%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU584^1 : 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 09:35:25 AM UTC 2026
% Result : Theorem 27.42s 5.39s
% Output : Refutation 27.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 5
% Syntax : Number of formulae : 46 ( 33 unt; 0 typ; 0 def)
% Number of atoms : 1761 ( 456 equ; 0 cnn)
% Maximal formula atoms : 102 ( 38 avg)
% Number of connectives : 1087 ( 12 ~; 7 |; 305 &; 312 @)
% ( 0 <=>; 428 =>; 0 <=; 0 <~>)
% Maximal formula depth : 109 ( 18 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 171 ( 167 usr; 107 con; 0-4 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 95 ( 38 ^; 48 !; 9 ?; 95 :)
% 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_138,type,
sK4: $i > $i ).
thf(func_def_139,type,
sK5: $i > $i ).
thf(func_def_140,type,
sK6: $i > $i > $i ).
thf(func_def_141,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_142,type,
sK8: $i > $i > $i ).
thf(func_def_143,type,
sK9: $i > $i > $i ).
thf(func_def_144,type,
sK10: $i > $i > $i ).
thf(func_def_145,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_146,type,
sK12: $i > $i ).
thf(func_def_147,type,
sK13: $i > $i > $i ).
thf(func_def_148,type,
sK14: $i > $i > $i ).
thf(func_def_149,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_150,type,
sK16: $i > $i ).
thf(func_def_151,type,
sK17: ( $i > $o ) > $i ).
thf(func_def_152,type,
sK18: $i > $i > $i ).
thf(func_def_153,type,
sK19: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_154,type,
sK20: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_155,type,
sK21: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_156,type,
sK22: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_157,type,
sK23: $i > $i > $i ).
thf(func_def_158,type,
sK24: ( $i > $o ) > $i ).
thf(func_def_159,type,
sK25: $i > $i ).
thf(func_def_160,type,
sK26: ( $i > $o ) > $i > $i ).
thf(func_def_161,type,
sK27: $i > $i > $i ).
thf(func_def_162,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_163,type,
sK29: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_164,type,
sK30: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_165,type,
sK31: $o > $i > $i > $i ).
thf(func_def_166,type,
sK32: $i > $i ).
thf(func_def_167,type,
sK33: $i > $i > $i > $i ).
thf(func_def_168,type,
sK34: $i > $i > $i ).
thf(func_def_169,type,
sK35: $i > $i > $i ).
thf(func_def_170,type,
sK36: $i > $i > $i ).
thf(func_def_171,type,
sK37: $i > $i > $i ).
thf(func_def_172,type,
sK38: $i > $i > $i ).
thf(func_def_173,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_174,type,
sK40: ( $i > $o ) > $i > $i ).
thf(func_def_175,type,
sK41: $i > $i ).
thf(func_def_176,type,
sK42: ( $i > $o ) > $i > $i ).
thf(func_def_177,type,
sK43: ( $i > $i > $o ) > $i > $i ).
thf(func_def_178,type,
sK44: ( $i > $i > $o ) > $i > $i ).
thf(func_def_179,type,
sK45: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_180,type,
sK46: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_181,type,
sK47: ( $i > $o ) > $i ).
thf(func_def_182,type,
sK48: ( $i > $o ) > $i ).
thf(func_def_183,type,
sK49: ( $i > $o ) > ( $i > $o ) > $i > $i > $i ).
thf(func_def_184,type,
sK50: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_185,type,
sK51: $i > ( $i > $o ) > $i ).
thf(func_def_186,type,
ph52:
!>[X0: $tType] : X0 ).
thf(f13197,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f13186]) ).
thf(f13186,plain,
$true = $false,
inference(superposition,[status(thm)],[f13184,f351]) ).
thf(f351,plain,
( $true
= ( in @ sK2 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f312]) ).
thf(f312,plain,
( ( exuE1 = $true )
& ( setoftrueEq = $true )
& ( subsetemptysetimpeq = $true )
& ( notdexE = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( emptyinPowerset = $true )
& ( subPowSU = $true )
& ( omega__Cong = $true )
& ( omegaIndAx = $true )
& ( subsetTrans = $true )
& ( setadjoinIR = $true )
& ( subsetI1 = $true )
& ( subsetRefl = $true )
& ( subset2powerset = $true )
& ( notequalI2 = $true )
& ( setunionI = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( descrp = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( descr__Cong = $true )
& ( noeltsimpempty = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetimpfalse = $true )
& ( upairsetIR = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstrER = $true )
& ( replAx = $true )
& ( upairsetE = $true )
& ( sepInPowerset = $true )
& ( exu__Cong = $true )
& ( exuI3 = $true )
& ( dsetconstr__Cong = $true )
& ( prop2set2propI = $true )
& ( powersetE = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( setbeta = $true )
& ( subsetI2 = $true )
& ( setext = $true )
& ( setunionAx = $true )
& ( uniqinunit = $true )
& ( exuE3u = $true )
& ( powersetE1 = $true )
& ( upairset2IR = $true )
& ( emptysetsubset = $true )
& ( vacuousDall = $true )
& ( singletonsswitch = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( eqimpsubset2 = $true )
& ( powersetI = $true )
& ( powerset__Cong = $true )
& ( emptysetE = $true )
& ( setadjoinOr = $true )
& ( powersetI1 = $true )
& ( nonemptyI = $true )
& ( notinemptyset = $true )
& ( setadjoinSub2 = $true )
& ( notsubsetI = $true )
& ( upairsetIL = $true )
& ( subsetE2 = $true )
& ( emptyinunitempty = $true )
& ( inPowerset = $true )
& ( prop2setI = $true )
& ( binunionIL = $true )
& ( wellorderingAx = $true )
& ( eqinunit = $true )
& ( exuE3e = $true )
& ( inCongP = $true )
& ( exuI1 = $true )
& ( exuE2 = $true )
& ( eqimpsubset1 = $true )
& ( prop2setE = $true )
& ( quantDeMorgan1 = $true )
& ( in__Cong = $true )
& ( setunionE = $true )
& ( powersetAx = $true )
& ( quantDeMorgan2 = $true )
& ( notinsingleton = $true )
& ( dsetconstrEL = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrI = $true )
& ( setadjoinSub = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( omegaSAx = $true )
& ( nonemptyE1 = $true )
& ( setunion__Cong = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( subsetE = $true )
& ( setadjoinAx = $true )
& ( foundationAx = $true )
& ( sepSubset = $true )
& ( notequalI1 = $true )
& ( $true
!= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ sK2 @ sK1 ) )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f310,f311]) ).
thf(f311,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
=> ( ( $true
!= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) )
& ( $true
= ( in @ sK2 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f310,plain,
( ( exuE1 = $true )
& ( setoftrueEq = $true )
& ( subsetemptysetimpeq = $true )
& ( notdexE = $true )
& ( setextsub = $true )
& ( emptyset__Cong = $true )
& ( emptyinPowerset = $true )
& ( subPowSU = $true )
& ( omega__Cong = $true )
& ( omegaIndAx = $true )
& ( subsetTrans = $true )
& ( setadjoinIR = $true )
& ( subsetI1 = $true )
& ( subsetRefl = $true )
& ( subset2powerset = $true )
& ( notequalI2 = $true )
& ( setunionI = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( descrp = $true )
& ( emptyInPowerset = $true )
& ( notdallE = $true )
& ( descr__Cong = $true )
& ( noeltsimpempty = $true )
& ( quantDeMorgan4 = $true )
& ( emptysetimpfalse = $true )
& ( upairsetIR = $true )
& ( setadjoin__Cong = $true )
& ( dsetconstrER = $true )
& ( replAx = $true )
& ( upairsetE = $true )
& ( sepInPowerset = $true )
& ( exu__Cong = $true )
& ( exuI3 = $true )
& ( dsetconstr__Cong = $true )
& ( prop2set2propI = $true )
& ( powersetE = $true )
& ( exuEu = $true )
& ( exuI2 = $true )
& ( setbeta = $true )
& ( subsetI2 = $true )
& ( setext = $true )
& ( setunionAx = $true )
& ( uniqinunit = $true )
& ( exuE3u = $true )
& ( powersetE1 = $true )
& ( upairset2IR = $true )
& ( emptysetsubset = $true )
& ( vacuousDall = $true )
& ( singletonsswitch = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( eqimpsubset2 = $true )
& ( powersetI = $true )
& ( powerset__Cong = $true )
& ( emptysetE = $true )
& ( setadjoinOr = $true )
& ( powersetI1 = $true )
& ( nonemptyI = $true )
& ( notinemptyset = $true )
& ( setadjoinSub2 = $true )
& ( notsubsetI = $true )
& ( upairsetIL = $true )
& ( subsetE2 = $true )
& ( emptyinunitempty = $true )
& ( inPowerset = $true )
& ( prop2setI = $true )
& ( binunionIL = $true )
& ( wellorderingAx = $true )
& ( eqinunit = $true )
& ( exuE3e = $true )
& ( inCongP = $true )
& ( exuI1 = $true )
& ( exuE2 = $true )
& ( eqimpsubset1 = $true )
& ( prop2setE = $true )
& ( quantDeMorgan1 = $true )
& ( in__Cong = $true )
& ( setunionE = $true )
& ( powersetAx = $true )
& ( quantDeMorgan2 = $true )
& ( notinsingleton = $true )
& ( dsetconstrEL = $true )
& ( quantDeMorgan3 = $true )
& ( dsetconstrI = $true )
& ( setadjoinSub = $true )
& ( emptysetAx = $true )
& ( emptyE1 = $true )
& ( omegaSAx = $true )
& ( nonemptyE1 = $true )
& ( setunion__Cong = $true )
& ( emptyI = $true )
& ( setadjoinIL = $true )
& ( subsetE = $true )
& ( setadjoinAx = $true )
& ( foundationAx = $true )
& ( sepSubset = $true )
& ( notequalI1 = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( powersetsubset = $true )
& ( nonemptyImpWitness = $true ) ),
inference(flattening,[status(thm)],[f309]) ).
thf(f309,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ ( binunion @ X0 @ X1 ) ) )
& ( $true
= ( in @ X2 @ X1 ) ) )
& ( 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)],[f120]) ).
thf(f120,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X1 ) )
=> ( $true
= ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f119]) ).
thf(f119,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X2 @ X1 )
=> ( in @ X2 @ ( binunion @ X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f105]) ).
thf(f105,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
=> ! [X3: $i,X4: $i,X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f104]) ).
thf(f104,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
=> ! [X3: $i,X4: $i,X1: $i] :
( ( in @ X1 @ X4 )
=> ( in @ X1 @ ( binunion @ X3 @ X4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2THF_17274.p',binunionIR) ).
thf(f13184,plain,
( $false
= ( in @ sK2 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f13175]) ).
thf(f13175,plain,
( ( $false
= ( in @ sK2 @ sK1 ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f5914,f1529]) ).
thf(f1529,plain,
! [X2: $i,X1: $i] :
( $true
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1528]) ).
thf(f1528,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f1527]) ).
thf(f1527,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1526]) ).
thf(f1526,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f571]) ).
thf(f571,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f469,f404]) ).
thf(f404,plain,
upairset2IR = $true,
inference(cnf_transformation,[status(thm)],[f312]) ).
thf(f469,plain,
( upairset2IR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f189]) ).
thf(f189,plain,
( upairset2IR
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] : ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y0 @ emptyset ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f188]) ).
thf(f188,plain,
! [X0: $i,X1: $i] :
( ( in @ X1 @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) )
= upairset2IR ),
inference(rectify,[status(thm)],[f103]) ).
thf(f103,axiom,
! [X1: $i,X2: $i] :
( ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
= upairset2IR ),
file('/export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2THF_17274.p',upairset2IR) ).
thf(f5914,plain,
! [X0: $i] :
( ( ( in @ X0 @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) )
= $false )
| ( ( in @ sK2 @ X0 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f5729]) ).
thf(f5729,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( in @ sK2 @ X0 )
= $false )
| ( ( in @ X0 @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) )
= $false ) ),
inference(superposition,[status(thm)],[f808,f923]) ).
thf(f923,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setunion @ X3 ) )
= $true )
| ( $false
= ( in @ X2 @ X1 ) )
| ( ( in @ X1 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f922]) ).
thf(f922,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X2 @ X1 ) )
| ( $true
= ( ( in @ X1 @ X3 )
=> ( in @ X2 @ ( setunion @ X3 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f921]) ).
thf(f921,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ X3 )
=> ( in @ X2 @ ( setunion @ X3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f920]) ).
thf(f920,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X2 @ ( setunion @ Y0 ) ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f919]) ).
thf(f919,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X2 @ X1 )
=> ( ( in @ X1 @ Y0 )
=> ( in @ X2 @ ( setunion @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f918]) ).
thf(f918,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f917]) ).
thf(f917,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y0 @ X1 )
=> ( ( in @ X1 @ Y1 )
=> ( in @ Y0 @ ( setunion @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f916]) ).
thf(f916,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y1 @ ( setunion @ Y2 ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f556]) ).
thf(f556,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y1 @ ( setunion @ Y2 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f454,f434]) ).
thf(f434,plain,
setunionI = $true,
inference(cnf_transformation,[status(thm)],[f312]) ).
thf(f454,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y1 @ ( setunion @ Y2 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f199]) ).
thf(f199,plain,
( setunionI
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y1 @ Y0 )
=> ( ( in @ Y0 @ Y2 )
=> ( in @ Y1 @ ( setunion @ Y2 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f198]) ).
thf(f198,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X1 @ X2 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X1 @ ( setunion @ X0 ) ) ) )
= setunionI ),
inference(rectify,[status(thm)],[f41]) ).
thf(f41,axiom,
! [X3: $i,X1: $i,X4: $i] :
( ( ( in @ X1 @ X4 )
=> ( ( in @ X4 @ X3 )
=> ( in @ X1 @ ( setunion @ X3 ) ) ) )
= setunionI ),
file('/export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2THF_17274.p',setunionI) ).
thf(f808,plain,
( ( in @ sK2 @ ( setunion @ ( setadjoin @ sK0 @ ( setadjoin @ sK1 @ emptyset ) ) ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f552]) ).
thf(f552,plain,
( $true
!= ( in @ sK2
@ ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
@ sK0
@ sK1 ) ) ),
inference(definition_unfolding,[status(thm)],[f352,f472]) ).
thf(f472,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f213]) ).
thf(f213,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f212]) ).
thf(f212,plain,
( ( ^ [X0: $i,X1: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) )
= binunion ),
inference(rectify,[status(thm)],[f101]) ).
thf(f101,axiom,
( ( ^ [X1: $i,X2: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) )
= binunion ),
file('/export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2THF_17274.p',binunion) ).
thf(f352,plain,
( $true
!= ( in @ sK2 @ ( binunion @ sK0 @ sK1 ) ) ),
inference(cnf_transformation,[status(thm)],[f312]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU584^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n001.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:28:20 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.21/0.48 ---- Original DTF file ---
% 0.21/0.48 thf(spec,logic,$$dhol).
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 % File : SEU584^1 : TPTP v9.2.1. Released v3.7.0.
% 0.21/0.48 % Domain : Set Theory
% 0.21/0.48 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.21/0.48 % Version : Especial.
% 0.21/0.48 % English : (! A:i.! B:i.! x:i.in x B -> in x (binunion A B))
% 0.21/0.48
% 0.21/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.21/0.48 % Source : [Bro08]
% 0.21/0.48 % Names : ZFC086g [Bro08]
% 0.21/0.48
% 0.21/0.48 % Status : Theorem
% 0.21/0.48 % Rating : 0.22 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.29 v6.1.0, 0.71 v6.0.0, 0.43 v5.5.0, 0.83 v5.4.0, 0.60 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.21/0.48 % Syntax : Number of formulae : 220 ( 103 unt; 116 typ; 103 def)
% 0.21/0.48 % Number of atoms : 550 ( 152 equ; 0 cnn)
% 0.21/0.48 % Maximal formula atoms : 102 ( 5 avg)
% 0.21/0.48 % Number of connectives : 865 ( 29 ~; 5 |; 27 &; 544 @)
% 0.21/0.48 % ( 14 <=>; 246 =>; 0 <=; 0 <~>)
% 0.21/0.48 % Maximal formula depth : 108 ( 2 avg)
% 0.21/0.48 % Number of types : 2 ( 0 usr)
% 0.21/0.48 % Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% 0.21/0.48 % Number of symbols : 119 ( 116 usr; 104 con; 0-2 aty)
% 0.21/0.48 % Number of variables : 304 ( 32 ^; 244 !; 28 ?; 304 :)
% 0.21/0.48 % SPC : TH0_THM_EQU_NAR
% 0.21/0.48
% 0.21/0.48 % Comments : http://mathgate.info/detsetitem.php?id=160
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 thf(in_type,type,
% 0.21/0.48 in: $i > $i > $o ).
% 0.21/0.48
% 0.21/0.48 thf(exu_type,type,
% 0.21/0.48 exu: ( $i > $o ) > $o ).
% 0.21/0.48
% 0.21/0.48 thf(exu,definition,
% 0.21/0.48 ( exu
% 0.21/0.48 = ( ^ [Xphi: $i > $o] :
% 0.21/0.48 ? [Xx: $i] :
% 0.21/0.48 ( ( Xphi @ Xx )
% 0.21/0.48 & ! [Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xy )
% 0.21/0.48 => ( Xx = Xy ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setextAx_type,type,
% 0.21/0.48 setextAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setextAx,definition,
% 0.21/0.48 ( setextAx
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 <=> ( in @ Xx @ B ) )
% 0.21/0.48 => ( A = B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptyset_type,type,
% 0.21/0.48 emptyset: $i ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetAx_type,type,
% 0.21/0.48 emptysetAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetAx,definition,
% 0.21/0.48 ( emptysetAx
% 0.21/0.48 = ( ! [Xx: $i] :
% 0.21/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoin_type,type,
% 0.21/0.48 setadjoin: $i > $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinAx_type,type,
% 0.21/0.48 setadjoinAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinAx,definition,
% 0.21/0.48 ( setadjoinAx
% 0.21/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.48 <=> ( ( Xy = Xx )
% 0.21/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(powerset_type,type,
% 0.21/0.48 powerset: $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(powersetAx_type,type,
% 0.21/0.48 powersetAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(powersetAx,definition,
% 0.21/0.48 ( powersetAx
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.48 <=> ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setunion_type,type,
% 0.21/0.48 setunion: $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(setunionAx_type,type,
% 0.21/0.48 setunionAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setunionAx,definition,
% 0.21/0.48 ( setunionAx
% 0.21/0.48 = ( ! [A: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.48 <=> ? [B: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 & ( in @ B @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(omega_type,type,
% 0.21/0.48 omega: $i ).
% 0.21/0.48
% 0.21/0.48 thf(omega0Ax_type,type,
% 0.21/0.48 omega0Ax: $o ).
% 0.21/0.48
% 0.21/0.48 thf(omega0Ax,definition,
% 0.21/0.48 ( omega0Ax
% 0.21/0.48 = ( in @ emptyset @ omega ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(omegaSAx_type,type,
% 0.21/0.48 omegaSAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(omegaSAx,definition,
% 0.21/0.48 ( omegaSAx
% 0.21/0.48 = ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ omega )
% 0.21/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(omegaIndAx_type,type,
% 0.21/0.48 omegaIndAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(omegaIndAx,definition,
% 0.21/0.48 ( omegaIndAx
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ( ( in @ emptyset @ A )
% 0.21/0.48 & ! [Xx: $i] :
% 0.21/0.48 ( ( ( in @ Xx @ omega )
% 0.21/0.48 & ( in @ Xx @ A ) )
% 0.21/0.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ omega )
% 0.21/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(replAx_type,type,
% 0.21/0.48 replAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(replAx,definition,
% 0.21/0.48 ( replAx
% 0.21/0.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( exu
% 0.21/0.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.21/0.48 => ? [B: $i] :
% 0.21/0.48 ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 <=> ? [Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ A )
% 0.21/0.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(foundationAx_type,type,
% 0.21/0.48 foundationAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(foundationAx,definition,
% 0.21/0.48 ( foundationAx
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.21/0.48 => ? [B: $i] :
% 0.21/0.48 ( ( in @ B @ A )
% 0.21/0.48 & ~ ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(wellorderingAx_type,type,
% 0.21/0.48 wellorderingAx: $o ).
% 0.21/0.48
% 0.21/0.48 thf(wellorderingAx,definition,
% 0.21/0.48 ( wellorderingAx
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ? [B: $i] :
% 0.21/0.48 ( ! [C: $i] :
% 0.21/0.48 ( ( in @ C @ B )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ C )
% 0.21/0.48 => ( in @ Xx @ A ) ) )
% 0.21/0.48 & ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( ( in @ Xx @ A )
% 0.21/0.48 & ( in @ Xy @ A ) )
% 0.21/0.48 => ( ! [C: $i] :
% 0.21/0.48 ( ( in @ C @ B )
% 0.21/0.48 => ( ( in @ Xx @ C )
% 0.21/0.48 <=> ( in @ Xy @ C ) ) )
% 0.21/0.48 => ( Xx = Xy ) ) )
% 0.21/0.48 & ! [C: $i,D: $i] :
% 0.21/0.48 ( ( ( in @ C @ B )
% 0.21/0.48 & ( in @ D @ B ) )
% 0.21/0.48 => ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ C )
% 0.21/0.48 => ( in @ Xx @ D ) )
% 0.21/0.48 | ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ D )
% 0.21/0.48 => ( in @ Xx @ C ) ) ) )
% 0.21/0.48 & ! [C: $i] :
% 0.21/0.48 ( ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ C )
% 0.21/0.48 => ( in @ Xx @ A ) )
% 0.21/0.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.21/0.48 => ? [D: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ D @ B )
% 0.21/0.48 & ( in @ Xx @ C )
% 0.21/0.48 & ~ ? [Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ D )
% 0.21/0.48 & ( in @ Xy @ C ) )
% 0.21/0.48 & ! [E: $i] :
% 0.21/0.48 ( ( in @ E @ B )
% 0.21/0.48 => ( ! [Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ E )
% 0.21/0.48 => ( in @ Xy @ D ) )
% 0.21/0.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(descr_type,type,
% 0.21/0.48 descr: ( $i > $o ) > $i ).
% 0.21/0.48
% 0.21/0.48 thf(descrp_type,type,
% 0.21/0.48 descrp: $o ).
% 0.21/0.48
% 0.21/0.48 thf(descrp,definition,
% 0.21/0.48 ( descrp
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 => ( Xphi
% 0.21/0.48 @ ( descr
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstr_type,type,
% 0.21/0.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstrI_type,type,
% 0.21/0.48 dsetconstrI: $o ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstrI,definition,
% 0.21/0.48 ( dsetconstrI
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( ( Xphi @ Xx )
% 0.21/0.48 => ( in @ Xx
% 0.21/0.48 @ ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstrEL_type,type,
% 0.21/0.48 dsetconstrEL: $o ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstrEL,definition,
% 0.21/0.48 ( dsetconstrEL
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx
% 0.21/0.48 @ ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.48 => ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstrER_type,type,
% 0.21/0.48 dsetconstrER: $o ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstrER,definition,
% 0.21/0.48 ( dsetconstrER
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx
% 0.21/0.48 @ ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exuE1_type,type,
% 0.21/0.48 exuE1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exuE1,definition,
% 0.21/0.48 ( exuE1
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 => ? [Xx: $i] :
% 0.21/0.48 ( ( Xphi @ Xx )
% 0.21/0.48 & ! [Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xy )
% 0.21/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(prop2set_type,type,
% 0.21/0.48 prop2set: $o > $i ).
% 0.21/0.48
% 0.21/0.48 thf(prop2setE_type,type,
% 0.21/0.48 prop2setE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(prop2setE,definition,
% 0.21/0.48 ( prop2setE
% 0.21/0.48 = ( ! [Xphi: $o,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.21/0.48 => Xphi ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetE_type,type,
% 0.21/0.48 emptysetE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetE,definition,
% 0.21/0.48 ( emptysetE
% 0.21/0.48 = ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ emptyset )
% 0.21/0.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetimpfalse_type,type,
% 0.21/0.48 emptysetimpfalse: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetimpfalse,definition,
% 0.21/0.48 ( emptysetimpfalse
% 0.21/0.48 = ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ emptyset )
% 0.21/0.48 => $false ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(notinemptyset_type,type,
% 0.21/0.48 notinemptyset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(notinemptyset,definition,
% 0.21/0.48 ( notinemptyset
% 0.21/0.48 = ( ! [Xx: $i] :
% 0.21/0.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exuE3e_type,type,
% 0.21/0.48 exuE3e: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exuE3e,definition,
% 0.21/0.48 ( exuE3e
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setext_type,type,
% 0.21/0.48 setext: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setext,definition,
% 0.21/0.48 ( setext
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( in @ Xx @ B ) )
% 0.21/0.48 => ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 => ( in @ Xx @ A ) )
% 0.21/0.48 => ( A = B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptyI_type,type,
% 0.21/0.48 emptyI: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptyI,definition,
% 0.21/0.48 ( emptyI
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ~ ( in @ Xx @ A )
% 0.21/0.48 => ( A = emptyset ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(noeltsimpempty_type,type,
% 0.21/0.48 noeltsimpempty: $o ).
% 0.21/0.48
% 0.21/0.48 thf(noeltsimpempty,definition,
% 0.21/0.48 ( noeltsimpempty
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ~ ( in @ Xx @ A )
% 0.21/0.48 => ( A = emptyset ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setbeta_type,type,
% 0.21/0.48 setbeta: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setbeta,definition,
% 0.21/0.48 ( setbeta
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( ( in @ Xx
% 0.21/0.48 @ ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.21/0.48 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(nonempty_type,type,
% 0.21/0.48 nonempty: $i > $o ).
% 0.21/0.48
% 0.21/0.48 thf(nonempty,definition,
% 0.21/0.48 ( nonempty
% 0.21/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(nonemptyE1_type,type,
% 0.21/0.48 nonemptyE1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(nonemptyE1,definition,
% 0.21/0.48 ( nonemptyE1
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ( nonempty @ A )
% 0.21/0.48 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(nonemptyI_type,type,
% 0.21/0.48 nonemptyI: $o ).
% 0.21/0.48
% 0.21/0.48 thf(nonemptyI,definition,
% 0.21/0.48 ( nonemptyI
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( ( Xphi @ Xx )
% 0.21/0.48 => ( nonempty
% 0.21/0.48 @ ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(nonemptyI1_type,type,
% 0.21/0.48 nonemptyI1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(nonemptyI1,definition,
% 0.21/0.48 ( nonemptyI1
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.21/0.48 => ( nonempty @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinIL_type,type,
% 0.21/0.48 setadjoinIL: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinIL,definition,
% 0.21/0.48 ( setadjoinIL
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptyinunitempty_type,type,
% 0.21/0.48 emptyinunitempty: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptyinunitempty,definition,
% 0.21/0.48 ( emptyinunitempty
% 0.21/0.48 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinIR_type,type,
% 0.21/0.48 setadjoinIR: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinIR,definition,
% 0.21/0.48 ( setadjoinIR
% 0.21/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ A )
% 0.21/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinE_type,type,
% 0.21/0.48 setadjoinE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinE,definition,
% 0.21/0.48 ( setadjoinE
% 0.21/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.48 => ! [Xphi: $o] :
% 0.21/0.48 ( ( ( Xy = Xx )
% 0.21/0.48 => Xphi )
% 0.21/0.48 => ( ( ( in @ Xy @ A )
% 0.21/0.48 => Xphi )
% 0.21/0.48 => Xphi ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinOr_type,type,
% 0.21/0.48 setadjoinOr: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinOr,definition,
% 0.21/0.48 ( setadjoinOr
% 0.21/0.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.21/0.48 => ( ( Xy = Xx )
% 0.21/0.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setoftrueEq_type,type,
% 0.21/0.48 setoftrueEq: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setoftrueEq,definition,
% 0.21/0.48 ( setoftrueEq
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xx: $i] : $true )
% 0.21/0.48 = A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(powersetI_type,type,
% 0.21/0.48 powersetI: $o ).
% 0.21/0.48
% 0.21/0.48 thf(powersetI,definition,
% 0.21/0.48 ( powersetI
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 => ( in @ Xx @ A ) )
% 0.21/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptyinPowerset_type,type,
% 0.21/0.48 emptyinPowerset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptyinPowerset,definition,
% 0.21/0.48 ( emptyinPowerset
% 0.21/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptyInPowerset_type,type,
% 0.21/0.48 emptyInPowerset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptyInPowerset,definition,
% 0.21/0.48 ( emptyInPowerset
% 0.21/0.48 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(powersetE_type,type,
% 0.21/0.48 powersetE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(powersetE,definition,
% 0.21/0.48 ( powersetE
% 0.21/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.48 => ( ( in @ Xx @ B )
% 0.21/0.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setunionI_type,type,
% 0.21/0.48 setunionI: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setunionI,definition,
% 0.21/0.48 ( setunionI
% 0.21/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 => ( ( in @ B @ A )
% 0.21/0.48 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setunionE_type,type,
% 0.21/0.48 setunionE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setunionE,definition,
% 0.21/0.48 ( setunionE
% 0.21/0.48 = ( ! [A: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ ( setunion @ A ) )
% 0.21/0.48 => ! [Xphi: $o] :
% 0.21/0.48 ( ! [B: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 => ( ( in @ B @ A )
% 0.21/0.48 => Xphi ) )
% 0.21/0.48 => Xphi ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subPowSU_type,type,
% 0.21/0.48 subPowSU: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subPowSU,definition,
% 0.21/0.48 ( subPowSU
% 0.21/0.48 = ( ! [A: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exuE2_type,type,
% 0.21/0.48 exuE2: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exuE2,definition,
% 0.21/0.48 ( exuE2
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 => ? [Xx: $i] :
% 0.21/0.48 ! [Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xy )
% 0.21/0.48 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(nonemptyImpWitness_type,type,
% 0.21/0.48 nonemptyImpWitness: $o ).
% 0.21/0.48
% 0.21/0.48 thf(nonemptyImpWitness,definition,
% 0.21/0.48 ( nonemptyImpWitness
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ( nonempty @ A )
% 0.21/0.48 => ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 & $true ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(uniqinunit_type,type,
% 0.21/0.48 uniqinunit: $o ).
% 0.21/0.48
% 0.21/0.48 thf(uniqinunit,definition,
% 0.21/0.48 ( uniqinunit
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.48 => ( Xx = Xy ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(notinsingleton_type,type,
% 0.21/0.48 notinsingleton: $o ).
% 0.21/0.48
% 0.21/0.48 thf(notinsingleton,definition,
% 0.21/0.48 ( notinsingleton
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xx != Xy )
% 0.21/0.48 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(eqinunit_type,type,
% 0.21/0.48 eqinunit: $o ).
% 0.21/0.48
% 0.21/0.48 thf(eqinunit,definition,
% 0.21/0.48 ( eqinunit
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xx = Xy )
% 0.21/0.48 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(singletonsswitch_type,type,
% 0.21/0.48 singletonsswitch: $o ).
% 0.21/0.48
% 0.21/0.48 thf(singletonsswitch,definition,
% 0.21/0.48 ( singletonsswitch
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.21/0.48 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(upairsetE_type,type,
% 0.21/0.48 upairsetE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(upairsetE,definition,
% 0.21/0.48 ( upairsetE
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.21/0.48 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.21/0.48 => ( ( Xz = Xx )
% 0.21/0.48 | ( Xz = Xy ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(upairsetIL_type,type,
% 0.21/0.48 upairsetIL: $o ).
% 0.21/0.48
% 0.21/0.48 thf(upairsetIL,definition,
% 0.21/0.48 ( upairsetIL
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(upairsetIR_type,type,
% 0.21/0.48 upairsetIR: $o ).
% 0.21/0.48
% 0.21/0.48 thf(upairsetIR,definition,
% 0.21/0.48 ( upairsetIR
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptyE1_type,type,
% 0.21/0.48 emptyE1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptyE1,definition,
% 0.21/0.48 ( emptyE1
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 & ( Xphi @ Xx ) )
% 0.21/0.48 => ( ( ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 = emptyset )
% 0.21/0.48 => $false ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(vacuousDall_type,type,
% 0.21/0.48 vacuousDall: $o ).
% 0.21/0.48
% 0.21/0.48 thf(vacuousDall,definition,
% 0.21/0.48 ( vacuousDall
% 0.21/0.48 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ emptyset )
% 0.21/0.48 => ( Xphi @ Xx ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(quantDeMorgan1_type,type,
% 0.21/0.48 quantDeMorgan1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(quantDeMorgan1,definition,
% 0.21/0.48 ( quantDeMorgan1
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( ~ ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( Xphi @ Xx ) )
% 0.21/0.48 => ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(quantDeMorgan2_type,type,
% 0.21/0.48 quantDeMorgan2: $o ).
% 0.21/0.48
% 0.21/0.48 thf(quantDeMorgan2,definition,
% 0.21/0.48 ( quantDeMorgan2
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ~ ( Xphi @ Xx ) )
% 0.21/0.48 => ~ ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(quantDeMorgan3_type,type,
% 0.21/0.48 quantDeMorgan3: $o ).
% 0.21/0.48
% 0.21/0.48 thf(quantDeMorgan3,definition,
% 0.21/0.48 ( quantDeMorgan3
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( ~ ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 & ( Xphi @ Xx ) )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(quantDeMorgan4_type,type,
% 0.21/0.48 quantDeMorgan4: $o ).
% 0.21/0.48
% 0.21/0.48 thf(quantDeMorgan4,definition,
% 0.21/0.48 ( quantDeMorgan4
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 & ~ ( Xphi @ Xx ) )
% 0.21/0.48 => ~ ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(prop2setI_type,type,
% 0.21/0.48 prop2setI: $o ).
% 0.21/0.48
% 0.21/0.48 thf(prop2setI,definition,
% 0.21/0.48 ( prop2setI
% 0.21/0.48 = ( ! [Xphi: $o] :
% 0.21/0.48 ( Xphi
% 0.21/0.48 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(set2prop_type,type,
% 0.21/0.48 set2prop: $i > $o ).
% 0.21/0.48
% 0.21/0.48 thf(prop2set2propI_type,type,
% 0.21/0.48 prop2set2propI: $o ).
% 0.21/0.48
% 0.21/0.48 thf(prop2set2propI,definition,
% 0.21/0.48 ( prop2set2propI
% 0.21/0.48 = ( ! [Xphi: $o] :
% 0.21/0.48 ( Xphi
% 0.21/0.48 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(notdexE_type,type,
% 0.21/0.48 notdexE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(notdexE,definition,
% 0.21/0.48 ( notdexE
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( ~ ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 & ( Xphi @ Xx ) )
% 0.21/0.48 => ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(notdallE_type,type,
% 0.21/0.48 notdallE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(notdallE,definition,
% 0.21/0.48 ( notdallE
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( ~ ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( Xphi @ Xx ) )
% 0.21/0.48 => ? [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exuI1_type,type,
% 0.21/0.48 exuI1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exuI1,definition,
% 0.21/0.48 ( exuI1
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ? [Xx: $i] :
% 0.21/0.48 ( ( Xphi @ Xx )
% 0.21/0.48 & ! [Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xy )
% 0.21/0.48 => ( Xx = Xy ) ) )
% 0.21/0.48 => ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exuI3_type,type,
% 0.21/0.48 exuI3: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exuI3,definition,
% 0.21/0.48 ( exuI3
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.21/0.48 => ( ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xx )
% 0.21/0.48 => ( ( Xphi @ Xy )
% 0.21/0.48 => ( Xx = Xy ) ) )
% 0.21/0.48 => ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exuI2_type,type,
% 0.21/0.48 exuI2: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exuI2,definition,
% 0.21/0.48 ( exuI2
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ? [Xx: $i] :
% 0.21/0.48 ! [Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xy )
% 0.21/0.48 <=> ( Xy = Xx ) )
% 0.21/0.48 => ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(inCongP_type,type,
% 0.21/0.48 inCongP: $o ).
% 0.21/0.48
% 0.21/0.48 thf(inCongP,definition,
% 0.21/0.48 ( inCongP
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xx = Xy )
% 0.21/0.48 => ( ( in @ Xx @ A )
% 0.21/0.48 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(in__Cong_type,type,
% 0.21/0.48 in__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(in__Cong,definition,
% 0.21/0.48 ( in__Cong
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xx = Xy )
% 0.21/0.48 => ( ( in @ Xx @ A )
% 0.21/0.48 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exuE3u_type,type,
% 0.21/0.48 exuE3u: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exuE3u,definition,
% 0.21/0.48 ( exuE3u
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 => ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xx )
% 0.21/0.48 => ( ( Xphi @ Xy )
% 0.21/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exu__Cong_type,type,
% 0.21/0.48 exu__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exu__Cong,definition,
% 0.21/0.48 ( exu__Cong
% 0.21/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xx = Xy )
% 0.21/0.48 => ( ( Xphi @ Xx )
% 0.21/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.21/0.48 => ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 <=> ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptyset__Cong_type,type,
% 0.21/0.48 emptyset__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptyset__Cong,definition,
% 0.21/0.48 ( emptyset__Cong
% 0.21/0.48 = ( emptyset = emptyset ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoin__Cong_type,type,
% 0.21/0.48 setadjoin__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoin__Cong,definition,
% 0.21/0.48 ( setadjoin__Cong
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xx = Xy )
% 0.21/0.48 => ! [Xz: $i,Xu: $i] :
% 0.21/0.48 ( ( Xz = Xu )
% 0.21/0.48 => ( ( setadjoin @ Xx @ Xz )
% 0.21/0.48 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(powerset__Cong_type,type,
% 0.21/0.48 powerset__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(powerset__Cong,definition,
% 0.21/0.48 ( powerset__Cong
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ( ( powerset @ A )
% 0.21/0.48 = ( powerset @ B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setunion__Cong_type,type,
% 0.21/0.48 setunion__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setunion__Cong,definition,
% 0.21/0.48 ( setunion__Cong
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ( ( setunion @ A )
% 0.21/0.48 = ( setunion @ B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(omega__Cong_type,type,
% 0.21/0.48 omega__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(omega__Cong,definition,
% 0.21/0.48 ( omega__Cong
% 0.21/0.48 = ( omega = omega ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(exuEu_type,type,
% 0.21/0.48 exuEu: $o ).
% 0.21/0.48
% 0.21/0.48 thf(exuEu,definition,
% 0.21/0.48 ( exuEu
% 0.21/0.48 = ( ! [Xphi: $i > $o] :
% 0.21/0.48 ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 => ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xphi @ Xx )
% 0.21/0.48 => ( ( Xphi @ Xy )
% 0.21/0.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(descr__Cong_type,type,
% 0.21/0.48 descr__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(descr__Cong,definition,
% 0.21/0.48 ( descr__Cong
% 0.21/0.48 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.48 ( ! [Xx: $i,Xy: $i] :
% 0.21/0.48 ( ( Xx = Xy )
% 0.21/0.48 => ( ( Xphi @ Xx )
% 0.21/0.48 <=> ( Xpsi @ Xy ) ) )
% 0.21/0.48 => ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 => ( ( exu
% 0.21/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.21/0.48 => ( ( descr
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 = ( descr
% 0.21/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstr__Cong_type,type,
% 0.21/0.48 dsetconstr__Cong: $o ).
% 0.21/0.48
% 0.21/0.48 thf(dsetconstr__Cong,definition,
% 0.21/0.48 ( dsetconstr__Cong
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ! [Xy: $i] :
% 0.21/0.48 ( ( in @ Xy @ B )
% 0.21/0.48 => ( ( Xx = Xy )
% 0.21/0.48 => ( ( Xphi @ Xx )
% 0.21/0.48 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.21/0.48 => ( ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 = ( dsetconstr @ B
% 0.21/0.48 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subset_type,type,
% 0.21/0.48 subset: $i > $i > $o ).
% 0.21/0.48
% 0.21/0.48 thf(disjoint_type,type,
% 0.21/0.48 disjoint: $i > $i > $o ).
% 0.21/0.48
% 0.21/0.48 thf(setsmeet_type,type,
% 0.21/0.48 setsmeet: $i > $i > $o ).
% 0.21/0.48
% 0.21/0.48 thf(subsetI1_type,type,
% 0.21/0.48 subsetI1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subsetI1,definition,
% 0.21/0.48 ( subsetI1
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( in @ Xx @ B ) )
% 0.21/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(eqimpsubset2_type,type,
% 0.21/0.48 eqimpsubset2: $o ).
% 0.21/0.48
% 0.21/0.48 thf(eqimpsubset2,definition,
% 0.21/0.48 ( eqimpsubset2
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(eqimpsubset1_type,type,
% 0.21/0.48 eqimpsubset1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(eqimpsubset1,definition,
% 0.21/0.48 ( eqimpsubset1
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( A = B )
% 0.21/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subsetI2_type,type,
% 0.21/0.48 subsetI2: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subsetI2,definition,
% 0.21/0.48 ( subsetI2
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ! [Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( in @ Xx @ B ) )
% 0.21/0.48 => ( subset @ A @ B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetsubset_type,type,
% 0.21/0.48 emptysetsubset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(emptysetsubset,definition,
% 0.21/0.48 ( emptysetsubset
% 0.21/0.48 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subsetE_type,type,
% 0.21/0.48 subsetE: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subsetE,definition,
% 0.21/0.48 ( subsetE
% 0.21/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.48 ( ( subset @ A @ B )
% 0.21/0.48 => ( ( in @ Xx @ A )
% 0.21/0.48 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subsetE2_type,type,
% 0.21/0.48 subsetE2: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subsetE2,definition,
% 0.21/0.48 ( subsetE2
% 0.21/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.48 ( ( subset @ A @ B )
% 0.21/0.48 => ( ~ ( in @ Xx @ B )
% 0.21/0.48 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(notsubsetI_type,type,
% 0.21/0.48 notsubsetI: $o ).
% 0.21/0.48
% 0.21/0.48 thf(notsubsetI,definition,
% 0.21/0.48 ( notsubsetI
% 0.21/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( ~ ( in @ Xx @ B )
% 0.21/0.48 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(notequalI1_type,type,
% 0.21/0.48 notequalI1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(notequalI1,definition,
% 0.21/0.48 ( notequalI1
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ~ ( subset @ A @ B )
% 0.21/0.48 => ( A != B ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(notequalI2_type,type,
% 0.21/0.48 notequalI2: $o ).
% 0.21/0.48
% 0.21/0.48 thf(notequalI2,definition,
% 0.21/0.48 ( notequalI2
% 0.21/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( ~ ( in @ Xx @ B )
% 0.21/0.48 => ( A != B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subsetRefl_type,type,
% 0.21/0.48 subsetRefl: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subsetRefl,definition,
% 0.21/0.48 ( subsetRefl
% 0.21/0.48 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subsetTrans_type,type,
% 0.21/0.48 subsetTrans: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subsetTrans,definition,
% 0.21/0.48 ( subsetTrans
% 0.21/0.48 = ( ! [A: $i,B: $i,C: $i] :
% 0.21/0.48 ( ( subset @ A @ B )
% 0.21/0.48 => ( ( subset @ B @ C )
% 0.21/0.48 => ( subset @ A @ C ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinSub_type,type,
% 0.21/0.48 setadjoinSub: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinSub,definition,
% 0.21/0.48 ( setadjoinSub
% 0.21/0.48 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinSub2_type,type,
% 0.21/0.48 setadjoinSub2: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setadjoinSub2,definition,
% 0.21/0.48 ( setadjoinSub2
% 0.21/0.48 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.21/0.48 ( ( subset @ A @ B )
% 0.21/0.48 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subset2powerset_type,type,
% 0.21/0.48 subset2powerset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subset2powerset,definition,
% 0.21/0.48 ( subset2powerset
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( subset @ A @ B )
% 0.21/0.48 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(setextsub_type,type,
% 0.21/0.48 setextsub: $o ).
% 0.21/0.48
% 0.21/0.48 thf(setextsub,definition,
% 0.21/0.48 ( setextsub
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( subset @ A @ B )
% 0.21/0.48 => ( ( subset @ B @ A )
% 0.21/0.48 => ( A = B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(subsetemptysetimpeq_type,type,
% 0.21/0.48 subsetemptysetimpeq: $o ).
% 0.21/0.48
% 0.21/0.48 thf(subsetemptysetimpeq,definition,
% 0.21/0.48 ( subsetemptysetimpeq
% 0.21/0.48 = ( ! [A: $i] :
% 0.21/0.48 ( ( subset @ A @ emptyset )
% 0.21/0.48 => ( A = emptyset ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(powersetI1_type,type,
% 0.21/0.48 powersetI1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(powersetI1,definition,
% 0.21/0.48 ( powersetI1
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( subset @ B @ A )
% 0.21/0.48 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(powersetE1_type,type,
% 0.21/0.48 powersetE1: $o ).
% 0.21/0.48
% 0.21/0.48 thf(powersetE1,definition,
% 0.21/0.48 ( powersetE1
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( in @ B @ ( powerset @ A ) )
% 0.21/0.48 => ( subset @ B @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(inPowerset_type,type,
% 0.21/0.48 inPowerset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(inPowerset,definition,
% 0.21/0.48 ( inPowerset
% 0.21/0.48 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(powersetsubset_type,type,
% 0.21/0.48 powersetsubset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(powersetsubset,definition,
% 0.21/0.48 ( powersetsubset
% 0.21/0.48 = ( ! [A: $i,B: $i] :
% 0.21/0.48 ( ( subset @ A @ B )
% 0.21/0.48 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(sepInPowerset_type,type,
% 0.21/0.48 sepInPowerset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(sepInPowerset,definition,
% 0.21/0.48 ( sepInPowerset
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( in
% 0.21/0.48 @ ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 @ ( powerset @ A ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(sepSubset_type,type,
% 0.21/0.48 sepSubset: $o ).
% 0.21/0.48
% 0.21/0.48 thf(sepSubset,definition,
% 0.21/0.48 ( sepSubset
% 0.21/0.48 = ( ! [A: $i,Xphi: $i > $o] :
% 0.21/0.48 ( subset
% 0.21/0.48 @ ( dsetconstr @ A
% 0.21/0.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.21/0.48 @ A ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(binunion_type,type,
% 0.21/0.48 binunion: $i > $i > $i ).
% 0.21/0.48
% 0.21/0.48 thf(binunion,definition,
% 0.21/0.48 ( binunion
% 0.21/0.48 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(binunionIL_type,type,
% 0.21/0.48 binunionIL: $o ).
% 0.21/0.48
% 0.21/0.48 thf(binunionIL,definition,
% 0.21/0.48 ( binunionIL
% 0.21/0.48 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ A )
% 0.21/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(upairset2IR_type,type,
% 0.21/0.48 upairset2IR: $o ).
% 0.21/0.48
% 0.21/0.48 thf(upairset2IR,definition,
% 0.21/0.48 ( upairset2IR
% 0.21/0.48 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 thf(binunionIR,conjecture,
% 0.21/0.48 ( setextAx
% 0.21/0.48 => ( emptysetAx
% 0.21/0.48 => ( setadjoinAx
% 0.21/0.48 => ( powersetAx
% 0.21/0.48 => ( setunionAx
% 0.21/0.48 => ( omega0Ax
% 0.21/0.48 => ( omegaSAx
% 0.21/0.48 => ( omegaIndAx
% 0.21/0.48 => ( replAx
% 0.21/0.48 => ( foundationAx
% 0.21/0.48 => ( wellorderingAx
% 0.21/0.48 => ( descrp
% 0.21/0.48 => ( dsetconstrI
% 0.21/0.48 => ( dsetconstrEL
% 0.21/0.48 => ( dsetconstrER
% 0.21/0.48 => ( exuE1
% 0.21/0.48 => ( prop2setE
% 0.21/0.48 => ( emptysetE
% 0.21/0.48 => ( emptysetimpfalse
% 0.21/0.48 => ( notinemptyset
% 0.21/0.48 => ( exuE3e
% 0.21/0.48 => ( setext
% 0.21/0.48 => ( emptyI
% 0.21/0.48 => ( noeltsimpempty
% 0.21/0.48 => ( setbeta
% 0.21/0.48 => ( nonemptyE1
% 0.21/0.48 => ( nonemptyI
% 0.21/0.48 => ( nonemptyI1
% 0.21/0.48 => ( setadjoinIL
% 0.21/0.48 => ( emptyinunitempty
% 0.21/0.48 => ( setadjoinIR
% 0.21/0.48 => ( setadjoinE
% 0.21/0.48 => ( setadjoinOr
% 0.21/0.48 => ( setoftrueEq
% 0.21/0.48 => ( powersetI
% 0.21/0.48 => ( emptyinPowerset
% 0.21/0.48 => ( emptyInPowerset
% 0.21/0.48 => ( powersetE
% 0.21/0.48 => ( setunionI
% 0.21/0.48 => ( setunionE
% 0.21/0.48 => ( subPowSU
% 0.21/0.48 => ( exuE2
% 0.21/0.48 => ( nonemptyImpWitness
% 0.21/0.48 => ( uniqinunit
% 0.21/0.48 => ( notinsingleton
% 0.21/0.48 => ( eqinunit
% 0.21/0.48 => ( singletonsswitch
% 0.21/0.48 => ( upairsetE
% 0.21/0.48 => ( upairsetIL
% 0.21/0.48 => ( upairsetIR
% 0.21/0.48 => ( emptyE1
% 0.21/0.48 => ( vacuousDall
% 0.21/0.48 => ( quantDeMorgan1
% 0.21/0.48 => ( quantDeMorgan2
% 0.21/0.48 => ( quantDeMorgan3
% 0.21/0.48 => ( quantDeMorgan4
% 0.21/0.48 => ( prop2setI
% 0.21/0.48 => ( prop2set2propI
% 0.21/0.48 => ( notdexE
% 0.21/0.48 => ( notdallE
% 0.21/0.48 => ( exuI1
% 0.21/0.48 => ( exuI3
% 0.21/0.48 => ( exuI2
% 0.21/0.48 => ( inCongP
% 0.21/0.48 => ( in__Cong
% 0.21/0.48 => ( exuE3u
% 0.21/0.48 => ( exu__Cong
% 0.21/0.48 => ( emptyset__Cong
% 0.21/0.48 => ( setadjoin__Cong
% 0.21/0.48 => ( powerset__Cong
% 0.21/0.48 => ( setunion__Cong
% 0.21/0.48 => ( omega__Cong
% 0.21/0.48 => ( exuEu
% 0.21/0.48 => ( descr__Cong
% 0.21/0.48 => ( dsetconstr__Cong
% 0.21/0.48 => ( subsetI1
% 0.21/0.48 => ( eqimpsubset2
% 0.21/0.48 => ( eqimpsubset1
% 0.21/0.48 => ( subsetI2
% 0.21/0.48 => ( emptysetsubset
% 0.21/0.48 => ( subsetE
% 0.21/0.48 => ( subsetE2
% 0.21/0.48 => ( notsubsetI
% 0.21/0.48 => ( notequalI1
% 0.21/0.48 => ( notequalI2
% 0.21/0.48 => ( subsetRefl
% 0.21/0.48 => ( subsetTrans
% 0.21/0.48 => ( setadjoinSub
% 0.21/0.48 => ( setadjoinSub2
% 0.21/0.48 => ( subset2powerset
% 0.21/0.48 => ( setextsub
% 0.21/0.48 => ( subsetemptysetimpeq
% 0.21/0.48 => ( powersetI1
% 0.21/0.48 => ( powersetE1
% 0.21/0.48 => ( inPowerset
% 0.21/0.48 => ( powersetsubset
% 0.21/0.48 => ( sepInPowerset
% 0.21/0.48 => ( sepSubset
% 0.21/0.48 => ( binunionIL
% 0.21/0.48 => ( upairset2IR
% 0.21/0.48 => ! [A: $i,B: $i,Xx: $i] :
% 0.21/0.48 ( ( in @ Xx @ B )
% 0.21/0.48 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.21/0.48
% 0.21/0.48 %------------------------------------------------------------------------------
% 0.21/0.48 ------------------------
% 2.57/1.65 ---- Embedded in THF ---
% 2.57/1.65 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.57/1.65 %%% Generated on Tue Feb 24 12:28:21 EST 2026
% 2.57/1.65 %%% using '$$dhol' embedding, version 1.3.0.
% 2.57/1.65 %%% Logic specification used:
% 2.57/1.65 %%% thf(spec, logic, $$dhol).
% 2.57/1.65
% 2.57/1.65 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2DTF17274.p
% See solution above
% 2.57/1.65 ------------------------
% 2.57/1.67 ---- Cleaned THF ---
% 2.57/1.67 thf(in_type,type,
% 2.57/1.67 in: $i > $i > $o ).
% 2.57/1.67
% 2.57/1.67 thf(exu_type,type,
% 2.57/1.67 exu: ( $i > $o ) > $o ).
% 2.57/1.67
% 2.57/1.67 thf(exu,definition,
% 2.57/1.67 ( exu
% 2.57/1.67 = ( ^ [Xphi: $i > $o] :
% 2.57/1.67 ? [Xx: $i] :
% 2.57/1.67 ( ( Xphi @ Xx )
% 2.57/1.67 & ! [Xy: $i] :
% 2.57/1.67 ( ( Xphi @ Xy )
% 2.57/1.67 => ( Xx = Xy ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setextAx_type,type,
% 2.57/1.67 setextAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setextAx,definition,
% 2.57/1.67 ( setextAx
% 2.57/1.67 = ( ! [A: $i,B: $i] :
% 2.57/1.67 ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ A )
% 2.57/1.67 <=> ( in @ Xx @ B ) )
% 2.57/1.67 => ( A = B ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(emptyset_type,type,
% 2.57/1.67 emptyset: $i ).
% 2.57/1.67
% 2.57/1.67 thf(emptysetAx_type,type,
% 2.57/1.67 emptysetAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(emptysetAx,definition,
% 2.57/1.67 ( emptysetAx
% 2.57/1.67 = ( ! [Xx: $i] :
% 2.57/1.67 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoin_type,type,
% 2.57/1.67 setadjoin: $i > $i > $i ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinAx_type,type,
% 2.57/1.67 setadjoinAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinAx,definition,
% 2.57/1.67 ( setadjoinAx
% 2.57/1.67 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.57/1.67 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.57/1.67 <=> ( ( Xy = Xx )
% 2.57/1.67 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(powerset_type,type,
% 2.57/1.67 powerset: $i > $i ).
% 2.57/1.67
% 2.57/1.67 thf(powersetAx_type,type,
% 2.57/1.67 powersetAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(powersetAx,definition,
% 2.57/1.67 ( powersetAx
% 2.57/1.67 = ( ! [A: $i,B: $i] :
% 2.57/1.67 ( ( in @ B @ ( powerset @ A ) )
% 2.57/1.67 <=> ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ B )
% 2.57/1.67 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setunion_type,type,
% 2.57/1.67 setunion: $i > $i ).
% 2.57/1.67
% 2.57/1.67 thf(setunionAx_type,type,
% 2.57/1.67 setunionAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setunionAx,definition,
% 2.57/1.67 ( setunionAx
% 2.57/1.67 = ( ! [A: $i,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ ( setunion @ A ) )
% 2.57/1.67 <=> ? [B: $i] :
% 2.57/1.67 ( ( in @ Xx @ B )
% 2.57/1.67 & ( in @ B @ A ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(omega_type,type,
% 2.57/1.67 omega: $i ).
% 2.57/1.67
% 2.57/1.67 thf(omega0Ax_type,type,
% 2.57/1.67 omega0Ax: $o ).
% 2.57/1.67
% 2.57/1.67 thf(omega0Ax,definition,
% 2.57/1.67 ( omega0Ax
% 2.57/1.67 = ( in @ emptyset @ omega ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(omegaSAx_type,type,
% 2.57/1.67 omegaSAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(omegaSAx,definition,
% 2.57/1.67 ( omegaSAx
% 2.57/1.67 = ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ omega )
% 2.57/1.67 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(omegaIndAx_type,type,
% 2.57/1.67 omegaIndAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(omegaIndAx,definition,
% 2.57/1.67 ( omegaIndAx
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ( ( ( in @ emptyset @ A )
% 2.57/1.67 & ! [Xx: $i] :
% 2.57/1.67 ( ( ( in @ Xx @ omega )
% 2.57/1.67 & ( in @ Xx @ A ) )
% 2.57/1.67 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.57/1.67 => ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ omega )
% 2.57/1.67 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(replAx_type,type,
% 2.57/1.67 replAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(replAx,definition,
% 2.57/1.67 ( replAx
% 2.57/1.67 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.57/1.67 ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ A )
% 2.57/1.67 => ( exu
% 2.57/1.67 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.57/1.67 => ? [B: $i] :
% 2.57/1.67 ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ B )
% 2.57/1.67 <=> ? [Xy: $i] :
% 2.57/1.67 ( ( in @ Xy @ A )
% 2.57/1.67 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(foundationAx_type,type,
% 2.57/1.67 foundationAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(foundationAx,definition,
% 2.57/1.67 ( foundationAx
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.57/1.67 => ? [B: $i] :
% 2.57/1.67 ( ( in @ B @ A )
% 2.57/1.67 & ~ ? [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ B )
% 2.57/1.67 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(wellorderingAx_type,type,
% 2.57/1.67 wellorderingAx: $o ).
% 2.57/1.67
% 2.57/1.67 thf(wellorderingAx,definition,
% 2.57/1.67 ( wellorderingAx
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ? [B: $i] :
% 2.57/1.67 ( ! [C: $i] :
% 2.57/1.67 ( ( in @ C @ B )
% 2.57/1.67 => ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ C )
% 2.57/1.67 => ( in @ Xx @ A ) ) )
% 2.57/1.67 & ! [Xx: $i,Xy: $i] :
% 2.57/1.67 ( ( ( in @ Xx @ A )
% 2.57/1.67 & ( in @ Xy @ A ) )
% 2.57/1.67 => ( ! [C: $i] :
% 2.57/1.67 ( ( in @ C @ B )
% 2.57/1.67 => ( ( in @ Xx @ C )
% 2.57/1.67 <=> ( in @ Xy @ C ) ) )
% 2.57/1.67 => ( Xx = Xy ) ) )
% 2.57/1.67 & ! [C: $i,D: $i] :
% 2.57/1.67 ( ( ( in @ C @ B )
% 2.57/1.67 & ( in @ D @ B ) )
% 2.57/1.67 => ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ C )
% 2.57/1.67 => ( in @ Xx @ D ) )
% 2.57/1.67 | ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ D )
% 2.57/1.67 => ( in @ Xx @ C ) ) ) )
% 2.57/1.67 & ! [C: $i] :
% 2.57/1.67 ( ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ C )
% 2.57/1.67 => ( in @ Xx @ A ) )
% 2.57/1.67 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.57/1.67 => ? [D: $i,Xx: $i] :
% 2.57/1.67 ( ( in @ D @ B )
% 2.57/1.67 & ( in @ Xx @ C )
% 2.57/1.67 & ~ ? [Xy: $i] :
% 2.57/1.67 ( ( in @ Xy @ D )
% 2.57/1.67 & ( in @ Xy @ C ) )
% 2.57/1.67 & ! [E: $i] :
% 2.57/1.67 ( ( in @ E @ B )
% 2.57/1.67 => ( ! [Xy: $i] :
% 2.57/1.67 ( ( in @ Xy @ E )
% 2.57/1.67 => ( in @ Xy @ D ) )
% 2.57/1.67 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(descr_type,type,
% 2.57/1.67 descr: ( $i > $o ) > $i ).
% 2.57/1.67
% 2.57/1.67 thf(descrp_type,type,
% 2.57/1.67 descrp: $o ).
% 2.57/1.67
% 2.57/1.67 thf(descrp,definition,
% 2.57/1.67 ( descrp
% 2.57/1.67 = ( ! [Xphi: $i > $o] :
% 2.57/1.67 ( ( exu
% 2.57/1.67 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.67 => ( Xphi
% 2.57/1.67 @ ( descr
% 2.57/1.67 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(dsetconstr_type,type,
% 2.57/1.67 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.57/1.67
% 2.57/1.67 thf(dsetconstrI_type,type,
% 2.57/1.67 dsetconstrI: $o ).
% 2.57/1.67
% 2.57/1.67 thf(dsetconstrI,definition,
% 2.57/1.67 ( dsetconstrI
% 2.57/1.67 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ A )
% 2.57/1.67 => ( ( Xphi @ Xx )
% 2.57/1.67 => ( in @ Xx
% 2.57/1.67 @ ( dsetconstr @ A
% 2.57/1.67 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(dsetconstrEL_type,type,
% 2.57/1.67 dsetconstrEL: $o ).
% 2.57/1.67
% 2.57/1.67 thf(dsetconstrEL,definition,
% 2.57/1.67 ( dsetconstrEL
% 2.57/1.67 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx
% 2.57/1.67 @ ( dsetconstr @ A
% 2.57/1.67 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.57/1.67 => ( in @ Xx @ A ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(dsetconstrER_type,type,
% 2.57/1.67 dsetconstrER: $o ).
% 2.57/1.67
% 2.57/1.67 thf(dsetconstrER,definition,
% 2.57/1.67 ( dsetconstrER
% 2.57/1.67 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx
% 2.57/1.67 @ ( dsetconstr @ A
% 2.57/1.67 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.57/1.67 => ( Xphi @ Xx ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(exuE1_type,type,
% 2.57/1.67 exuE1: $o ).
% 2.57/1.67
% 2.57/1.67 thf(exuE1,definition,
% 2.57/1.67 ( exuE1
% 2.57/1.67 = ( ! [Xphi: $i > $o] :
% 2.57/1.67 ( ( exu
% 2.57/1.67 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.67 => ? [Xx: $i] :
% 2.57/1.67 ( ( Xphi @ Xx )
% 2.57/1.67 & ! [Xy: $i] :
% 2.57/1.67 ( ( Xphi @ Xy )
% 2.57/1.67 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(prop2set_type,type,
% 2.57/1.67 prop2set: $o > $i ).
% 2.57/1.67
% 2.57/1.67 thf(prop2setE_type,type,
% 2.57/1.67 prop2setE: $o ).
% 2.57/1.67
% 2.57/1.67 thf(prop2setE,definition,
% 2.57/1.67 ( prop2setE
% 2.57/1.67 = ( ! [Xphi: $o,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.57/1.67 => Xphi ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(emptysetE_type,type,
% 2.57/1.67 emptysetE: $o ).
% 2.57/1.67
% 2.57/1.67 thf(emptysetE,definition,
% 2.57/1.67 ( emptysetE
% 2.57/1.67 = ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ emptyset )
% 2.57/1.67 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(emptysetimpfalse_type,type,
% 2.57/1.67 emptysetimpfalse: $o ).
% 2.57/1.67
% 2.57/1.67 thf(emptysetimpfalse,definition,
% 2.57/1.67 ( emptysetimpfalse
% 2.57/1.67 = ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ emptyset )
% 2.57/1.67 => $false ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(notinemptyset_type,type,
% 2.57/1.67 notinemptyset: $o ).
% 2.57/1.67
% 2.57/1.67 thf(notinemptyset,definition,
% 2.57/1.67 ( notinemptyset
% 2.57/1.67 = ( ! [Xx: $i] :
% 2.57/1.67 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(exuE3e_type,type,
% 2.57/1.67 exuE3e: $o ).
% 2.57/1.67
% 2.57/1.67 thf(exuE3e,definition,
% 2.57/1.67 ( exuE3e
% 2.57/1.67 = ( ! [Xphi: $i > $o] :
% 2.57/1.67 ( ( exu
% 2.57/1.67 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.67 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setext_type,type,
% 2.57/1.67 setext: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setext,definition,
% 2.57/1.67 ( setext
% 2.57/1.67 = ( ! [A: $i,B: $i] :
% 2.57/1.67 ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ A )
% 2.57/1.67 => ( in @ Xx @ B ) )
% 2.57/1.67 => ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ B )
% 2.57/1.67 => ( in @ Xx @ A ) )
% 2.57/1.67 => ( A = B ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(emptyI_type,type,
% 2.57/1.67 emptyI: $o ).
% 2.57/1.67
% 2.57/1.67 thf(emptyI,definition,
% 2.57/1.67 ( emptyI
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ( ! [Xx: $i] :
% 2.57/1.67 ~ ( in @ Xx @ A )
% 2.57/1.67 => ( A = emptyset ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(noeltsimpempty_type,type,
% 2.57/1.67 noeltsimpempty: $o ).
% 2.57/1.67
% 2.57/1.67 thf(noeltsimpempty,definition,
% 2.57/1.67 ( noeltsimpempty
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ( ! [Xx: $i] :
% 2.57/1.67 ~ ( in @ Xx @ A )
% 2.57/1.67 => ( A = emptyset ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setbeta_type,type,
% 2.57/1.67 setbeta: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setbeta,definition,
% 2.57/1.67 ( setbeta
% 2.57/1.67 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ A )
% 2.57/1.67 => ( ( in @ Xx
% 2.57/1.67 @ ( dsetconstr @ A
% 2.57/1.67 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.57/1.67 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(nonempty_type,type,
% 2.57/1.67 nonempty: $i > $o ).
% 2.57/1.67
% 2.57/1.67 thf(nonempty,definition,
% 2.57/1.67 ( nonempty
% 2.57/1.67 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(nonemptyE1_type,type,
% 2.57/1.67 nonemptyE1: $o ).
% 2.57/1.67
% 2.57/1.67 thf(nonemptyE1,definition,
% 2.57/1.67 ( nonemptyE1
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ( ( nonempty @ A )
% 2.57/1.67 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(nonemptyI_type,type,
% 2.57/1.67 nonemptyI: $o ).
% 2.57/1.67
% 2.57/1.67 thf(nonemptyI,definition,
% 2.57/1.67 ( nonemptyI
% 2.57/1.67 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ A )
% 2.57/1.67 => ( ( Xphi @ Xx )
% 2.57/1.67 => ( nonempty
% 2.57/1.67 @ ( dsetconstr @ A
% 2.57/1.67 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(nonemptyI1_type,type,
% 2.57/1.67 nonemptyI1: $o ).
% 2.57/1.67
% 2.57/1.67 thf(nonemptyI1,definition,
% 2.57/1.67 ( nonemptyI1
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.57/1.67 => ( nonempty @ A ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinIL_type,type,
% 2.57/1.67 setadjoinIL: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinIL,definition,
% 2.57/1.67 ( setadjoinIL
% 2.57/1.67 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(emptyinunitempty_type,type,
% 2.57/1.67 emptyinunitempty: $o ).
% 2.57/1.67
% 2.57/1.67 thf(emptyinunitempty,definition,
% 2.57/1.67 ( emptyinunitempty
% 2.57/1.67 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinIR_type,type,
% 2.57/1.67 setadjoinIR: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinIR,definition,
% 2.57/1.67 ( setadjoinIR
% 2.57/1.67 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.57/1.67 ( ( in @ Xy @ A )
% 2.57/1.67 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinE_type,type,
% 2.57/1.67 setadjoinE: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinE,definition,
% 2.57/1.67 ( setadjoinE
% 2.57/1.67 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.57/1.67 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.57/1.67 => ! [Xphi: $o] :
% 2.57/1.67 ( ( ( Xy = Xx )
% 2.57/1.67 => Xphi )
% 2.57/1.67 => ( ( ( in @ Xy @ A )
% 2.57/1.67 => Xphi )
% 2.57/1.67 => Xphi ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinOr_type,type,
% 2.57/1.67 setadjoinOr: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setadjoinOr,definition,
% 2.57/1.67 ( setadjoinOr
% 2.57/1.67 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.57/1.67 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.57/1.67 => ( ( Xy = Xx )
% 2.57/1.67 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setoftrueEq_type,type,
% 2.57/1.67 setoftrueEq: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setoftrueEq,definition,
% 2.57/1.67 ( setoftrueEq
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ( ( dsetconstr @ A
% 2.57/1.67 @ ^ [Xx: $i] : $true )
% 2.57/1.67 = A ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(powersetI_type,type,
% 2.57/1.67 powersetI: $o ).
% 2.57/1.67
% 2.57/1.67 thf(powersetI,definition,
% 2.57/1.67 ( powersetI
% 2.57/1.67 = ( ! [A: $i,B: $i] :
% 2.57/1.67 ( ! [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ B )
% 2.57/1.67 => ( in @ Xx @ A ) )
% 2.57/1.67 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(emptyinPowerset_type,type,
% 2.57/1.67 emptyinPowerset: $o ).
% 2.57/1.67
% 2.57/1.67 thf(emptyinPowerset,definition,
% 2.57/1.67 ( emptyinPowerset
% 2.57/1.67 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(emptyInPowerset_type,type,
% 2.57/1.67 emptyInPowerset: $o ).
% 2.57/1.67
% 2.57/1.67 thf(emptyInPowerset,definition,
% 2.57/1.67 ( emptyInPowerset
% 2.57/1.67 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(powersetE_type,type,
% 2.57/1.67 powersetE: $o ).
% 2.57/1.67
% 2.57/1.67 thf(powersetE,definition,
% 2.57/1.67 ( powersetE
% 2.57/1.67 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.67 ( ( in @ B @ ( powerset @ A ) )
% 2.57/1.67 => ( ( in @ Xx @ B )
% 2.57/1.67 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setunionI_type,type,
% 2.57/1.67 setunionI: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setunionI,definition,
% 2.57/1.67 ( setunionI
% 2.57/1.67 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.57/1.67 ( ( in @ Xx @ B )
% 2.57/1.67 => ( ( in @ B @ A )
% 2.57/1.67 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(setunionE_type,type,
% 2.57/1.67 setunionE: $o ).
% 2.57/1.67
% 2.57/1.67 thf(setunionE,definition,
% 2.57/1.67 ( setunionE
% 2.57/1.67 = ( ! [A: $i,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ ( setunion @ A ) )
% 2.57/1.67 => ! [Xphi: $o] :
% 2.57/1.67 ( ! [B: $i] :
% 2.57/1.67 ( ( in @ Xx @ B )
% 2.57/1.67 => ( ( in @ B @ A )
% 2.57/1.67 => Xphi ) )
% 2.57/1.67 => Xphi ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(subPowSU_type,type,
% 2.57/1.67 subPowSU: $o ).
% 2.57/1.67
% 2.57/1.67 thf(subPowSU,definition,
% 2.57/1.67 ( subPowSU
% 2.57/1.67 = ( ! [A: $i,Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ A )
% 2.57/1.67 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(exuE2_type,type,
% 2.57/1.67 exuE2: $o ).
% 2.57/1.67
% 2.57/1.67 thf(exuE2,definition,
% 2.57/1.67 ( exuE2
% 2.57/1.67 = ( ! [Xphi: $i > $o] :
% 2.57/1.67 ( ( exu
% 2.57/1.67 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.67 => ? [Xx: $i] :
% 2.57/1.67 ! [Xy: $i] :
% 2.57/1.67 ( ( Xphi @ Xy )
% 2.57/1.67 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(nonemptyImpWitness_type,type,
% 2.57/1.67 nonemptyImpWitness: $o ).
% 2.57/1.67
% 2.57/1.67 thf(nonemptyImpWitness,definition,
% 2.57/1.67 ( nonemptyImpWitness
% 2.57/1.67 = ( ! [A: $i] :
% 2.57/1.67 ( ( nonempty @ A )
% 2.57/1.67 => ? [Xx: $i] :
% 2.57/1.67 ( ( in @ Xx @ A )
% 2.57/1.67 & $true ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(uniqinunit_type,type,
% 2.57/1.67 uniqinunit: $o ).
% 2.57/1.67
% 2.57/1.67 thf(uniqinunit,definition,
% 2.57/1.67 ( uniqinunit
% 2.57/1.67 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.67 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.57/1.67 => ( Xx = Xy ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(notinsingleton_type,type,
% 2.57/1.67 notinsingleton: $o ).
% 2.57/1.67
% 2.57/1.67 thf(notinsingleton,definition,
% 2.57/1.67 ( notinsingleton
% 2.57/1.67 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.67 ( ( Xx != Xy )
% 2.57/1.67 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(eqinunit_type,type,
% 2.57/1.67 eqinunit: $o ).
% 2.57/1.67
% 2.57/1.67 thf(eqinunit,definition,
% 2.57/1.67 ( eqinunit
% 2.57/1.67 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.67 ( ( Xx = Xy )
% 2.57/1.67 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(singletonsswitch_type,type,
% 2.57/1.67 singletonsswitch: $o ).
% 2.57/1.67
% 2.57/1.67 thf(singletonsswitch,definition,
% 2.57/1.67 ( singletonsswitch
% 2.57/1.67 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.67 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.57/1.67 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(upairsetE_type,type,
% 2.57/1.67 upairsetE: $o ).
% 2.57/1.67
% 2.57/1.67 thf(upairsetE,definition,
% 2.57/1.67 ( upairsetE
% 2.57/1.67 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.57/1.67 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.57/1.67 => ( ( Xz = Xx )
% 2.57/1.67 | ( Xz = Xy ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(upairsetIL_type,type,
% 2.57/1.67 upairsetIL: $o ).
% 2.57/1.67
% 2.57/1.67 thf(upairsetIL,definition,
% 2.57/1.67 ( upairsetIL
% 2.57/1.67 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.67
% 2.57/1.67 thf(upairsetIR_type,type,
% 2.57/1.67 upairsetIR: $o ).
% 2.57/1.67
% 2.57/1.67 thf(upairsetIR,definition,
% 2.57/1.67 ( upairsetIR
% 2.57/1.67 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(emptyE1_type,type,
% 2.57/1.68 emptyE1: $o ).
% 2.57/1.68
% 2.57/1.68 thf(emptyE1,definition,
% 2.57/1.68 ( emptyE1
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( ? [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 & ( Xphi @ Xx ) )
% 2.57/1.68 => ( ( ( dsetconstr @ A
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 = emptyset )
% 2.57/1.68 => $false ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(vacuousDall_type,type,
% 2.57/1.68 vacuousDall: $o ).
% 2.57/1.68
% 2.57/1.68 thf(vacuousDall,definition,
% 2.57/1.68 ( vacuousDall
% 2.57/1.68 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ emptyset )
% 2.57/1.68 => ( Xphi @ Xx ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(quantDeMorgan1_type,type,
% 2.57/1.68 quantDeMorgan1: $o ).
% 2.57/1.68
% 2.57/1.68 thf(quantDeMorgan1,definition,
% 2.57/1.68 ( quantDeMorgan1
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( ~ ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ( Xphi @ Xx ) )
% 2.57/1.68 => ? [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(quantDeMorgan2_type,type,
% 2.57/1.68 quantDeMorgan2: $o ).
% 2.57/1.68
% 2.57/1.68 thf(quantDeMorgan2,definition,
% 2.57/1.68 ( quantDeMorgan2
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ~ ( Xphi @ Xx ) )
% 2.57/1.68 => ~ ? [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(quantDeMorgan3_type,type,
% 2.57/1.68 quantDeMorgan3: $o ).
% 2.57/1.68
% 2.57/1.68 thf(quantDeMorgan3,definition,
% 2.57/1.68 ( quantDeMorgan3
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( ~ ? [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 & ( Xphi @ Xx ) )
% 2.57/1.68 => ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(quantDeMorgan4_type,type,
% 2.57/1.68 quantDeMorgan4: $o ).
% 2.57/1.68
% 2.57/1.68 thf(quantDeMorgan4,definition,
% 2.57/1.68 ( quantDeMorgan4
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( ? [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 & ~ ( Xphi @ Xx ) )
% 2.57/1.68 => ~ ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(prop2setI_type,type,
% 2.57/1.68 prop2setI: $o ).
% 2.57/1.68
% 2.57/1.68 thf(prop2setI,definition,
% 2.57/1.68 ( prop2setI
% 2.57/1.68 = ( ! [Xphi: $o] :
% 2.57/1.68 ( Xphi
% 2.57/1.68 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(set2prop_type,type,
% 2.57/1.68 set2prop: $i > $o ).
% 2.57/1.68
% 2.57/1.68 thf(prop2set2propI_type,type,
% 2.57/1.68 prop2set2propI: $o ).
% 2.57/1.68
% 2.57/1.68 thf(prop2set2propI,definition,
% 2.57/1.68 ( prop2set2propI
% 2.57/1.68 = ( ! [Xphi: $o] :
% 2.57/1.68 ( Xphi
% 2.57/1.68 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(notdexE_type,type,
% 2.57/1.68 notdexE: $o ).
% 2.57/1.68
% 2.57/1.68 thf(notdexE,definition,
% 2.57/1.68 ( notdexE
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( ~ ? [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 & ( Xphi @ Xx ) )
% 2.57/1.68 => ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(notdallE_type,type,
% 2.57/1.68 notdallE: $o ).
% 2.57/1.68
% 2.57/1.68 thf(notdallE,definition,
% 2.57/1.68 ( notdallE
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( ~ ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ( Xphi @ Xx ) )
% 2.57/1.68 => ? [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(exuI1_type,type,
% 2.57/1.68 exuI1: $o ).
% 2.57/1.68
% 2.57/1.68 thf(exuI1,definition,
% 2.57/1.68 ( exuI1
% 2.57/1.68 = ( ! [Xphi: $i > $o] :
% 2.57/1.68 ( ? [Xx: $i] :
% 2.57/1.68 ( ( Xphi @ Xx )
% 2.57/1.68 & ! [Xy: $i] :
% 2.57/1.68 ( ( Xphi @ Xy )
% 2.57/1.68 => ( Xx = Xy ) ) )
% 2.57/1.68 => ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(exuI3_type,type,
% 2.57/1.68 exuI3: $o ).
% 2.57/1.68
% 2.57/1.68 thf(exuI3,definition,
% 2.57/1.68 ( exuI3
% 2.57/1.68 = ( ! [Xphi: $i > $o] :
% 2.57/1.68 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.57/1.68 => ( ! [Xx: $i,Xy: $i] :
% 2.57/1.68 ( ( Xphi @ Xx )
% 2.57/1.68 => ( ( Xphi @ Xy )
% 2.57/1.68 => ( Xx = Xy ) ) )
% 2.57/1.68 => ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(exuI2_type,type,
% 2.57/1.68 exuI2: $o ).
% 2.57/1.68
% 2.57/1.68 thf(exuI2,definition,
% 2.57/1.68 ( exuI2
% 2.57/1.68 = ( ! [Xphi: $i > $o] :
% 2.57/1.68 ( ? [Xx: $i] :
% 2.57/1.68 ! [Xy: $i] :
% 2.57/1.68 ( ( Xphi @ Xy )
% 2.57/1.68 <=> ( Xy = Xx ) )
% 2.57/1.68 => ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(inCongP_type,type,
% 2.57/1.68 inCongP: $o ).
% 2.57/1.68
% 2.57/1.68 thf(inCongP,definition,
% 2.57/1.68 ( inCongP
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( A = B )
% 2.57/1.68 => ! [Xx: $i,Xy: $i] :
% 2.57/1.68 ( ( Xx = Xy )
% 2.57/1.68 => ( ( in @ Xx @ A )
% 2.57/1.68 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(in__Cong_type,type,
% 2.57/1.68 in__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(in__Cong,definition,
% 2.57/1.68 ( in__Cong
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( A = B )
% 2.57/1.68 => ! [Xx: $i,Xy: $i] :
% 2.57/1.68 ( ( Xx = Xy )
% 2.57/1.68 => ( ( in @ Xx @ A )
% 2.57/1.68 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(exuE3u_type,type,
% 2.57/1.68 exuE3u: $o ).
% 2.57/1.68
% 2.57/1.68 thf(exuE3u,definition,
% 2.57/1.68 ( exuE3u
% 2.57/1.68 = ( ! [Xphi: $i > $o] :
% 2.57/1.68 ( ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 => ! [Xx: $i,Xy: $i] :
% 2.57/1.68 ( ( Xphi @ Xx )
% 2.57/1.68 => ( ( Xphi @ Xy )
% 2.57/1.68 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(exu__Cong_type,type,
% 2.57/1.68 exu__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(exu__Cong,definition,
% 2.57/1.68 ( exu__Cong
% 2.57/1.68 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.57/1.68 ( ! [Xx: $i,Xy: $i] :
% 2.57/1.68 ( ( Xx = Xy )
% 2.57/1.68 => ( ( Xphi @ Xx )
% 2.57/1.68 <=> ( Xpsi @ Xy ) ) )
% 2.57/1.68 => ( ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 <=> ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(emptyset__Cong_type,type,
% 2.57/1.68 emptyset__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(emptyset__Cong,definition,
% 2.57/1.68 ( emptyset__Cong
% 2.57/1.68 = ( emptyset = emptyset ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(setadjoin__Cong_type,type,
% 2.57/1.68 setadjoin__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(setadjoin__Cong,definition,
% 2.57/1.68 ( setadjoin__Cong
% 2.57/1.68 = ( ! [Xx: $i,Xy: $i] :
% 2.57/1.68 ( ( Xx = Xy )
% 2.57/1.68 => ! [Xz: $i,Xu: $i] :
% 2.57/1.68 ( ( Xz = Xu )
% 2.57/1.68 => ( ( setadjoin @ Xx @ Xz )
% 2.57/1.68 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(powerset__Cong_type,type,
% 2.57/1.68 powerset__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(powerset__Cong,definition,
% 2.57/1.68 ( powerset__Cong
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( A = B )
% 2.57/1.68 => ( ( powerset @ A )
% 2.57/1.68 = ( powerset @ B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(setunion__Cong_type,type,
% 2.57/1.68 setunion__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(setunion__Cong,definition,
% 2.57/1.68 ( setunion__Cong
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( A = B )
% 2.57/1.68 => ( ( setunion @ A )
% 2.57/1.68 = ( setunion @ B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(omega__Cong_type,type,
% 2.57/1.68 omega__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(omega__Cong,definition,
% 2.57/1.68 ( omega__Cong
% 2.57/1.68 = ( omega = omega ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(exuEu_type,type,
% 2.57/1.68 exuEu: $o ).
% 2.57/1.68
% 2.57/1.68 thf(exuEu,definition,
% 2.57/1.68 ( exuEu
% 2.57/1.68 = ( ! [Xphi: $i > $o] :
% 2.57/1.68 ( ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 => ! [Xx: $i,Xy: $i] :
% 2.57/1.68 ( ( Xphi @ Xx )
% 2.57/1.68 => ( ( Xphi @ Xy )
% 2.57/1.68 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(descr__Cong_type,type,
% 2.57/1.68 descr__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(descr__Cong,definition,
% 2.57/1.68 ( descr__Cong
% 2.57/1.68 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.57/1.68 ( ! [Xx: $i,Xy: $i] :
% 2.57/1.68 ( ( Xx = Xy )
% 2.57/1.68 => ( ( Xphi @ Xx )
% 2.57/1.68 <=> ( Xpsi @ Xy ) ) )
% 2.57/1.68 => ( ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 => ( ( exu
% 2.57/1.68 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.57/1.68 => ( ( descr
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 = ( descr
% 2.57/1.68 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(dsetconstr__Cong_type,type,
% 2.57/1.68 dsetconstr__Cong: $o ).
% 2.57/1.68
% 2.57/1.68 thf(dsetconstr__Cong,definition,
% 2.57/1.68 ( dsetconstr__Cong
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( A = B )
% 2.57/1.68 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.57/1.68 ( ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ! [Xy: $i] :
% 2.57/1.68 ( ( in @ Xy @ B )
% 2.57/1.68 => ( ( Xx = Xy )
% 2.57/1.68 => ( ( Xphi @ Xx )
% 2.57/1.68 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.57/1.68 => ( ( dsetconstr @ A
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 = ( dsetconstr @ B
% 2.57/1.68 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(subset_type,type,
% 2.57/1.68 subset: $i > $i > $o ).
% 2.57/1.68
% 2.57/1.68 thf(disjoint_type,type,
% 2.57/1.68 disjoint: $i > $i > $o ).
% 2.57/1.68
% 2.57/1.68 thf(setsmeet_type,type,
% 2.57/1.68 setsmeet: $i > $i > $o ).
% 2.57/1.68
% 2.57/1.68 thf(subsetI1_type,type,
% 2.57/1.68 subsetI1: $o ).
% 2.57/1.68
% 2.57/1.68 thf(subsetI1,definition,
% 2.57/1.68 ( subsetI1
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ( in @ Xx @ B ) )
% 2.57/1.68 => ( subset @ A @ B ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(eqimpsubset2_type,type,
% 2.57/1.68 eqimpsubset2: $o ).
% 2.57/1.68
% 2.57/1.68 thf(eqimpsubset2,definition,
% 2.57/1.68 ( eqimpsubset2
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( A = B )
% 2.57/1.68 => ( subset @ B @ A ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(eqimpsubset1_type,type,
% 2.57/1.68 eqimpsubset1: $o ).
% 2.57/1.68
% 2.57/1.68 thf(eqimpsubset1,definition,
% 2.57/1.68 ( eqimpsubset1
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( A = B )
% 2.57/1.68 => ( subset @ A @ B ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(subsetI2_type,type,
% 2.57/1.68 subsetI2: $o ).
% 2.57/1.68
% 2.57/1.68 thf(subsetI2,definition,
% 2.57/1.68 ( subsetI2
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ! [Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ( in @ Xx @ B ) )
% 2.57/1.68 => ( subset @ A @ B ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(emptysetsubset_type,type,
% 2.57/1.68 emptysetsubset: $o ).
% 2.57/1.68
% 2.57/1.68 thf(emptysetsubset,definition,
% 2.57/1.68 ( emptysetsubset
% 2.57/1.68 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(subsetE_type,type,
% 2.57/1.68 subsetE: $o ).
% 2.57/1.68
% 2.57/1.68 thf(subsetE,definition,
% 2.57/1.68 ( subsetE
% 2.57/1.68 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.68 ( ( subset @ A @ B )
% 2.57/1.68 => ( ( in @ Xx @ A )
% 2.57/1.68 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(subsetE2_type,type,
% 2.57/1.68 subsetE2: $o ).
% 2.57/1.68
% 2.57/1.68 thf(subsetE2,definition,
% 2.57/1.68 ( subsetE2
% 2.57/1.68 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.68 ( ( subset @ A @ B )
% 2.57/1.68 => ( ~ ( in @ Xx @ B )
% 2.57/1.68 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(notsubsetI_type,type,
% 2.57/1.68 notsubsetI: $o ).
% 2.57/1.68
% 2.57/1.68 thf(notsubsetI,definition,
% 2.57/1.68 ( notsubsetI
% 2.57/1.68 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ( ~ ( in @ Xx @ B )
% 2.57/1.68 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(notequalI1_type,type,
% 2.57/1.68 notequalI1: $o ).
% 2.57/1.68
% 2.57/1.68 thf(notequalI1,definition,
% 2.57/1.68 ( notequalI1
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ~ ( subset @ A @ B )
% 2.57/1.68 => ( A != B ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(notequalI2_type,type,
% 2.57/1.68 notequalI2: $o ).
% 2.57/1.68
% 2.57/1.68 thf(notequalI2,definition,
% 2.57/1.68 ( notequalI2
% 2.57/1.68 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ( ~ ( in @ Xx @ B )
% 2.57/1.68 => ( A != B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(subsetRefl_type,type,
% 2.57/1.68 subsetRefl: $o ).
% 2.57/1.68
% 2.57/1.68 thf(subsetRefl,definition,
% 2.57/1.68 ( subsetRefl
% 2.57/1.68 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(subsetTrans_type,type,
% 2.57/1.68 subsetTrans: $o ).
% 2.57/1.68
% 2.57/1.68 thf(subsetTrans,definition,
% 2.57/1.68 ( subsetTrans
% 2.57/1.68 = ( ! [A: $i,B: $i,C: $i] :
% 2.57/1.68 ( ( subset @ A @ B )
% 2.57/1.68 => ( ( subset @ B @ C )
% 2.57/1.68 => ( subset @ A @ C ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(setadjoinSub_type,type,
% 2.57/1.68 setadjoinSub: $o ).
% 2.57/1.68
% 2.57/1.68 thf(setadjoinSub,definition,
% 2.57/1.68 ( setadjoinSub
% 2.57/1.68 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(setadjoinSub2_type,type,
% 2.57/1.68 setadjoinSub2: $o ).
% 2.57/1.68
% 2.57/1.68 thf(setadjoinSub2,definition,
% 2.57/1.68 ( setadjoinSub2
% 2.57/1.68 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.57/1.68 ( ( subset @ A @ B )
% 2.57/1.68 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(subset2powerset_type,type,
% 2.57/1.68 subset2powerset: $o ).
% 2.57/1.68
% 2.57/1.68 thf(subset2powerset,definition,
% 2.57/1.68 ( subset2powerset
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( subset @ A @ B )
% 2.57/1.68 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(setextsub_type,type,
% 2.57/1.68 setextsub: $o ).
% 2.57/1.68
% 2.57/1.68 thf(setextsub,definition,
% 2.57/1.68 ( setextsub
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( subset @ A @ B )
% 2.57/1.68 => ( ( subset @ B @ A )
% 2.57/1.68 => ( A = B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(subsetemptysetimpeq_type,type,
% 2.57/1.68 subsetemptysetimpeq: $o ).
% 2.57/1.68
% 2.57/1.68 thf(subsetemptysetimpeq,definition,
% 2.57/1.68 ( subsetemptysetimpeq
% 2.57/1.68 = ( ! [A: $i] :
% 2.57/1.68 ( ( subset @ A @ emptyset )
% 2.57/1.68 => ( A = emptyset ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(powersetI1_type,type,
% 2.57/1.68 powersetI1: $o ).
% 2.57/1.68
% 2.57/1.68 thf(powersetI1,definition,
% 2.57/1.68 ( powersetI1
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( subset @ B @ A )
% 2.57/1.68 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(powersetE1_type,type,
% 2.57/1.68 powersetE1: $o ).
% 2.57/1.68
% 2.57/1.68 thf(powersetE1,definition,
% 2.57/1.68 ( powersetE1
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( in @ B @ ( powerset @ A ) )
% 2.57/1.68 => ( subset @ B @ A ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(inPowerset_type,type,
% 2.57/1.68 inPowerset: $o ).
% 2.57/1.68
% 2.57/1.68 thf(inPowerset,definition,
% 2.57/1.68 ( inPowerset
% 2.57/1.68 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(powersetsubset_type,type,
% 2.57/1.68 powersetsubset: $o ).
% 2.57/1.68
% 2.57/1.68 thf(powersetsubset,definition,
% 2.57/1.68 ( powersetsubset
% 2.57/1.68 = ( ! [A: $i,B: $i] :
% 2.57/1.68 ( ( subset @ A @ B )
% 2.57/1.68 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(sepInPowerset_type,type,
% 2.57/1.68 sepInPowerset: $o ).
% 2.57/1.68
% 2.57/1.68 thf(sepInPowerset,definition,
% 2.57/1.68 ( sepInPowerset
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( in
% 2.57/1.68 @ ( dsetconstr @ A
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 @ ( powerset @ A ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(sepSubset_type,type,
% 2.57/1.68 sepSubset: $o ).
% 2.57/1.68
% 2.57/1.68 thf(sepSubset,definition,
% 2.57/1.68 ( sepSubset
% 2.57/1.68 = ( ! [A: $i,Xphi: $i > $o] :
% 2.57/1.68 ( subset
% 2.57/1.68 @ ( dsetconstr @ A
% 2.57/1.68 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.57/1.68 @ A ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(binunion_type,type,
% 2.57/1.68 binunion: $i > $i > $i ).
% 2.57/1.68
% 2.57/1.68 thf(binunion,definition,
% 2.57/1.68 ( binunion
% 2.57/1.68 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(binunionIL_type,type,
% 2.57/1.68 binunionIL: $o ).
% 2.57/1.68
% 2.57/1.68 thf(binunionIL,definition,
% 2.57/1.68 ( binunionIL
% 2.57/1.68 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ A )
% 2.57/1.68 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(upairset2IR_type,type,
% 2.57/1.68 upairset2IR: $o ).
% 2.57/1.68
% 2.57/1.68 thf(upairset2IR,definition,
% 2.57/1.68 ( upairset2IR
% 2.57/1.68 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.57/1.68
% 2.57/1.68 thf(binunionIR,conjecture,
% 2.57/1.68 ( setextAx
% 2.57/1.68 => ( emptysetAx
% 2.57/1.68 => ( setadjoinAx
% 2.57/1.68 => ( powersetAx
% 2.57/1.68 => ( setunionAx
% 2.57/1.68 => ( omega0Ax
% 2.57/1.68 => ( omegaSAx
% 2.57/1.68 => ( omegaIndAx
% 2.57/1.68 => ( replAx
% 2.57/1.68 => ( foundationAx
% 2.57/1.68 => ( wellorderingAx
% 2.57/1.68 => ( descrp
% 2.57/1.68 => ( dsetconstrI
% 2.57/1.68 => ( dsetconstrEL
% 2.57/1.68 => ( dsetconstrER
% 2.57/1.68 => ( exuE1
% 2.57/1.68 => ( prop2setE
% 2.57/1.68 => ( emptysetE
% 2.57/1.68 => ( emptysetimpfalse
% 2.57/1.68 => ( notinemptyset
% 2.57/1.68 => ( exuE3e
% 2.57/1.68 => ( setext
% 2.57/1.68 => ( emptyI
% 2.57/1.68 => ( noeltsimpempty
% 2.57/1.68 => ( setbeta
% 2.57/1.68 => ( nonemptyE1
% 2.57/1.68 => ( nonemptyI
% 2.57/1.68 => ( nonemptyI1
% 2.57/1.68 => ( setadjoinIL
% 2.57/1.68 => ( emptyinunitempty
% 2.57/1.68 => ( setadjoinIR
% 2.57/1.68 => ( setadjoinE
% 2.57/1.68 => ( setadjoinOr
% 2.57/1.68 => ( setoftrueEq
% 2.57/1.68 => ( powersetI
% 2.57/1.68 => ( emptyinPowerset
% 2.57/1.68 => ( emptyInPowerset
% 2.57/1.68 => ( powersetE
% 2.57/1.68 => ( setunionI
% 2.57/1.68 => ( setunionE
% 2.57/1.68 => ( subPowSU
% 2.57/1.68 => ( exuE2
% 2.57/1.68 => ( nonemptyImpWitness
% 2.57/1.68 => ( uniqinunit
% 2.57/1.68 => ( notinsingleton
% 2.57/1.68 => ( eqinunit
% 2.57/1.68 => ( singletonsswitch
% 2.57/1.68 => ( upairsetE
% 2.57/1.68 => ( upairsetIL
% 2.57/1.68 => ( upairsetIR
% 2.57/1.68 => ( emptyE1
% 2.57/1.68 => ( vacuousDall
% 2.57/1.68 => ( quantDeMorgan1
% 2.57/1.68 => ( quantDeMorgan2
% 2.57/1.68 => ( quantDeMorgan3
% 2.57/1.68 => ( quantDeMorgan4
% 2.57/1.68 => ( prop2setI
% 2.57/1.68 => ( prop2set2propI
% 2.57/1.68 => ( notdexE
% 2.57/1.68 => ( notdallE
% 2.57/1.68 => ( exuI1
% 2.57/1.68 => ( exuI3
% 2.57/1.68 => ( exuI2
% 2.57/1.68 => ( inCongP
% 2.57/1.68 => ( in__Cong
% 2.57/1.68 => ( exuE3u
% 2.57/1.68 => ( exu__Cong
% 2.57/1.68 => ( emptyset__Cong
% 2.57/1.68 => ( setadjoin__Cong
% 2.57/1.68 => ( powerset__Cong
% 2.57/1.68 => ( setunion__Cong
% 2.57/1.68 => ( omega__Cong
% 2.57/1.68 => ( exuEu
% 2.57/1.68 => ( descr__Cong
% 2.57/1.68 => ( dsetconstr__Cong
% 2.57/1.68 => ( subsetI1
% 2.57/1.68 => ( eqimpsubset2
% 2.57/1.68 => ( eqimpsubset1
% 2.57/1.68 => ( subsetI2
% 2.57/1.68 => ( emptysetsubset
% 2.57/1.68 => ( subsetE
% 2.57/1.68 => ( subsetE2
% 2.57/1.68 => ( notsubsetI
% 2.57/1.68 => ( notequalI1
% 2.57/1.68 => ( notequalI2
% 2.57/1.68 => ( subsetRefl
% 2.57/1.68 => ( subsetTrans
% 2.57/1.68 => ( setadjoinSub
% 2.57/1.68 => ( setadjoinSub2
% 2.57/1.68 => ( subset2powerset
% 2.57/1.68 => ( setextsub
% 2.57/1.68 => ( subsetemptysetimpeq
% 2.57/1.68 => ( powersetI1
% 2.57/1.68 => ( powersetE1
% 2.57/1.68 => ( inPowerset
% 2.57/1.68 => ( powersetsubset
% 2.57/1.68 => ( sepInPowerset
% 2.57/1.68 => ( sepSubset
% 2.57/1.68 => ( binunionIL
% 2.57/1.68 => ( upairset2IR
% 2.57/1.68 => ! [A: $i,B: $i,Xx: $i] :
% 2.57/1.68 ( ( in @ Xx @ B )
% 2.57/1.68 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.57/1.68 ------------------------
% 2.69/1.70 % (17378)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/2Mi)
% 2.69/1.70 % (17381)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/18Mi)
% 2.69/1.70 % (17377)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_17274 for (2999ds/27Mi)
% 2.69/1.70 % (17374)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/183Mi)
% 2.69/1.70 % (17380)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_17274 for (2999ds/275Mi)
% 2.69/1.70 % (17379)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_17274 for (2999ds/2Mi)
% 2.69/1.70 % (17376)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_17274 for (2999ds/4Mi)
% 2.69/1.70 % (17379)Instruction limit reached!
% 2.69/1.70 % (17379)------------------------------
% 2.69/1.70 % (17379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.70 % (17379)Termination reason: Unknown
% 2.69/1.70 % (17379)Termination phase: shuffling
% 2.69/1.70
% 2.69/1.70 % (17379)Memory used [KB]: 1151
% 2.69/1.70 % (17379)Time elapsed: 0.003 s
% 2.69/1.70 % (17379)Instructions burned: 3 (million)
% 2.69/1.70 % (17379)------------------------------
% 2.69/1.70 % (17379)------------------------------
% 2.69/1.70 % (17378)Instruction limit reached!
% 2.69/1.70 % (17378)------------------------------
% 2.69/1.70 % (17378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.70 % (17378)Termination reason: Unknown
% 2.69/1.70 % (17378)Termination phase: shuffling
% 2.69/1.70
% 2.69/1.70 % (17378)Memory used [KB]: 1151
% 2.69/1.70 % (17378)Time elapsed: 0.003 s
% 2.69/1.70 % (17378)Instructions burned: 2 (million)
% 2.69/1.70 % (17378)------------------------------
% 2.69/1.70 % (17378)------------------------------
% 2.69/1.70 % (17376)Instruction limit reached!
% 2.69/1.70 % (17376)------------------------------
% 2.69/1.70 % (17376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.70 % (17376)Termination reason: Unknown
% 2.69/1.70 % (17376)Termination phase: shuffling
% 2.69/1.70
% 2.69/1.70 % (17376)Memory used [KB]: 1279
% 2.69/1.70 % (17376)Time elapsed: 0.004 s
% 2.69/1.70 % (17376)Instructions burned: 4 (million)
% 2.69/1.70 % (17376)------------------------------
% 2.69/1.70 % (17376)------------------------------
% 2.69/1.71 % (17381)Instruction limit reached!
% 2.69/1.71 % (17381)------------------------------
% 2.69/1.71 % (17381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.71 % (17381)Termination reason: Unknown
% 2.69/1.71 % (17381)Termination phase: Preprocessing 3
% 2.69/1.71
% 2.69/1.71 % (17381)Memory used [KB]: 1663
% 2.69/1.71 % (17381)Time elapsed: 0.012 s
% 2.69/1.71 % (17381)Instructions burned: 19 (million)
% 2.69/1.71 % (17381)------------------------------
% 2.69/1.71 % (17381)------------------------------
% 2.69/1.71 % (17377)Instruction limit reached!
% 2.69/1.71 % (17377)------------------------------
% 2.69/1.71 % (17377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.71 % (17377)Termination reason: Unknown
% 2.69/1.71 % (17377)Termination phase: Property scanning
% 2.69/1.71
% 2.69/1.71 % (17377)Memory used [KB]: 1535
% 2.69/1.71 % (17377)Time elapsed: 0.015 s
% 2.69/1.71 % (17377)Instructions burned: 29 (million)
% 2.69/1.71 % (17377)------------------------------
% 2.69/1.71 % (17377)------------------------------
% 2.69/1.72 % (17382)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/3Mi)
% 2.69/1.72 % (17383)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_17274 for (2999ds/37Mi)
% 2.69/1.72 % (17384)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_17274 for (2999ds/15Mi)
% 2.69/1.72 % (17382)Instruction limit reached!
% 2.69/1.72 % (17382)------------------------------
% 2.69/1.72 % (17382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.72 % (17382)Termination reason: Unknown
% 2.69/1.72 % (17382)Termination phase: shuffling
% 2.69/1.72
% 2.69/1.72 % (17382)Memory used [KB]: 1151
% 2.69/1.72 % (17382)Time elapsed: 0.003 s
% 2.69/1.72 % (17382)Instructions burned: 3 (million)
% 2.69/1.72 % (17382)------------------------------
% 2.69/1.72 % (17382)------------------------------
% 2.69/1.73 % (17384)Instruction limit reached!
% 2.69/1.73 % (17384)------------------------------
% 2.69/1.73 % (17384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.73 % (17384)Termination reason: Unknown
% 2.69/1.73 % (17384)Termination phase: Naming
% 2.69/1.73
% 2.69/1.73 % (17384)Memory used [KB]: 1535
% 2.69/1.73 % (17384)Time elapsed: 0.009 s
% 2.69/1.73 % (17384)Instructions burned: 15 (million)
% 2.69/1.73 % (17384)------------------------------
% 2.69/1.73 % (17384)------------------------------
% 2.69/1.73 % (17385)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_17274 for (2999ds/3Mi)
% 2.69/1.73 % (17385)Instruction limit reached!
% 2.69/1.73 % (17385)------------------------------
% 2.69/1.73 % (17385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.73 % (17385)Termination reason: Unknown
% 2.69/1.73 % (17385)Termination phase: shuffling
% 2.69/1.73
% 2.69/1.73 % (17385)Memory used [KB]: 1151
% 2.69/1.73 % (17385)Time elapsed: 0.003 s
% 2.69/1.73 % (17385)Instructions burned: 3 (million)
% 2.69/1.73 % (17385)------------------------------
% 2.69/1.73 % (17385)------------------------------
% 2.69/1.73 % (17386)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_17274 for (2999ds/1041Mi)
% 2.69/1.74 % (17383)Instruction limit reached!
% 2.69/1.74 % (17383)------------------------------
% 2.69/1.74 % (17383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.74 % (17383)Termination reason: Unknown
% 2.69/1.74 % (17383)Termination phase: Function definition elimination
% 2.69/1.74
% 2.69/1.74 % (17383)Memory used [KB]: 1535
% 2.69/1.74 % (17383)Time elapsed: 0.018 s
% 2.69/1.74 % (17383)Instructions burned: 38 (million)
% 2.69/1.74 % (17383)------------------------------
% 2.69/1.74 % (17383)------------------------------
% 2.69/1.74 % (17387)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/7Mi)
% 2.69/1.74 % (17387)Instruction limit reached!
% 2.69/1.74 % (17387)------------------------------
% 2.69/1.74 % (17387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.74 % (17387)Termination reason: Unknown
% 2.69/1.74 % (17387)Termination phase: shuffling
% 2.69/1.74
% 2.69/1.74 % (17387)Memory used [KB]: 1279
% 2.69/1.74 % (17387)Time elapsed: 0.005 s
% 2.69/1.74 % (17387)Instructions burned: 8 (million)
% 2.69/1.74 % (17387)------------------------------
% 2.69/1.74 % (17387)------------------------------
% 2.69/1.74 % (17388)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/16Mi)
% 2.69/1.75 % (17389)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_17274 for (2999ds/3Mi)
% 2.69/1.75 % (17389)Instruction limit reached!
% 2.69/1.75 % (17389)------------------------------
% 2.69/1.75 % (17389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.75 % (17389)Termination reason: Unknown
% 2.69/1.75 % (17389)Termination phase: shuffling
% 2.69/1.75
% 2.69/1.75 % (17389)Memory used [KB]: 1151
% 2.69/1.75 % (17389)Time elapsed: 0.003 s
% 2.69/1.75 % (17389)Instructions burned: 3 (million)
% 2.69/1.75 % (17389)------------------------------
% 2.69/1.75 % (17389)------------------------------
% 2.69/1.75 % (17388)Instruction limit reached!
% 2.69/1.75 % (17388)------------------------------
% 2.69/1.75 % (17388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.75 % (17388)Termination reason: Unknown
% 2.69/1.75 % (17388)Termination phase: Property scanning
% 2.69/1.75
% 2.69/1.75 % (17388)Memory used [KB]: 1407
% 2.69/1.75 % (17388)Time elapsed: 0.009 s
% 2.69/1.75 % (17388)Instructions burned: 16 (million)
% 2.69/1.75 % (17388)------------------------------
% 2.69/1.75 % (17388)------------------------------
% 2.69/1.75 % (17390)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_17274 for (2999ds/3Mi)
% 2.69/1.75 % (17390)Instruction limit reached!
% 2.69/1.75 % (17390)------------------------------
% 2.69/1.75 % (17390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.75 % (17390)Termination reason: Unknown
% 2.69/1.75 % (17390)Termination phase: shuffling
% 2.69/1.75
% 2.69/1.75 % (17390)Memory used [KB]: 1151
% 2.69/1.75 % (17390)Time elapsed: 0.003 s
% 2.69/1.75 % (17390)Instructions burned: 3 (million)
% 2.69/1.75 % (17390)------------------------------
% 2.69/1.75 % (17390)------------------------------
% 2.69/1.76 % (17391)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/7Mi)
% 2.69/1.76 % (17391)Instruction limit reached!
% 2.69/1.76 % (17391)------------------------------
% 2.69/1.76 % (17391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.76 % (17391)Termination reason: Unknown
% 2.69/1.76 % (17391)Termination phase: shuffling
% 2.69/1.76
% 2.69/1.76 % (17391)Memory used [KB]: 1279
% 2.69/1.76 % (17391)Time elapsed: 0.005 s
% 2.69/1.76 % (17391)Instructions burned: 7 (million)
% 2.69/1.76 % (17391)------------------------------
% 2.69/1.76 % (17391)------------------------------
% 2.69/1.76 % (17392)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/3Mi)
% 2.69/1.76 % (17392)Instruction limit reached!
% 2.69/1.76 % (17392)------------------------------
% 2.69/1.76 % (17392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.76 % (17392)Termination reason: Unknown
% 2.69/1.76 % (17392)Termination phase: shuffling
% 2.69/1.76
% 2.69/1.76 % (17392)Memory used [KB]: 1151
% 2.69/1.76 % (17392)Time elapsed: 0.003 s
% 2.69/1.76 % (17392)Instructions burned: 3 (million)
% 2.69/1.76 % (17392)------------------------------
% 2.69/1.76 % (17392)------------------------------
% 2.69/1.77 % (17393)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/4Mi)
% 2.69/1.77 % (17393)Instruction limit reached!
% 2.69/1.77 % (17393)------------------------------
% 2.69/1.77 % (17393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.77 % (17393)Termination reason: Unknown
% 2.69/1.77 % (17393)Termination phase: shuffling
% 2.69/1.77
% 2.69/1.77 % (17393)Memory used [KB]: 1279
% 2.69/1.77 % (17393)Time elapsed: 0.004 s
% 2.69/1.77 % (17393)Instructions burned: 6 (million)
% 2.69/1.77 % (17393)------------------------------
% 2.69/1.77 % (17393)------------------------------
% 2.69/1.77 % (17394)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/18Mi)
% 2.69/1.77 % (17395)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/710Mi)
% 2.69/1.78 % (17394)Instruction limit reached!
% 2.69/1.78 % (17394)------------------------------
% 2.69/1.78 % (17394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.78 % (17394)Termination reason: Unknown
% 2.69/1.78 % (17394)Termination phase: Property scanning
% 2.69/1.78
% 2.69/1.78 % (17394)Memory used [KB]: 1407
% 2.69/1.78 % (17394)Time elapsed: 0.010 s
% 2.69/1.78 % (17394)Instructions burned: 18 (million)
% 2.69/1.78 % (17394)------------------------------
% 2.69/1.78 % (17394)------------------------------
% 2.69/1.78 % (17396)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/6Mi)
% 2.69/1.78 % (17396)Instruction limit reached!
% 2.69/1.78 % (17396)------------------------------
% 2.69/1.78 % (17396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.78 % (17396)Termination reason: Unknown
% 2.69/1.78 % (17396)Termination phase: shuffling
% 2.69/1.78
% 2.69/1.78 % (17396)Memory used [KB]: 1279
% 2.69/1.78 % (17396)Time elapsed: 0.005 s
% 2.69/1.78 % (17396)Instructions burned: 7 (million)
% 2.69/1.78 % (17396)------------------------------
% 2.69/1.78 % (17396)------------------------------
% 2.69/1.78 % (17397)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_17274 for (2999ds/902Mi)
% 2.69/1.79 % (17374)Instruction limit reached!
% 2.69/1.79 % (17374)------------------------------
% 2.69/1.79 % (17374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.79 % (17374)Termination reason: Unknown
% 2.69/1.79 % (17374)Termination phase: Saturation
% 2.69/1.79
% 2.69/1.79 % (17374)Memory used [KB]: 6908
% 2.69/1.79 % (17374)Time elapsed: 0.091 s
% 2.69/1.79 % (17374)Instructions burned: 184 (million)
% 2.69/1.79 % (17374)------------------------------
% 2.69/1.79 % (17374)------------------------------
% 2.69/1.79 % (17398)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_17274 for (2999ds/21Mi)
% 2.69/1.80 % (17399)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_17274 for (2999ds/5Mi)
% 2.69/1.80 % (17399)Instruction limit reached!
% 2.69/1.80 % (17399)------------------------------
% 2.69/1.80 % (17399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.80 % (17399)Termination reason: Unknown
% 2.69/1.80 % (17399)Termination phase: shuffling
% 2.69/1.80
% 2.69/1.80 % (17399)Memory used [KB]: 1279
% 2.69/1.80 % (17399)Time elapsed: 0.004 s
% 2.69/1.80 % (17399)Instructions burned: 6 (million)
% 2.69/1.80 % (17399)------------------------------
% 2.69/1.80 % (17399)------------------------------
% 2.69/1.80 % (17398)Instruction limit reached!
% 2.69/1.80 % (17398)------------------------------
% 2.69/1.80 % (17398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.80 % (17398)Termination reason: Unknown
% 2.69/1.80 % (17398)Termination phase: Property scanning
% 2.69/1.80
% 2.69/1.80 % (17398)Memory used [KB]: 1407
% 2.69/1.80 % (17398)Time elapsed: 0.011 s
% 2.69/1.80 % (17398)Instructions burned: 21 (million)
% 2.69/1.80 % (17398)------------------------------
% 2.69/1.80 % (17398)------------------------------
% 2.69/1.81 % (17400)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_17274 for (2999ds/6Mi)
% 2.69/1.81 % (17400)Instruction limit reached!
% 2.69/1.81 % (17400)------------------------------
% 2.69/1.81 % (17400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.81 % (17400)Termination reason: Unknown
% 2.69/1.81 % (17400)Termination phase: shuffling
% 2.69/1.81
% 2.69/1.81 % (17400)Memory used [KB]: 1279
% 2.69/1.81 % (17400)Time elapsed: 0.005 s
% 2.69/1.81 % (17400)Instructions burned: 8 (million)
% 2.69/1.81 % (17400)------------------------------
% 2.69/1.81 % (17400)------------------------------
% 2.69/1.82 % (17401)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_17274 for (2998ds/377Mi)
% 2.69/1.82 % (17402)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_17274 for (2998ds/779Mi)
% 2.69/1.83 % (17403)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_17274 for (2998ds/19Mi)
% 2.69/1.83 % (17403)Instruction limit reached!
% 2.69/1.83 % (17403)------------------------------
% 2.69/1.83 % (17403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.83 % (17403)Termination reason: Unknown
% 2.69/1.83 % (17403)Termination phase: Property scanning
% 2.69/1.83
% 2.69/1.83 % (17403)Memory used [KB]: 1407
% 2.69/1.83 % (17403)Time elapsed: 0.010 s
% 2.69/1.83 % (17403)Instructions burned: 19 (million)
% 2.69/1.83 % (17403)------------------------------
% 2.69/1.83 % (17403)------------------------------
% 2.69/1.84 % (17380)Instruction limit reached!
% 2.69/1.84 % (17380)------------------------------
% 2.69/1.84 % (17380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.84 % (17380)Termination reason: Unknown
% 2.69/1.84 % (17380)Termination phase: Saturation
% 2.69/1.84
% 2.69/1.84 % (17380)Memory used [KB]: 7547
% 2.69/1.84 % (17380)Time elapsed: 0.142 s
% 2.69/1.84 % (17380)Instructions burned: 275 (million)
% 2.69/1.84 % (17380)------------------------------
% 2.69/1.84 % (17380)------------------------------
% 2.69/1.85 % (17404)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_17274 for (2998ds/879Mi)
% 2.69/1.86 % (17405)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_17274 for (2998ds/17Mi)
% 2.69/1.87 % (17405)Instruction limit reached!
% 2.69/1.87 % (17405)------------------------------
% 2.69/1.87 % (17405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.87 % (17405)Termination reason: Unknown
% 2.69/1.87 % (17405)Termination phase: Property scanning
% 2.69/1.87
% 2.69/1.87 % (17405)Memory used [KB]: 1407
% 2.69/1.87 % (17405)Time elapsed: 0.010 s
% 2.69/1.87 % (17405)Instructions burned: 18 (million)
% 2.69/1.87 % (17405)------------------------------
% 2.69/1.87 % (17405)------------------------------
% 2.69/1.88 % (17406)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_17274 for (2998ds/3Mi)
% 2.69/1.88 % (17406)Instruction limit reached!
% 2.69/1.88 % (17406)------------------------------
% 2.69/1.88 % (17406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.88 % (17406)Termination reason: Unknown
% 2.69/1.88 % (17406)Termination phase: shuffling
% 2.69/1.88
% 2.69/1.88 % (17406)Memory used [KB]: 1151
% 2.69/1.88 % (17406)Time elapsed: 0.003 s
% 2.69/1.88 % (17406)Instructions burned: 3 (million)
% 2.69/1.88 % (17406)------------------------------
% 2.69/1.88 % (17406)------------------------------
% 2.69/1.90 % (17407)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_17274 for (2997ds/30Mi)
% 2.69/1.91 % (17407)Instruction limit reached!
% 2.69/1.91 % (17407)------------------------------
% 2.69/1.91 % (17407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.91 % (17407)Termination reason: Unknown
% 2.69/1.91 % (17407)Termination phase: Property scanning
% 2.69/1.91
% 2.69/1.91 % (17407)Memory used [KB]: 1535
% 2.69/1.91 % (17407)Time elapsed: 0.016 s
% 2.69/1.91 % (17407)Instructions burned: 31 (million)
% 2.69/1.91 % (17407)------------------------------
% 2.69/1.91 % (17407)------------------------------
% 2.69/1.93 % (17408)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_17274 for (2997ds/127Mi)
% 2.69/1.99 % (17408)Instruction limit reached!
% 2.69/1.99 % (17408)------------------------------
% 2.69/1.99 % (17408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/1.99 % (17408)Termination reason: Unknown
% 2.69/1.99 % (17408)Termination phase: Saturation
% 2.69/1.99
% 2.69/1.99 % (17408)Memory used [KB]: 6780
% 2.69/1.99 % (17408)Time elapsed: 0.063 s
% 2.69/1.99 % (17408)Instructions burned: 128 (million)
% 2.69/1.99 % (17408)------------------------------
% 2.69/1.99 % (17408)------------------------------
% 2.69/2.00 % (17401)Instruction limit reached!
% 2.69/2.00 % (17401)------------------------------
% 2.69/2.00 % (17401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/2.00 % (17401)Termination reason: Unknown
% 2.69/2.00 % (17401)Termination phase: Saturation
% 2.69/2.00
% 2.69/2.00 % (17401)Memory used [KB]: 7164
% 2.69/2.00 % (17401)Time elapsed: 0.208 s
% 2.69/2.00 % (17401)Instructions burned: 378 (million)
% 2.69/2.00 % (17401)------------------------------
% 2.69/2.00 % (17401)------------------------------
% 2.69/2.01 % (17409)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_17274 for (2996ds/100Mi)
% 2.69/2.02 % (17410)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_17274 for (2996ds/3Mi)
% 2.69/2.02 % (17410)Instruction limit reached!
% 2.69/2.02 % (17410)------------------------------
% 2.69/2.02 % (17410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.69/2.02 % (17410)Termination reason: Unknown
% 2.69/2.02 % (17410)Termination phase: shuffling
% 2.69/2.02
% 2.69/2.02 % (17410)Memory used [KB]: 1151
% 2.69/2.02 % (17410)Time elapsed: 0.003 s
% 2.69/2.02 % (17410)Instructions burned: 3 (million)
% 2.69/2.02 % (17410)------------------------------
% 2.69/2.02 % (17410)------------------------------
% 4.98/2.04 % (17411)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_17274 for (2996ds/20Mi)
% 4.98/2.05 % (17411)Instruction limit reached!
% 4.98/2.05 % (17411)------------------------------
% 4.98/2.05 % (17411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.98/2.05 % (17411)Termination reason: Unknown
% 4.98/2.05 % (17411)Termination phase: Preprocessing 3
% 4.98/2.05
% 4.98/2.05 % (17411)Memory used [KB]: 1407
% 4.98/2.05 % (17411)Time elapsed: 0.012 s
% 4.98/2.05 % (17411)Instructions burned: 21 (million)
% 4.98/2.05 % (17411)------------------------------
% 4.98/2.05 % (17411)------------------------------
% 4.98/2.06 % (17409)Instruction limit reached!
% 4.98/2.06 % (17409)------------------------------
% 4.98/2.06 % (17409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.98/2.06 % (17409)Termination reason: Unknown
% 4.98/2.06 % (17409)Termination phase: Saturation
% 4.98/2.06
% 4.98/2.06 % (17409)Memory used [KB]: 6268
% 4.98/2.06 % (17409)Time elapsed: 0.049 s
% 4.98/2.06 % (17409)Instructions burned: 100 (million)
% 4.98/2.06 % (17409)------------------------------
% 4.98/2.06 % (17409)------------------------------
% 4.98/2.06 % (17412)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_17274 for (2996ds/86Mi)
% 4.98/2.07 % (17413)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_17274 for (2996ds/107Mi)
% 4.98/2.10 % (17412)Instruction limit reached!
% 4.98/2.10 % (17412)------------------------------
% 4.98/2.10 % (17412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.98/2.10 % (17412)Termination reason: Unknown
% 4.98/2.10 % (17412)Termination phase: Saturation
% 4.98/2.10
% 4.98/2.10 % (17412)Memory used [KB]: 6396
% 4.98/2.10 % (17412)Time elapsed: 0.041 s
% 4.98/2.10 % (17412)Instructions burned: 87 (million)
% 4.98/2.10 % (17412)------------------------------
% 4.98/2.10 % (17412)------------------------------
% 4.98/2.12 % (17402)Instruction limit reached!
% 4.98/2.12 % (17402)------------------------------
% 4.98/2.12 % (17402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.98/2.12 % (17402)Termination reason: Unknown
% 4.98/2.12 % (17402)Termination phase: Saturation
% 4.98/2.12
% 4.98/2.12 % (17402)Memory used [KB]: 6652
% 4.98/2.12 % (17402)Time elapsed: 0.298 s
% 4.98/2.12 % (17402)Instructions burned: 780 (million)
% 4.98/2.12 % (17402)------------------------------
% 4.98/2.12 % (17402)------------------------------
% 4.98/2.12 % (17414)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_17274 for (2995ds/39Mi)
% 4.98/2.12 % (17413)Instruction limit reached!
% 4.98/2.12 % (17413)------------------------------
% 4.98/2.12 % (17413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 4.98/2.12 % (17413)Termination reason: Unknown
% 4.98/2.12 % (17413)Termination phase: Saturation
% 4.98/2.12
% 4.98/2.12 % (17413)Memory used [KB]: 6652
% 4.98/2.12 % (17413)Time elapsed: 0.050 s
% 4.98/2.12 % (17413)Instructions burned: 108 (million)
% 4.98/2.12 % (17413)------------------------------
% 4.98/2.12 % (17413)------------------------------
% 5.69/2.13 % (17415)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_17274 for (2995ds/448Mi)
% 5.69/2.13 % (17386)Instruction limit reached!
% 5.69/2.13 % (17386)------------------------------
% 5.69/2.13 % (17386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.13 % (17386)Termination reason: Unknown
% 5.69/2.13 % (17386)Termination phase: Saturation
% 5.69/2.13
% 5.69/2.13 % (17386)Memory used [KB]: 7803
% 5.69/2.13 % (17386)Time elapsed: 0.406 s
% 5.69/2.13 % (17386)Instructions burned: 1042 (million)
% 5.69/2.13 % (17386)------------------------------
% 5.69/2.13 % (17386)------------------------------
% 5.69/2.14 % (17414)Instruction limit reached!
% 5.69/2.14 % (17414)------------------------------
% 5.69/2.14 % (17414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.14 % (17414)Termination reason: Unknown
% 5.69/2.14 % (17414)Termination phase: Function definition elimination
% 5.69/2.14
% 5.69/2.14 % (17414)Memory used [KB]: 1535
% 5.69/2.14 % (17414)Time elapsed: 0.019 s
% 5.69/2.14 % (17414)Instructions burned: 39 (million)
% 5.69/2.14 % (17414)------------------------------
% 5.69/2.14 % (17414)------------------------------
% 5.69/2.14 % (17416)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_17274 for (2995ds/46Mi)
% 5.69/2.14 % (17395)Instruction limit reached!
% 5.69/2.14 % (17395)------------------------------
% 5.69/2.14 % (17395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.14 % (17395)Termination reason: Unknown
% 5.69/2.14 % (17395)Termination phase: Saturation
% 5.69/2.14
% 5.69/2.14 % (17395)Memory used [KB]: 8955
% 5.69/2.14 % (17395)Time elapsed: 0.370 s
% 5.69/2.14 % (17395)Instructions burned: 711 (million)
% 5.69/2.14 % (17395)------------------------------
% 5.69/2.14 % (17395)------------------------------
% 5.69/2.15 % (17417)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_17274 for (2995ds/98Mi)
% 5.69/2.15 % (17418)ott+1002_1:1_apa=on:au=on:bd=off:cnfonf=off:fd=off:sos=on:sp=weighted_frequency:i=507:si=on:rtra=on_0 on DTF2THF_17274 for (2995ds/507Mi)
% 5.69/2.16 % (17416)Instruction limit reached!
% 5.69/2.16 % (17416)------------------------------
% 5.69/2.16 % (17416)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.16 % (17416)Termination reason: Unknown
% 5.69/2.16 % (17416)Termination phase: Twee Goal Transformation
% 5.69/2.16
% 5.69/2.16 % (17416)Memory used [KB]: 1535
% 5.69/2.16 % (17416)Time elapsed: 0.022 s
% 5.69/2.16 % (17416)Instructions burned: 47 (million)
% 5.69/2.16 % (17416)------------------------------
% 5.69/2.16 % (17416)------------------------------
% 5.69/2.16 % (17419)dis+1010_2:3_amm=off:fd=preordered:ixr=off:nm=0:pe=on:piset=equals:prag=on:sac=on:tgt=ground:i=149:si=on:rtra=on_0 on DTF2THF_17274 for (2995ds/149Mi)
% 5.69/2.17 % (17420)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_17274 for (2995ds/39Mi)
% 5.69/2.19 % (17420)Instruction limit reached!
% 5.69/2.19 % (17420)------------------------------
% 5.69/2.19 % (17420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.19 % (17420)Termination reason: Unknown
% 5.69/2.19 % (17420)Termination phase: Property scanning
% 5.69/2.19
% 5.69/2.19 % (17420)Memory used [KB]: 1535
% 5.69/2.19 % (17420)Time elapsed: 0.019 s
% 5.69/2.19 % (17420)Instructions burned: 39 (million)
% 5.69/2.19 % (17420)------------------------------
% 5.69/2.19 % (17420)------------------------------
% 5.69/2.19 % (17417)Instruction limit reached!
% 5.69/2.19 % (17417)------------------------------
% 5.69/2.19 % (17417)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 5.69/2.19 % (17417)Termination reason: Unknown
% 5.69/2.19 % (17417)Termination phase: Saturation
% 5.69/2.19
% 5.69/2.19 % (17417)Memory used [KB]: 1663
% 5.69/2.19 % (17417)Time elapsed: 0.043 s
% 5.69/2.19 % (17417)Instructions burned: 99 (million)
% 5.69/2.19 % (17417)------------------------------
% 5.69/2.19 % (17417)------------------------------
% 6.04/2.21 % (17421)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_17274 for (2994ds/6Mi)
% 6.04/2.21 % (17422)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=1087:si=on:rtra=on_0 on DTF2THF_17274 for (2994ds/1087Mi)
% 6.04/2.21 % (17421)Instruction limit reached!
% 6.04/2.21 % (17421)------------------------------
% 6.04/2.21 % (17421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.21 % (17421)Termination reason: Unknown
% 6.04/2.21 % (17421)Termination phase: shuffling
% 6.04/2.21
% 6.04/2.21 % (17421)Memory used [KB]: 1279
% 6.04/2.21 % (17421)Time elapsed: 0.005 s
% 6.04/2.21 % (17421)Instructions burned: 7 (million)
% 6.04/2.21 % (17421)------------------------------
% 6.04/2.21 % (17421)------------------------------
% 6.04/2.23 % (17423)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_17274 for (2994ds/47Mi)
% 6.04/2.23 % (17397)Instruction limit reached!
% 6.04/2.23 % (17397)------------------------------
% 6.04/2.23 % (17397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.23 % (17397)Termination reason: Unknown
% 6.04/2.23 % (17397)Termination phase: Saturation
% 6.04/2.23
% 6.04/2.23 % (17397)Memory used [KB]: 9594
% 6.04/2.23 % (17397)Time elapsed: 0.466 s
% 6.04/2.23 % (17397)Instructions burned: 902 (million)
% 6.04/2.23 % (17397)------------------------------
% 6.04/2.23 % (17397)------------------------------
% 6.04/2.23 % (17419)Instruction limit reached!
% 6.04/2.23 % (17419)------------------------------
% 6.04/2.23 % (17419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.23 % (17419)Termination reason: Unknown
% 6.04/2.23 % (17419)Termination phase: Saturation
% 6.04/2.23
% 6.04/2.23 % (17419)Memory used [KB]: 6652
% 6.04/2.23 % (17419)Time elapsed: 0.075 s
% 6.04/2.23 % (17419)Instructions burned: 150 (million)
% 6.04/2.23 % (17419)------------------------------
% 6.04/2.23 % (17419)------------------------------
% 6.04/2.25 % (17424)lrs+1010_1:128_av=off:cbe=off:cnfonf=lazy_simp:fsr=off:ntd=on:ss=axioms:st=1.5:i=44:si=on:rtra=on_0 on DTF2THF_17274 for (2994ds/44Mi)
% 6.04/2.25 % (17423)Instruction limit reached!
% 6.04/2.25 % (17423)------------------------------
% 6.04/2.25 % (17423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.25 % (17423)Termination reason: Unknown
% 6.04/2.25 % (17423)Termination phase: Saturation
% 6.04/2.25
% 6.04/2.25 % (17423)Memory used [KB]: 6012
% 6.04/2.25 % (17423)Time elapsed: 0.023 s
% 6.04/2.25 % (17423)Instructions burned: 47 (million)
% 6.04/2.25 % (17423)------------------------------
% 6.04/2.25 % (17423)------------------------------
% 6.04/2.25 % (17425)dis+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=432:si=on:rtra=on_0 on DTF2THF_17274 for (2994ds/432Mi)
% 6.04/2.26 % (17424)Instruction limit reached!
% 6.04/2.26 % (17424)------------------------------
% 6.04/2.26 % (17424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.26 % (17424)Termination reason: Unknown
% 6.04/2.26 % (17424)Termination phase: Property scanning
% 6.04/2.26
% 6.04/2.26 % (17424)Memory used [KB]: 1535
% 6.04/2.26 % (17424)Time elapsed: 0.021 s
% 6.04/2.26 % (17424)Instructions burned: 45 (million)
% 6.04/2.26 % (17424)------------------------------
% 6.04/2.26 % (17424)------------------------------
% 6.04/2.27 % (17426)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_17274 for (2994ds/62Mi)
% 6.04/2.28 % (17427)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17274 for (2994ds/31Mi)
% 6.04/2.29 % (17404)Instruction limit reached!
% 6.04/2.29 % (17404)------------------------------
% 6.04/2.29 % (17404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.29 % (17404)Termination reason: Unknown
% 6.04/2.29 % (17404)Termination phase: Saturation
% 6.04/2.29
% 6.04/2.29 % (17404)Memory used [KB]: 7675
% 6.04/2.29 % (17404)Time elapsed: 0.439 s
% 6.04/2.29 % (17404)Instructions burned: 879 (million)
% 6.04/2.29 % (17404)------------------------------
% 6.04/2.29 % (17404)------------------------------
% 6.04/2.29 % (17426)Instruction limit reached!
% 6.04/2.29 % (17426)------------------------------
% 6.04/2.29 % (17426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.29 % (17426)Termination reason: Unknown
% 6.04/2.29 % (17426)Termination phase: Saturation
% 6.04/2.29
% 6.04/2.29 % (17426)Memory used [KB]: 6140
% 6.04/2.29 % (17426)Time elapsed: 0.029 s
% 6.04/2.29 % (17426)Instructions burned: 63 (million)
% 6.04/2.29 % (17426)------------------------------
% 6.04/2.29 % (17426)------------------------------
% 6.04/2.30 % (17427)Instruction limit reached!
% 6.04/2.30 % (17427)------------------------------
% 6.04/2.30 % (17427)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.04/2.30 % (17427)Termination reason: Unknown
% 6.04/2.30 % (17427)Termination phase: Property scanning
% 6.04/2.30
% 6.04/2.30 % (17427)Memory used [KB]: 1535
% 6.04/2.30 % (17427)Time elapsed: 0.016 s
% 6.04/2.30 % (17427)Instructions burned: 32 (million)
% 6.04/2.30 % (17427)------------------------------
% 6.04/2.30 % (17427)------------------------------
% 6.44/2.30 % (17415)Instruction limit reached!
% 6.44/2.30 % (17415)------------------------------
% 6.44/2.30 % (17415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.30 % (17415)Termination reason: Unknown
% 6.44/2.30 % (17415)Termination phase: Saturation
% 6.44/2.30
% 6.44/2.30 % (17415)Memory used [KB]: 6268
% 6.44/2.30 % (17415)Time elapsed: 0.167 s
% 6.44/2.30 % (17415)Instructions burned: 449 (million)
% 6.44/2.30 % (17415)------------------------------
% 6.44/2.30 % (17415)------------------------------
% 6.44/2.30 % (17428)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/96Mi)
% 6.44/2.31 % (17429)lrs+1002_1:4_au=on:cbe=off:cnfonf=lazy_pi_sigma_gen:hud=15:inj=on:nwc=4.0:s2a=on:sac=on:sp=reverse_arity:i=453:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/453Mi)
% 6.44/2.31 % (17430)lrs-1004_1:1_au=on:bsd=on:cbe=off:cnfonf=off:fe=axiom:fsd=on:i=71:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/71Mi)
% 6.44/2.31 % (17431)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/83Mi)
% 6.44/2.34 % (17430)Instruction limit reached!
% 6.44/2.34 % (17430)------------------------------
% 6.44/2.34 % (17430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.34 % (17430)Termination reason: Unknown
% 6.44/2.34 % (17430)Termination phase: Saturation
% 6.44/2.34
% 6.44/2.34 % (17430)Memory used [KB]: 6268
% 6.44/2.34 % (17430)Time elapsed: 0.034 s
% 6.44/2.34 % (17430)Instructions burned: 71 (million)
% 6.44/2.34 % (17430)------------------------------
% 6.44/2.34 % (17430)------------------------------
% 6.44/2.35 % (17428)Instruction limit reached!
% 6.44/2.35 % (17428)------------------------------
% 6.44/2.35 % (17428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.35 % (17428)Termination reason: Unknown
% 6.44/2.35 % (17428)Termination phase: Saturation
% 6.44/2.35
% 6.44/2.35 % (17428)Memory used [KB]: 6524
% 6.44/2.35 % (17428)Time elapsed: 0.046 s
% 6.44/2.35 % (17428)Instructions burned: 97 (million)
% 6.44/2.35 % (17428)------------------------------
% 6.44/2.35 % (17428)------------------------------
% 6.44/2.35 % (17431)Instruction limit reached!
% 6.44/2.35 % (17431)------------------------------
% 6.44/2.35 % (17431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.35 % (17431)Termination reason: Unknown
% 6.44/2.35 % (17431)Termination phase: Saturation
% 6.44/2.35
% 6.44/2.35 % (17431)Memory used [KB]: 6268
% 6.44/2.35 % (17431)Time elapsed: 0.039 s
% 6.44/2.35 % (17431)Instructions burned: 84 (million)
% 6.44/2.35 % (17431)------------------------------
% 6.44/2.35 % (17431)------------------------------
% 6.44/2.36 % (17432)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/11Mi)
% 6.44/2.36 % (17433)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_gen_be_off:fsr=off:spb=non_intro:i=41:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/41Mi)
% 6.44/2.37 % (17432)Instruction limit reached!
% 6.44/2.37 % (17432)------------------------------
% 6.44/2.37 % (17432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.37 % (17432)Termination reason: Unknown
% 6.44/2.37 % (17432)Termination phase: shuffling
% 6.44/2.37
% 6.44/2.37 % (17432)Memory used [KB]: 1407
% 6.44/2.37 % (17432)Time elapsed: 0.007 s
% 6.44/2.37 % (17432)Instructions burned: 11 (million)
% 6.44/2.37 % (17432)------------------------------
% 6.44/2.37 % (17432)------------------------------
% 6.44/2.37 % (17434)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/6Mi)
% 6.44/2.37 % (17434)Instruction limit reached!
% 6.44/2.37 % (17434)------------------------------
% 6.44/2.37 % (17434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.37 % (17434)Termination reason: Unknown
% 6.44/2.37 % (17434)Termination phase: shuffling
% 6.44/2.37
% 6.44/2.37 % (17434)Memory used [KB]: 1279
% 6.44/2.37 % (17434)Time elapsed: 0.005 s
% 6.44/2.37 % (17434)Instructions burned: 8 (million)
% 6.44/2.37 % (17434)------------------------------
% 6.44/2.37 % (17434)------------------------------
% 6.44/2.38 % (17435)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/150Mi)
% 6.44/2.38 % (17433)Instruction limit reached!
% 6.44/2.38 % (17433)------------------------------
% 6.44/2.38 % (17433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.44/2.38 % (17433)Termination reason: Unknown
% 6.44/2.38 % (17433)Termination phase: Property scanning
% 6.44/2.38
% 6.44/2.38 % (17433)Memory used [KB]: 1535
% 6.44/2.38 % (17433)Time elapsed: 0.020 s
% 6.44/2.38 % (17433)Instructions burned: 42 (million)
% 6.44/2.38 % (17433)------------------------------
% 6.44/2.38 % (17433)------------------------------
% 6.44/2.39 % (17436)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_17274 for (2993ds/343Mi)
% 6.85/2.40 % (17437)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=109:si=on:rtra=on_0 on DTF2THF_17274 for (2992ds/109Mi)
% 6.85/2.40 % (17418)Instruction limit reached!
% 6.85/2.40 % (17418)------------------------------
% 6.85/2.40 % (17418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.40 % (17418)Termination reason: Unknown
% 6.85/2.40 % (17418)Termination phase: Saturation
% 6.85/2.40
% 6.85/2.40 % (17418)Memory used [KB]: 7164
% 6.85/2.40 % (17418)Time elapsed: 0.253 s
% 6.85/2.40 % (17418)Instructions burned: 508 (million)
% 6.85/2.40 % (17418)------------------------------
% 6.85/2.40 % (17418)------------------------------
% 6.85/2.42 % (17438)dis+10_1:1_au=on:c=on:e2e=on:fsr=off:sos=all:sp=const_frequency:ss=axioms:i=253:si=on:rtra=on_0 on DTF2THF_17274 for (2992ds/253Mi)
% 6.85/2.42 % (17425)Instruction limit reached!
% 6.85/2.42 % (17425)------------------------------
% 6.85/2.42 % (17425)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.42 % (17425)Termination reason: Unknown
% 6.85/2.42 % (17425)Termination phase: Saturation
% 6.85/2.42
% 6.85/2.42 % (17425)Memory used [KB]: 2558
% 6.85/2.42 % (17425)Time elapsed: 0.175 s
% 6.85/2.42 % (17425)Instructions burned: 433 (million)
% 6.85/2.42 % (17425)------------------------------
% 6.85/2.42 % (17425)------------------------------
% 6.85/2.44 % (17439)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_17274 for (2992ds/140Mi)
% 6.85/2.45 % (17437)Instruction limit reached!
% 6.85/2.45 % (17437)------------------------------
% 6.85/2.45 % (17437)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.45 % (17437)Termination reason: Unknown
% 6.85/2.45 % (17437)Termination phase: Saturation
% 6.85/2.45
% 6.85/2.45 % (17437)Memory used [KB]: 6652
% 6.85/2.45 % (17437)Time elapsed: 0.051 s
% 6.85/2.45 % (17437)Instructions burned: 109 (million)
% 6.85/2.45 % (17437)------------------------------
% 6.85/2.45 % (17437)------------------------------
% 6.85/2.46 % (17435)Instruction limit reached!
% 6.85/2.46 % (17435)------------------------------
% 6.85/2.46 % (17435)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.46 % (17435)Termination reason: Unknown
% 6.85/2.46 % (17435)Termination phase: Saturation
% 6.85/2.46
% 6.85/2.46 % (17435)Memory used [KB]: 7164
% 6.85/2.46 % (17435)Time elapsed: 0.077 s
% 6.85/2.46 % (17435)Instructions burned: 151 (million)
% 6.85/2.46 % (17435)------------------------------
% 6.85/2.46 % (17435)------------------------------
% 6.85/2.47 % (17440)dis+1010_16:1_acc=model:au=on:avsq=on:cond=fast:plsq=on:plsqc=2:plsqr=9267,262144:i=614:si=on:rtra=on_0 on DTF2THF_17274 for (2992ds/614Mi)
% 6.85/2.47 % (17441)lrs+1002_1:1_e2e=on:fde=unused:fe=axiom:prag=on:sd=1:sos=on:ss=axioms:st=2.0:i=202:si=on:rtra=on_0 on DTF2THF_17274 for (2992ds/202Mi)
% 6.85/2.48 % (17429)Instruction limit reached!
% 6.85/2.48 % (17429)------------------------------
% 6.85/2.48 % (17429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.85/2.48 % (17429)Termination reason: Unknown
% 6.85/2.48 % (17429)Termination phase: Saturation
% 6.85/2.48
% 6.85/2.48 % (17429)Memory used [KB]: 6268
% 6.85/2.48 % (17429)Time elapsed: 0.174 s
% 6.85/2.48 % (17429)Instructions burned: 453 (million)
% 6.85/2.48 % (17429)------------------------------
% 6.85/2.48 % (17429)------------------------------
% 7.65/2.50 % (17439)Refutation not found, incomplete strategy
% 7.65/2.50 % (17439)------------------------------
% 7.65/2.50 % (17439)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.50 % (17439)Termination reason: Refutation not found, incomplete strategy
% 7.65/2.50
% 7.65/2.50
% 7.65/2.50 % (17439)Memory used [KB]: 6140
% 7.65/2.50 % (17439)Time elapsed: 0.058 s
% 7.65/2.50 % (17439)Instructions burned: 123 (million)
% 7.65/2.50 % (17439)------------------------------
% 7.65/2.50 % (17439)------------------------------
% 7.65/2.50 % (17442)dis+1002_1:1_au=on:cs=on:ins=3:kws=inv_frequency:nwc=10.0:ss=axioms:st=3.0:i=339:si=on:rtra=on_0 on DTF2THF_17274 for (2991ds/339Mi)
% 7.65/2.51 % (17443)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=283:si=on:rtra=on_0 on DTF2THF_17274 for (2991ds/283Mi)
% 7.65/2.55 % (17438)Instruction limit reached!
% 7.65/2.55 % (17438)------------------------------
% 7.65/2.55 % (17438)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.55 % (17438)Termination reason: Unknown
% 7.65/2.55 % (17438)Termination phase: Saturation
% 7.65/2.55
% 7.65/2.55 % (17438)Memory used [KB]: 7675
% 7.65/2.55 % (17438)Time elapsed: 0.127 s
% 7.65/2.55 % (17438)Instructions burned: 253 (million)
% 7.65/2.55 % (17438)------------------------------
% 7.65/2.55 % (17438)------------------------------
% 7.65/2.55 % (17436)Instruction limit reached!
% 7.65/2.55 % (17436)------------------------------
% 7.65/2.55 % (17436)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.55 % (17436)Termination reason: Unknown
% 7.65/2.55 % (17436)Termination phase: Saturation
% 7.65/2.55
% 7.65/2.55 % (17436)Memory used [KB]: 7164
% 7.65/2.55 % (17436)Time elapsed: 0.167 s
% 7.65/2.55 % (17436)Instructions burned: 344 (million)
% 7.65/2.55 % (17436)------------------------------
% 7.65/2.55 % (17436)------------------------------
% 7.65/2.56 % (17444)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_17274 for (2991ds/134Mi)
% 7.65/2.57 % (17445)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_17274 for (2991ds/298Mi)
% 7.65/2.58 % (17441)Instruction limit reached!
% 7.65/2.58 % (17441)------------------------------
% 7.65/2.58 % (17441)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.65/2.58 % (17441)Termination reason: Unknown
% 7.65/2.58 % (17441)Termination phase: Saturation
% 7.65/2.58
% 7.65/2.58 % (17441)Memory used [KB]: 7547
% 7.65/2.58 % (17441)Time elapsed: 0.107 s
% 7.65/2.58 % (17441)Instructions burned: 203 (million)
% 7.65/2.58 % (17441)------------------------------
% 7.65/2.58 % (17441)------------------------------
% 7.65/2.60 % (17446)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_17274 for (2990ds/192Mi)
% 8.18/2.63 % (17444)Instruction limit reached!
% 8.18/2.63 % (17444)------------------------------
% 8.18/2.63 % (17444)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.63 % (17444)Termination reason: Unknown
% 8.18/2.63 % (17444)Termination phase: Saturation
% 8.18/2.63
% 8.18/2.63 % (17444)Memory used [KB]: 6780
% 8.18/2.63 % (17444)Time elapsed: 0.066 s
% 8.18/2.63 % (17444)Instructions burned: 135 (million)
% 8.18/2.63 % (17444)------------------------------
% 8.18/2.63 % (17444)------------------------------
% 8.18/2.63 % (17443)Instruction limit reached!
% 8.18/2.63 % (17443)------------------------------
% 8.18/2.63 % (17443)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.63 % (17443)Termination reason: Unknown
% 8.18/2.63 % (17443)Termination phase: Saturation
% 8.18/2.63
% 8.18/2.63 % (17443)Memory used [KB]: 8059
% 8.18/2.63 % (17443)Time elapsed: 0.116 s
% 8.18/2.63 % (17443)Instructions burned: 285 (million)
% 8.18/2.63 % (17443)------------------------------
% 8.18/2.63 % (17443)------------------------------
% 8.18/2.64 % (17447)lrs+10_1:1_bd=off:hud=1:nm=0:prag=on:sd=2:sgt=32:sos=all:ss=axioms:i=258:si=on:rtra=on_0 on DTF2THF_17274 for (2990ds/258Mi)
% 8.18/2.64 % (17448)lrs+1002_1:1024_au=on:cond=fast:ntd=on:piset=and:plsq=on:plsqc=1:plsqr=183491,1048576:sac=on:tgt=ground:i=90:si=on:rtra=on_0 on DTF2THF_17274 for (2990ds/90Mi)
% 8.18/2.66 % (17442)Instruction limit reached!
% 8.18/2.66 % (17442)------------------------------
% 8.18/2.66 % (17442)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.66 % (17442)Termination reason: Unknown
% 8.18/2.66 % (17442)Termination phase: Saturation
% 8.18/2.66
% 8.18/2.66 % (17442)Memory used [KB]: 7036
% 8.18/2.66 % (17442)Time elapsed: 0.161 s
% 8.18/2.66 % (17442)Instructions burned: 339 (million)
% 8.18/2.66 % (17442)------------------------------
% 8.18/2.66 % (17442)------------------------------
% 8.18/2.67 % (17449)dis+1004_16:1_avsq=on:avsqr=1,16:cnfonf=lazy_gen:cs=on:fe=off:tgt=ground:tnu=1:i=231:si=on:rtra=on_0 on DTF2THF_17274 for (2990ds/231Mi)
% 8.18/2.69 % (17448)Instruction limit reached!
% 8.18/2.69 % (17448)------------------------------
% 8.18/2.69 % (17448)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.69 % (17448)Termination reason: Unknown
% 8.18/2.69 % (17448)Termination phase: Saturation
% 8.18/2.69
% 8.18/2.69 % (17448)Memory used [KB]: 6524
% 8.18/2.69 % (17448)Time elapsed: 0.043 s
% 8.18/2.69 % (17448)Instructions burned: 90 (million)
% 8.18/2.69 % (17448)------------------------------
% 8.18/2.69 % (17448)------------------------------
% 8.18/2.69 % (17446)Instruction limit reached!
% 8.18/2.69 % (17446)------------------------------
% 8.18/2.69 % (17446)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.69 % (17446)Termination reason: Unknown
% 8.18/2.69 % (17446)Termination phase: Saturation
% 8.18/2.69
% 8.18/2.69 % (17446)Memory used [KB]: 7036
% 8.18/2.69 % (17446)Time elapsed: 0.095 s
% 8.18/2.69 % (17446)Instructions burned: 193 (million)
% 8.18/2.69 % (17446)------------------------------
% 8.18/2.69 % (17446)------------------------------
% 8.18/2.69 % (17445)Instruction limit reached!
% 8.18/2.69 % (17445)------------------------------
% 8.18/2.69 % (17445)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.18/2.69 % (17445)Termination reason: Unknown
% 8.18/2.69 % (17445)Termination phase: Saturation
% 8.18/2.69
% 8.18/2.69 % (17445)Memory used [KB]: 6396
% 8.18/2.69 % (17445)Time elapsed: 0.127 s
% 8.18/2.69 % (17445)Instructions burned: 298 (million)
% 8.18/2.69 % (17445)------------------------------
% 8.18/2.69 % (17445)------------------------------
% 8.88/2.70 % (17450)lrs+1002_1:1_au=on:s2a=on:sgt=32:slsq=on:slsqc=1:slsql=off:ss=axioms:i=458:si=on:rtra=on_0 on DTF2THF_17274 for (2989ds/458Mi)
% 8.88/2.70 % (17451)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17274 for (2989ds/31Mi)
% 8.88/2.71 % (17453)lrs+10_1:1_cnfonf=lazy_gen:kws=inv_precedence:nwc=10.0:s2a=on:sp=weighted_frequency:ss=axioms:i=297:si=on:rtra=on_0 on DTF2THF_17274 for (2989ds/297Mi)
% 8.88/2.72 % (17451)Instruction limit reached!
% 8.88/2.72 % (17451)------------------------------
% 8.88/2.72 % (17451)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.88/2.72 % (17451)Termination reason: Unknown
% 8.88/2.72 % (17451)Termination phase: Property scanning
% 8.88/2.72
% 8.88/2.72 % (17451)Memory used [KB]: 1535
% 8.88/2.72 % (17451)Time elapsed: 0.016 s
% 8.88/2.72 % (17451)Instructions burned: 31 (million)
% 8.88/2.72 % (17451)------------------------------
% 8.88/2.72 % (17451)------------------------------
% 8.88/2.74 % (17454)dis+2_1:4_amm=off:au=on:cbe=off:cnfonf=lazy_gen:hfaw=0:hfsq=on:hfsql=off:plsq=on:plsqc=1:plsqr=35,4:sac=on:i=987:si=on:rtra=on_0 on DTF2THF_17274 for (2989ds/987Mi)
% 8.88/2.76 % (17422)Instruction limit reached!
% 8.88/2.76 % (17422)------------------------------
% 8.88/2.76 % (17422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.88/2.76 % (17422)Termination reason: Unknown
% 8.88/2.76 % (17422)Termination phase: Saturation
% 8.88/2.76
% 8.88/2.76 % (17422)Memory used [KB]: 9850
% 8.88/2.76 % (17422)Time elapsed: 0.557 s
% 8.88/2.76 % (17422)Instructions burned: 1088 (million)
% 8.88/2.76 % (17422)------------------------------
% 8.88/2.76 % (17422)------------------------------
% 8.88/2.77 % (17447)Instruction limit reached!
% 8.88/2.77 % (17447)------------------------------
% 8.88/2.77 % (17447)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.88/2.77 % (17447)Termination reason: Unknown
% 8.88/2.77 % (17447)Termination phase: Saturation
% 8.88/2.77
% 8.88/2.77 % (17447)Memory used [KB]: 7036
% 8.88/2.77 % (17447)Time elapsed: 0.127 s
% 8.88/2.77 % (17447)Instructions burned: 259 (million)
% 8.88/2.77 % (17447)------------------------------
% 8.88/2.77 % (17447)------------------------------
% 8.88/2.77 % (17440)Instruction limit reached!
% 8.88/2.77 % (17440)------------------------------
% 8.88/2.77 % (17440)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.88/2.77 % (17440)Termination reason: Unknown
% 8.88/2.77 % (17440)Termination phase: Saturation
% 8.88/2.77
% 8.88/2.77 % (17440)Memory used [KB]: 7931
% 8.88/2.77 % (17440)Time elapsed: 0.306 s
% 8.88/2.77 % (17440)Instructions burned: 614 (million)
% 8.88/2.77 % (17440)------------------------------
% 8.88/2.77 % (17440)------------------------------
% 8.88/2.78 % (17455)lrs+10_1:1024_avsq=on:avsqc=4:avsqr=584411,1048576:bd=off:bet=on:br=off:chr=on:fsd=on:fsdmm=1:hud=10:nm=0:ntd=on:nwc=9.0:piset=or:plsq=on:plsqc=2:plsql=on:plsqr=852219,1048576:rawr=on:sp=const_frequency:spb=units:i=182:si=on:rtra=on_0 on DTF2THF_17274 for (2989ds/182Mi)
% 8.88/2.79 % (17456)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=182:si=on:rtra=on_0 on DTF2THF_17274 for (2989ds/182Mi)
% 8.88/2.79 % (17457)dis+10_1:8_cha=on:cnfonf=lazy_pi_sigma_gen:fe=axiom:hud=5:plsq=on:plsqr=32,1:prag=on:sos=all:i=154:si=on:rtra=on_0 on DTF2THF_17274 for (2989ds/154Mi)
% 8.88/2.79 % (17449)Instruction limit reached!
% 8.88/2.79 % (17449)------------------------------
% 8.88/2.79 % (17449)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.88/2.79 % (17449)Termination reason: Unknown
% 8.88/2.79 % (17449)Termination phase: Saturation
% 8.88/2.79
% 8.88/2.79 % (17449)Memory used [KB]: 9466
% 8.88/2.79 % (17449)Time elapsed: 0.116 s
% 8.88/2.79 % (17449)Instructions burned: 232 (million)
% 8.88/2.79 % (17449)------------------------------
% 8.88/2.79 % (17449)------------------------------
% 10.08/2.80 % (17458)dis+1003_1:64_atotf=0.4:au=on:fsr=off:hflw=5:hfsq=on:hfsqc=20:hfsql=off:plsq=on:plsqc=1:plsqr=32,1:i=79:si=on:rtra=on_0 on DTF2THF_17274 for (2988ds/79Mi)
% 10.08/2.83 % (17453)Instruction limit reached!
% 10.08/2.83 % (17453)------------------------------
% 10.08/2.83 % (17453)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.83 % (17453)Termination reason: Unknown
% 10.08/2.83 % (17453)Termination phase: Saturation
% 10.08/2.83
% 10.08/2.83 % (17453)Memory used [KB]: 7419
% 10.08/2.83 % (17453)Time elapsed: 0.119 s
% 10.08/2.83 % (17453)Instructions burned: 299 (million)
% 10.08/2.83 % (17453)------------------------------
% 10.08/2.83 % (17453)------------------------------
% 10.08/2.84 % (17458)Instruction limit reached!
% 10.08/2.84 % (17458)------------------------------
% 10.08/2.84 % (17458)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.84 % (17458)Termination reason: Unknown
% 10.08/2.84 % (17458)Termination phase: Saturation
% 10.08/2.84
% 10.08/2.84 % (17458)Memory used [KB]: 6268
% 10.08/2.84 % (17458)Time elapsed: 0.038 s
% 10.08/2.84 % (17458)Instructions burned: 80 (million)
% 10.08/2.84 % (17458)------------------------------
% 10.08/2.84 % (17458)------------------------------
% 10.08/2.84 % (17459)dis+1010_5:2_anc=all_dependent:awrs=converge:bd=off:bet=on:c=on:cha=on:cnfonf=lazy_not_gen_be_off:fe=axiom:hud=5:kws=precedence:piset=and:prag=on:s2a=on:sac=on:slsq=on:slsqc=1:sp=reverse_arity:ss=axioms:st=1.5:i=216:si=on:rtra=on_0 on DTF2THF_17274 for (2988ds/216Mi)
% 10.08/2.85 % (17457)Instruction limit reached!
% 10.08/2.85 % (17457)------------------------------
% 10.08/2.85 % (17457)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.85 % (17457)Termination reason: Unknown
% 10.08/2.85 % (17457)Termination phase: Saturation
% 10.08/2.85
% 10.08/2.85 % (17457)Memory used [KB]: 6140
% 10.08/2.85 % (17457)Time elapsed: 0.063 s
% 10.08/2.85 % (17457)Instructions burned: 155 (million)
% 10.08/2.85 % (17457)------------------------------
% 10.08/2.85 % (17457)------------------------------
% 10.08/2.86 % (17460)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_17274 for (2988ds/114Mi)
% 10.08/2.86 % (17461)dis+1002_1:1_acc=on:au=on:bd=off:e2e=on:sgt=8:ss=axioms:i=922:si=on:rtra=on_0 on DTF2THF_17274 for (2988ds/922Mi)
% 10.08/2.87 % (17455)Instruction limit reached!
% 10.08/2.87 % (17455)------------------------------
% 10.08/2.87 % (17455)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.87 % (17455)Termination reason: Unknown
% 10.08/2.87 % (17455)Termination phase: Saturation
% 10.08/2.87
% 10.08/2.87 % (17455)Memory used [KB]: 6908
% 10.08/2.87 % (17455)Time elapsed: 0.090 s
% 10.08/2.87 % (17455)Instructions burned: 183 (million)
% 10.08/2.87 % (17455)------------------------------
% 10.08/2.87 % (17455)------------------------------
% 10.08/2.88 % (17456)Instruction limit reached!
% 10.08/2.88 % (17456)------------------------------
% 10.08/2.88 % (17456)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.08/2.88 % (17456)Termination reason: Unknown
% 10.08/2.88 % (17456)Termination phase: Saturation
% 10.08/2.88
% 10.08/2.88 % (17456)Memory used [KB]: 8443
% 10.08/2.88 % (17456)Time elapsed: 0.094 s
% 10.08/2.88 % (17456)Instructions burned: 182 (million)
% 10.08/2.88 % (17456)------------------------------
% 10.08/2.88 % (17456)------------------------------
% 10.08/2.89 % (17462)lrs+10_1:128_au=on:bd=off:cnfonf=lazy_not_gen_be_off:nwc=10.0:piset=and:i=182:si=on:rtra=on_0 on DTF2THF_17274 for (2988ds/182Mi)
% 10.08/2.89 % (17463)ott+1010_1:1024_au=on:av=off:c=on:cnfonf=conj_eager:piset=equals:s2a=on:sp=occurrence:spb=units:ss=axioms:i=164:si=on:rtra=on_0 on DTF2THF_17274 for (2988ds/164Mi)
% 10.56/2.91 % (17460)Instruction limit reached!
% 10.56/2.91 % (17460)------------------------------
% 10.56/2.91 % (17460)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.56/2.91 % (17460)Termination reason: Unknown
% 10.56/2.91 % (17460)Termination phase: Saturation
% 10.56/2.91
% 10.56/2.91 % (17460)Memory used [KB]: 6780
% 10.56/2.91 % (17460)Time elapsed: 0.054 s
% 10.56/2.91 % (17460)Instructions burned: 114 (million)
% 10.56/2.91 % (17460)------------------------------
% 10.56/2.91 % (17460)------------------------------
% 10.56/2.93 % (17464)lrs+1004_1:1_cnfonf=lazy_pi_sigma_gen:fe=off:gs=on:hud=10:prag=on:tnu=1:i=50:si=on:rtra=on_0 on DTF2THF_17274 for (2987ds/50Mi)
% 10.56/2.93 % (17459)Instruction limit reached!
% 10.56/2.93 % (17459)------------------------------
% 10.56/2.93 % (17459)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.56/2.93 % (17459)Termination reason: Unknown
% 10.56/2.93 % (17459)Termination phase: Saturation
% 10.56/2.93
% 10.56/2.93 % (17459)Memory used [KB]: 7036
% 10.56/2.93 % (17459)Time elapsed: 0.087 s
% 10.56/2.93 % (17459)Instructions burned: 217 (million)
% 10.56/2.93 % (17459)------------------------------
% 10.56/2.93 % (17459)------------------------------
% 10.56/2.93 % (17450)Instruction limit reached!
% 10.56/2.93 % (17450)------------------------------
% 10.56/2.93 % (17450)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.56/2.93 % (17450)Termination reason: Unknown
% 10.56/2.93 % (17450)Termination phase: Saturation
% 10.56/2.93
% 10.56/2.93 % (17450)Memory used [KB]: 7419
% 10.56/2.93 % (17450)Time elapsed: 0.229 s
% 10.56/2.93 % (17450)Instructions burned: 459 (million)
% 10.56/2.93 % (17450)------------------------------
% 10.56/2.93 % (17450)------------------------------
% 10.56/2.95 % (17465)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_17274 for (2987ds/368Mi)
% 10.56/2.95 % (17466)dis+2_1:1_bd=off:e2e=on:hud=1:nm=3:piset=or:prag=on:s2a=on:sp=const_max:i=1021:si=on:rtra=on_0 on DTF2THF_17274 for (2987ds/1021Mi)
% 10.56/2.95 % (17464)Instruction limit reached!
% 10.56/2.95 % (17464)------------------------------
% 10.56/2.95 % (17464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.56/2.95 % (17464)Termination reason: Unknown
% 10.56/2.95 % (17464)Termination phase: Saturation
% 10.56/2.95
% 10.56/2.95 % (17464)Memory used [KB]: 10618
% 10.56/2.95 % (17464)Time elapsed: 0.024 s
% 10.56/2.95 % (17464)Instructions burned: 50 (million)
% 10.56/2.95 % (17464)------------------------------
% 10.56/2.95 % (17464)------------------------------
% 10.56/2.96 % (17462)Instruction limit reached!
% 10.56/2.96 % (17462)------------------------------
% 10.56/2.96 % (17462)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.56/2.96 % (17462)Termination reason: Unknown
% 10.56/2.96 % (17462)Termination phase: Saturation
% 10.56/2.96
% 10.56/2.96 % (17462)Memory used [KB]: 6268
% 10.56/2.96 % (17462)Time elapsed: 0.075 s
% 10.56/2.96 % (17462)Instructions burned: 184 (million)
% 10.56/2.96 % (17462)------------------------------
% 10.56/2.96 % (17462)------------------------------
% 10.56/2.96 % (17467)dis+10_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:i=267:si=on:rtra=on_0 on DTF2THF_17274 for (2987ds/267Mi)
% 10.56/2.97 % (17463)Instruction limit reached!
% 10.56/2.97 % (17463)------------------------------
% 10.56/2.97 % (17463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.56/2.97 % (17463)Termination reason: Unknown
% 10.56/2.97 % (17463)Termination phase: Saturation
% 10.56/2.97
% 10.56/2.97 % (17463)Memory used [KB]: 2174
% 10.56/2.97 % (17463)Time elapsed: 0.077 s
% 10.56/2.97 % (17463)Instructions burned: 166 (million)
% 10.56/2.97 % (17463)------------------------------
% 10.56/2.97 % (17463)------------------------------
% 10.56/2.98 % (17468)dis+21_1:5_au=on:ntd=on:nwc=5.0:s2a=on:ss=axioms:st=5.0:i=204:si=on:rtra=on_0 on DTF2THF_17274 for (2987ds/204Mi)
% 10.56/2.99 % (17469)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17274 for (2987ds/26Mi)
% 10.56/3.00 % (17469)Instruction limit reached!
% 10.56/3.00 % (17469)------------------------------
% 10.56/3.00 % (17469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 10.56/3.00 % (17469)Termination reason: Unknown
% 10.56/3.00 % (17469)Termination phase: Property scanning
% 10.56/3.00
% 10.56/3.00 % (17469)Memory used [KB]: 1535
% 10.56/3.00 % (17469)Time elapsed: 0.013 s
% 10.56/3.00 % (17469)Instructions burned: 26 (million)
% 10.56/3.00 % (17469)------------------------------
% 10.56/3.00 % (17469)------------------------------
% 10.56/3.01 % (17470)dis+1002_1:1_bd=preordered:c=on:cbe=off:cnfonf=lazy_not_gen_be_off:hud=10:ixr=off:prag=on:i=53:si=on:rtra=on_0 on DTF2THF_17274 for (2986ds/53Mi)
% 11.97/3.04 % (17470)Instruction limit reached!
% 11.97/3.04 % (17470)------------------------------
% 11.97/3.04 % (17470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.04 % (17470)Termination reason: Unknown
% 11.97/3.04 % (17470)Termination phase: Saturation
% 11.97/3.04
% 11.97/3.04 % (17470)Memory used [KB]: 6140
% 11.97/3.04 % (17470)Time elapsed: 0.025 s
% 11.97/3.04 % (17470)Instructions burned: 53 (million)
% 11.97/3.04 % (17470)------------------------------
% 11.97/3.04 % (17470)------------------------------
% 11.97/3.05 % (17471)dis+1002_1:1_aac=none:au=on:e2e=on:nm=2:nwc=10.0:sd=1:ss=axioms:st=3.0:i=4436:si=on:rtra=on_0 on DTF2THF_17274 for (2986ds/4436Mi)
% 11.97/3.07 % (17467)Instruction limit reached!
% 11.97/3.07 % (17467)------------------------------
% 11.97/3.07 % (17467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.07 % (17467)Termination reason: Unknown
% 11.97/3.07 % (17467)Termination phase: Saturation
% 11.97/3.07
% 11.97/3.07 % (17467)Memory used [KB]: 7931
% 11.97/3.07 % (17467)Time elapsed: 0.109 s
% 11.97/3.07 % (17467)Instructions burned: 267 (million)
% 11.97/3.07 % (17467)------------------------------
% 11.97/3.07 % (17467)------------------------------
% 11.97/3.07 % (17468)Instruction limit reached!
% 11.97/3.07 % (17468)------------------------------
% 11.97/3.07 % (17468)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.07 % (17468)Termination reason: Unknown
% 11.97/3.07 % (17468)Termination phase: Saturation
% 11.97/3.07
% 11.97/3.07 % (17468)Memory used [KB]: 6908
% 11.97/3.07 % (17468)Time elapsed: 0.100 s
% 11.97/3.07 % (17468)Instructions burned: 204 (million)
% 11.97/3.07 % (17468)------------------------------
% 11.97/3.07 % (17468)------------------------------
% 11.97/3.08 % (17465)Instruction limit reached!
% 11.97/3.08 % (17465)------------------------------
% 11.97/3.08 % (17465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.08 % (17465)Termination reason: Unknown
% 11.97/3.08 % (17465)Termination phase: Saturation
% 11.97/3.08
% 11.97/3.08 % (17465)Memory used [KB]: 6908
% 11.97/3.08 % (17465)Time elapsed: 0.141 s
% 11.97/3.08 % (17465)Instructions burned: 368 (million)
% 11.97/3.08 % (17465)------------------------------
% 11.97/3.08 % (17465)------------------------------
% 11.97/3.09 % (17472)dis+1010_1:1_acc=model:avsq=on:ixr=off:prag=on:s2a=on:sac=on:i=1539:si=on:rtra=on_0 on DTF2THF_17274 for (2986ds/1539Mi)
% 11.97/3.09 % (17473)lrs+2_1:1_bd=off:e2e=on:fde=none:kws=inv_precedence:plsq=on:plsqr=32,1:sos=on:i=408:si=on:rtra=on_0 on DTF2THF_17274 for (2986ds/408Mi)
% 11.97/3.10 % (17474)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=5205:si=on:rtra=on_0 on DTF2THF_17274 for (2986ds/5205Mi)
% 11.97/3.11 % (17454)Instruction limit reached!
% 11.97/3.11 % (17454)------------------------------
% 11.97/3.11 % (17454)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 11.97/3.11 % (17454)Termination reason: Unknown
% 11.97/3.11 % (17454)Termination phase: Saturation
% 11.97/3.11
% 11.97/3.11 % (17454)Memory used [KB]: 7803
% 11.97/3.11 % (17454)Time elapsed: 0.374 s
% 11.97/3.11 % (17454)Instructions burned: 989 (million)
% 11.97/3.11 % (17454)------------------------------
% 11.97/3.11 % (17454)------------------------------
% 11.97/3.12 % (17475)dis+1010_1:4_au=on:av=off:cbe=off:nwc=10.0:s2a=on:s2at=3.0:sd=2:ss=axioms:st=5.0:i=1913:si=on:rtra=on_0 on DTF2THF_17274 for (2985ds/1913Mi)
% 12.83/3.30 % (17473)Instruction limit reached!
% 12.83/3.30 % (17473)------------------------------
% 12.83/3.30 % (17473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.83/3.30 % (17473)Termination reason: Unknown
% 12.83/3.30 % (17473)Termination phase: Saturation
% 12.83/3.30
% 12.83/3.30 % (17473)Memory used [KB]: 8571
% 12.83/3.30 % (17473)Time elapsed: 0.231 s
% 12.83/3.30 % (17473)Instructions burned: 408 (million)
% 12.83/3.30 % (17473)------------------------------
% 12.83/3.30 % (17473)------------------------------
% 12.83/3.32 % (17476)lrs+2_1:1_bd=off:cbe=off:piset=equals:sd=1:sgt=20:sos=all:ss=axioms:i=4350:si=on:rtra=on_0 on DTF2THF_17274 for (2983ds/4350Mi)
% 12.83/3.33 % (17461)Instruction limit reached!
% 12.83/3.33 % (17461)------------------------------
% 12.83/3.33 % (17461)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.83/3.33 % (17461)Termination reason: Unknown
% 12.83/3.33 % (17461)Termination phase: Saturation
% 12.83/3.33
% 12.83/3.33 % (17461)Memory used [KB]: 8955
% 12.83/3.33 % (17461)Time elapsed: 0.464 s
% 12.83/3.33 % (17461)Instructions burned: 922 (million)
% 12.83/3.33 % (17461)------------------------------
% 12.83/3.33 % (17461)------------------------------
% 12.83/3.34 % (17477)ott+1010_1:4_cbe=off:chr=on:hfsq=on:hfsqr=1,16:hud=3:sac=on:sp=unary_frequency:ss=axioms:st=5.0:tnu=2:i=68:si=on:rtra=on_0 on DTF2THF_17274 for (2983ds/68Mi)
% 12.83/3.37 % (17477)Instruction limit reached!
% 12.83/3.37 % (17477)------------------------------
% 12.83/3.37 % (17477)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 12.83/3.37 % (17477)Termination reason: Unknown
% 12.83/3.37 % (17477)Termination phase: Saturation
% 12.83/3.37
% 12.83/3.37 % (17477)Memory used [KB]: 6268
% 12.83/3.37 % (17477)Time elapsed: 0.032 s
% 12.83/3.37 % (17477)Instructions burned: 68 (million)
% 12.83/3.37 % (17477)------------------------------
% 12.83/3.37 % (17477)------------------------------
% 12.83/3.39 % (17478)dis+10_1:1_au=on:nwc=5.0:s2a=on:s2at=2.0:sac=on:sd=7:ss=axioms:st=2.0:i=358:si=on:rtra=on_0 on DTF2THF_17274 for (2982ds/358Mi)
% 13.26/3.46 % (17466)Instruction limit reached!
% 13.26/3.46 % (17466)------------------------------
% 13.26/3.46 % (17466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/3.46 % (17466)Termination reason: Unknown
% 13.26/3.46 % (17466)Termination phase: Saturation
% 13.26/3.46
% 13.26/3.46 % (17466)Memory used [KB]: 9594
% 13.26/3.46 % (17466)Time elapsed: 0.518 s
% 13.26/3.46 % (17466)Instructions burned: 1023 (million)
% 13.26/3.46 % (17466)------------------------------
% 13.26/3.46 % (17466)------------------------------
% 13.26/3.48 % (17479)lrs+1010_1:16_add=large:amm=off:anc=all_dependent:chr=on:fd=off:ins=2:sp=const_max:tnu=5:uhcvi=on:i=31:si=on:rtra=on_0 on DTF2THF_17274 for (2982ds/31Mi)
% 13.26/3.49 % (17479)Instruction limit reached!
% 13.26/3.49 % (17479)------------------------------
% 13.26/3.49 % (17479)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.26/3.49 % (17479)Termination reason: Unknown
% 13.26/3.49 % (17479)Termination phase: Property scanning
% 13.26/3.49
% 13.26/3.49 % (17479)Memory used [KB]: 1535
% 13.26/3.49 % (17479)Time elapsed: 0.016 s
% 13.26/3.49 % (17479)Instructions burned: 31 (million)
% 13.26/3.49 % (17479)------------------------------
% 13.26/3.49 % (17479)------------------------------
% 13.37/3.51 % (17480)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_17274 for (2981ds/279Mi)
% 13.37/3.56 % (17478)Instruction limit reached!
% 13.37/3.56 % (17478)------------------------------
% 13.37/3.56 % (17478)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.37/3.56 % (17478)Termination reason: Unknown
% 13.37/3.56 % (17478)Termination phase: Saturation
% 13.37/3.56
% 13.37/3.56 % (17478)Memory used [KB]: 7036
% 13.37/3.56 % (17478)Time elapsed: 0.174 s
% 13.37/3.56 % (17478)Instructions burned: 358 (million)
% 13.37/3.56 % (17478)------------------------------
% 13.37/3.56 % (17478)------------------------------
% 13.37/3.58 % (17481)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_17274 for (2981ds/258Mi)
% 13.56/3.62 % (17480)Instruction limit reached!
% 13.56/3.62 % (17480)------------------------------
% 13.56/3.62 % (17480)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/3.62 % (17480)Termination reason: Unknown
% 13.56/3.62 % (17480)Termination phase: Saturation
% 13.56/3.62
% 13.56/3.62 % (17480)Memory used [KB]: 6268
% 13.56/3.62 % (17480)Time elapsed: 0.112 s
% 13.56/3.62 % (17480)Instructions burned: 281 (million)
% 13.56/3.62 % (17480)------------------------------
% 13.56/3.62 % (17480)------------------------------
% 13.56/3.64 % (17482)dis+2_1:1024_atotf=0.0802881:au=on:bs=unit_only:cnfonf=lazy_not_gen_be_off:fde=none:nwc=10.0:prag=on:i=26:si=on:rtra=on_0 on DTF2THF_17274 for (2980ds/26Mi)
% 13.56/3.65 % (17482)Instruction limit reached!
% 13.56/3.65 % (17482)------------------------------
% 13.56/3.65 % (17482)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.56/3.65 % (17482)Termination reason: Unknown
% 13.56/3.65 % (17482)Termination phase: Property scanning
% 13.56/3.65
% 13.56/3.65 % (17482)Memory used [KB]: 1535
% 13.56/3.65 % (17482)Time elapsed: 0.014 s
% 13.56/3.65 % (17482)Instructions burned: 27 (million)
% 13.56/3.65 % (17482)------------------------------
% 13.56/3.65 % (17482)------------------------------
% 13.56/3.66 % (17483)lrs+1010_1:1_au=on:cbe=off:cnfonf=lazy_not_be_gen:ntd=on:pe=on:i=995:si=on:rtra=on_0 on DTF2THF_17274 for (2980ds/995Mi)
% 13.70/3.70 % (17481)Instruction limit reached!
% 13.70/3.70 % (17481)------------------------------
% 13.70/3.70 % (17481)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.70/3.70 % (17481)Termination reason: Unknown
% 13.70/3.70 % (17481)Termination phase: Saturation
% 13.70/3.70
% 13.70/3.70 % (17481)Memory used [KB]: 7547
% 13.70/3.70 % (17481)Time elapsed: 0.120 s
% 13.70/3.70 % (17481)Instructions burned: 258 (million)
% 13.70/3.70 % (17481)------------------------------
% 13.70/3.70 % (17481)------------------------------
% 13.70/3.71 % (17484)dis+10_1:8_amm=sco:cbe=off:hflw=5:hfsq=on:hfsqc=14:hfsql=off:hfsqr=4,1:hud=5:ile=on:lma=on:nm=2:ntd=on:prag=on:sac=on:sp=frequency:i=373:si=on:rtra=on_0 on DTF2THF_17274 for (2979ds/373Mi)
% 13.84/3.86 % (17472)Instruction limit reached!
% 13.84/3.86 % (17472)------------------------------
% 13.84/3.86 % (17472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 13.84/3.86 % (17472)Termination reason: Unknown
% 13.84/3.86 % (17472)Termination phase: Saturation
% 13.84/3.86
% 13.84/3.86 % (17472)Memory used [KB]: 8699
% 13.84/3.86 % (17472)Time elapsed: 0.799 s
% 13.84/3.86 % (17472)Instructions burned: 1540 (million)
% 13.84/3.86 % (17472)------------------------------
% 13.84/3.86 % (17472)------------------------------
% 13.84/3.89 % (17485)lrs+1010_1:128_au=on:cnfonf=lazy_pi_sigma_gen:hflw=4:hfsq=on:hfsqc=20:hfsql=off:i=253:si=on:rtra=on_0 on DTF2THF_17274 for (2978ds/253Mi)
% 14.63/3.90 % (17484)Instruction limit reached!
% 14.63/3.90 % (17484)------------------------------
% 14.63/3.90 % (17484)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.63/3.90 % (17484)Termination reason: Unknown
% 14.63/3.90 % (17484)Termination phase: Saturation
% 14.63/3.90
% 14.63/3.90 % (17484)Memory used [KB]: 7164
% 14.63/3.90 % (17484)Time elapsed: 0.185 s
% 14.63/3.90 % (17484)Instructions burned: 373 (million)
% 14.63/3.90 % (17484)------------------------------
% 14.63/3.90 % (17484)------------------------------
% 14.63/3.91 % (17486)lrs+1002_1:14_au=on:bd=off:e2e=on:fde=unused:sac=on:sos=on:i=832:si=on:rtra=on_0 on DTF2THF_17274 for (2977ds/832Mi)
% 14.63/3.96 % (17475)Instruction limit reached!
% 14.63/3.96 % (17475)------------------------------
% 14.63/3.96 % (17475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.63/3.96 % (17475)Termination reason: Unknown
% 14.63/3.96 % (17475)Termination phase: Saturation
% 14.63/3.96
% 14.63/3.96 % (17475)Memory used [KB]: 3198
% 14.63/3.96 % (17475)Time elapsed: 0.851 s
% 14.63/3.96 % (17475)Instructions burned: 1916 (million)
% 14.63/3.96 % (17475)------------------------------
% 14.63/3.96 % (17475)------------------------------
% 14.63/3.97 % (17488)lrs+1010_1:1_chr=on:cnfonf=lazy_not_be_gen:gs=on:hud=5:plsq=on:plsqc=1:plsqr=5,1:prag=on:rawr=on:i=668:si=on:rtra=on_0 on DTF2THF_17274 for (2977ds/668Mi)
% 14.63/3.99 % (17485)Instruction limit reached!
% 14.63/3.99 % (17485)------------------------------
% 14.63/3.99 % (17485)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 14.63/3.99 % (17485)Termination reason: Unknown
% 14.63/3.99 % (17485)Termination phase: Saturation
% 14.63/3.99
% 14.63/3.99 % (17485)Memory used [KB]: 6268
% 14.63/3.99 % (17485)Time elapsed: 0.100 s
% 14.63/3.99 % (17485)Instructions burned: 255 (million)
% 14.63/3.99 % (17485)------------------------------
% 14.63/3.99 % (17485)------------------------------
% 18.87/4.02 % (17489)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=40:si=on:rtra=on_0 on DTF2THF_17274 for (2976ds/40Mi)
% 18.87/4.04 % (17489)Instruction limit reached!
% 18.87/4.04 % (17489)------------------------------
% 18.87/4.04 % (17489)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.87/4.04 % (17489)Termination reason: Unknown
% 18.87/4.04 % (17489)Termination phase: Property scanning
% 18.87/4.04
% 18.87/4.04 % (17489)Memory used [KB]: 1535
% 18.87/4.04 % (17489)Time elapsed: 0.020 s
% 18.87/4.04 % (17489)Instructions burned: 40 (million)
% 18.87/4.04 % (17489)------------------------------
% 18.87/4.04 % (17489)------------------------------
% 18.87/4.06 % (17490)lrs+1010_1:1_cnfonf=lazy_pi_sigma_gen:fd=off:ntd=on:sd=1:sgt=32:sos=on:ss=axioms:i=294:si=on:rtra=on_0 on DTF2THF_17274 for (2976ds/294Mi)
% 18.87/4.06 % (17483)Instruction limit reached!
% 18.87/4.06 % (17483)------------------------------
% 18.87/4.06 % (17483)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 18.87/4.06 % (17483)Termination reason: Unknown
% 18.87/4.06 % (17483)Termination phase: Saturation
% 18.87/4.06
% 18.87/4.06 % (17483)Memory used [KB]: 7675
% 18.87/4.06 % (17483)Time elapsed: 0.396 s
% 18.87/4.06 % (17483)Instructions burned: 995 (million)
% 18.87/4.06 % (17483)------------------------------
% 18.87/4.06 % (17483)------------------------------
% 18.87/4.08 % (17491)dis+1010_1:1_avsq=on:fe=off:fsr=off:hud=10:plsq=on:plsqr=32,1:prag=on:i=187:si=on:rtra=on_0 on DTF2THF_17274 for (2976ds/187Mi)
% 19.46/4.17 % (17491)Instruction limit reached!
% 19.46/4.17 % (17491)------------------------------
% 19.46/4.17 % (17491)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.46/4.17 % (17491)Termination reason: Unknown
% 19.46/4.17 % (17491)Termination phase: Saturation
% 19.46/4.17
% 19.46/4.17 % (17491)Memory used [KB]: 7036
% 19.46/4.17 % (17491)Time elapsed: 0.093 s
% 19.46/4.17 % (17491)Instructions burned: 187 (million)
% 19.46/4.17 % (17491)------------------------------
% 19.46/4.17 % (17491)------------------------------
% 19.46/4.18 % (17490)Instruction limit reached!
% 19.46/4.18 % (17490)------------------------------
% 19.46/4.18 % (17490)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 19.46/4.18 % (17490)Termination reason: Unknown
% 19.46/4.18 % (17490)Termination phase: Saturation
% 19.46/4.18
% 19.46/4.18 % (17490)Memory used [KB]: 6140
% 19.46/4.18 % (17490)Time elapsed: 0.126 s
% 19.46/4.18 % (17490)Instructions burned: 294 (million)
% 19.46/4.18 % (17490)------------------------------
% 19.46/4.18 % (17490)------------------------------
% 19.46/4.18 % (17492)lrs+1010_2:3_au=on:fsr=off:sd=4:ss=axioms:st=1.5:i=371:si=on:rtra=on_0 on DTF2THF_17274 for (2975ds/371Mi)
% 20.12/4.20 % (17493)dis+1003_1:1_au=on:bd=preordered:fde=none:ixr=off:nwc=10.0:i=1827:si=on:rtra=on_0 on DTF2THF_17274 for (2974ds/1827Mi)
% 20.12/4.23 % (17488)Instruction limit reached!
% 20.12/4.23 % (17488)------------------------------
% 20.12/4.23 % (17488)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.12/4.23 % (17488)Termination reason: Unknown
% 20.12/4.23 % (17488)Termination phase: Saturation
% 20.12/4.23
% 20.12/4.23 % (17488)Memory used [KB]: 12281
% 20.12/4.23 % (17488)Time elapsed: 0.246 s
% 20.12/4.23 % (17488)Instructions burned: 670 (million)
% 20.12/4.23 % (17488)------------------------------
% 20.12/4.23 % (17488)------------------------------
% 20.12/4.25 % (17494)lrs+10_1:1_av=off:bd=off:cnfonf=lazy_gen:fe=off:hud=10:plsq=on:plsqc=1:plsqr=32,1:tnu=1:i=70:si=on:rtra=on_0 on DTF2THF_17274 for (2974ds/70Mi)
% 20.12/4.28 % (17494)Instruction limit reached!
% 20.12/4.28 % (17494)------------------------------
% 20.12/4.28 % (17494)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.12/4.28 % (17494)Termination reason: Unknown
% 20.12/4.28 % (17494)Termination phase: Saturation
% 20.12/4.28
% 20.12/4.28 % (17494)Memory used [KB]: 1663
% 20.12/4.28 % (17494)Time elapsed: 0.033 s
% 20.12/4.28 % (17494)Instructions burned: 72 (million)
% 20.12/4.28 % (17494)------------------------------
% 20.12/4.28 % (17494)------------------------------
% 20.12/4.29 % (17495)lrs+10_1:20_bd=off:cnfonf=lazy_not_be_gen:fe=axiom:hud=10:ins=1:nm=20:prag=on:sos=on:i=316:si=on:rtra=on_0 on DTF2THF_17274 for (2974ds/316Mi)
% 20.61/4.33 % (17486)Instruction limit reached!
% 20.61/4.33 % (17486)------------------------------
% 20.61/4.33 % (17486)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.61/4.33 % (17486)Termination reason: Unknown
% 20.61/4.33 % (17486)Termination phase: Saturation
% 20.61/4.33
% 20.61/4.33 % (17486)Memory used [KB]: 8315
% 20.61/4.33 % (17486)Time elapsed: 0.422 s
% 20.61/4.33 % (17486)Instructions burned: 833 (million)
% 20.61/4.33 % (17486)------------------------------
% 20.61/4.33 % (17486)------------------------------
% 20.61/4.35 % (17492)Instruction limit reached!
% 20.61/4.35 % (17492)------------------------------
% 20.61/4.35 % (17492)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 20.61/4.35 % (17492)Termination reason: Unknown
% 20.61/4.35 % (17492)Termination phase: Saturation
% 20.61/4.35
% 20.61/4.35 % (17492)Memory used [KB]: 7036
% 20.61/4.35 % (17492)Time elapsed: 0.166 s
% 20.61/4.35 % (17492)Instructions burned: 371 (million)
% 20.61/4.35 % (17492)------------------------------
% 20.61/4.35 % (17492)------------------------------
% 20.61/4.35 % (17496)ott+1010_1:1_cnfonf=lazy_gen:fe=off:plsq=on:plsqc=1:plsqr=3548551,65536:s2a=on:i=932:si=on:rtra=on_0 on DTF2THF_17274 for (2973ds/932Mi)
% 20.61/4.36 % (17497)lrs+1010_1:128_au=on:bd=preordered:cnfonf=lazy_pi_sigma_gen:plsq=on:plsqc=1:plsqr=32,1:sos=all:sp=occurrence:i=4714:si=on:rtra=on_0 on DTF2THF_17274 for (2973ds/4714Mi)
% 21.13/4.42 % (17495)Instruction limit reached!
% 21.13/4.42 % (17495)------------------------------
% 21.13/4.42 % (17495)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 21.13/4.42 % (17495)Termination reason: Unknown
% 21.13/4.42 % (17495)Termination phase: Saturation
% 21.13/4.42
% 21.13/4.42 % (17495)Memory used [KB]: 6780
% 21.13/4.42 % (17495)Time elapsed: 0.130 s
% 21.13/4.42 % (17495)Instructions burned: 318 (million)
% 21.13/4.42 % (17495)------------------------------
% 21.13/4.42 % (17495)------------------------------
% 21.13/4.44 % (17498)dis+10_1:1_au=on:e2e=on:fde=none:nwc=10.0:s2a=on:s2at=2.0:i=8250:si=on:rtra=on_0 on DTF2THF_17274 for (2972ds/8250Mi)
% 22.17/4.73 % (17496)Instruction limit reached!
% 22.17/4.73 % (17496)------------------------------
% 22.17/4.73 % (17496)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 22.17/4.73 % (17496)Termination reason: Unknown
% 22.17/4.73 % (17496)Termination phase: Saturation
% 22.17/4.73
% 22.17/4.73 % (17496)Memory used [KB]: 8187
% 22.17/4.73 % (17496)Time elapsed: 0.380 s
% 22.17/4.73 % (17496)Instructions burned: 932 (million)
% 22.17/4.73 % (17496)------------------------------
% 22.17/4.73 % (17496)------------------------------
% 22.17/4.75 % (17499)lrs+1002_1:1_apa=on:cnfonf=off:fd=off:flr=on:hud=1:lcm=reverse:prag=on:sd=1:sos=on:ss=axioms:i=770:si=on:rtra=on_0 on DTF2THF_17274 for (2969ds/770Mi)
% 25.92/5.09 % (17499)Instruction limit reached!
% 25.92/5.09 % (17499)------------------------------
% 25.92/5.09 % (17499)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.92/5.09 % (17499)Termination reason: Unknown
% 25.92/5.09 % (17499)Termination phase: Saturation
% 25.92/5.09
% 25.92/5.09 % (17499)Memory used [KB]: 6396
% 25.92/5.09 % (17499)Time elapsed: 0.346 s
% 25.92/5.09 % (17499)Instructions burned: 771 (million)
% 25.92/5.09 % (17499)------------------------------
% 25.92/5.09 % (17499)------------------------------
% 25.92/5.11 % (17500)ott+1010_5:1_av=off:fe=off:ins=1:kws=precedence:sp=reverse_arity:i=794:si=on:rtra=on_0 on DTF2THF_17274 for (2965ds/794Mi)
% 25.92/5.12 % (17493)Instruction limit reached!
% 25.92/5.12 % (17493)------------------------------
% 25.92/5.12 % (17493)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 25.92/5.12 % (17493)Termination reason: Unknown
% 25.92/5.12 % (17493)Termination phase: Saturation
% 25.92/5.12
% 25.92/5.12 % (17493)Memory used [KB]: 14583
% 25.92/5.12 % (17493)Time elapsed: 0.915 s
% 25.92/5.12 % (17493)Instructions burned: 1827 (million)
% 25.92/5.12 % (17493)------------------------------
% 25.92/5.12 % (17493)------------------------------
% 26.61/5.13 % (17501)dis+1002_1:1_au=on:avsq=on:avsqr=1,16:cond=on:sp=frequency:i=464:si=on:rtra=on_0 on DTF2THF_17274 for (2965ds/464Mi)
% 26.97/5.23 % (17474)Instruction limit reached!
% 26.97/5.23 % (17474)------------------------------
% 26.97/5.23 % (17474)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.97/5.23 % (17474)Termination reason: Unknown
% 26.97/5.23 % (17474)Termination phase: Saturation
% 26.97/5.23
% 26.97/5.23 % (17474)Memory used [KB]: 11769
% 26.97/5.23 % (17474)Time elapsed: 2.157 s
% 26.97/5.23 % (17474)Instructions burned: 5207 (million)
% 26.97/5.23 % (17474)------------------------------
% 26.97/5.23 % (17474)------------------------------
% 26.97/5.25 % (17503)ott+21_1:3_avsq=on:bd=off:cnfonf=lazy_gen:fe=off:hud=10:ixr=off:plsq=on:plsqc=1:plsqr=32,1:prag=on:tnu=1:i=1376:si=on:rtra=on_0 on DTF2THF_17274 for (2964ds/1376Mi)
% 26.97/5.29 % (17471)Instruction limit reached!
% 26.97/5.29 % (17471)------------------------------
% 26.97/5.29 % (17471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 26.97/5.29 % (17471)Termination reason: Unknown
% 26.97/5.29 % (17471)Termination phase: Saturation
% 26.97/5.29
% 26.97/5.29 % (17471)Memory used [KB]: 14456
% 26.97/5.29 % (17471)Time elapsed: 2.261 s
% 26.97/5.29 % (17471)Instructions burned: 4436 (million)
% 26.97/5.29 % (17471)------------------------------
% 26.97/5.29 % (17471)------------------------------
% 27.42/5.31 % (17504)dis+10_1:1_etr=on:plsq=on:plsqc=1:plsqr=32,1:i=906:si=on:rtra=on_0 on DTF2THF_17274 for (2963ds/906Mi)
% 27.42/5.37 % (17501)Instruction limit reached!
% 27.42/5.37 % (17501)------------------------------
% 27.42/5.37 % (17501)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.42/5.37 % (17501)Termination reason: Unknown
% 27.42/5.37 % (17501)Termination phase: Saturation
% 27.42/5.37
% 27.42/5.37 % (17501)Memory used [KB]: 7419
% 27.42/5.37 % (17501)Time elapsed: 0.235 s
% 27.42/5.37 % (17501)Instructions burned: 464 (million)
% 27.42/5.37 % (17501)------------------------------
% 27.42/5.37 % (17501)------------------------------
% 27.42/5.38 % (17505)lrs+1002_1:16_bd=off:e2e=on:fde=unused:kws=precedence:sac=on:sos=on:ss=axioms:i=434:si=on:rtra=on_0 on DTF2THF_17274 for (2963ds/434Mi)
% 27.42/5.38 % (17476)First to succeed.
% 27.42/5.39 % (17476)Refutation found. Thanks to Tanya!
% 27.42/5.39 % SZS status Theorem for DTF2THF_17274
% 27.42/5.39 % SZS output start Proof for DTF2THF_17274
% 27.42/5.39 thf(func_def_0, type, in: $i > $i > $o).
% 27.42/5.39 thf(func_def_1, type, exu: ($i > $o) > $o).
% 27.42/5.39 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 27.42/5.39 thf(func_def_8, type, powerset: $i > $i).
% 27.42/5.39 thf(func_def_10, type, setunion: $i > $i).
% 27.42/5.39 thf(func_def_19, type, descr: ($i > $o) > $i).
% 27.42/5.39 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_26, type, prop2set: $o > $i).
% 27.42/5.39 thf(func_def_36, type, nonempty: $i > $o).
% 27.42/5.39 thf(func_def_69, type, set2prop: $i > $o).
% 27.42/5.39 thf(func_def_88, type, subset: $i > $i > $o).
% 27.42/5.39 thf(func_def_89, type, disjoint: $i > $i > $o).
% 27.42/5.39 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 27.42/5.39 thf(func_def_114, type, binunion: $i > $i > $i).
% 27.42/5.39 thf(func_def_138, type, sK4: $i > $i).
% 27.42/5.39 thf(func_def_139, type, sK5: $i > $i).
% 27.42/5.39 thf(func_def_140, type, sK6: $i > $i > $i).
% 27.42/5.39 thf(func_def_141, type, sK7: ($i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_142, type, sK8: $i > $i > $i).
% 27.42/5.39 thf(func_def_143, type, sK9: $i > $i > $i).
% 27.42/5.39 thf(func_def_144, type, sK10: $i > $i > $i).
% 27.42/5.39 thf(func_def_145, type, sK11: ($i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_146, type, sK12: $i > $i).
% 27.42/5.39 thf(func_def_147, type, sK13: $i > $i > $i).
% 27.42/5.39 thf(func_def_148, type, sK14: $i > $i > $i).
% 27.42/5.39 thf(func_def_149, type, sK15: ($i > $o) > $i).
% 27.42/5.39 thf(func_def_150, type, sK16: $i > $i).
% 27.42/5.39 thf(func_def_151, type, sK17: ($i > $o) > $i).
% 27.42/5.39 thf(func_def_152, type, sK18: $i > $i > $i).
% 27.42/5.39 thf(func_def_153, type, sK19: ($i > $o) > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_154, type, sK20: ($i > $o) > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_155, type, sK21: ($i > $o) > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_156, type, sK22: ($i > $o) > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_157, type, sK23: $i > $i > $i).
% 27.42/5.39 thf(func_def_158, type, sK24: ($i > $o) > $i).
% 27.42/5.39 thf(func_def_159, type, sK25: $i > $i).
% 27.42/5.39 thf(func_def_160, type, sK26: ($i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_161, type, sK27: $i > $i > $i).
% 27.42/5.39 thf(func_def_162, type, sK28: ($i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_163, type, sK29: ($i > $o) > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_164, type, sK30: ($i > $o) > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_165, type, sK31: $o > $i > $i > $i).
% 27.42/5.39 thf(func_def_166, type, sK32: $i > $i).
% 27.42/5.39 thf(func_def_167, type, sK33: $i > $i > $i > $i).
% 27.42/5.39 thf(func_def_168, type, sK34: $i > $i > $i).
% 27.42/5.39 thf(func_def_169, type, sK35: $i > $i > $i).
% 27.42/5.39 thf(func_def_170, type, sK36: $i > $i > $i).
% 27.42/5.39 thf(func_def_171, type, sK37: $i > $i > $i).
% 27.42/5.39 thf(func_def_172, type, sK38: $i > $i > $i).
% 27.42/5.39 thf(func_def_173, type, sK39: ($i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_174, type, sK40: ($i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_175, type, sK41: $i > $i).
% 27.42/5.39 thf(func_def_176, type, sK42: ($i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_177, type, sK43: ($i > $i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_178, type, sK44: ($i > $i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_179, type, sK45: $i > ($i > $i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_180, type, sK46: $i > ($i > $i > $o) > $i > $i).
% 27.42/5.39 thf(func_def_181, type, sK47: ($i > $o) > $i).
% 27.42/5.39 thf(func_def_182, type, sK48: ($i > $o) > $i).
% 27.42/5.39 thf(func_def_183, type, sK49: ($i > $o) > ($i > $o) > $i > $i > $i).
% 27.42/5.39 thf(func_def_184, type, sK50: $i > $i > ($i > $o) > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_185, type, sK51: $i > ($i > $o) > $i).
% 27.42/5.39 thf(func_def_186, type, ph52: !>[X0: $tType]:(X0)).
% 27.42/5.39 thf(f13197,plain,(
% 27.42/5.39 $false),
% 27.42/5.39 inference(trivial_inequality_removal,[status(thm)],[f13186])).
% 27.42/5.39 thf(f13186,plain,(
% 27.42/5.39 ($true = $false)),
% 27.42/5.39 inference(superposition,[status(thm)],[f13184,f351])).
% 27.42/5.39 thf(f351,plain,(
% 27.42/5.39 ($true = (in @ sK2 @ sK1))),
% 27.42/5.39 inference(cnf_transformation,[status(thm)],[f312])).
% 27.42/5.39 thf(f312,plain,(
% 27.42/5.39 (exuE1 = $true) & (setoftrueEq = $true) & (subsetemptysetimpeq = $true) & (notdexE = $true) & (setextsub = $true) & (emptyset__Cong = $true) & (emptyinPowerset = $true) & (subPowSU = $true) & (omega__Cong = $true) & (omegaIndAx = $true) & (subsetTrans = $true) & (setadjoinIR = $true) & (subsetI1 = $true) & (subsetRefl = $true) & (subset2powerset = $true) & (notequalI2 = $true) & (setunionI = $true) & (setadjoinE = $true) & (omega0Ax = $true) & (descrp = $true) & (emptyInPowerset = $true) & (notdallE = $true) & (descr__Cong = $true) & (noeltsimpempty = $true) & (quantDeMorgan4 = $true) & (emptysetimpfalse = $true) & (upairsetIR = $true) & (setadjoin__Cong = $true) & (dsetconstrER = $true) & (replAx = $true) & (upairsetE = $true) & (sepInPowerset = $true) & (exu__Cong = $true) & (exuI3 = $true) & (dsetconstr__Cong = $true) & (prop2set2propI = $true) & (powersetE = $true) & (exuEu = $true) & (exuI2 = $true) & (setbeta = $true) & (subsetI2 = $true) & (setext = $true) & (setunionAx = $true) & (uniqinunit = $true) & (exuE3u = $true) & (powersetE1 = $true) & (upairset2IR = $true) & (emptysetsubset = $true) & (vacuousDall = $true) & (singletonsswitch = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (eqimpsubset2 = $true) & (powersetI = $true) & (powerset__Cong = $true) & (emptysetE = $true) & (setadjoinOr = $true) & (powersetI1 = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (setadjoinSub2 = $true) & (notsubsetI = $true) & (upairsetIL = $true) & (subsetE2 = $true) & (emptyinunitempty = $true) & (inPowerset = $true) & (prop2setI = $true) & (binunionIL = $true) & (wellorderingAx = $true) & (eqinunit = $true) & (exuE3e = $true) & (inCongP = $true) & (exuI1 = $true) & (exuE2 = $true) & (eqimpsubset1 = $true) & (prop2setE = $true) & (quantDeMorgan1 = $true) & (in__Cong = $true) & (setunionE = $true) & (powersetAx = $true) & (quantDeMorgan2 = $true) & (notinsingleton = $true) & (dsetconstrEL = $true) & (quantDeMorgan3 = $true) & (dsetconstrI = $true) & (setadjoinSub = $true) & (emptysetAx = $true) & (emptyE1 = $true) & (omegaSAx = $true) & (nonemptyE1 = $true) & (setunion__Cong = $true) & (emptyI = $true) & (setadjoinIL = $true) & (subsetE = $true) & (setadjoinAx = $true) & (foundationAx = $true) & (sepSubset = $true) & (notequalI1 = $true) & (($true != (in @ sK2 @ (binunion @ sK0 @ sK1))) & ($true = (in @ sK2 @ sK1))) & (powersetsubset = $true) & (nonemptyImpWitness = $true)),
% 27.42/5.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f310,f311])).
% 27.42/5.39 thf(f311,plain,(
% 27.42/5.39 ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (binunion @ X0 @ X1))) & ($true = (in @ X2 @ X1))) => (($true != (in @ sK2 @ (binunion @ sK0 @ sK1))) & ($true = (in @ sK2 @ sK1)))),
% 27.42/5.39 introduced(definition,[],[choice_axiom])).
% 27.42/5.39 thf(f310,plain,(
% 27.42/5.39 (exuE1 = $true) & (setoftrueEq = $true) & (subsetemptysetimpeq = $true) & (notdexE = $true) & (setextsub = $true) & (emptyset__Cong = $true) & (emptyinPowerset = $true) & (subPowSU = $true) & (omega__Cong = $true) & (omegaIndAx = $true) & (subsetTrans = $true) & (setadjoinIR = $true) & (subsetI1 = $true) & (subsetRefl = $true) & (subset2powerset = $true) & (notequalI2 = $true) & (setunionI = $true) & (setadjoinE = $true) & (omega0Ax = $true) & (descrp = $true) & (emptyInPowerset = $true) & (notdallE = $true) & (descr__Cong = $true) & (noeltsimpempty = $true) & (quantDeMorgan4 = $true) & (emptysetimpfalse = $true) & (upairsetIR = $true) & (setadjoin__Cong = $true) & (dsetconstrER = $true) & (replAx = $true) & (upairsetE = $true) & (sepInPowerset = $true) & (exu__Cong = $true) & (exuI3 = $true) & (dsetconstr__Cong = $true) & (prop2set2propI = $true) & (powersetE = $true) & (exuEu = $true) & (exuI2 = $true) & (setbeta = $true) & (subsetI2 = $true) & (setext = $true) & (setunionAx = $true) & (uniqinunit = $true) & (exuE3u = $true) & (powersetE1 = $true) & (upairset2IR = $true) & (emptysetsubset = $true) & (vacuousDall = $true) & (singletonsswitch = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (eqimpsubset2 = $true) & (powersetI = $true) & (powerset__Cong = $true) & (emptysetE = $true) & (setadjoinOr = $true) & (powersetI1 = $true) & (nonemptyI = $true) & (notinemptyset = $true) & (setadjoinSub2 = $true) & (notsubsetI = $true) & (upairsetIL = $true) & (subsetE2 = $true) & (emptyinunitempty = $true) & (inPowerset = $true) & (prop2setI = $true) & (binunionIL = $true) & (wellorderingAx = $true) & (eqinunit = $true) & (exuE3e = $true) & (inCongP = $true) & (exuI1 = $true) & (exuE2 = $true) & (eqimpsubset1 = $true) & (prop2setE = $true) & (quantDeMorgan1 = $true) & (in__Cong = $true) & (setunionE = $true) & (powersetAx = $true) & (quantDeMorgan2 = $true) & (notinsingleton = $true) & (dsetconstrEL = $true) & (quantDeMorgan3 = $true) & (dsetconstrI = $true) & (setadjoinSub = $true) & (emptysetAx = $true) & (emptyE1 = $true) & (omegaSAx = $true) & (nonemptyE1 = $true) & (setunion__Cong = $true) & (emptyI = $true) & (setadjoinIL = $true) & (subsetE = $true) & (setadjoinAx = $true) & (foundationAx = $true) & (sepSubset = $true) & (notequalI1 = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (binunion @ X0 @ X1))) & ($true = (in @ X2 @ X1))) & (powersetsubset = $true) & (nonemptyImpWitness = $true)),
% 27.42/5.39 inference(flattening,[status(thm)],[f309])).
% 27.42/5.39 thf(f309,plain,(
% 27.42/5.39 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ (binunion @ X0 @ X1))) & ($true = (in @ X2 @ X1))) & (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)),
% 27.42/5.39 inference(ennf_transformation,[status(thm)],[f120])).
% 27.42/5.39 thf(f120,plain,(
% 27.42/5.39 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X1)) => ($true = (in @ X2 @ (binunion @ X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.42/5.39 inference(fool_elimination,[status(thm)],[f119])).
% 27.42/5.39 thf(f119,plain,(
% 27.42/5.39 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ X1) => (in @ X2 @ (binunion @ X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.42/5.39 inference(rectify,[status(thm)],[f105])).
% 27.42/5.39 thf(f105,negated_conjecture,(
% 27.42/5.39 ~(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 => ! [X3 : $i,X4 : $i,X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ (binunion @ X3 @ X4)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.42/5.39 inference(negated_conjecture,[status(cth)],[f104])).
% 27.42/5.39 thf(f104,conjecture,(
% 27.42/5.39 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 => ! [X3 : $i,X4 : $i,X1 : $i] : ((in @ X1 @ X4) => (in @ X1 @ (binunion @ X3 @ X4))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 27.42/5.39 file('/export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2THF_17274.p',binunionIR)).
% 27.42/5.39 thf(f13184,plain,(
% 27.42/5.39 ($false = (in @ sK2 @ sK1))),
% 27.42/5.39 inference(trivial_inequality_removal,[status(thm)],[f13175])).
% 27.42/5.39 thf(f13175,plain,(
% 27.42/5.39 ($false = (in @ sK2 @ sK1)) | ($true = $false)),
% 27.42/5.39 inference(superposition,[status(thm)],[f5914,f1529])).
% 27.42/5.39 thf(f1529,plain,(
% 27.42/5.39 ( ! [X2 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X1 @ emptyset))))) )),
% 27.42/5.39 inference(beta_eta_normalization,[status(thm)],[f1528])).
% 27.42/5.39 thf(f1528,plain,(
% 27.42/5.39 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset)))) @ X2))) )),
% 27.42/5.39 inference(pi_clausification,[status(thm)],[f1527])).
% 27.42/5.39 thf(f1527,plain,(
% 27.42/5.39 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ X1 @ emptyset))))))) )),
% 27.42/5.39 inference(beta_eta_normalization,[status(thm)],[f1526])).
% 27.42/5.39 thf(f1526,plain,(
% 27.42/5.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset)))))) @ X1))) )),
% 27.42/5.39 inference(pi_clausification,[status(thm)],[f571])).
% 27.42/5.39 thf(f571,plain,(
% 27.42/5.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 27.42/5.39 inference(definition_unfolding,[status(thm)],[f469,f404])).
% 27.42/5.39 thf(f404,plain,(
% 27.42/5.39 (upairset2IR = $true)),
% 27.42/5.39 inference(cnf_transformation,[status(thm)],[f312])).
% 27.42/5.39 thf(f469,plain,(
% 27.42/5.39 (upairset2IR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 27.42/5.39 inference(cnf_transformation,[status(thm)],[f189])).
% 27.42/5.39 thf(f189,plain,(
% 27.42/5.39 (upairset2IR = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y0 @ emptyset))))))))),
% 27.42/5.39 inference(fool_elimination,[status(thm)],[f188])).
% 27.42/5.39 thf(f188,plain,(
% 27.42/5.39 (! [X0 : $i,X1 : $i] : (in @ X1 @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset))) = upairset2IR)),
% 27.42/5.39 inference(rectify,[status(thm)],[f103])).
% 27.42/5.39 thf(f103,axiom,(
% 27.42/5.39 (! [X1 : $i,X2 : $i] : (in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) = upairset2IR)),
% 27.42/5.39 file('/export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2THF_17274.p',upairset2IR)).
% 27.42/5.39 thf(f5914,plain,(
% 27.42/5.39 ( ! [X0 : $i] : (((in @ X0 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) = $false) | ((in @ sK2 @ X0) = $false)) )),
% 27.42/5.39 inference(trivial_inequality_removal,[status(thm)],[f5729])).
% 27.42/5.39 thf(f5729,plain,(
% 27.42/5.39 ( ! [X0 : $i] : (($true != $true) | ((in @ sK2 @ X0) = $false) | ((in @ X0 @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset))) = $false)) )),
% 27.42/5.39 inference(superposition,[status(thm)],[f808,f923])).
% 27.42/5.39 thf(f923,plain,(
% 27.42/5.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X2 @ (setunion @ X3)) = $true) | ($false = (in @ X2 @ X1)) | ((in @ X1 @ X3) = $false)) )),
% 27.42/5.39 inference(binary_proxy_clausification,[status(thm)],[f922])).
% 27.42/5.39 thf(f922,plain,(
% 27.42/5.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X2 @ X1)) | ($true = ((in @ X1 @ X3) => (in @ X2 @ (setunion @ X3))))) )),
% 27.42/5.39 inference(binary_proxy_clausification,[status(thm)],[f921])).
% 27.42/5.39 thf(f921,plain,(
% 27.42/5.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((in @ X2 @ X1) => ((in @ X1 @ X3) => (in @ X2 @ (setunion @ X3)))))) )),
% 27.42/5.39 inference(beta_eta_normalization,[status(thm)],[f920])).
% 27.42/5.39 thf(f920,plain,(
% 27.42/5.39 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ X2 @ X1) => ((in @ X1 @ Y0) => (in @ X2 @ (setunion @ Y0))))) @ X3))) )),
% 27.42/5.39 inference(pi_clausification,[status(thm)],[f919])).
% 27.42/5.39 thf(f919,plain,(
% 27.42/5.39 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ X2 @ X1) => ((in @ X1 @ Y0) => (in @ X2 @ (setunion @ Y0)))))))) )),
% 27.42/5.39 inference(beta_eta_normalization,[status(thm)],[f918])).
% 27.42/5.39 thf(f918,plain,(
% 27.42/5.39 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ X1 @ Y1) => (in @ Y0 @ (setunion @ Y1))))))) @ X2))) )),
% 27.42/5.39 inference(pi_clausification,[status(thm)],[f917])).
% 27.42/5.39 thf(f917,plain,(
% 27.42/5.39 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y0 @ X1) => ((in @ X1 @ Y1) => (in @ Y0 @ (setunion @ Y1)))))))))) )),
% 27.42/5.39 inference(beta_eta_normalization,[status(thm)],[f916])).
% 27.42/5.39 thf(f916,plain,(
% 27.42/5.39 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2))))))))) @ X1))) )),
% 27.42/5.39 inference(pi_clausification,[status(thm)],[f556])).
% 27.42/5.39 thf(f556,plain,(
% 27.42/5.39 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))))),
% 27.42/5.39 inference(definition_unfolding,[status(thm)],[f454,f434])).
% 27.42/5.39 thf(f434,plain,(
% 27.42/5.39 (setunionI = $true)),
% 27.42/5.39 inference(cnf_transformation,[status(thm)],[f312])).
% 27.42/5.39 thf(f454,plain,(
% 27.42/5.39 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))))),
% 27.42/5.39 inference(cnf_transformation,[status(thm)],[f199])).
% 27.42/5.39 thf(f199,plain,(
% 27.42/5.39 (setunionI = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y1 @ Y0) => ((in @ Y0 @ Y2) => (in @ Y1 @ (setunion @ Y2)))))))))))),
% 27.42/5.39 inference(fool_elimination,[status(thm)],[f198])).
% 27.42/5.39 thf(f198,plain,(
% 27.42/5.39 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X1 @ X2) => ((in @ X2 @ X0) => (in @ X1 @ (setunion @ X0)))) = setunionI)),
% 27.42/5.39 inference(rectify,[status(thm)],[f41])).
% 27.42/5.39 thf(f41,axiom,(
% 27.42/5.39 (! [X3 : $i,X1 : $i,X4 : $i] : ((in @ X1 @ X4) => ((in @ X4 @ X3) => (in @ X1 @ (setunion @ X3)))) = setunionI)),
% 27.42/5.39 file('/export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2THF_17274.p',setunionI)).
% 27.42/5.39 thf(f808,plain,(
% 27.42/5.39 ((in @ sK2 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ sK1 @ emptyset)))) != $true)),
% 27.42/5.39 inference(beta_eta_normalization,[status(thm)],[f552])).
% 27.42/5.39 thf(f552,plain,(
% 27.42/5.39 ($true != (in @ sK2 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ sK0 @ sK1)))),
% 27.42/5.39 inference(definition_unfolding,[status(thm)],[f352,f472])).
% 27.42/5.39 thf(f472,plain,(
% 27.42/5.39 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 27.42/5.39 inference(cnf_transformation,[status(thm)],[f213])).
% 27.42/5.39 thf(f213,plain,(
% 27.42/5.39 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 27.42/5.39 inference(fool_elimination,[status(thm)],[f212])).
% 27.42/5.39 thf(f212,plain,(
% 27.42/5.39 ((^[X0 : $i, X1 : $i] : (setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))) = binunion)),
% 27.42/5.39 inference(rectify,[status(thm)],[f101])).
% 27.42/5.39 thf(f101,axiom,(
% 27.42/5.39 ((^[X1 : $i, X2 : $i] : (setunion @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))) = binunion)),
% 27.42/5.39 file('/export/starexec/sandbox/tmp/tmp.Tmlf9EryTJ/DTF2THF_17274.p',binunion)).
% 27.42/5.39 thf(f352,plain,(
% 27.42/5.39 ($true != (in @ sK2 @ (binunion @ sK0 @ sK1)))),
% 27.42/5.39 inference(cnf_transformation,[status(thm)],[f312])).
% 27.42/5.39 % SZS output end Proof for DTF2THF_17274
% 27.42/5.39 % (17476)------------------------------
% 27.42/5.39 % (17476)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 27.42/5.39 % (17476)Termination reason: Refutation
% 27.42/5.39
% 27.42/5.39 % (17476)Memory used [KB]: 10746
% 27.42/5.39 % (17476)Time elapsed: 2.073 s
% 27.42/5.39 % (17476)Instructions burned: 4142 (million)
% 27.42/5.39 % (17476)------------------------------
% 27.42/5.39 % (17476)------------------------------
% 27.42/5.39 % (17373)Success in time 3.701 s
%------------------------------------------------------------------------------