%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU595^1 : 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 : n017.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 09:35:29 AM UTC 2026
% Result : Theorem 2.24s 1.77s
% Output : Refutation 2.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 9
% Syntax : Number of formulae : 86 ( 56 unt; 0 typ; 2 def)
% Number of atoms : 2119 ( 548 equ; 0 cnn)
% Maximal formula atoms : 113 ( 24 avg)
% Number of connectives : 1523 ( 22 ~; 31 |; 338 &; 526 @)
% ( 2 <=>; 547 =>; 0 <=; 0 <~>)
% Maximal formula depth : 120 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 184 ( 180 usr; 121 con; 0-4 aty)
% ( 57 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 217 ( 90 ^; 118 !; 9 ?; 217 :)
% 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_149,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_150,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_151,type,
sK6: ( $i > $o ) > $i > $i ).
thf(func_def_152,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK8: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_154,type,
sK9: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_155,type,
sK10: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_156,type,
sK11: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_157,type,
sK12: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_158,type,
sK13: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_159,type,
sK14: $i > $i > $i ).
thf(func_def_160,type,
sK15: $i > $i > $i ).
thf(func_def_161,type,
sK16: $i > $i > $i ).
thf(func_def_162,type,
sK17: $o > $i > $i > $i ).
thf(func_def_163,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_164,type,
sK19: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_165,type,
sK20: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_166,type,
sK21: $i > $i ).
thf(func_def_167,type,
sK22: $i > $i > $i ).
thf(func_def_168,type,
sK23: $i > $i > $i ).
thf(func_def_169,type,
sK24: $i > $i > $i ).
thf(func_def_170,type,
sK25: $i > ( $i > $o ) > $i ).
thf(func_def_171,type,
sK26: $i > $i ).
thf(func_def_172,type,
sK27: $i > $i ).
thf(func_def_173,type,
sK28: $i > $i ).
thf(func_def_174,type,
sK29: $i > $i > $i ).
thf(func_def_175,type,
sK30: $i > $i > $i ).
thf(func_def_176,type,
sK31: $i > $i > $i ).
thf(func_def_177,type,
sK32: $i > $i ).
thf(func_def_178,type,
sK33: $i > $i > $i ).
thf(func_def_179,type,
sK34: $i > $i > $i ).
thf(func_def_180,type,
sK35: $i > $i > $i ).
thf(func_def_181,type,
sK36: $i > $i > $i > $i ).
thf(func_def_182,type,
sK37: $i > $i ).
thf(func_def_183,type,
sK38: ( $i > $i > $o ) > $i > $i ).
thf(func_def_184,type,
sK39: ( $i > $i > $o ) > $i > $i ).
thf(func_def_185,type,
sK40: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_186,type,
sK41: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_187,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_188,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_189,type,
sK44: ( $i > $o ) > $i ).
thf(func_def_190,type,
sK45: ( $i > $o ) > $i > $i ).
thf(func_def_191,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_192,type,
sK47: ( $i > $o ) > $i > $i ).
thf(func_def_193,type,
sK48: $i > $i ).
thf(func_def_194,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_195,type,
ph50:
!>[X0: $tType] : X0 ).
thf(f3113,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1752,f2159,f3112]) ).
thf(f3112,plain,
~ spl3_1,
inference(avatar_contradiction_clause,[status(thm)],[f3111]) ).
thf(f3111,plain,
( $false
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f3110]) ).
thf(f3110,plain,
( ( $true = $false )
| ~ spl3_1 ),
inference(forward_demodulation,[status(thm)],[f3098,f2168]) ).
thf(f2168,plain,
( ( ( in @ sK0 @ sK2 )
= $false )
| ~ spl3_1 ),
inference(trivial_inequality_removal,[status(thm)],[f2162]) ).
thf(f2162,plain,
( ( $true != $true )
| ( ( in @ sK0 @ sK2 )
= $false )
| ~ spl3_1 ),
inference(superposition,[status(thm)],[f562,f1736]) ).
thf(f1736,plain,
( ! [X4: $o] :
( ( $true = X4 )
| ( $false = X4 ) )
| ~ spl3_1 ),
inference(avatar_component_clause,[status(thm)],[f1735]) ).
thf(f1735,definition,
( spl3_1
<=> ! [X4: $o] :
( ( $true = X4 )
| ( $false = X4 ) ) ),
introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition]) ).
thf(f562,plain,
( ( in @ sK0 @ sK2 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f345]) ).
thf(f345,plain,
( ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( subsetI2 = $true )
& ( noeltsimpempty = $true )
& ( upairsetIL = $true )
& ( upairset2IR = $true )
& ( binunionRsub = $true )
& ( ( in @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) )
& ( notequalI2 = $true )
& ( binunionE = $true )
& ( setbeta = $true )
& ( binunionEcases = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyI1 = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan3 = $true )
& ( emptyI = $true )
& ( eqimpsubset2 = $true )
& ( foundationAx = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( subsetRefl = $true )
& ( setadjoinAx = $true )
& ( singletonsswitch = $true )
& ( omega0Ax = $true )
& ( setadjoinIR = $true )
& ( powersetAx = $true )
& ( setextsub = $true )
& ( setext = $true )
& ( sepSubset = $true )
& ( upairsetE = $true )
& ( powerset__Cong = $true )
& ( emptyinPowerset = $true )
& ( emptyInPowerset = $true )
& ( emptysetsubset = $true )
& ( subsetTrans = $true )
& ( setunionE = $true )
& ( replAx = $true )
& ( setadjoinSub = $true )
& ( sepInPowerset = $true )
& ( setadjoinE = $true )
& ( omegaIndAx = $true )
& ( uniqinunit = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( exuEu = $true )
& ( setadjoinSub2 = $true )
& ( exuI3 = $true )
& ( setextAx = $true )
& ( setadjoinIL = $true )
& ( setunionAx = $true )
& ( exuI2 = $true )
& ( quantDeMorgan4 = $true )
& ( notinemptyset = $true )
& ( powersetE = $true )
& ( subset2powerset = $true )
& ( descr__Cong = $true )
& ( wellorderingAx = $true )
& ( emptyinunitempty = $true )
& ( binintersectLsub = $true )
& ( binunionIL = $true )
& ( subsetI1 = $true )
& ( binintersectI = $true )
& ( emptysetE = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( subsetE = $true )
& ( emptyset__Cong = $true )
& ( exuI1 = $true )
& ( dsetconstrI = $true )
& ( emptysetimpfalse = $true )
& ( emptyE1 = $true )
& ( dsetconstrEL = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( in__Cong = $true )
& ( subsetE2 = $true )
& ( exuE3u = $true )
& ( binintersectEL = $true )
& ( binunionIR = $true )
& ( notsubsetI = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionI = $true )
& ( powersetI1 = $true )
& ( exu__Cong = $true )
& ( omega__Cong = $true )
& ( setoftrueEq = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( exuE2 = $true )
& ( quantDeMorgan2 = $true )
& ( notdexE = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyE1 = $true )
& ( upairsetIR = $true )
& ( inPowerset = $true )
& ( notequalI1 = $true )
& ( eqinunit = $true )
& ( setunion__Cong = $true )
& ( omegaSAx = $true )
& ( exuE3e = $true )
& ( subPowSU = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( vacuousDall = $true )
& ( prop2setE = $true )
& ( prop2setI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f343,f344]) ).
thf(f344,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
=> ( ( ( in @ sK0 @ sK2 )
!= $true )
& ( $true
= ( in @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f343,plain,
( ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( subsetI2 = $true )
& ( noeltsimpempty = $true )
& ( upairsetIL = $true )
& ( upairset2IR = $true )
& ( binunionRsub = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
& ( notequalI2 = $true )
& ( binunionE = $true )
& ( setbeta = $true )
& ( binunionEcases = $true )
& ( dsetconstr__Cong = $true )
& ( nonemptyI1 = $true )
& ( prop2set2propI = $true )
& ( quantDeMorgan3 = $true )
& ( emptyI = $true )
& ( eqimpsubset2 = $true )
& ( foundationAx = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( subsetRefl = $true )
& ( setadjoinAx = $true )
& ( singletonsswitch = $true )
& ( omega0Ax = $true )
& ( setadjoinIR = $true )
& ( powersetAx = $true )
& ( setextsub = $true )
& ( setext = $true )
& ( sepSubset = $true )
& ( upairsetE = $true )
& ( powerset__Cong = $true )
& ( emptyinPowerset = $true )
& ( emptyInPowerset = $true )
& ( emptysetsubset = $true )
& ( subsetTrans = $true )
& ( setunionE = $true )
& ( replAx = $true )
& ( setadjoinSub = $true )
& ( sepInPowerset = $true )
& ( setadjoinE = $true )
& ( omegaIndAx = $true )
& ( uniqinunit = $true )
& ( nonemptyI = $true )
& ( descrp = $true )
& ( exuEu = $true )
& ( setadjoinSub2 = $true )
& ( exuI3 = $true )
& ( setextAx = $true )
& ( setadjoinIL = $true )
& ( setunionAx = $true )
& ( exuI2 = $true )
& ( quantDeMorgan4 = $true )
& ( notinemptyset = $true )
& ( powersetE = $true )
& ( subset2powerset = $true )
& ( descr__Cong = $true )
& ( wellorderingAx = $true )
& ( emptyinunitempty = $true )
& ( binintersectLsub = $true )
& ( binunionIL = $true )
& ( subsetI1 = $true )
& ( binintersectI = $true )
& ( emptysetE = $true )
& ( notinsingleton = $true )
& ( eqimpsubset1 = $true )
& ( subsetE = $true )
& ( emptyset__Cong = $true )
& ( exuI1 = $true )
& ( dsetconstrI = $true )
& ( emptysetimpfalse = $true )
& ( emptyE1 = $true )
& ( dsetconstrEL = $true )
& ( notdallE = $true )
& ( binintersectSubset5 = $true )
& ( in__Cong = $true )
& ( subsetE2 = $true )
& ( exuE3u = $true )
& ( binintersectEL = $true )
& ( binunionIR = $true )
& ( notsubsetI = $true )
& ( subsetemptysetimpeq = $true )
& ( setunionI = $true )
& ( powersetI1 = $true )
& ( exu__Cong = $true )
& ( omega__Cong = $true )
& ( setoftrueEq = $true )
& ( setadjoin__Cong = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( exuE2 = $true )
& ( quantDeMorgan2 = $true )
& ( notdexE = $true )
& ( nonemptyImpWitness = $true )
& ( nonemptyE1 = $true )
& ( upairsetIR = $true )
& ( inPowerset = $true )
& ( notequalI1 = $true )
& ( eqinunit = $true )
& ( setunion__Cong = $true )
& ( omegaSAx = $true )
& ( exuE3e = $true )
& ( subPowSU = $true )
& ( binunionLsub = $true )
& ( powersetsubset = $true )
& ( powersetI = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( vacuousDall = $true )
& ( prop2setE = $true )
& ( prop2setI = $true ) ),
inference(flattening,[status(thm)],[f342]) ).
thf(f342,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X0 @ X2 ) )
& ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) ) )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $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)],[f174]) ).
thf(f174,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 )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X0 @ ( binintersect @ X1 @ X2 ) ) )
=> ( $true
= ( in @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f173]) ).
thf(f173,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
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ ( binintersect @ X1 @ X2 ) )
=> ( in @ X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f116]) ).
thf(f116,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f115]) ).
thf(f115,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ! [X1: $i,X3: $i,X4: $i] :
( ( in @ X1 @ ( binintersect @ X3 @ X4 ) )
=> ( in @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',binintersectER) ).
thf(f3098,plain,
( ( in @ sK0 @ sK2 )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f3097]) ).
thf(f3097,plain,
( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ sK2 )
@ sK0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f3086]) ).
thf(f3086,plain,
( ( $true
= ( ^ [Y0: $i] : ( in @ Y0 @ sK2 )
@ sK0 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f1653,f1524]) ).
thf(f1524,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( $false
= ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) ) )
| ( $true
= ( X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1523]) ).
thf(f1523,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
=> ( X3 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1522]) ).
thf(f1522,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f1521]) ).
thf(f1521,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1520]) ).
thf(f1520,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1519]) ).
thf(f1519,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1518]) ).
thf(f1518,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1517]) ).
thf(f1517,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( Y2 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f683]) ).
thf(f683,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f461,f368]) ).
thf(f368,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f259]) ).
thf(f259,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f258]) ).
thf(f258,plain,
( dsetconstrER
= ( ! [X0: $i > $o,X1: $i,X2: $i] :
( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
( dsetconstrER
= ( ! [X0: $i > $o,X1: $i,X3: $i] :
( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',dsetconstrER) ).
thf(f461,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f345]) ).
thf(f1653,plain,
( $true
= ( in @ sK0
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ Y0 @ sK2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f584]) ).
thf(f584,plain,
( $true
= ( in @ sK0
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK1
@ sK2 ) ) ),
inference(definition_unfolding,[status(thm)],[f561,f411]) ).
thf(f411,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f293]) ).
thf(f293,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f292]) ).
thf(f292,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.rHmzVjta6m/DTF2THF_13088.p',binintersect) ).
thf(f561,plain,
( $true
= ( in @ sK0 @ ( binintersect @ sK1 @ sK2 ) ) ),
inference(cnf_transformation,[status(thm)],[f345]) ).
thf(f2159,plain,
~ spl3_5,
inference(avatar_contradiction_clause,[status(thm)],[f2158]) ).
thf(f2158,plain,
( $false
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f2157]) ).
thf(f2157,plain,
( ( $true = $false )
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f601,f1957]) ).
thf(f1957,plain,
( ! [X2: $i,X3: $i] :
( ( in @ X2 @ X3 )
= $false )
| ~ spl3_5 ),
inference(trivial_inequality_removal,[status(thm)],[f1956]) ).
thf(f1956,plain,
( ! [X2: $i,X3: $i] :
( ( ( in @ X2 @ X3 )
= $false )
| ( $true = $false ) )
| ~ spl3_5 ),
inference(forward_demodulation,[status(thm)],[f1162,f1751]) ).
thf(f1751,plain,
( ! [X2: $i,X3: $i,X1: $i] :
( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
= $false )
| ~ spl3_5 ),
inference(avatar_component_clause,[status(thm)],[f1750]) ).
thf(f1750,definition,
( spl3_5
<=> ! [X2: $i,X1: $i,X3: $i] :
( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition]) ).
thf(f1162,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( binunion @ X3 @ X1 ) )
= $true )
| ( ( in @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1161]) ).
thf(f1161,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( binunion @ X3 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1160]) ).
thf(f1160,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( binunion @ Y0 @ X1 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f1159]) ).
thf(f1159,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ Y0 )
=> ( in @ X2 @ ( binunion @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1158]) ).
thf(f1158,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binunion @ Y1 @ X1 ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1157]) ).
thf(f1157,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ Y1 )
=> ( in @ Y0 @ ( binunion @ Y1 @ X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1156]) ).
thf(f1156,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y2 @ Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f637]) ).
thf(f637,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y2 @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f508,f347]) ).
thf(f347,plain,
( binunionIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f151]) ).
thf(f151,plain,
( binunionIL
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y2 )
=> ( in @ Y1 @ ( binunion @ Y2 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f150]) ).
thf(f150,plain,
( binunionIL
= ( ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( in @ X1 @ ( binunion @ X0 @ X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f101]) ).
thf(f101,axiom,
( binunionIL
= ( ! [X3: $i,X1: $i,X4: $i] :
( ( in @ X1 @ X3 )
=> ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',binunionIL) ).
thf(f508,plain,
binunionIL = $true,
inference(cnf_transformation,[status(thm)],[f345]) ).
thf(f601,plain,
( ( in @ emptyset @ omega )
= $true ),
inference(definition_unfolding,[status(thm)],[f544,f386]) ).
thf(f386,plain,
( omega0Ax
= ( in @ emptyset @ omega ) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
thf(f7,axiom,
( omega0Ax
= ( in @ emptyset @ omega ) ),
file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',omega0Ax) ).
thf(f544,plain,
omega0Ax = $true,
inference(cnf_transformation,[status(thm)],[f345]) ).
thf(f1752,plain,
( spl3_1
| spl3_5 ),
inference(avatar_split_clause,[status(thm)],[f1204,f1750,f1735]) ).
thf(f1204,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true = X4 )
| ( $false = X4 )
| ( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
= $false ) ),
inference(duplicate_literal_removal,[status(thm)],[f1202]) ).
thf(f1202,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
= $false )
| ( $true = X4 )
| ( $false = X4 )
| ( $false = X4 ) ),
inference(binary_proxy_clausification,[status(thm)],[f1201]) ).
thf(f1201,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
= $false )
| ( $true = X4 )
| ( $false = X4 )
| ( $false
= ( ( in @ X1 @ X3 )
=> X4 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1196]) ).
thf(f1196,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( ( ( in @ X1 @ X3 )
=> X4 )
=> X4 )
= $true )
| ( $false = X4 )
| ( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1195]) ).
thf(f1195,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( ( in @ X1 @ X2 )
=> X4 )
= $false )
| ( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
= $false )
| ( ( ( ( in @ X1 @ X3 )
=> X4 )
=> X4 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1194]) ).
thf(f1194,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( $true
= ( ( ( in @ X1 @ X2 )
=> X4 )
=> ( ( ( in @ X1 @ X3 )
=> X4 )
=> X4 ) ) )
| ( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1193]) ).
thf(f1193,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X1 @ X2 )
=> X4 )
=> ( ( ( in @ X1 @ X3 )
=> X4 )
=> X4 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1192]) ).
thf(f1192,plain,
! [X2: $i,X3: $i,X1: $i,X4: $o] :
( ( ^ [Y0: $o] :
( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X1 @ X2 )
=> Y0 )
=> ( ( ( in @ X1 @ X3 )
=> Y0 )
=> Y0 ) ) )
@ X4 )
= $true ),
inference(pi_clausification,[status(thm)],[f1191]) ).
thf(f1191,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( !! @ $o
@ ^ [Y0: $o] :
( ( in @ X1 @ ( binunion @ X2 @ X3 ) )
=> ( ( ( in @ X1 @ X2 )
=> Y0 )
=> ( ( ( in @ X1 @ X3 )
=> Y0 )
=> Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1190]) ).
thf(f1190,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ X1 @ ( binunion @ X2 @ Y0 ) )
=> ( ( ( in @ X1 @ X2 )
=> Y1 )
=> ( ( ( in @ X1 @ Y0 )
=> Y1 )
=> Y1 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f1189]) ).
thf(f1189,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $o
@ ^ [Y1: $o] :
( ( in @ X1 @ ( binunion @ X2 @ Y0 ) )
=> ( ( ( in @ X1 @ X2 )
=> Y1 )
=> ( ( ( in @ X1 @ Y0 )
=> Y1 )
=> Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1188]) ).
thf(f1188,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ X1 @ ( binunion @ Y0 @ Y1 ) )
=> ( ( ( in @ X1 @ Y0 )
=> Y2 )
=> ( ( ( in @ X1 @ Y1 )
=> Y2 )
=> Y2 ) ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1187]) ).
thf(f1187,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $o
@ ^ [Y2: $o] :
( ( in @ X1 @ ( binunion @ Y0 @ Y1 ) )
=> ( ( ( in @ X1 @ Y0 )
=> Y2 )
=> ( ( ( in @ X1 @ Y1 )
=> Y2 )
=> Y2 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1186]) ).
thf(f1186,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $o
@ ^ [Y3: $o] :
( ( in @ Y0 @ ( binunion @ Y1 @ Y2 ) )
=> ( ( ( in @ Y0 @ Y1 )
=> Y3 )
=> ( ( ( in @ Y0 @ Y2 )
=> Y3 )
=> Y3 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f588]) ).
thf(f588,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $o
@ ^ [Y3: $o] :
( ( in @ Y0 @ ( binunion @ Y1 @ Y2 ) )
=> ( ( ( in @ Y0 @ Y1 )
=> Y3 )
=> ( ( ( in @ Y0 @ Y2 )
=> Y3 )
=> Y3 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f557,f445]) ).
thf(f445,plain,
( binunionEcases
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $o
@ ^ [Y3: $o] :
( ( in @ Y0 @ ( binunion @ Y1 @ Y2 ) )
=> ( ( ( in @ Y0 @ Y1 )
=> Y3 )
=> ( ( ( in @ Y0 @ Y2 )
=> Y3 )
=> Y3 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f239]) ).
thf(f239,plain,
( binunionEcases
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( !! @ $o
@ ^ [Y3: $o] :
( ( in @ Y0 @ ( binunion @ Y1 @ Y2 ) )
=> ( ( ( in @ Y0 @ Y1 )
=> Y3 )
=> ( ( ( in @ Y0 @ Y2 )
=> Y3 )
=> Y3 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f238]) ).
thf(f238,plain,
( binunionEcases
= ( ! [X0: $o,X1: $i,X2: $i,X3: $i] :
( ( in @ X3 @ ( binunion @ X2 @ X1 ) )
=> ( ( ( in @ X3 @ X2 )
=> X0 )
=> ( ( ( in @ X3 @ X1 )
=> X0 )
=> X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f104]) ).
thf(f104,axiom,
( binunionEcases
= ( ! [X0: $o,X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ ( binunion @ X3 @ X4 ) )
=> ( ( ( in @ X1 @ X3 )
=> X0 )
=> ( ( ( in @ X1 @ X4 )
=> X0 )
=> X0 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',binunionEcases) ).
thf(f557,plain,
binunionEcases = $true,
inference(cnf_transformation,[status(thm)],[f345]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU595^1 : 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
% 0.17/0.34 % Computer : n017.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:26:26 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU595^1 : TPTP v9.2.1. Released v3.7.0.
% 0.28/0.47 % Domain : Set Theory
% 0.28/0.47 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.28/0.47 % Version : Especial.
% 0.28/0.47 % English : (! A:i.! B:i.! x:i.in x (binintersect A B) -> in x B)
% 0.28/0.47
% 0.28/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.28/0.47 % Source : [Bro08]
% 0.28/0.47 % Names : ZFC097g [Bro08]
% 0.28/0.47
% 0.28/0.47 % Status : Theorem
% 0.28/0.47 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.30 v8.2.0, 0.54 v8.1.0, 0.45 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 v5.2.0, 0.80 v5.0.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.28/0.47 % Syntax : Number of formulae : 243 ( 114 unt; 128 typ; 114 def)
% 0.28/0.47 % Number of atoms : 607 ( 165 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 113 ( 5 avg)
% 0.28/0.47 % Number of connectives : 954 ( 29 ~; 6 |; 27 &; 607 @)
% 0.28/0.47 % ( 14 <=>; 271 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 119 ( 2 avg)
% 0.28/0.47 % Number of types : 2 ( 0 usr)
% 0.28/0.47 % Number of type conns : 59 ( 59 >; 0 *; 0 +; 0 <<)
% 0.28/0.47 % Number of symbols : 131 ( 128 usr; 115 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 334 ( 33 ^; 273 !; 28 ?; 334 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=168
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 thf(in_type,type,
% 0.28/0.47 in: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu_type,type,
% 0.28/0.47 exu: ( $i > $o ) > $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu,definition,
% 0.28/0.47 ( exu
% 0.28/0.47 = ( ^ [Xphi: $i > $o] :
% 0.28/0.47 ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextAx_type,type,
% 0.28/0.47 setextAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextAx,definition,
% 0.28/0.47 ( setextAx
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xx @ B ) )
% 0.28/0.47 => ( A = B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset_type,type,
% 0.28/0.47 emptyset: $i ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetAx_type,type,
% 0.28/0.47 emptysetAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetAx,definition,
% 0.28/0.47 ( emptysetAx
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin_type,type,
% 0.28/0.47 setadjoin: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinAx_type,type,
% 0.28/0.47 setadjoinAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinAx,definition,
% 0.28/0.47 ( setadjoinAx
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 <=> ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powerset_type,type,
% 0.28/0.47 powerset: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(powersetAx_type,type,
% 0.28/0.47 powersetAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetAx,definition,
% 0.28/0.47 ( powersetAx
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 <=> ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion_type,type,
% 0.28/0.47 setunion: $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(setunionAx_type,type,
% 0.28/0.47 setunionAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionAx,definition,
% 0.28/0.47 ( setunionAx
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 <=> ? [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omega_type,type,
% 0.28/0.47 omega: $i ).
% 0.28/0.47
% 0.28/0.47 thf(omega0Ax_type,type,
% 0.28/0.47 omega0Ax: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omega0Ax,definition,
% 0.28/0.47 ( omega0Ax
% 0.28/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omegaSAx_type,type,
% 0.28/0.47 omegaSAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omegaSAx,definition,
% 0.28/0.47 ( omegaSAx
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ omega )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omegaIndAx_type,type,
% 0.28/0.47 omegaIndAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omegaIndAx,definition,
% 0.28/0.47 ( omegaIndAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( ( in @ emptyset @ A )
% 0.28/0.47 & ! [Xx: $i] :
% 0.28/0.47 ( ( ( in @ Xx @ omega )
% 0.28/0.47 & ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ omega )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(replAx_type,type,
% 0.28/0.47 replAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(replAx,definition,
% 0.28/0.47 ( replAx
% 0.28/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.28/0.47 => ? [B: $i] :
% 0.28/0.47 ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 <=> ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(foundationAx_type,type,
% 0.28/0.47 foundationAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(foundationAx,definition,
% 0.28/0.47 ( foundationAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ? [B: $i] :
% 0.28/0.47 ( ( in @ B @ A )
% 0.28/0.47 & ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderingAx_type,type,
% 0.28/0.47 wellorderingAx: $o ).
% 0.28/0.47
% 0.28/0.47 thf(wellorderingAx,definition,
% 0.28/0.47 ( wellorderingAx
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ? [B: $i] :
% 0.28/0.47 ( ! [C: $i] :
% 0.28/0.47 ( ( in @ C @ B )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ A ) ) )
% 0.28/0.47 & ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( ( in @ Xx @ A )
% 0.28/0.47 & ( in @ Xy @ A ) )
% 0.28/0.47 => ( ! [C: $i] :
% 0.28/0.47 ( ( in @ C @ B )
% 0.28/0.47 => ( ( in @ Xx @ C )
% 0.28/0.47 <=> ( in @ Xy @ C ) ) )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 & ! [C: $i,D: $i] :
% 0.28/0.47 ( ( ( in @ C @ B )
% 0.28/0.47 & ( in @ D @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ D ) )
% 0.28/0.47 | ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ D )
% 0.28/0.47 => ( in @ Xx @ C ) ) ) )
% 0.28/0.47 & ! [C: $i] :
% 0.28/0.47 ( ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ C )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.28/0.47 => ? [D: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ D @ B )
% 0.28/0.47 & ( in @ Xx @ C )
% 0.28/0.47 & ~ ? [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ D )
% 0.28/0.47 & ( in @ Xy @ C ) )
% 0.28/0.47 & ! [E: $i] :
% 0.28/0.47 ( ( in @ E @ B )
% 0.28/0.47 => ( ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ E )
% 0.28/0.47 => ( in @ Xy @ D ) )
% 0.28/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(descr_type,type,
% 0.28/0.47 descr: ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(descrp_type,type,
% 0.28/0.47 descrp: $o ).
% 0.28/0.47
% 0.28/0.47 thf(descrp,definition,
% 0.28/0.47 ( descrp
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ( Xphi
% 0.28/0.47 @ ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr_type,type,
% 0.28/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrI_type,type,
% 0.28/0.47 dsetconstrI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrI,definition,
% 0.28/0.47 ( dsetconstrI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrEL_type,type,
% 0.28/0.47 dsetconstrEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrEL,definition,
% 0.28/0.47 ( dsetconstrEL
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER_type,type,
% 0.28/0.47 dsetconstrER: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstrER,definition,
% 0.28/0.47 ( dsetconstrER
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE1_type,type,
% 0.28/0.47 exuE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE1,definition,
% 0.28/0.47 ( exuE1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set_type,type,
% 0.28/0.47 prop2set: $o > $i ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE_type,type,
% 0.28/0.47 prop2setE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setE,definition,
% 0.28/0.47 ( prop2setE
% 0.28/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE_type,type,
% 0.28/0.47 emptysetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetE,definition,
% 0.28/0.47 ( emptysetE
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse_type,type,
% 0.28/0.47 emptysetimpfalse: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetimpfalse,definition,
% 0.28/0.47 ( emptysetimpfalse
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => $false ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset_type,type,
% 0.28/0.47 notinemptyset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinemptyset,definition,
% 0.28/0.47 ( notinemptyset
% 0.28/0.47 = ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e_type,type,
% 0.28/0.47 exuE3e: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3e,definition,
% 0.28/0.47 ( exuE3e
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setext_type,type,
% 0.28/0.47 setext: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setext,definition,
% 0.28/0.47 ( setext
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI_type,type,
% 0.28/0.47 emptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyI,definition,
% 0.28/0.47 ( emptyI
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty_type,type,
% 0.28/0.47 noeltsimpempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(noeltsimpempty,definition,
% 0.28/0.47 ( noeltsimpempty
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ~ ( in @ Xx @ A )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta_type,type,
% 0.28/0.47 setbeta: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setbeta,definition,
% 0.28/0.47 ( setbeta
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.28/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty_type,type,
% 0.28/0.47 nonempty: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonempty,definition,
% 0.28/0.47 ( nonempty
% 0.28/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1_type,type,
% 0.28/0.47 nonemptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyE1,definition,
% 0.28/0.47 ( nonemptyE1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI_type,type,
% 0.28/0.47 nonemptyI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI,definition,
% 0.28/0.47 ( nonemptyI
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 => ( nonempty
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1_type,type,
% 0.28/0.47 nonemptyI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyI1,definition,
% 0.28/0.47 ( nonemptyI1
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.28/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL_type,type,
% 0.28/0.47 setadjoinIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIL,definition,
% 0.28/0.47 ( setadjoinIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty_type,type,
% 0.28/0.47 emptyinunitempty: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinunitempty,definition,
% 0.28/0.47 ( emptyinunitempty
% 0.28/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR_type,type,
% 0.28/0.47 setadjoinIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinIR,definition,
% 0.28/0.47 ( setadjoinIR
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ A )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE_type,type,
% 0.28/0.47 setadjoinE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinE,definition,
% 0.28/0.47 ( setadjoinE
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ( ( Xy = Xx )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xy @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr_type,type,
% 0.28/0.47 setadjoinOr: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinOr,definition,
% 0.28/0.47 ( setadjoinOr
% 0.28/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.28/0.47 => ( ( Xy = Xx )
% 0.28/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq_type,type,
% 0.28/0.47 setoftrueEq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setoftrueEq,definition,
% 0.28/0.47 ( setoftrueEq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : $true )
% 0.28/0.47 = A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI_type,type,
% 0.28/0.47 powersetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI,definition,
% 0.28/0.47 ( powersetI
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset_type,type,
% 0.28/0.47 emptyinPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyinPowerset,definition,
% 0.28/0.47 ( emptyinPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset_type,type,
% 0.28/0.47 emptyInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyInPowerset,definition,
% 0.28/0.47 ( emptyInPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE_type,type,
% 0.28/0.47 powersetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE,definition,
% 0.28/0.47 ( powersetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI_type,type,
% 0.28/0.47 setunionI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionI,definition,
% 0.28/0.47 ( setunionI
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE_type,type,
% 0.28/0.47 setunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunionE,definition,
% 0.28/0.47 ( setunionE
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.28/0.47 => ! [Xphi: $o] :
% 0.28/0.47 ( ! [B: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( ( in @ B @ A )
% 0.28/0.47 => Xphi ) )
% 0.28/0.47 => Xphi ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU_type,type,
% 0.28/0.47 subPowSU: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subPowSU,definition,
% 0.28/0.47 ( subPowSU
% 0.28/0.47 = ( ! [A: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2_type,type,
% 0.28/0.47 exuE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE2,definition,
% 0.28/0.47 ( exuE2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness_type,type,
% 0.28/0.47 nonemptyImpWitness: $o ).
% 0.28/0.47
% 0.28/0.47 thf(nonemptyImpWitness,definition,
% 0.28/0.47 ( nonemptyImpWitness
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( nonempty @ A )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & $true ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit_type,type,
% 0.28/0.47 uniqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(uniqinunit,definition,
% 0.28/0.47 ( uniqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton_type,type,
% 0.28/0.47 notinsingleton: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notinsingleton,definition,
% 0.28/0.47 ( notinsingleton
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx != Xy )
% 0.28/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit_type,type,
% 0.28/0.47 eqinunit: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqinunit,definition,
% 0.28/0.47 ( eqinunit
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch_type,type,
% 0.28/0.47 singletonsswitch: $o ).
% 0.28/0.47
% 0.28/0.47 thf(singletonsswitch,definition,
% 0.28/0.47 ( singletonsswitch
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.28/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE_type,type,
% 0.28/0.47 upairsetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetE,definition,
% 0.28/0.47 ( upairsetE
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.28/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.28/0.47 => ( ( Xz = Xx )
% 0.28/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIL_type,type,
% 0.28/0.47 upairsetIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIL,definition,
% 0.28/0.47 ( upairsetIL
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIR_type,type,
% 0.28/0.47 upairsetIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairsetIR,definition,
% 0.28/0.47 ( upairsetIR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyE1_type,type,
% 0.28/0.47 emptyE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyE1,definition,
% 0.28/0.47 ( emptyE1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ( ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = emptyset )
% 0.28/0.47 => $false ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(vacuousDall_type,type,
% 0.28/0.47 vacuousDall: $o ).
% 0.28/0.47
% 0.28/0.47 thf(vacuousDall,definition,
% 0.28/0.47 ( vacuousDall
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ emptyset )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan1_type,type,
% 0.28/0.47 quantDeMorgan1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan1,definition,
% 0.28/0.47 ( quantDeMorgan1
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan2_type,type,
% 0.28/0.47 quantDeMorgan2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan2,definition,
% 0.28/0.47 ( quantDeMorgan2
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan3_type,type,
% 0.28/0.47 quantDeMorgan3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan3,definition,
% 0.28/0.47 ( quantDeMorgan3
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4_type,type,
% 0.28/0.47 quantDeMorgan4: $o ).
% 0.28/0.47
% 0.28/0.47 thf(quantDeMorgan4,definition,
% 0.28/0.47 ( quantDeMorgan4
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) )
% 0.28/0.47 => ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI_type,type,
% 0.28/0.47 prop2setI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2setI,definition,
% 0.28/0.47 ( prop2setI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(set2prop_type,type,
% 0.28/0.47 set2prop: $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI_type,type,
% 0.28/0.47 prop2set2propI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(prop2set2propI,definition,
% 0.28/0.47 ( prop2set2propI
% 0.28/0.47 = ( ! [Xphi: $o] :
% 0.28/0.47 ( Xphi
% 0.28/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE_type,type,
% 0.28/0.47 notdexE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdexE,definition,
% 0.28/0.47 ( notdexE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE_type,type,
% 0.28/0.47 notdallE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notdallE,definition,
% 0.28/0.47 ( notdallE
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( ~ ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( Xphi @ Xx ) )
% 0.28/0.47 => ? [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1_type,type,
% 0.28/0.47 exuI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI1,definition,
% 0.28/0.47 ( exuI1
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 & ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3_type,type,
% 0.28/0.47 exuI3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI3,definition,
% 0.28/0.47 ( exuI3
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.28/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2_type,type,
% 0.28/0.47 exuI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuI2,definition,
% 0.28/0.47 ( exuI2
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ? [Xx: $i] :
% 0.28/0.47 ! [Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xy )
% 0.28/0.47 <=> ( Xy = Xx ) )
% 0.28/0.47 => ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP_type,type,
% 0.28/0.47 inCongP: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inCongP,definition,
% 0.28/0.47 ( inCongP
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong_type,type,
% 0.28/0.47 in__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(in__Cong,definition,
% 0.28/0.47 ( in__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u_type,type,
% 0.28/0.47 exuE3u: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuE3u,definition,
% 0.28/0.47 ( exuE3u
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong_type,type,
% 0.28/0.47 exu__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exu__Cong,definition,
% 0.28/0.47 ( exu__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 <=> ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong_type,type,
% 0.28/0.47 emptyset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptyset__Cong,definition,
% 0.28/0.47 ( emptyset__Cong
% 0.28/0.47 = ( emptyset = emptyset ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong_type,type,
% 0.28/0.47 setadjoin__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoin__Cong,definition,
% 0.28/0.47 ( setadjoin__Cong
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ! [Xz: $i,Xu: $i] :
% 0.28/0.47 ( ( Xz = Xu )
% 0.28/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.28/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powerset__Cong_type,type,
% 0.28/0.47 powerset__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powerset__Cong,definition,
% 0.28/0.47 ( powerset__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( powerset @ A )
% 0.28/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong_type,type,
% 0.28/0.47 setunion__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setunion__Cong,definition,
% 0.28/0.47 ( setunion__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( ( setunion @ A )
% 0.28/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(omega__Cong_type,type,
% 0.28/0.47 omega__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(omega__Cong,definition,
% 0.28/0.47 ( omega__Cong
% 0.28/0.47 = ( omega = omega ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(exuEu_type,type,
% 0.28/0.47 exuEu: $o ).
% 0.28/0.47
% 0.28/0.47 thf(exuEu,definition,
% 0.28/0.47 ( exuEu
% 0.28/0.47 = ( ! [Xphi: $i > $o] :
% 0.28/0.47 ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xphi @ Xx )
% 0.28/0.47 => ( ( Xphi @ Xy )
% 0.28/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(descr__Cong_type,type,
% 0.28/0.47 descr__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(descr__Cong,definition,
% 0.28/0.47 ( descr__Cong
% 0.28/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.28/0.47 ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 => ( ( exu
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.28/0.47 => ( ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = ( descr
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr__Cong_type,type,
% 0.28/0.47 dsetconstr__Cong: $o ).
% 0.28/0.47
% 0.28/0.47 thf(dsetconstr__Cong,definition,
% 0.28/0.47 ( dsetconstr__Cong
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ! [Xy: $i] :
% 0.28/0.47 ( ( in @ Xy @ B )
% 0.28/0.47 => ( ( Xx = Xy )
% 0.28/0.47 => ( ( Xphi @ Xx )
% 0.28/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.28/0.47 => ( ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 = ( dsetconstr @ B
% 0.28/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subset_type,type,
% 0.28/0.47 subset: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(disjoint_type,type,
% 0.28/0.47 disjoint: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(setsmeet_type,type,
% 0.28/0.47 setsmeet: $i > $i > $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI1_type,type,
% 0.28/0.47 subsetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI1,definition,
% 0.28/0.47 ( subsetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset2_type,type,
% 0.28/0.47 eqimpsubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset2,definition,
% 0.28/0.47 ( eqimpsubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset1_type,type,
% 0.28/0.47 eqimpsubset1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(eqimpsubset1,definition,
% 0.28/0.47 ( eqimpsubset1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( A = B )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI2_type,type,
% 0.28/0.47 subsetI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetI2,definition,
% 0.28/0.47 ( subsetI2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ! [Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) )
% 0.28/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetsubset_type,type,
% 0.28/0.47 emptysetsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(emptysetsubset,definition,
% 0.28/0.47 ( emptysetsubset
% 0.28/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE_type,type,
% 0.28/0.47 subsetE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE,definition,
% 0.28/0.47 ( subsetE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE2_type,type,
% 0.28/0.47 subsetE2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetE2,definition,
% 0.28/0.47 ( subsetE2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notsubsetI_type,type,
% 0.28/0.47 notsubsetI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notsubsetI,definition,
% 0.28/0.47 ( notsubsetI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI1_type,type,
% 0.28/0.47 notequalI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI1,definition,
% 0.28/0.47 ( notequalI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ~ ( subset @ A @ B )
% 0.28/0.47 => ( A != B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI2_type,type,
% 0.28/0.47 notequalI2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(notequalI2,definition,
% 0.28/0.47 ( notequalI2
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ~ ( in @ Xx @ B )
% 0.28/0.47 => ( A != B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetRefl_type,type,
% 0.28/0.47 subsetRefl: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetRefl,definition,
% 0.28/0.47 ( subsetRefl
% 0.28/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTrans_type,type,
% 0.28/0.47 subsetTrans: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetTrans,definition,
% 0.28/0.47 ( subsetTrans
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( subset @ B @ C )
% 0.28/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub_type,type,
% 0.28/0.47 setadjoinSub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub,definition,
% 0.28/0.47 ( setadjoinSub
% 0.28/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub2_type,type,
% 0.28/0.47 setadjoinSub2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setadjoinSub2,definition,
% 0.28/0.47 ( setadjoinSub2
% 0.28/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subset2powerset_type,type,
% 0.28/0.47 subset2powerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subset2powerset,definition,
% 0.28/0.47 ( subset2powerset
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(setextsub_type,type,
% 0.28/0.47 setextsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(setextsub,definition,
% 0.28/0.47 ( setextsub
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( subset @ B @ A )
% 0.28/0.47 => ( A = B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(subsetemptysetimpeq_type,type,
% 0.28/0.47 subsetemptysetimpeq: $o ).
% 0.28/0.47
% 0.28/0.47 thf(subsetemptysetimpeq,definition,
% 0.28/0.47 ( subsetemptysetimpeq
% 0.28/0.47 = ( ! [A: $i] :
% 0.28/0.47 ( ( subset @ A @ emptyset )
% 0.28/0.47 => ( A = emptyset ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1_type,type,
% 0.28/0.47 powersetI1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetI1,definition,
% 0.28/0.47 ( powersetI1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ B @ A )
% 0.28/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE1_type,type,
% 0.28/0.47 powersetE1: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetE1,definition,
% 0.28/0.47 ( powersetE1
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(inPowerset_type,type,
% 0.28/0.47 inPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(inPowerset,definition,
% 0.28/0.47 ( inPowerset
% 0.28/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(powersetsubset_type,type,
% 0.28/0.47 powersetsubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(powersetsubset,definition,
% 0.28/0.47 ( powersetsubset
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sepInPowerset_type,type,
% 0.28/0.47 sepInPowerset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(sepInPowerset,definition,
% 0.28/0.47 ( sepInPowerset
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( in
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(sepSubset_type,type,
% 0.28/0.47 sepSubset: $o ).
% 0.28/0.47
% 0.28/0.47 thf(sepSubset,definition,
% 0.28/0.47 ( sepSubset
% 0.28/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.28/0.47 ( subset
% 0.28/0.47 @ ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.28/0.47 @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunion_type,type,
% 0.28/0.47 binunion: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIL_type,type,
% 0.28/0.47 binunionIL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIL,definition,
% 0.28/0.47 ( binunionIL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2IR_type,type,
% 0.28/0.47 upairset2IR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(upairset2IR,definition,
% 0.28/0.47 ( upairset2IR
% 0.28/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIR_type,type,
% 0.28/0.47 binunionIR: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionIR,definition,
% 0.28/0.47 ( binunionIR
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionEcases_type,type,
% 0.28/0.47 binunionEcases: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionEcases,definition,
% 0.28/0.47 ( binunionEcases
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( ( in @ Xx @ A )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => ( ( ( in @ Xx @ B )
% 0.28/0.47 => Xphi )
% 0.28/0.47 => Xphi ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE_type,type,
% 0.28/0.47 binunionE: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionE,definition,
% 0.28/0.47 ( binunionE
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.28/0.47 => ( ( in @ Xx @ A )
% 0.28/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub_type,type,
% 0.28/0.47 binunionLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionLsub,definition,
% 0.28/0.47 ( binunionLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub_type,type,
% 0.28/0.47 binunionRsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binunionRsub,definition,
% 0.28/0.47 ( binunionRsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersect_type,type,
% 0.28/0.47 binintersect: $i > $i > $i ).
% 0.28/0.47
% 0.28/0.47 thf(binintersect,definition,
% 0.28/0.47 ( binintersect
% 0.28/0.47 = ( ^ [A: $i,B: $i] :
% 0.28/0.47 ( dsetconstr @ A
% 0.28/0.47 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI_type,type,
% 0.28/0.47 binintersectI: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectI,definition,
% 0.28/0.47 ( binintersectI
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ A )
% 0.28/0.47 => ( ( in @ Xx @ B )
% 0.28/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5_type,type,
% 0.28/0.47 binintersectSubset5: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset5,definition,
% 0.28/0.47 ( binintersectSubset5
% 0.28/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.28/0.47 ( ( subset @ C @ A )
% 0.28/0.47 => ( ( subset @ C @ B )
% 0.28/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL_type,type,
% 0.28/0.47 binintersectEL: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectEL,definition,
% 0.28/0.47 ( binintersectEL
% 0.28/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub_type,type,
% 0.28/0.47 binintersectLsub: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectLsub,definition,
% 0.28/0.47 ( binintersectLsub
% 0.28/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2_type,type,
% 0.28/0.47 binintersectSubset2: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset2,definition,
% 0.28/0.47 ( binintersectSubset2
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( subset @ A @ B )
% 0.28/0.47 => ( ( binintersect @ A @ B )
% 0.28/0.47 = A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3_type,type,
% 0.28/0.47 binintersectSubset3: $o ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectSubset3,definition,
% 0.28/0.47 ( binintersectSubset3
% 0.28/0.47 = ( ! [A: $i,B: $i] :
% 0.28/0.47 ( ( ( binintersect @ A @ B )
% 0.28/0.47 = B )
% 0.28/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 thf(binintersectER,conjecture,
% 0.28/0.47 ( setextAx
% 0.28/0.47 => ( emptysetAx
% 0.28/0.47 => ( setadjoinAx
% 0.28/0.47 => ( powersetAx
% 0.28/0.47 => ( setunionAx
% 0.28/0.47 => ( omega0Ax
% 0.28/0.47 => ( omegaSAx
% 0.28/0.47 => ( omegaIndAx
% 0.28/0.47 => ( replAx
% 0.28/0.47 => ( foundationAx
% 0.28/0.47 => ( wellorderingAx
% 0.28/0.47 => ( descrp
% 0.28/0.47 => ( dsetconstrI
% 0.28/0.47 => ( dsetconstrEL
% 0.28/0.47 => ( dsetconstrER
% 0.28/0.47 => ( exuE1
% 0.28/0.47 => ( prop2setE
% 0.28/0.47 => ( emptysetE
% 0.28/0.47 => ( emptysetimpfalse
% 0.28/0.47 => ( notinemptyset
% 0.28/0.47 => ( exuE3e
% 0.28/0.47 => ( setext
% 0.28/0.47 => ( emptyI
% 0.28/0.47 => ( noeltsimpempty
% 0.28/0.47 => ( setbeta
% 0.28/0.47 => ( nonemptyE1
% 0.28/0.47 => ( nonemptyI
% 0.28/0.47 => ( nonemptyI1
% 0.28/0.47 => ( setadjoinIL
% 0.28/0.47 => ( emptyinunitempty
% 0.28/0.47 => ( setadjoinIR
% 0.28/0.47 => ( setadjoinE
% 0.28/0.47 => ( setadjoinOr
% 0.28/0.47 => ( setoftrueEq
% 0.28/0.47 => ( powersetI
% 0.28/0.47 => ( emptyinPowerset
% 0.28/0.47 => ( emptyInPowerset
% 0.28/0.47 => ( powersetE
% 0.28/0.47 => ( setunionI
% 0.28/0.47 => ( setunionE
% 0.28/0.47 => ( subPowSU
% 0.28/0.47 => ( exuE2
% 0.28/0.47 => ( nonemptyImpWitness
% 0.28/0.47 => ( uniqinunit
% 0.28/0.47 => ( notinsingleton
% 0.28/0.47 => ( eqinunit
% 0.28/0.47 => ( singletonsswitch
% 0.28/0.47 => ( upairsetE
% 0.28/0.47 => ( upairsetIL
% 0.28/0.47 => ( upairsetIR
% 0.28/0.47 => ( emptyE1
% 0.28/0.47 => ( vacuousDall
% 0.28/0.47 => ( quantDeMorgan1
% 0.28/0.47 => ( quantDeMorgan2
% 0.28/0.47 => ( quantDeMorgan3
% 0.28/0.47 => ( quantDeMorgan4
% 0.28/0.47 => ( prop2setI
% 0.28/0.47 => ( prop2set2propI
% 0.28/0.47 => ( notdexE
% 0.28/0.47 => ( notdallE
% 0.28/0.47 => ( exuI1
% 0.28/0.47 => ( exuI3
% 0.28/0.47 => ( exuI2
% 0.28/0.47 => ( inCongP
% 0.28/0.47 => ( in__Cong
% 0.28/0.47 => ( exuE3u
% 0.28/0.47 => ( exu__Cong
% 0.28/0.47 => ( emptyset__Cong
% 0.28/0.47 => ( setadjoin__Cong
% 0.28/0.47 => ( powerset__Cong
% 0.28/0.47 => ( setunion__Cong
% 0.28/0.47 => ( omega__Cong
% 0.28/0.47 => ( exuEu
% 0.28/0.47 => ( descr__Cong
% 0.28/0.47 => ( dsetconstr__Cong
% 0.28/0.47 => ( subsetI1
% 0.28/0.47 => ( eqimpsubset2
% 0.28/0.47 => ( eqimpsubset1
% 0.28/0.47 => ( subsetI2
% 0.28/0.47 => ( emptysetsubset
% 0.28/0.47 => ( subsetE
% 0.28/0.47 => ( subsetE2
% 0.28/0.47 => ( notsubsetI
% 0.28/0.47 => ( notequalI1
% 0.28/0.47 => ( notequalI2
% 0.28/0.47 => ( subsetRefl
% 0.28/0.47 => ( subsetTrans
% 0.28/0.47 => ( setadjoinSub
% 0.28/0.47 => ( setadjoinSub2
% 0.28/0.47 => ( subset2powerset
% 0.28/0.47 => ( setextsub
% 0.28/0.47 => ( subsetemptysetimpeq
% 0.28/0.47 => ( powersetI1
% 0.28/0.47 => ( powersetE1
% 0.28/0.47 => ( inPowerset
% 0.28/0.47 => ( powersetsubset
% 0.28/0.47 => ( sepInPowerset
% 0.28/0.47 => ( sepSubset
% 0.28/0.47 => ( binunionIL
% 0.28/0.47 => ( upairset2IR
% 0.28/0.47 => ( binunionIR
% 0.28/0.47 => ( binunionEcases
% 0.28/0.47 => ( binunionE
% 0.28/0.47 => ( binunionLsub
% 0.28/0.47 => ( binunionRsub
% 0.28/0.47 => ( binintersectI
% 0.28/0.47 => ( binintersectSubset5
% 0.28/0.47 => ( binintersectEL
% 0.28/0.47 => ( binintersectLsub
% 0.28/0.47 => ( binintersectSubset2
% 0.28/0.47 => ( binintersectSubset3
% 0.28/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.28/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.28/0.47 => ( in @ Xx @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.28/0.47
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.11/1.44 ---- Embedded in THF ---
% 2.11/1.44 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.11/1.44 %%% Generated on Tue Feb 24 12:26:27 EST 2026
% 2.11/1.44 %%% using '$$dhol' embedding, version 1.3.0.
% 2.11/1.44 %%% Logic specification used:
% 2.11/1.44 %%% thf(spec, logic, $$dhol).
% 2.11/1.44
% 2.11/1.44 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2DTF13088.p
% See solution above
% 2.11/1.44 ------------------------
% 2.11/1.45 ---- Cleaned THF ---
% 2.11/1.46 thf(in_type,type,
% 2.11/1.46 in: $i > $i > $o ).
% 2.11/1.46
% 2.11/1.46 thf(exu_type,type,
% 2.11/1.46 exu: ( $i > $o ) > $o ).
% 2.11/1.46
% 2.11/1.46 thf(exu,definition,
% 2.11/1.46 ( exu
% 2.11/1.46 = ( ^ [Xphi: $i > $o] :
% 2.11/1.46 ? [Xx: $i] :
% 2.11/1.46 ( ( Xphi @ Xx )
% 2.11/1.46 & ! [Xy: $i] :
% 2.11/1.46 ( ( Xphi @ Xy )
% 2.11/1.46 => ( Xx = Xy ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setextAx_type,type,
% 2.11/1.46 setextAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setextAx,definition,
% 2.11/1.46 ( setextAx
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 <=> ( in @ Xx @ B ) )
% 2.11/1.46 => ( A = B ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptyset_type,type,
% 2.11/1.46 emptyset: $i ).
% 2.11/1.46
% 2.11/1.46 thf(emptysetAx_type,type,
% 2.11/1.46 emptysetAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptysetAx,definition,
% 2.11/1.46 ( emptysetAx
% 2.11/1.46 = ( ! [Xx: $i] :
% 2.11/1.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoin_type,type,
% 2.11/1.46 setadjoin: $i > $i > $i ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinAx_type,type,
% 2.11/1.46 setadjoinAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinAx,definition,
% 2.11/1.46 ( setadjoinAx
% 2.11/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.11/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.11/1.46 <=> ( ( Xy = Xx )
% 2.11/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(powerset_type,type,
% 2.11/1.46 powerset: $i > $i ).
% 2.11/1.46
% 2.11/1.46 thf(powersetAx_type,type,
% 2.11/1.46 powersetAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(powersetAx,definition,
% 2.11/1.46 ( powersetAx
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.11/1.46 <=> ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setunion_type,type,
% 2.11/1.46 setunion: $i > $i ).
% 2.11/1.46
% 2.11/1.46 thf(setunionAx_type,type,
% 2.11/1.46 setunionAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setunionAx,definition,
% 2.11/1.46 ( setunionAx
% 2.11/1.46 = ( ! [A: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.11/1.46 <=> ? [B: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 & ( in @ B @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(omega_type,type,
% 2.11/1.46 omega: $i ).
% 2.11/1.46
% 2.11/1.46 thf(omega0Ax_type,type,
% 2.11/1.46 omega0Ax: $o ).
% 2.11/1.46
% 2.11/1.46 thf(omega0Ax,definition,
% 2.11/1.46 ( omega0Ax
% 2.11/1.46 = ( in @ emptyset @ omega ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(omegaSAx_type,type,
% 2.11/1.46 omegaSAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(omegaSAx,definition,
% 2.11/1.46 ( omegaSAx
% 2.11/1.46 = ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ omega )
% 2.11/1.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(omegaIndAx_type,type,
% 2.11/1.46 omegaIndAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(omegaIndAx,definition,
% 2.11/1.46 ( omegaIndAx
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ( ( in @ emptyset @ A )
% 2.11/1.46 & ! [Xx: $i] :
% 2.11/1.46 ( ( ( in @ Xx @ omega )
% 2.11/1.46 & ( in @ Xx @ A ) )
% 2.11/1.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.11/1.46 => ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ omega )
% 2.11/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(replAx_type,type,
% 2.11/1.46 replAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(replAx,definition,
% 2.11/1.46 ( replAx
% 2.11/1.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( exu
% 2.11/1.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.11/1.46 => ? [B: $i] :
% 2.11/1.46 ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 <=> ? [Xy: $i] :
% 2.11/1.46 ( ( in @ Xy @ A )
% 2.11/1.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(foundationAx_type,type,
% 2.11/1.46 foundationAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(foundationAx,definition,
% 2.11/1.46 ( foundationAx
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.11/1.46 => ? [B: $i] :
% 2.11/1.46 ( ( in @ B @ A )
% 2.11/1.46 & ~ ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(wellorderingAx_type,type,
% 2.11/1.46 wellorderingAx: $o ).
% 2.11/1.46
% 2.11/1.46 thf(wellorderingAx,definition,
% 2.11/1.46 ( wellorderingAx
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ? [B: $i] :
% 2.11/1.46 ( ! [C: $i] :
% 2.11/1.46 ( ( in @ C @ B )
% 2.11/1.46 => ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ C )
% 2.11/1.46 => ( in @ Xx @ A ) ) )
% 2.11/1.46 & ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( ( in @ Xx @ A )
% 2.11/1.46 & ( in @ Xy @ A ) )
% 2.11/1.46 => ( ! [C: $i] :
% 2.11/1.46 ( ( in @ C @ B )
% 2.11/1.46 => ( ( in @ Xx @ C )
% 2.11/1.46 <=> ( in @ Xy @ C ) ) )
% 2.11/1.46 => ( Xx = Xy ) ) )
% 2.11/1.46 & ! [C: $i,D: $i] :
% 2.11/1.46 ( ( ( in @ C @ B )
% 2.11/1.46 & ( in @ D @ B ) )
% 2.11/1.46 => ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ C )
% 2.11/1.46 => ( in @ Xx @ D ) )
% 2.11/1.46 | ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ D )
% 2.11/1.46 => ( in @ Xx @ C ) ) ) )
% 2.11/1.46 & ! [C: $i] :
% 2.11/1.46 ( ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ C )
% 2.11/1.46 => ( in @ Xx @ A ) )
% 2.11/1.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.11/1.46 => ? [D: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ D @ B )
% 2.11/1.46 & ( in @ Xx @ C )
% 2.11/1.46 & ~ ? [Xy: $i] :
% 2.11/1.46 ( ( in @ Xy @ D )
% 2.11/1.46 & ( in @ Xy @ C ) )
% 2.11/1.46 & ! [E: $i] :
% 2.11/1.46 ( ( in @ E @ B )
% 2.11/1.46 => ( ! [Xy: $i] :
% 2.11/1.46 ( ( in @ Xy @ E )
% 2.11/1.46 => ( in @ Xy @ D ) )
% 2.11/1.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(descr_type,type,
% 2.11/1.46 descr: ( $i > $o ) > $i ).
% 2.11/1.46
% 2.11/1.46 thf(descrp_type,type,
% 2.11/1.46 descrp: $o ).
% 2.11/1.46
% 2.11/1.46 thf(descrp,definition,
% 2.11/1.46 ( descrp
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 => ( Xphi
% 2.11/1.46 @ ( descr
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstr_type,type,
% 2.11/1.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstrI_type,type,
% 2.11/1.46 dsetconstrI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstrI,definition,
% 2.11/1.46 ( dsetconstrI
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( ( Xphi @ Xx )
% 2.11/1.46 => ( in @ Xx
% 2.11/1.46 @ ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstrEL_type,type,
% 2.11/1.46 dsetconstrEL: $o ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstrEL,definition,
% 2.11/1.46 ( dsetconstrEL
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx
% 2.11/1.46 @ ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.11/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstrER_type,type,
% 2.11/1.46 dsetconstrER: $o ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstrER,definition,
% 2.11/1.46 ( dsetconstrER
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx
% 2.11/1.46 @ ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.11/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exuE1_type,type,
% 2.11/1.46 exuE1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exuE1,definition,
% 2.11/1.46 ( exuE1
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 => ? [Xx: $i] :
% 2.11/1.46 ( ( Xphi @ Xx )
% 2.11/1.46 & ! [Xy: $i] :
% 2.11/1.46 ( ( Xphi @ Xy )
% 2.11/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(prop2set_type,type,
% 2.11/1.46 prop2set: $o > $i ).
% 2.11/1.46
% 2.11/1.46 thf(prop2setE_type,type,
% 2.11/1.46 prop2setE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(prop2setE,definition,
% 2.11/1.46 ( prop2setE
% 2.11/1.46 = ( ! [Xphi: $o,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.11/1.46 => Xphi ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptysetE_type,type,
% 2.11/1.46 emptysetE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptysetE,definition,
% 2.11/1.46 ( emptysetE
% 2.11/1.46 = ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ emptyset )
% 2.11/1.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptysetimpfalse_type,type,
% 2.11/1.46 emptysetimpfalse: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptysetimpfalse,definition,
% 2.11/1.46 ( emptysetimpfalse
% 2.11/1.46 = ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ emptyset )
% 2.11/1.46 => $false ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(notinemptyset_type,type,
% 2.11/1.46 notinemptyset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(notinemptyset,definition,
% 2.11/1.46 ( notinemptyset
% 2.11/1.46 = ( ! [Xx: $i] :
% 2.11/1.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exuE3e_type,type,
% 2.11/1.46 exuE3e: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exuE3e,definition,
% 2.11/1.46 ( exuE3e
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setext_type,type,
% 2.11/1.46 setext: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setext,definition,
% 2.11/1.46 ( setext
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( in @ Xx @ B ) )
% 2.11/1.46 => ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 => ( in @ Xx @ A ) )
% 2.11/1.46 => ( A = B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptyI_type,type,
% 2.11/1.46 emptyI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptyI,definition,
% 2.11/1.46 ( emptyI
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ~ ( in @ Xx @ A )
% 2.11/1.46 => ( A = emptyset ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(noeltsimpempty_type,type,
% 2.11/1.46 noeltsimpempty: $o ).
% 2.11/1.46
% 2.11/1.46 thf(noeltsimpempty,definition,
% 2.11/1.46 ( noeltsimpempty
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ~ ( in @ Xx @ A )
% 2.11/1.46 => ( A = emptyset ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setbeta_type,type,
% 2.11/1.46 setbeta: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setbeta,definition,
% 2.11/1.46 ( setbeta
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( ( in @ Xx
% 2.11/1.46 @ ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.11/1.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(nonempty_type,type,
% 2.11/1.46 nonempty: $i > $o ).
% 2.11/1.46
% 2.11/1.46 thf(nonempty,definition,
% 2.11/1.46 ( nonempty
% 2.11/1.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(nonemptyE1_type,type,
% 2.11/1.46 nonemptyE1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(nonemptyE1,definition,
% 2.11/1.46 ( nonemptyE1
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ( nonempty @ A )
% 2.11/1.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(nonemptyI_type,type,
% 2.11/1.46 nonemptyI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(nonemptyI,definition,
% 2.11/1.46 ( nonemptyI
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( ( Xphi @ Xx )
% 2.11/1.46 => ( nonempty
% 2.11/1.46 @ ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(nonemptyI1_type,type,
% 2.11/1.46 nonemptyI1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(nonemptyI1,definition,
% 2.11/1.46 ( nonemptyI1
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.11/1.46 => ( nonempty @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinIL_type,type,
% 2.11/1.46 setadjoinIL: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinIL,definition,
% 2.11/1.46 ( setadjoinIL
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptyinunitempty_type,type,
% 2.11/1.46 emptyinunitempty: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptyinunitempty,definition,
% 2.11/1.46 ( emptyinunitempty
% 2.11/1.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinIR_type,type,
% 2.11/1.46 setadjoinIR: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinIR,definition,
% 2.11/1.46 ( setadjoinIR
% 2.11/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.11/1.46 ( ( in @ Xy @ A )
% 2.11/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinE_type,type,
% 2.11/1.46 setadjoinE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinE,definition,
% 2.11/1.46 ( setadjoinE
% 2.11/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.11/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.11/1.46 => ! [Xphi: $o] :
% 2.11/1.46 ( ( ( Xy = Xx )
% 2.11/1.46 => Xphi )
% 2.11/1.46 => ( ( ( in @ Xy @ A )
% 2.11/1.46 => Xphi )
% 2.11/1.46 => Xphi ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinOr_type,type,
% 2.11/1.46 setadjoinOr: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinOr,definition,
% 2.11/1.46 ( setadjoinOr
% 2.11/1.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.11/1.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.11/1.46 => ( ( Xy = Xx )
% 2.11/1.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setoftrueEq_type,type,
% 2.11/1.46 setoftrueEq: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setoftrueEq,definition,
% 2.11/1.46 ( setoftrueEq
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xx: $i] : $true )
% 2.11/1.46 = A ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(powersetI_type,type,
% 2.11/1.46 powersetI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(powersetI,definition,
% 2.11/1.46 ( powersetI
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 => ( in @ Xx @ A ) )
% 2.11/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptyinPowerset_type,type,
% 2.11/1.46 emptyinPowerset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptyinPowerset,definition,
% 2.11/1.46 ( emptyinPowerset
% 2.11/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptyInPowerset_type,type,
% 2.11/1.46 emptyInPowerset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptyInPowerset,definition,
% 2.11/1.46 ( emptyInPowerset
% 2.11/1.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(powersetE_type,type,
% 2.11/1.46 powersetE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(powersetE,definition,
% 2.11/1.46 ( powersetE
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.11/1.46 => ( ( in @ Xx @ B )
% 2.11/1.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setunionI_type,type,
% 2.11/1.46 setunionI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setunionI,definition,
% 2.11/1.46 ( setunionI
% 2.11/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 => ( ( in @ B @ A )
% 2.11/1.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setunionE_type,type,
% 2.11/1.46 setunionE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setunionE,definition,
% 2.11/1.46 ( setunionE
% 2.11/1.46 = ( ! [A: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ ( setunion @ A ) )
% 2.11/1.46 => ! [Xphi: $o] :
% 2.11/1.46 ( ! [B: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 => ( ( in @ B @ A )
% 2.11/1.46 => Xphi ) )
% 2.11/1.46 => Xphi ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subPowSU_type,type,
% 2.11/1.46 subPowSU: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subPowSU,definition,
% 2.11/1.46 ( subPowSU
% 2.11/1.46 = ( ! [A: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exuE2_type,type,
% 2.11/1.46 exuE2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exuE2,definition,
% 2.11/1.46 ( exuE2
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 => ? [Xx: $i] :
% 2.11/1.46 ! [Xy: $i] :
% 2.11/1.46 ( ( Xphi @ Xy )
% 2.11/1.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(nonemptyImpWitness_type,type,
% 2.11/1.46 nonemptyImpWitness: $o ).
% 2.11/1.46
% 2.11/1.46 thf(nonemptyImpWitness,definition,
% 2.11/1.46 ( nonemptyImpWitness
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ( nonempty @ A )
% 2.11/1.46 => ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 & $true ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(uniqinunit_type,type,
% 2.11/1.46 uniqinunit: $o ).
% 2.11/1.46
% 2.11/1.46 thf(uniqinunit,definition,
% 2.11/1.46 ( uniqinunit
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.11/1.46 => ( Xx = Xy ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(notinsingleton_type,type,
% 2.11/1.46 notinsingleton: $o ).
% 2.11/1.46
% 2.11/1.46 thf(notinsingleton,definition,
% 2.11/1.46 ( notinsingleton
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xx != Xy )
% 2.11/1.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(eqinunit_type,type,
% 2.11/1.46 eqinunit: $o ).
% 2.11/1.46
% 2.11/1.46 thf(eqinunit,definition,
% 2.11/1.46 ( eqinunit
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xx = Xy )
% 2.11/1.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(singletonsswitch_type,type,
% 2.11/1.46 singletonsswitch: $o ).
% 2.11/1.46
% 2.11/1.46 thf(singletonsswitch,definition,
% 2.11/1.46 ( singletonsswitch
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.11/1.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(upairsetE_type,type,
% 2.11/1.46 upairsetE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(upairsetE,definition,
% 2.11/1.46 ( upairsetE
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.11/1.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.11/1.46 => ( ( Xz = Xx )
% 2.11/1.46 | ( Xz = Xy ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(upairsetIL_type,type,
% 2.11/1.46 upairsetIL: $o ).
% 2.11/1.46
% 2.11/1.46 thf(upairsetIL,definition,
% 2.11/1.46 ( upairsetIL
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(upairsetIR_type,type,
% 2.11/1.46 upairsetIR: $o ).
% 2.11/1.46
% 2.11/1.46 thf(upairsetIR,definition,
% 2.11/1.46 ( upairsetIR
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptyE1_type,type,
% 2.11/1.46 emptyE1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptyE1,definition,
% 2.11/1.46 ( emptyE1
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 & ( Xphi @ Xx ) )
% 2.11/1.46 => ( ( ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 = emptyset )
% 2.11/1.46 => $false ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(vacuousDall_type,type,
% 2.11/1.46 vacuousDall: $o ).
% 2.11/1.46
% 2.11/1.46 thf(vacuousDall,definition,
% 2.11/1.46 ( vacuousDall
% 2.11/1.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ emptyset )
% 2.11/1.46 => ( Xphi @ Xx ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(quantDeMorgan1_type,type,
% 2.11/1.46 quantDeMorgan1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(quantDeMorgan1,definition,
% 2.11/1.46 ( quantDeMorgan1
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( ~ ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( Xphi @ Xx ) )
% 2.11/1.46 => ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(quantDeMorgan2_type,type,
% 2.11/1.46 quantDeMorgan2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(quantDeMorgan2,definition,
% 2.11/1.46 ( quantDeMorgan2
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ~ ( Xphi @ Xx ) )
% 2.11/1.46 => ~ ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(quantDeMorgan3_type,type,
% 2.11/1.46 quantDeMorgan3: $o ).
% 2.11/1.46
% 2.11/1.46 thf(quantDeMorgan3,definition,
% 2.11/1.46 ( quantDeMorgan3
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( ~ ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 & ( Xphi @ Xx ) )
% 2.11/1.46 => ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(quantDeMorgan4_type,type,
% 2.11/1.46 quantDeMorgan4: $o ).
% 2.11/1.46
% 2.11/1.46 thf(quantDeMorgan4,definition,
% 2.11/1.46 ( quantDeMorgan4
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 & ~ ( Xphi @ Xx ) )
% 2.11/1.46 => ~ ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(prop2setI_type,type,
% 2.11/1.46 prop2setI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(prop2setI,definition,
% 2.11/1.46 ( prop2setI
% 2.11/1.46 = ( ! [Xphi: $o] :
% 2.11/1.46 ( Xphi
% 2.11/1.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(set2prop_type,type,
% 2.11/1.46 set2prop: $i > $o ).
% 2.11/1.46
% 2.11/1.46 thf(prop2set2propI_type,type,
% 2.11/1.46 prop2set2propI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(prop2set2propI,definition,
% 2.11/1.46 ( prop2set2propI
% 2.11/1.46 = ( ! [Xphi: $o] :
% 2.11/1.46 ( Xphi
% 2.11/1.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(notdexE_type,type,
% 2.11/1.46 notdexE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(notdexE,definition,
% 2.11/1.46 ( notdexE
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( ~ ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 & ( Xphi @ Xx ) )
% 2.11/1.46 => ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(notdallE_type,type,
% 2.11/1.46 notdallE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(notdallE,definition,
% 2.11/1.46 ( notdallE
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( ~ ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( Xphi @ Xx ) )
% 2.11/1.46 => ? [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exuI1_type,type,
% 2.11/1.46 exuI1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exuI1,definition,
% 2.11/1.46 ( exuI1
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ? [Xx: $i] :
% 2.11/1.46 ( ( Xphi @ Xx )
% 2.11/1.46 & ! [Xy: $i] :
% 2.11/1.46 ( ( Xphi @ Xy )
% 2.11/1.46 => ( Xx = Xy ) ) )
% 2.11/1.46 => ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exuI3_type,type,
% 2.11/1.46 exuI3: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exuI3,definition,
% 2.11/1.46 ( exuI3
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.11/1.46 => ( ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xphi @ Xx )
% 2.11/1.46 => ( ( Xphi @ Xy )
% 2.11/1.46 => ( Xx = Xy ) ) )
% 2.11/1.46 => ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exuI2_type,type,
% 2.11/1.46 exuI2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exuI2,definition,
% 2.11/1.46 ( exuI2
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ? [Xx: $i] :
% 2.11/1.46 ! [Xy: $i] :
% 2.11/1.46 ( ( Xphi @ Xy )
% 2.11/1.46 <=> ( Xy = Xx ) )
% 2.11/1.46 => ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(inCongP_type,type,
% 2.11/1.46 inCongP: $o ).
% 2.11/1.46
% 2.11/1.46 thf(inCongP,definition,
% 2.11/1.46 ( inCongP
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( A = B )
% 2.11/1.46 => ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xx = Xy )
% 2.11/1.46 => ( ( in @ Xx @ A )
% 2.11/1.46 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(in__Cong_type,type,
% 2.11/1.46 in__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(in__Cong,definition,
% 2.11/1.46 ( in__Cong
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( A = B )
% 2.11/1.46 => ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xx = Xy )
% 2.11/1.46 => ( ( in @ Xx @ A )
% 2.11/1.46 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exuE3u_type,type,
% 2.11/1.46 exuE3u: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exuE3u,definition,
% 2.11/1.46 ( exuE3u
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 => ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xphi @ Xx )
% 2.11/1.46 => ( ( Xphi @ Xy )
% 2.11/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exu__Cong_type,type,
% 2.11/1.46 exu__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exu__Cong,definition,
% 2.11/1.46 ( exu__Cong
% 2.11/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.11/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xx = Xy )
% 2.11/1.46 => ( ( Xphi @ Xx )
% 2.11/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.11/1.46 => ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 <=> ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptyset__Cong_type,type,
% 2.11/1.46 emptyset__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptyset__Cong,definition,
% 2.11/1.46 ( emptyset__Cong
% 2.11/1.46 = ( emptyset = emptyset ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoin__Cong_type,type,
% 2.11/1.46 setadjoin__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoin__Cong,definition,
% 2.11/1.46 ( setadjoin__Cong
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xx = Xy )
% 2.11/1.46 => ! [Xz: $i,Xu: $i] :
% 2.11/1.46 ( ( Xz = Xu )
% 2.11/1.46 => ( ( setadjoin @ Xx @ Xz )
% 2.11/1.46 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(powerset__Cong_type,type,
% 2.11/1.46 powerset__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(powerset__Cong,definition,
% 2.11/1.46 ( powerset__Cong
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( A = B )
% 2.11/1.46 => ( ( powerset @ A )
% 2.11/1.46 = ( powerset @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setunion__Cong_type,type,
% 2.11/1.46 setunion__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setunion__Cong,definition,
% 2.11/1.46 ( setunion__Cong
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( A = B )
% 2.11/1.46 => ( ( setunion @ A )
% 2.11/1.46 = ( setunion @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(omega__Cong_type,type,
% 2.11/1.46 omega__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(omega__Cong,definition,
% 2.11/1.46 ( omega__Cong
% 2.11/1.46 = ( omega = omega ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(exuEu_type,type,
% 2.11/1.46 exuEu: $o ).
% 2.11/1.46
% 2.11/1.46 thf(exuEu,definition,
% 2.11/1.46 ( exuEu
% 2.11/1.46 = ( ! [Xphi: $i > $o] :
% 2.11/1.46 ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 => ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xphi @ Xx )
% 2.11/1.46 => ( ( Xphi @ Xy )
% 2.11/1.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(descr__Cong_type,type,
% 2.11/1.46 descr__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(descr__Cong,definition,
% 2.11/1.46 ( descr__Cong
% 2.11/1.46 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.11/1.46 ( ! [Xx: $i,Xy: $i] :
% 2.11/1.46 ( ( Xx = Xy )
% 2.11/1.46 => ( ( Xphi @ Xx )
% 2.11/1.46 <=> ( Xpsi @ Xy ) ) )
% 2.11/1.46 => ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 => ( ( exu
% 2.11/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.11/1.46 => ( ( descr
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 = ( descr
% 2.11/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstr__Cong_type,type,
% 2.11/1.46 dsetconstr__Cong: $o ).
% 2.11/1.46
% 2.11/1.46 thf(dsetconstr__Cong,definition,
% 2.11/1.46 ( dsetconstr__Cong
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( A = B )
% 2.11/1.46 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ! [Xy: $i] :
% 2.11/1.46 ( ( in @ Xy @ B )
% 2.11/1.46 => ( ( Xx = Xy )
% 2.11/1.46 => ( ( Xphi @ Xx )
% 2.11/1.46 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.11/1.46 => ( ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 = ( dsetconstr @ B
% 2.11/1.46 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subset_type,type,
% 2.11/1.46 subset: $i > $i > $o ).
% 2.11/1.46
% 2.11/1.46 thf(disjoint_type,type,
% 2.11/1.46 disjoint: $i > $i > $o ).
% 2.11/1.46
% 2.11/1.46 thf(setsmeet_type,type,
% 2.11/1.46 setsmeet: $i > $i > $o ).
% 2.11/1.46
% 2.11/1.46 thf(subsetI1_type,type,
% 2.11/1.46 subsetI1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subsetI1,definition,
% 2.11/1.46 ( subsetI1
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( in @ Xx @ B ) )
% 2.11/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(eqimpsubset2_type,type,
% 2.11/1.46 eqimpsubset2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(eqimpsubset2,definition,
% 2.11/1.46 ( eqimpsubset2
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( A = B )
% 2.11/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(eqimpsubset1_type,type,
% 2.11/1.46 eqimpsubset1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(eqimpsubset1,definition,
% 2.11/1.46 ( eqimpsubset1
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( A = B )
% 2.11/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subsetI2_type,type,
% 2.11/1.46 subsetI2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subsetI2,definition,
% 2.11/1.46 ( subsetI2
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ! [Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( in @ Xx @ B ) )
% 2.11/1.46 => ( subset @ A @ B ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(emptysetsubset_type,type,
% 2.11/1.46 emptysetsubset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(emptysetsubset,definition,
% 2.11/1.46 ( emptysetsubset
% 2.11/1.46 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subsetE_type,type,
% 2.11/1.46 subsetE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subsetE,definition,
% 2.11/1.46 ( subsetE
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( subset @ A @ B )
% 2.11/1.46 => ( ( in @ Xx @ A )
% 2.11/1.46 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subsetE2_type,type,
% 2.11/1.46 subsetE2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subsetE2,definition,
% 2.11/1.46 ( subsetE2
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( subset @ A @ B )
% 2.11/1.46 => ( ~ ( in @ Xx @ B )
% 2.11/1.46 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(notsubsetI_type,type,
% 2.11/1.46 notsubsetI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(notsubsetI,definition,
% 2.11/1.46 ( notsubsetI
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( ~ ( in @ Xx @ B )
% 2.11/1.46 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(notequalI1_type,type,
% 2.11/1.46 notequalI1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(notequalI1,definition,
% 2.11/1.46 ( notequalI1
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ~ ( subset @ A @ B )
% 2.11/1.46 => ( A != B ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(notequalI2_type,type,
% 2.11/1.46 notequalI2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(notequalI2,definition,
% 2.11/1.46 ( notequalI2
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( ~ ( in @ Xx @ B )
% 2.11/1.46 => ( A != B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subsetRefl_type,type,
% 2.11/1.46 subsetRefl: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subsetRefl,definition,
% 2.11/1.46 ( subsetRefl
% 2.11/1.46 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subsetTrans_type,type,
% 2.11/1.46 subsetTrans: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subsetTrans,definition,
% 2.11/1.46 ( subsetTrans
% 2.11/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.11/1.46 ( ( subset @ A @ B )
% 2.11/1.46 => ( ( subset @ B @ C )
% 2.11/1.46 => ( subset @ A @ C ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinSub_type,type,
% 2.11/1.46 setadjoinSub: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinSub,definition,
% 2.11/1.46 ( setadjoinSub
% 2.11/1.46 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinSub2_type,type,
% 2.11/1.46 setadjoinSub2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setadjoinSub2,definition,
% 2.11/1.46 ( setadjoinSub2
% 2.11/1.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.11/1.46 ( ( subset @ A @ B )
% 2.11/1.46 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subset2powerset_type,type,
% 2.11/1.46 subset2powerset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subset2powerset,definition,
% 2.11/1.46 ( subset2powerset
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( subset @ A @ B )
% 2.11/1.46 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(setextsub_type,type,
% 2.11/1.46 setextsub: $o ).
% 2.11/1.46
% 2.11/1.46 thf(setextsub,definition,
% 2.11/1.46 ( setextsub
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( subset @ A @ B )
% 2.11/1.46 => ( ( subset @ B @ A )
% 2.11/1.46 => ( A = B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(subsetemptysetimpeq_type,type,
% 2.11/1.46 subsetemptysetimpeq: $o ).
% 2.11/1.46
% 2.11/1.46 thf(subsetemptysetimpeq,definition,
% 2.11/1.46 ( subsetemptysetimpeq
% 2.11/1.46 = ( ! [A: $i] :
% 2.11/1.46 ( ( subset @ A @ emptyset )
% 2.11/1.46 => ( A = emptyset ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(powersetI1_type,type,
% 2.11/1.46 powersetI1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(powersetI1,definition,
% 2.11/1.46 ( powersetI1
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( subset @ B @ A )
% 2.11/1.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(powersetE1_type,type,
% 2.11/1.46 powersetE1: $o ).
% 2.11/1.46
% 2.11/1.46 thf(powersetE1,definition,
% 2.11/1.46 ( powersetE1
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( in @ B @ ( powerset @ A ) )
% 2.11/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(inPowerset_type,type,
% 2.11/1.46 inPowerset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(inPowerset,definition,
% 2.11/1.46 ( inPowerset
% 2.11/1.46 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(powersetsubset_type,type,
% 2.11/1.46 powersetsubset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(powersetsubset,definition,
% 2.11/1.46 ( powersetsubset
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( subset @ A @ B )
% 2.11/1.46 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(sepInPowerset_type,type,
% 2.11/1.46 sepInPowerset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(sepInPowerset,definition,
% 2.11/1.46 ( sepInPowerset
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( in
% 2.11/1.46 @ ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 @ ( powerset @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(sepSubset_type,type,
% 2.11/1.46 sepSubset: $o ).
% 2.11/1.46
% 2.11/1.46 thf(sepSubset,definition,
% 2.11/1.46 ( sepSubset
% 2.11/1.46 = ( ! [A: $i,Xphi: $i > $o] :
% 2.11/1.46 ( subset
% 2.11/1.46 @ ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.11/1.46 @ A ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binunion_type,type,
% 2.11/1.46 binunion: $i > $i > $i ).
% 2.11/1.46
% 2.11/1.46 thf(binunionIL_type,type,
% 2.11/1.46 binunionIL: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binunionIL,definition,
% 2.11/1.46 ( binunionIL
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(upairset2IR_type,type,
% 2.11/1.46 upairset2IR: $o ).
% 2.11/1.46
% 2.11/1.46 thf(upairset2IR,definition,
% 2.11/1.46 ( upairset2IR
% 2.11/1.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binunionIR_type,type,
% 2.11/1.46 binunionIR: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binunionIR,definition,
% 2.11/1.46 ( binunionIR
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ B )
% 2.11/1.46 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binunionEcases_type,type,
% 2.11/1.46 binunionEcases: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binunionEcases,definition,
% 2.11/1.46 ( binunionEcases
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.11/1.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.11/1.46 => ( ( ( in @ Xx @ A )
% 2.11/1.46 => Xphi )
% 2.11/1.46 => ( ( ( in @ Xx @ B )
% 2.11/1.46 => Xphi )
% 2.11/1.46 => Xphi ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binunionE_type,type,
% 2.11/1.46 binunionE: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binunionE,definition,
% 2.11/1.46 ( binunionE
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.11/1.46 => ( ( in @ Xx @ A )
% 2.11/1.46 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binunionLsub_type,type,
% 2.11/1.46 binunionLsub: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binunionLsub,definition,
% 2.11/1.46 ( binunionLsub
% 2.11/1.46 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binunionRsub_type,type,
% 2.11/1.46 binunionRsub: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binunionRsub,definition,
% 2.11/1.46 ( binunionRsub
% 2.11/1.46 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binintersect_type,type,
% 2.11/1.46 binintersect: $i > $i > $i ).
% 2.11/1.46
% 2.11/1.46 thf(binintersect,definition,
% 2.11/1.46 ( binintersect
% 2.11/1.46 = ( ^ [A: $i,B: $i] :
% 2.11/1.46 ( dsetconstr @ A
% 2.11/1.46 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectI_type,type,
% 2.11/1.46 binintersectI: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectI,definition,
% 2.11/1.46 ( binintersectI
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ A )
% 2.11/1.46 => ( ( in @ Xx @ B )
% 2.11/1.46 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectSubset5_type,type,
% 2.11/1.46 binintersectSubset5: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectSubset5,definition,
% 2.11/1.46 ( binintersectSubset5
% 2.11/1.46 = ( ! [A: $i,B: $i,C: $i] :
% 2.11/1.46 ( ( subset @ C @ A )
% 2.11/1.46 => ( ( subset @ C @ B )
% 2.11/1.46 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectEL_type,type,
% 2.11/1.46 binintersectEL: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectEL,definition,
% 2.11/1.46 ( binintersectEL
% 2.11/1.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.11/1.46 => ( in @ Xx @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectLsub_type,type,
% 2.11/1.46 binintersectLsub: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectLsub,definition,
% 2.11/1.46 ( binintersectLsub
% 2.11/1.46 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectSubset2_type,type,
% 2.11/1.46 binintersectSubset2: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectSubset2,definition,
% 2.11/1.46 ( binintersectSubset2
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( subset @ A @ B )
% 2.11/1.46 => ( ( binintersect @ A @ B )
% 2.11/1.46 = A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectSubset3_type,type,
% 2.11/1.46 binintersectSubset3: $o ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectSubset3,definition,
% 2.11/1.46 ( binintersectSubset3
% 2.11/1.46 = ( ! [A: $i,B: $i] :
% 2.11/1.46 ( ( ( binintersect @ A @ B )
% 2.11/1.46 = B )
% 2.11/1.46 => ( subset @ B @ A ) ) ) ) ).
% 2.11/1.46
% 2.11/1.46 thf(binintersectER,conjecture,
% 2.11/1.46 ( setextAx
% 2.11/1.46 => ( emptysetAx
% 2.11/1.46 => ( setadjoinAx
% 2.11/1.46 => ( powersetAx
% 2.11/1.46 => ( setunionAx
% 2.11/1.46 => ( omega0Ax
% 2.11/1.46 => ( omegaSAx
% 2.11/1.46 => ( omegaIndAx
% 2.11/1.46 => ( replAx
% 2.11/1.46 => ( foundationAx
% 2.11/1.46 => ( wellorderingAx
% 2.11/1.46 => ( descrp
% 2.11/1.46 => ( dsetconstrI
% 2.11/1.46 => ( dsetconstrEL
% 2.11/1.46 => ( dsetconstrER
% 2.11/1.46 => ( exuE1
% 2.11/1.46 => ( prop2setE
% 2.11/1.46 => ( emptysetE
% 2.11/1.46 => ( emptysetimpfalse
% 2.11/1.46 => ( notinemptyset
% 2.11/1.46 => ( exuE3e
% 2.11/1.46 => ( setext
% 2.11/1.46 => ( emptyI
% 2.11/1.46 => ( noeltsimpempty
% 2.11/1.46 => ( setbeta
% 2.11/1.46 => ( nonemptyE1
% 2.11/1.46 => ( nonemptyI
% 2.11/1.46 => ( nonemptyI1
% 2.11/1.46 => ( setadjoinIL
% 2.11/1.46 => ( emptyinunitempty
% 2.11/1.46 => ( setadjoinIR
% 2.11/1.46 => ( setadjoinE
% 2.11/1.46 => ( setadjoinOr
% 2.11/1.46 => ( setoftrueEq
% 2.11/1.46 => ( powersetI
% 2.11/1.46 => ( emptyinPowerset
% 2.11/1.46 => ( emptyInPowerset
% 2.11/1.46 => ( powersetE
% 2.11/1.46 => ( setunionI
% 2.11/1.46 => ( setunionE
% 2.11/1.46 => ( subPowSU
% 2.11/1.46 => ( exuE2
% 2.11/1.46 => ( nonemptyImpWitness
% 2.11/1.46 => ( uniqinunit
% 2.11/1.46 => ( notinsingleton
% 2.11/1.46 => ( eqinunit
% 2.11/1.46 => ( singletonsswitch
% 2.11/1.46 => ( upairsetE
% 2.11/1.46 => ( upairsetIL
% 2.11/1.46 => ( upairsetIR
% 2.11/1.46 => ( emptyE1
% 2.11/1.46 => ( vacuousDall
% 2.11/1.46 => ( quantDeMorgan1
% 2.11/1.46 => ( quantDeMorgan2
% 2.11/1.46 => ( quantDeMorgan3
% 2.11/1.46 => ( quantDeMorgan4
% 2.11/1.46 => ( prop2setI
% 2.11/1.46 => ( prop2set2propI
% 2.11/1.46 => ( notdexE
% 2.11/1.46 => ( notdallE
% 2.11/1.46 => ( exuI1
% 2.11/1.46 => ( exuI3
% 2.11/1.46 => ( exuI2
% 2.11/1.46 => ( inCongP
% 2.11/1.46 => ( in__Cong
% 2.11/1.46 => ( exuE3u
% 2.11/1.46 => ( exu__Cong
% 2.11/1.46 => ( emptyset__Cong
% 2.11/1.46 => ( setadjoin__Cong
% 2.11/1.46 => ( powerset__Cong
% 2.11/1.46 => ( setunion__Cong
% 2.11/1.46 => ( omega__Cong
% 2.11/1.46 => ( exuEu
% 2.11/1.46 => ( descr__Cong
% 2.11/1.46 => ( dsetconstr__Cong
% 2.11/1.46 => ( subsetI1
% 2.11/1.46 => ( eqimpsubset2
% 2.11/1.46 => ( eqimpsubset1
% 2.11/1.46 => ( subsetI2
% 2.11/1.46 => ( emptysetsubset
% 2.11/1.46 => ( subsetE
% 2.11/1.46 => ( subsetE2
% 2.11/1.46 => ( notsubsetI
% 2.11/1.46 => ( notequalI1
% 2.11/1.46 => ( notequalI2
% 2.11/1.46 => ( subsetRefl
% 2.11/1.46 => ( subsetTrans
% 2.11/1.46 => ( setadjoinSub
% 2.11/1.46 => ( setadjoinSub2
% 2.11/1.46 => ( subset2powerset
% 2.11/1.46 => ( setextsub
% 2.11/1.46 => ( subsetemptysetimpeq
% 2.11/1.46 => ( powersetI1
% 2.11/1.46 => ( powersetE1
% 2.11/1.46 => ( inPowerset
% 2.11/1.46 => ( powersetsubset
% 2.11/1.46 => ( sepInPowerset
% 2.11/1.46 => ( sepSubset
% 2.11/1.46 => ( binunionIL
% 2.11/1.46 => ( upairset2IR
% 2.11/1.46 => ( binunionIR
% 2.11/1.46 => ( binunionEcases
% 2.11/1.46 => ( binunionE
% 2.11/1.46 => ( binunionLsub
% 2.11/1.46 => ( binunionRsub
% 2.11/1.46 => ( binintersectI
% 2.11/1.46 => ( binintersectSubset5
% 2.11/1.46 => ( binintersectEL
% 2.11/1.46 => ( binintersectLsub
% 2.11/1.46 => ( binintersectSubset2
% 2.11/1.46 => ( binintersectSubset3
% 2.11/1.46 => ! [A: $i,B: $i,Xx: $i] :
% 2.11/1.46 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 2.11/1.46 => ( in @ Xx @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.11/1.46 ------------------------
% 2.11/1.48 % (13366)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/183Mi)
% 2.11/1.48 % (13372)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/18Mi)
% 2.11/1.48 % (13369)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/2Mi)
% 2.11/1.48 % (13369)Instruction limit reached!
% 2.11/1.48 % (13369)------------------------------
% 2.11/1.48 % (13369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.48 % (13369)Termination reason: Unknown
% 2.11/1.48 % (13369)Termination phase: shuffling
% 2.11/1.48
% 2.11/1.48 % (13369)Memory used [KB]: 1151
% 2.11/1.48 % (13369)Time elapsed: 0.002 s
% 2.11/1.48 % (13369)Instructions burned: 2 (million)
% 2.11/1.48 % (13369)------------------------------
% 2.11/1.48 % (13369)------------------------------
% 2.11/1.48 % (13372)Instruction limit reached!
% 2.11/1.48 % (13372)------------------------------
% 2.11/1.48 % (13372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.48 % (13372)Termination reason: Unknown
% 2.11/1.48 % (13372)Termination phase: Preprocessing 3
% 2.11/1.48
% 2.11/1.48 % (13372)Memory used [KB]: 1535
% 2.11/1.48 % (13372)Time elapsed: 0.007 s
% 2.11/1.48 % (13372)Instructions burned: 18 (million)
% 2.11/1.48 % (13372)------------------------------
% 2.11/1.48 % (13372)------------------------------
% 2.11/1.48 % (13367)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_13088 for (2999ds/4Mi)
% 2.11/1.48 % (13368)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_13088 for (2999ds/27Mi)
% 2.11/1.48 % (13370)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_13088 for (2999ds/2Mi)
% 2.11/1.48 % (13371)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_13088 for (2999ds/275Mi)
% 2.11/1.49 % (13370)Instruction limit reached!
% 2.11/1.49 % (13370)------------------------------
% 2.11/1.49 % (13370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.49 % (13370)Termination reason: Unknown
% 2.11/1.49 % (13370)Termination phase: shuffling
% 2.11/1.49
% 2.11/1.49 % (13370)Memory used [KB]: 1151
% 2.11/1.49 % (13370)Time elapsed: 0.003 s
% 2.11/1.49 % (13370)Instructions burned: 2 (million)
% 2.11/1.49 % (13370)------------------------------
% 2.11/1.49 % (13370)------------------------------
% 2.11/1.49 % (13367)Instruction limit reached!
% 2.11/1.49 % (13367)------------------------------
% 2.11/1.49 % (13367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.49 % (13367)Termination reason: Unknown
% 2.11/1.49 % (13367)Termination phase: shuffling
% 2.11/1.49
% 2.11/1.49 % (13367)Memory used [KB]: 1279
% 2.11/1.49 % (13367)Time elapsed: 0.005 s
% 2.11/1.49 % (13367)Instructions burned: 5 (million)
% 2.11/1.49 % (13367)------------------------------
% 2.11/1.49 % (13367)------------------------------
% 2.11/1.49 % (13374)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/3Mi)
% 2.11/1.49 % (13374)Instruction limit reached!
% 2.11/1.49 % (13374)------------------------------
% 2.11/1.49 % (13374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.11/1.49 % (13374)Termination reason: Unknown
% 2.11/1.49 % (13374)Termination phase: shuffling
% 2.11/1.49
% 2.11/1.49 % (13374)Memory used [KB]: 1151
% 2.11/1.49 % (13374)Time elapsed: 0.002 s
% 2.11/1.49 % (13374)Instructions burned: 3 (million)
% 2.11/1.49 % (13374)------------------------------
% 2.11/1.49 % (13374)------------------------------
% 2.11/1.49 % (13375)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_13088 for (2999ds/37Mi)
% 2.24/1.50 % (13368)Instruction limit reached!
% 2.24/1.50 % (13368)------------------------------
% 2.24/1.50 % (13368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.50 % (13368)Termination reason: Unknown
% 2.24/1.50 % (13368)Termination phase: Property scanning
% 2.24/1.50
% 2.24/1.50 % (13368)Memory used [KB]: 1535
% 2.24/1.50 % (13368)Time elapsed: 0.016 s
% 2.24/1.50 % (13368)Instructions burned: 27 (million)
% 2.24/1.50 % (13368)------------------------------
% 2.24/1.50 % (13368)------------------------------
% 2.24/1.50 % (13378)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_13088 for (2999ds/1041Mi)
% 2.24/1.50 % (13376)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_13088 for (2999ds/15Mi)
% 2.24/1.50 % (13375)Instruction limit reached!
% 2.24/1.50 % (13375)------------------------------
% 2.24/1.50 % (13375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.50 % (13375)Termination reason: Unknown
% 2.24/1.50 % (13375)Termination phase: Property scanning
% 2.24/1.50
% 2.24/1.50 % (13375)Memory used [KB]: 1535
% 2.24/1.50 % (13375)Time elapsed: 0.012 s
% 2.24/1.50 % (13375)Instructions burned: 37 (million)
% 2.24/1.50 % (13375)------------------------------
% 2.24/1.50 % (13375)------------------------------
% 2.24/1.50 % (13377)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_13088 for (2999ds/3Mi)
% 2.24/1.51 % (13377)Instruction limit reached!
% 2.24/1.51 % (13377)------------------------------
% 2.24/1.51 % (13377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.51 % (13377)Termination reason: Unknown
% 2.24/1.51 % (13377)Termination phase: shuffling
% 2.24/1.51
% 2.24/1.51 % (13377)Memory used [KB]: 1151
% 2.24/1.51 % (13377)Time elapsed: 0.004 s
% 2.24/1.51 % (13377)Instructions burned: 4 (million)
% 2.24/1.51 % (13377)------------------------------
% 2.24/1.51 % (13377)------------------------------
% 2.24/1.51 % (13376)Instruction limit reached!
% 2.24/1.51 % (13376)------------------------------
% 2.24/1.51 % (13376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.51 % (13376)Termination reason: Unknown
% 2.24/1.51 % (13376)Termination phase: Naming
% 2.24/1.51
% 2.24/1.51 % (13376)Memory used [KB]: 1407
% 2.24/1.51 % (13376)Time elapsed: 0.011 s
% 2.24/1.51 % (13376)Instructions burned: 16 (million)
% 2.24/1.51 % (13376)------------------------------
% 2.24/1.51 % (13376)------------------------------
% 2.24/1.51 % (13380)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/16Mi)
% 2.24/1.52 % (13379)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/7Mi)
% 2.24/1.52 % (13380)Instruction limit reached!
% 2.24/1.52 % (13380)------------------------------
% 2.24/1.52 % (13380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.52 % (13380)Termination reason: Unknown
% 2.24/1.52 % (13380)Termination phase: Property scanning
% 2.24/1.52
% 2.24/1.52 % (13380)Memory used [KB]: 1535
% 2.24/1.52 % (13380)Time elapsed: 0.006 s
% 2.24/1.52 % (13380)Instructions burned: 17 (million)
% 2.24/1.52 % (13380)------------------------------
% 2.24/1.52 % (13380)------------------------------
% 2.24/1.52 % (13379)Instruction limit reached!
% 2.24/1.52 % (13379)------------------------------
% 2.24/1.52 % (13379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.52 % (13379)Termination reason: Unknown
% 2.24/1.52 % (13379)Termination phase: shuffling
% 2.24/1.52
% 2.24/1.52 % (13379)Memory used [KB]: 1279
% 2.24/1.52 % (13379)Time elapsed: 0.006 s
% 2.24/1.52 % (13379)Instructions burned: 8 (million)
% 2.24/1.52 % (13379)------------------------------
% 2.24/1.52 % (13379)------------------------------
% 2.24/1.52 % (13381)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_13088 for (2999ds/3Mi)
% 2.24/1.53 % (13381)Instruction limit reached!
% 2.24/1.53 % (13381)------------------------------
% 2.24/1.53 % (13381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.53 % (13381)Termination reason: Unknown
% 2.24/1.53 % (13381)Termination phase: shuffling
% 2.24/1.53
% 2.24/1.53 % (13381)Memory used [KB]: 1151
% 2.24/1.53 % (13381)Time elapsed: 0.003 s
% 2.24/1.53 % (13381)Instructions burned: 4 (million)
% 2.24/1.53 % (13381)------------------------------
% 2.24/1.53 % (13381)------------------------------
% 2.24/1.53 % (13383)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/7Mi)
% 2.24/1.53 % (13382)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_13088 for (2999ds/3Mi)
% 2.24/1.53 % (13383)Instruction limit reached!
% 2.24/1.53 % (13383)------------------------------
% 2.24/1.53 % (13383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.53 % (13383)Termination reason: Unknown
% 2.24/1.53 % (13383)Termination phase: shuffling
% 2.24/1.53
% 2.24/1.53 % (13383)Memory used [KB]: 1279
% 2.24/1.53 % (13383)Time elapsed: 0.003 s
% 2.24/1.53 % (13383)Instructions burned: 7 (million)
% 2.24/1.53 % (13383)------------------------------
% 2.24/1.53 % (13383)------------------------------
% 2.24/1.53 % (13366)Instruction limit reached!
% 2.24/1.53 % (13366)------------------------------
% 2.24/1.53 % (13366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.53 % (13366)Termination reason: Unknown
% 2.24/1.53 % (13366)Termination phase: Saturation
% 2.24/1.53
% 2.24/1.53 % (13366)Memory used [KB]: 6908
% 2.24/1.53 % (13366)Time elapsed: 0.055 s
% 2.24/1.53 % (13366)Instructions burned: 183 (million)
% 2.24/1.53 % (13366)------------------------------
% 2.24/1.53 % (13366)------------------------------
% 2.24/1.53 % (13382)Instruction limit reached!
% 2.24/1.53 % (13382)------------------------------
% 2.24/1.53 % (13382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.53 % (13382)Termination reason: Unknown
% 2.24/1.53 % (13382)Termination phase: shuffling
% 2.24/1.53
% 2.24/1.53 % (13382)Memory used [KB]: 1151
% 2.24/1.53 % (13382)Time elapsed: 0.004 s
% 2.24/1.53 % (13382)Instructions burned: 4 (million)
% 2.24/1.53 % (13382)------------------------------
% 2.24/1.53 % (13382)------------------------------
% 2.24/1.54 % (13384)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/3Mi)
% 2.24/1.54 % (13385)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/4Mi)
% 2.24/1.54 % (13386)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/18Mi)
% 2.24/1.54 % (13384)Instruction limit reached!
% 2.24/1.54 % (13384)------------------------------
% 2.24/1.54 % (13384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.54 % (13384)Termination reason: Unknown
% 2.24/1.54 % (13384)Termination phase: shuffling
% 2.24/1.54
% 2.24/1.54 % (13384)Memory used [KB]: 1279
% 2.24/1.54 % (13384)Time elapsed: 0.004 s
% 2.24/1.54 % (13384)Instructions burned: 4 (million)
% 2.24/1.54 % (13384)------------------------------
% 2.24/1.54 % (13384)------------------------------
% 2.24/1.54 % (13387)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/710Mi)
% 2.24/1.54 % (13385)Instruction limit reached!
% 2.24/1.54 % (13385)------------------------------
% 2.24/1.54 % (13385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.54 % (13385)Termination reason: Unknown
% 2.24/1.54 % (13385)Termination phase: shuffling
% 2.24/1.54
% 2.24/1.54 % (13385)Memory used [KB]: 1279
% 2.24/1.54 % (13385)Time elapsed: 0.003 s
% 2.24/1.54 % (13385)Instructions burned: 6 (million)
% 2.24/1.54 % (13385)------------------------------
% 2.24/1.54 % (13385)------------------------------
% 2.24/1.54 % (13386)Instruction limit reached!
% 2.24/1.54 % (13386)------------------------------
% 2.24/1.54 % (13386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.54 % (13386)Termination reason: Unknown
% 2.24/1.54 % (13386)Termination phase: Property scanning
% 2.24/1.54
% 2.24/1.54 % (13386)Memory used [KB]: 1535
% 2.24/1.54 % (13386)Time elapsed: 0.006 s
% 2.24/1.54 % (13386)Instructions burned: 19 (million)
% 2.24/1.54 % (13386)------------------------------
% 2.24/1.54 % (13386)------------------------------
% 2.24/1.55 % (13388)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/6Mi)
% 2.24/1.55 % (13390)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_13088 for (2999ds/21Mi)
% 2.24/1.55 % (13388)Instruction limit reached!
% 2.24/1.55 % (13388)------------------------------
% 2.24/1.55 % (13388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.55 % (13388)Termination reason: Unknown
% 2.24/1.55 % (13388)Termination phase: shuffling
% 2.24/1.55
% 2.24/1.55 % (13388)Memory used [KB]: 1279
% 2.24/1.55 % (13388)Time elapsed: 0.005 s
% 2.24/1.55 % (13388)Instructions burned: 6 (million)
% 2.24/1.55 % (13388)------------------------------
% 2.24/1.55 % (13388)------------------------------
% 2.24/1.55 % (13391)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/5Mi)
% 2.24/1.56 % (13391)Instruction limit reached!
% 2.24/1.56 % (13391)------------------------------
% 2.24/1.56 % (13391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.56 % (13391)Termination reason: Unknown
% 2.24/1.56 % (13391)Termination phase: shuffling
% 2.24/1.56
% 2.24/1.56 % (13391)Memory used [KB]: 1279
% 2.24/1.56 % (13391)Time elapsed: 0.003 s
% 2.24/1.56 % (13391)Instructions burned: 7 (million)
% 2.24/1.56 % (13391)------------------------------
% 2.24/1.56 % (13391)------------------------------
% 2.24/1.56 % (13390)Instruction limit reached!
% 2.24/1.56 % (13390)------------------------------
% 2.24/1.56 % (13390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.56 % (13390)Termination reason: Unknown
% 2.24/1.56 % (13390)Termination phase: Property scanning
% 2.24/1.56
% 2.24/1.56 % (13390)Memory used [KB]: 1535
% 2.24/1.56 % (13390)Time elapsed: 0.008 s
% 2.24/1.56 % (13390)Instructions burned: 21 (million)
% 2.24/1.56 % (13390)------------------------------
% 2.24/1.56 % (13390)------------------------------
% 2.24/1.56 % (13389)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_13088 for (2999ds/902Mi)
% 2.24/1.56 % (13393)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13088 for (2999ds/377Mi)
% 2.24/1.57 % (13394)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_13088 for (2999ds/779Mi)
% 2.24/1.57 % (13392)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_13088 for (2999ds/6Mi)
% 2.24/1.57 % (13392)Instruction limit reached!
% 2.24/1.57 % (13392)------------------------------
% 2.24/1.57 % (13392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.57 % (13392)Termination reason: Unknown
% 2.24/1.57 % (13392)Termination phase: shuffling
% 2.24/1.57
% 2.24/1.57 % (13392)Memory used [KB]: 1279
% 2.24/1.57 % (13392)Time elapsed: 0.004 s
% 2.24/1.57 % (13392)Instructions burned: 6 (million)
% 2.24/1.57 % (13392)------------------------------
% 2.24/1.57 % (13392)------------------------------
% 2.24/1.58 % (13395)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_13088 for (2999ds/19Mi)
% 2.24/1.59 % (13395)Instruction limit reached!
% 2.24/1.59 % (13395)------------------------------
% 2.24/1.59 % (13395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.59 % (13395)Termination reason: Unknown
% 2.24/1.59 % (13395)Termination phase: Property scanning
% 2.24/1.59
% 2.24/1.59 % (13395)Memory used [KB]: 1535
% 2.24/1.59 % (13395)Time elapsed: 0.008 s
% 2.24/1.59 % (13395)Instructions burned: 22 (million)
% 2.24/1.59 % (13395)------------------------------
% 2.24/1.59 % (13395)------------------------------
% 2.24/1.60 % (13396)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13088 for (2998ds/879Mi)
% 2.24/1.61 % (13371)Instruction limit reached!
% 2.24/1.61 % (13371)------------------------------
% 2.24/1.61 % (13371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.61 % (13371)Termination reason: Unknown
% 2.24/1.61 % (13371)Termination phase: Saturation
% 2.24/1.61
% 2.24/1.61 % (13371)Memory used [KB]: 7675
% 2.24/1.61 % (13371)Time elapsed: 0.126 s
% 2.24/1.61 % (13371)Instructions burned: 276 (million)
% 2.24/1.61 % (13371)------------------------------
% 2.24/1.61 % (13371)------------------------------
% 2.24/1.62 % (13397)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13088 for (2998ds/17Mi)
% 2.24/1.62 % (13397)Instruction limit reached!
% 2.24/1.62 % (13397)------------------------------
% 2.24/1.62 % (13397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.62 % (13397)Termination reason: Unknown
% 2.24/1.62 % (13397)Termination phase: Property scanning
% 2.24/1.62
% 2.24/1.62 % (13397)Memory used [KB]: 1535
% 2.24/1.62 % (13397)Time elapsed: 0.007 s
% 2.24/1.62 % (13397)Instructions burned: 18 (million)
% 2.24/1.62 % (13397)------------------------------
% 2.24/1.62 % (13397)------------------------------
% 2.24/1.63 % (13398)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13088 for (2998ds/3Mi)
% 2.24/1.64 % (13398)Instruction limit reached!
% 2.24/1.64 % (13398)------------------------------
% 2.24/1.64 % (13398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.64 % (13398)Termination reason: Unknown
% 2.24/1.64 % (13398)Termination phase: shuffling
% 2.24/1.64
% 2.24/1.64 % (13398)Memory used [KB]: 1279
% 2.24/1.64 % (13398)Time elapsed: 0.003 s
% 2.24/1.64 % (13398)Instructions burned: 4 (million)
% 2.24/1.64 % (13398)------------------------------
% 2.24/1.64 % (13398)------------------------------
% 2.24/1.65 % (13399)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13088 for (2998ds/30Mi)
% 2.24/1.65 % (13399)Instruction limit reached!
% 2.24/1.65 % (13399)------------------------------
% 2.24/1.65 % (13399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.65 % (13399)Termination reason: Unknown
% 2.24/1.65 % (13399)Termination phase: Property scanning
% 2.24/1.65
% 2.24/1.65 % (13399)Memory used [KB]: 1535
% 2.24/1.65 % (13399)Time elapsed: 0.011 s
% 2.24/1.65 % (13399)Instructions burned: 33 (million)
% 2.24/1.65 % (13399)------------------------------
% 2.24/1.65 % (13399)------------------------------
% 2.24/1.66 % (13400)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13088 for (2998ds/127Mi)
% 2.24/1.68 % (13393)Instruction limit reached!
% 2.24/1.68 % (13393)------------------------------
% 2.24/1.68 % (13393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.68 % (13393)Termination reason: Unknown
% 2.24/1.68 % (13393)Termination phase: Saturation
% 2.24/1.68
% 2.24/1.68 % (13393)Memory used [KB]: 7164
% 2.24/1.68 % (13393)Time elapsed: 0.115 s
% 2.24/1.68 % (13393)Instructions burned: 377 (million)
% 2.24/1.68 % (13393)------------------------------
% 2.24/1.68 % (13393)------------------------------
% 2.24/1.69 % (13401)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13088 for (2997ds/100Mi)
% 2.24/1.70 % (13400)Instruction limit reached!
% 2.24/1.70 % (13400)------------------------------
% 2.24/1.70 % (13400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.70 % (13400)Termination reason: Unknown
% 2.24/1.70 % (13400)Termination phase: Saturation
% 2.24/1.70
% 2.24/1.70 % (13400)Memory used [KB]: 6780
% 2.24/1.70 % (13400)Time elapsed: 0.040 s
% 2.24/1.70 % (13400)Instructions burned: 129 (million)
% 2.24/1.70 % (13400)------------------------------
% 2.24/1.70 % (13400)------------------------------
% 2.24/1.71 % (13402)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_13088 for (2997ds/3Mi)
% 2.24/1.71 % (13402)Instruction limit reached!
% 2.24/1.71 % (13402)------------------------------
% 2.24/1.71 % (13402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.71 % (13402)Termination reason: Unknown
% 2.24/1.71 % (13402)Termination phase: shuffling
% 2.24/1.71
% 2.24/1.71 % (13402)Memory used [KB]: 1279
% 2.24/1.71 % (13402)Time elapsed: 0.003 s
% 2.24/1.71 % (13402)Instructions burned: 4 (million)
% 2.24/1.71 % (13402)------------------------------
% 2.24/1.71 % (13402)------------------------------
% 2.24/1.72 % (13401)Instruction limit reached!
% 2.24/1.72 % (13401)------------------------------
% 2.24/1.72 % (13401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.72 % (13401)Termination reason: Unknown
% 2.24/1.72 % (13401)Termination phase: Saturation
% 2.24/1.72
% 2.24/1.72 % (13401)Memory used [KB]: 6396
% 2.24/1.72 % (13401)Time elapsed: 0.030 s
% 2.24/1.72 % (13401)Instructions burned: 103 (million)
% 2.24/1.72 % (13401)------------------------------
% 2.24/1.72 % (13401)------------------------------
% 2.24/1.72 % (13403)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_13088 for (2997ds/20Mi)
% 2.24/1.73 % (13404)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_13088 for (2997ds/86Mi)
% 2.24/1.73 % (13403)Instruction limit reached!
% 2.24/1.73 % (13403)------------------------------
% 2.24/1.73 % (13403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.73 % (13403)Termination reason: Unknown
% 2.24/1.73 % (13403)Termination phase: Preprocessing 1
% 2.24/1.73
% 2.24/1.73 % (13403)Memory used [KB]: 1407
% 2.24/1.73 % (13403)Time elapsed: 0.008 s
% 2.24/1.73 % (13403)Instructions burned: 20 (million)
% 2.24/1.73 % (13403)------------------------------
% 2.24/1.73 % (13403)------------------------------
% 2.24/1.74 % (13405)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_13088 for (2997ds/107Mi)
% 2.24/1.75 % (13404)Instruction limit reached!
% 2.24/1.75 % (13404)------------------------------
% 2.24/1.75 % (13404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.75 % (13404)Termination reason: Unknown
% 2.24/1.75 % (13404)Termination phase: Saturation
% 2.24/1.75
% 2.24/1.75 % (13404)Memory used [KB]: 6396
% 2.24/1.75 % (13404)Time elapsed: 0.025 s
% 2.24/1.75 % (13404)Instructions burned: 89 (million)
% 2.24/1.75 % (13404)------------------------------
% 2.24/1.75 % (13404)------------------------------
% 2.24/1.77 % (13394)Instruction limit reached!
% 2.24/1.77 % (13394)------------------------------
% 2.24/1.77 % (13394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.77 % (13394)Termination reason: Unknown
% 2.24/1.77 % (13394)Termination phase: Saturation
% 2.24/1.77
% 2.24/1.77 % (13394)Memory used [KB]: 6524
% 2.24/1.77 % (13394)Time elapsed: 0.200 s
% 2.24/1.77 % (13394)Instructions burned: 781 (million)
% 2.24/1.77 % (13394)------------------------------
% 2.24/1.77 % (13394)------------------------------
% 2.24/1.77 % (13387)Instruction limit reached!
% 2.24/1.77 % (13387)------------------------------
% 2.24/1.77 % (13387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.77 % (13387)Termination reason: Unknown
% 2.24/1.77 % (13387)Termination phase: Saturation
% 2.24/1.77
% 2.24/1.77 % (13387)Memory used [KB]: 8955
% 2.24/1.77 % (13387)Time elapsed: 0.228 s
% 2.24/1.77 % (13387)Instructions burned: 710 (million)
% 2.24/1.77 % (13387)------------------------------
% 2.24/1.77 % (13387)------------------------------
% 2.24/1.77 % (13406)lrs+2_1:1024_cnfonf=lazy_gen:fe=off:hud=15:plsq=on:plsqc=1:plsqr=32,1:i=39:si=on:rtra=on_0 on DTF2THF_13088 for (2997ds/39Mi)
% 2.24/1.77 % (13396)First to succeed.
% 2.24/1.77 % (13378)Instruction limit reached!
% 2.24/1.77 % (13378)------------------------------
% 2.24/1.77 % (13378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.77 % (13378)Termination reason: Unknown
% 2.24/1.77 % (13378)Termination phase: Saturation
% 2.24/1.77
% 2.24/1.77 % (13378)Memory used [KB]: 8059
% 2.24/1.77 % (13378)Time elapsed: 0.272 s
% 2.24/1.77 % (13378)Instructions burned: 1044 (million)
% 2.24/1.77 % (13378)------------------------------
% 2.24/1.77 % (13378)------------------------------
% 2.24/1.77 % (13405)Instruction limit reached!
% 2.24/1.77 % (13405)------------------------------
% 2.24/1.77 % (13405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.77 % (13405)Termination reason: Unknown
% 2.24/1.77 % (13405)Termination phase: Saturation
% 2.24/1.77
% 2.24/1.77 % (13405)Memory used [KB]: 6652
% 2.24/1.77 % (13405)Time elapsed: 0.033 s
% 2.24/1.77 % (13405)Instructions burned: 109 (million)
% 2.24/1.77 % (13405)------------------------------
% 2.24/1.77 % (13405)------------------------------
% 2.24/1.77 % (13396)Refutation found. Thanks to Tanya!
% 2.24/1.77 % SZS status Theorem for DTF2THF_13088
% 2.24/1.77 % SZS output start Proof for DTF2THF_13088
% 2.24/1.77 thf(func_def_0, type, in: $i > $i > $o).
% 2.24/1.77 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.24/1.77 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.24/1.77 thf(func_def_8, type, powerset: $i > $i).
% 2.24/1.77 thf(func_def_10, type, setunion: $i > $i).
% 2.24/1.77 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.24/1.77 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_26, type, prop2set: $o > $i).
% 2.24/1.77 thf(func_def_36, type, nonempty: $i > $o).
% 2.24/1.77 thf(func_def_69, type, set2prop: $i > $o).
% 2.24/1.77 thf(func_def_88, type, subset: $i > $i > $o).
% 2.24/1.77 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.24/1.77 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.24/1.77 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.24/1.77 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.24/1.77 thf(func_def_149, type, sK4: ($i > $o) > $i).
% 2.24/1.77 thf(func_def_150, type, sK5: ($i > $o) > $i).
% 2.24/1.77 thf(func_def_151, type, sK6: ($i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_152, type, sK7: ($i > $o) > $i).
% 2.24/1.77 thf(func_def_153, type, sK8: ($i > $o) > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_154, type, sK9: ($i > $o) > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_155, type, sK10: ($i > $o) > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_156, type, sK11: ($i > $o) > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_157, type, sK12: ($i > $o) > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_158, type, sK13: ($i > $o) > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_159, type, sK14: $i > $i > $i).
% 2.24/1.77 thf(func_def_160, type, sK15: $i > $i > $i).
% 2.24/1.77 thf(func_def_161, type, sK16: $i > $i > $i).
% 2.24/1.77 thf(func_def_162, type, sK17: $o > $i > $i > $i).
% 2.24/1.77 thf(func_def_163, type, sK18: ($i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_164, type, sK19: ($i > $o) > $i > ($i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_165, type, sK20: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_166, type, sK21: $i > $i).
% 2.24/1.77 thf(func_def_167, type, sK22: $i > $i > $i).
% 2.24/1.77 thf(func_def_168, type, sK23: $i > $i > $i).
% 2.24/1.77 thf(func_def_169, type, sK24: $i > $i > $i).
% 2.24/1.77 thf(func_def_170, type, sK25: $i > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_171, type, sK26: $i > $i).
% 2.24/1.77 thf(func_def_172, type, sK27: $i > $i).
% 2.24/1.77 thf(func_def_173, type, sK28: $i > $i).
% 2.24/1.77 thf(func_def_174, type, sK29: $i > $i > $i).
% 2.24/1.77 thf(func_def_175, type, sK30: $i > $i > $i).
% 2.24/1.77 thf(func_def_176, type, sK31: $i > $i > $i).
% 2.24/1.77 thf(func_def_177, type, sK32: $i > $i).
% 2.24/1.77 thf(func_def_178, type, sK33: $i > $i > $i).
% 2.24/1.77 thf(func_def_179, type, sK34: $i > $i > $i).
% 2.24/1.77 thf(func_def_180, type, sK35: $i > $i > $i).
% 2.24/1.77 thf(func_def_181, type, sK36: $i > $i > $i > $i).
% 2.24/1.77 thf(func_def_182, type, sK37: $i > $i).
% 2.24/1.77 thf(func_def_183, type, sK38: ($i > $i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_184, type, sK39: ($i > $i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_185, type, sK40: ($i > $i > $o) > $i > $i > $i).
% 2.24/1.77 thf(func_def_186, type, sK41: ($i > $i > $o) > $i > $i > $i).
% 2.24/1.77 thf(func_def_187, type, sK42: ($i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_188, type, sK43: ($i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_189, type, sK44: ($i > $o) > $i).
% 2.24/1.77 thf(func_def_190, type, sK45: ($i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_191, type, sK46: ($i > $o) > $i).
% 2.24/1.77 thf(func_def_192, type, sK47: ($i > $o) > $i > $i).
% 2.24/1.77 thf(func_def_193, type, sK48: $i > $i).
% 2.24/1.77 thf(func_def_194, type, sK49: $i > ($i > $o) > $i).
% 2.24/1.77 thf(func_def_195, type, ph50: !>[X0: $tType]:(X0)).
% 2.24/1.77 thf(f3113,plain,(
% 2.24/1.77 $false),
% 2.24/1.77 inference(avatar_sat_refutation,[status(thm)],[f1752,f2159,f3112])).
% 2.24/1.77 thf(f3112,plain,(
% 2.24/1.77 ~spl3_1),
% 2.24/1.77 inference(avatar_contradiction_clause,[status(thm)],[f3111])).
% 2.24/1.77 thf(f3111,plain,(
% 2.24/1.77 $false | ~spl3_1),
% 2.24/1.77 inference(trivial_inequality_removal,[status(thm)],[f3110])).
% 2.24/1.77 thf(f3110,plain,(
% 2.24/1.77 ($true = $false) | ~spl3_1),
% 2.24/1.77 inference(forward_demodulation,[status(thm)],[f3098,f2168])).
% 2.24/1.77 thf(f2168,plain,(
% 2.24/1.77 ((in @ sK0 @ sK2) = $false) | ~spl3_1),
% 2.24/1.77 inference(trivial_inequality_removal,[status(thm)],[f2162])).
% 2.24/1.77 thf(f2162,plain,(
% 2.24/1.77 ($true != $true) | ((in @ sK0 @ sK2) = $false) | ~spl3_1),
% 2.24/1.77 inference(superposition,[status(thm)],[f562,f1736])).
% 2.24/1.77 thf(f1736,plain,(
% 2.24/1.77 ( ! [X4 : $o] : (($true = X4) | ($false = X4)) ) | ~spl3_1),
% 2.24/1.77 inference(avatar_component_clause,[status(thm)],[f1735])).
% 2.24/1.77 thf(f1735,definition,(
% 2.24/1.77 spl3_1 <=> ! [X4 : $o] : (($true = X4) | ($false = X4))),
% 2.24/1.77 introduced(definition,[new_symbols(naming,[spl3_1])],[avatar_definition])).
% 2.24/1.77 thf(f562,plain,(
% 2.24/1.77 ((in @ sK0 @ sK2) != $true)),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f345])).
% 2.24/1.77 thf(f345,plain,(
% 2.24/1.77 (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (subsetI2 = $true) & (noeltsimpempty = $true) & (upairsetIL = $true) & (upairset2IR = $true) & (binunionRsub = $true) & (((in @ sK0 @ sK2) != $true) & ($true = (in @ sK0 @ (binintersect @ sK1 @ sK2)))) & (notequalI2 = $true) & (binunionE = $true) & (setbeta = $true) & (binunionEcases = $true) & (dsetconstr__Cong = $true) & (nonemptyI1 = $true) & (prop2set2propI = $true) & (quantDeMorgan3 = $true) & (emptyI = $true) & (eqimpsubset2 = $true) & (foundationAx = $true) & (inCongP = $true) & (powersetE1 = $true) & (subsetRefl = $true) & (setadjoinAx = $true) & (singletonsswitch = $true) & (omega0Ax = $true) & (setadjoinIR = $true) & (powersetAx = $true) & (setextsub = $true) & (setext = $true) & (sepSubset = $true) & (upairsetE = $true) & (powerset__Cong = $true) & (emptyinPowerset = $true) & (emptyInPowerset = $true) & (emptysetsubset = $true) & (subsetTrans = $true) & (setunionE = $true) & (replAx = $true) & (setadjoinSub = $true) & (sepInPowerset = $true) & (setadjoinE = $true) & (omegaIndAx = $true) & (uniqinunit = $true) & (nonemptyI = $true) & (descrp = $true) & (exuEu = $true) & (setadjoinSub2 = $true) & (exuI3 = $true) & (setextAx = $true) & (setadjoinIL = $true) & (setunionAx = $true) & (exuI2 = $true) & (quantDeMorgan4 = $true) & (notinemptyset = $true) & (powersetE = $true) & (subset2powerset = $true) & (descr__Cong = $true) & (wellorderingAx = $true) & (emptyinunitempty = $true) & (binintersectLsub = $true) & (binunionIL = $true) & (subsetI1 = $true) & (binintersectI = $true) & (emptysetE = $true) & (notinsingleton = $true) & (eqimpsubset1 = $true) & (subsetE = $true) & (emptyset__Cong = $true) & (exuI1 = $true) & (dsetconstrI = $true) & (emptysetimpfalse = $true) & (emptyE1 = $true) & (dsetconstrEL = $true) & (notdallE = $true) & (binintersectSubset5 = $true) & (in__Cong = $true) & (subsetE2 = $true) & (exuE3u = $true) & (binintersectEL = $true) & (binunionIR = $true) & (notsubsetI = $true) & (subsetemptysetimpeq = $true) & (setunionI = $true) & (powersetI1 = $true) & (exu__Cong = $true) & (omega__Cong = $true) & (setoftrueEq = $true) & (setadjoin__Cong = $true) & (quantDeMorgan1 = $true) & (setadjoinOr = $true) & (emptysetAx = $true) & (exuE2 = $true) & (quantDeMorgan2 = $true) & (notdexE = $true) & (nonemptyImpWitness = $true) & (nonemptyE1 = $true) & (upairsetIR = $true) & (inPowerset = $true) & (notequalI1 = $true) & (eqinunit = $true) & (setunion__Cong = $true) & (omegaSAx = $true) & (exuE3e = $true) & (subPowSU = $true) & (binunionLsub = $true) & (powersetsubset = $true) & (powersetI = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (vacuousDall = $true) & (prop2setE = $true) & (prop2setI = $true)),
% 2.24/1.77 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f343,f344])).
% 2.24/1.77 thf(f344,plain,(
% 2.24/1.77 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ($true = (in @ X0 @ (binintersect @ X1 @ X2)))) => (((in @ sK0 @ sK2) != $true) & ($true = (in @ sK0 @ (binintersect @ sK1 @ sK2))))),
% 2.24/1.77 introduced(definition,[],[choice_axiom])).
% 2.24/1.77 thf(f343,plain,(
% 2.24/1.77 (binintersectSubset3 = $true) & (binintersectSubset2 = $true) & (subsetI2 = $true) & (noeltsimpempty = $true) & (upairsetIL = $true) & (upairset2IR = $true) & (binunionRsub = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ($true = (in @ X0 @ (binintersect @ X1 @ X2)))) & (notequalI2 = $true) & (binunionE = $true) & (setbeta = $true) & (binunionEcases = $true) & (dsetconstr__Cong = $true) & (nonemptyI1 = $true) & (prop2set2propI = $true) & (quantDeMorgan3 = $true) & (emptyI = $true) & (eqimpsubset2 = $true) & (foundationAx = $true) & (inCongP = $true) & (powersetE1 = $true) & (subsetRefl = $true) & (setadjoinAx = $true) & (singletonsswitch = $true) & (omega0Ax = $true) & (setadjoinIR = $true) & (powersetAx = $true) & (setextsub = $true) & (setext = $true) & (sepSubset = $true) & (upairsetE = $true) & (powerset__Cong = $true) & (emptyinPowerset = $true) & (emptyInPowerset = $true) & (emptysetsubset = $true) & (subsetTrans = $true) & (setunionE = $true) & (replAx = $true) & (setadjoinSub = $true) & (sepInPowerset = $true) & (setadjoinE = $true) & (omegaIndAx = $true) & (uniqinunit = $true) & (nonemptyI = $true) & (descrp = $true) & (exuEu = $true) & (setadjoinSub2 = $true) & (exuI3 = $true) & (setextAx = $true) & (setadjoinIL = $true) & (setunionAx = $true) & (exuI2 = $true) & (quantDeMorgan4 = $true) & (notinemptyset = $true) & (powersetE = $true) & (subset2powerset = $true) & (descr__Cong = $true) & (wellorderingAx = $true) & (emptyinunitempty = $true) & (binintersectLsub = $true) & (binunionIL = $true) & (subsetI1 = $true) & (binintersectI = $true) & (emptysetE = $true) & (notinsingleton = $true) & (eqimpsubset1 = $true) & (subsetE = $true) & (emptyset__Cong = $true) & (exuI1 = $true) & (dsetconstrI = $true) & (emptysetimpfalse = $true) & (emptyE1 = $true) & (dsetconstrEL = $true) & (notdallE = $true) & (binintersectSubset5 = $true) & (in__Cong = $true) & (subsetE2 = $true) & (exuE3u = $true) & (binintersectEL = $true) & (binunionIR = $true) & (notsubsetI = $true) & (subsetemptysetimpeq = $true) & (setunionI = $true) & (powersetI1 = $true) & (exu__Cong = $true) & (omega__Cong = $true) & (setoftrueEq = $true) & (setadjoin__Cong = $true) & (quantDeMorgan1 = $true) & (setadjoinOr = $true) & (emptysetAx = $true) & (exuE2 = $true) & (quantDeMorgan2 = $true) & (notdexE = $true) & (nonemptyImpWitness = $true) & (nonemptyE1 = $true) & (upairsetIR = $true) & (inPowerset = $true) & (notequalI1 = $true) & (eqinunit = $true) & (setunion__Cong = $true) & (omegaSAx = $true) & (exuE3e = $true) & (subPowSU = $true) & (binunionLsub = $true) & (powersetsubset = $true) & (powersetI = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (vacuousDall = $true) & (prop2setE = $true) & (prop2setI = $true)),
% 2.24/1.77 inference(flattening,[status(thm)],[f342])).
% 2.24/1.77 thf(f342,plain,(
% 2.24/1.77 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X0 @ X2)) & ($true = (in @ X0 @ (binintersect @ X1 @ X2)))) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $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)),
% 2.24/1.77 inference(ennf_transformation,[status(thm)],[f174])).
% 2.24/1.77 thf(f174,plain,(
% 2.24/1.77 ~((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) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X0 @ (binintersect @ X1 @ X2))) => ($true = (in @ X0 @ X2))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.24/1.77 inference(fool_elimination,[status(thm)],[f173])).
% 2.24/1.77 thf(f173,plain,(
% 2.24/1.77 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (binintersect @ X1 @ X2)) => (in @ X0 @ X2)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.24/1.77 inference(rectify,[status(thm)],[f116])).
% 2.24/1.77 thf(f116,negated_conjecture,(
% 2.24/1.77 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.24/1.77 inference(negated_conjecture,[status(cth)],[f115])).
% 2.24/1.77 thf(f115,conjecture,(
% 2.24/1.77 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => ! [X1 : $i,X3 : $i,X4 : $i] : ((in @ X1 @ (binintersect @ X3 @ X4)) => (in @ X1 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.24/1.77 file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',binintersectER)).
% 2.24/1.77 thf(f3098,plain,(
% 2.24/1.77 ((in @ sK0 @ sK2) = $true)),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f3097])).
% 2.24/1.77 thf(f3097,plain,(
% 2.24/1.77 ($true = ((^[Y0 : $i]: (in @ Y0 @ sK2)) @ sK0))),
% 2.24/1.77 inference(trivial_inequality_removal,[status(thm)],[f3086])).
% 2.24/1.77 thf(f3086,plain,(
% 2.24/1.77 ($true = ((^[Y0 : $i]: (in @ Y0 @ sK2)) @ sK0)) | ($true = $false)),
% 2.24/1.77 inference(superposition,[status(thm)],[f1653,f1524])).
% 2.24/1.77 thf(f1524,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($false = (in @ X2 @ (dsetconstr @ X1 @ X3))) | ($true = (X3 @ X2))) )),
% 2.24/1.77 inference(binary_proxy_clausification,[status(thm)],[f1523])).
% 2.24/1.77 thf(f1523,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ (dsetconstr @ X1 @ X3)) => (X3 @ X2)))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1522])).
% 2.24/1.77 thf(f1522,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ X2))) @ X3))) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f1521])).
% 2.24/1.77 thf(f1521,plain,(
% 2.24/1.77 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ X2)))))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1520])).
% 2.24/1.77 thf(f1520,plain,(
% 2.24/1.77 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (Y1 @ Y0))))) @ X2))) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f1519])).
% 2.24/1.77 thf(f1519,plain,(
% 2.24/1.77 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (Y1 @ Y0)))))))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1518])).
% 2.24/1.77 thf(f1518,plain,(
% 2.24/1.77 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1))))))) @ X1))) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f1517])).
% 2.24/1.77 thf(f1517,plain,(
% 2.24/1.77 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))) = $true)),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f683])).
% 2.24/1.77 thf(f683,plain,(
% 2.24/1.77 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))) = $true)),
% 2.24/1.77 inference(definition_unfolding,[status(thm)],[f461,f368])).
% 2.24/1.77 thf(f368,plain,(
% 2.24/1.77 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f259])).
% 2.24/1.77 thf(f259,plain,(
% 2.24/1.77 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 2.24/1.77 inference(fool_elimination,[status(thm)],[f258])).
% 2.24/1.77 thf(f258,plain,(
% 2.24/1.77 (dsetconstrER = ! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X1)))),
% 2.24/1.77 inference(rectify,[status(thm)],[f16])).
% 2.24/1.77 thf(f16,axiom,(
% 2.24/1.77 (dsetconstrER = ! [X0 : $i > $o,X1 : $i,X3 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)))),
% 2.24/1.77 file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',dsetconstrER)).
% 2.24/1.77 thf(f461,plain,(
% 2.24/1.77 (dsetconstrER = $true)),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f345])).
% 2.24/1.77 thf(f1653,plain,(
% 2.24/1.77 ($true = (in @ sK0 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ Y0 @ sK2)))))),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f584])).
% 2.24/1.77 thf(f584,plain,(
% 2.24/1.77 ($true = (in @ sK0 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK1 @ sK2)))),
% 2.24/1.77 inference(definition_unfolding,[status(thm)],[f561,f411])).
% 2.24/1.77 thf(f411,plain,(
% 2.24/1.77 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f293])).
% 2.24/1.77 thf(f293,plain,(
% 2.24/1.77 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 2.24/1.77 inference(fool_elimination,[status(thm)],[f292])).
% 2.24/1.77 thf(f292,plain,(
% 2.24/1.77 ((^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))) = binintersect)),
% 2.24/1.77 inference(rectify,[status(thm)],[f108])).
% 2.24/1.77 thf(f108,axiom,(
% 2.24/1.77 ((^[X3 : $i, X4 : $i] : (dsetconstr @ X3 @ (^[X1 : $i] : (in @ X1 @ X4)))) = binintersect)),
% 2.24/1.77 file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',binintersect)).
% 2.24/1.77 thf(f561,plain,(
% 2.24/1.77 ($true = (in @ sK0 @ (binintersect @ sK1 @ sK2)))),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f345])).
% 2.24/1.77 thf(f2159,plain,(
% 2.24/1.77 ~spl3_5),
% 2.24/1.77 inference(avatar_contradiction_clause,[status(thm)],[f2158])).
% 2.24/1.77 thf(f2158,plain,(
% 2.24/1.77 $false | ~spl3_5),
% 2.24/1.77 inference(trivial_inequality_removal,[status(thm)],[f2157])).
% 2.24/1.77 thf(f2157,plain,(
% 2.24/1.77 ($true = $false) | ~spl3_5),
% 2.24/1.77 inference(forward_demodulation,[status(thm)],[f601,f1957])).
% 2.24/1.77 thf(f1957,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i] : (((in @ X2 @ X3) = $false)) ) | ~spl3_5),
% 2.24/1.77 inference(trivial_inequality_removal,[status(thm)],[f1956])).
% 2.24/1.77 thf(f1956,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i] : (((in @ X2 @ X3) = $false) | ($true = $false)) ) | ~spl3_5),
% 2.24/1.77 inference(forward_demodulation,[status(thm)],[f1162,f1751])).
% 2.24/1.77 thf(f1751,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X1 @ (binunion @ X2 @ X3)) = $false)) ) | ~spl3_5),
% 2.24/1.77 inference(avatar_component_clause,[status(thm)],[f1750])).
% 2.24/1.77 thf(f1750,definition,(
% 2.24/1.77 spl3_5 <=> ! [X2 : $i,X1 : $i,X3 : $i] : ((in @ X1 @ (binunion @ X2 @ X3)) = $false)),
% 2.24/1.77 introduced(definition,[new_symbols(naming,[spl3_5])],[avatar_definition])).
% 2.24/1.77 thf(f1162,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (binunion @ X3 @ X1)) = $true) | ((in @ X2 @ X3) = $false)) )),
% 2.24/1.77 inference(binary_proxy_clausification,[status(thm)],[f1161])).
% 2.24/1.77 thf(f1161,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X3) => (in @ X2 @ (binunion @ X3 @ X1))))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1160])).
% 2.24/1.77 thf(f1160,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X2 @ Y0) => (in @ X2 @ (binunion @ Y0 @ X1)))) @ X3) = $true)) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f1159])).
% 2.24/1.77 thf(f1159,plain,(
% 2.24/1.77 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ Y0) => (in @ X2 @ (binunion @ Y0 @ X1))))))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1158])).
% 2.24/1.77 thf(f1158,plain,(
% 2.24/1.77 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y1 @ X1)))))) @ X2))) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f1157])).
% 2.24/1.77 thf(f1157,plain,(
% 2.24/1.77 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ Y1) => (in @ Y0 @ (binunion @ Y1 @ X1))))))))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1156])).
% 2.24/1.77 thf(f1156,plain,(
% 2.24/1.77 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y2 @ Y0)))))))) @ X1))) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f637])).
% 2.24/1.77 thf(f637,plain,(
% 2.24/1.77 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y2 @ Y0))))))))) = $true)),
% 2.24/1.77 inference(definition_unfolding,[status(thm)],[f508,f347])).
% 2.24/1.77 thf(f347,plain,(
% 2.24/1.77 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y2 @ Y0))))))))))),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f151])).
% 2.24/1.77 thf(f151,plain,(
% 2.24/1.77 (binunionIL = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y2) => (in @ Y1 @ (binunion @ Y2 @ Y0))))))))))),
% 2.24/1.77 inference(fool_elimination,[status(thm)],[f150])).
% 2.24/1.77 thf(f150,plain,(
% 2.24/1.77 (binunionIL = ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X0) => (in @ X1 @ (binunion @ X0 @ X2))))),
% 2.24/1.77 inference(rectify,[status(thm)],[f101])).
% 2.24/1.77 thf(f101,axiom,(
% 2.24/1.77 (binunionIL = ! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X3) => (in @ X1 @ (binunion @ X3 @ X4))))),
% 2.24/1.77 file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',binunionIL)).
% 2.24/1.77 thf(f508,plain,(
% 2.24/1.77 (binunionIL = $true)),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f345])).
% 2.24/1.77 thf(f601,plain,(
% 2.24/1.77 ((in @ emptyset @ omega) = $true)),
% 2.24/1.77 inference(definition_unfolding,[status(thm)],[f544,f386])).
% 2.24/1.77 thf(f386,plain,(
% 2.24/1.77 (omega0Ax = (in @ emptyset @ omega))),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f7])).
% 2.24/1.77 thf(f7,axiom,(
% 2.24/1.77 (omega0Ax = (in @ emptyset @ omega))),
% 2.24/1.77 file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',omega0Ax)).
% 2.24/1.77 thf(f544,plain,(
% 2.24/1.77 (omega0Ax = $true)),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f345])).
% 2.24/1.77 thf(f1752,plain,(
% 2.24/1.77 spl3_1 | spl3_5),
% 2.24/1.77 inference(avatar_split_clause,[status(thm)],[f1204,f1750,f1735])).
% 2.24/1.77 thf(f1204,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = X4) | ($false = X4) | ((in @ X1 @ (binunion @ X2 @ X3)) = $false)) )),
% 2.24/1.77 inference(duplicate_literal_removal,[status(thm)],[f1202])).
% 2.24/1.77 thf(f1202,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((in @ X1 @ (binunion @ X2 @ X3)) = $false) | ($true = X4) | ($false = X4) | ($false = X4)) )),
% 2.24/1.77 inference(binary_proxy_clausification,[status(thm)],[f1201])).
% 2.24/1.77 thf(f1201,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((in @ X1 @ (binunion @ X2 @ X3)) = $false) | ($true = X4) | ($false = X4) | ($false = ((in @ X1 @ X3) => X4))) )),
% 2.24/1.77 inference(binary_proxy_clausification,[status(thm)],[f1196])).
% 2.24/1.77 thf(f1196,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (((((in @ X1 @ X3) => X4) => X4) = $true) | ($false = X4) | ((in @ X1 @ (binunion @ X2 @ X3)) = $false)) )),
% 2.24/1.77 inference(binary_proxy_clausification,[status(thm)],[f1195])).
% 2.24/1.77 thf(f1195,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : ((((in @ X1 @ X2) => X4) = $false) | ((in @ X1 @ (binunion @ X2 @ X3)) = $false) | ((((in @ X1 @ X3) => X4) => X4) = $true)) )),
% 2.24/1.77 inference(binary_proxy_clausification,[status(thm)],[f1194])).
% 2.24/1.77 thf(f1194,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : (($true = (((in @ X1 @ X2) => X4) => (((in @ X1 @ X3) => X4) => X4))) | ((in @ X1 @ (binunion @ X2 @ X3)) = $false)) )),
% 2.24/1.77 inference(binary_proxy_clausification,[status(thm)],[f1193])).
% 2.24/1.77 thf(f1193,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : ((((in @ X1 @ (binunion @ X2 @ X3)) => (((in @ X1 @ X2) => X4) => (((in @ X1 @ X3) => X4) => X4))) = $true)) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1192])).
% 2.24/1.77 thf(f1192,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i,X4 : $o] : ((((^[Y0 : $o]: ((in @ X1 @ (binunion @ X2 @ X3)) => (((in @ X1 @ X2) => Y0) => (((in @ X1 @ X3) => Y0) => Y0)))) @ X4) = $true)) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f1191])).
% 2.24/1.77 thf(f1191,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = (!! @ $o @ (^[Y0 : $o]: ((in @ X1 @ (binunion @ X2 @ X3)) => (((in @ X1 @ X2) => Y0) => (((in @ X1 @ X3) => Y0) => Y0))))))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1190])).
% 2.24/1.77 thf(f1190,plain,(
% 2.24/1.77 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ X1 @ (binunion @ X2 @ Y0)) => (((in @ X1 @ X2) => Y1) => (((in @ X1 @ Y0) => Y1) => Y1)))))) @ X3))) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f1189])).
% 2.24/1.77 thf(f1189,plain,(
% 2.24/1.77 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $o @ (^[Y1 : $o]: ((in @ X1 @ (binunion @ X2 @ Y0)) => (((in @ X1 @ X2) => Y1) => (((in @ X1 @ Y0) => Y1) => Y1))))))))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1188])).
% 2.24/1.77 thf(f1188,plain,(
% 2.24/1.77 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ X1 @ (binunion @ Y0 @ Y1)) => (((in @ X1 @ Y0) => Y2) => (((in @ X1 @ Y1) => Y2) => Y2)))))))) @ X2) = $true)) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f1187])).
% 2.24/1.77 thf(f1187,plain,(
% 2.24/1.77 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $o @ (^[Y2 : $o]: ((in @ X1 @ (binunion @ Y0 @ Y1)) => (((in @ X1 @ Y0) => Y2) => (((in @ X1 @ Y1) => Y2) => Y2))))))))))) )),
% 2.24/1.77 inference(beta_eta_normalization,[status(thm)],[f1186])).
% 2.24/1.77 thf(f1186,plain,(
% 2.24/1.77 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3)))))))))) @ X1) = $true)) )),
% 2.24/1.77 inference(pi_clausification,[status(thm)],[f588])).
% 2.24/1.77 thf(f588,plain,(
% 2.24/1.77 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))))),
% 2.24/1.77 inference(definition_unfolding,[status(thm)],[f557,f445])).
% 2.24/1.77 thf(f445,plain,(
% 2.24/1.77 (binunionEcases = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))))),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f239])).
% 2.24/1.77 thf(f239,plain,(
% 2.24/1.77 (binunionEcases = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: (!! @ $o @ (^[Y3 : $o]: ((in @ Y0 @ (binunion @ Y1 @ Y2)) => (((in @ Y0 @ Y1) => Y3) => (((in @ Y0 @ Y2) => Y3) => Y3))))))))))))),
% 2.24/1.77 inference(fool_elimination,[status(thm)],[f238])).
% 2.24/1.77 thf(f238,plain,(
% 2.24/1.77 (binunionEcases = ! [X0 : $o,X1 : $i,X2 : $i,X3 : $i] : ((in @ X3 @ (binunion @ X2 @ X1)) => (((in @ X3 @ X2) => X0) => (((in @ X3 @ X1) => X0) => X0))))),
% 2.24/1.77 inference(rectify,[status(thm)],[f104])).
% 2.24/1.77 thf(f104,axiom,(
% 2.24/1.77 (binunionEcases = ! [X0 : $o,X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ (binunion @ X3 @ X4)) => (((in @ X1 @ X3) => X0) => (((in @ X1 @ X4) => X0) => X0))))),
% 2.24/1.77 file('/export/starexec/sandbox/tmp/tmp.rHmzVjta6m/DTF2THF_13088.p',binunionEcases)).
% 2.24/1.77 thf(f557,plain,(
% 2.24/1.77 (binunionEcases = $true)),
% 2.24/1.77 inference(cnf_transformation,[status(thm)],[f345])).
% 2.24/1.77 % SZS output end Proof for DTF2THF_13088
% 2.24/1.77 % (13396)------------------------------
% 2.24/1.77 % (13396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.24/1.77 % (13396)Termination reason: Refutation
% 2.24/1.77
% 2.24/1.77 % (13396)Memory used [KB]: 7291
% 2.24/1.77 % (13396)Time elapsed: 0.176 s
% 2.24/1.77 % (13396)Instructions burned: 505 (million)
% 2.24/1.77 % (13396)------------------------------
% 2.24/1.77 % (13396)------------------------------
% 2.24/1.77 % (13365)Success in time 0.316 s
%------------------------------------------------------------------------------