18/1.56 % (25516)------------------------------
% 2.18/1.56 % (25516)------------------------------
% 2.18/1.57 % (25517)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_25294 for (2998ds/30Mi)
% 2.18/1.58 % (25517)Instruction limit reached!
% 2.18/1.58 % (25517)------------------------------
% 2.18/1.58 % (25517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.58 % (25517)Termination reason: Unknown
% 2.18/1.58 % (25517)Termination phase: Property scanning
% 2.18/1.58
% 2.18/1.58 % (25517)Memory used [KB]: 1535
% 2.18/1.58 % (25517)Time elapsed: 0.009 s
% 2.18/1.58 % (25517)Instructions burned: 30 (million)
% 2.18/1.58 % (25517)------------------------------
% 2.18/1.58 % (25517)------------------------------
% 2.18/1.59 % (25518)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_25294 for (2998ds/127Mi)
% 2.18/1.63 % (25518)Instruction limit reached!
% 2.18/1.63 % (25518)------------------------------
% 2.18/1.63 % (25518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.63 % (25518)Termination reason: Unknown
% 2.18/1.63 % (25518)Termination phase: Saturation
% 2.18/1.63
% 2.18/1.63 % (25518)Memory used [KB]: 6780
% 2.18/1.63 % (25518)Time elapsed: 0.041 s
% 2.18/1.63 % (25518)Instructions burned: 127 (million)
% 2.18/1.63 % (25518)------------------------------
% 2.18/1.63 % (25518)------------------------------
% 2.18/1.65 % (25533)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_25294 for (2997ds/100Mi)
% 2.18/1.69 % (25511)Instruction limit reached!
% 2.18/1.69 % (25511)------------------------------
% 2.18/1.69 % (25511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.69 % (25511)Termination reason: Unknown
% 2.18/1.69 % (25511)Termination phase: Saturation
% 2.18/1.69
% 2.18/1.69 % (25511)Memory used [KB]: 7164
% 2.18/1.69 % (25511)Time elapsed: 0.171 s
% 2.18/1.69 % (25511)Instructions burned: 378 (million)
% 2.18/1.69 % (25511)------------------------------
% 2.18/1.69 % (25511)------------------------------
% 2.18/1.70 % (25533)Instruction limit reached!
% 2.18/1.70 % (25533)------------------------------
% 2.18/1.70 % (25533)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.70 % (25533)Termination reason: Unknown
% 2.18/1.70 % (25533)Termination phase: Saturation
% 2.18/1.70
% 2.18/1.70 % (25533)Memory used [KB]: 6396
% 2.18/1.70 % (25533)Time elapsed: 0.053 s
% 2.18/1.70 % (25533)Instructions burned: 101 (million)
% 2.18/1.70 % (25533)------------------------------
% 2.18/1.70 % (25533)------------------------------
% 2.18/1.70 % (25550)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_25294 for (2997ds/3Mi)
% 2.18/1.71 % (25550)Instruction limit reached!
% 2.18/1.71 % (25550)------------------------------
% 2.18/1.71 % (25550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.71 % (25550)Termination reason: Unknown
% 2.18/1.71 % (25550)Termination phase: shuffling
% 2.18/1.71
% 2.18/1.71 % (25550)Memory used [KB]: 1279
% 2.18/1.71 % (25550)Time elapsed: 0.003 s
% 2.18/1.71 % (25550)Instructions burned: 5 (million)
% 2.18/1.71 % (25550)------------------------------
% 2.18/1.71 % (25550)------------------------------
% 2.18/1.71 % (25552)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_25294 for (2997ds/20Mi)
% 2.18/1.72 % (25552)Instruction limit reached!
% 2.18/1.72 % (25552)------------------------------
% 2.18/1.72 % (25552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.72 % (25552)Termination reason: Unknown
% 2.18/1.72 % (25552)Termination phase: Preprocessing 2
% 2.18/1.72
% 2.18/1.72 % (25552)Memory used [KB]: 1407
% 2.18/1.72 % (25552)Time elapsed: 0.007 s
% 2.18/1.72 % (25552)Instructions burned: 21 (million)
% 2.18/1.72 % (25552)------------------------------
% 2.18/1.72 % (25552)------------------------------
% 2.18/1.72 % (25554)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_25294 for (2997ds/86Mi)
% 2.18/1.73 % (25505)Instruction limit reached!
% 2.18/1.73 % (25505)------------------------------
% 2.18/1.73 % (25505)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.73 % (25505)Termination reason: Unknown
% 2.18/1.73 % (25505)Termination phase: Saturation
% 2.18/1.73
% 2.18/1.73 % (25505)Memory used [KB]: 8955
% 2.18/1.73 % (25505)Time elapsed: 0.255 s
% 2.18/1.73 % (25505)Instructions burned: 710 (million)
% 2.18/1.73 % (25505)------------------------------
% 2.18/1.73 % (25505)------------------------------
% 2.18/1.73 % (25557)lrs+1010_1:1_au=on:cbe=off:nm=2:ntd=on:sd=2:ss=axioms:st=5.0:i=107:si=on:rtra=on_0 on DTF2THF_25294 for (2996ds/107Mi)
% 2.18/1.73 % (25514)First to succeed.
% 2.18/1.74 % (25514)Refutation found. Thanks to Tanya!
% 2.18/1.74 % SZS status Theorem for DTF2THF_25294
% 2.18/1.74 % SZS output start Proof for DTF2THF_25294
% 2.18/1.74 thf(func_def_0, type, in: $i > $i > $o).
% 2.18/1.74 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.18/1.74 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.18/1.74 thf(func_def_8, type, powerset: $i > $i).
% 2.18/1.74 thf(func_def_10, type, setunion: $i > $i).
% 2.18/1.74 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.18/1.74 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_26, type, prop2set: $o > $i).
% 2.18/1.74 thf(func_def_36, type, nonempty: $i > $o).
% 2.18/1.74 thf(func_def_69, type, set2prop: $i > $o).
% 2.18/1.74 thf(func_def_88, type, subset: $i > $i > $o).
% 2.18/1.74 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.18/1.74 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.18/1.74 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.18/1.74 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.18/1.74 thf(func_def_146, type, sK4: ($i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_147, type, sK5: $i > $i > $i).
% 2.18/1.74 thf(func_def_148, type, sK6: $i > $i > $i).
% 2.18/1.74 thf(func_def_149, type, sK7: ($i > $i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_150, type, sK8: ($i > $i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_151, type, sK9: $i > ($i > $i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_152, type, sK10: $i > ($i > $i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_153, type, sK11: ($i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_154, type, sK12: $i > $i).
% 2.18/1.74 thf(func_def_155, type, sK13: $i > $i).
% 2.18/1.74 thf(func_def_156, type, sK14: $i > $i > $i).
% 2.18/1.74 thf(func_def_157, type, sK15: $i > $i).
% 2.18/1.74 thf(func_def_158, type, sK16: $i > $i > $i).
% 2.18/1.74 thf(func_def_159, type, sK17: $i > $i > $i).
% 2.18/1.74 thf(func_def_160, type, sK18: $i > $i > $i).
% 2.18/1.74 thf(func_def_161, type, sK19: ($i > $o) > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_162, type, sK20: ($i > $o) > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_163, type, sK21: ($i > $o) > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_164, type, sK22: ($i > $o) > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_165, type, sK23: ($i > $o) > $i).
% 2.18/1.74 thf(func_def_166, type, sK24: $i > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_167, type, sK25: ($i > $o) > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_168, type, sK26: ($i > $o) > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_169, type, sK27: $i > $i).
% 2.18/1.74 thf(func_def_170, type, sK28: $i > $i > $i > $i).
% 2.18/1.74 thf(func_def_171, type, sK29: $i > $i > $i).
% 2.18/1.74 thf(func_def_172, type, sK30: $i > $i > $i).
% 2.18/1.74 thf(func_def_173, type, sK31: $i > $i > $i).
% 2.18/1.74 thf(func_def_174, type, sK32: $i > $i).
% 2.18/1.74 thf(func_def_175, type, sK33: $i > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_176, type, sK34: ($i > $o) > ($i > $o) > $i > $i > $i).
% 2.18/1.74 thf(func_def_177, type, sK35: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_178, type, sK36: $i > $i).
% 2.18/1.74 thf(func_def_179, type, sK37: $i > ($i > $o) > $i).
% 2.18/1.74 thf(func_def_180, type, sK38: ($i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_181, type, sK39: ($i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_182, type, sK40: ($i > $o) > $i).
% 2.18/1.74 thf(func_def_183, type, sK41: ($i > $o) > $i).
% 2.18/1.74 thf(func_def_184, type, sK42: $i > $i > $i).
% 2.18/1.74 thf(func_def_185, type, sK43: $i > $i > $i).
% 2.18/1.74 thf(func_def_186, type, sK44: $i > $o > $i > $i).
% 2.18/1.74 thf(func_def_187, type, sK45: ($i > $o) > $i > $i).
% 2.18/1.74 thf(func_def_188, type, sK46: ($i > $o) > $i).
% 2.18/1.74 thf(func_def_189, type, sK47: ($i > $o) > $i).
% 2.18/1.74 thf(func_def_190, type, sK48: $i > $i).
% 2.18/1.74 thf(func_def_191, type, ph49: !>[X0: $tType]:(X0)).
% 2.18/1.74 thf(f3267,plain,(
% 2.18/1.74 $false),
% 2.18/1.74 inference(avatar_sat_refutation,[status(thm)],[f2795,f3266])).
% 2.18/1.74 thf(f3266,plain,(
% 2.18/1.74 spl3_2),
% 2.18/1.74 inference(avatar_split_clause,[status(thm)],[f1802,f1682])).
% 2.18/1.74 thf(f1682,definition,(
% 2.18/1.74 spl3_2 <=> ! [X3 : $o] : (($true = X3) | ($false = X3))),
% 2.18/1.74 introduced(definition,[new_symbols(naming,[spl3_2])],[avatar_definition])).
% 2.18/1.74 thf(f1802,plain,(
% 2.18/1.74 ( ! [X0 : $o] : (($false = X0) | ($true = X0)) )),
% 2.18/1.74 inference(trivial_inequality_removal,[status(thm)],[f1795])).
% 2.18/1.74 thf(f1795,plain,(
% 2.18/1.74 ( ! [X0 : $o] : (($true = X0) | ($false = $true) | ($false = X0)) )),
% 2.18/1.74 inference(superposition,[status(thm)],[f1258,f1241])).
% 2.18/1.74 thf(f1241,plain,(
% 2.18/1.74 ( ! [X1 : $o] : (((in @ emptyset @ (prop2set @ X1)) = $true) | ($false = X1)) )),
% 2.18/1.74 inference(binary_proxy_clausification,[status(thm)],[f1240])).
% 2.18/1.74 thf(f1240,plain,(
% 2.18/1.74 ( ! [X1 : $o] : (((X1 => (in @ emptyset @ (prop2set @ X1))) = $true)) )),
% 2.18/1.74 inference(beta_eta_normalization,[status(thm)],[f1239])).
% 2.18/1.74 thf(f1239,plain,(
% 2.18/1.74 ( ! [X1 : $o] : ((((^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0)))) @ X1) = $true)) )),
% 2.18/1.74 inference(pi_clausification,[status(thm)],[f612])).
% 2.18/1.74 thf(f612,plain,(
% 2.18/1.74 ((!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))) = $true)),
% 2.18/1.74 inference(definition_unfolding,[status(thm)],[f502,f467])).
% 2.18/1.74 thf(f467,plain,(
% 2.18/1.74 (prop2setI = $true)),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f333])).
% 2.18/1.74 thf(f333,plain,(
% 2.18/1.74 (exuE3e = $true) & (quantDeMorgan2 = $true) & (exuI2 = $true) & (noeltsimpempty = $true) & (descrp = $true) & (setunionE = $true) & (binunionIL = $true) & (emptyI = $true) & (exuE2 = $true) & (upairsetE = $true) & (binunionRsub = $true) & (dsetconstrEL = $true) & (nonemptyImpWitness = $true) & (sepSubset = $true) & (omega0Ax = $true) & (setext = $true) & (binunionE = $true) & (in__Cong = $true) & (prop2setI = $true) & (inPowerset = $true) & (setbeta = $true) & (emptyE1 = $true) & (wellorderingAx = $true) & (exuI3 = $true) & (binunionIR = $true) & (replAx = $true) & (prop2setE = $true) & (inCongP = $true) & (powerset__Cong = $true) & (setunionI = $true) & (setextsub = $true) & (setadjoinAx = $true) & (setadjoinOr = $true) & (foundationAx = $true) & (subsetI2 = $true) & (exuE3u = $true) & (subsetTrans = $true) & (eqimpsubset1 = $true) & (emptysetE = $true) & (quantDeMorgan4 = $true) & (exuE1 = $true) & (exuEu = $true) & (omega__Cong = $true) & (dsetconstrER = $true) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (singletonsswitch = $true) & (notequalI2 = $true) & (notdexE = $true) & (dsetconstrI = $true) & (emptyinunitempty = $true) & (subsetE = $true) & (setadjoinE = $true) & (emptyinPowerset = $true) & (quantDeMorgan3 = $true) & (notsubsetI = $true) & (setadjoinIL = $true) & (notinemptyset = $true) & (prop2set2propI = $true) & (notdallE = $true) & (binintersectSubset5 = $true) & (omegaIndAx = $true) & (setadjoinIR = $true) & (emptysetimpfalse = $true) & (setunion__Cong = $true) & (powersetAx = $true) & (((in @ sK2 @ (binintersect @ sK1 @ sK0)) = $true) & ((in @ sK2 @ sK1) != $true)) & (binunionLsub = $true) & (subset2powerset = $true) & (setunionAx = $true) & (quantDeMorgan1 = $true) & (powersetI = $true) & (powersetI1 = $true) & (emptysetsubset = $true) & (emptyset__Cong = $true) & (subsetemptysetimpeq = $true) & (exu__Cong = $true) & (powersetE1 = $true) & (nonemptyI1 = $true) & (setadjoin__Cong = $true) & (upairsetIR = $true) & (nonemptyI = $true) & (exuI1 = $true) & (subsetE2 = $true) & (dsetconstr__Cong = $true) & (powersetE = $true) & (sepInPowerset = $true) & (subPowSU = $true) & (notequalI1 = $true) & (setadjoinSub = $true) & (subsetI1 = $true) & (vacuousDall = $true) & (eqimpsubset2 = $true) & (omegaSAx = $true) & (descr__Cong = $true) & (uniqinunit = $true) & (emptyInPowerset = $true) & (notinsingleton = $true) & (binunionEcases = $true) & (emptysetAx = $true) & (upairsetIL = $true) & (subsetRefl = $true) & (binintersectI = $true) & (setextAx = $true) & (nonemptyE1 = $true) & (powersetsubset = $true) & (eqinunit = $true) & (upairset2IR = $true)),
% 2.18/1.74 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f331,f332])).
% 2.18/1.74 thf(f332,plain,(
% 2.18/1.74 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true)) => (((in @ sK2 @ (binintersect @ sK1 @ sK0)) = $true) & ((in @ sK2 @ sK1) != $true))),
% 2.18/1.74 introduced(definition,[],[choice_axiom])).
% 2.18/1.74 thf(f331,plain,(
% 2.18/1.74 (exuE3e = $true) & (quantDeMorgan2 = $true) & (exuI2 = $true) & (noeltsimpempty = $true) & (descrp = $true) & (setunionE = $true) & (binunionIL = $true) & (emptyI = $true) & (exuE2 = $true) & (upairsetE = $true) & (binunionRsub = $true) & (dsetconstrEL = $true) & (nonemptyImpWitness = $true) & (sepSubset = $true) & (omega0Ax = $true) & (setext = $true) & (binunionE = $true) & (in__Cong = $true) & (prop2setI = $true) & (inPowerset = $true) & (setbeta = $true) & (emptyE1 = $true) & (wellorderingAx = $true) & (exuI3 = $true) & (binunionIR = $true) & (replAx = $true) & (prop2setE = $true) & (inCongP = $true) & (powerset__Cong = $true) & (setunionI = $true) & (setextsub = $true) & (setadjoinAx = $true) & (setadjoinOr = $true) & (foundationAx = $true) & (subsetI2 = $true) & (exuE3u = $true) & (subsetTrans = $true) & (eqimpsubset1 = $true) & (emptysetE = $true) & (quantDeMorgan4 = $true) & (exuE1 = $true) & (exuEu = $true) & (omega__Cong = $true) & (dsetconstrER = $true) & (setadjoinSub2 = $true) & (setoftrueEq = $true) & (singletonsswitch = $true) & (notequalI2 = $true) & (notdexE = $true) & (dsetconstrI = $true) & (emptyinunitempty = $true) & (subsetE = $true) & (setadjoinE = $true) & (emptyinPowerset = $true) & (quantDeMorgan3 = $true) & (notsubsetI = $true) & (setadjoinIL = $true) & (notinemptyset = $true) & (prop2set2propI = $true) & (notdallE = $true) & (binintersectSubset5 = $true) & (omegaIndAx = $true) & (setadjoinIR = $true) & (emptysetimpfalse = $true) & (setunion__Cong = $true) & (powersetAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true)) & (binunionLsub = $true) & (subset2powerset = $true) & (setunionAx = $true) & (quantDeMorgan1 = $true) & (powersetI = $true) & (powersetI1 = $true) & (emptysetsubset = $true) & (emptyset__Cong = $true) & (subsetemptysetimpeq = $true) & (exu__Cong = $true) & (powersetE1 = $true) & (nonemptyI1 = $true) & (setadjoin__Cong = $true) & (upairsetIR = $true) & (nonemptyI = $true) & (exuI1 = $true) & (subsetE2 = $true) & (dsetconstr__Cong = $true) & (powersetE = $true) & (sepInPowerset = $true) & (subPowSU = $true) & (notequalI1 = $true) & (setadjoinSub = $true) & (subsetI1 = $true) & (vacuousDall = $true) & (eqimpsubset2 = $true) & (omegaSAx = $true) & (descr__Cong = $true) & (uniqinunit = $true) & (emptyInPowerset = $true) & (notinsingleton = $true) & (binunionEcases = $true) & (emptysetAx = $true) & (upairsetIL = $true) & (subsetRefl = $true) & (binintersectI = $true) & (setextAx = $true) & (nonemptyE1 = $true) & (powersetsubset = $true) & (eqinunit = $true) & (upairset2IR = $true)),
% 2.18/1.74 inference(flattening,[status(thm)],[f330])).
% 2.18/1.74 thf(f330,plain,(
% 2.18/1.74 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) & ((in @ X2 @ X1) != $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.18/1.74 inference(ennf_transformation,[status(thm)],[f279])).
% 2.18/1.74 thf(f279,plain,(
% 2.18/1.74 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X2 @ (binintersect @ X1 @ X0)) = $true) => ((in @ X2 @ X1) = $true)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.18/1.74 inference(fool_elimination,[status(thm)],[f278])).
% 2.18/1.74 thf(f278,plain,(
% 2.18/1.74 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (binintersect @ X1 @ X0)) => (in @ X2 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.18/1.74 inference(rectify,[status(thm)],[f112])).
% 2.18/1.74 thf(f112,negated_conjecture,(
% 2.18/1.74 ~(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 => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X3)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.18/1.74 inference(negated_conjecture,[status(cth)],[f111])).
% 2.18/1.74 thf(f111,conjecture,(
% 2.18/1.74 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 => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.18/1.74 file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',binintersectEL)).
% 2.18/1.74 thf(f502,plain,(
% 2.18/1.74 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f248])).
% 2.18/1.74 thf(f248,plain,(
% 2.18/1.74 (prop2setI = (!! @ $o @ (^[Y0 : $o]: (Y0 => (in @ emptyset @ (prop2set @ Y0))))))),
% 2.18/1.74 inference(fool_elimination,[status(thm)],[f247])).
% 2.18/1.74 thf(f247,plain,(
% 2.18/1.74 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 2.18/1.74 inference(rectify,[status(thm)],[f59])).
% 2.18/1.74 thf(f59,axiom,(
% 2.18/1.74 (prop2setI = ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))),
% 2.18/1.74 file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',prop2setI)).
% 2.18/1.74 thf(f1258,plain,(
% 2.18/1.74 ( ! [X2 : $i,X1 : $o] : (($false = (in @ X2 @ (prop2set @ X1))) | ($true = X1)) )),
% 2.18/1.74 inference(binary_proxy_clausification,[status(thm)],[f1257])).
% 2.18/1.74 thf(f1257,plain,(
% 2.18/1.74 ( ! [X2 : $i,X1 : $o] : ((((in @ X2 @ (prop2set @ X1)) => X1) = $true)) )),
% 2.18/1.74 inference(beta_eta_normalization,[status(thm)],[f1256])).
% 2.18/1.74 thf(f1256,plain,(
% 2.18/1.74 ( ! [X2 : $i,X1 : $o] : ((((^[Y0 : $i]: ((in @ Y0 @ (prop2set @ X1)) => X1)) @ X2) = $true)) )),
% 2.18/1.74 inference(pi_clausification,[status(thm)],[f1255])).
% 2.18/1.74 thf(f1255,plain,(
% 2.18/1.74 ( ! [X1 : $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (prop2set @ X1)) => X1))) = $true)) )),
% 2.18/1.74 inference(beta_eta_normalization,[status(thm)],[f1254])).
% 2.18/1.74 thf(f1254,plain,(
% 2.18/1.74 ( ! [X1 : $o] : ((((^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0)))) @ X1) = $true)) )),
% 2.18/1.74 inference(pi_clausification,[status(thm)],[f561])).
% 2.18/1.74 thf(f561,plain,(
% 2.18/1.74 ((!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))) = $true)),
% 2.18/1.74 inference(definition_unfolding,[status(thm)],[f459,f345])).
% 2.18/1.74 thf(f345,plain,(
% 2.18/1.74 (prop2setE = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))))),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f297])).
% 2.18/1.74 thf(f297,plain,(
% 2.18/1.74 (prop2setE = (!! @ $o @ (^[Y0 : $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (prop2set @ Y0)) => Y0))))))),
% 2.18/1.74 inference(fool_elimination,[status(thm)],[f296])).
% 2.18/1.74 thf(f296,plain,(
% 2.18/1.74 (prop2setE = ! [X0 : $i,X1 : $o] : ((in @ X0 @ (prop2set @ X1)) => X1))),
% 2.18/1.74 inference(rectify,[status(thm)],[f18])).
% 2.18/1.74 thf(f18,axiom,(
% 2.18/1.74 (prop2setE = ! [X1 : $i,X0 : $o] : ((in @ X1 @ (prop2set @ X0)) => X0))),
% 2.18/1.74 file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',prop2setE)).
% 2.18/1.74 thf(f459,plain,(
% 2.18/1.74 (prop2setE = $true)),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f333])).
% 2.18/1.74 thf(f2795,plain,(
% 2.18/1.74 ~spl3_2),
% 2.18/1.74 inference(avatar_contradiction_clause,[status(thm)],[f2794])).
% 2.18/1.74 thf(f2794,plain,(
% 2.18/1.74 $false | ~spl3_2),
% 2.18/1.74 inference(trivial_inequality_removal,[status(thm)],[f2793])).
% 2.18/1.74 thf(f2793,plain,(
% 2.18/1.74 ($false = $true) | ~spl3_2),
% 2.18/1.74 inference(forward_demodulation,[status(thm)],[f2782,f1729])).
% 2.18/1.74 thf(f1729,plain,(
% 2.18/1.74 ($false = (in @ sK2 @ sK1)) | ~spl3_2),
% 2.18/1.74 inference(trivial_inequality_removal,[status(thm)],[f1727])).
% 2.18/1.74 thf(f1727,plain,(
% 2.18/1.74 ($false = (in @ sK2 @ sK1)) | ($true != $true) | ~spl3_2),
% 2.18/1.74 inference(superposition,[status(thm)],[f418,f1683])).
% 2.18/1.74 thf(f1683,plain,(
% 2.18/1.74 ( ! [X3 : $o] : (($true = X3) | ($false = X3)) ) | ~spl3_2),
% 2.18/1.74 inference(avatar_component_clause,[status(thm)],[f1682])).
% 2.18/1.74 thf(f418,plain,(
% 2.18/1.74 ((in @ sK2 @ sK1) != $true)),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f333])).
% 2.18/1.74 thf(f2782,plain,(
% 2.18/1.74 ((in @ sK2 @ sK1) = $true)),
% 2.18/1.74 inference(trivial_inequality_removal,[status(thm)],[f2772])).
% 2.18/1.74 thf(f2772,plain,(
% 2.18/1.74 ((in @ sK2 @ sK1) = $true) | ($false = $true)),
% 2.18/1.74 inference(superposition,[status(thm)],[f846,f1003])).
% 2.18/1.74 thf(f1003,plain,(
% 2.18/1.74 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : (($false = (in @ X2 @ (dsetconstr @ X3 @ X1))) | ((in @ X2 @ X3) = $true)) )),
% 2.18/1.74 inference(binary_proxy_clausification,[status(thm)],[f1002])).
% 2.18/1.74 thf(f1002,plain,(
% 2.18/1.74 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((in @ X2 @ (dsetconstr @ X3 @ X1)) => (in @ X2 @ X3)) = $true)) )),
% 2.18/1.74 inference(beta_eta_normalization,[status(thm)],[f1001])).
% 2.18/1.74 thf(f1001,plain,(
% 2.18/1.74 ( ! [X2 : $i,X3 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: ((in @ X2 @ (dsetconstr @ Y0 @ X1)) => (in @ X2 @ Y0))) @ X3) = $true)) )),
% 2.18/1.74 inference(pi_clausification,[status(thm)],[f1000])).
% 2.18/1.74 thf(f1000,plain,(
% 2.18/1.74 ( ! [X2 : $i,X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ (dsetconstr @ Y0 @ X1)) => (in @ X2 @ Y0)))) = $true)) )),
% 2.18/1.74 inference(beta_eta_normalization,[status(thm)],[f999])).
% 2.18/1.74 thf(f999,plain,(
% 2.18/1.74 ( ! [X2 : $i,X1 : $i > $o] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (dsetconstr @ Y1 @ X1)) => (in @ Y0 @ Y1))))) @ X2) = $true)) )),
% 2.18/1.74 inference(pi_clausification,[status(thm)],[f998])).
% 2.18/1.74 thf(f998,plain,(
% 2.18/1.74 ( ! [X1 : $i > $o] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ (dsetconstr @ Y1 @ X1)) => (in @ Y0 @ Y1)))))) = $true)) )),
% 2.18/1.74 inference(beta_eta_normalization,[status(thm)],[f997])).
% 2.18/1.74 thf(f997,plain,(
% 2.18/1.74 ( ! [X1 : $i > $o] : ((((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (in @ Y1 @ Y2))))))) @ X1) = $true)) )),
% 2.18/1.74 inference(pi_clausification,[status(thm)],[f996])).
% 2.18/1.74 thf(f996,plain,(
% 2.18/1.74 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ Y0)) => (in @ Y1 @ Y2)))))))) = $true)),
% 2.18/1.74 inference(beta_eta_normalization,[status(thm)],[f609])).
% 2.18/1.74 thf(f609,plain,(
% 2.18/1.74 ((!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (in @ Y1 @ Y2)))))))) = $true)),
% 2.18/1.74 inference(definition_unfolding,[status(thm)],[f499,f474])).
% 2.18/1.74 thf(f474,plain,(
% 2.18/1.74 (dsetconstrEL = $true)),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f333])).
% 2.18/1.74 thf(f499,plain,(
% 2.18/1.74 (dsetconstrEL = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (in @ Y1 @ Y2)))))))))),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f269])).
% 2.18/1.74 thf(f269,plain,(
% 2.18/1.74 (dsetconstrEL = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ (dsetconstr @ Y2 @ (^[Y3 : $i]: (Y0 @ Y3)))) => (in @ Y1 @ Y2)))))))))),
% 2.18/1.74 inference(fool_elimination,[status(thm)],[f268])).
% 2.18/1.74 thf(f268,plain,(
% 2.18/1.74 (! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X1 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X2 @ X3)))) => (in @ X1 @ X0)) = dsetconstrEL)),
% 2.18/1.74 inference(rectify,[status(thm)],[f15])).
% 2.18/1.74 thf(f15,axiom,(
% 2.18/1.74 (! [X3 : $i,X1 : $i,X0 : $i > $o] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (in @ X1 @ X3)) = dsetconstrEL)),
% 2.18/1.74 file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',dsetconstrEL)).
% 2.18/1.74 thf(f846,plain,(
% 2.18/1.74 ((in @ sK2 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ Y0 @ sK0)))) = $true)),
% 2.18/1.74 inference(beta_eta_normalization,[status(thm)],[f584])).
% 2.18/1.74 thf(f584,plain,(
% 2.18/1.74 ((in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK1 @ sK0)) = $true)),
% 2.18/1.74 inference(definition_unfolding,[status(thm)],[f419,f550])).
% 2.18/1.74 thf(f550,plain,(
% 2.18/1.74 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f267])).
% 2.18/1.74 thf(f267,plain,(
% 2.18/1.74 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 2.18/1.74 inference(fool_elimination,[status(thm)],[f266])).
% 2.18/1.74 thf(f266,plain,(
% 2.18/1.74 ((^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))) = binintersect)),
% 2.18/1.74 inference(rectify,[status(thm)],[f108])).
% 2.18/1.74 thf(f108,axiom,(
% 2.18/1.74 ((^[X3 : $i, X4 : $i] : (dsetconstr @ X3 @ (^[X1 : $i] : (in @ X1 @ X4)))) = binintersect)),
% 2.18/1.74 file('/export/starexec/sandbox/tmp/tmp.NobyZbPNbN/DTF2THF_25294.p',binintersect)).
% 2.18/1.74 thf(f419,plain,(
% 2.18/1.74 ((in @ sK2 @ (binintersect @ sK1 @ sK0)) = $true)),
% 2.18/1.74 inference(cnf_transformation,[status(thm)],[f333])).
% 2.18/1.74 % SZS output end Proof for DTF2THF_25294
% 2.18/1.74 % (25514)------------------------------
% 2.18/1.74 % (25514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.18/1.74 % (25514)Termination reason: Refutation
% 2.18/1.74
% 2.18/1.74 % (25514)Memory used [KB]: 7291
% 2.18/1.74 % (25514)Time elapsed: 0.194 s
% 2.18/1.74 % (25514)Instructions burned: 467 (million)
% 2.18/1.74 % (25514)------------------------------
% 2.18/1.74 % (25514)------------------------------
% 2.18/1.74 % (25484)Success in time 0.336 s
%------------------------------------------------------------------------------