%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU589^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n026.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 09:35:27 AM UTC 2026
% Result : Theorem 2.41s 1.82s
% Output : Refutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 25 unt; 0 typ; 0 def)
% Number of atoms : 1823 ( 476 equ; 0 cnn)
% Maximal formula atoms : 108 ( 46 avg)
% Number of connectives : 1087 ( 12 ~; 8 |; 325 &; 270 @)
% ( 0 <=>; 454 =>; 0 <=; 0 <~>)
% Maximal formula depth : 115 ( 22 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 21 ( 21 >; 0 *; 0 +; 0 <<)
% Number of symbols : 174 ( 170 usr; 111 con; 0-4 aty)
% ( 18 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 89 ( 44 ^; 36 !; 9 ?; 89 :)
% 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_143,type,
sK4: $i > $i ).
thf(func_def_144,type,
sK5: $i > $i ).
thf(func_def_145,type,
sK6: $i > $i > $i ).
thf(func_def_146,type,
sK7: $i > $i > $i ).
thf(func_def_147,type,
sK8: $i > $i > $i ).
thf(func_def_148,type,
sK9: $i > $i > $i > $i ).
thf(func_def_149,type,
sK10: $i > $i ).
thf(func_def_150,type,
sK11: $i > $i > $i ).
thf(func_def_151,type,
sK12: $i > $i > $i ).
thf(func_def_152,type,
sK13: $i > $i ).
thf(func_def_153,type,
sK14: $i > $i > $i ).
thf(func_def_154,type,
sK15: $i > $i > $i ).
thf(func_def_155,type,
sK16: $i > ( $i > $o ) > $i ).
thf(func_def_156,type,
sK17: ( $i > $o ) > $i ).
thf(func_def_157,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_158,type,
sK19: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_159,type,
sK20: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_160,type,
sK21: $i > $i ).
thf(func_def_161,type,
sK22: ( $i > $o ) > $i > $i ).
thf(func_def_162,type,
sK23: ( $i > $o ) > $i > $i ).
thf(func_def_163,type,
sK24: ( $i > $o ) > $i ).
thf(func_def_164,type,
sK25: $i > $i ).
thf(func_def_165,type,
sK26: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_166,type,
sK27: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_167,type,
sK28: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_168,type,
sK29: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_169,type,
sK30: ( $i > $i > $o ) > $i > $i ).
thf(func_def_170,type,
sK31: ( $i > $i > $o ) > $i > $i ).
thf(func_def_171,type,
sK32: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_172,type,
sK33: ( $i > $i > $o ) > $i > $i ).
thf(func_def_173,type,
sK34: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_174,type,
sK35: ( $i > $o ) > $i ).
thf(func_def_175,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_176,type,
sK37: ( $i > $o ) > $i ).
thf(func_def_177,type,
sK38: $i > $i ).
thf(func_def_178,type,
sK39: $i > $o > $i > $i ).
thf(func_def_179,type,
sK40: $i > $i > $i ).
thf(func_def_180,type,
sK41: $i > ( $i > $o ) > $i ).
thf(func_def_181,type,
sK42: $i > ( $i > $o ) > $i ).
thf(func_def_182,type,
sK43: $i > ( $i > $o ) > $i ).
thf(func_def_183,type,
sK44: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_184,type,
sK45: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_185,type,
sK46: $i > $i > $i ).
thf(func_def_186,type,
sK47: $i > $i > $i ).
thf(func_def_187,type,
sK48: $i > $i > $i ).
thf(func_def_188,type,
sK49: $i > ( $i > $o ) > $i ).
thf(func_def_189,type,
ph50:
!>[X0: $tType] : X0 ).
thf(f3101,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f3100]) ).
thf(f3100,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f369,f3099]) ).
thf(f3099,plain,
( $false
= ( in @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f3098]) ).
thf(f3098,plain,
( ( $true = $false )
| ( $false
= ( in @ sK2 @ sK1 ) ) ),
inference(forward_demodulation,[status(thm)],[f3094,f368]) ).
thf(f368,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f327]) ).
thf(f327,plain,
( ( nonemptyI = $true )
& ( quantDeMorgan1 = $true )
& ( powerset__Cong = $true )
& ( exuE1 = $true )
& ( subsetE = $true )
& ( setadjoinSub2 = $true )
& ( in__Cong = $true )
& ( emptyE1 = $true )
& ( dsetconstrEL = $true )
& ( replAx = $true )
& ( setbeta = $true )
& ( omega0Ax = $true )
& ( powersetsubset = $true )
& ( subsetI1 = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( omega__Cong = $true )
& ( notequalI2 = $true )
& ( emptysetimpfalse = $true )
& ( subsetE2 = $true )
& ( emptysetE = $true )
& ( upairsetIL = $true )
& ( setunionI = $true )
& ( subset2powerset = $true )
& ( binunionLsub = $true )
& ( eqinunit = $true )
& ( binunionE = $true )
& ( setunion__Cong = $true )
& ( noeltsimpempty = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan2 = $true )
& ( sepSubset = $true )
& ( notsubsetI = $true )
& ( notinsingleton = $true )
& ( exuI3 = $true )
& ( emptysetsubset = $true )
& ( nonemptyI1 = $true )
& ( singletonsswitch = $true )
& ( dsetconstrER = $true )
& ( exuI2 = $true )
& ( setadjoinIR = $true )
& ( dsetconstr__Cong = $true )
& ( setoftrueEq = $true )
& ( setextAx = $true )
& ( uniqinunit = $true )
& ( upairsetIR = $true )
& ( notequalI1 = $true )
& ( exuE3e = $true )
& ( subsetTrans = $true )
& ( setunionE = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan3 = $true )
& ( exuEu = $true )
& ( wellorderingAx = $true )
& ( powersetE1 = $true )
& ( prop2setI = $true )
& ( binunionIR = $true )
& ( setadjoinE = $true )
& ( omegaIndAx = $true )
& ( inPowerset = $true )
& ( nonemptyE1 = $true )
& ( sepInPowerset = $true )
& ( vacuousDall = $true )
& ( notdallE = $true )
& ( setadjoinIL = $true )
& ( inCongP = $true )
& ( descrp = $true )
& ( upairset2IR = $true )
& ( subPowSU = $true )
& ( subsetRefl = $true )
& ( powersetE = $true )
& ( prop2setE = $true )
& ( emptyset__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( binunionEcases = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( binunionIL = $true )
& ( emptyI = $true )
& ( dsetconstrI = $true )
& ( exuE3u = $true )
& ( exu__Cong = $true )
& ( exuE2 = $true )
& ( prop2set2propI = $true )
& ( binunionRsub = $true )
& ( subsetemptysetimpeq = $true )
& ( powersetI = $true )
& ( setextsub = $true )
& ( notinemptyset = $true )
& ( notdexE = $true )
& ( subsetI2 = $true )
& ( setadjoinAx = $true )
& ( exuI1 = $true )
& ( omegaSAx = $true )
& ( setext = $true )
& ( setadjoinOr = $true )
& ( setadjoin__Cong = $true )
& ( foundationAx = $true )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
!= ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) ) )
& ( descr__Cong = $true )
& ( powersetI1 = $true )
& ( upairsetE = $true )
& ( eqimpsubset1 = $true )
& ( emptyinunitempty = $true )
& ( nonemptyImpWitness = $true )
& ( emptyinPowerset = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f325,f326]) ).
thf(f326,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X2 @ X0 ) )
& ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true ) )
=> ( ( $true
= ( in @ sK2 @ sK1 ) )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
!= ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f325,plain,
( ( nonemptyI = $true )
& ( quantDeMorgan1 = $true )
& ( powerset__Cong = $true )
& ( exuE1 = $true )
& ( subsetE = $true )
& ( setadjoinSub2 = $true )
& ( in__Cong = $true )
& ( emptyE1 = $true )
& ( dsetconstrEL = $true )
& ( replAx = $true )
& ( setbeta = $true )
& ( omega0Ax = $true )
& ( powersetsubset = $true )
& ( subsetI1 = $true )
& ( emptyInPowerset = $true )
& ( eqimpsubset2 = $true )
& ( omega__Cong = $true )
& ( notequalI2 = $true )
& ( emptysetimpfalse = $true )
& ( subsetE2 = $true )
& ( emptysetE = $true )
& ( upairsetIL = $true )
& ( setunionI = $true )
& ( subset2powerset = $true )
& ( binunionLsub = $true )
& ( eqinunit = $true )
& ( binunionE = $true )
& ( setunion__Cong = $true )
& ( noeltsimpempty = $true )
& ( emptysetAx = $true )
& ( quantDeMorgan2 = $true )
& ( sepSubset = $true )
& ( notsubsetI = $true )
& ( notinsingleton = $true )
& ( exuI3 = $true )
& ( emptysetsubset = $true )
& ( nonemptyI1 = $true )
& ( singletonsswitch = $true )
& ( dsetconstrER = $true )
& ( exuI2 = $true )
& ( setadjoinIR = $true )
& ( dsetconstr__Cong = $true )
& ( setoftrueEq = $true )
& ( setextAx = $true )
& ( uniqinunit = $true )
& ( upairsetIR = $true )
& ( notequalI1 = $true )
& ( exuE3e = $true )
& ( subsetTrans = $true )
& ( setunionE = $true )
& ( setadjoinSub = $true )
& ( quantDeMorgan3 = $true )
& ( exuEu = $true )
& ( wellorderingAx = $true )
& ( powersetE1 = $true )
& ( prop2setI = $true )
& ( binunionIR = $true )
& ( setadjoinE = $true )
& ( omegaIndAx = $true )
& ( inPowerset = $true )
& ( nonemptyE1 = $true )
& ( sepInPowerset = $true )
& ( vacuousDall = $true )
& ( notdallE = $true )
& ( setadjoinIL = $true )
& ( inCongP = $true )
& ( descrp = $true )
& ( upairset2IR = $true )
& ( subPowSU = $true )
& ( subsetRefl = $true )
& ( powersetE = $true )
& ( prop2setE = $true )
& ( emptyset__Cong = $true )
& ( quantDeMorgan4 = $true )
& ( binunionEcases = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( binunionIL = $true )
& ( emptyI = $true )
& ( dsetconstrI = $true )
& ( exuE3u = $true )
& ( exu__Cong = $true )
& ( exuE2 = $true )
& ( prop2set2propI = $true )
& ( binunionRsub = $true )
& ( subsetemptysetimpeq = $true )
& ( powersetI = $true )
& ( setextsub = $true )
& ( notinemptyset = $true )
& ( notdexE = $true )
& ( subsetI2 = $true )
& ( setadjoinAx = $true )
& ( exuI1 = $true )
& ( omegaSAx = $true )
& ( setext = $true )
& ( setadjoinOr = $true )
& ( setadjoin__Cong = $true )
& ( foundationAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
& ( $true
= ( in @ X2 @ X0 ) )
& ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true ) )
& ( descr__Cong = $true )
& ( powersetI1 = $true )
& ( upairsetE = $true )
& ( eqimpsubset1 = $true )
& ( emptyinunitempty = $true )
& ( nonemptyImpWitness = $true )
& ( emptyinPowerset = $true ) ),
inference(flattening,[status(thm)],[f324]) ).
thf(f324,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
!= $true )
& ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( 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)],[f161]) ).
thf(f161,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( ( $true
= ( in @ X2 @ X0 ) )
=> ( ( in @ X2 @ ( binintersect @ X1 @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f160]) ).
thf(f160,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ ( binintersect @ X1 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f110]) ).
thf(f110,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
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X4 )
=> ( in @ X1 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f109]) ).
thf(f109,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
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X1 @ X4 )
=> ( in @ X1 @ ( binintersect @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yYawlLAc0c/DTF2THF_5165.p',binintersectI) ).
thf(f3094,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ( $false
= ( in @ sK2 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3093]) ).
thf(f3093,plain,
( ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ sK0 )
@ sK2 ) )
| ( $false
= ( in @ sK2 @ sK1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f3085]) ).
thf(f3085,plain,
( ( $true != $true )
| ( $false
= ( ^ [Y0: $i] : ( in @ Y0 @ sK0 )
@ sK2 ) )
| ( $false
= ( in @ sK2 @ sK1 ) ) ),
inference(superposition,[status(thm)],[f1369,f1118]) ).
thf(f1118,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( $true
= ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) )
| ( $false
= ( X2 @ X3 ) )
| ( ( in @ X3 @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f1117]) ).
thf(f1117,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( ( ( in @ X3 @ X1 )
= $false )
| ( $true
= ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1116]) ).
thf(f1116,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ( in @ X3 @ X1 )
=> ( ( X2 @ X3 )
=> ( in @ X3 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1115]) ).
thf(f1115,plain,
! [X2: $i > $o,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f1114]) ).
thf(f1114,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
=> ( ( X2 @ Y0 )
=> ( in @ Y0 @ ( dsetconstr @ X1 @ X2 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1113]) ).
thf(f1113,plain,
! [X2: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1112]) ).
thf(f1112,plain,
! [X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
=> ( ( Y0 @ Y1 )
=> ( in @ Y1 @ ( dsetconstr @ X1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1111]) ).
thf(f1111,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f1110]) ).
thf(f1110,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2 @ ( dsetconstr @ Y0 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f635]) ).
thf(f635,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f529,f388]) ).
thf(f388,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f327]) ).
thf(f529,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f163]) ).
thf(f163,plain,
( dsetconstrI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
=> ( ( Y1 @ Y2 )
=> ( in @ Y2
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y1 @ Y3 ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f162]) ).
thf(f162,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( in @ X0 @ X2 )
=> ( ( X1 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X1 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( dsetconstrI
= ( ! [X1: $i,X0: $i > $o,X3: $i] :
( ( in @ X1 @ X3 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.yYawlLAc0c/DTF2THF_5165.p',dsetconstrI) ).
thf(f1369,plain,
( $true
!= ( in @ sK2
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] : ( in @ Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f571]) ).
thf(f571,plain,
( $true
!= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) )
@ sK1
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f367,f349]) ).
thf(f349,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f230]) ).
thf(f230,plain,
( binintersect
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] : ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f229]) ).
thf(f229,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/sandbox2/tmp/tmp.yYawlLAc0c/DTF2THF_5165.p',binintersect) ).
thf(f367,plain,
( $true
!= ( in @ sK2 @ ( binintersect @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f327]) ).
thf(f369,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f327]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU589^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n026.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 12:28:10 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.47 ---- Original DTF file ---
% 0.28/0.47 thf(spec,logic,$$dhol).
% 0.28/0.47 %------------------------------------------------------------------------------
% 0.28/0.47 % File : SEU589^1 : 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 A -> in x B -> in x (binintersect A 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 : ZFC091g [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 : 231 ( 108 unt; 122 typ; 108 def)
% 0.28/0.47 % Number of atoms : 577 ( 157 equ; 0 cnn)
% 0.28/0.47 % Maximal formula atoms : 108 ( 5 avg)
% 0.28/0.47 % Number of connectives : 910 ( 29 ~; 6 |; 27 &; 575 @)
% 0.28/0.47 % ( 14 <=>; 259 =>; 0 <=; 0 <~>)
% 0.28/0.47 % Maximal formula depth : 114 ( 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 : 125 ( 122 usr; 109 con; 0-2 aty)
% 0.28/0.47 % Number of variables : 319 ( 33 ^; 258 !; 28 ?; 319 :)
% 0.28/0.47 % SPC : TH0_THM_EQU_NAR
% 0.28/0.47
% 0.28/0.47 % Comments : http://mathgate.info/detsetitem.php?id=166
% 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,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 => ! [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 %------------------------------------------------------------------------------
% 0.28/0.47 ------------------------
% 2.27/1.46 ---- Embedded in THF ---
% 2.27/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.27/1.46 %%% Generated on Tue Feb 24 12:28:11 EST 2026
% 2.27/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 2.27/1.46 %%% Logic specification used:
% 2.27/1.46 %%% thf(spec, logic, $$dhol).
% 2.27/1.46
% 2.27/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.yYawlLAc0c/DTF2DTF5165.p
% See solution above
% 2.27/1.46 ------------------------
% 2.27/1.49 ---- Cleaned THF ---
% 2.27/1.49 thf(in_type,type,
% 2.27/1.49 in: $i > $i > $o ).
% 2.27/1.49
% 2.27/1.49 thf(exu_type,type,
% 2.27/1.49 exu: ( $i > $o ) > $o ).
% 2.27/1.49
% 2.27/1.49 thf(exu,definition,
% 2.27/1.49 ( exu
% 2.27/1.49 = ( ^ [Xphi: $i > $o] :
% 2.27/1.49 ? [Xx: $i] :
% 2.27/1.49 ( ( Xphi @ Xx )
% 2.27/1.49 & ! [Xy: $i] :
% 2.27/1.49 ( ( Xphi @ Xy )
% 2.27/1.49 => ( Xx = Xy ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setextAx_type,type,
% 2.27/1.49 setextAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setextAx,definition,
% 2.27/1.49 ( setextAx
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 <=> ( in @ Xx @ B ) )
% 2.27/1.49 => ( A = B ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptyset_type,type,
% 2.27/1.49 emptyset: $i ).
% 2.27/1.49
% 2.27/1.49 thf(emptysetAx_type,type,
% 2.27/1.49 emptysetAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptysetAx,definition,
% 2.27/1.49 ( emptysetAx
% 2.27/1.49 = ( ! [Xx: $i] :
% 2.27/1.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoin_type,type,
% 2.27/1.49 setadjoin: $i > $i > $i ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinAx_type,type,
% 2.27/1.49 setadjoinAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinAx,definition,
% 2.27/1.49 ( setadjoinAx
% 2.27/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.27/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.27/1.49 <=> ( ( Xy = Xx )
% 2.27/1.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(powerset_type,type,
% 2.27/1.49 powerset: $i > $i ).
% 2.27/1.49
% 2.27/1.49 thf(powersetAx_type,type,
% 2.27/1.49 powersetAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(powersetAx,definition,
% 2.27/1.49 ( powersetAx
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( in @ B @ ( powerset @ A ) )
% 2.27/1.49 <=> ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setunion_type,type,
% 2.27/1.49 setunion: $i > $i ).
% 2.27/1.49
% 2.27/1.49 thf(setunionAx_type,type,
% 2.27/1.49 setunionAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setunionAx,definition,
% 2.27/1.49 ( setunionAx
% 2.27/1.49 = ( ! [A: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ ( setunion @ A ) )
% 2.27/1.49 <=> ? [B: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 & ( in @ B @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(omega_type,type,
% 2.27/1.49 omega: $i ).
% 2.27/1.49
% 2.27/1.49 thf(omega0Ax_type,type,
% 2.27/1.49 omega0Ax: $o ).
% 2.27/1.49
% 2.27/1.49 thf(omega0Ax,definition,
% 2.27/1.49 ( omega0Ax
% 2.27/1.49 = ( in @ emptyset @ omega ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(omegaSAx_type,type,
% 2.27/1.49 omegaSAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(omegaSAx,definition,
% 2.27/1.49 ( omegaSAx
% 2.27/1.49 = ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ omega )
% 2.27/1.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(omegaIndAx_type,type,
% 2.27/1.49 omegaIndAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(omegaIndAx,definition,
% 2.27/1.49 ( omegaIndAx
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ( ( in @ emptyset @ A )
% 2.27/1.49 & ! [Xx: $i] :
% 2.27/1.49 ( ( ( in @ Xx @ omega )
% 2.27/1.49 & ( in @ Xx @ A ) )
% 2.27/1.49 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.27/1.49 => ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ omega )
% 2.27/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(replAx_type,type,
% 2.27/1.49 replAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(replAx,definition,
% 2.27/1.49 ( replAx
% 2.27/1.49 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( exu
% 2.27/1.49 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.27/1.49 => ? [B: $i] :
% 2.27/1.49 ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 <=> ? [Xy: $i] :
% 2.27/1.49 ( ( in @ Xy @ A )
% 2.27/1.49 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(foundationAx_type,type,
% 2.27/1.49 foundationAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(foundationAx,definition,
% 2.27/1.49 ( foundationAx
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.27/1.49 => ? [B: $i] :
% 2.27/1.49 ( ( in @ B @ A )
% 2.27/1.49 & ~ ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(wellorderingAx_type,type,
% 2.27/1.49 wellorderingAx: $o ).
% 2.27/1.49
% 2.27/1.49 thf(wellorderingAx,definition,
% 2.27/1.49 ( wellorderingAx
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ? [B: $i] :
% 2.27/1.49 ( ! [C: $i] :
% 2.27/1.49 ( ( in @ C @ B )
% 2.27/1.49 => ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ C )
% 2.27/1.49 => ( in @ Xx @ A ) ) )
% 2.27/1.49 & ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( ( in @ Xx @ A )
% 2.27/1.49 & ( in @ Xy @ A ) )
% 2.27/1.49 => ( ! [C: $i] :
% 2.27/1.49 ( ( in @ C @ B )
% 2.27/1.49 => ( ( in @ Xx @ C )
% 2.27/1.49 <=> ( in @ Xy @ C ) ) )
% 2.27/1.49 => ( Xx = Xy ) ) )
% 2.27/1.49 & ! [C: $i,D: $i] :
% 2.27/1.49 ( ( ( in @ C @ B )
% 2.27/1.49 & ( in @ D @ B ) )
% 2.27/1.49 => ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ C )
% 2.27/1.49 => ( in @ Xx @ D ) )
% 2.27/1.49 | ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ D )
% 2.27/1.49 => ( in @ Xx @ C ) ) ) )
% 2.27/1.49 & ! [C: $i] :
% 2.27/1.49 ( ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ C )
% 2.27/1.49 => ( in @ Xx @ A ) )
% 2.27/1.49 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.27/1.49 => ? [D: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ D @ B )
% 2.27/1.49 & ( in @ Xx @ C )
% 2.27/1.49 & ~ ? [Xy: $i] :
% 2.27/1.49 ( ( in @ Xy @ D )
% 2.27/1.49 & ( in @ Xy @ C ) )
% 2.27/1.49 & ! [E: $i] :
% 2.27/1.49 ( ( in @ E @ B )
% 2.27/1.49 => ( ! [Xy: $i] :
% 2.27/1.49 ( ( in @ Xy @ E )
% 2.27/1.49 => ( in @ Xy @ D ) )
% 2.27/1.49 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(descr_type,type,
% 2.27/1.49 descr: ( $i > $o ) > $i ).
% 2.27/1.49
% 2.27/1.49 thf(descrp_type,type,
% 2.27/1.49 descrp: $o ).
% 2.27/1.49
% 2.27/1.49 thf(descrp,definition,
% 2.27/1.49 ( descrp
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 => ( Xphi
% 2.27/1.49 @ ( descr
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstr_type,type,
% 2.27/1.49 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstrI_type,type,
% 2.27/1.49 dsetconstrI: $o ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstrI,definition,
% 2.27/1.49 ( dsetconstrI
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( ( Xphi @ Xx )
% 2.27/1.49 => ( in @ Xx
% 2.27/1.49 @ ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstrEL_type,type,
% 2.27/1.49 dsetconstrEL: $o ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstrEL,definition,
% 2.27/1.49 ( dsetconstrEL
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx
% 2.27/1.49 @ ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.27/1.49 => ( in @ Xx @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstrER_type,type,
% 2.27/1.49 dsetconstrER: $o ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstrER,definition,
% 2.27/1.49 ( dsetconstrER
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx
% 2.27/1.49 @ ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.27/1.49 => ( Xphi @ Xx ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exuE1_type,type,
% 2.27/1.49 exuE1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exuE1,definition,
% 2.27/1.49 ( exuE1
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 => ? [Xx: $i] :
% 2.27/1.49 ( ( Xphi @ Xx )
% 2.27/1.49 & ! [Xy: $i] :
% 2.27/1.49 ( ( Xphi @ Xy )
% 2.27/1.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(prop2set_type,type,
% 2.27/1.49 prop2set: $o > $i ).
% 2.27/1.49
% 2.27/1.49 thf(prop2setE_type,type,
% 2.27/1.49 prop2setE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(prop2setE,definition,
% 2.27/1.49 ( prop2setE
% 2.27/1.49 = ( ! [Xphi: $o,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.27/1.49 => Xphi ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptysetE_type,type,
% 2.27/1.49 emptysetE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptysetE,definition,
% 2.27/1.49 ( emptysetE
% 2.27/1.49 = ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ emptyset )
% 2.27/1.49 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptysetimpfalse_type,type,
% 2.27/1.49 emptysetimpfalse: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptysetimpfalse,definition,
% 2.27/1.49 ( emptysetimpfalse
% 2.27/1.49 = ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ emptyset )
% 2.27/1.49 => $false ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(notinemptyset_type,type,
% 2.27/1.49 notinemptyset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(notinemptyset,definition,
% 2.27/1.49 ( notinemptyset
% 2.27/1.49 = ( ! [Xx: $i] :
% 2.27/1.49 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exuE3e_type,type,
% 2.27/1.49 exuE3e: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exuE3e,definition,
% 2.27/1.49 ( exuE3e
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setext_type,type,
% 2.27/1.49 setext: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setext,definition,
% 2.27/1.49 ( setext
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( in @ Xx @ B ) )
% 2.27/1.49 => ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 => ( in @ Xx @ A ) )
% 2.27/1.49 => ( A = B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptyI_type,type,
% 2.27/1.49 emptyI: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptyI,definition,
% 2.27/1.49 ( emptyI
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ~ ( in @ Xx @ A )
% 2.27/1.49 => ( A = emptyset ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(noeltsimpempty_type,type,
% 2.27/1.49 noeltsimpempty: $o ).
% 2.27/1.49
% 2.27/1.49 thf(noeltsimpempty,definition,
% 2.27/1.49 ( noeltsimpempty
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ~ ( in @ Xx @ A )
% 2.27/1.49 => ( A = emptyset ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setbeta_type,type,
% 2.27/1.49 setbeta: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setbeta,definition,
% 2.27/1.49 ( setbeta
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( ( in @ Xx
% 2.27/1.49 @ ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.27/1.49 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(nonempty_type,type,
% 2.27/1.49 nonempty: $i > $o ).
% 2.27/1.49
% 2.27/1.49 thf(nonempty,definition,
% 2.27/1.49 ( nonempty
% 2.27/1.49 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(nonemptyE1_type,type,
% 2.27/1.49 nonemptyE1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(nonemptyE1,definition,
% 2.27/1.49 ( nonemptyE1
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ( nonempty @ A )
% 2.27/1.49 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(nonemptyI_type,type,
% 2.27/1.49 nonemptyI: $o ).
% 2.27/1.49
% 2.27/1.49 thf(nonemptyI,definition,
% 2.27/1.49 ( nonemptyI
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( ( Xphi @ Xx )
% 2.27/1.49 => ( nonempty
% 2.27/1.49 @ ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(nonemptyI1_type,type,
% 2.27/1.49 nonemptyI1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(nonemptyI1,definition,
% 2.27/1.49 ( nonemptyI1
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.27/1.49 => ( nonempty @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinIL_type,type,
% 2.27/1.49 setadjoinIL: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinIL,definition,
% 2.27/1.49 ( setadjoinIL
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptyinunitempty_type,type,
% 2.27/1.49 emptyinunitempty: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptyinunitempty,definition,
% 2.27/1.49 ( emptyinunitempty
% 2.27/1.49 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinIR_type,type,
% 2.27/1.49 setadjoinIR: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinIR,definition,
% 2.27/1.49 ( setadjoinIR
% 2.27/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.27/1.49 ( ( in @ Xy @ A )
% 2.27/1.49 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinE_type,type,
% 2.27/1.49 setadjoinE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinE,definition,
% 2.27/1.49 ( setadjoinE
% 2.27/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.27/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.27/1.49 => ! [Xphi: $o] :
% 2.27/1.49 ( ( ( Xy = Xx )
% 2.27/1.49 => Xphi )
% 2.27/1.49 => ( ( ( in @ Xy @ A )
% 2.27/1.49 => Xphi )
% 2.27/1.49 => Xphi ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinOr_type,type,
% 2.27/1.49 setadjoinOr: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinOr,definition,
% 2.27/1.49 ( setadjoinOr
% 2.27/1.49 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.27/1.49 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.27/1.49 => ( ( Xy = Xx )
% 2.27/1.49 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setoftrueEq_type,type,
% 2.27/1.49 setoftrueEq: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setoftrueEq,definition,
% 2.27/1.49 ( setoftrueEq
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xx: $i] : $true )
% 2.27/1.49 = A ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(powersetI_type,type,
% 2.27/1.49 powersetI: $o ).
% 2.27/1.49
% 2.27/1.49 thf(powersetI,definition,
% 2.27/1.49 ( powersetI
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 => ( in @ Xx @ A ) )
% 2.27/1.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptyinPowerset_type,type,
% 2.27/1.49 emptyinPowerset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptyinPowerset,definition,
% 2.27/1.49 ( emptyinPowerset
% 2.27/1.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptyInPowerset_type,type,
% 2.27/1.49 emptyInPowerset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptyInPowerset,definition,
% 2.27/1.49 ( emptyInPowerset
% 2.27/1.49 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(powersetE_type,type,
% 2.27/1.49 powersetE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(powersetE,definition,
% 2.27/1.49 ( powersetE
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ B @ ( powerset @ A ) )
% 2.27/1.49 => ( ( in @ Xx @ B )
% 2.27/1.49 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setunionI_type,type,
% 2.27/1.49 setunionI: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setunionI,definition,
% 2.27/1.49 ( setunionI
% 2.27/1.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 => ( ( in @ B @ A )
% 2.27/1.49 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setunionE_type,type,
% 2.27/1.49 setunionE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setunionE,definition,
% 2.27/1.49 ( setunionE
% 2.27/1.49 = ( ! [A: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ ( setunion @ A ) )
% 2.27/1.49 => ! [Xphi: $o] :
% 2.27/1.49 ( ! [B: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 => ( ( in @ B @ A )
% 2.27/1.49 => Xphi ) )
% 2.27/1.49 => Xphi ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subPowSU_type,type,
% 2.27/1.49 subPowSU: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subPowSU,definition,
% 2.27/1.49 ( subPowSU
% 2.27/1.49 = ( ! [A: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exuE2_type,type,
% 2.27/1.49 exuE2: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exuE2,definition,
% 2.27/1.49 ( exuE2
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 => ? [Xx: $i] :
% 2.27/1.49 ! [Xy: $i] :
% 2.27/1.49 ( ( Xphi @ Xy )
% 2.27/1.49 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(nonemptyImpWitness_type,type,
% 2.27/1.49 nonemptyImpWitness: $o ).
% 2.27/1.49
% 2.27/1.49 thf(nonemptyImpWitness,definition,
% 2.27/1.49 ( nonemptyImpWitness
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ( nonempty @ A )
% 2.27/1.49 => ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 & $true ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(uniqinunit_type,type,
% 2.27/1.49 uniqinunit: $o ).
% 2.27/1.49
% 2.27/1.49 thf(uniqinunit,definition,
% 2.27/1.49 ( uniqinunit
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.27/1.49 => ( Xx = Xy ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(notinsingleton_type,type,
% 2.27/1.49 notinsingleton: $o ).
% 2.27/1.49
% 2.27/1.49 thf(notinsingleton,definition,
% 2.27/1.49 ( notinsingleton
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xx != Xy )
% 2.27/1.49 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(eqinunit_type,type,
% 2.27/1.49 eqinunit: $o ).
% 2.27/1.49
% 2.27/1.49 thf(eqinunit,definition,
% 2.27/1.49 ( eqinunit
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xx = Xy )
% 2.27/1.49 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(singletonsswitch_type,type,
% 2.27/1.49 singletonsswitch: $o ).
% 2.27/1.49
% 2.27/1.49 thf(singletonsswitch,definition,
% 2.27/1.49 ( singletonsswitch
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.27/1.49 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(upairsetE_type,type,
% 2.27/1.49 upairsetE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(upairsetE,definition,
% 2.27/1.49 ( upairsetE
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.27/1.49 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.27/1.49 => ( ( Xz = Xx )
% 2.27/1.49 | ( Xz = Xy ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(upairsetIL_type,type,
% 2.27/1.49 upairsetIL: $o ).
% 2.27/1.49
% 2.27/1.49 thf(upairsetIL,definition,
% 2.27/1.49 ( upairsetIL
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(upairsetIR_type,type,
% 2.27/1.49 upairsetIR: $o ).
% 2.27/1.49
% 2.27/1.49 thf(upairsetIR,definition,
% 2.27/1.49 ( upairsetIR
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptyE1_type,type,
% 2.27/1.49 emptyE1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptyE1,definition,
% 2.27/1.49 ( emptyE1
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 & ( Xphi @ Xx ) )
% 2.27/1.49 => ( ( ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 = emptyset )
% 2.27/1.49 => $false ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(vacuousDall_type,type,
% 2.27/1.49 vacuousDall: $o ).
% 2.27/1.49
% 2.27/1.49 thf(vacuousDall,definition,
% 2.27/1.49 ( vacuousDall
% 2.27/1.49 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ emptyset )
% 2.27/1.49 => ( Xphi @ Xx ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(quantDeMorgan1_type,type,
% 2.27/1.49 quantDeMorgan1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(quantDeMorgan1,definition,
% 2.27/1.49 ( quantDeMorgan1
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( ~ ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( Xphi @ Xx ) )
% 2.27/1.49 => ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(quantDeMorgan2_type,type,
% 2.27/1.49 quantDeMorgan2: $o ).
% 2.27/1.49
% 2.27/1.49 thf(quantDeMorgan2,definition,
% 2.27/1.49 ( quantDeMorgan2
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ~ ( Xphi @ Xx ) )
% 2.27/1.49 => ~ ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(quantDeMorgan3_type,type,
% 2.27/1.49 quantDeMorgan3: $o ).
% 2.27/1.49
% 2.27/1.49 thf(quantDeMorgan3,definition,
% 2.27/1.49 ( quantDeMorgan3
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( ~ ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 & ( Xphi @ Xx ) )
% 2.27/1.49 => ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(quantDeMorgan4_type,type,
% 2.27/1.49 quantDeMorgan4: $o ).
% 2.27/1.49
% 2.27/1.49 thf(quantDeMorgan4,definition,
% 2.27/1.49 ( quantDeMorgan4
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 & ~ ( Xphi @ Xx ) )
% 2.27/1.49 => ~ ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(prop2setI_type,type,
% 2.27/1.49 prop2setI: $o ).
% 2.27/1.49
% 2.27/1.49 thf(prop2setI,definition,
% 2.27/1.49 ( prop2setI
% 2.27/1.49 = ( ! [Xphi: $o] :
% 2.27/1.49 ( Xphi
% 2.27/1.49 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(set2prop_type,type,
% 2.27/1.49 set2prop: $i > $o ).
% 2.27/1.49
% 2.27/1.49 thf(prop2set2propI_type,type,
% 2.27/1.49 prop2set2propI: $o ).
% 2.27/1.49
% 2.27/1.49 thf(prop2set2propI,definition,
% 2.27/1.49 ( prop2set2propI
% 2.27/1.49 = ( ! [Xphi: $o] :
% 2.27/1.49 ( Xphi
% 2.27/1.49 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(notdexE_type,type,
% 2.27/1.49 notdexE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(notdexE,definition,
% 2.27/1.49 ( notdexE
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( ~ ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 & ( Xphi @ Xx ) )
% 2.27/1.49 => ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(notdallE_type,type,
% 2.27/1.49 notdallE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(notdallE,definition,
% 2.27/1.49 ( notdallE
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( ~ ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( Xphi @ Xx ) )
% 2.27/1.49 => ? [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exuI1_type,type,
% 2.27/1.49 exuI1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exuI1,definition,
% 2.27/1.49 ( exuI1
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ? [Xx: $i] :
% 2.27/1.49 ( ( Xphi @ Xx )
% 2.27/1.49 & ! [Xy: $i] :
% 2.27/1.49 ( ( Xphi @ Xy )
% 2.27/1.49 => ( Xx = Xy ) ) )
% 2.27/1.49 => ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exuI3_type,type,
% 2.27/1.49 exuI3: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exuI3,definition,
% 2.27/1.49 ( exuI3
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.27/1.49 => ( ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xphi @ Xx )
% 2.27/1.49 => ( ( Xphi @ Xy )
% 2.27/1.49 => ( Xx = Xy ) ) )
% 2.27/1.49 => ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exuI2_type,type,
% 2.27/1.49 exuI2: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exuI2,definition,
% 2.27/1.49 ( exuI2
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ? [Xx: $i] :
% 2.27/1.49 ! [Xy: $i] :
% 2.27/1.49 ( ( Xphi @ Xy )
% 2.27/1.49 <=> ( Xy = Xx ) )
% 2.27/1.49 => ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(inCongP_type,type,
% 2.27/1.49 inCongP: $o ).
% 2.27/1.49
% 2.27/1.49 thf(inCongP,definition,
% 2.27/1.49 ( inCongP
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( A = B )
% 2.27/1.49 => ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xx = Xy )
% 2.27/1.49 => ( ( in @ Xx @ A )
% 2.27/1.49 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(in__Cong_type,type,
% 2.27/1.49 in__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(in__Cong,definition,
% 2.27/1.49 ( in__Cong
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( A = B )
% 2.27/1.49 => ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xx = Xy )
% 2.27/1.49 => ( ( in @ Xx @ A )
% 2.27/1.49 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exuE3u_type,type,
% 2.27/1.49 exuE3u: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exuE3u,definition,
% 2.27/1.49 ( exuE3u
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 => ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xphi @ Xx )
% 2.27/1.49 => ( ( Xphi @ Xy )
% 2.27/1.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exu__Cong_type,type,
% 2.27/1.49 exu__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exu__Cong,definition,
% 2.27/1.49 ( exu__Cong
% 2.27/1.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.27/1.49 ( ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xx = Xy )
% 2.27/1.49 => ( ( Xphi @ Xx )
% 2.27/1.49 <=> ( Xpsi @ Xy ) ) )
% 2.27/1.49 => ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 <=> ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptyset__Cong_type,type,
% 2.27/1.49 emptyset__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptyset__Cong,definition,
% 2.27/1.49 ( emptyset__Cong
% 2.27/1.49 = ( emptyset = emptyset ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoin__Cong_type,type,
% 2.27/1.49 setadjoin__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoin__Cong,definition,
% 2.27/1.49 ( setadjoin__Cong
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xx = Xy )
% 2.27/1.49 => ! [Xz: $i,Xu: $i] :
% 2.27/1.49 ( ( Xz = Xu )
% 2.27/1.49 => ( ( setadjoin @ Xx @ Xz )
% 2.27/1.49 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(powerset__Cong_type,type,
% 2.27/1.49 powerset__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(powerset__Cong,definition,
% 2.27/1.49 ( powerset__Cong
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( A = B )
% 2.27/1.49 => ( ( powerset @ A )
% 2.27/1.49 = ( powerset @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setunion__Cong_type,type,
% 2.27/1.49 setunion__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setunion__Cong,definition,
% 2.27/1.49 ( setunion__Cong
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( A = B )
% 2.27/1.49 => ( ( setunion @ A )
% 2.27/1.49 = ( setunion @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(omega__Cong_type,type,
% 2.27/1.49 omega__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(omega__Cong,definition,
% 2.27/1.49 ( omega__Cong
% 2.27/1.49 = ( omega = omega ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(exuEu_type,type,
% 2.27/1.49 exuEu: $o ).
% 2.27/1.49
% 2.27/1.49 thf(exuEu,definition,
% 2.27/1.49 ( exuEu
% 2.27/1.49 = ( ! [Xphi: $i > $o] :
% 2.27/1.49 ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 => ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xphi @ Xx )
% 2.27/1.49 => ( ( Xphi @ Xy )
% 2.27/1.49 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(descr__Cong_type,type,
% 2.27/1.49 descr__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(descr__Cong,definition,
% 2.27/1.49 ( descr__Cong
% 2.27/1.49 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.27/1.49 ( ! [Xx: $i,Xy: $i] :
% 2.27/1.49 ( ( Xx = Xy )
% 2.27/1.49 => ( ( Xphi @ Xx )
% 2.27/1.49 <=> ( Xpsi @ Xy ) ) )
% 2.27/1.49 => ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 => ( ( exu
% 2.27/1.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.27/1.49 => ( ( descr
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 = ( descr
% 2.27/1.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstr__Cong_type,type,
% 2.27/1.49 dsetconstr__Cong: $o ).
% 2.27/1.49
% 2.27/1.49 thf(dsetconstr__Cong,definition,
% 2.27/1.49 ( dsetconstr__Cong
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( A = B )
% 2.27/1.49 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ! [Xy: $i] :
% 2.27/1.49 ( ( in @ Xy @ B )
% 2.27/1.49 => ( ( Xx = Xy )
% 2.27/1.49 => ( ( Xphi @ Xx )
% 2.27/1.49 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.27/1.49 => ( ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 = ( dsetconstr @ B
% 2.27/1.49 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subset_type,type,
% 2.27/1.49 subset: $i > $i > $o ).
% 2.27/1.49
% 2.27/1.49 thf(disjoint_type,type,
% 2.27/1.49 disjoint: $i > $i > $o ).
% 2.27/1.49
% 2.27/1.49 thf(setsmeet_type,type,
% 2.27/1.49 setsmeet: $i > $i > $o ).
% 2.27/1.49
% 2.27/1.49 thf(subsetI1_type,type,
% 2.27/1.49 subsetI1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subsetI1,definition,
% 2.27/1.49 ( subsetI1
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( in @ Xx @ B ) )
% 2.27/1.49 => ( subset @ A @ B ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(eqimpsubset2_type,type,
% 2.27/1.49 eqimpsubset2: $o ).
% 2.27/1.49
% 2.27/1.49 thf(eqimpsubset2,definition,
% 2.27/1.49 ( eqimpsubset2
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( A = B )
% 2.27/1.49 => ( subset @ B @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(eqimpsubset1_type,type,
% 2.27/1.49 eqimpsubset1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(eqimpsubset1,definition,
% 2.27/1.49 ( eqimpsubset1
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( A = B )
% 2.27/1.49 => ( subset @ A @ B ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subsetI2_type,type,
% 2.27/1.49 subsetI2: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subsetI2,definition,
% 2.27/1.49 ( subsetI2
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ! [Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( in @ Xx @ B ) )
% 2.27/1.49 => ( subset @ A @ B ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(emptysetsubset_type,type,
% 2.27/1.49 emptysetsubset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(emptysetsubset,definition,
% 2.27/1.49 ( emptysetsubset
% 2.27/1.49 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subsetE_type,type,
% 2.27/1.49 subsetE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subsetE,definition,
% 2.27/1.49 ( subsetE
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( subset @ A @ B )
% 2.27/1.49 => ( ( in @ Xx @ A )
% 2.27/1.49 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subsetE2_type,type,
% 2.27/1.49 subsetE2: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subsetE2,definition,
% 2.27/1.49 ( subsetE2
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( subset @ A @ B )
% 2.27/1.49 => ( ~ ( in @ Xx @ B )
% 2.27/1.49 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(notsubsetI_type,type,
% 2.27/1.49 notsubsetI: $o ).
% 2.27/1.49
% 2.27/1.49 thf(notsubsetI,definition,
% 2.27/1.49 ( notsubsetI
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( ~ ( in @ Xx @ B )
% 2.27/1.49 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(notequalI1_type,type,
% 2.27/1.49 notequalI1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(notequalI1,definition,
% 2.27/1.49 ( notequalI1
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ~ ( subset @ A @ B )
% 2.27/1.49 => ( A != B ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(notequalI2_type,type,
% 2.27/1.49 notequalI2: $o ).
% 2.27/1.49
% 2.27/1.49 thf(notequalI2,definition,
% 2.27/1.49 ( notequalI2
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( ~ ( in @ Xx @ B )
% 2.27/1.49 => ( A != B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subsetRefl_type,type,
% 2.27/1.49 subsetRefl: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subsetRefl,definition,
% 2.27/1.49 ( subsetRefl
% 2.27/1.49 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subsetTrans_type,type,
% 2.27/1.49 subsetTrans: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subsetTrans,definition,
% 2.27/1.49 ( subsetTrans
% 2.27/1.49 = ( ! [A: $i,B: $i,C: $i] :
% 2.27/1.49 ( ( subset @ A @ B )
% 2.27/1.49 => ( ( subset @ B @ C )
% 2.27/1.49 => ( subset @ A @ C ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinSub_type,type,
% 2.27/1.49 setadjoinSub: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinSub,definition,
% 2.27/1.49 ( setadjoinSub
% 2.27/1.49 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinSub2_type,type,
% 2.27/1.49 setadjoinSub2: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setadjoinSub2,definition,
% 2.27/1.49 ( setadjoinSub2
% 2.27/1.49 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.27/1.49 ( ( subset @ A @ B )
% 2.27/1.49 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subset2powerset_type,type,
% 2.27/1.49 subset2powerset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subset2powerset,definition,
% 2.27/1.49 ( subset2powerset
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( subset @ A @ B )
% 2.27/1.49 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(setextsub_type,type,
% 2.27/1.49 setextsub: $o ).
% 2.27/1.49
% 2.27/1.49 thf(setextsub,definition,
% 2.27/1.49 ( setextsub
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( subset @ A @ B )
% 2.27/1.49 => ( ( subset @ B @ A )
% 2.27/1.49 => ( A = B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(subsetemptysetimpeq_type,type,
% 2.27/1.49 subsetemptysetimpeq: $o ).
% 2.27/1.49
% 2.27/1.49 thf(subsetemptysetimpeq,definition,
% 2.27/1.49 ( subsetemptysetimpeq
% 2.27/1.49 = ( ! [A: $i] :
% 2.27/1.49 ( ( subset @ A @ emptyset )
% 2.27/1.49 => ( A = emptyset ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(powersetI1_type,type,
% 2.27/1.49 powersetI1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(powersetI1,definition,
% 2.27/1.49 ( powersetI1
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( subset @ B @ A )
% 2.27/1.49 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(powersetE1_type,type,
% 2.27/1.49 powersetE1: $o ).
% 2.27/1.49
% 2.27/1.49 thf(powersetE1,definition,
% 2.27/1.49 ( powersetE1
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( in @ B @ ( powerset @ A ) )
% 2.27/1.49 => ( subset @ B @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(inPowerset_type,type,
% 2.27/1.49 inPowerset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(inPowerset,definition,
% 2.27/1.49 ( inPowerset
% 2.27/1.49 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(powersetsubset_type,type,
% 2.27/1.49 powersetsubset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(powersetsubset,definition,
% 2.27/1.49 ( powersetsubset
% 2.27/1.49 = ( ! [A: $i,B: $i] :
% 2.27/1.49 ( ( subset @ A @ B )
% 2.27/1.49 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(sepInPowerset_type,type,
% 2.27/1.49 sepInPowerset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(sepInPowerset,definition,
% 2.27/1.49 ( sepInPowerset
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( in
% 2.27/1.49 @ ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 @ ( powerset @ A ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(sepSubset_type,type,
% 2.27/1.49 sepSubset: $o ).
% 2.27/1.49
% 2.27/1.49 thf(sepSubset,definition,
% 2.27/1.49 ( sepSubset
% 2.27/1.49 = ( ! [A: $i,Xphi: $i > $o] :
% 2.27/1.49 ( subset
% 2.27/1.49 @ ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.27/1.49 @ A ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(binunion_type,type,
% 2.27/1.49 binunion: $i > $i > $i ).
% 2.27/1.49
% 2.27/1.49 thf(binunionIL_type,type,
% 2.27/1.49 binunionIL: $o ).
% 2.27/1.49
% 2.27/1.49 thf(binunionIL,definition,
% 2.27/1.49 ( binunionIL
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(upairset2IR_type,type,
% 2.27/1.49 upairset2IR: $o ).
% 2.27/1.49
% 2.27/1.49 thf(upairset2IR,definition,
% 2.27/1.49 ( upairset2IR
% 2.27/1.49 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(binunionIR_type,type,
% 2.27/1.49 binunionIR: $o ).
% 2.27/1.49
% 2.27/1.49 thf(binunionIR,definition,
% 2.27/1.49 ( binunionIR
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ B )
% 2.27/1.49 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(binunionEcases_type,type,
% 2.27/1.49 binunionEcases: $o ).
% 2.27/1.49
% 2.27/1.49 thf(binunionEcases,definition,
% 2.27/1.49 ( binunionEcases
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.27/1.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.27/1.49 => ( ( ( in @ Xx @ A )
% 2.27/1.49 => Xphi )
% 2.27/1.49 => ( ( ( in @ Xx @ B )
% 2.27/1.49 => Xphi )
% 2.27/1.49 => Xphi ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(binunionE_type,type,
% 2.27/1.49 binunionE: $o ).
% 2.27/1.49
% 2.27/1.49 thf(binunionE,definition,
% 2.27/1.49 ( binunionE
% 2.27/1.49 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.27/1.49 => ( ( in @ Xx @ A )
% 2.27/1.49 | ( in @ Xx @ B ) ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(binunionLsub_type,type,
% 2.27/1.49 binunionLsub: $o ).
% 2.27/1.49
% 2.27/1.49 thf(binunionLsub,definition,
% 2.27/1.49 ( binunionLsub
% 2.27/1.49 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(binunionRsub_type,type,
% 2.27/1.49 binunionRsub: $o ).
% 2.27/1.49
% 2.27/1.49 thf(binunionRsub,definition,
% 2.27/1.49 ( binunionRsub
% 2.27/1.49 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(binintersect_type,type,
% 2.27/1.49 binintersect: $i > $i > $i ).
% 2.27/1.49
% 2.27/1.49 thf(binintersect,definition,
% 2.27/1.49 ( binintersect
% 2.27/1.49 = ( ^ [A: $i,B: $i] :
% 2.27/1.49 ( dsetconstr @ A
% 2.27/1.49 @ ^ [Xx: $i] : ( in @ Xx @ B ) ) ) ) ).
% 2.27/1.49
% 2.27/1.49 thf(binintersectI,conjecture,
% 2.27/1.49 ( setextAx
% 2.27/1.49 => ( emptysetAx
% 2.27/1.49 => ( setadjoinAx
% 2.27/1.49 => ( powersetAx
% 2.27/1.49 => ( setunionAx
% 2.27/1.49 => ( omega0Ax
% 2.27/1.49 => ( omegaSAx
% 2.27/1.49 => ( omegaIndAx
% 2.27/1.49 => ( replAx
% 2.27/1.49 => ( foundationAx
% 2.27/1.49 => ( wellorderingAx
% 2.27/1.49 => ( descrp
% 2.27/1.49 => ( dsetconstrI
% 2.27/1.49 => ( dsetconstrEL
% 2.27/1.49 => ( dsetconstrER
% 2.27/1.49 => ( exuE1
% 2.27/1.49 => ( prop2setE
% 2.27/1.49 => ( emptysetE
% 2.27/1.49 => ( emptysetimpfalse
% 2.27/1.49 => ( notinemptyset
% 2.27/1.49 => ( exuE3e
% 2.27/1.49 => ( setext
% 2.27/1.49 => ( emptyI
% 2.27/1.49 => ( noeltsimpempty
% 2.27/1.49 => ( setbeta
% 2.27/1.49 => ( nonemptyE1
% 2.27/1.49 => ( nonemptyI
% 2.27/1.49 => ( nonemptyI1
% 2.27/1.49 => ( setadjoinIL
% 2.27/1.49 => ( emptyinunitempty
% 2.27/1.49 => ( setadjoinIR
% 2.27/1.49 => ( setadjoinE
% 2.27/1.49 => ( setadjoinOr
% 2.27/1.49 => ( setoftrueEq
% 2.27/1.49 => ( powersetI
% 2.27/1.49 => ( emptyinPowerset
% 2.27/1.49 => ( emptyInPowerset
% 2.27/1.49 => ( powersetE
% 2.27/1.49 => ( setunionI
% 2.27/1.49 => ( setunionE
% 2.27/1.49 => ( subPowSU
% 2.27/1.49 => ( exuE2
% 2.27/1.49 => ( nonemptyImpWitness
% 2.27/1.49 => ( uniqinunit
% 2.27/1.49 => ( notinsingleton
% 2.27/1.49 => ( eqinunit
% 2.27/1.49 => ( singletonsswitch
% 2.27/1.49 => ( upairsetE
% 2.27/1.49 => ( upairsetIL
% 2.27/1.49 => ( upairsetIR
% 2.27/1.49 => ( emptyE1
% 2.27/1.49 => ( vacuousDall
% 2.27/1.49 => ( quantDeMorgan1
% 2.27/1.49 => ( quantDeMorgan2
% 2.27/1.49 => ( quantDeMorgan3
% 2.27/1.49 => ( quantDeMorgan4
% 2.27/1.49 => ( prop2setI
% 2.27/1.49 => ( prop2set2propI
% 2.27/1.49 => ( notdexE
% 2.27/1.49 => ( notdallE
% 2.27/1.49 => ( exuI1
% 2.27/1.49 => ( exuI3
% 2.27/1.49 => ( exuI2
% 2.27/1.49 => ( inCongP
% 2.27/1.49 => ( in__Cong
% 2.27/1.49 => ( exuE3u
% 2.27/1.49 => ( exu__Cong
% 2.27/1.49 => ( emptyset__Cong
% 2.27/1.49 => ( setadjoin__Cong
% 2.27/1.49 => ( powerset__Cong
% 2.27/1.49 => ( setunion__Cong
% 2.27/1.49 => ( omega__Cong
% 2.27/1.49 => ( exuEu
% 2.27/1.49 => ( descr__Cong
% 2.27/1.49 => ( dsetconstr__Cong
% 2.27/1.49 => ( subsetI1
% 2.27/1.49 => ( eqimpsubset2
% 2.27/1.49 => ( eqimpsubset1
% 2.27/1.49 => ( subsetI2
% 2.27/1.49 => ( emptysetsubset
% 2.27/1.49 => ( subsetE
% 2.27/1.49 => ( subsetE2
% 2.27/1.49 => ( notsubsetI
% 2.27/1.49 => ( notequalI1
% 2.27/1.49 => ( notequalI2
% 2.27/1.49 => ( subsetRefl
% 2.27/1.49 => ( subsetTrans
% 2.27/1.49 => ( setadjoinSub
% 2.27/1.49 => ( setadjoinSub2
% 2.27/1.49 => ( subset2powerset
% 2.27/1.49 => ( setextsub
% 2.27/1.49 => ( subsetemptysetimpeq
% 2.27/1.49 => ( powersetI1
% 2.27/1.49 => ( powersetE1
% 2.27/1.49 => ( inPowerset
% 2.27/1.49 => ( powersetsubset
% 2.27/1.49 => ( sepInPowerset
% 2.27/1.49 => ( sepSubset
% 2.27/1.49 => ( binunionIL
% 2.27/1.49 => ( upairset2IR
% 2.27/1.49 => ( binunionIR
% 2.27/1.49 => ( binunionEcases
% 2.27/1.49 => ( binunionE
% 2.27/1.49 => ( binunionLsub
% 2.27/1.49 => ( binunionRsub
% 2.27/1.49 => ! [A: $i,B: $i,Xx: $i] :
% 2.27/1.49 ( ( in @ Xx @ A )
% 2.27/1.49 => ( ( in @ Xx @ B )
% 2.27/1.49 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.27/1.49 ------------------------
% 2.41/1.51 % (5438)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_5165 for (2999ds/27Mi)
% 2.41/1.51 % (5439)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/2Mi)
% 2.41/1.51 % (5439)Instruction limit reached!
% 2.41/1.51 % (5439)------------------------------
% 2.41/1.51 % (5439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.51 % (5439)Termination reason: Unknown
% 2.41/1.51 % (5439)Termination phase: shuffling
% 2.41/1.51
% 2.41/1.51 % (5439)Memory used [KB]: 1151
% 2.41/1.51 % (5439)Time elapsed: 0.002 s
% 2.41/1.51 % (5439)Instructions burned: 3 (million)
% 2.41/1.51 % (5439)------------------------------
% 2.41/1.51 % (5439)------------------------------
% 2.41/1.52 % (5437)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_5165 for (2999ds/4Mi)
% 2.41/1.52 % (5436)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/183Mi)
% 2.41/1.52 % (5440)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_5165 for (2999ds/2Mi)
% 2.41/1.52 % (5441)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_5165 for (2999ds/275Mi)
% 2.41/1.52 % (5442)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/18Mi)
% 2.41/1.52 % (5438)Instruction limit reached!
% 2.41/1.52 % (5438)------------------------------
% 2.41/1.52 % (5438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.52 % (5438)Termination reason: Unknown
% 2.41/1.52 % (5438)Termination phase: Property scanning
% 2.41/1.52
% 2.41/1.52 % (5438)Memory used [KB]: 1535
% 2.41/1.52 % (5438)Time elapsed: 0.009 s
% 2.41/1.52 % (5438)Instructions burned: 27 (million)
% 2.41/1.52 % (5438)------------------------------
% 2.41/1.52 % (5438)------------------------------
% 2.41/1.52 % (5440)Instruction limit reached!
% 2.41/1.52 % (5440)------------------------------
% 2.41/1.52 % (5440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.52 % (5440)Termination reason: Unknown
% 2.41/1.52 % (5440)Termination phase: shuffling
% 2.41/1.52
% 2.41/1.52 % (5440)Memory used [KB]: 1151
% 2.41/1.52 % (5440)Time elapsed: 0.003 s
% 2.41/1.52 % (5440)Instructions burned: 2 (million)
% 2.41/1.52 % (5440)------------------------------
% 2.41/1.52 % (5440)------------------------------
% 2.41/1.52 % (5437)Instruction limit reached!
% 2.41/1.52 % (5437)------------------------------
% 2.41/1.52 % (5437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.52 % (5437)Termination reason: Unknown
% 2.41/1.52 % (5437)Termination phase: shuffling
% 2.41/1.52
% 2.41/1.52 % (5437)Memory used [KB]: 1151
% 2.41/1.52 % (5437)Time elapsed: 0.004 s
% 2.41/1.52 % (5437)Instructions burned: 4 (million)
% 2.41/1.52 % (5437)------------------------------
% 2.41/1.52 % (5437)------------------------------
% 2.41/1.52 % (5443)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/3Mi)
% 2.41/1.52 % (5443)Instruction limit reached!
% 2.41/1.52 % (5443)------------------------------
% 2.41/1.52 % (5443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.52 % (5443)Termination reason: Unknown
% 2.41/1.52 % (5443)Termination phase: shuffling
% 2.41/1.52
% 2.41/1.52 % (5443)Memory used [KB]: 1279
% 2.41/1.52 % (5443)Time elapsed: 0.003 s
% 2.41/1.52 % (5443)Instructions burned: 4 (million)
% 2.41/1.52 % (5443)------------------------------
% 2.41/1.52 % (5443)------------------------------
% 2.41/1.53 % (5444)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_5165 for (2999ds/37Mi)
% 2.41/1.53 % (5442)Instruction limit reached!
% 2.41/1.53 % (5442)------------------------------
% 2.41/1.53 % (5442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.53 % (5442)Termination reason: Unknown
% 2.41/1.53 % (5442)Termination phase: Preprocessing 3
% 2.41/1.53
% 2.41/1.53 % (5442)Memory used [KB]: 1535
% 2.41/1.53 % (5442)Time elapsed: 0.013 s
% 2.41/1.53 % (5442)Instructions burned: 19 (million)
% 2.41/1.53 % (5442)------------------------------
% 2.41/1.53 % (5442)------------------------------
% 2.41/1.53 % (5447)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_5165 for (2999ds/1041Mi)
% 2.41/1.53 % (5446)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_5165 for (2999ds/3Mi)
% 2.41/1.54 % (5445)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_5165 for (2999ds/15Mi)
% 2.41/1.54 % (5446)Instruction limit reached!
% 2.41/1.54 % (5446)------------------------------
% 2.41/1.54 % (5446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.54 % (5446)Termination reason: Unknown
% 2.41/1.54 % (5446)Termination phase: shuffling
% 2.41/1.54
% 2.41/1.54 % (5446)Memory used [KB]: 1279
% 2.41/1.54 % (5446)Time elapsed: 0.004 s
% 2.41/1.54 % (5446)Instructions burned: 5 (million)
% 2.41/1.54 % (5446)------------------------------
% 2.41/1.54 % (5446)------------------------------
% 2.41/1.54 % (5444)Instruction limit reached!
% 2.41/1.54 % (5444)------------------------------
% 2.41/1.54 % (5444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.54 % (5444)Termination reason: Unknown
% 2.41/1.54 % (5444)Termination phase: Function definition elimination
% 2.41/1.54
% 2.41/1.54 % (5444)Memory used [KB]: 1535
% 2.41/1.54 % (5444)Time elapsed: 0.012 s
% 2.41/1.54 % (5444)Instructions burned: 38 (million)
% 2.41/1.54 % (5444)------------------------------
% 2.41/1.54 % (5444)------------------------------
% 2.41/1.55 % (5445)Instruction limit reached!
% 2.41/1.55 % (5445)------------------------------
% 2.41/1.55 % (5445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.55 % (5445)Termination reason: Unknown
% 2.41/1.55 % (5445)Termination phase: Naming
% 2.41/1.55
% 2.41/1.55 % (5445)Memory used [KB]: 1535
% 2.41/1.55 % (5445)Time elapsed: 0.011 s
% 2.41/1.55 % (5445)Instructions burned: 16 (million)
% 2.41/1.55 % (5445)------------------------------
% 2.41/1.55 % (5445)------------------------------
% 2.41/1.55 % (5448)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/7Mi)
% 2.41/1.55 % (5450)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_5165 for (2999ds/3Mi)
% 2.41/1.55 % (5450)Instruction limit reached!
% 2.41/1.55 % (5450)------------------------------
% 2.41/1.55 % (5450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.55 % (5450)Termination reason: Unknown
% 2.41/1.55 % (5450)Termination phase: shuffling
% 2.41/1.55
% 2.41/1.55 % (5450)Memory used [KB]: 1279
% 2.41/1.55 % (5450)Time elapsed: 0.003 s
% 2.41/1.55 % (5450)Instructions burned: 4 (million)
% 2.41/1.55 % (5450)------------------------------
% 2.41/1.55 % (5450)------------------------------
% 2.41/1.55 % (5449)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/16Mi)
% 2.41/1.55 % (5448)Instruction limit reached!
% 2.41/1.55 % (5448)------------------------------
% 2.41/1.55 % (5448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.55 % (5448)Termination reason: Unknown
% 2.41/1.55 % (5448)Termination phase: shuffling
% 2.41/1.55
% 2.41/1.55 % (5448)Memory used [KB]: 1279
% 2.41/1.55 % (5448)Time elapsed: 0.006 s
% 2.41/1.55 % (5448)Instructions burned: 8 (million)
% 2.41/1.55 % (5448)------------------------------
% 2.41/1.55 % (5448)------------------------------
% 2.41/1.56 % (5449)Instruction limit reached!
% 2.41/1.56 % (5449)------------------------------
% 2.41/1.56 % (5449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.56 % (5449)Termination reason: Unknown
% 2.41/1.56 % (5449)Termination phase: Property scanning
% 2.41/1.56
% 2.41/1.56 % (5449)Memory used [KB]: 1407
% 2.41/1.56 % (5449)Time elapsed: 0.007 s
% 2.41/1.56 % (5449)Instructions burned: 18 (million)
% 2.41/1.56 % (5449)------------------------------
% 2.41/1.56 % (5449)------------------------------
% 2.41/1.56 % (5451)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_5165 for (2999ds/3Mi)
% 2.41/1.56 % (5451)Instruction limit reached!
% 2.41/1.56 % (5451)------------------------------
% 2.41/1.56 % (5451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.56 % (5451)Termination reason: Unknown
% 2.41/1.56 % (5451)Termination phase: shuffling
% 2.41/1.56
% 2.41/1.56 % (5451)Memory used [KB]: 1151
% 2.41/1.56 % (5451)Time elapsed: 0.003 s
% 2.41/1.56 % (5451)Instructions burned: 3 (million)
% 2.41/1.56 % (5451)------------------------------
% 2.41/1.56 % (5451)------------------------------
% 2.41/1.56 % (5453)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/3Mi)
% 2.41/1.57 % (5454)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/4Mi)
% 2.41/1.57 % (5454)Instruction limit reached!
% 2.41/1.57 % (5454)------------------------------
% 2.41/1.57 % (5454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.57 % (5454)Termination reason: Unknown
% 2.41/1.57 % (5454)Termination phase: shuffling
% 2.41/1.57
% 2.41/1.57 % (5454)Memory used [KB]: 1151
% 2.41/1.57 % (5454)Time elapsed: 0.003 s
% 2.41/1.57 % (5454)Instructions burned: 4 (million)
% 2.41/1.57 % (5454)------------------------------
% 2.41/1.57 % (5454)------------------------------
% 2.41/1.57 % (5453)Instruction limit reached!
% 2.41/1.57 % (5453)------------------------------
% 2.41/1.57 % (5453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.57 % (5453)Termination reason: Unknown
% 2.41/1.57 % (5453)Termination phase: shuffling
% 2.41/1.57
% 2.41/1.57 % (5453)Memory used [KB]: 1279
% 2.41/1.57 % (5453)Time elapsed: 0.003 s
% 2.41/1.57 % (5453)Instructions burned: 5 (million)
% 2.41/1.57 % (5453)------------------------------
% 2.41/1.57 % (5453)------------------------------
% 2.41/1.57 % (5452)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/7Mi)
% 2.41/1.57 % (5452)Instruction limit reached!
% 2.41/1.57 % (5452)------------------------------
% 2.41/1.57 % (5452)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.57 % (5452)Termination reason: Unknown
% 2.41/1.57 % (5452)Termination phase: shuffling
% 2.41/1.57
% 2.41/1.57 % (5452)Memory used [KB]: 1279
% 2.41/1.57 % (5452)Time elapsed: 0.006 s
% 2.41/1.57 % (5452)Instructions burned: 8 (million)
% 2.41/1.57 % (5452)------------------------------
% 2.41/1.57 % (5452)------------------------------
% 2.41/1.57 % (5455)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/18Mi)
% 2.41/1.58 % (5456)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/710Mi)
% 2.41/1.58 % (5455)Instruction limit reached!
% 2.41/1.58 % (5455)------------------------------
% 2.41/1.58 % (5455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.58 % (5455)Termination reason: Unknown
% 2.41/1.58 % (5455)Termination phase: Property scanning
% 2.41/1.58
% 2.41/1.58 % (5455)Memory used [KB]: 1407
% 2.41/1.58 % (5455)Time elapsed: 0.007 s
% 2.41/1.58 % (5455)Instructions burned: 22 (million)
% 2.41/1.58 % (5455)------------------------------
% 2.41/1.58 % (5455)------------------------------
% 2.41/1.58 % (5457)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/6Mi)
% 2.41/1.58 % (5457)Instruction limit reached!
% 2.41/1.58 % (5457)------------------------------
% 2.41/1.58 % (5457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.58 % (5457)Termination reason: Unknown
% 2.41/1.58 % (5457)Termination phase: shuffling
% 2.41/1.58
% 2.41/1.58 % (5457)Memory used [KB]: 1279
% 2.41/1.58 % (5457)Time elapsed: 0.003 s
% 2.41/1.58 % (5457)Instructions burned: 6 (million)
% 2.41/1.58 % (5457)------------------------------
% 2.41/1.58 % (5457)------------------------------
% 2.41/1.59 % (5459)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_5165 for (2999ds/21Mi)
% 2.41/1.59 % (5458)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_5165 for (2999ds/902Mi)
% 2.41/1.59 % (5460)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/5Mi)
% 2.41/1.59 % (5460)Instruction limit reached!
% 2.41/1.59 % (5460)------------------------------
% 2.41/1.59 % (5460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.59 % (5460)Termination reason: Unknown
% 2.41/1.59 % (5460)Termination phase: shuffling
% 2.41/1.59
% 2.41/1.59 % (5460)Memory used [KB]: 1279
% 2.41/1.59 % (5460)Time elapsed: 0.004 s
% 2.41/1.59 % (5460)Instructions burned: 7 (million)
% 2.41/1.59 % (5460)------------------------------
% 2.41/1.59 % (5460)------------------------------
% 2.41/1.59 % (5459)Instruction limit reached!
% 2.41/1.59 % (5459)------------------------------
% 2.41/1.59 % (5459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.59 % (5459)Termination reason: Unknown
% 2.41/1.59 % (5459)Termination phase: Property scanning
% 2.41/1.59
% 2.41/1.59 % (5459)Memory used [KB]: 1407
% 2.41/1.59 % (5459)Time elapsed: 0.007 s
% 2.41/1.59 % (5459)Instructions burned: 21 (million)
% 2.41/1.59 % (5459)------------------------------
% 2.41/1.59 % (5459)------------------------------
% 2.41/1.60 % (5462)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5165 for (2999ds/377Mi)
% 2.41/1.60 % (5461)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_5165 for (2999ds/6Mi)
% 2.41/1.60 % (5461)Instruction limit reached!
% 2.41/1.60 % (5461)------------------------------
% 2.41/1.60 % (5461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.60 % (5461)Termination reason: Unknown
% 2.41/1.60 % (5461)Termination phase: shuffling
% 2.41/1.60
% 2.41/1.60 % (5461)Memory used [KB]: 1279
% 2.41/1.60 % (5461)Time elapsed: 0.004 s
% 2.41/1.60 % (5461)Instructions burned: 8 (million)
% 2.41/1.60 % (5461)------------------------------
% 2.41/1.60 % (5461)------------------------------
% 2.41/1.61 % (5463)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_5165 for (2999ds/779Mi)
% 2.41/1.62 % (5436)Instruction limit reached!
% 2.41/1.62 % (5436)------------------------------
% 2.41/1.62 % (5436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.62 % (5436)Termination reason: Unknown
% 2.41/1.62 % (5436)Termination phase: Saturation
% 2.41/1.62
% 2.41/1.62 % (5436)Memory used [KB]: 6908
% 2.41/1.62 % (5436)Time elapsed: 0.103 s
% 2.41/1.62 % (5436)Instructions burned: 183 (million)
% 2.41/1.62 % (5436)------------------------------
% 2.41/1.62 % (5436)------------------------------
% 2.41/1.64 % (5464)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_5165 for (2998ds/19Mi)
% 2.41/1.65 % (5464)Instruction limit reached!
% 2.41/1.65 % (5464)------------------------------
% 2.41/1.65 % (5464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.65 % (5464)Termination reason: Unknown
% 2.41/1.65 % (5464)Termination phase: Property scanning
% 2.41/1.65
% 2.41/1.65 % (5464)Memory used [KB]: 1407
% 2.41/1.65 % (5464)Time elapsed: 0.012 s
% 2.41/1.65 % (5464)Instructions burned: 20 (million)
% 2.41/1.65 % (5464)------------------------------
% 2.41/1.65 % (5464)------------------------------
% 2.41/1.66 % (5465)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_5165 for (2998ds/879Mi)
% 2.41/1.67 % (5441)Instruction limit reached!
% 2.41/1.67 % (5441)------------------------------
% 2.41/1.67 % (5441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.67 % (5441)Termination reason: Unknown
% 2.41/1.67 % (5441)Termination phase: Saturation
% 2.41/1.67
% 2.41/1.67 % (5441)Memory used [KB]: 7675
% 2.41/1.67 % (5441)Time elapsed: 0.151 s
% 2.41/1.67 % (5441)Instructions burned: 277 (million)
% 2.41/1.67 % (5441)------------------------------
% 2.41/1.67 % (5441)------------------------------
% 2.41/1.68 % (5466)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_5165 for (2998ds/17Mi)
% 2.41/1.68 % (5466)Instruction limit reached!
% 2.41/1.68 % (5466)------------------------------
% 2.41/1.68 % (5466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.68 % (5466)Termination reason: Unknown
% 2.41/1.68 % (5466)Termination phase: Property scanning
% 2.41/1.68
% 2.41/1.68 % (5466)Memory used [KB]: 1407
% 2.41/1.68 % (5466)Time elapsed: 0.006 s
% 2.41/1.68 % (5466)Instructions burned: 17 (million)
% 2.41/1.68 % (5466)------------------------------
% 2.41/1.68 % (5466)------------------------------
% 2.41/1.69 % (5467)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5165 for (2998ds/3Mi)
% 2.41/1.69 % (5467)Instruction limit reached!
% 2.41/1.69 % (5467)------------------------------
% 2.41/1.69 % (5467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.69 % (5467)Termination reason: Unknown
% 2.41/1.69 % (5467)Termination phase: shuffling
% 2.41/1.69
% 2.41/1.69 % (5467)Memory used [KB]: 1279
% 2.41/1.69 % (5467)Time elapsed: 0.003 s
% 2.41/1.69 % (5467)Instructions burned: 4 (million)
% 2.41/1.69 % (5467)------------------------------
% 2.41/1.69 % (5467)------------------------------
% 2.41/1.70 % (5468)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_5165 for (2998ds/30Mi)
% 2.41/1.71 % (5468)Instruction limit reached!
% 2.41/1.71 % (5468)------------------------------
% 2.41/1.71 % (5468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.71 % (5468)Termination reason: Unknown
% 2.41/1.71 % (5468)Termination phase: Property scanning
% 2.41/1.71
% 2.41/1.71 % (5468)Memory used [KB]: 1535
% 2.41/1.71 % (5468)Time elapsed: 0.011 s
% 2.41/1.71 % (5468)Instructions burned: 33 (million)
% 2.41/1.71 % (5468)------------------------------
% 2.41/1.71 % (5468)------------------------------
% 2.41/1.72 % (5462)Instruction limit reached!
% 2.41/1.72 % (5462)------------------------------
% 2.41/1.72 % (5462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.72 % (5462)Termination reason: Unknown
% 2.41/1.72 % (5462)Termination phase: Saturation
% 2.41/1.72
% 2.41/1.72 % (5462)Memory used [KB]: 7291
% 2.41/1.72 % (5462)Time elapsed: 0.117 s
% 2.41/1.72 % (5462)Instructions burned: 379 (million)
% 2.41/1.72 % (5462)------------------------------
% 2.41/1.72 % (5462)------------------------------
% 2.41/1.72 % (5469)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_5165 for (2997ds/127Mi)
% 2.41/1.73 % (5470)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_5165 for (2997ds/100Mi)
% 2.41/1.76 % (5470)Instruction limit reached!
% 2.41/1.76 % (5470)------------------------------
% 2.41/1.76 % (5470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.76 % (5470)Termination reason: Unknown
% 2.41/1.76 % (5470)Termination phase: Saturation
% 2.41/1.76
% 2.41/1.76 % (5470)Memory used [KB]: 6268
% 2.41/1.76 % (5470)Time elapsed: 0.029 s
% 2.41/1.76 % (5470)Instructions burned: 101 (million)
% 2.41/1.76 % (5470)------------------------------
% 2.41/1.76 % (5470)------------------------------
% 2.41/1.76 % (5469)Instruction limit reached!
% 2.41/1.76 % (5469)------------------------------
% 2.41/1.76 % (5469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.76 % (5469)Termination reason: Unknown
% 2.41/1.76 % (5469)Termination phase: Saturation
% 2.41/1.76
% 2.41/1.76 % (5469)Memory used [KB]: 6780
% 2.41/1.76 % (5469)Time elapsed: 0.041 s
% 2.41/1.76 % (5469)Instructions burned: 129 (million)
% 2.41/1.76 % (5469)------------------------------
% 2.41/1.76 % (5469)------------------------------
% 2.41/1.77 % (5471)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_5165 for (2997ds/3Mi)
% 2.41/1.77 % (5471)Instruction limit reached!
% 2.41/1.77 % (5471)------------------------------
% 2.41/1.77 % (5471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.77 % (5471)Termination reason: Unknown
% 2.41/1.77 % (5471)Termination phase: shuffling
% 2.41/1.77
% 2.41/1.77 % (5471)Memory used [KB]: 1151
% 2.41/1.77 % (5471)Time elapsed: 0.002 s
% 2.41/1.77 % (5471)Instructions burned: 3 (million)
% 2.41/1.77 % (5471)------------------------------
% 2.41/1.77 % (5471)------------------------------
% 2.41/1.77 % (5472)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_5165 for (2997ds/20Mi)
% 2.41/1.78 % (5473)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_5165 for (2997ds/86Mi)
% 2.41/1.78 % (5472)Instruction limit reached!
% 2.41/1.78 % (5472)------------------------------
% 2.41/1.78 % (5472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.78 % (5472)Termination reason: Unknown
% 2.41/1.78 % (5472)Termination phase: Preprocessing 2
% 2.41/1.78
% 2.41/1.78 % (5472)Memory used [KB]: 1407
% 2.41/1.78 % (5472)Time elapsed: 0.008 s
% 2.41/1.78 % (5472)Instructions burned: 20 (million)
% 2.41/1.78 % (5472)------------------------------
% 2.41/1.78 % (5472)------------------------------
% 2.41/1.79 % (5474)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_5165 for (2997ds/107Mi)
% 2.41/1.79 % (5447)Instruction limit reached!
% 2.41/1.79 % (5447)------------------------------
% 2.41/1.79 % (5447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.79 % (5447)Termination reason: Unknown
% 2.41/1.79 % (5447)Termination phase: Saturation
% 2.41/1.79
% 2.41/1.79 % (5447)Memory used [KB]: 7931
% 2.41/1.79 % (5447)Time elapsed: 0.258 s
% 2.41/1.79 % (5447)Instructions burned: 1041 (million)
% 2.41/1.79 % (5447)------------------------------
% 2.41/1.79 % (5447)------------------------------
% 2.41/1.80 % (5456)Instruction limit reached!
% 2.41/1.80 % (5456)------------------------------
% 2.41/1.80 % (5456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.80 % (5456)Termination reason: Unknown
% 2.41/1.80 % (5456)Termination phase: Saturation
% 2.41/1.80
% 2.41/1.80 % (5456)Memory used [KB]: 8571
% 2.41/1.80 % (5456)Time elapsed: 0.223 s
% 2.41/1.80 % (5456)Instructions burned: 710 (million)
% 2.41/1.80 % (5456)------------------------------
% 2.41/1.80 % (5456)------------------------------
% 2.41/1.80 % (5473)Instruction limit reached!
% 2.41/1.80 % (5473)------------------------------
% 2.41/1.80 % (5473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.80 % (5473)Termination reason: Unknown
% 2.41/1.80 % (5473)Termination phase: Saturation
% 2.41/1.80
% 2.41/1.80 % (5473)Memory used [KB]: 6396
% 2.41/1.80 % (5473)Time elapsed: 0.024 s
% 2.41/1.80 % (5473)Instructions burned: 88 (million)
% 2.41/1.80 % (5473)------------------------------
% 2.41/1.80 % (5473)------------------------------
% 2.41/1.80 % (5475)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_5165 for (2997ds/39Mi)
% 2.41/1.81 % (5476)dis+10_1:1_cnfonf=lazy_not_gen:fsr=off:kws=precedence:nwc=5.0:s2a=on:ss=axioms:st=1.5:i=448:si=on:rtra=on_0 on DTF2THF_5165 for (2996ds/448Mi)
% 2.41/1.81 % (5477)lrs+10_1:512_au=on:fde=unused:lma=on:nm=32:plsq=on:plsqc=1:plsqr=16121663,131072:sfv=off:sp=const_max:ss=axioms:st=3.0:tgt=full:i=46:si=on:rtra=on_0 on DTF2THF_5165 for (2996ds/46Mi)
% 2.41/1.81 % (5475)Instruction limit reached!
% 2.41/1.81 % (5475)------------------------------
% 2.41/1.81 % (5475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.81 % (5475)Termination reason: Unknown
% 2.41/1.81 % (5475)Termination phase: Function definition elimination
% 2.41/1.81
% 2.41/1.81 % (5475)Memory used [KB]: 1535
% 2.41/1.81 % (5475)Time elapsed: 0.011 s
% 2.41/1.81 % (5475)Instructions burned: 40 (million)
% 2.41/1.81 % (5475)------------------------------
% 2.41/1.81 % (5475)------------------------------
% 2.41/1.82 % (5463)Instruction limit reached!
% 2.41/1.82 % (5463)------------------------------
% 2.41/1.82 % (5463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.82 % (5463)Termination reason: Unknown
% 2.41/1.82 % (5463)Termination phase: Saturation
% 2.41/1.82
% 2.41/1.82 % (5463)Memory used [KB]: 6780
% 2.41/1.82 % (5463)Time elapsed: 0.203 s
% 2.41/1.82 % (5463)Instructions burned: 779 (million)
% 2.41/1.82 % (5463)------------------------------
% 2.41/1.82 % (5463)------------------------------
% 2.41/1.82 % (5478)lrs+10_1:10_au=on:av=off:cbe=off:cnfonf=lazy_pi_sigma_gen:ntd=on:plsq=on:plsqc=1:plsqr=32,1:i=98:si=on:rtra=on_0 on DTF2THF_5165 for (2996ds/98Mi)
% 2.41/1.82 % (5465)First to succeed.
% 2.41/1.82 % (5474)Instruction limit reached!
% 2.41/1.82 % (5474)------------------------------
% 2.41/1.82 % (5474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.82 % (5474)Termination reason: Unknown
% 2.41/1.82 % (5474)Termination phase: Saturation
% 2.41/1.82
% 2.41/1.82 % (5474)Memory used [KB]: 6524
% 2.41/1.82 % (5474)Time elapsed: 0.033 s
% 2.41/1.82 % (5474)Instructions burned: 109 (million)
% 2.41/1.82 % (5474)------------------------------
% 2.41/1.82 % (5474)------------------------------
% 2.41/1.82 % (5477)Instruction limit reached!
% 2.41/1.82 % (5477)------------------------------
% 2.41/1.82 % (5477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.82 % (5477)Termination reason: Unknown
% 2.41/1.82 % (5477)Termination phase: Twee Goal Transformation
% 2.41/1.82
% 2.41/1.82 % (5477)Memory used [KB]: 1535
% 2.41/1.82 % (5477)Time elapsed: 0.013 s
% 2.41/1.82 % (5477)Instructions burned: 46 (million)
% 2.41/1.82 % (5477)------------------------------
% 2.41/1.82 % (5477)------------------------------
% 2.41/1.82 % (5465)Refutation found. Thanks to Tanya!
% 2.41/1.82 % SZS status Theorem for DTF2THF_5165
% 2.41/1.82 % SZS output start Proof for DTF2THF_5165
% 2.41/1.82 thf(func_def_0, type, in: $i > $i > $o).
% 2.41/1.82 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.41/1.82 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.41/1.82 thf(func_def_8, type, powerset: $i > $i).
% 2.41/1.82 thf(func_def_10, type, setunion: $i > $i).
% 2.41/1.82 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.41/1.82 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_26, type, prop2set: $o > $i).
% 2.41/1.82 thf(func_def_36, type, nonempty: $i > $o).
% 2.41/1.82 thf(func_def_69, type, set2prop: $i > $o).
% 2.41/1.82 thf(func_def_88, type, subset: $i > $i > $o).
% 2.41/1.82 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.41/1.82 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.41/1.82 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.41/1.82 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.41/1.82 thf(func_def_143, type, sK4: $i > $i).
% 2.41/1.82 thf(func_def_144, type, sK5: $i > $i).
% 2.41/1.82 thf(func_def_145, type, sK6: $i > $i > $i).
% 2.41/1.82 thf(func_def_146, type, sK7: $i > $i > $i).
% 2.41/1.82 thf(func_def_147, type, sK8: $i > $i > $i).
% 2.41/1.82 thf(func_def_148, type, sK9: $i > $i > $i > $i).
% 2.41/1.82 thf(func_def_149, type, sK10: $i > $i).
% 2.41/1.82 thf(func_def_150, type, sK11: $i > $i > $i).
% 2.41/1.82 thf(func_def_151, type, sK12: $i > $i > $i).
% 2.41/1.82 thf(func_def_152, type, sK13: $i > $i).
% 2.41/1.82 thf(func_def_153, type, sK14: $i > $i > $i).
% 2.41/1.82 thf(func_def_154, type, sK15: $i > $i > $i).
% 2.41/1.82 thf(func_def_155, type, sK16: $i > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_156, type, sK17: ($i > $o) > $i).
% 2.41/1.82 thf(func_def_157, type, sK18: ($i > $o) > $i > $i).
% 2.41/1.82 thf(func_def_158, type, sK19: ($i > $o) > $i > ($i > $o) > $i > $i).
% 2.41/1.82 thf(func_def_159, type, sK20: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_160, type, sK21: $i > $i).
% 2.41/1.82 thf(func_def_161, type, sK22: ($i > $o) > $i > $i).
% 2.41/1.82 thf(func_def_162, type, sK23: ($i > $o) > $i > $i).
% 2.41/1.82 thf(func_def_163, type, sK24: ($i > $o) > $i).
% 2.41/1.82 thf(func_def_164, type, sK25: $i > $i).
% 2.41/1.82 thf(func_def_165, type, sK26: ($i > $o) > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_166, type, sK27: ($i > $o) > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_167, type, sK28: ($i > $o) > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_168, type, sK29: ($i > $o) > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_169, type, sK30: ($i > $i > $o) > $i > $i).
% 2.41/1.82 thf(func_def_170, type, sK31: ($i > $i > $o) > $i > $i).
% 2.41/1.82 thf(func_def_171, type, sK32: ($i > $i > $o) > $i > $i > $i).
% 2.41/1.82 thf(func_def_172, type, sK33: ($i > $i > $o) > $i > $i).
% 2.41/1.82 thf(func_def_173, type, sK34: ($i > $i > $o) > $i > $i > $i).
% 2.41/1.82 thf(func_def_174, type, sK35: ($i > $o) > $i).
% 2.41/1.82 thf(func_def_175, type, sK36: ($i > $o) > $i).
% 2.41/1.82 thf(func_def_176, type, sK37: ($i > $o) > $i).
% 2.41/1.82 thf(func_def_177, type, sK38: $i > $i).
% 2.41/1.82 thf(func_def_178, type, sK39: $i > $o > $i > $i).
% 2.41/1.82 thf(func_def_179, type, sK40: $i > $i > $i).
% 2.41/1.82 thf(func_def_180, type, sK41: $i > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_181, type, sK42: $i > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_182, type, sK43: $i > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_183, type, sK44: ($i > $o) > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_184, type, sK45: ($i > $o) > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_185, type, sK46: $i > $i > $i).
% 2.41/1.82 thf(func_def_186, type, sK47: $i > $i > $i).
% 2.41/1.82 thf(func_def_187, type, sK48: $i > $i > $i).
% 2.41/1.82 thf(func_def_188, type, sK49: $i > ($i > $o) > $i).
% 2.41/1.82 thf(func_def_189, type, ph50: !>[X0: $tType]:(X0)).
% 2.41/1.82 thf(f3101,plain,(
% 2.41/1.82 $false),
% 2.41/1.82 inference(trivial_inequality_removal,[status(thm)],[f3100])).
% 2.41/1.82 thf(f3100,plain,(
% 2.41/1.82 ($true = $false)),
% 2.41/1.82 inference(backward_demodulation,[status(thm)],[f369,f3099])).
% 2.41/1.82 thf(f3099,plain,(
% 2.41/1.82 ($false = (in @ sK2 @ sK1))),
% 2.41/1.82 inference(trivial_inequality_removal,[status(thm)],[f3098])).
% 2.41/1.82 thf(f3098,plain,(
% 2.41/1.82 ($true = $false) | ($false = (in @ sK2 @ sK1))),
% 2.41/1.82 inference(forward_demodulation,[status(thm)],[f3094,f368])).
% 2.41/1.82 thf(f368,plain,(
% 2.41/1.82 ($true = (in @ sK2 @ sK0))),
% 2.41/1.82 inference(cnf_transformation,[status(thm)],[f327])).
% 2.41/1.82 thf(f327,plain,(
% 2.41/1.82 (nonemptyI = $true) & (quantDeMorgan1 = $true) & (powerset__Cong = $true) & (exuE1 = $true) & (subsetE = $true) & (setadjoinSub2 = $true) & (in__Cong = $true) & (emptyE1 = $true) & (dsetconstrEL = $true) & (replAx = $true) & (setbeta = $true) & (omega0Ax = $true) & (powersetsubset = $true) & (subsetI1 = $true) & (emptyInPowerset = $true) & (eqimpsubset2 = $true) & (omega__Cong = $true) & (notequalI2 = $true) & (emptysetimpfalse = $true) & (subsetE2 = $true) & (emptysetE = $true) & (upairsetIL = $true) & (setunionI = $true) & (subset2powerset = $true) & (binunionLsub = $true) & (eqinunit = $true) & (binunionE = $true) & (setunion__Cong = $true) & (noeltsimpempty = $true) & (emptysetAx = $true) & (quantDeMorgan2 = $true) & (sepSubset = $true) & (notsubsetI = $true) & (notinsingleton = $true) & (exuI3 = $true) & (emptysetsubset = $true) & (nonemptyI1 = $true) & (singletonsswitch = $true) & (dsetconstrER = $true) & (exuI2 = $true) & (setadjoinIR = $true) & (dsetconstr__Cong = $true) & (setoftrueEq = $true) & (setextAx = $true) & (uniqinunit = $true) & (upairsetIR = $true) & (notequalI1 = $true) & (exuE3e = $true) & (subsetTrans = $true) & (setunionE = $true) & (setadjoinSub = $true) & (quantDeMorgan3 = $true) & (exuEu = $true) & (wellorderingAx = $true) & (powersetE1 = $true) & (prop2setI = $true) & (binunionIR = $true) & (setadjoinE = $true) & (omegaIndAx = $true) & (inPowerset = $true) & (nonemptyE1 = $true) & (sepInPowerset = $true) & (vacuousDall = $true) & (notdallE = $true) & (setadjoinIL = $true) & (inCongP = $true) & (descrp = $true) & (upairset2IR = $true) & (subPowSU = $true) & (subsetRefl = $true) & (powersetE = $true) & (prop2setE = $true) & (emptyset__Cong = $true) & (quantDeMorgan4 = $true) & (binunionEcases = $true) & (setunionAx = $true) & (powersetAx = $true) & (binunionIL = $true) & (emptyI = $true) & (dsetconstrI = $true) & (exuE3u = $true) & (exu__Cong = $true) & (exuE2 = $true) & (prop2set2propI = $true) & (binunionRsub = $true) & (subsetemptysetimpeq = $true) & (powersetI = $true) & (setextsub = $true) & (notinemptyset = $true) & (notdexE = $true) & (subsetI2 = $true) & (setadjoinAx = $true) & (exuI1 = $true) & (omegaSAx = $true) & (setext = $true) & (setadjoinOr = $true) & (setadjoin__Cong = $true) & (foundationAx = $true) & (($true = (in @ sK2 @ sK1)) & ($true = (in @ sK2 @ sK0)) & ($true != (in @ sK2 @ (binintersect @ sK1 @ sK0)))) & (descr__Cong = $true) & (powersetI1 = $true) & (upairsetE = $true) & (eqimpsubset1 = $true) & (emptyinunitempty = $true) & (nonemptyImpWitness = $true) & (emptyinPowerset = $true)),
% 2.41/1.82 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f325,f326])).
% 2.41/1.82 thf(f326,plain,(
% 2.41/1.82 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) & ($true = (in @ X2 @ X0)) & ((in @ X2 @ (binintersect @ X1 @ X0)) != $true)) => (($true = (in @ sK2 @ sK1)) & ($true = (in @ sK2 @ sK0)) & ($true != (in @ sK2 @ (binintersect @ sK1 @ sK0))))),
% 2.41/1.82 introduced(definition,[],[choice_axiom])).
% 2.41/1.82 thf(f325,plain,(
% 2.41/1.82 (nonemptyI = $true) & (quantDeMorgan1 = $true) & (powerset__Cong = $true) & (exuE1 = $true) & (subsetE = $true) & (setadjoinSub2 = $true) & (in__Cong = $true) & (emptyE1 = $true) & (dsetconstrEL = $true) & (replAx = $true) & (setbeta = $true) & (omega0Ax = $true) & (powersetsubset = $true) & (subsetI1 = $true) & (emptyInPowerset = $true) & (eqimpsubset2 = $true) & (omega__Cong = $true) & (notequalI2 = $true) & (emptysetimpfalse = $true) & (subsetE2 = $true) & (emptysetE = $true) & (upairsetIL = $true) & (setunionI = $true) & (subset2powerset = $true) & (binunionLsub = $true) & (eqinunit = $true) & (binunionE = $true) & (setunion__Cong = $true) & (noeltsimpempty = $true) & (emptysetAx = $true) & (quantDeMorgan2 = $true) & (sepSubset = $true) & (notsubsetI = $true) & (notinsingleton = $true) & (exuI3 = $true) & (emptysetsubset = $true) & (nonemptyI1 = $true) & (singletonsswitch = $true) & (dsetconstrER = $true) & (exuI2 = $true) & (setadjoinIR = $true) & (dsetconstr__Cong = $true) & (setoftrueEq = $true) & (setextAx = $true) & (uniqinunit = $true) & (upairsetIR = $true) & (notequalI1 = $true) & (exuE3e = $true) & (subsetTrans = $true) & (setunionE = $true) & (setadjoinSub = $true) & (quantDeMorgan3 = $true) & (exuEu = $true) & (wellorderingAx = $true) & (powersetE1 = $true) & (prop2setI = $true) & (binunionIR = $true) & (setadjoinE = $true) & (omegaIndAx = $true) & (inPowerset = $true) & (nonemptyE1 = $true) & (sepInPowerset = $true) & (vacuousDall = $true) & (notdallE = $true) & (setadjoinIL = $true) & (inCongP = $true) & (descrp = $true) & (upairset2IR = $true) & (subPowSU = $true) & (subsetRefl = $true) & (powersetE = $true) & (prop2setE = $true) & (emptyset__Cong = $true) & (quantDeMorgan4 = $true) & (binunionEcases = $true) & (setunionAx = $true) & (powersetAx = $true) & (binunionIL = $true) & (emptyI = $true) & (dsetconstrI = $true) & (exuE3u = $true) & (exu__Cong = $true) & (exuE2 = $true) & (prop2set2propI = $true) & (binunionRsub = $true) & (subsetemptysetimpeq = $true) & (powersetI = $true) & (setextsub = $true) & (notinemptyset = $true) & (notdexE = $true) & (subsetI2 = $true) & (setadjoinAx = $true) & (exuI1 = $true) & (omegaSAx = $true) & (setext = $true) & (setadjoinOr = $true) & (setadjoin__Cong = $true) & (foundationAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) & ($true = (in @ X2 @ X0)) & ((in @ X2 @ (binintersect @ X1 @ X0)) != $true)) & (descr__Cong = $true) & (powersetI1 = $true) & (upairsetE = $true) & (eqimpsubset1 = $true) & (emptyinunitempty = $true) & (nonemptyImpWitness = $true) & (emptyinPowerset = $true)),
% 2.41/1.82 inference(flattening,[status(thm)],[f324])).
% 2.41/1.82 thf(f324,plain,(
% 2.41/1.82 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ (binintersect @ X1 @ X0)) != $true) & ($true = (in @ X2 @ X0))) & ($true = (in @ X2 @ X1))) & (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)),
% 2.41/1.82 inference(ennf_transformation,[status(thm)],[f161])).
% 2.41/1.82 thf(f161,plain,(
% 2.41/1.82 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) => (($true = (in @ X2 @ X0)) => ((in @ X2 @ (binintersect @ X1 @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.41/1.82 inference(fool_elimination,[status(thm)],[f160])).
% 2.41/1.82 thf(f160,plain,(
% 2.41/1.82 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ (binintersect @ X1 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.41/1.82 inference(rectify,[status(thm)],[f110])).
% 2.41/1.82 thf(f110,negated_conjecture,(
% 2.41/1.82 ~(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 => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (binintersect @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.41/1.82 inference(negated_conjecture,[status(cth)],[f109])).
% 2.41/1.82 thf(f109,conjecture,(
% 2.41/1.82 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 => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ X3) => ((in @ X1 @ X4) => (in @ X1 @ (binintersect @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.41/1.82 file('/export/starexec/sandbox2/tmp/tmp.yYawlLAc0c/DTF2THF_5165.p',binintersectI)).
% 2.41/1.82 thf(f3094,plain,(
% 2.41/1.82 ($false = (in @ sK2 @ sK1)) | ($false = (in @ sK2 @ sK0))),
% 2.41/1.82 inference(beta_eta_normalization,[status(thm)],[f3093])).
% 2.41/1.82 thf(f3093,plain,(
% 2.41/1.82 ($false = ((^[Y0 : $i]: (in @ Y0 @ sK0)) @ sK2)) | ($false = (in @ sK2 @ sK1))),
% 2.41/1.82 inference(trivial_inequality_removal,[status(thm)],[f3085])).
% 2.41/1.82 thf(f3085,plain,(
% 2.41/1.82 ($true != $true) | ($false = ((^[Y0 : $i]: (in @ Y0 @ sK0)) @ sK2)) | ($false = (in @ sK2 @ sK1))),
% 2.41/1.82 inference(superposition,[status(thm)],[f1369,f1118])).
% 2.41/1.82 thf(f1118,plain,(
% 2.41/1.82 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = (in @ X3 @ (dsetconstr @ X1 @ X2))) | ($false = (X2 @ X3)) | ((in @ X3 @ X1) = $false)) )),
% 2.41/1.82 inference(binary_proxy_clausification,[status(thm)],[f1117])).
% 2.41/1.82 thf(f1117,plain,(
% 2.41/1.82 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (((in @ X3 @ X1) = $false) | ($true = ((X2 @ X3) => (in @ X3 @ (dsetconstr @ X1 @ X2))))) )),
% 2.41/1.82 inference(binary_proxy_clausification,[status(thm)],[f1116])).
% 2.41/1.82 thf(f1116,plain,(
% 2.41/1.82 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((in @ X3 @ X1) => ((X2 @ X3) => (in @ X3 @ (dsetconstr @ X1 @ X2)))))) )),
% 2.41/1.82 inference(beta_eta_normalization,[status(thm)],[f1115])).
% 2.41/1.82 thf(f1115,plain,(
% 2.41/1.82 ( ! [X2 : $i > $o,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ X2))))) @ X3))) )),
% 2.41/1.82 inference(pi_clausification,[status(thm)],[f1114])).
% 2.41/1.82 thf(f1114,plain,(
% 2.41/1.82 ( ! [X2 : $i > $o,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) => ((X2 @ Y0) => (in @ Y0 @ (dsetconstr @ X1 @ X2)))))))) )),
% 2.41/1.82 inference(beta_eta_normalization,[status(thm)],[f1113])).
% 2.41/1.82 thf(f1113,plain,(
% 2.41/1.82 ( ! [X2 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ X1 @ Y0))))))) @ X2))) )),
% 2.41/1.82 inference(pi_clausification,[status(thm)],[f1112])).
% 2.41/1.82 thf(f1112,plain,(
% 2.41/1.82 ( ! [X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) => ((Y0 @ Y1) => (in @ Y1 @ (dsetconstr @ X1 @ Y0)))))))))) )),
% 2.41/1.82 inference(beta_eta_normalization,[status(thm)],[f1111])).
% 2.41/1.82 thf(f1111,plain,(
% 2.41/1.82 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ Y1))))))))) @ X1))) )),
% 2.41/1.82 inference(pi_clausification,[status(thm)],[f1110])).
% 2.41/1.82 thf(f1110,plain,(
% 2.41/1.82 ((!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ Y1)))))))))) = $true)),
% 2.41/1.82 inference(beta_eta_normalization,[status(thm)],[f635])).
% 2.41/1.82 thf(f635,plain,(
% 2.41/1.82 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 2.41/1.82 inference(definition_unfolding,[status(thm)],[f529,f388])).
% 2.41/1.82 thf(f388,plain,(
% 2.41/1.82 (dsetconstrI = $true)),
% 2.41/1.82 inference(cnf_transformation,[status(thm)],[f327])).
% 2.41/1.82 thf(f529,plain,(
% 2.41/1.82 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 2.41/1.82 inference(cnf_transformation,[status(thm)],[f163])).
% 2.41/1.82 thf(f163,plain,(
% 2.41/1.82 (dsetconstrI = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) => ((Y1 @ Y2) => (in @ Y2 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y1 @ Y3)))))))))))))),
% 2.41/1.82 inference(fool_elimination,[status(thm)],[f162])).
% 2.41/1.82 thf(f162,plain,(
% 2.41/1.82 (dsetconstrI = ! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X0 @ X2) => ((X1 @ X0) => (in @ X0 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X1 @ X3)))))))),
% 2.41/1.82 inference(rectify,[status(thm)],[f14])).
% 2.41/1.82 thf(f14,axiom,(
% 2.41/1.82 (dsetconstrI = ! [X1 : $i,X0 : $i > $o,X3 : $i] : ((in @ X1 @ X3) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))),
% 2.41/1.82 file('/export/starexec/sandbox2/tmp/tmp.yYawlLAc0c/DTF2THF_5165.p',dsetconstrI)).
% 2.41/1.82 thf(f1369,plain,(
% 2.41/1.82 ($true != (in @ sK2 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (in @ Y0 @ sK0)))))),
% 2.41/1.82 inference(beta_eta_normalization,[status(thm)],[f571])).
% 2.41/1.82 thf(f571,plain,(
% 2.41/1.82 ($true != (in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))) @ sK1 @ sK0)))),
% 2.41/1.82 inference(definition_unfolding,[status(thm)],[f367,f349])).
% 2.41/1.82 thf(f349,plain,(
% 2.41/1.82 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 2.41/1.82 inference(cnf_transformation,[status(thm)],[f230])).
% 2.41/1.82 thf(f230,plain,(
% 2.41/1.82 (binintersect = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (in @ Y2 @ Y1)))))))),
% 2.41/1.82 inference(fool_elimination,[status(thm)],[f229])).
% 2.41/1.82 thf(f229,plain,(
% 2.41/1.82 ((^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (in @ X2 @ X1)))) = binintersect)),
% 2.41/1.82 inference(rectify,[status(thm)],[f108])).
% 2.41/1.82 thf(f108,axiom,(
% 2.41/1.82 ((^[X3 : $i, X4 : $i] : (dsetconstr @ X3 @ (^[X1 : $i] : (in @ X1 @ X4)))) = binintersect)),
% 2.41/1.82 file('/export/starexec/sandbox2/tmp/tmp.yYawlLAc0c/DTF2THF_5165.p',binintersect)).
% 2.41/1.82 thf(f367,plain,(
% 2.41/1.82 ($true != (in @ sK2 @ (binintersect @ sK1 @ sK0)))),
% 2.41/1.82 inference(cnf_transformation,[status(thm)],[f327])).
% 2.41/1.82 thf(f369,plain,(
% 2.41/1.82 ($true = (in @ sK2 @ sK1))),
% 2.41/1.82 inference(cnf_transformation,[status(thm)],[f327])).
% 2.41/1.82 % SZS output end Proof for DTF2THF_5165
% 2.41/1.82 % (5465)------------------------------
% 2.41/1.82 % (5465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.41/1.82 % (5465)Termination reason: Refutation
% 2.41/1.82
% 2.41/1.82 % (5465)Memory used [KB]: 7291
% 2.41/1.82 % (5465)Time elapsed: 0.164 s
% 2.41/1.82 % (5465)Instructions burned: 475 (million)
% 2.41/1.82 % (5465)------------------------------
% 2.41/1.82 % (5465)------------------------------
% 2.41/1.82 % (5435)Success in time 0.329 s
%------------------------------------------------------------------------------