%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU603^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n001.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 09:35:33 AM UTC 2026
% Result : Theorem 2.43s 1.69s
% Output : Refutation 2.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 4
% Syntax : Number of formulae : 37 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 2322 ( 638 equ; 0 cnn)
% Maximal formula atoms : 121 ( 62 avg)
% Number of connectives : 1228 ( 18 ~; 2 |; 362 &; 215 @)
% ( 0 <=>; 613 =>; 0 <=; 0 <~>)
% Maximal formula depth : 128 ( 28 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 192 ( 188 usr; 125 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_135,type,
regular: $i > $o ).
thf(func_def_136,type,
setminus: $i > $i > $i ).
thf(func_def_159,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_160,type,
sK5: $i > $i > $i ).
thf(func_def_161,type,
sK6: $i > ( $i > $o ) > $i ).
thf(func_def_162,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_163,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_164,type,
sK9: $i > $i ).
thf(func_def_165,type,
sK10: $i > $i > $i ).
thf(func_def_166,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_167,type,
sK12: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_168,type,
sK13: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_169,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_170,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_171,type,
sK16: $i > $i ).
thf(func_def_172,type,
sK17: $i > $i > $i ).
thf(func_def_173,type,
sK18: $i > ( $i > $o ) > $i ).
thf(func_def_174,type,
sK19: $i > $i > $i ).
thf(func_def_175,type,
sK20: ( $i > $o ) > $i ).
thf(func_def_176,type,
sK21: $i > $i > $i ).
thf(func_def_177,type,
sK22: ( $i > $i > $o ) > $i > $i ).
thf(func_def_178,type,
sK23: ( $i > $i > $o ) > $i > $i ).
thf(func_def_179,type,
sK24: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_180,type,
sK25: ( $i > $i > $o ) > $i > $i ).
thf(func_def_181,type,
sK26: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_182,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_183,type,
sK28: $i > $i > $i ).
thf(func_def_184,type,
sK29: $i > $i > $i ).
thf(func_def_185,type,
sK30: $i > $i ).
thf(func_def_186,type,
sK31: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_187,type,
sK32: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_188,type,
sK33: ( $i > $o ) > $i > $i ).
thf(func_def_189,type,
sK34: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_190,type,
sK35: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_191,type,
sK36: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_192,type,
sK37: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_193,type,
sK38: $i > ( $i > $o ) > $i ).
thf(func_def_194,type,
sK39: $i > $i > $o > $i ).
thf(func_def_195,type,
sK40: $i > $i ).
thf(func_def_196,type,
sK41: $i > $i > $i ).
thf(func_def_197,type,
sK42: $i > $i > $i ).
thf(func_def_198,type,
sK43: $i > $i > $i ).
thf(func_def_199,type,
sK44: $i > $i > $i > $i ).
thf(func_def_200,type,
sK45: $i > $i ).
thf(func_def_201,type,
sK46: ( $i > $o ) > $i > $i ).
thf(func_def_202,type,
sK47: $i > $i ).
thf(func_def_203,type,
sK48: $i > $i > $i ).
thf(func_def_204,type,
sK49: $i > $i > $i ).
thf(func_def_205,type,
sK50: $i > $i > $i ).
thf(func_def_206,type,
sK51: $i > $i ).
thf(func_def_207,type,
ph52:
!>[X0: $tType] : X0 ).
thf(f3182,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f3181]) ).
thf(f3181,plain,
$true = $false,
inference(backward_demodulation,[status(thm)],[f440,f3180]) ).
thf(f3180,plain,
( ( in @ sK2 @ sK0 )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f3179]) ).
thf(f3179,plain,
( $true
= ( ~ ( in @ sK2 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f3178]) ).
thf(f3178,plain,
( $true
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK0 )
@ sK2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f3164]) ).
thf(f3164,plain,
( ( $true
= ( ^ [Y0: $i] :
~ ( in @ Y0 @ sK0 )
@ sK2 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f1191,f920]) ).
thf(f920,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
= $false )
| ( $true
= ( X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f919]) ).
thf(f919,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ( in @ X2 @ ( dsetconstr @ X1 @ X3 ) )
=> ( X3 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f918]) ).
thf(f918,plain,
! [X2: $i,X3: $i > $o,X1: $i] :
( $true
= ( ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ X2 ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f917]) ).
thf(f917,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( in @ X2 @ ( dsetconstr @ X1 @ Y0 ) )
=> ( Y0 @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f916]) ).
thf(f916,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( Y1 @ Y0 ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f915]) ).
thf(f915,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( in @ Y0 @ ( dsetconstr @ X1 @ Y1 ) )
=> ( Y1 @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f914]) ).
thf(f914,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( Y2 @ Y1 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f913]) ).
thf(f913,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1 @ ( dsetconstr @ Y0 @ Y2 ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f682]) ).
thf(f682,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f561,f530]) ).
thf(f530,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f370]) ).
thf(f370,plain,
( ( powersetsubset = $true )
& ( binintersectSubset1 = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( subsetI1 = $true )
& ( binintersectLsub = $true )
& ( notinemptyset = $true )
& ( subsetE = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIR = $true )
& ( dsetconstrER = $true )
& ( descr__Cong = $true )
& ( prop2setE = $true )
& ( binunionIL = $true )
& ( prop2setI = $true )
& ( binintersectEL = $true )
& ( emptysetAx = $true )
& ( uniqinunit = $true )
& ( subsetE2 = $true )
& ( dsetconstrI = $true )
& ( setminusEL = $true )
& ( notequalI1 = $true )
& ( omega__Cong = $true )
& ( binintersectSubset3 = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIL = $true )
& ( subsetTrans = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( subsetI2 = $true )
& ( exuE1 = $true )
& ( setunionAx = $true )
& ( notsubsetI = $true )
& ( binunionLsub = $true )
& ( setadjoinSub2 = $true )
& ( quantDeMorgan1 = $true )
& ( exuE3u = $true )
& ( powersetAx = $true )
& ( exuI2 = $true )
& ( setadjoinSub = $true )
& ( setadjoinE = $true )
& ( nonemptyI1 = $true )
& ( singletonsswitch = $true )
& ( setunionE = $true )
& ( noeltsimpempty = $true )
& ( binunionEcases = $true )
& ( setunionI = $true )
& ( binintersectER = $true )
& ( sepSubset = $true )
& ( eqimpsubset2 = $true )
& ( upairsetE = $true )
& ( emptyInPowerset = $true )
& ( upairset2IR = $true )
& ( binintersectSubset4 = $true )
& ( disjointsetsI1 = $true )
& ( binintersectSubset5 = $true )
& ( setunion__Cong = $true )
& ( setadjoinOr = $true )
& ( setminusI = $true )
& ( setadjoin__Cong = $true )
& ( inPowerset = $true )
& ( prop2set2propI = $true )
& ( binunionIR = $true )
& ( binintersectRsub = $true )
& ( binunionE = $true )
& ( powersetI1 = $true )
& ( replAx = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( binintersectSubset2 = $true )
& ( exu__Cong = $true )
& ( exuE3e = $true )
& ( eqimpsubset1 = $true )
& ( notdexE = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( setext = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE = $true )
& ( notequalI2 = $true )
& ( setadjoinIR = $true )
& ( omega0Ax = $true )
& ( setextAx = $true )
& ( foundationAx = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( setbeta = $true )
& ( subPowSU = $true )
& ( eqinunit = $true )
& ( emptyE1 = $true )
& ( emptysetE = $true )
& ( emptysetimpfalse = $true )
& ( exuEu = $true )
& ( omegaSAx = $true )
& ( powersetI = $true )
& ( bs114d = $true )
& ( dsetconstrEL = $true )
& ( exuI1 = $true )
& ( descrp = $true )
& ( emptyset__Cong = $true )
& ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) )
& ( wellorderingAx = $true )
& ( nonemptyE1 = $true )
& ( notinsingleton = $true )
& ( exuE2 = $true )
& ( quantDeMorgan4 = $true )
& ( subsetRefl = $true )
& ( emptyinunitempty = $true )
& ( sepInPowerset = $true )
& ( omegaIndAx = $true )
& ( emptysetsubset = $true )
& ( setoftrueEq = $true )
& ( exuI3 = $true )
& ( emptyinPowerset = $true )
& ( binintersectI = $true )
& ( in__Cong = $true )
& ( powerset__Cong = $true )
& ( notdallE = $true )
& ( setadjoinAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f368,f369]) ).
thf(f369,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
=> ( ( $true
= ( in @ sK2 @ sK0 ) )
& ( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f368,plain,
( ( powersetsubset = $true )
& ( binintersectSubset1 = $true )
& ( inCongP = $true )
& ( powersetE1 = $true )
& ( subsetI1 = $true )
& ( binintersectLsub = $true )
& ( notinemptyset = $true )
& ( subsetE = $true )
& ( binunionRsub = $true )
& ( quantDeMorgan3 = $true )
& ( upairsetIR = $true )
& ( dsetconstrER = $true )
& ( descr__Cong = $true )
& ( prop2setE = $true )
& ( binunionIL = $true )
& ( prop2setI = $true )
& ( binintersectEL = $true )
& ( emptysetAx = $true )
& ( uniqinunit = $true )
& ( subsetE2 = $true )
& ( dsetconstrI = $true )
& ( setminusEL = $true )
& ( notequalI1 = $true )
& ( omega__Cong = $true )
& ( binintersectSubset3 = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIL = $true )
& ( subsetTrans = $true )
& ( subsetemptysetimpeq = $true )
& ( upairsetIL = $true )
& ( subsetI2 = $true )
& ( exuE1 = $true )
& ( setunionAx = $true )
& ( notsubsetI = $true )
& ( binunionLsub = $true )
& ( setadjoinSub2 = $true )
& ( quantDeMorgan1 = $true )
& ( exuE3u = $true )
& ( powersetAx = $true )
& ( exuI2 = $true )
& ( setadjoinSub = $true )
& ( setadjoinE = $true )
& ( nonemptyI1 = $true )
& ( singletonsswitch = $true )
& ( setunionE = $true )
& ( noeltsimpempty = $true )
& ( binunionEcases = $true )
& ( setunionI = $true )
& ( binintersectER = $true )
& ( sepSubset = $true )
& ( eqimpsubset2 = $true )
& ( upairsetE = $true )
& ( emptyInPowerset = $true )
& ( upairset2IR = $true )
& ( binintersectSubset4 = $true )
& ( disjointsetsI1 = $true )
& ( binintersectSubset5 = $true )
& ( setunion__Cong = $true )
& ( setadjoinOr = $true )
& ( setminusI = $true )
& ( setadjoin__Cong = $true )
& ( inPowerset = $true )
& ( prop2set2propI = $true )
& ( binunionIR = $true )
& ( binintersectRsub = $true )
& ( binunionE = $true )
& ( powersetI1 = $true )
& ( replAx = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( binintersectSubset2 = $true )
& ( exu__Cong = $true )
& ( exuE3e = $true )
& ( eqimpsubset1 = $true )
& ( notdexE = $true )
& ( vacuousDall = $true )
& ( nonemptyI = $true )
& ( setext = $true )
& ( nonemptyImpWitness = $true )
& ( powersetE = $true )
& ( notequalI2 = $true )
& ( setadjoinIR = $true )
& ( omega0Ax = $true )
& ( setextAx = $true )
& ( foundationAx = $true )
& ( emptyI = $true )
& ( dsetconstr__Cong = $true )
& ( setbeta = $true )
& ( subPowSU = $true )
& ( eqinunit = $true )
& ( emptyE1 = $true )
& ( emptysetE = $true )
& ( emptysetimpfalse = $true )
& ( exuEu = $true )
& ( omegaSAx = $true )
& ( powersetI = $true )
& ( bs114d = $true )
& ( dsetconstrEL = $true )
& ( exuI1 = $true )
& ( descrp = $true )
& ( emptyset__Cong = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
& ( wellorderingAx = $true )
& ( nonemptyE1 = $true )
& ( notinsingleton = $true )
& ( exuE2 = $true )
& ( quantDeMorgan4 = $true )
& ( subsetRefl = $true )
& ( emptyinunitempty = $true )
& ( sepInPowerset = $true )
& ( omegaIndAx = $true )
& ( emptysetsubset = $true )
& ( setoftrueEq = $true )
& ( exuI3 = $true )
& ( emptyinPowerset = $true )
& ( binintersectI = $true )
& ( in__Cong = $true )
& ( powerset__Cong = $true )
& ( notdallE = $true )
& ( setadjoinAx = $true ) ),
inference(flattening,[status(thm)],[f367]) ).
thf(f367,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) ) )
& ( setminusEL = $true )
& ( setminusI = $true )
& ( bs114d = $true )
& ( binintersectSubset1 = $true )
& ( binintersectSubset4 = $true )
& ( binintersectRsub = $true )
& ( disjointsetsI1 = $true )
& ( binintersectER = $true )
& ( binintersectSubset3 = $true )
& ( binintersectSubset2 = $true )
& ( binintersectLsub = $true )
& ( binintersectEL = $true )
& ( binintersectSubset5 = $true )
& ( binintersectI = $true )
& ( binunionRsub = $true )
& ( binunionLsub = $true )
& ( binunionE = $true )
& ( binunionEcases = $true )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f366]) ).
thf(f366,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f137]) ).
thf(f137,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ( ( binunionEcases = $true )
=> ( ( binunionE = $true )
=> ( ( binunionLsub = $true )
=> ( ( binunionRsub = $true )
=> ( ( binintersectI = $true )
=> ( ( binintersectSubset5 = $true )
=> ( ( binintersectEL = $true )
=> ( ( binintersectLsub = $true )
=> ( ( binintersectSubset2 = $true )
=> ( ( binintersectSubset3 = $true )
=> ( ( binintersectER = $true )
=> ( ( disjointsetsI1 = $true )
=> ( ( binintersectRsub = $true )
=> ( ( binintersectSubset4 = $true )
=> ( ( binintersectSubset1 = $true )
=> ( ( bs114d = $true )
=> ( ( setminusI = $true )
=> ( ( setminusEL = $true )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ ( setminus @ X1 @ X0 ) ) )
=> ( $true
!= ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f136]) ).
thf(f136,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ ( setminus @ X1 @ X0 ) )
=> ~ ( in @ X2 @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f124]) ).
thf(f124,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ ( setminus @ X3 @ X4 ) )
=> ~ ( in @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f123]) ).
thf(f123,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ( binunionEcases
=> ( binunionE
=> ( binunionLsub
=> ( binunionRsub
=> ( binintersectI
=> ( binintersectSubset5
=> ( binintersectEL
=> ( binintersectLsub
=> ( binintersectSubset2
=> ( binintersectSubset3
=> ( binintersectER
=> ( disjointsetsI1
=> ( binintersectRsub
=> ( binintersectSubset4
=> ( binintersectSubset1
=> ( bs114d
=> ( setminusI
=> ( setminusEL
=> ! [X4: $i,X3: $i,X1: $i] :
( ( in @ X1 @ ( setminus @ X3 @ X4 ) )
=> ~ ( in @ X1 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ji351ajFME/DTF2THF_19448.p',setminusER) ).
thf(f561,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f333]) ).
thf(f333,plain,
( dsetconstrER
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( in @ Y1
@ ( dsetconstr @ Y0
@ ^ [Y3: $i] : ( Y2 @ Y3 ) ) )
=> ( Y2 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f332]) ).
thf(f332,plain,
! [X0: $i > $o,X1: $i,X2: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X2
@ ^ [X3: $i] : ( X0 @ X3 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X0: $i > $o,X1: $i,X3: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.Ji351ajFME/DTF2THF_19448.p',dsetconstrER) ).
thf(f1191,plain,
( $true
= ( in @ sK2
@ ( dsetconstr @ sK1
@ ^ [Y0: $i] :
~ ( in @ Y0 @ sK0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f653]) ).
thf(f653,plain,
( $true
= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) )
@ sK1
@ sK0 ) ) ),
inference(definition_unfolding,[status(thm)],[f439,f571]) ).
thf(f571,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
thf(f203,plain,
( setminus
= ( ^ [Y0: $i,Y1: $i] :
( dsetconstr @ Y0
@ ^ [Y2: $i] :
~ ( in @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f202]) ).
thf(f202,plain,
( setminus
= ( ^ [X0: $i,X1: $i] :
( dsetconstr @ X0
@ ^ [X2: $i] :
~ ( in @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f120]) ).
thf(f120,axiom,
( setminus
= ( ^ [X3: $i,X4: $i] :
( dsetconstr @ X3
@ ^ [X1: $i] :
~ ( in @ X1 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ji351ajFME/DTF2THF_19448.p',setminus) ).
thf(f439,plain,
( $true
= ( in @ sK2 @ ( setminus @ sK1 @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
thf(f440,plain,
( $true
= ( in @ sK2 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f370]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU603^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n001.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:28:50 EST 2026
% 0.16/0.35 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.47 thf(spec,logic,$$dhol).
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 % File : SEU603^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.47 % Domain : Set Theory
% 0.20/0.47 % Problem : Preliminary Notions - Operations on Sets - Set Difference
% 0.20/0.47 % Version : Especial.
% 0.20/0.47 % English : (! A:i.! B:i.! x:i.in x (setminus A B) -> ~(in x B))
% 0.20/0.47
% 0.20/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.47 % Source : [Bro08]
% 0.20/0.47 % Names : ZFC105g [Bro08]
% 0.20/0.47
% 0.20/0.47 % Status : Theorem
% 0.20/0.47 % Rating : 0.33 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.29 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.20/0.47 % Syntax : Number of formulae : 261 ( 122 unt; 138 typ; 122 def)
% 0.20/0.47 % Number of atoms : 647 ( 177 equ; 0 cnn)
% 0.20/0.47 % Maximal formula atoms : 121 ( 5 avg)
% 0.20/0.47 % Number of connectives : 1022 ( 33 ~; 6 |; 28 &; 655 @)
% 0.20/0.47 % ( 14 <=>; 286 =>; 0 <=; 0 <~>)
% 0.20/0.47 % Maximal formula depth : 127 ( 2 avg)
% 0.20/0.47 % Number of types : 2 ( 0 usr)
% 0.20/0.47 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.20/0.47 % Number of symbols : 141 ( 138 usr; 123 con; 0-2 aty)
% 0.20/0.47 % Number of variables : 355 ( 33 ^; 293 !; 29 ?; 355 :)
% 0.20/0.47 % SPC : TH0_THM_EQU_NAR
% 0.20/0.47
% 0.20/0.47 % Comments : http://mathgate.info/detsetitem.php?id=278
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 thf(in_type,type,
% 0.20/0.47 in: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(exu_type,type,
% 0.20/0.47 exu: ( $i > $o ) > $o ).
% 0.20/0.47
% 0.20/0.47 thf(exu,definition,
% 0.20/0.47 ( exu
% 0.20/0.47 = ( ^ [Xphi: $i > $o] :
% 0.20/0.47 ? [Xx: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 & ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setextAx_type,type,
% 0.20/0.47 setextAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setextAx,definition,
% 0.20/0.47 ( setextAx
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 <=> ( in @ Xx @ B ) )
% 0.20/0.47 => ( A = B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyset_type,type,
% 0.20/0.47 emptyset: $i ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetAx_type,type,
% 0.20/0.47 emptysetAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetAx,definition,
% 0.20/0.47 ( emptysetAx
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoin_type,type,
% 0.20/0.47 setadjoin: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinAx_type,type,
% 0.20/0.47 setadjoinAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinAx,definition,
% 0.20/0.47 ( setadjoinAx
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.47 <=> ( ( Xy = Xx )
% 0.20/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powerset_type,type,
% 0.20/0.47 powerset: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(powersetAx_type,type,
% 0.20/0.47 powersetAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetAx,definition,
% 0.20/0.47 ( powersetAx
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.47 <=> ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunion_type,type,
% 0.20/0.47 setunion: $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(setunionAx_type,type,
% 0.20/0.47 setunionAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionAx,definition,
% 0.20/0.47 ( setunionAx
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.47 <=> ? [B: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(omega_type,type,
% 0.20/0.47 omega: $i ).
% 0.20/0.47
% 0.20/0.47 thf(omega0Ax_type,type,
% 0.20/0.47 omega0Ax: $o ).
% 0.20/0.47
% 0.20/0.47 thf(omega0Ax,definition,
% 0.20/0.47 ( omega0Ax
% 0.20/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(omegaSAx_type,type,
% 0.20/0.47 omegaSAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(omegaSAx,definition,
% 0.20/0.47 ( omegaSAx
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ omega )
% 0.20/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(omegaIndAx_type,type,
% 0.20/0.47 omegaIndAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(omegaIndAx,definition,
% 0.20/0.47 ( omegaIndAx
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( ( in @ emptyset @ A )
% 0.20/0.47 & ! [Xx: $i] :
% 0.20/0.47 ( ( ( in @ Xx @ omega )
% 0.20/0.47 & ( in @ Xx @ A ) )
% 0.20/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ omega )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(replAx_type,type,
% 0.20/0.47 replAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(replAx,definition,
% 0.20/0.47 ( replAx
% 0.20/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( exu
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.47 => ? [B: $i] :
% 0.20/0.47 ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 <=> ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(foundationAx_type,type,
% 0.20/0.47 foundationAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(foundationAx,definition,
% 0.20/0.47 ( foundationAx
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.47 => ? [B: $i] :
% 0.20/0.47 ( ( in @ B @ A )
% 0.20/0.47 & ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(wellorderingAx_type,type,
% 0.20/0.47 wellorderingAx: $o ).
% 0.20/0.47
% 0.20/0.47 thf(wellorderingAx,definition,
% 0.20/0.47 ( wellorderingAx
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ? [B: $i] :
% 0.20/0.47 ( ! [C: $i] :
% 0.20/0.47 ( ( in @ C @ B )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ A ) ) )
% 0.20/0.47 & ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( ( in @ Xx @ A )
% 0.20/0.47 & ( in @ Xy @ A ) )
% 0.20/0.47 => ( ! [C: $i] :
% 0.20/0.47 ( ( in @ C @ B )
% 0.20/0.47 => ( ( in @ Xx @ C )
% 0.20/0.47 <=> ( in @ Xy @ C ) ) )
% 0.20/0.47 => ( Xx = Xy ) ) )
% 0.20/0.47 & ! [C: $i,D: $i] :
% 0.20/0.47 ( ( ( in @ C @ B )
% 0.20/0.47 & ( in @ D @ B ) )
% 0.20/0.47 => ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ D ) )
% 0.20/0.47 | ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ D )
% 0.20/0.47 => ( in @ Xx @ C ) ) ) )
% 0.20/0.47 & ! [C: $i] :
% 0.20/0.47 ( ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ C )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.47 => ? [D: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ D @ B )
% 0.20/0.47 & ( in @ Xx @ C )
% 0.20/0.47 & ~ ? [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ D )
% 0.20/0.47 & ( in @ Xy @ C ) )
% 0.20/0.47 & ! [E: $i] :
% 0.20/0.47 ( ( in @ E @ B )
% 0.20/0.47 => ( ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ E )
% 0.20/0.47 => ( in @ Xy @ D ) )
% 0.20/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(descr_type,type,
% 0.20/0.47 descr: ( $i > $o ) > $i ).
% 0.20/0.47
% 0.20/0.47 thf(descrp_type,type,
% 0.20/0.47 descrp: $o ).
% 0.20/0.47
% 0.20/0.47 thf(descrp,definition,
% 0.20/0.47 ( descrp
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ( Xphi
% 0.20/0.47 @ ( descr
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstr_type,type,
% 0.20/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrI_type,type,
% 0.20/0.47 dsetconstrI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrI,definition,
% 0.20/0.47 ( dsetconstrI
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 => ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrEL_type,type,
% 0.20/0.47 dsetconstrEL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrEL,definition,
% 0.20/0.47 ( dsetconstrEL
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrER_type,type,
% 0.20/0.47 dsetconstrER: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstrER,definition,
% 0.20/0.47 ( dsetconstrER
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE1_type,type,
% 0.20/0.47 exuE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE1,definition,
% 0.20/0.47 ( exuE1
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 & ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(prop2set_type,type,
% 0.20/0.47 prop2set: $o > $i ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setE_type,type,
% 0.20/0.47 prop2setE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setE,definition,
% 0.20/0.47 ( prop2setE
% 0.20/0.47 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.47 => Xphi ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetE_type,type,
% 0.20/0.47 emptysetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetE,definition,
% 0.20/0.47 ( emptysetE
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ emptyset )
% 0.20/0.47 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetimpfalse_type,type,
% 0.20/0.47 emptysetimpfalse: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetimpfalse,definition,
% 0.20/0.47 ( emptysetimpfalse
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ emptyset )
% 0.20/0.47 => $false ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notinemptyset_type,type,
% 0.20/0.47 notinemptyset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notinemptyset,definition,
% 0.20/0.47 ( notinemptyset
% 0.20/0.47 = ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3e_type,type,
% 0.20/0.47 exuE3e: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3e,definition,
% 0.20/0.47 ( exuE3e
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setext_type,type,
% 0.20/0.47 setext: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setext,definition,
% 0.20/0.47 ( setext
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) )
% 0.20/0.47 => ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 => ( A = B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyI_type,type,
% 0.20/0.47 emptyI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyI,definition,
% 0.20/0.47 ( emptyI
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ A )
% 0.20/0.47 => ( A = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(noeltsimpempty_type,type,
% 0.20/0.47 noeltsimpempty: $o ).
% 0.20/0.47
% 0.20/0.47 thf(noeltsimpempty,definition,
% 0.20/0.47 ( noeltsimpempty
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ A )
% 0.20/0.47 => ( A = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setbeta_type,type,
% 0.20/0.47 setbeta: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setbeta,definition,
% 0.20/0.47 ( setbeta
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.47 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonempty_type,type,
% 0.20/0.47 nonempty: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonempty,definition,
% 0.20/0.47 ( nonempty
% 0.20/0.47 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyE1_type,type,
% 0.20/0.47 nonemptyE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyE1,definition,
% 0.20/0.47 ( nonemptyE1
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( nonempty @ A )
% 0.20/0.47 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyI_type,type,
% 0.20/0.47 nonemptyI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyI,definition,
% 0.20/0.47 ( nonemptyI
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 => ( nonempty
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyI1_type,type,
% 0.20/0.47 nonemptyI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyI1,definition,
% 0.20/0.47 ( nonemptyI1
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.47 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinIL_type,type,
% 0.20/0.47 setadjoinIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinIL,definition,
% 0.20/0.47 ( setadjoinIL
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyinunitempty_type,type,
% 0.20/0.47 emptyinunitempty: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyinunitempty,definition,
% 0.20/0.47 ( emptyinunitempty
% 0.20/0.47 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinIR_type,type,
% 0.20/0.47 setadjoinIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinIR,definition,
% 0.20/0.47 ( setadjoinIR
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ A )
% 0.20/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinE_type,type,
% 0.20/0.47 setadjoinE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinE,definition,
% 0.20/0.47 ( setadjoinE
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.47 => ! [Xphi: $o] :
% 0.20/0.47 ( ( ( Xy = Xx )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => ( ( ( in @ Xy @ A )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinOr_type,type,
% 0.20/0.47 setadjoinOr: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinOr,definition,
% 0.20/0.47 ( setadjoinOr
% 0.20/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.47 => ( ( Xy = Xx )
% 0.20/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setoftrueEq_type,type,
% 0.20/0.47 setoftrueEq: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setoftrueEq,definition,
% 0.20/0.47 ( setoftrueEq
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : $true )
% 0.20/0.47 = A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI_type,type,
% 0.20/0.47 powersetI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI,definition,
% 0.20/0.47 ( powersetI
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) )
% 0.20/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyinPowerset_type,type,
% 0.20/0.47 emptyinPowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyinPowerset,definition,
% 0.20/0.47 ( emptyinPowerset
% 0.20/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyInPowerset_type,type,
% 0.20/0.47 emptyInPowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyInPowerset,definition,
% 0.20/0.47 ( emptyInPowerset
% 0.20/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetE_type,type,
% 0.20/0.47 powersetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetE,definition,
% 0.20/0.47 ( powersetE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunionI_type,type,
% 0.20/0.47 setunionI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionI,definition,
% 0.20/0.47 ( setunionI
% 0.20/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( ( in @ B @ A )
% 0.20/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunionE_type,type,
% 0.20/0.47 setunionE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunionE,definition,
% 0.20/0.47 ( setunionE
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.47 => ! [Xphi: $o] :
% 0.20/0.47 ( ! [B: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( ( in @ B @ A )
% 0.20/0.47 => Xphi ) )
% 0.20/0.47 => Xphi ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subPowSU_type,type,
% 0.20/0.47 subPowSU: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subPowSU,definition,
% 0.20/0.47 ( subPowSU
% 0.20/0.47 = ( ! [A: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE2_type,type,
% 0.20/0.47 exuE2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE2,definition,
% 0.20/0.47 ( exuE2
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyImpWitness_type,type,
% 0.20/0.47 nonemptyImpWitness: $o ).
% 0.20/0.47
% 0.20/0.47 thf(nonemptyImpWitness,definition,
% 0.20/0.47 ( nonemptyImpWitness
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( nonempty @ A )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & $true ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(uniqinunit_type,type,
% 0.20/0.47 uniqinunit: $o ).
% 0.20/0.47
% 0.20/0.47 thf(uniqinunit,definition,
% 0.20/0.47 ( uniqinunit
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notinsingleton_type,type,
% 0.20/0.47 notinsingleton: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notinsingleton,definition,
% 0.20/0.47 ( notinsingleton
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx != Xy )
% 0.20/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(eqinunit_type,type,
% 0.20/0.47 eqinunit: $o ).
% 0.20/0.47
% 0.20/0.47 thf(eqinunit,definition,
% 0.20/0.47 ( eqinunit
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(singletonsswitch_type,type,
% 0.20/0.47 singletonsswitch: $o ).
% 0.20/0.47
% 0.20/0.47 thf(singletonsswitch,definition,
% 0.20/0.47 ( singletonsswitch
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetE_type,type,
% 0.20/0.47 upairsetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetE,definition,
% 0.20/0.47 ( upairsetE
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.20/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.20/0.47 => ( ( Xz = Xx )
% 0.20/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetIL_type,type,
% 0.20/0.47 upairsetIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetIL,definition,
% 0.20/0.47 ( upairsetIL
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetIR_type,type,
% 0.20/0.47 upairsetIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairsetIR,definition,
% 0.20/0.47 ( upairsetIR
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyE1_type,type,
% 0.20/0.47 emptyE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyE1,definition,
% 0.20/0.47 ( emptyE1
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) )
% 0.20/0.47 => ( ( ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 = emptyset )
% 0.20/0.47 => $false ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(vacuousDall_type,type,
% 0.20/0.47 vacuousDall: $o ).
% 0.20/0.47
% 0.20/0.47 thf(vacuousDall,definition,
% 0.20/0.47 ( vacuousDall
% 0.20/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ emptyset )
% 0.20/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan1_type,type,
% 0.20/0.47 quantDeMorgan1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan1,definition,
% 0.20/0.47 ( quantDeMorgan1
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ~ ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan2_type,type,
% 0.20/0.47 quantDeMorgan2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan2,definition,
% 0.20/0.47 ( quantDeMorgan2
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ~ ( Xphi @ Xx ) )
% 0.20/0.47 => ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan3_type,type,
% 0.20/0.47 quantDeMorgan3: $o ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan3,definition,
% 0.20/0.47 ( quantDeMorgan3
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan4_type,type,
% 0.20/0.47 quantDeMorgan4: $o ).
% 0.20/0.47
% 0.20/0.47 thf(quantDeMorgan4,definition,
% 0.20/0.47 ( quantDeMorgan4
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ~ ( Xphi @ Xx ) )
% 0.20/0.47 => ~ ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setI_type,type,
% 0.20/0.47 prop2setI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2setI,definition,
% 0.20/0.47 ( prop2setI
% 0.20/0.47 = ( ! [Xphi: $o] :
% 0.20/0.47 ( Xphi
% 0.20/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(set2prop_type,type,
% 0.20/0.47 set2prop: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2set2propI_type,type,
% 0.20/0.47 prop2set2propI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(prop2set2propI,definition,
% 0.20/0.47 ( prop2set2propI
% 0.20/0.47 = ( ! [Xphi: $o] :
% 0.20/0.47 ( Xphi
% 0.20/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notdexE_type,type,
% 0.20/0.47 notdexE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notdexE,definition,
% 0.20/0.47 ( notdexE
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( Xphi @ Xx ) )
% 0.20/0.47 => ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notdallE_type,type,
% 0.20/0.47 notdallE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notdallE,definition,
% 0.20/0.47 ( notdallE
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( ~ ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( Xphi @ Xx ) )
% 0.20/0.47 => ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuI1_type,type,
% 0.20/0.47 exuI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuI1,definition,
% 0.20/0.47 ( exuI1
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 & ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) )
% 0.20/0.47 => ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuI3_type,type,
% 0.20/0.47 exuI3: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuI3,definition,
% 0.20/0.47 ( exuI3
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.20/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) )
% 0.20/0.47 => ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuI2_type,type,
% 0.20/0.47 exuI2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuI2,definition,
% 0.20/0.47 ( exuI2
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ? [Xx: $i] :
% 0.20/0.47 ! [Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xy )
% 0.20/0.47 <=> ( Xy = Xx ) )
% 0.20/0.47 => ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(inCongP_type,type,
% 0.20/0.47 inCongP: $o ).
% 0.20/0.47
% 0.20/0.47 thf(inCongP,definition,
% 0.20/0.47 ( inCongP
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(in__Cong_type,type,
% 0.20/0.47 in__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(in__Cong,definition,
% 0.20/0.47 ( in__Cong
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3u_type,type,
% 0.20/0.47 exuE3u: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuE3u,definition,
% 0.20/0.47 ( exuE3u
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exu__Cong_type,type,
% 0.20/0.47 exu__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exu__Cong,definition,
% 0.20/0.47 ( exu__Cong
% 0.20/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.47 => ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 <=> ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptyset__Cong_type,type,
% 0.20/0.47 emptyset__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptyset__Cong,definition,
% 0.20/0.47 ( emptyset__Cong
% 0.20/0.47 = ( emptyset = emptyset ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoin__Cong_type,type,
% 0.20/0.47 setadjoin__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoin__Cong,definition,
% 0.20/0.47 ( setadjoin__Cong
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ! [Xz: $i,Xu: $i] :
% 0.20/0.47 ( ( Xz = Xu )
% 0.20/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.20/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powerset__Cong_type,type,
% 0.20/0.47 powerset__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powerset__Cong,definition,
% 0.20/0.47 ( powerset__Cong
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( ( powerset @ A )
% 0.20/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setunion__Cong_type,type,
% 0.20/0.47 setunion__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setunion__Cong,definition,
% 0.20/0.47 ( setunion__Cong
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( ( setunion @ A )
% 0.20/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(omega__Cong_type,type,
% 0.20/0.47 omega__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(omega__Cong,definition,
% 0.20/0.47 ( omega__Cong
% 0.20/0.47 = ( omega = omega ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(exuEu_type,type,
% 0.20/0.47 exuEu: $o ).
% 0.20/0.47
% 0.20/0.47 thf(exuEu,definition,
% 0.20/0.47 ( exuEu
% 0.20/0.47 = ( ! [Xphi: $i > $o] :
% 0.20/0.47 ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xphi @ Xx )
% 0.20/0.47 => ( ( Xphi @ Xy )
% 0.20/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(descr__Cong_type,type,
% 0.20/0.47 descr__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(descr__Cong,definition,
% 0.20/0.47 ( descr__Cong
% 0.20/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.20/0.47 ( ( Xx = Xy )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.20/0.47 => ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 => ( ( exu
% 0.20/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.20/0.47 => ( ( descr
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 = ( descr
% 0.20/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstr__Cong_type,type,
% 0.20/0.47 dsetconstr__Cong: $o ).
% 0.20/0.47
% 0.20/0.47 thf(dsetconstr__Cong,definition,
% 0.20/0.47 ( dsetconstr__Cong
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ! [Xy: $i] :
% 0.20/0.47 ( ( in @ Xy @ B )
% 0.20/0.47 => ( ( Xx = Xy )
% 0.20/0.47 => ( ( Xphi @ Xx )
% 0.20/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.20/0.47 => ( ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 = ( dsetconstr @ B
% 0.20/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subset_type,type,
% 0.20/0.47 subset: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(disjoint_type,type,
% 0.20/0.47 disjoint: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(setsmeet_type,type,
% 0.20/0.47 setsmeet: $i > $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetI1_type,type,
% 0.20/0.47 subsetI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetI1,definition,
% 0.20/0.47 ( subsetI1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(eqimpsubset2_type,type,
% 0.20/0.47 eqimpsubset2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(eqimpsubset2,definition,
% 0.20/0.47 ( eqimpsubset2
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(eqimpsubset1_type,type,
% 0.20/0.47 eqimpsubset1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(eqimpsubset1,definition,
% 0.20/0.47 ( eqimpsubset1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( A = B )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetI2_type,type,
% 0.20/0.47 subsetI2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetI2,definition,
% 0.20/0.47 ( subsetI2
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ! [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetsubset_type,type,
% 0.20/0.47 emptysetsubset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(emptysetsubset,definition,
% 0.20/0.47 ( emptysetsubset
% 0.20/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE_type,type,
% 0.20/0.47 subsetE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE,definition,
% 0.20/0.47 ( subsetE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE2_type,type,
% 0.20/0.47 subsetE2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetE2,definition,
% 0.20/0.47 ( subsetE2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notsubsetI_type,type,
% 0.20/0.47 notsubsetI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notsubsetI,definition,
% 0.20/0.47 ( notsubsetI
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notequalI1_type,type,
% 0.20/0.47 notequalI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notequalI1,definition,
% 0.20/0.47 ( notequalI1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ~ ( subset @ A @ B )
% 0.20/0.47 => ( A != B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(notequalI2_type,type,
% 0.20/0.47 notequalI2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(notequalI2,definition,
% 0.20/0.47 ( notequalI2
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ( A != B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetRefl_type,type,
% 0.20/0.47 subsetRefl: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetRefl,definition,
% 0.20/0.47 ( subsetRefl
% 0.20/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetTrans_type,type,
% 0.20/0.47 subsetTrans: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetTrans,definition,
% 0.20/0.47 ( subsetTrans
% 0.20/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( subset @ B @ C )
% 0.20/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinSub_type,type,
% 0.20/0.47 setadjoinSub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinSub,definition,
% 0.20/0.47 ( setadjoinSub
% 0.20/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinSub2_type,type,
% 0.20/0.47 setadjoinSub2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setadjoinSub2,definition,
% 0.20/0.47 ( setadjoinSub2
% 0.20/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subset2powerset_type,type,
% 0.20/0.47 subset2powerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subset2powerset,definition,
% 0.20/0.47 ( subset2powerset
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setextsub_type,type,
% 0.20/0.47 setextsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setextsub,definition,
% 0.20/0.47 ( setextsub
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( subset @ B @ A )
% 0.20/0.47 => ( A = B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(subsetemptysetimpeq_type,type,
% 0.20/0.47 subsetemptysetimpeq: $o ).
% 0.20/0.47
% 0.20/0.47 thf(subsetemptysetimpeq,definition,
% 0.20/0.47 ( subsetemptysetimpeq
% 0.20/0.47 = ( ! [A: $i] :
% 0.20/0.47 ( ( subset @ A @ emptyset )
% 0.20/0.47 => ( A = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI1_type,type,
% 0.20/0.47 powersetI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetI1,definition,
% 0.20/0.47 ( powersetI1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ B @ A )
% 0.20/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetE1_type,type,
% 0.20/0.47 powersetE1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetE1,definition,
% 0.20/0.47 ( powersetE1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(inPowerset_type,type,
% 0.20/0.47 inPowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(inPowerset,definition,
% 0.20/0.47 ( inPowerset
% 0.20/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(powersetsubset_type,type,
% 0.20/0.47 powersetsubset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(powersetsubset,definition,
% 0.20/0.47 ( powersetsubset
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sepInPowerset_type,type,
% 0.20/0.47 sepInPowerset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(sepInPowerset,definition,
% 0.20/0.47 ( sepInPowerset
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( in
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(sepSubset_type,type,
% 0.20/0.47 sepSubset: $o ).
% 0.20/0.47
% 0.20/0.47 thf(sepSubset,definition,
% 0.20/0.47 ( sepSubset
% 0.20/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.20/0.47 ( subset
% 0.20/0.47 @ ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.47 @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunion_type,type,
% 0.20/0.47 binunion: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(binunionIL_type,type,
% 0.20/0.47 binunionIL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionIL,definition,
% 0.20/0.47 ( binunionIL
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(upairset2IR_type,type,
% 0.20/0.47 upairset2IR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(upairset2IR,definition,
% 0.20/0.47 ( upairset2IR
% 0.20/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionIR_type,type,
% 0.20/0.47 binunionIR: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionIR,definition,
% 0.20/0.47 ( binunionIR
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionEcases_type,type,
% 0.20/0.47 binunionEcases: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionEcases,definition,
% 0.20/0.47 ( binunionEcases
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.20/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.47 => ( ( ( in @ Xx @ A )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => ( ( ( in @ Xx @ B )
% 0.20/0.47 => Xphi )
% 0.20/0.47 => Xphi ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionE_type,type,
% 0.20/0.47 binunionE: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionE,definition,
% 0.20/0.47 ( binunionE
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.20/0.47 => ( ( in @ Xx @ A )
% 0.20/0.47 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionLsub_type,type,
% 0.20/0.47 binunionLsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionLsub,definition,
% 0.20/0.47 ( binunionLsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binunionRsub_type,type,
% 0.20/0.47 binunionRsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binunionRsub,definition,
% 0.20/0.47 ( binunionRsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersect_type,type,
% 0.20/0.47 binintersect: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectI_type,type,
% 0.20/0.47 binintersectI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectI,definition,
% 0.20/0.47 ( binintersectI
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset5_type,type,
% 0.20/0.47 binintersectSubset5: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset5,definition,
% 0.20/0.47 ( binintersectSubset5
% 0.20/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.47 ( ( subset @ C @ A )
% 0.20/0.47 => ( ( subset @ C @ B )
% 0.20/0.47 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectEL_type,type,
% 0.20/0.47 binintersectEL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectEL,definition,
% 0.20/0.47 ( binintersectEL
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectLsub_type,type,
% 0.20/0.47 binintersectLsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectLsub,definition,
% 0.20/0.47 ( binintersectLsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset2_type,type,
% 0.20/0.47 binintersectSubset2: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset2,definition,
% 0.20/0.47 ( binintersectSubset2
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ A @ B )
% 0.20/0.47 => ( ( binintersect @ A @ B )
% 0.20/0.47 = A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset3_type,type,
% 0.20/0.47 binintersectSubset3: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset3,definition,
% 0.20/0.47 ( binintersectSubset3
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( ( binintersect @ A @ B )
% 0.20/0.47 = B )
% 0.20/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectER_type,type,
% 0.20/0.47 binintersectER: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectER,definition,
% 0.20/0.47 ( binintersectER
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.20/0.47 => ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(disjointsetsI1_type,type,
% 0.20/0.47 disjointsetsI1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(disjointsetsI1,definition,
% 0.20/0.47 ( disjointsetsI1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ~ ? [Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 & ( in @ Xx @ B ) )
% 0.20/0.47 => ( ( binintersect @ A @ B )
% 0.20/0.47 = emptyset ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectRsub_type,type,
% 0.20/0.47 binintersectRsub: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectRsub,definition,
% 0.20/0.47 ( binintersectRsub
% 0.20/0.47 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset4_type,type,
% 0.20/0.47 binintersectSubset4: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset4,definition,
% 0.20/0.47 ( binintersectSubset4
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( subset @ B @ A )
% 0.20/0.47 => ( ( binintersect @ A @ B )
% 0.20/0.47 = B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset1_type,type,
% 0.20/0.47 binintersectSubset1: $o ).
% 0.20/0.47
% 0.20/0.47 thf(binintersectSubset1,definition,
% 0.20/0.47 ( binintersectSubset1
% 0.20/0.47 = ( ! [A: $i,B: $i] :
% 0.20/0.47 ( ( ( binintersect @ A @ B )
% 0.20/0.47 = A )
% 0.20/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(bs114d_type,type,
% 0.20/0.47 bs114d: $o ).
% 0.20/0.47
% 0.20/0.47 thf(bs114d,definition,
% 0.20/0.47 ( bs114d
% 0.20/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.20/0.47 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.20/0.47 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(regular_type,type,
% 0.20/0.47 regular: $i > $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminus_type,type,
% 0.20/0.47 setminus: $i > $i > $i ).
% 0.20/0.47
% 0.20/0.47 thf(setminus,definition,
% 0.20/0.47 ( setminus
% 0.20/0.47 = ( ^ [A: $i,B: $i] :
% 0.20/0.47 ( dsetconstr @ A
% 0.20/0.47 @ ^ [Xx: $i] :
% 0.20/0.47 ~ ( in @ Xx @ B ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusI_type,type,
% 0.20/0.47 setminusI: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusI,definition,
% 0.20/0.47 ( setminusI
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ A )
% 0.20/0.47 => ( ~ ( in @ Xx @ B )
% 0.20/0.47 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusEL_type,type,
% 0.20/0.47 setminusEL: $o ).
% 0.20/0.47
% 0.20/0.47 thf(setminusEL,definition,
% 0.20/0.47 ( setminusEL
% 0.20/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 thf(setminusER,conjecture,
% 0.20/0.47 ( setextAx
% 0.20/0.47 => ( emptysetAx
% 0.20/0.47 => ( setadjoinAx
% 0.20/0.47 => ( powersetAx
% 0.20/0.47 => ( setunionAx
% 0.20/0.47 => ( omega0Ax
% 0.20/0.47 => ( omegaSAx
% 0.20/0.47 => ( omegaIndAx
% 0.20/0.47 => ( replAx
% 0.20/0.47 => ( foundationAx
% 0.20/0.47 => ( wellorderingAx
% 0.20/0.47 => ( descrp
% 0.20/0.47 => ( dsetconstrI
% 0.20/0.47 => ( dsetconstrEL
% 0.20/0.47 => ( dsetconstrER
% 0.20/0.47 => ( exuE1
% 0.20/0.47 => ( prop2setE
% 0.20/0.47 => ( emptysetE
% 0.20/0.47 => ( emptysetimpfalse
% 0.20/0.47 => ( notinemptyset
% 0.20/0.47 => ( exuE3e
% 0.20/0.47 => ( setext
% 0.20/0.47 => ( emptyI
% 0.20/0.47 => ( noeltsimpempty
% 0.20/0.47 => ( setbeta
% 0.20/0.47 => ( nonemptyE1
% 0.20/0.47 => ( nonemptyI
% 0.20/0.47 => ( nonemptyI1
% 0.20/0.47 => ( setadjoinIL
% 0.20/0.47 => ( emptyinunitempty
% 0.20/0.47 => ( setadjoinIR
% 0.20/0.47 => ( setadjoinE
% 0.20/0.47 => ( setadjoinOr
% 0.20/0.47 => ( setoftrueEq
% 0.20/0.47 => ( powersetI
% 0.20/0.47 => ( emptyinPowerset
% 0.20/0.47 => ( emptyInPowerset
% 0.20/0.47 => ( powersetE
% 0.20/0.47 => ( setunionI
% 0.20/0.47 => ( setunionE
% 0.20/0.47 => ( subPowSU
% 0.20/0.47 => ( exuE2
% 0.20/0.47 => ( nonemptyImpWitness
% 0.20/0.47 => ( uniqinunit
% 0.20/0.47 => ( notinsingleton
% 0.20/0.47 => ( eqinunit
% 0.20/0.47 => ( singletonsswitch
% 0.20/0.47 => ( upairsetE
% 0.20/0.47 => ( upairsetIL
% 0.20/0.47 => ( upairsetIR
% 0.20/0.47 => ( emptyE1
% 0.20/0.47 => ( vacuousDall
% 0.20/0.47 => ( quantDeMorgan1
% 0.20/0.47 => ( quantDeMorgan2
% 0.20/0.47 => ( quantDeMorgan3
% 0.20/0.47 => ( quantDeMorgan4
% 0.20/0.47 => ( prop2setI
% 0.20/0.47 => ( prop2set2propI
% 0.20/0.47 => ( notdexE
% 0.20/0.47 => ( notdallE
% 0.20/0.47 => ( exuI1
% 0.20/0.47 => ( exuI3
% 0.20/0.47 => ( exuI2
% 0.20/0.47 => ( inCongP
% 0.20/0.47 => ( in__Cong
% 0.20/0.47 => ( exuE3u
% 0.20/0.47 => ( exu__Cong
% 0.20/0.47 => ( emptyset__Cong
% 0.20/0.47 => ( setadjoin__Cong
% 0.20/0.47 => ( powerset__Cong
% 0.20/0.47 => ( setunion__Cong
% 0.20/0.47 => ( omega__Cong
% 0.20/0.47 => ( exuEu
% 0.20/0.47 => ( descr__Cong
% 0.20/0.47 => ( dsetconstr__Cong
% 0.20/0.47 => ( subsetI1
% 0.20/0.47 => ( eqimpsubset2
% 0.20/0.47 => ( eqimpsubset1
% 0.20/0.47 => ( subsetI2
% 0.20/0.47 => ( emptysetsubset
% 0.20/0.47 => ( subsetE
% 0.20/0.47 => ( subsetE2
% 0.20/0.47 => ( notsubsetI
% 0.20/0.47 => ( notequalI1
% 0.20/0.47 => ( notequalI2
% 0.20/0.47 => ( subsetRefl
% 0.20/0.47 => ( subsetTrans
% 0.20/0.47 => ( setadjoinSub
% 0.20/0.47 => ( setadjoinSub2
% 0.20/0.47 => ( subset2powerset
% 0.20/0.47 => ( setextsub
% 0.20/0.47 => ( subsetemptysetimpeq
% 0.20/0.47 => ( powersetI1
% 0.20/0.47 => ( powersetE1
% 0.20/0.47 => ( inPowerset
% 0.20/0.47 => ( powersetsubset
% 0.20/0.47 => ( sepInPowerset
% 0.20/0.47 => ( sepSubset
% 0.20/0.47 => ( binunionIL
% 0.20/0.47 => ( upairset2IR
% 0.20/0.47 => ( binunionIR
% 0.20/0.47 => ( binunionEcases
% 0.20/0.47 => ( binunionE
% 0.20/0.47 => ( binunionLsub
% 0.20/0.47 => ( binunionRsub
% 0.20/0.47 => ( binintersectI
% 0.20/0.47 => ( binintersectSubset5
% 0.20/0.47 => ( binintersectEL
% 0.20/0.47 => ( binintersectLsub
% 0.20/0.47 => ( binintersectSubset2
% 0.20/0.47 => ( binintersectSubset3
% 0.20/0.47 => ( binintersectER
% 0.20/0.47 => ( disjointsetsI1
% 0.20/0.47 => ( binintersectRsub
% 0.20/0.47 => ( binintersectSubset4
% 0.20/0.47 => ( binintersectSubset1
% 0.20/0.47 => ( bs114d
% 0.20/0.47 => ( setminusI
% 0.20/0.47 => ( setminusEL
% 0.20/0.47 => ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.47 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.20/0.47 => ~ ( in @ Xx @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.47
% 0.20/0.47 %------------------------------------------------------------------------------
% 0.20/0.47 ------------------------
% 0.31/1.40 ---- Embedded in THF ---
% 0.31/1.40 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.40 %%% Generated on Tue Feb 24 12:28:51 EST 2026
% 0.31/1.40 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.40 %%% Logic specification used:
% 0.31/1.40 %%% thf(spec, logic, $$dhol).
% 0.31/1.40
% 0.31/1.40 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ji351ajFME/DTF2DTF19448.p
% See solution above
% 0.31/1.40 ------------------------
% 0.31/1.42 ---- Cleaned THF ---
% 0.31/1.42 thf(in_type,type,
% 0.31/1.42 in: $i > $i > $o ).
% 0.31/1.42
% 0.31/1.42 thf(exu_type,type,
% 0.31/1.42 exu: ( $i > $o ) > $o ).
% 0.31/1.42
% 0.31/1.42 thf(exu,definition,
% 0.31/1.42 ( exu
% 0.31/1.42 = ( ^ [Xphi: $i > $o] :
% 0.31/1.42 ? [Xx: $i] :
% 0.31/1.42 ( ( Xphi @ Xx )
% 0.31/1.42 & ! [Xy: $i] :
% 0.31/1.42 ( ( Xphi @ Xy )
% 0.31/1.42 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setextAx_type,type,
% 0.31/1.42 setextAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setextAx,definition,
% 0.31/1.42 ( setextAx
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 <=> ( in @ Xx @ B ) )
% 0.31/1.42 => ( A = B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptyset_type,type,
% 0.31/1.42 emptyset: $i ).
% 0.31/1.42
% 0.31/1.42 thf(emptysetAx_type,type,
% 0.31/1.42 emptysetAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptysetAx,definition,
% 0.31/1.42 ( emptysetAx
% 0.31/1.42 = ( ! [Xx: $i] :
% 0.31/1.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoin_type,type,
% 0.31/1.42 setadjoin: $i > $i > $i ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinAx_type,type,
% 0.31/1.42 setadjoinAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinAx,definition,
% 0.31/1.42 ( setadjoinAx
% 0.31/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/1.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/1.42 <=> ( ( Xy = Xx )
% 0.31/1.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(powerset_type,type,
% 0.31/1.42 powerset: $i > $i ).
% 0.31/1.42
% 0.31/1.42 thf(powersetAx_type,type,
% 0.31/1.42 powersetAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(powersetAx,definition,
% 0.31/1.42 ( powersetAx
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( in @ B @ ( powerset @ A ) )
% 0.31/1.42 <=> ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setunion_type,type,
% 0.31/1.42 setunion: $i > $i ).
% 0.31/1.42
% 0.31/1.42 thf(setunionAx_type,type,
% 0.31/1.42 setunionAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setunionAx,definition,
% 0.31/1.42 ( setunionAx
% 0.31/1.42 = ( ! [A: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/1.42 <=> ? [B: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(omega_type,type,
% 0.31/1.42 omega: $i ).
% 0.31/1.42
% 0.31/1.42 thf(omega0Ax_type,type,
% 0.31/1.42 omega0Ax: $o ).
% 0.31/1.42
% 0.31/1.42 thf(omega0Ax,definition,
% 0.31/1.42 ( omega0Ax
% 0.31/1.42 = ( in @ emptyset @ omega ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(omegaSAx_type,type,
% 0.31/1.42 omegaSAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(omegaSAx,definition,
% 0.31/1.42 ( omegaSAx
% 0.31/1.42 = ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ omega )
% 0.31/1.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(omegaIndAx_type,type,
% 0.31/1.42 omegaIndAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(omegaIndAx,definition,
% 0.31/1.42 ( omegaIndAx
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ( ( in @ emptyset @ A )
% 0.31/1.42 & ! [Xx: $i] :
% 0.31/1.42 ( ( ( in @ Xx @ omega )
% 0.31/1.42 & ( in @ Xx @ A ) )
% 0.31/1.42 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/1.42 => ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ omega )
% 0.31/1.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(replAx_type,type,
% 0.31/1.42 replAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(replAx,definition,
% 0.31/1.42 ( replAx
% 0.31/1.42 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( exu
% 0.31/1.42 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/1.42 => ? [B: $i] :
% 0.31/1.42 ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 <=> ? [Xy: $i] :
% 0.31/1.42 ( ( in @ Xy @ A )
% 0.31/1.42 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(foundationAx_type,type,
% 0.31/1.42 foundationAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(foundationAx,definition,
% 0.31/1.42 ( foundationAx
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/1.42 => ? [B: $i] :
% 0.31/1.42 ( ( in @ B @ A )
% 0.31/1.42 & ~ ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(wellorderingAx_type,type,
% 0.31/1.42 wellorderingAx: $o ).
% 0.31/1.42
% 0.31/1.42 thf(wellorderingAx,definition,
% 0.31/1.42 ( wellorderingAx
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ? [B: $i] :
% 0.31/1.42 ( ! [C: $i] :
% 0.31/1.42 ( ( in @ C @ B )
% 0.31/1.42 => ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ C )
% 0.31/1.42 => ( in @ Xx @ A ) ) )
% 0.31/1.42 & ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( ( in @ Xx @ A )
% 0.31/1.42 & ( in @ Xy @ A ) )
% 0.31/1.42 => ( ! [C: $i] :
% 0.31/1.42 ( ( in @ C @ B )
% 0.31/1.42 => ( ( in @ Xx @ C )
% 0.31/1.42 <=> ( in @ Xy @ C ) ) )
% 0.31/1.42 => ( Xx = Xy ) ) )
% 0.31/1.42 & ! [C: $i,D: $i] :
% 0.31/1.42 ( ( ( in @ C @ B )
% 0.31/1.42 & ( in @ D @ B ) )
% 0.31/1.42 => ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ C )
% 0.31/1.42 => ( in @ Xx @ D ) )
% 0.31/1.42 | ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ D )
% 0.31/1.42 => ( in @ Xx @ C ) ) ) )
% 0.31/1.42 & ! [C: $i] :
% 0.31/1.42 ( ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ C )
% 0.31/1.42 => ( in @ Xx @ A ) )
% 0.31/1.42 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/1.42 => ? [D: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ D @ B )
% 0.31/1.42 & ( in @ Xx @ C )
% 0.31/1.42 & ~ ? [Xy: $i] :
% 0.31/1.42 ( ( in @ Xy @ D )
% 0.31/1.42 & ( in @ Xy @ C ) )
% 0.31/1.42 & ! [E: $i] :
% 0.31/1.42 ( ( in @ E @ B )
% 0.31/1.42 => ( ! [Xy: $i] :
% 0.31/1.42 ( ( in @ Xy @ E )
% 0.31/1.42 => ( in @ Xy @ D ) )
% 0.31/1.42 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(descr_type,type,
% 0.31/1.42 descr: ( $i > $o ) > $i ).
% 0.31/1.42
% 0.31/1.42 thf(descrp_type,type,
% 0.31/1.42 descrp: $o ).
% 0.31/1.42
% 0.31/1.42 thf(descrp,definition,
% 0.31/1.42 ( descrp
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 => ( Xphi
% 0.31/1.42 @ ( descr
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstr_type,type,
% 0.31/1.42 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstrI_type,type,
% 0.31/1.42 dsetconstrI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstrI,definition,
% 0.31/1.42 ( dsetconstrI
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( ( Xphi @ Xx )
% 0.31/1.42 => ( in @ Xx
% 0.31/1.42 @ ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstrEL_type,type,
% 0.31/1.42 dsetconstrEL: $o ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstrEL,definition,
% 0.31/1.42 ( dsetconstrEL
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx
% 0.31/1.42 @ ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/1.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstrER_type,type,
% 0.31/1.42 dsetconstrER: $o ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstrER,definition,
% 0.31/1.42 ( dsetconstrER
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx
% 0.31/1.42 @ ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/1.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exuE1_type,type,
% 0.31/1.42 exuE1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exuE1,definition,
% 0.31/1.42 ( exuE1
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 => ? [Xx: $i] :
% 0.31/1.42 ( ( Xphi @ Xx )
% 0.31/1.42 & ! [Xy: $i] :
% 0.31/1.42 ( ( Xphi @ Xy )
% 0.31/1.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(prop2set_type,type,
% 0.31/1.42 prop2set: $o > $i ).
% 0.31/1.42
% 0.31/1.42 thf(prop2setE_type,type,
% 0.31/1.42 prop2setE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(prop2setE,definition,
% 0.31/1.42 ( prop2setE
% 0.31/1.42 = ( ! [Xphi: $o,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.31/1.42 => Xphi ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptysetE_type,type,
% 0.31/1.42 emptysetE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptysetE,definition,
% 0.31/1.42 ( emptysetE
% 0.31/1.42 = ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ emptyset )
% 0.31/1.42 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptysetimpfalse_type,type,
% 0.31/1.42 emptysetimpfalse: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptysetimpfalse,definition,
% 0.31/1.42 ( emptysetimpfalse
% 0.31/1.42 = ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ emptyset )
% 0.31/1.42 => $false ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(notinemptyset_type,type,
% 0.31/1.42 notinemptyset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(notinemptyset,definition,
% 0.31/1.42 ( notinemptyset
% 0.31/1.42 = ( ! [Xx: $i] :
% 0.31/1.42 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exuE3e_type,type,
% 0.31/1.42 exuE3e: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exuE3e,definition,
% 0.31/1.42 ( exuE3e
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setext_type,type,
% 0.31/1.42 setext: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setext,definition,
% 0.31/1.42 ( setext
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( in @ Xx @ B ) )
% 0.31/1.42 => ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 => ( in @ Xx @ A ) )
% 0.31/1.42 => ( A = B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptyI_type,type,
% 0.31/1.42 emptyI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptyI,definition,
% 0.31/1.42 ( emptyI
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ~ ( in @ Xx @ A )
% 0.31/1.42 => ( A = emptyset ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(noeltsimpempty_type,type,
% 0.31/1.42 noeltsimpempty: $o ).
% 0.31/1.42
% 0.31/1.42 thf(noeltsimpempty,definition,
% 0.31/1.42 ( noeltsimpempty
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ~ ( in @ Xx @ A )
% 0.31/1.42 => ( A = emptyset ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setbeta_type,type,
% 0.31/1.42 setbeta: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setbeta,definition,
% 0.31/1.42 ( setbeta
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( ( in @ Xx
% 0.31/1.42 @ ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/1.42 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(nonempty_type,type,
% 0.31/1.42 nonempty: $i > $o ).
% 0.31/1.42
% 0.31/1.42 thf(nonempty,definition,
% 0.31/1.42 ( nonempty
% 0.31/1.42 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(nonemptyE1_type,type,
% 0.31/1.42 nonemptyE1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(nonemptyE1,definition,
% 0.31/1.42 ( nonemptyE1
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ( nonempty @ A )
% 0.31/1.42 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(nonemptyI_type,type,
% 0.31/1.42 nonemptyI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(nonemptyI,definition,
% 0.31/1.42 ( nonemptyI
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( ( Xphi @ Xx )
% 0.31/1.42 => ( nonempty
% 0.31/1.42 @ ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(nonemptyI1_type,type,
% 0.31/1.42 nonemptyI1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(nonemptyI1,definition,
% 0.31/1.42 ( nonemptyI1
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/1.42 => ( nonempty @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinIL_type,type,
% 0.31/1.42 setadjoinIL: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinIL,definition,
% 0.31/1.42 ( setadjoinIL
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptyinunitempty_type,type,
% 0.31/1.42 emptyinunitempty: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptyinunitempty,definition,
% 0.31/1.42 ( emptyinunitempty
% 0.31/1.42 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinIR_type,type,
% 0.31/1.42 setadjoinIR: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinIR,definition,
% 0.31/1.42 ( setadjoinIR
% 0.31/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/1.42 ( ( in @ Xy @ A )
% 0.31/1.42 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinE_type,type,
% 0.31/1.42 setadjoinE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinE,definition,
% 0.31/1.42 ( setadjoinE
% 0.31/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/1.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/1.42 => ! [Xphi: $o] :
% 0.31/1.42 ( ( ( Xy = Xx )
% 0.31/1.42 => Xphi )
% 0.31/1.42 => ( ( ( in @ Xy @ A )
% 0.31/1.42 => Xphi )
% 0.31/1.42 => Xphi ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinOr_type,type,
% 0.31/1.42 setadjoinOr: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinOr,definition,
% 0.31/1.42 ( setadjoinOr
% 0.31/1.42 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/1.42 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/1.42 => ( ( Xy = Xx )
% 0.31/1.42 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setoftrueEq_type,type,
% 0.31/1.42 setoftrueEq: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setoftrueEq,definition,
% 0.31/1.42 ( setoftrueEq
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xx: $i] : $true )
% 0.31/1.42 = A ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(powersetI_type,type,
% 0.31/1.42 powersetI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(powersetI,definition,
% 0.31/1.42 ( powersetI
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 => ( in @ Xx @ A ) )
% 0.31/1.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptyinPowerset_type,type,
% 0.31/1.42 emptyinPowerset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptyinPowerset,definition,
% 0.31/1.42 ( emptyinPowerset
% 0.31/1.42 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptyInPowerset_type,type,
% 0.31/1.42 emptyInPowerset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptyInPowerset,definition,
% 0.31/1.42 ( emptyInPowerset
% 0.31/1.42 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(powersetE_type,type,
% 0.31/1.42 powersetE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(powersetE,definition,
% 0.31/1.42 ( powersetE
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ B @ ( powerset @ A ) )
% 0.31/1.42 => ( ( in @ Xx @ B )
% 0.31/1.42 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setunionI_type,type,
% 0.31/1.42 setunionI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setunionI,definition,
% 0.31/1.42 ( setunionI
% 0.31/1.42 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 => ( ( in @ B @ A )
% 0.31/1.42 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setunionE_type,type,
% 0.31/1.42 setunionE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setunionE,definition,
% 0.31/1.42 ( setunionE
% 0.31/1.42 = ( ! [A: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/1.42 => ! [Xphi: $o] :
% 0.31/1.42 ( ! [B: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 => ( ( in @ B @ A )
% 0.31/1.42 => Xphi ) )
% 0.31/1.42 => Xphi ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subPowSU_type,type,
% 0.31/1.42 subPowSU: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subPowSU,definition,
% 0.31/1.42 ( subPowSU
% 0.31/1.42 = ( ! [A: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exuE2_type,type,
% 0.31/1.42 exuE2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exuE2,definition,
% 0.31/1.42 ( exuE2
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 => ? [Xx: $i] :
% 0.31/1.42 ! [Xy: $i] :
% 0.31/1.42 ( ( Xphi @ Xy )
% 0.31/1.42 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(nonemptyImpWitness_type,type,
% 0.31/1.42 nonemptyImpWitness: $o ).
% 0.31/1.42
% 0.31/1.42 thf(nonemptyImpWitness,definition,
% 0.31/1.42 ( nonemptyImpWitness
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ( nonempty @ A )
% 0.31/1.42 => ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & $true ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(uniqinunit_type,type,
% 0.31/1.42 uniqinunit: $o ).
% 0.31/1.42
% 0.31/1.42 thf(uniqinunit,definition,
% 0.31/1.42 ( uniqinunit
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/1.42 => ( Xx = Xy ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(notinsingleton_type,type,
% 0.31/1.42 notinsingleton: $o ).
% 0.31/1.42
% 0.31/1.42 thf(notinsingleton,definition,
% 0.31/1.42 ( notinsingleton
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xx != Xy )
% 0.31/1.42 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(eqinunit_type,type,
% 0.31/1.42 eqinunit: $o ).
% 0.31/1.42
% 0.31/1.42 thf(eqinunit,definition,
% 0.31/1.42 ( eqinunit
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xx = Xy )
% 0.31/1.42 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(singletonsswitch_type,type,
% 0.31/1.42 singletonsswitch: $o ).
% 0.31/1.42
% 0.31/1.42 thf(singletonsswitch,definition,
% 0.31/1.42 ( singletonsswitch
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.31/1.42 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(upairsetE_type,type,
% 0.31/1.42 upairsetE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(upairsetE,definition,
% 0.31/1.42 ( upairsetE
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.31/1.42 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.31/1.42 => ( ( Xz = Xx )
% 0.31/1.42 | ( Xz = Xy ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(upairsetIL_type,type,
% 0.31/1.42 upairsetIL: $o ).
% 0.31/1.42
% 0.31/1.42 thf(upairsetIL,definition,
% 0.31/1.42 ( upairsetIL
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(upairsetIR_type,type,
% 0.31/1.42 upairsetIR: $o ).
% 0.31/1.42
% 0.31/1.42 thf(upairsetIR,definition,
% 0.31/1.42 ( upairsetIR
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptyE1_type,type,
% 0.31/1.42 emptyE1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptyE1,definition,
% 0.31/1.42 ( emptyE1
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & ( Xphi @ Xx ) )
% 0.31/1.42 => ( ( ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 = emptyset )
% 0.31/1.42 => $false ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(vacuousDall_type,type,
% 0.31/1.42 vacuousDall: $o ).
% 0.31/1.42
% 0.31/1.42 thf(vacuousDall,definition,
% 0.31/1.42 ( vacuousDall
% 0.31/1.42 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ emptyset )
% 0.31/1.42 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(quantDeMorgan1_type,type,
% 0.31/1.42 quantDeMorgan1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(quantDeMorgan1,definition,
% 0.31/1.42 ( quantDeMorgan1
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( ~ ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( Xphi @ Xx ) )
% 0.31/1.42 => ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(quantDeMorgan2_type,type,
% 0.31/1.42 quantDeMorgan2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(quantDeMorgan2,definition,
% 0.31/1.42 ( quantDeMorgan2
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ~ ( Xphi @ Xx ) )
% 0.31/1.42 => ~ ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(quantDeMorgan3_type,type,
% 0.31/1.42 quantDeMorgan3: $o ).
% 0.31/1.42
% 0.31/1.42 thf(quantDeMorgan3,definition,
% 0.31/1.42 ( quantDeMorgan3
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( ~ ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & ( Xphi @ Xx ) )
% 0.31/1.42 => ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(quantDeMorgan4_type,type,
% 0.31/1.42 quantDeMorgan4: $o ).
% 0.31/1.42
% 0.31/1.42 thf(quantDeMorgan4,definition,
% 0.31/1.42 ( quantDeMorgan4
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & ~ ( Xphi @ Xx ) )
% 0.31/1.42 => ~ ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(prop2setI_type,type,
% 0.31/1.42 prop2setI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(prop2setI,definition,
% 0.31/1.42 ( prop2setI
% 0.31/1.42 = ( ! [Xphi: $o] :
% 0.31/1.42 ( Xphi
% 0.31/1.42 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(set2prop_type,type,
% 0.31/1.42 set2prop: $i > $o ).
% 0.31/1.42
% 0.31/1.42 thf(prop2set2propI_type,type,
% 0.31/1.42 prop2set2propI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(prop2set2propI,definition,
% 0.31/1.42 ( prop2set2propI
% 0.31/1.42 = ( ! [Xphi: $o] :
% 0.31/1.42 ( Xphi
% 0.31/1.42 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(notdexE_type,type,
% 0.31/1.42 notdexE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(notdexE,definition,
% 0.31/1.42 ( notdexE
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( ~ ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & ( Xphi @ Xx ) )
% 0.31/1.42 => ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(notdallE_type,type,
% 0.31/1.42 notdallE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(notdallE,definition,
% 0.31/1.42 ( notdallE
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( ~ ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( Xphi @ Xx ) )
% 0.31/1.42 => ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exuI1_type,type,
% 0.31/1.42 exuI1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exuI1,definition,
% 0.31/1.42 ( exuI1
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ? [Xx: $i] :
% 0.31/1.42 ( ( Xphi @ Xx )
% 0.31/1.42 & ! [Xy: $i] :
% 0.31/1.42 ( ( Xphi @ Xy )
% 0.31/1.42 => ( Xx = Xy ) ) )
% 0.31/1.42 => ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exuI3_type,type,
% 0.31/1.42 exuI3: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exuI3,definition,
% 0.31/1.42 ( exuI3
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.31/1.42 => ( ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xphi @ Xx )
% 0.31/1.42 => ( ( Xphi @ Xy )
% 0.31/1.42 => ( Xx = Xy ) ) )
% 0.31/1.42 => ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exuI2_type,type,
% 0.31/1.42 exuI2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exuI2,definition,
% 0.31/1.42 ( exuI2
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ? [Xx: $i] :
% 0.31/1.42 ! [Xy: $i] :
% 0.31/1.42 ( ( Xphi @ Xy )
% 0.31/1.42 <=> ( Xy = Xx ) )
% 0.31/1.42 => ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(inCongP_type,type,
% 0.31/1.42 inCongP: $o ).
% 0.31/1.42
% 0.31/1.42 thf(inCongP,definition,
% 0.31/1.42 ( inCongP
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( A = B )
% 0.31/1.42 => ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xx = Xy )
% 0.31/1.42 => ( ( in @ Xx @ A )
% 0.31/1.42 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(in__Cong_type,type,
% 0.31/1.42 in__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(in__Cong,definition,
% 0.31/1.42 ( in__Cong
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( A = B )
% 0.31/1.42 => ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xx = Xy )
% 0.31/1.42 => ( ( in @ Xx @ A )
% 0.31/1.42 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exuE3u_type,type,
% 0.31/1.42 exuE3u: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exuE3u,definition,
% 0.31/1.42 ( exuE3u
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 => ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xphi @ Xx )
% 0.31/1.42 => ( ( Xphi @ Xy )
% 0.31/1.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exu__Cong_type,type,
% 0.31/1.42 exu__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exu__Cong,definition,
% 0.31/1.42 ( exu__Cong
% 0.31/1.42 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/1.42 ( ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xx = Xy )
% 0.31/1.42 => ( ( Xphi @ Xx )
% 0.31/1.42 <=> ( Xpsi @ Xy ) ) )
% 0.31/1.42 => ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 <=> ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptyset__Cong_type,type,
% 0.31/1.42 emptyset__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptyset__Cong,definition,
% 0.31/1.42 ( emptyset__Cong
% 0.31/1.42 = ( emptyset = emptyset ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoin__Cong_type,type,
% 0.31/1.42 setadjoin__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoin__Cong,definition,
% 0.31/1.42 ( setadjoin__Cong
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xx = Xy )
% 0.31/1.42 => ! [Xz: $i,Xu: $i] :
% 0.31/1.42 ( ( Xz = Xu )
% 0.31/1.42 => ( ( setadjoin @ Xx @ Xz )
% 0.31/1.42 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(powerset__Cong_type,type,
% 0.31/1.42 powerset__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(powerset__Cong,definition,
% 0.31/1.42 ( powerset__Cong
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( A = B )
% 0.31/1.42 => ( ( powerset @ A )
% 0.31/1.42 = ( powerset @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setunion__Cong_type,type,
% 0.31/1.42 setunion__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setunion__Cong,definition,
% 0.31/1.42 ( setunion__Cong
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( A = B )
% 0.31/1.42 => ( ( setunion @ A )
% 0.31/1.42 = ( setunion @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(omega__Cong_type,type,
% 0.31/1.42 omega__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(omega__Cong,definition,
% 0.31/1.42 ( omega__Cong
% 0.31/1.42 = ( omega = omega ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(exuEu_type,type,
% 0.31/1.42 exuEu: $o ).
% 0.31/1.42
% 0.31/1.42 thf(exuEu,definition,
% 0.31/1.42 ( exuEu
% 0.31/1.42 = ( ! [Xphi: $i > $o] :
% 0.31/1.42 ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 => ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xphi @ Xx )
% 0.31/1.42 => ( ( Xphi @ Xy )
% 0.31/1.42 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(descr__Cong_type,type,
% 0.31/1.42 descr__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(descr__Cong,definition,
% 0.31/1.42 ( descr__Cong
% 0.31/1.42 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/1.42 ( ! [Xx: $i,Xy: $i] :
% 0.31/1.42 ( ( Xx = Xy )
% 0.31/1.42 => ( ( Xphi @ Xx )
% 0.31/1.42 <=> ( Xpsi @ Xy ) ) )
% 0.31/1.42 => ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 => ( ( exu
% 0.31/1.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.31/1.42 => ( ( descr
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 = ( descr
% 0.31/1.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstr__Cong_type,type,
% 0.31/1.42 dsetconstr__Cong: $o ).
% 0.31/1.42
% 0.31/1.42 thf(dsetconstr__Cong,definition,
% 0.31/1.42 ( dsetconstr__Cong
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( A = B )
% 0.31/1.42 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ! [Xy: $i] :
% 0.31/1.42 ( ( in @ Xy @ B )
% 0.31/1.42 => ( ( Xx = Xy )
% 0.31/1.42 => ( ( Xphi @ Xx )
% 0.31/1.42 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.31/1.42 => ( ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 = ( dsetconstr @ B
% 0.31/1.42 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subset_type,type,
% 0.31/1.42 subset: $i > $i > $o ).
% 0.31/1.42
% 0.31/1.42 thf(disjoint_type,type,
% 0.31/1.42 disjoint: $i > $i > $o ).
% 0.31/1.42
% 0.31/1.42 thf(setsmeet_type,type,
% 0.31/1.42 setsmeet: $i > $i > $o ).
% 0.31/1.42
% 0.31/1.42 thf(subsetI1_type,type,
% 0.31/1.42 subsetI1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subsetI1,definition,
% 0.31/1.42 ( subsetI1
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( in @ Xx @ B ) )
% 0.31/1.42 => ( subset @ A @ B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(eqimpsubset2_type,type,
% 0.31/1.42 eqimpsubset2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(eqimpsubset2,definition,
% 0.31/1.42 ( eqimpsubset2
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( A = B )
% 0.31/1.42 => ( subset @ B @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(eqimpsubset1_type,type,
% 0.31/1.42 eqimpsubset1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(eqimpsubset1,definition,
% 0.31/1.42 ( eqimpsubset1
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( A = B )
% 0.31/1.42 => ( subset @ A @ B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subsetI2_type,type,
% 0.31/1.42 subsetI2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subsetI2,definition,
% 0.31/1.42 ( subsetI2
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ! [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( in @ Xx @ B ) )
% 0.31/1.42 => ( subset @ A @ B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(emptysetsubset_type,type,
% 0.31/1.42 emptysetsubset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(emptysetsubset,definition,
% 0.31/1.42 ( emptysetsubset
% 0.31/1.42 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subsetE_type,type,
% 0.31/1.42 subsetE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subsetE,definition,
% 0.31/1.42 ( subsetE
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( subset @ A @ B )
% 0.31/1.42 => ( ( in @ Xx @ A )
% 0.31/1.42 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subsetE2_type,type,
% 0.31/1.42 subsetE2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subsetE2,definition,
% 0.31/1.42 ( subsetE2
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( subset @ A @ B )
% 0.31/1.42 => ( ~ ( in @ Xx @ B )
% 0.31/1.42 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(notsubsetI_type,type,
% 0.31/1.42 notsubsetI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(notsubsetI,definition,
% 0.31/1.42 ( notsubsetI
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( ~ ( in @ Xx @ B )
% 0.31/1.42 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(notequalI1_type,type,
% 0.31/1.42 notequalI1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(notequalI1,definition,
% 0.31/1.42 ( notequalI1
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ~ ( subset @ A @ B )
% 0.31/1.42 => ( A != B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(notequalI2_type,type,
% 0.31/1.42 notequalI2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(notequalI2,definition,
% 0.31/1.42 ( notequalI2
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( ~ ( in @ Xx @ B )
% 0.31/1.42 => ( A != B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subsetRefl_type,type,
% 0.31/1.42 subsetRefl: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subsetRefl,definition,
% 0.31/1.42 ( subsetRefl
% 0.31/1.42 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subsetTrans_type,type,
% 0.31/1.42 subsetTrans: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subsetTrans,definition,
% 0.31/1.42 ( subsetTrans
% 0.31/1.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/1.42 ( ( subset @ A @ B )
% 0.31/1.42 => ( ( subset @ B @ C )
% 0.31/1.42 => ( subset @ A @ C ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinSub_type,type,
% 0.31/1.42 setadjoinSub: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinSub,definition,
% 0.31/1.42 ( setadjoinSub
% 0.31/1.42 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinSub2_type,type,
% 0.31/1.42 setadjoinSub2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setadjoinSub2,definition,
% 0.31/1.42 ( setadjoinSub2
% 0.31/1.42 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.31/1.42 ( ( subset @ A @ B )
% 0.31/1.42 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subset2powerset_type,type,
% 0.31/1.42 subset2powerset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subset2powerset,definition,
% 0.31/1.42 ( subset2powerset
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( subset @ A @ B )
% 0.31/1.42 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setextsub_type,type,
% 0.31/1.42 setextsub: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setextsub,definition,
% 0.31/1.42 ( setextsub
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( subset @ A @ B )
% 0.31/1.42 => ( ( subset @ B @ A )
% 0.31/1.42 => ( A = B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(subsetemptysetimpeq_type,type,
% 0.31/1.42 subsetemptysetimpeq: $o ).
% 0.31/1.42
% 0.31/1.42 thf(subsetemptysetimpeq,definition,
% 0.31/1.42 ( subsetemptysetimpeq
% 0.31/1.42 = ( ! [A: $i] :
% 0.31/1.42 ( ( subset @ A @ emptyset )
% 0.31/1.42 => ( A = emptyset ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(powersetI1_type,type,
% 0.31/1.42 powersetI1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(powersetI1,definition,
% 0.31/1.42 ( powersetI1
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( subset @ B @ A )
% 0.31/1.42 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(powersetE1_type,type,
% 0.31/1.42 powersetE1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(powersetE1,definition,
% 0.31/1.42 ( powersetE1
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( in @ B @ ( powerset @ A ) )
% 0.31/1.42 => ( subset @ B @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(inPowerset_type,type,
% 0.31/1.42 inPowerset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(inPowerset,definition,
% 0.31/1.42 ( inPowerset
% 0.31/1.42 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(powersetsubset_type,type,
% 0.31/1.42 powersetsubset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(powersetsubset,definition,
% 0.31/1.42 ( powersetsubset
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( subset @ A @ B )
% 0.31/1.42 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(sepInPowerset_type,type,
% 0.31/1.42 sepInPowerset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(sepInPowerset,definition,
% 0.31/1.42 ( sepInPowerset
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( in
% 0.31/1.42 @ ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 @ ( powerset @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(sepSubset_type,type,
% 0.31/1.42 sepSubset: $o ).
% 0.31/1.42
% 0.31/1.42 thf(sepSubset,definition,
% 0.31/1.42 ( sepSubset
% 0.31/1.42 = ( ! [A: $i,Xphi: $i > $o] :
% 0.31/1.42 ( subset
% 0.31/1.42 @ ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.42 @ A ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binunion_type,type,
% 0.31/1.42 binunion: $i > $i > $i ).
% 0.31/1.42
% 0.31/1.42 thf(binunionIL_type,type,
% 0.31/1.42 binunionIL: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binunionIL,definition,
% 0.31/1.42 ( binunionIL
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(upairset2IR_type,type,
% 0.31/1.42 upairset2IR: $o ).
% 0.31/1.42
% 0.31/1.42 thf(upairset2IR,definition,
% 0.31/1.42 ( upairset2IR
% 0.31/1.42 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binunionIR_type,type,
% 0.31/1.42 binunionIR: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binunionIR,definition,
% 0.31/1.42 ( binunionIR
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ B )
% 0.31/1.42 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binunionEcases_type,type,
% 0.31/1.42 binunionEcases: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binunionEcases,definition,
% 0.31/1.42 ( binunionEcases
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.31/1.42 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.31/1.42 => ( ( ( in @ Xx @ A )
% 0.31/1.42 => Xphi )
% 0.31/1.42 => ( ( ( in @ Xx @ B )
% 0.31/1.42 => Xphi )
% 0.31/1.42 => Xphi ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binunionE_type,type,
% 0.31/1.42 binunionE: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binunionE,definition,
% 0.31/1.42 ( binunionE
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.31/1.42 => ( ( in @ Xx @ A )
% 0.31/1.42 | ( in @ Xx @ B ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binunionLsub_type,type,
% 0.31/1.42 binunionLsub: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binunionLsub,definition,
% 0.31/1.42 ( binunionLsub
% 0.31/1.42 = ( ! [A: $i,B: $i] : ( subset @ A @ ( binunion @ A @ B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binunionRsub_type,type,
% 0.31/1.42 binunionRsub: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binunionRsub,definition,
% 0.31/1.42 ( binunionRsub
% 0.31/1.42 = ( ! [A: $i,B: $i] : ( subset @ B @ ( binunion @ A @ B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersect_type,type,
% 0.31/1.42 binintersect: $i > $i > $i ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectI_type,type,
% 0.31/1.42 binintersectI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectI,definition,
% 0.31/1.42 ( binintersectI
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( ( in @ Xx @ B )
% 0.31/1.42 => ( in @ Xx @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset5_type,type,
% 0.31/1.42 binintersectSubset5: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset5,definition,
% 0.31/1.42 ( binintersectSubset5
% 0.31/1.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/1.42 ( ( subset @ C @ A )
% 0.31/1.42 => ( ( subset @ C @ B )
% 0.31/1.42 => ( subset @ C @ ( binintersect @ A @ B ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectEL_type,type,
% 0.31/1.42 binintersectEL: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectEL,definition,
% 0.31/1.42 ( binintersectEL
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.31/1.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectLsub_type,type,
% 0.31/1.42 binintersectLsub: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectLsub,definition,
% 0.31/1.42 ( binintersectLsub
% 0.31/1.42 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ A ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset2_type,type,
% 0.31/1.42 binintersectSubset2: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset2,definition,
% 0.31/1.42 ( binintersectSubset2
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( subset @ A @ B )
% 0.31/1.42 => ( ( binintersect @ A @ B )
% 0.31/1.42 = A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset3_type,type,
% 0.31/1.42 binintersectSubset3: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset3,definition,
% 0.31/1.42 ( binintersectSubset3
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( ( binintersect @ A @ B )
% 0.31/1.42 = B )
% 0.31/1.42 => ( subset @ B @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectER_type,type,
% 0.31/1.42 binintersectER: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectER,definition,
% 0.31/1.42 ( binintersectER
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( binintersect @ A @ B ) )
% 0.31/1.42 => ( in @ Xx @ B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(disjointsetsI1_type,type,
% 0.31/1.42 disjointsetsI1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(disjointsetsI1,definition,
% 0.31/1.42 ( disjointsetsI1
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ~ ? [Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 & ( in @ Xx @ B ) )
% 0.31/1.42 => ( ( binintersect @ A @ B )
% 0.31/1.42 = emptyset ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectRsub_type,type,
% 0.31/1.42 binintersectRsub: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectRsub,definition,
% 0.31/1.42 ( binintersectRsub
% 0.31/1.42 = ( ! [A: $i,B: $i] : ( subset @ ( binintersect @ A @ B ) @ B ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset4_type,type,
% 0.31/1.42 binintersectSubset4: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset4,definition,
% 0.31/1.42 ( binintersectSubset4
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( subset @ B @ A )
% 0.31/1.42 => ( ( binintersect @ A @ B )
% 0.31/1.42 = B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset1_type,type,
% 0.31/1.42 binintersectSubset1: $o ).
% 0.31/1.42
% 0.31/1.42 thf(binintersectSubset1,definition,
% 0.31/1.42 ( binintersectSubset1
% 0.31/1.42 = ( ! [A: $i,B: $i] :
% 0.31/1.42 ( ( ( binintersect @ A @ B )
% 0.31/1.42 = A )
% 0.31/1.42 => ( subset @ A @ B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(bs114d_type,type,
% 0.31/1.42 bs114d: $o ).
% 0.31/1.42
% 0.31/1.42 thf(bs114d,definition,
% 0.31/1.42 ( bs114d
% 0.31/1.42 = ( ! [A: $i,B: $i,C: $i] :
% 0.31/1.42 ( ( binintersect @ A @ ( binunion @ B @ C ) )
% 0.31/1.42 = ( binunion @ ( binintersect @ A @ B ) @ ( binintersect @ A @ C ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(regular_type,type,
% 0.31/1.42 regular: $i > $o ).
% 0.31/1.42
% 0.31/1.42 thf(setminus_type,type,
% 0.31/1.42 setminus: $i > $i > $i ).
% 0.31/1.42
% 0.31/1.42 thf(setminus,definition,
% 0.31/1.42 ( setminus
% 0.31/1.42 = ( ^ [A: $i,B: $i] :
% 0.31/1.42 ( dsetconstr @ A
% 0.31/1.42 @ ^ [Xx: $i] :
% 0.31/1.42 ~ ( in @ Xx @ B ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setminusI_type,type,
% 0.31/1.42 setminusI: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setminusI,definition,
% 0.31/1.42 ( setminusI
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ A )
% 0.31/1.42 => ( ~ ( in @ Xx @ B )
% 0.31/1.42 => ( in @ Xx @ ( setminus @ A @ B ) ) ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setminusEL_type,type,
% 0.31/1.42 setminusEL: $o ).
% 0.31/1.42
% 0.31/1.42 thf(setminusEL,definition,
% 0.31/1.42 ( setminusEL
% 0.31/1.42 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/1.42 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/1.42
% 0.31/1.42 thf(setminusER,conjecture,
% 0.31/1.42 ( setextAx
% 0.31/1.42 => ( emptysetAx
% 0.31/1.42 => ( setadjoinAx
% 0.31/1.42 => ( powersetAx
% 0.31/1.42 => ( setunionAx
% 0.31/1.42 => ( omega0Ax
% 0.31/1.42 => ( omegaSAx
% 0.31/1.42 => ( omegaIndAx
% 0.31/1.42 => ( replAx
% 0.31/1.42 => ( foundationAx
% 0.31/1.42 => ( wellorderingAx
% 0.31/1.42 => ( descrp
% 0.31/1.42 => ( dsetconstrI
% 0.31/1.42 => ( dsetconstrEL
% 0.31/1.42 => ( dsetconstrER
% 0.31/1.42 => ( exuE1
% 0.31/1.42 => ( prop2setE
% 0.31/1.42 => ( emptysetE
% 0.31/1.42 => ( emptysetimpfalse
% 0.31/1.42 => ( notinemptyset
% 0.31/1.42 => ( exuE3e
% 0.31/1.42 => ( setext
% 0.31/1.42 => ( emptyI
% 0.31/1.42 => ( noeltsimpempty
% 0.31/1.42 => ( setbeta
% 0.31/1.42 => ( nonemptyE1
% 0.31/1.42 => ( nonemptyI
% 0.31/1.42 => ( nonemptyI1
% 0.31/1.42 => ( setadjoinIL
% 0.31/1.42 => ( emptyinunitempty
% 0.31/1.42 => ( setadjoinIR
% 0.31/1.42 => ( setadjoinE
% 0.31/1.42 => ( setadjoinOr
% 0.31/1.42 => ( setoftrueEq
% 0.31/1.42 => ( powersetI
% 0.31/1.42 => ( emptyinPowerset
% 0.31/1.42 => ( emptyInPowerset
% 0.31/1.42 => ( powersetE
% 0.31/1.42 => ( setunionI
% 0.31/1.42 => ( setunionE
% 0.31/1.42 => ( subPowSU
% 0.31/1.42 => ( exuE2
% 0.31/1.42 => ( nonemptyImpWitness
% 0.31/1.42 => ( uniqinunit
% 0.31/1.42 => ( notinsingleton
% 0.31/1.42 => ( eqinunit
% 0.31/1.42 => ( singletonsswitch
% 0.31/1.42 => ( upairsetE
% 0.31/1.42 => ( upairsetIL
% 0.31/1.42 => ( upairsetIR
% 0.31/1.42 => ( emptyE1
% 0.31/1.42 => ( vacuousDall
% 0.31/1.42 => ( quantDeMorgan1
% 0.31/1.42 => ( quantDeMorgan2
% 0.31/1.42 => ( quantDeMorgan3
% 0.31/1.42 => ( quantDeMorgan4
% 0.31/1.42 => ( prop2setI
% 0.31/1.42 => ( prop2set2propI
% 0.31/1.42 => ( notdexE
% 0.31/1.42 => ( notdallE
% 0.31/1.42 => ( exuI1
% 0.31/1.42 => ( exuI3
% 0.31/1.42 => ( exuI2
% 0.31/1.42 => ( inCongP
% 0.31/1.42 => ( in__Cong
% 0.31/1.42 => ( exuE3u
% 0.31/1.42 => ( exu__Cong
% 0.31/1.42 => ( emptyset__Cong
% 0.31/1.42 => ( setadjoin__Cong
% 0.31/1.42 => ( powerset__Cong
% 0.31/1.42 => ( setunion__Cong
% 0.31/1.42 => ( omega__Cong
% 0.31/1.42 => ( exuEu
% 0.31/1.42 => ( descr__Cong
% 0.31/1.42 => ( dsetconstr__Cong
% 0.31/1.42 => ( subsetI1
% 0.31/1.42 => ( eqimpsubset2
% 0.31/1.42 => ( eqimpsubset1
% 0.31/1.42 => ( subsetI2
% 0.31/1.42 => ( emptysetsubset
% 0.31/1.42 => ( subsetE
% 0.31/1.42 => ( subsetE2
% 0.31/1.42 => ( notsubsetI
% 0.31/1.42 => ( notequalI1
% 0.31/1.42 => ( notequalI2
% 0.31/1.42 => ( subsetRefl
% 0.31/1.42 => ( subsetTrans
% 0.31/1.42 => ( setadjoinSub
% 0.31/1.42 => ( setadjoinSub2
% 0.31/1.42 => ( subset2powerset
% 0.31/1.42 => ( setextsub
% 0.31/1.42 => ( subsetemptysetimpeq
% 0.31/1.42 => ( powersetI1
% 0.31/1.42 => ( powersetE1
% 0.31/1.42 => ( inPowerset
% 0.31/1.42 => ( powersetsubset
% 0.31/1.42 => ( sepInPowerset
% 0.31/1.42 => ( sepSubset
% 0.31/1.42 => ( binunionIL
% 0.31/1.42 => ( upairset2IR
% 0.31/1.42 => ( binunionIR
% 0.31/1.42 => ( binunionEcases
% 0.31/1.42 => ( binunionE
% 0.31/1.42 => ( binunionLsub
% 0.31/1.42 => ( binunionRsub
% 0.31/1.42 => ( binintersectI
% 0.31/1.42 => ( binintersectSubset5
% 0.31/1.42 => ( binintersectEL
% 0.31/1.42 => ( binintersectLsub
% 0.31/1.42 => ( binintersectSubset2
% 0.31/1.42 => ( binintersectSubset3
% 0.31/1.42 => ( binintersectER
% 0.31/1.42 => ( disjointsetsI1
% 0.31/1.42 => ( binintersectRsub
% 0.31/1.42 => ( binintersectSubset4
% 0.31/1.42 => ( binintersectSubset1
% 0.31/1.42 => ( bs114d
% 0.31/1.42 => ( setminusI
% 0.31/1.42 => ( setminusEL
% 0.31/1.42 => ! [A: $i,B: $i,Xx: $i] :
% 0.31/1.42 ( ( in @ Xx @ ( setminus @ A @ B ) )
% 0.31/1.42 => ~ ( in @ Xx @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.42 ------------------------
% 0.31/1.44 % (19780)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_19448 for (2999ds/4Mi)
% 0.31/1.44 % (19783)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_19448 for (2999ds/2Mi)
% 0.31/1.44 % (19784)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_19448 for (2999ds/275Mi)
% 0.31/1.44 % (19780)Instruction limit reached!
% 0.31/1.44 % (19780)------------------------------
% 0.31/1.44 % (19780)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.44 % (19780)Termination reason: Unknown
% 0.31/1.44 % (19780)Termination phase: shuffling
% 0.31/1.44
% 0.31/1.44 % (19780)Memory used [KB]: 1279
% 0.31/1.44 % (19780)Time elapsed: 0.003 s
% 0.31/1.44 % (19780)Instructions burned: 5 (million)
% 0.31/1.44 % (19780)------------------------------
% 0.31/1.44 % (19780)------------------------------
% 0.31/1.44 % (19783)Instruction limit reached!
% 0.31/1.44 % (19783)------------------------------
% 0.31/1.44 % (19783)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.44 % (19783)Termination reason: Unknown
% 0.31/1.44 % (19783)Termination phase: shuffling
% 0.31/1.44
% 0.31/1.44 % (19783)Memory used [KB]: 1151
% 0.31/1.44 % (19783)Time elapsed: 0.002 s
% 0.31/1.44 % (19783)Instructions burned: 3 (million)
% 0.31/1.44 % (19783)------------------------------
% 0.31/1.44 % (19783)------------------------------
% 0.31/1.45 % (19779)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/183Mi)
% 0.31/1.45 % (19781)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_19448 for (2999ds/27Mi)
% 0.31/1.45 % (19782)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/2Mi)
% 0.31/1.45 % (19785)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/18Mi)
% 0.31/1.45 % (19782)Instruction limit reached!
% 0.31/1.45 % (19782)------------------------------
% 0.31/1.45 % (19782)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.45 % (19782)Termination reason: Unknown
% 0.31/1.45 % (19782)Termination phase: shuffling
% 0.31/1.45
% 0.31/1.45 % (19782)Memory used [KB]: 1151
% 0.31/1.45 % (19782)Time elapsed: 0.004 s
% 0.31/1.45 % (19782)Instructions burned: 3 (million)
% 0.31/1.45 % (19782)------------------------------
% 0.31/1.45 % (19782)------------------------------
% 0.31/1.45 % (19786)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/3Mi)
% 0.31/1.45 % (19786)Instruction limit reached!
% 0.31/1.45 % (19786)------------------------------
% 0.31/1.45 % (19786)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.45 % (19786)Termination reason: Unknown
% 0.31/1.45 % (19786)Termination phase: shuffling
% 0.31/1.45
% 0.31/1.45 % (19786)Memory used [KB]: 1279
% 0.31/1.45 % (19786)Time elapsed: 0.002 s
% 0.31/1.45 % (19786)Instructions burned: 4 (million)
% 0.31/1.45 % (19786)------------------------------
% 0.31/1.45 % (19786)------------------------------
% 0.31/1.45 % (19787)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_19448 for (2999ds/37Mi)
% 0.31/1.46 % (19785)Instruction limit reached!
% 0.31/1.46 % (19785)------------------------------
% 0.31/1.46 % (19785)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.46 % (19785)Termination reason: Unknown
% 0.31/1.46 % (19785)Termination phase: Preprocessing 3
% 0.31/1.46
% 0.31/1.46 % (19785)Memory used [KB]: 1535
% 0.31/1.46 % (19785)Time elapsed: 0.013 s
% 0.31/1.46 % (19785)Instructions burned: 19 (million)
% 0.31/1.46 % (19785)------------------------------
% 0.31/1.46 % (19785)------------------------------
% 0.31/1.46 % (19789)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_19448 for (2999ds/3Mi)
% 0.31/1.46 % (19781)Instruction limit reached!
% 0.31/1.46 % (19781)------------------------------
% 0.31/1.46 % (19781)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.46 % (19781)Termination reason: Unknown
% 0.31/1.46 % (19781)Termination phase: Property scanning
% 0.31/1.46
% 0.31/1.46 % (19781)Memory used [KB]: 1535
% 0.31/1.46 % (19781)Time elapsed: 0.016 s
% 0.31/1.46 % (19781)Instructions burned: 27 (million)
% 0.31/1.46 % (19781)------------------------------
% 0.31/1.46 % (19781)------------------------------
% 0.31/1.46 % (19787)Instruction limit reached!
% 0.31/1.46 % (19787)------------------------------
% 0.31/1.46 % (19787)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.46 % (19787)Termination reason: Unknown
% 0.31/1.46 % (19787)Termination phase: Property scanning
% 0.31/1.46
% 0.31/1.46 % (19787)Memory used [KB]: 1663
% 0.31/1.46 % (19787)Time elapsed: 0.012 s
% 0.31/1.46 % (19787)Instructions burned: 37 (million)
% 0.31/1.46 % (19787)------------------------------
% 0.31/1.46 % (19787)------------------------------
% 0.31/1.46 % (19789)Instruction limit reached!
% 0.31/1.46 % (19789)------------------------------
% 0.31/1.46 % (19789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.46 % (19789)Termination reason: Unknown
% 0.31/1.46 % (19789)Termination phase: shuffling
% 0.31/1.46
% 0.31/1.46 % (19789)Memory used [KB]: 1279
% 0.31/1.46 % (19789)Time elapsed: 0.002 s
% 0.31/1.46 % (19789)Instructions burned: 4 (million)
% 0.31/1.46 % (19789)------------------------------
% 0.31/1.46 % (19789)------------------------------
% 0.31/1.47 % (19788)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_19448 for (2999ds/15Mi)
% 0.31/1.47 % (19793)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_19448 for (2999ds/3Mi)
% 0.31/1.47 % (19792)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/16Mi)
% 0.31/1.47 % (19793)Instruction limit reached!
% 0.31/1.47 % (19793)------------------------------
% 0.31/1.47 % (19793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.47 % (19793)Termination reason: Unknown
% 0.31/1.47 % (19793)Termination phase: shuffling
% 0.31/1.47
% 0.31/1.47 % (19793)Memory used [KB]: 1151
% 0.31/1.47 % (19793)Time elapsed: 0.002 s
% 0.31/1.47 % (19793)Instructions burned: 4 (million)
% 0.31/1.47 % (19793)------------------------------
% 0.31/1.47 % (19793)------------------------------
% 0.31/1.47 % (19788)Instruction limit reached!
% 0.31/1.47 % (19788)------------------------------
% 0.31/1.47 % (19788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.47 % (19788)Termination reason: Unknown
% 0.31/1.47 % (19788)Termination phase: Preprocessing 1
% 0.31/1.47
% 0.31/1.47 % (19788)Memory used [KB]: 1407
% 0.31/1.47 % (19788)Time elapsed: 0.010 s
% 0.31/1.47 % (19788)Instructions burned: 15 (million)
% 0.31/1.47 % (19788)------------------------------
% 0.31/1.47 % (19788)------------------------------
% 0.31/1.47 % (19790)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_19448 for (2999ds/1041Mi)
% 0.31/1.48 % (19792)Instruction limit reached!
% 0.31/1.48 % (19792)------------------------------
% 0.31/1.48 % (19792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.48 % (19792)Termination reason: Unknown
% 0.31/1.48 % (19792)Termination phase: Property scanning
% 0.31/1.48
% 0.31/1.48 % (19792)Memory used [KB]: 1535
% 0.31/1.48 % (19792)Time elapsed: 0.007 s
% 0.31/1.48 % (19792)Instructions burned: 18 (million)
% 0.31/1.48 % (19792)------------------------------
% 0.31/1.48 % (19792)------------------------------
% 0.31/1.48 % (19791)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/7Mi)
% 0.31/1.48 % (19794)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_19448 for (2999ds/3Mi)
% 0.31/1.48 % (19794)Instruction limit reached!
% 0.31/1.48 % (19794)------------------------------
% 0.31/1.48 % (19794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.48 % (19794)Termination reason: Unknown
% 0.31/1.48 % (19794)Termination phase: shuffling
% 0.31/1.48
% 0.31/1.48 % (19794)Memory used [KB]: 1151
% 0.31/1.48 % (19794)Time elapsed: 0.002 s
% 0.31/1.48 % (19794)Instructions burned: 3 (million)
% 0.31/1.48 % (19794)------------------------------
% 0.31/1.48 % (19794)------------------------------
% 0.31/1.48 % (19791)Instruction limit reached!
% 0.31/1.48 % (19791)------------------------------
% 0.31/1.48 % (19791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.48 % (19791)Termination reason: Unknown
% 0.31/1.48 % (19791)Termination phase: shuffling
% 0.31/1.48
% 0.31/1.48 % (19791)Memory used [KB]: 1279
% 0.31/1.48 % (19791)Time elapsed: 0.006 s
% 0.31/1.48 % (19791)Instructions burned: 8 (million)
% 0.31/1.48 % (19791)------------------------------
% 0.31/1.48 % (19791)------------------------------
% 0.31/1.49 % (19795)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/7Mi)
% 0.31/1.49 % (19796)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/3Mi)
% 0.31/1.49 % (19796)Instruction limit reached!
% 0.31/1.49 % (19796)------------------------------
% 0.31/1.49 % (19796)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.49 % (19796)Termination reason: Unknown
% 0.31/1.49 % (19796)Termination phase: shuffling
% 0.31/1.49
% 0.31/1.49 % (19796)Memory used [KB]: 1279
% 0.31/1.49 % (19796)Time elapsed: 0.003 s
% 0.31/1.49 % (19796)Instructions burned: 4 (million)
% 0.31/1.49 % (19796)------------------------------
% 0.31/1.49 % (19796)------------------------------
% 0.31/1.49 % (19795)Instruction limit reached!
% 0.31/1.49 % (19795)------------------------------
% 0.31/1.49 % (19795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.49 % (19795)Termination reason: Unknown
% 0.31/1.49 % (19795)Termination phase: shuffling
% 0.31/1.49
% 0.31/1.49 % (19795)Memory used [KB]: 1279
% 0.31/1.49 % (19795)Time elapsed: 0.003 s
% 0.31/1.49 % (19795)Instructions burned: 7 (million)
% 0.31/1.49 % (19795)------------------------------
% 0.31/1.49 % (19795)------------------------------
% 0.31/1.49 % (19797)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/4Mi)
% 0.31/1.49 % (19797)Instruction limit reached!
% 0.31/1.49 % (19797)------------------------------
% 0.31/1.49 % (19797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.49 % (19797)Termination reason: Unknown
% 0.31/1.49 % (19797)Termination phase: shuffling
% 0.31/1.49
% 0.31/1.49 % (19797)Memory used [KB]: 1279
% 0.31/1.49 % (19797)Time elapsed: 0.003 s
% 0.31/1.49 % (19797)Instructions burned: 7 (million)
% 0.31/1.49 % (19797)------------------------------
% 0.31/1.49 % (19797)------------------------------
% 2.43/1.50 % (19799)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/710Mi)
% 2.43/1.50 % (19800)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/6Mi)
% 2.43/1.50 % (19798)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/18Mi)
% 2.43/1.50 % (19800)Instruction limit reached!
% 2.43/1.50 % (19800)------------------------------
% 2.43/1.50 % (19800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.50 % (19800)Termination reason: Unknown
% 2.43/1.50 % (19800)Termination phase: shuffling
% 2.43/1.50
% 2.43/1.50 % (19800)Memory used [KB]: 1279
% 2.43/1.50 % (19800)Time elapsed: 0.004 s
% 2.43/1.50 % (19800)Instructions burned: 7 (million)
% 2.43/1.50 % (19800)------------------------------
% 2.43/1.50 % (19800)------------------------------
% 2.43/1.50 % (19801)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_19448 for (2999ds/902Mi)
% 2.43/1.51 % (19798)Instruction limit reached!
% 2.43/1.51 % (19798)------------------------------
% 2.43/1.51 % (19798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.51 % (19798)Termination reason: Unknown
% 2.43/1.51 % (19798)Termination phase: Property scanning
% 2.43/1.51
% 2.43/1.51 % (19798)Memory used [KB]: 1535
% 2.43/1.51 % (19798)Time elapsed: 0.012 s
% 2.43/1.51 % (19798)Instructions burned: 19 (million)
% 2.43/1.51 % (19798)------------------------------
% 2.43/1.51 % (19798)------------------------------
% 2.43/1.51 % (19802)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_19448 for (2999ds/21Mi)
% 2.43/1.52 % (19802)Instruction limit reached!
% 2.43/1.52 % (19802)------------------------------
% 2.43/1.52 % (19802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (19802)Termination reason: Unknown
% 2.43/1.52 % (19802)Termination phase: Property scanning
% 2.43/1.52
% 2.43/1.52 % (19802)Memory used [KB]: 1535
% 2.43/1.52 % (19802)Time elapsed: 0.008 s
% 2.43/1.52 % (19802)Instructions burned: 22 (million)
% 2.43/1.52 % (19802)------------------------------
% 2.43/1.52 % (19802)------------------------------
% 2.43/1.52 % (19784)Instruction limit reached!
% 2.43/1.52 % (19784)------------------------------
% 2.43/1.52 % (19784)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.52 % (19784)Termination reason: Unknown
% 2.43/1.52 % (19784)Termination phase: Saturation
% 2.43/1.52
% 2.43/1.52 % (19784)Memory used [KB]: 7675
% 2.43/1.52 % (19784)Time elapsed: 0.087 s
% 2.43/1.52 % (19784)Instructions burned: 276 (million)
% 2.43/1.52 % (19784)------------------------------
% 2.43/1.52 % (19784)------------------------------
% 2.43/1.53 % (19803)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/5Mi)
% 2.43/1.53 % (19804)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_19448 for (2999ds/6Mi)
% 2.43/1.53 % (19803)Instruction limit reached!
% 2.43/1.53 % (19803)------------------------------
% 2.43/1.53 % (19803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.53 % (19803)Termination reason: Unknown
% 2.43/1.53 % (19803)Termination phase: shuffling
% 2.43/1.53
% 2.43/1.53 % (19803)Memory used [KB]: 1279
% 2.43/1.53 % (19803)Time elapsed: 0.004 s
% 2.43/1.53 % (19803)Instructions burned: 5 (million)
% 2.43/1.53 % (19803)------------------------------
% 2.43/1.53 % (19803)------------------------------
% 2.43/1.53 % (19804)Instruction limit reached!
% 2.43/1.53 % (19804)------------------------------
% 2.43/1.53 % (19804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.53 % (19804)Termination reason: Unknown
% 2.43/1.53 % (19804)Termination phase: shuffling
% 2.43/1.53
% 2.43/1.53 % (19804)Memory used [KB]: 1279
% 2.43/1.53 % (19804)Time elapsed: 0.004 s
% 2.43/1.53 % (19804)Instructions burned: 8 (million)
% 2.43/1.53 % (19804)------------------------------
% 2.43/1.53 % (19804)------------------------------
% 2.43/1.53 % (19805)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19448 for (2999ds/377Mi)
% 2.43/1.54 % (19801)Refutation not found, incomplete strategy
% 2.43/1.54 % (19801)------------------------------
% 2.43/1.54 % (19801)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.54 % (19801)Termination reason: Refutation not found, incomplete strategy
% 2.43/1.54
% 2.43/1.54
% 2.43/1.54 % (19801)Memory used [KB]: 7164
% 2.43/1.54 % (19801)Time elapsed: 0.037 s
% 2.43/1.54 % (19801)Instructions burned: 119 (million)
% 2.43/1.54 % (19801)------------------------------
% 2.43/1.54 % (19801)------------------------------
% 2.43/1.54 % (19807)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_19448 for (2999ds/19Mi)
% 2.43/1.54 % (19779)Instruction limit reached!
% 2.43/1.54 % (19779)------------------------------
% 2.43/1.54 % (19779)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.54 % (19779)Termination reason: Unknown
% 2.43/1.54 % (19779)Termination phase: Saturation
% 2.43/1.54
% 2.43/1.54 % (19779)Memory used [KB]: 7036
% 2.43/1.54 % (19779)Time elapsed: 0.096 s
% 2.43/1.54 % (19779)Instructions burned: 184 (million)
% 2.43/1.54 % (19779)------------------------------
% 2.43/1.54 % (19779)------------------------------
% 2.43/1.54 % (19806)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_19448 for (2999ds/779Mi)
% 2.43/1.55 % (19807)Instruction limit reached!
% 2.43/1.55 % (19807)------------------------------
% 2.43/1.55 % (19807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.55 % (19807)Termination reason: Unknown
% 2.43/1.55 % (19807)Termination phase: Property scanning
% 2.43/1.55
% 2.43/1.55 % (19807)Memory used [KB]: 1535
% 2.43/1.55 % (19807)Time elapsed: 0.008 s
% 2.43/1.55 % (19807)Instructions burned: 22 (million)
% 2.43/1.55 % (19807)------------------------------
% 2.43/1.55 % (19807)------------------------------
% 2.43/1.55 % (19808)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19448 for (2998ds/879Mi)
% 2.43/1.55 % (19809)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19448 for (2998ds/17Mi)
% 2.43/1.56 % (19809)Instruction limit reached!
% 2.43/1.56 % (19809)------------------------------
% 2.43/1.56 % (19809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.56 % (19809)Termination reason: Unknown
% 2.43/1.56 % (19809)Termination phase: shuffling
% 2.43/1.56
% 2.43/1.56 % (19809)Memory used [KB]: 1535
% 2.43/1.56 % (19809)Time elapsed: 0.007 s
% 2.43/1.56 % (19809)Instructions burned: 18 (million)
% 2.43/1.56 % (19809)------------------------------
% 2.43/1.56 % (19809)------------------------------
% 2.43/1.56 % (19810)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19448 for (2998ds/3Mi)
% 2.43/1.56 % (19810)Instruction limit reached!
% 2.43/1.56 % (19810)------------------------------
% 2.43/1.56 % (19810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.56 % (19810)Termination reason: Unknown
% 2.43/1.56 % (19810)Termination phase: shuffling
% 2.43/1.56
% 2.43/1.56 % (19810)Memory used [KB]: 1279
% 2.43/1.56 % (19810)Time elapsed: 0.003 s
% 2.43/1.56 % (19810)Instructions burned: 4 (million)
% 2.43/1.56 % (19810)------------------------------
% 2.43/1.56 % (19810)------------------------------
% 2.43/1.57 % (19811)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19448 for (2998ds/30Mi)
% 2.43/1.57 % (19812)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19448 for (2998ds/127Mi)
% 2.43/1.57 % (19811)Instruction limit reached!
% 2.43/1.57 % (19811)------------------------------
% 2.43/1.57 % (19811)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.57 % (19811)Termination reason: Unknown
% 2.43/1.57 % (19811)Termination phase: Property scanning
% 2.43/1.57
% 2.43/1.57 % (19811)Memory used [KB]: 1535
% 2.43/1.57 % (19811)Time elapsed: 0.011 s
% 2.43/1.57 % (19811)Instructions burned: 31 (million)
% 2.43/1.57 % (19811)------------------------------
% 2.43/1.57 % (19811)------------------------------
% 2.43/1.58 % (19813)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19448 for (2998ds/100Mi)
% 2.43/1.60 % (19812)Instruction limit reached!
% 2.43/1.60 % (19812)------------------------------
% 2.43/1.60 % (19812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.60 % (19812)Termination reason: Unknown
% 2.43/1.60 % (19812)Termination phase: Saturation
% 2.43/1.60
% 2.43/1.60 % (19812)Memory used [KB]: 6780
% 2.43/1.60 % (19812)Time elapsed: 0.039 s
% 2.43/1.60 % (19812)Instructions burned: 129 (million)
% 2.43/1.60 % (19812)------------------------------
% 2.43/1.60 % (19812)------------------------------
% 2.43/1.61 % (19814)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_19448 for (2998ds/3Mi)
% 2.43/1.61 % (19813)Instruction limit reached!
% 2.43/1.61 % (19813)------------------------------
% 2.43/1.61 % (19813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.61 % (19813)Termination reason: Unknown
% 2.43/1.61 % (19813)Termination phase: Saturation
% 2.43/1.61
% 2.43/1.61 % (19813)Memory used [KB]: 6396
% 2.43/1.61 % (19813)Time elapsed: 0.032 s
% 2.43/1.61 % (19813)Instructions burned: 102 (million)
% 2.43/1.61 % (19813)------------------------------
% 2.43/1.61 % (19813)------------------------------
% 2.43/1.62 % (19814)Instruction limit reached!
% 2.43/1.62 % (19814)------------------------------
% 2.43/1.62 % (19814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.62 % (19814)Termination reason: Unknown
% 2.43/1.62 % (19814)Termination phase: shuffling
% 2.43/1.62
% 2.43/1.62 % (19814)Memory used [KB]: 1279
% 2.43/1.62 % (19814)Time elapsed: 0.002 s
% 2.43/1.62 % (19814)Instructions burned: 4 (million)
% 2.43/1.62 % (19814)------------------------------
% 2.43/1.62 % (19814)------------------------------
% 2.43/1.63 % (19815)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_19448 for (2998ds/20Mi)
% 2.43/1.63 % (19816)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_19448 for (2998ds/86Mi)
% 2.43/1.63 % (19815)Instruction limit reached!
% 2.43/1.63 % (19815)------------------------------
% 2.43/1.63 % (19815)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.63 % (19815)Termination reason: Unknown
% 2.43/1.63 % (19815)Termination phase: SInE selection
% 2.43/1.63
% 2.43/1.63 % (19815)Memory used [KB]: 1407
% 2.43/1.63 % (19815)Time elapsed: 0.008 s
% 2.43/1.63 % (19815)Instructions burned: 20 (million)
% 2.43/1.63 % (19815)------------------------------
% 2.43/1.63 % (19815)------------------------------
% 2.43/1.64 % (19817)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_19448 for (2997ds/107Mi)
% 2.43/1.65 % (19805)Instruction limit reached!
% 2.43/1.65 % (19805)------------------------------
% 2.43/1.65 % (19805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.65 % (19805)Termination reason: Unknown
% 2.43/1.65 % (19805)Termination phase: Saturation
% 2.43/1.65
% 2.43/1.65 % (19805)Memory used [KB]: 7291
% 2.43/1.65 % (19805)Time elapsed: 0.115 s
% 2.43/1.65 % (19805)Instructions burned: 377 (million)
% 2.43/1.65 % (19805)------------------------------
% 2.43/1.65 % (19805)------------------------------
% 2.43/1.65 % (19816)Instruction limit reached!
% 2.43/1.65 % (19816)------------------------------
% 2.43/1.65 % (19816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.65 % (19816)Termination reason: Unknown
% 2.43/1.65 % (19816)Termination phase: Saturation
% 2.43/1.65
% 2.43/1.65 % (19816)Memory used [KB]: 6268
% 2.43/1.65 % (19816)Time elapsed: 0.026 s
% 2.43/1.65 % (19816)Instructions burned: 86 (million)
% 2.43/1.65 % (19816)------------------------------
% 2.43/1.65 % (19816)------------------------------
% 2.43/1.66 % (19818)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_19448 for (2997ds/39Mi)
% 2.43/1.66 % (19819)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_19448 for (2997ds/448Mi)
% 2.43/1.67 % (19818)Instruction limit reached!
% 2.43/1.67 % (19818)------------------------------
% 2.43/1.67 % (19818)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.67 % (19818)Termination reason: Unknown
% 2.43/1.67 % (19818)Termination phase: Property scanning
% 2.43/1.67
% 2.43/1.67 % (19818)Memory used [KB]: 1663
% 2.43/1.67 % (19818)Time elapsed: 0.011 s
% 2.43/1.67 % (19818)Instructions burned: 39 (million)
% 2.43/1.67 % (19818)------------------------------
% 2.43/1.67 % (19818)------------------------------
% 2.43/1.67 % (19817)Instruction limit reached!
% 2.43/1.67 % (19817)------------------------------
% 2.43/1.67 % (19817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.67 % (19817)Termination reason: Unknown
% 2.43/1.67 % (19817)Termination phase: Saturation
% 2.43/1.67
% 2.43/1.67 % (19817)Memory used [KB]: 6652
% 2.43/1.67 % (19817)Time elapsed: 0.033 s
% 2.43/1.67 % (19817)Instructions burned: 109 (million)
% 2.43/1.67 % (19817)------------------------------
% 2.43/1.67 % (19817)------------------------------
% 2.43/1.68 % (19820)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_19448 for (2997ds/46Mi)
% 2.43/1.68 % (19821)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_19448 for (2997ds/98Mi)
% 2.43/1.69 % (19808)First to succeed.
% 2.43/1.69 % (19820)Instruction limit reached!
% 2.43/1.69 % (19820)------------------------------
% 2.43/1.69 % (19820)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.69 % (19820)Termination reason: Unknown
% 2.43/1.69 % (19820)Termination phase: Property scanning
% 2.43/1.69
% 2.43/1.69 % (19820)Memory used [KB]: 1535
% 2.43/1.69 % (19820)Time elapsed: 0.013 s
% 2.43/1.69 % (19820)Instructions burned: 46 (million)
% 2.43/1.69 % (19820)------------------------------
% 2.43/1.69 % (19820)------------------------------
% 2.43/1.69 % (19808)Refutation found. Thanks to Tanya!
% 2.43/1.69 % SZS status Theorem for DTF2THF_19448
% 2.43/1.69 % SZS output start Proof for DTF2THF_19448
% 2.43/1.69 thf(func_def_0, type, in: $i > $i > $o).
% 2.43/1.69 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.43/1.69 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.43/1.69 thf(func_def_8, type, powerset: $i > $i).
% 2.43/1.69 thf(func_def_10, type, setunion: $i > $i).
% 2.43/1.69 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.43/1.69 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_26, type, prop2set: $o > $i).
% 2.43/1.69 thf(func_def_36, type, nonempty: $i > $o).
% 2.43/1.69 thf(func_def_69, type, set2prop: $i > $o).
% 2.43/1.69 thf(func_def_88, type, subset: $i > $i > $o).
% 2.43/1.69 thf(func_def_89, type, disjoint: $i > $i > $o).
% 2.43/1.69 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 2.43/1.69 thf(func_def_114, type, binunion: $i > $i > $i).
% 2.43/1.69 thf(func_def_122, type, binintersect: $i > $i > $i).
% 2.43/1.69 thf(func_def_135, type, regular: $i > $o).
% 2.43/1.69 thf(func_def_136, type, setminus: $i > $i > $i).
% 2.43/1.69 thf(func_def_159, type, sK4: ($i > $o) > $i).
% 2.43/1.69 thf(func_def_160, type, sK5: $i > $i > $i).
% 2.43/1.69 thf(func_def_161, type, sK6: $i > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_162, type, sK7: ($i > $o) > $i).
% 2.43/1.69 thf(func_def_163, type, sK8: ($i > $o) > $i).
% 2.43/1.69 thf(func_def_164, type, sK9: $i > $i).
% 2.43/1.69 thf(func_def_165, type, sK10: $i > $i > $i).
% 2.43/1.69 thf(func_def_166, type, sK11: ($i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_167, type, sK12: ($i > $o) > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_168, type, sK13: ($i > $o) > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_169, type, sK14: ($i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_170, type, sK15: ($i > $o) > $i).
% 2.43/1.69 thf(func_def_171, type, sK16: $i > $i).
% 2.43/1.69 thf(func_def_172, type, sK17: $i > $i > $i).
% 2.43/1.69 thf(func_def_173, type, sK18: $i > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_174, type, sK19: $i > $i > $i).
% 2.43/1.69 thf(func_def_175, type, sK20: ($i > $o) > $i).
% 2.43/1.69 thf(func_def_176, type, sK21: $i > $i > $i).
% 2.43/1.69 thf(func_def_177, type, sK22: ($i > $i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_178, type, sK23: ($i > $i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_179, type, sK24: $i > ($i > $i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_180, type, sK25: ($i > $i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_181, type, sK26: $i > ($i > $i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_182, type, sK27: $i > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_183, type, sK28: $i > $i > $i).
% 2.43/1.69 thf(func_def_184, type, sK29: $i > $i > $i).
% 2.43/1.69 thf(func_def_185, type, sK30: $i > $i).
% 2.43/1.69 thf(func_def_186, type, sK31: ($i > $o) > $i > ($i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_187, type, sK32: $i > $i > ($i > $o) > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_188, type, sK33: ($i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_189, type, sK34: ($i > $o) > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_190, type, sK35: ($i > $o) > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_191, type, sK36: ($i > $o) > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_192, type, sK37: ($i > $o) > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_193, type, sK38: $i > ($i > $o) > $i).
% 2.43/1.69 thf(func_def_194, type, sK39: $i > $i > $o > $i).
% 2.43/1.69 thf(func_def_195, type, sK40: $i > $i).
% 2.43/1.69 thf(func_def_196, type, sK41: $i > $i > $i).
% 2.43/1.69 thf(func_def_197, type, sK42: $i > $i > $i).
% 2.43/1.69 thf(func_def_198, type, sK43: $i > $i > $i).
% 2.43/1.69 thf(func_def_199, type, sK44: $i > $i > $i > $i).
% 2.43/1.69 thf(func_def_200, type, sK45: $i > $i).
% 2.43/1.69 thf(func_def_201, type, sK46: ($i > $o) > $i > $i).
% 2.43/1.69 thf(func_def_202, type, sK47: $i > $i).
% 2.43/1.69 thf(func_def_203, type, sK48: $i > $i > $i).
% 2.43/1.69 thf(func_def_204, type, sK49: $i > $i > $i).
% 2.43/1.69 thf(func_def_205, type, sK50: $i > $i > $i).
% 2.43/1.69 thf(func_def_206, type, sK51: $i > $i).
% 2.43/1.69 thf(func_def_207, type, ph52: !>[X0: $tType]:(X0)).
% 2.43/1.69 thf(f3182,plain,(
% 2.43/1.69 $false),
% 2.43/1.69 inference(trivial_inequality_removal,[status(thm)],[f3181])).
% 2.43/1.69 thf(f3181,plain,(
% 2.43/1.69 ($true = $false)),
% 2.43/1.69 inference(backward_demodulation,[status(thm)],[f440,f3180])).
% 2.43/1.69 thf(f3180,plain,(
% 2.43/1.69 ((in @ sK2 @ sK0) = $false)),
% 2.43/1.69 inference(not_proxy_clausification,[status(thm)],[f3179])).
% 2.43/1.69 thf(f3179,plain,(
% 2.43/1.69 ($true = (~ (in @ sK2 @ sK0)))),
% 2.43/1.69 inference(beta_eta_normalization,[status(thm)],[f3178])).
% 2.43/1.69 thf(f3178,plain,(
% 2.43/1.69 ($true = ((^[Y0 : $i]: (~ (in @ Y0 @ sK0))) @ sK2))),
% 2.43/1.69 inference(trivial_inequality_removal,[status(thm)],[f3164])).
% 2.43/1.69 thf(f3164,plain,(
% 2.43/1.69 ($true = ((^[Y0 : $i]: (~ (in @ Y0 @ sK0))) @ sK2)) | ($true = $false)),
% 2.43/1.69 inference(superposition,[status(thm)],[f1191,f920])).
% 2.43/1.69 thf(f920,plain,(
% 2.43/1.69 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (((in @ X2 @ (dsetconstr @ X1 @ X3)) = $false) | ($true = (X3 @ X2))) )),
% 2.43/1.69 inference(binary_proxy_clausification,[status(thm)],[f919])).
% 2.43/1.69 thf(f919,plain,(
% 2.43/1.69 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((in @ X2 @ (dsetconstr @ X1 @ X3)) => (X3 @ X2)))) )),
% 2.43/1.69 inference(beta_eta_normalization,[status(thm)],[f918])).
% 2.43/1.69 thf(f918,plain,(
% 2.43/1.69 ( ! [X2 : $i,X3 : $i > $o,X1 : $i] : (($true = ((^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ X2))) @ X3))) )),
% 2.43/1.69 inference(pi_clausification,[status(thm)],[f917])).
% 2.43/1.69 thf(f917,plain,(
% 2.43/1.69 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ ($i > $o) @ (^[Y0 : $i > $o]: ((in @ X2 @ (dsetconstr @ X1 @ Y0)) => (Y0 @ X2)))))) )),
% 2.43/1.69 inference(beta_eta_normalization,[status(thm)],[f916])).
% 2.43/1.69 thf(f916,plain,(
% 2.43/1.69 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (Y1 @ Y0))))) @ X2))) )),
% 2.43/1.69 inference(pi_clausification,[status(thm)],[f915])).
% 2.43/1.69 thf(f915,plain,(
% 2.43/1.69 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ ($i > $o) @ (^[Y1 : $i > $o]: ((in @ Y0 @ (dsetconstr @ X1 @ Y1)) => (Y1 @ Y0)))))))) )),
% 2.43/1.69 inference(beta_eta_normalization,[status(thm)],[f914])).
% 2.43/1.69 thf(f914,plain,(
% 2.43/1.69 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1))))))) @ X1))) )),
% 2.43/1.69 inference(pi_clausification,[status(thm)],[f913])).
% 2.43/1.69 thf(f913,plain,(
% 2.43/1.69 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ Y2)) => (Y2 @ Y1)))))))))),
% 2.43/1.69 inference(beta_eta_normalization,[status(thm)],[f682])).
% 2.43/1.69 thf(f682,plain,(
% 2.43/1.69 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 2.43/1.69 inference(definition_unfolding,[status(thm)],[f561,f530])).
% 2.43/1.69 thf(f530,plain,(
% 2.43/1.69 (dsetconstrER = $true)),
% 2.43/1.69 inference(cnf_transformation,[status(thm)],[f370])).
% 2.43/1.69 thf(f370,plain,(
% 2.43/1.69 (powersetsubset = $true) & (binintersectSubset1 = $true) & (inCongP = $true) & (powersetE1 = $true) & (subsetI1 = $true) & (binintersectLsub = $true) & (notinemptyset = $true) & (subsetE = $true) & (binunionRsub = $true) & (quantDeMorgan3 = $true) & (upairsetIR = $true) & (dsetconstrER = $true) & (descr__Cong = $true) & (prop2setE = $true) & (binunionIL = $true) & (prop2setI = $true) & (binintersectEL = $true) & (emptysetAx = $true) & (uniqinunit = $true) & (subsetE2 = $true) & (dsetconstrI = $true) & (setminusEL = $true) & (notequalI1 = $true) & (omega__Cong = $true) & (binintersectSubset3 = $true) & (quantDeMorgan2 = $true) & (setadjoinIL = $true) & (subsetTrans = $true) & (subsetemptysetimpeq = $true) & (upairsetIL = $true) & (subsetI2 = $true) & (exuE1 = $true) & (setunionAx = $true) & (notsubsetI = $true) & (binunionLsub = $true) & (setadjoinSub2 = $true) & (quantDeMorgan1 = $true) & (exuE3u = $true) & (powersetAx = $true) & (exuI2 = $true) & (setadjoinSub = $true) & (setadjoinE = $true) & (nonemptyI1 = $true) & (singletonsswitch = $true) & (setunionE = $true) & (noeltsimpempty = $true) & (binunionEcases = $true) & (setunionI = $true) & (binintersectER = $true) & (sepSubset = $true) & (eqimpsubset2 = $true) & (upairsetE = $true) & (emptyInPowerset = $true) & (upairset2IR = $true) & (binintersectSubset4 = $true) & (disjointsetsI1 = $true) & (binintersectSubset5 = $true) & (setunion__Cong = $true) & (setadjoinOr = $true) & (setminusI = $true) & (setadjoin__Cong = $true) & (inPowerset = $true) & (prop2set2propI = $true) & (binunionIR = $true) & (binintersectRsub = $true) & (binunionE = $true) & (powersetI1 = $true) & (replAx = $true) & (setextsub = $true) & (subset2powerset = $true) & (binintersectSubset2 = $true) & (exu__Cong = $true) & (exuE3e = $true) & (eqimpsubset1 = $true) & (notdexE = $true) & (vacuousDall = $true) & (nonemptyI = $true) & (setext = $true) & (nonemptyImpWitness = $true) & (powersetE = $true) & (notequalI2 = $true) & (setadjoinIR = $true) & (omega0Ax = $true) & (setextAx = $true) & (foundationAx = $true) & (emptyI = $true) & (dsetconstr__Cong = $true) & (setbeta = $true) & (subPowSU = $true) & (eqinunit = $true) & (emptyE1 = $true) & (emptysetE = $true) & (emptysetimpfalse = $true) & (exuEu = $true) & (omegaSAx = $true) & (powersetI = $true) & (bs114d = $true) & (dsetconstrEL = $true) & (exuI1 = $true) & (descrp = $true) & (emptyset__Cong = $true) & (($true = (in @ sK2 @ sK0)) & ($true = (in @ sK2 @ (setminus @ sK1 @ sK0)))) & (wellorderingAx = $true) & (nonemptyE1 = $true) & (notinsingleton = $true) & (exuE2 = $true) & (quantDeMorgan4 = $true) & (subsetRefl = $true) & (emptyinunitempty = $true) & (sepInPowerset = $true) & (omegaIndAx = $true) & (emptysetsubset = $true) & (setoftrueEq = $true) & (exuI3 = $true) & (emptyinPowerset = $true) & (binintersectI = $true) & (in__Cong = $true) & (powerset__Cong = $true) & (notdallE = $true) & (setadjoinAx = $true)),
% 2.43/1.69 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f368,f369])).
% 2.43/1.69 thf(f369,plain,(
% 2.43/1.69 ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) => (($true = (in @ sK2 @ sK0)) & ($true = (in @ sK2 @ (setminus @ sK1 @ sK0))))),
% 2.43/1.69 introduced(definition,[],[choice_axiom])).
% 2.43/1.69 thf(f368,plain,(
% 2.43/1.69 (powersetsubset = $true) & (binintersectSubset1 = $true) & (inCongP = $true) & (powersetE1 = $true) & (subsetI1 = $true) & (binintersectLsub = $true) & (notinemptyset = $true) & (subsetE = $true) & (binunionRsub = $true) & (quantDeMorgan3 = $true) & (upairsetIR = $true) & (dsetconstrER = $true) & (descr__Cong = $true) & (prop2setE = $true) & (binunionIL = $true) & (prop2setI = $true) & (binintersectEL = $true) & (emptysetAx = $true) & (uniqinunit = $true) & (subsetE2 = $true) & (dsetconstrI = $true) & (setminusEL = $true) & (notequalI1 = $true) & (omega__Cong = $true) & (binintersectSubset3 = $true) & (quantDeMorgan2 = $true) & (setadjoinIL = $true) & (subsetTrans = $true) & (subsetemptysetimpeq = $true) & (upairsetIL = $true) & (subsetI2 = $true) & (exuE1 = $true) & (setunionAx = $true) & (notsubsetI = $true) & (binunionLsub = $true) & (setadjoinSub2 = $true) & (quantDeMorgan1 = $true) & (exuE3u = $true) & (powersetAx = $true) & (exuI2 = $true) & (setadjoinSub = $true) & (setadjoinE = $true) & (nonemptyI1 = $true) & (singletonsswitch = $true) & (setunionE = $true) & (noeltsimpempty = $true) & (binunionEcases = $true) & (setunionI = $true) & (binintersectER = $true) & (sepSubset = $true) & (eqimpsubset2 = $true) & (upairsetE = $true) & (emptyInPowerset = $true) & (upairset2IR = $true) & (binintersectSubset4 = $true) & (disjointsetsI1 = $true) & (binintersectSubset5 = $true) & (setunion__Cong = $true) & (setadjoinOr = $true) & (setminusI = $true) & (setadjoin__Cong = $true) & (inPowerset = $true) & (prop2set2propI = $true) & (binunionIR = $true) & (binintersectRsub = $true) & (binunionE = $true) & (powersetI1 = $true) & (replAx = $true) & (setextsub = $true) & (subset2powerset = $true) & (binintersectSubset2 = $true) & (exu__Cong = $true) & (exuE3e = $true) & (eqimpsubset1 = $true) & (notdexE = $true) & (vacuousDall = $true) & (nonemptyI = $true) & (setext = $true) & (nonemptyImpWitness = $true) & (powersetE = $true) & (notequalI2 = $true) & (setadjoinIR = $true) & (omega0Ax = $true) & (setextAx = $true) & (foundationAx = $true) & (emptyI = $true) & (dsetconstr__Cong = $true) & (setbeta = $true) & (subPowSU = $true) & (eqinunit = $true) & (emptyE1 = $true) & (emptysetE = $true) & (emptysetimpfalse = $true) & (exuEu = $true) & (omegaSAx = $true) & (powersetI = $true) & (bs114d = $true) & (dsetconstrEL = $true) & (exuI1 = $true) & (descrp = $true) & (emptyset__Cong = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) & (wellorderingAx = $true) & (nonemptyE1 = $true) & (notinsingleton = $true) & (exuE2 = $true) & (quantDeMorgan4 = $true) & (subsetRefl = $true) & (emptyinunitempty = $true) & (sepInPowerset = $true) & (omegaIndAx = $true) & (emptysetsubset = $true) & (setoftrueEq = $true) & (exuI3 = $true) & (emptyinPowerset = $true) & (binintersectI = $true) & (in__Cong = $true) & (powerset__Cong = $true) & (notdallE = $true) & (setadjoinAx = $true)),
% 2.43/1.69 inference(flattening,[status(thm)],[f367])).
% 2.43/1.69 thf(f367,plain,(
% 2.43/1.69 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ($true = (in @ X2 @ (setminus @ X1 @ X0)))) & (setminusEL = $true)) & (setminusI = $true)) & (bs114d = $true)) & (binintersectSubset1 = $true)) & (binintersectSubset4 = $true)) & (binintersectRsub = $true)) & (disjointsetsI1 = $true)) & (binintersectER = $true)) & (binintersectSubset3 = $true)) & (binintersectSubset2 = $true)) & (binintersectLsub = $true)) & (binintersectEL = $true)) & (binintersectSubset5 = $true)) & (binintersectI = $true)) & (binunionRsub = $true)) & (binunionLsub = $true)) & (binunionE = $true)) & (binunionEcases = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.43/1.69 inference(ennf_transformation,[status(thm)],[f366])).
% 2.43/1.69 thf(f366,plain,(
% 2.43/1.69 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ($true != (in @ X2 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.69 inference(flattening,[status(thm)],[f137])).
% 2.43/1.69 thf(f137,plain,(
% 2.43/1.69 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ((binunionEcases = $true) => ((binunionE = $true) => ((binunionLsub = $true) => ((binunionRsub = $true) => ((binintersectI = $true) => ((binintersectSubset5 = $true) => ((binintersectEL = $true) => ((binintersectLsub = $true) => ((binintersectSubset2 = $true) => ((binintersectSubset3 = $true) => ((binintersectER = $true) => ((disjointsetsI1 = $true) => ((binintersectRsub = $true) => ((binintersectSubset4 = $true) => ((binintersectSubset1 = $true) => ((bs114d = $true) => ((setminusI = $true) => ((setminusEL = $true) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ (setminus @ X1 @ X0))) => ~($true = (in @ X2 @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.69 inference(fool_elimination,[status(thm)],[f136])).
% 2.43/1.69 thf(f136,plain,(
% 2.43/1.69 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setminus @ X1 @ X0)) => ~(in @ X2 @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.69 inference(rectify,[status(thm)],[f124])).
% 2.43/1.69 thf(f124,negated_conjecture,(
% 2.43/1.69 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.69 inference(negated_conjecture,[status(cth)],[f123])).
% 2.43/1.69 thf(f123,conjecture,(
% 2.43/1.69 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => (binunionEcases => (binunionE => (binunionLsub => (binunionRsub => (binintersectI => (binintersectSubset5 => (binintersectEL => (binintersectLsub => (binintersectSubset2 => (binintersectSubset3 => (binintersectER => (disjointsetsI1 => (binintersectRsub => (binintersectSubset4 => (binintersectSubset1 => (bs114d => (setminusI => (setminusEL => ! [X4 : $i,X3 : $i,X1 : $i] : ((in @ X1 @ (setminus @ X3 @ X4)) => ~(in @ X1 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.43/1.69 file('/export/starexec/sandbox/tmp/tmp.Ji351ajFME/DTF2THF_19448.p',setminusER)).
% 2.43/1.69 thf(f561,plain,(
% 2.43/1.69 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 2.43/1.69 inference(cnf_transformation,[status(thm)],[f333])).
% 2.43/1.69 thf(f333,plain,(
% 2.43/1.69 (dsetconstrER = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ ($i > $o) @ (^[Y2 : $i > $o]: ((in @ Y1 @ (dsetconstr @ Y0 @ (^[Y3 : $i]: (Y2 @ Y3)))) => (Y2 @ Y1)))))))))),
% 2.43/1.69 inference(fool_elimination,[status(thm)],[f332])).
% 2.43/1.69 thf(f332,plain,(
% 2.43/1.69 (! [X0 : $i > $o,X1 : $i,X2 : $i] : ((in @ X1 @ (dsetconstr @ X2 @ (^[X3 : $i] : (X0 @ X3)))) => (X0 @ X1)) = dsetconstrER)),
% 2.43/1.69 inference(rectify,[status(thm)],[f16])).
% 2.43/1.69 thf(f16,axiom,(
% 2.43/1.69 (! [X0 : $i > $o,X1 : $i,X3 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)),
% 2.43/1.69 file('/export/starexec/sandbox/tmp/tmp.Ji351ajFME/DTF2THF_19448.p',dsetconstrER)).
% 2.43/1.69 thf(f1191,plain,(
% 2.43/1.69 ($true = (in @ sK2 @ (dsetconstr @ sK1 @ (^[Y0 : $i]: (~ (in @ Y0 @ sK0))))))),
% 2.43/1.69 inference(beta_eta_normalization,[status(thm)],[f653])).
% 2.43/1.69 thf(f653,plain,(
% 2.43/1.69 ($true = (in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))) @ sK1 @ sK0)))),
% 2.43/1.69 inference(definition_unfolding,[status(thm)],[f439,f571])).
% 2.43/1.69 thf(f571,plain,(
% 2.43/1.69 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 2.43/1.69 inference(cnf_transformation,[status(thm)],[f203])).
% 2.43/1.69 thf(f203,plain,(
% 2.43/1.69 (setminus = (^[Y0 : $i]: ((^[Y1 : $i]: (dsetconstr @ Y0 @ (^[Y2 : $i]: (~ (in @ Y2 @ Y1))))))))),
% 2.43/1.69 inference(fool_elimination,[status(thm)],[f202])).
% 2.43/1.69 thf(f202,plain,(
% 2.43/1.69 (setminus = (^[X0 : $i, X1 : $i] : (dsetconstr @ X0 @ (^[X2 : $i] : (~(in @ X2 @ X1))))))),
% 2.43/1.69 inference(rectify,[status(thm)],[f120])).
% 2.43/1.69 thf(f120,axiom,(
% 2.43/1.69 (setminus = (^[X3 : $i, X4 : $i] : (dsetconstr @ X3 @ (^[X1 : $i] : (~(in @ X1 @ X4))))))),
% 2.43/1.69 file('/export/starexec/sandbox/tmp/tmp.Ji351ajFME/DTF2THF_19448.p',setminus)).
% 2.43/1.69 thf(f439,plain,(
% 2.43/1.69 ($true = (in @ sK2 @ (setminus @ sK1 @ sK0)))),
% 2.43/1.69 inference(cnf_transformation,[status(thm)],[f370])).
% 2.43/1.69 thf(f440,plain,(
% 2.43/1.69 ($true = (in @ sK2 @ sK0))),
% 2.43/1.69 inference(cnf_transformation,[status(thm)],[f370])).
% 2.43/1.69 % SZS output end Proof for DTF2THF_19448
% 2.43/1.69 % (19808)------------------------------
% 2.43/1.69 % (19808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.43/1.69 % (19808)Termination reason: Refutation
% 2.43/1.69
% 2.43/1.69 % (19808)Memory used [KB]: 7419
% 2.43/1.69 % (19808)Time elapsed: 0.165 s
% 2.43/1.69 % (19808)Instructions burned: 449 (million)
% 2.43/1.69 % (19808)------------------------------
% 2.43/1.69 % (19808)------------------------------
% 2.43/1.69 % (19778)Success in time 0.269 s
%------------------------------------------------------------------------------