%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU585^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.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 9.54s 2.73s
% Output : Refutation 9.54s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 33 unt; 0 typ; 8 def)
% Number of atoms : 2059 ( 550 equ; 0 cnn)
% Maximal formula atoms : 107 ( 27 avg)
% Number of connectives : 1333 ( 44 ~; 57 |; 331 &; 423 @)
% ( 10 <=>; 436 =>; 0 <=; 0 <~>)
% Maximal formula depth : 113 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 214 ( 209 usr; 119 con; 0-4 aty)
% ( 23 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 118 ( 48 ^; 56 !; 14 ?; 118 :)
% 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_139,type,
sK5: $i > $i ).
thf(func_def_140,type,
sK6: ( $i > $o ) > $i ).
thf(func_def_141,type,
sK7: ( $i > $o ) > $i ).
thf(func_def_142,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_143,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_144,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_145,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_146,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_147,type,
sK13: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_148,type,
sK14: ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_149,type,
sK15: $i > $i ).
thf(func_def_150,type,
sK16: $i > $i ).
thf(func_def_151,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_152,type,
sK18: ( $i > $o ) > $i ).
thf(func_def_153,type,
sK19: $i > ( $i > $o ) > $i ).
thf(func_def_154,type,
sK20: $i > $i > $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 > $o ) > $i ).
thf(func_def_158,type,
sK24: $i > ( $i > $o ) > $i ).
thf(func_def_159,type,
sK25: $i > ( $i > $o ) > $i ).
thf(func_def_160,type,
sK26: $i > ( $i > $o ) > $i ).
thf(func_def_161,type,
sK27: $i > ( $i > $o ) > $i ).
thf(func_def_162,type,
sK28: $i > $i > $i ).
thf(func_def_163,type,
sK29: ( $i > $o ) > $i ).
thf(func_def_164,type,
sK30: ( $i > $o ) > $i > $i ).
thf(func_def_165,type,
sK31: $i > $i > $i ).
thf(func_def_166,type,
sK32: $i > $i > $i ).
thf(func_def_167,type,
sK33: $i > $i > $i ).
thf(func_def_168,type,
sK34: ( $i > $o ) > $i > $i ).
thf(func_def_169,type,
sK35: $i > $i > $i ).
thf(func_def_170,type,
sK36: ( $i > $o ) > $i ).
thf(func_def_171,type,
sK37: ( $i > $o ) > $i > $i ).
thf(func_def_172,type,
sK38: ( $i > $o ) > $i > $i ).
thf(func_def_173,type,
sK39: ( $i > $o ) > $i > $i ).
thf(func_def_174,type,
sK40: $o > $i > $i > $i ).
thf(func_def_175,type,
sK41: $i > ( $i > $o ) > $i ).
thf(func_def_176,type,
sK42: $i > $i ).
thf(func_def_177,type,
sK43: ( $i > $o ) > $i > $i ).
thf(func_def_178,type,
sK44: $i > ( $i > $i > $o ) > $i ).
thf(func_def_179,type,
sK45: $i > ( $i > $i > $o ) > $i ).
thf(func_def_180,type,
sK46: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_181,type,
sK47: ( $i > $o ) > $i > ( $i > $o ) > $i > $i ).
thf(func_def_182,type,
sK48: $i > $i > ( $i > $o ) > ( $i > $o ) > $i ).
thf(func_def_183,type,
sK49: ( $i > $o ) > $i > $i ).
thf(func_def_184,type,
sK50: $i > $i > $i ).
thf(func_def_185,type,
sK51: $i > $i ).
thf(func_def_186,type,
sK52: $i > $i > $i > $i ).
thf(func_def_187,type,
sK53: $i > $i > $i ).
thf(func_def_188,type,
sK54: $i > $i > $i ).
thf(func_def_189,type,
sK55: $i > $i > $i ).
thf(func_def_190,type,
sK56: $i > $i > $i ).
thf(func_def_191,type,
sK57: $i > $i > $i ).
thf(func_def_192,type,
sK58: $i > $i > $i ).
thf(func_def_193,type,
sK59: $i > $i ).
thf(func_def_194,type,
sK60: ( $i > $o ) > $i ).
thf(func_def_195,type,
sK61: ( $i > $o ) > $i > $i ).
thf(func_def_196,type,
sK62: $i > $i ).
thf(func_def_197,type,
sK63: $i > ( $i > $o ) > $i ).
thf(func_def_198,type,
ph64:
!>[X0: $tType] : X0 ).
thf(func_def_200,type,
sK66: $i > $i > $i > $i ).
thf(func_def_201,type,
sK67: $i > $i > $i ).
thf(func_def_202,type,
sK68: $i > $i > $i ).
thf(func_def_203,type,
sK69: $i > $i > $i ).
thf(func_def_204,type,
sK70: $i > $i ).
thf(func_def_205,type,
sK71: $i > $i > $i ).
thf(func_def_206,type,
sK72: $i > $i > $i ).
thf(func_def_207,type,
sK73: $i > $i ).
thf(func_def_208,type,
sK74: $i > $i ).
thf(func_def_209,type,
sK75: $i > $i > $i ).
thf(func_def_211,type,
sK77: $i > $i > $i > $i ).
thf(func_def_212,type,
sK78: $i > $i ).
thf(func_def_213,type,
sK79: $i > $i > $i ).
thf(func_def_214,type,
sK80: $i > $i > $i ).
thf(func_def_215,type,
sK81: $i > $i > $i ).
thf(func_def_216,type,
sK82: $i > $i > $i ).
thf(func_def_217,type,
sK83: $i > $i > $i ).
thf(func_def_218,type,
sK84: $i > $i > $i ).
thf(func_def_219,type,
sK85: $i > $i > $i ).
thf(func_def_220,type,
sK86: $i > $i > $i ).
thf(f4395,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1643,f1667,f1673,f2189,f3634,f4283,f4384,f4386,f4392]) ).
thf(f4392,plain,
( ( sK0 != sK76 )
| ( ( in @ sK3 @ sK76 )
!= $true )
| ( ( in @ sK3 @ sK0 )
= $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f4386,plain,
( ( sK2 != sK76 )
| ( ( in @ sK3 @ sK76 )
!= $true )
| ( ( in @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[],[theory_tautology_sat_conflict]) ).
thf(f4384,plain,
( spl4_15
| spl4_16
| ~ spl4_14 ),
inference(avatar_split_clause,[status(thm)],[f4371,f4280,f4381,f4377]) ).
thf(f4377,definition,
( spl4_15
<=> ( sK2 = sK76 ) ),
introduced(definition,[new_symbols(naming,[spl4_15])],[avatar_definition]) ).
thf(f4381,definition,
( spl4_16
<=> ( sK0 = sK76 ) ),
introduced(definition,[new_symbols(naming,[spl4_16])],[avatar_definition]) ).
thf(f4280,definition,
( spl4_14
<=> ( $true
= ( in @ sK76 @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl4_14])],[avatar_definition]) ).
thf(f4371,plain,
( ( sK2 = sK76 )
| ( sK0 = sK76 )
| ~ spl4_14 ),
inference(trivial_inequality_removal,[status(thm)],[f4356]) ).
thf(f4356,plain,
( ( sK2 = sK76 )
| ( sK0 = sK76 )
| ( $false = $true )
| ~ spl4_14 ),
inference(superposition,[status(thm)],[f1075,f4282]) ).
thf(f4282,plain,
( ( $true
= ( in @ sK76 @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
| ~ spl4_14 ),
inference(avatar_component_clause,[status(thm)],[f4280]) ).
thf(f1075,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( X1 = X2 )
| ( X1 = X3 ) ),
inference(equality_proxy_clausification,[status(thm)],[f1074]) ).
thf(f1074,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( ( X3 = X1 )
= $true )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f1073]) ).
thf(f1073,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) )
| ( ( X2 = X1 )
= $true )
| ( ( X3 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f1072]) ).
thf(f1072,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( ( X2 = X1 )
| ( X3 = X1 ) )
= $true )
| ( $false
= ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f1071]) ).
thf(f1071,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ X3 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( X3 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1070]) ).
thf(f1070,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( Y0 = X1 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f1069]) ).
thf(f1069,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ ( setadjoin @ Y0 @ emptyset ) ) )
=> ( ( X2 = X1 )
| ( Y0 = X1 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f1068]) ).
thf(f1068,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
=> ( ( Y0 = X1 )
| ( Y1 = X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f1067]) ).
thf(f1067,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ X1 @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
=> ( ( Y0 = X1 )
| ( Y1 = X1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1066]) ).
thf(f1066,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y0 ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f627]) ).
thf(f627,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f522,f358]) ).
thf(f358,plain,
upairsetE = $true,
inference(cnf_transformation,[status(thm)],[f315]) ).
thf(f315,plain,
( ( setextsub = $true )
& ( powerset__Cong = $true )
& ( omegaIndAx = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( notdallE = $true )
& ( exuE1 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( exuI3 = $true )
& ( subsetI2 = $true )
& ( foundationAx = $true )
& ( exuI2 = $true )
& ( prop2set2propI = $true )
& ( setadjoinSub2 = $true )
& ( in__Cong = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( eqimpsubset2 = $true )
& ( subsetE = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ( ( in @ sK3 @ ( binunion @ sK0 @ sK2 ) )
= $true )
& ( ( sK1 = $true )
| ( ( in @ sK3 @ sK2 )
!= $true ) )
& ( sK1 != $true )
& ( ( sK1 = $true )
| ( ( in @ sK3 @ sK0 )
!= $true ) )
& ( nonemptyI1 = $true )
& ( setunion__Cong = $true )
& ( dsetconstrER = $true )
& ( eqimpsubset1 = $true )
& ( sepSubset = $true )
& ( upairset2IR = $true )
& ( inCongP = $true )
& ( subsetRefl = $true )
& ( exuE3u = $true )
& ( setadjoinIL = $true )
& ( emptyset__Cong = $true )
& ( subPowSU = $true )
& ( quantDeMorgan2 = $true )
& ( subset2powerset = $true )
& ( exuE3e = $true )
& ( omega0Ax = $true )
& ( binunionIL = $true )
& ( vacuousDall = $true )
& ( nonemptyE1 = $true )
& ( setadjoinE = $true )
& ( prop2setI = $true )
& ( powersetI1 = $true )
& ( sepInPowerset = $true )
& ( notequalI1 = $true )
& ( setext = $true )
& ( setadjoinAx = $true )
& ( omega__Cong = $true )
& ( setextAx = $true )
& ( replAx = $true )
& ( powersetI = $true )
& ( powersetAx = $true )
& ( exuE2 = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinOr = $true )
& ( notequalI2 = $true )
& ( prop2setE = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinIR = $true )
& ( subsetI1 = $true )
& ( emptyinPowerset = $true )
& ( emptysetE = $true )
& ( upairsetE = $true )
& ( emptyInPowerset = $true )
& ( exu__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( exuEu = $true )
& ( upairsetIL = $true )
& ( inPowerset = $true )
& ( binunionIR = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( subsetTrans = $true )
& ( setunionAx = $true )
& ( notinemptyset = $true )
& ( powersetE = $true )
& ( setunionI = $true )
& ( upairsetIR = $true )
& ( dsetconstrEL = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetAx = $true )
& ( emptysetsubset = $true )
& ( emptyinunitempty = $true )
& ( notsubsetI = $true )
& ( setadjoinSub = $true )
& ( setunionE = $true )
& ( notdexE = $true )
& ( emptyE1 = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( uniqinunit = $true )
& ( setbeta = $true )
& ( singletonsswitch = $true )
& ( emptyI = $true )
& ( powersetE1 = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f313,f314]) ).
thf(f314,plain,
( ? [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
& ( ( $true = X1 )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( $true != X1 )
& ( ( $true = X1 )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
=> ( ( ( in @ sK3 @ ( binunion @ sK0 @ sK2 ) )
= $true )
& ( ( sK1 = $true )
| ( ( in @ sK3 @ sK2 )
!= $true ) )
& ( sK1 != $true )
& ( ( sK1 = $true )
| ( ( in @ sK3 @ sK0 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f313,plain,
( ( setextsub = $true )
& ( powerset__Cong = $true )
& ( omegaIndAx = $true )
& ( noeltsimpempty = $true )
& ( omegaSAx = $true )
& ( notdallE = $true )
& ( exuE1 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( exuI3 = $true )
& ( subsetI2 = $true )
& ( foundationAx = $true )
& ( exuI2 = $true )
& ( prop2set2propI = $true )
& ( setadjoinSub2 = $true )
& ( in__Cong = $true )
& ( descrp = $true )
& ( dsetconstrI = $true )
& ( eqimpsubset2 = $true )
& ( subsetE = $true )
& ( powersetsubset = $true )
& ( wellorderingAx = $true )
& ? [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
& ( ( $true = X1 )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( $true != X1 )
& ( ( $true = X1 )
| ( ( in @ X3 @ X0 )
!= $true ) ) )
& ( nonemptyI1 = $true )
& ( setunion__Cong = $true )
& ( dsetconstrER = $true )
& ( eqimpsubset1 = $true )
& ( sepSubset = $true )
& ( upairset2IR = $true )
& ( inCongP = $true )
& ( subsetRefl = $true )
& ( exuE3u = $true )
& ( setadjoinIL = $true )
& ( emptyset__Cong = $true )
& ( subPowSU = $true )
& ( quantDeMorgan2 = $true )
& ( subset2powerset = $true )
& ( exuE3e = $true )
& ( omega0Ax = $true )
& ( binunionIL = $true )
& ( vacuousDall = $true )
& ( nonemptyE1 = $true )
& ( setadjoinE = $true )
& ( prop2setI = $true )
& ( powersetI1 = $true )
& ( sepInPowerset = $true )
& ( notequalI1 = $true )
& ( setext = $true )
& ( setadjoinAx = $true )
& ( omega__Cong = $true )
& ( setextAx = $true )
& ( replAx = $true )
& ( powersetI = $true )
& ( powersetAx = $true )
& ( exuE2 = $true )
& ( setadjoin__Cong = $true )
& ( setadjoinOr = $true )
& ( notequalI2 = $true )
& ( prop2setE = $true )
& ( quantDeMorgan4 = $true )
& ( setadjoinIR = $true )
& ( subsetI1 = $true )
& ( emptyinPowerset = $true )
& ( emptysetE = $true )
& ( upairsetE = $true )
& ( emptyInPowerset = $true )
& ( exu__Cong = $true )
& ( subsetemptysetimpeq = $true )
& ( exuI1 = $true )
& ( subsetE2 = $true )
& ( exuEu = $true )
& ( upairsetIL = $true )
& ( inPowerset = $true )
& ( binunionIR = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( subsetTrans = $true )
& ( setunionAx = $true )
& ( notinemptyset = $true )
& ( powersetE = $true )
& ( setunionI = $true )
& ( upairsetIR = $true )
& ( dsetconstrEL = $true )
& ( nonemptyImpWitness = $true )
& ( emptysetAx = $true )
& ( emptysetsubset = $true )
& ( emptyinunitempty = $true )
& ( notsubsetI = $true )
& ( setadjoinSub = $true )
& ( setunionE = $true )
& ( notdexE = $true )
& ( emptyE1 = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( emptysetimpfalse = $true )
& ( uniqinunit = $true )
& ( setbeta = $true )
& ( singletonsswitch = $true )
& ( emptyI = $true )
& ( powersetE1 = $true ) ),
inference(flattening,[status(thm)],[f312]) ).
thf(f312,plain,
( ? [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( $true != X1 )
& ( ( $true = X1 )
| ( ( in @ X3 @ X2 )
!= $true ) )
& ( ( $true = X1 )
| ( ( in @ X3 @ X0 )
!= $true ) )
& ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true ) )
& ( binunionIR = $true )
& ( upairset2IR = $true )
& ( binunionIL = $true )
& ( sepSubset = $true )
& ( sepInPowerset = $true )
& ( powersetsubset = $true )
& ( inPowerset = $true )
& ( powersetE1 = $true )
& ( powersetI1 = $true )
& ( subsetemptysetimpeq = $true )
& ( setextsub = $true )
& ( subset2powerset = $true )
& ( setadjoinSub2 = $true )
& ( setadjoinSub = $true )
& ( subsetTrans = $true )
& ( subsetRefl = $true )
& ( notequalI2 = $true )
& ( notequalI1 = $true )
& ( notsubsetI = $true )
& ( subsetE2 = $true )
& ( subsetE = $true )
& ( emptysetsubset = $true )
& ( subsetI2 = $true )
& ( eqimpsubset1 = $true )
& ( eqimpsubset2 = $true )
& ( subsetI1 = $true )
& ( dsetconstr__Cong = $true )
& ( descr__Cong = $true )
& ( exuEu = $true )
& ( omega__Cong = $true )
& ( setunion__Cong = $true )
& ( powerset__Cong = $true )
& ( setadjoin__Cong = $true )
& ( emptyset__Cong = $true )
& ( exu__Cong = $true )
& ( exuE3u = $true )
& ( in__Cong = $true )
& ( inCongP = $true )
& ( exuI2 = $true )
& ( exuI3 = $true )
& ( exuI1 = $true )
& ( notdallE = $true )
& ( notdexE = $true )
& ( prop2set2propI = $true )
& ( prop2setI = $true )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f201]) ).
thf(f201,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ( ( prop2setI = $true )
=> ( ( prop2set2propI = $true )
=> ( ( notdexE = $true )
=> ( ( notdallE = $true )
=> ( ( exuI1 = $true )
=> ( ( exuI3 = $true )
=> ( ( exuI2 = $true )
=> ( ( inCongP = $true )
=> ( ( in__Cong = $true )
=> ( ( exuE3u = $true )
=> ( ( exu__Cong = $true )
=> ( ( emptyset__Cong = $true )
=> ( ( setadjoin__Cong = $true )
=> ( ( powerset__Cong = $true )
=> ( ( setunion__Cong = $true )
=> ( ( omega__Cong = $true )
=> ( ( exuEu = $true )
=> ( ( descr__Cong = $true )
=> ( ( dsetconstr__Cong = $true )
=> ( ( subsetI1 = $true )
=> ( ( eqimpsubset2 = $true )
=> ( ( eqimpsubset1 = $true )
=> ( ( subsetI2 = $true )
=> ( ( emptysetsubset = $true )
=> ( ( subsetE = $true )
=> ( ( subsetE2 = $true )
=> ( ( notsubsetI = $true )
=> ( ( notequalI1 = $true )
=> ( ( notequalI2 = $true )
=> ( ( subsetRefl = $true )
=> ( ( subsetTrans = $true )
=> ( ( setadjoinSub = $true )
=> ( ( setadjoinSub2 = $true )
=> ( ( subset2powerset = $true )
=> ( ( setextsub = $true )
=> ( ( subsetemptysetimpeq = $true )
=> ( ( powersetI1 = $true )
=> ( ( powersetE1 = $true )
=> ( ( inPowerset = $true )
=> ( ( powersetsubset = $true )
=> ( ( sepInPowerset = $true )
=> ( ( sepSubset = $true )
=> ( ( binunionIL = $true )
=> ( ( upairset2IR = $true )
=> ( ( binunionIR = $true )
=> ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
= $true )
=> ( ( ( ( in @ X3 @ X0 )
= $true )
=> ( $true = X1 ) )
=> ( ( ( ( in @ X3 @ X2 )
= $true )
=> ( $true = X1 ) )
=> ( $true = X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f200]) ).
thf(f200,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ! [X0: $i,X1: $o,X2: $i,X3: $i] :
( ( in @ X3 @ ( binunion @ X0 @ X2 ) )
=> ( ( ( in @ X3 @ X0 )
=> X1 )
=> ( ( ( in @ X3 @ X2 )
=> X1 )
=> X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f106]) ).
thf(f106,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ! [X3: $i,X0: $o,X4: $i,X1: $i] :
( ( in @ X1 @ ( binunion @ X3 @ X4 ) )
=> ( ( ( in @ X1 @ X3 )
=> X0 )
=> ( ( ( in @ X1 @ X4 )
=> X0 )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f105]) ).
thf(f105,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ( prop2setI
=> ( prop2set2propI
=> ( notdexE
=> ( notdallE
=> ( exuI1
=> ( exuI3
=> ( exuI2
=> ( inCongP
=> ( in__Cong
=> ( exuE3u
=> ( exu__Cong
=> ( emptyset__Cong
=> ( setadjoin__Cong
=> ( powerset__Cong
=> ( setunion__Cong
=> ( omega__Cong
=> ( exuEu
=> ( descr__Cong
=> ( dsetconstr__Cong
=> ( subsetI1
=> ( eqimpsubset2
=> ( eqimpsubset1
=> ( subsetI2
=> ( emptysetsubset
=> ( subsetE
=> ( subsetE2
=> ( notsubsetI
=> ( notequalI1
=> ( notequalI2
=> ( subsetRefl
=> ( subsetTrans
=> ( setadjoinSub
=> ( setadjoinSub2
=> ( subset2powerset
=> ( setextsub
=> ( subsetemptysetimpeq
=> ( powersetI1
=> ( powersetE1
=> ( inPowerset
=> ( powersetsubset
=> ( sepInPowerset
=> ( sepSubset
=> ( binunionIL
=> ( upairset2IR
=> ( binunionIR
=> ! [X3: $i,X0: $o,X4: $i,X1: $i] :
( ( in @ X1 @ ( binunion @ X3 @ X4 ) )
=> ( ( ( in @ X1 @ X3 )
=> X0 )
=> ( ( ( in @ X1 @ X4 )
=> X0 )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2THF_27107.p',binunionEcases) ).
thf(f522,plain,
( upairsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f203]) ).
thf(f203,plain,
( upairsetE
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y0 @ ( setadjoin @ Y1 @ ( setadjoin @ Y2 @ emptyset ) ) )
=> ( ( Y1 = Y0 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f202]) ).
thf(f202,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
=> ( ( X0 = X2 )
| ( X1 = X2 ) ) )
= upairsetE ),
inference(rectify,[status(thm)],[f50]) ).
thf(f50,axiom,
! [X2: $i,X1: $i,X8: $i] :
( ( ( in @ X8 @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) )
=> ( ( X2 = X8 )
| ( X1 = X8 ) ) )
= upairsetE ),
file('/export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2THF_27107.p',upairsetE) ).
thf(f4283,plain,
( spl4_14
| ~ spl4_10 ),
inference(avatar_split_clause,[status(thm)],[f3546,f2186,f4280]) ).
thf(f2186,definition,
( spl4_10
<=> ( ( in @ sK3 @ ( setunion @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition]) ).
thf(f3546,plain,
( ( $true
= ( in @ sK76 @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
| ~ spl4_10 ),
inference(binary_proxy_clausification,[status(thm)],[f3544]) ).
thf(f3544,plain,
( ( ( ( in @ sK76 @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) )
& ( in @ sK3 @ sK76 ) )
= $true )
| ~ spl4_10 ),
inference(beta_eta_normalization,[status(thm)],[f3543]) ).
thf(f3543,plain,
( ( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) )
& ( in @ sK3 @ Y0 ) )
@ sK76 )
= $true )
| ~ spl4_10 ),
inference(sigma_clausification,[status(thm)],[f3542]) ).
thf(f3542,plain,
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) )
& ( in @ sK3 @ Y0 ) ) )
= $true )
| ~ spl4_10 ),
inference(boolean_simplification,[status(thm)],[f3460]) ).
thf(f3460,plain,
( ( ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) )
& ( in @ sK3 @ Y0 ) ) ) )
= $true )
| ~ spl4_10 ),
inference(superposition,[status(thm)],[f812,f2188]) ).
thf(f2188,plain,
( ( ( in @ sK3 @ ( setunion @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
= $true )
| ~ spl4_10 ),
inference(avatar_component_clause,[status(thm)],[f2186]) ).
thf(f812,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setunion @ X1 ) )
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ X1 )
& ( in @ X2 @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f811]) ).
thf(f811,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
& ( in @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f810]) ).
thf(f810,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setunion @ X1 ) )
= ( ?? @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ X1 )
& ( in @ Y0 @ Y1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f809]) ).
thf(f809,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y1 @ Y2 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f592]) ).
thf(f592,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y1 @ Y2 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f486,f345]) ).
thf(f345,plain,
setunionAx = $true,
inference(cnf_transformation,[status(thm)],[f315]) ).
thf(f486,plain,
( setunionAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f169]) ).
thf(f169,plain,
( setunionAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setunion @ Y0 ) )
= ( ?? @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y0 )
& ( in @ Y1 @ Y2 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f168]) ).
thf(f168,plain,
! [X0: $i,X1: $i] :
( ( ( in @ X0 @ ( setunion @ X1 ) )
<=> ? [X2: $i] :
( ( in @ X0 @ X2 )
& ( in @ X2 @ X1 ) ) )
= setunionAx ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
! [X1: $i,X3: $i] :
( ( ( in @ X1 @ ( setunion @ X3 ) )
<=> ? [X4: $i] :
( ( in @ X1 @ X4 )
& ( in @ X4 @ X3 ) ) )
= setunionAx ),
file('/export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2THF_27107.p',setunionAx) ).
thf(f3634,plain,
( spl4_13
| ~ spl4_10 ),
inference(avatar_split_clause,[status(thm)],[f3545,f2186,f3631]) ).
thf(f3631,definition,
( spl4_13
<=> ( ( in @ sK3 @ sK76 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_13])],[avatar_definition]) ).
thf(f3545,plain,
( ( ( in @ sK3 @ sK76 )
= $true )
| ~ spl4_10 ),
inference(binary_proxy_clausification,[status(thm)],[f3544]) ).
thf(f2189,plain,
spl4_10,
inference(avatar_split_clause,[status(thm)],[f984,f2186]) ).
thf(f984,plain,
( ( in @ sK3 @ ( setunion @ ( setadjoin @ sK0 @ ( setadjoin @ sK2 @ emptyset ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f530]) ).
thf(f530,plain,
( ( in @ sK3
@ ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) )
@ sK0
@ sK2 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f403,f436]) ).
thf(f436,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
thf(f181,plain,
( binunion
= ( ^ [Y0: $i,Y1: $i] : ( setunion @ ( setadjoin @ Y0 @ ( setadjoin @ Y1 @ emptyset ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f180]) ).
thf(f180,plain,
( binunion
= ( ^ [X0: $i,X1: $i] : ( setunion @ ( setadjoin @ X0 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ),
inference(rectify,[status(thm)],[f101]) ).
thf(f101,axiom,
( binunion
= ( ^ [X1: $i,X2: $i] : ( setunion @ ( setadjoin @ X1 @ ( setadjoin @ X2 @ emptyset ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2THF_27107.p',binunion) ).
thf(f403,plain,
( ( in @ sK3 @ ( binunion @ sK0 @ sK2 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f315]) ).
thf(f1673,plain,
( ~ spl4_5
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f1668,f1640,f1670]) ).
thf(f1670,definition,
( spl4_5
<=> ( ( in @ sK3 @ sK2 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition]) ).
thf(f1640,definition,
( spl4_1
<=> ( sK1 = $true ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f1668,plain,
( ( ( in @ sK3 @ sK2 )
!= $true )
| spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f402,f1642]) ).
thf(f1642,plain,
( ( sK1 != $true )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f1640]) ).
thf(f402,plain,
( ( ( in @ sK3 @ sK2 )
!= $true )
| ( sK1 = $true ) ),
inference(cnf_transformation,[status(thm)],[f315]) ).
thf(f1667,plain,
( ~ spl4_4
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f1662,f1640,f1664]) ).
thf(f1664,definition,
( spl4_4
<=> ( ( in @ sK3 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition]) ).
thf(f1662,plain,
( ( ( in @ sK3 @ sK0 )
!= $true )
| spl4_1 ),
inference(subsumption_resolution,[status(thm)],[f400,f1642]) ).
thf(f400,plain,
( ( sK1 = $true )
| ( ( in @ sK3 @ sK0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f315]) ).
thf(f1643,plain,
~ spl4_1,
inference(avatar_split_clause,[status(thm)],[f401,f1640]) ).
thf(f401,plain,
sK1 != $true,
inference(cnf_transformation,[status(thm)],[f315]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU585^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n002.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 12:28:03 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.46 ---- Original DTF file ---
% 0.29/0.46 thf(spec,logic,$$dhol).
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 % File : SEU585^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.46 % Domain : Set Theory
% 0.29/0.46 % Problem : Preliminary Notions - Ops on Sets - Unions and Intersections
% 0.29/0.46 % Version : Especial.
% 0.29/0.46 % English : (! A:i.! B:i.! x:i.! phi:o.in x (binunion A B) ->
% 0.29/0.46 % (in x A -> phi) -> (in x B -> phi) -> phi)
% 0.29/0.46
% 0.29/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.46 % Source : [Bro08]
% 0.29/0.46 % Names : ZFC087g [Bro08]
% 0.29/0.46
% 0.29/0.46 % Status : Theorem
% 0.29/0.46 % Rating : 0.44 v9.1.0, 0.38 v9.0.0, 0.40 v8.2.0, 0.62 v8.1.0, 0.55 v7.5.0, 0.57 v7.4.0, 0.56 v7.2.0, 0.50 v7.1.0, 0.62 v7.0.0, 0.71 v6.4.0, 0.83 v6.3.0, 0.80 v6.2.0, 0.86 v6.1.0, 1.00 v5.4.0, 0.80 v5.2.0, 1.00 v5.0.0, 0.80 v4.1.0, 1.00 v3.7.0
% 0.29/0.46 % Syntax : Number of formulae : 222 ( 104 unt; 117 typ; 104 def)
% 0.29/0.46 % Number of atoms : 556 ( 153 equ; 0 cnn)
% 0.29/0.46 % Maximal formula atoms : 104 ( 5 avg)
% 0.29/0.46 % Number of connectives : 879 ( 29 ~; 5 |; 27 &; 552 @)
% 0.29/0.46 % ( 14 <=>; 252 =>; 0 <=; 0 <~>)
% 0.29/0.46 % Maximal formula depth : 112 ( 2 avg)
% 0.29/0.46 % Number of types : 2 ( 0 usr)
% 0.29/0.46 % Number of type conns : 57 ( 57 >; 0 *; 0 +; 0 <<)
% 0.29/0.46 % Number of symbols : 120 ( 117 usr; 105 con; 0-2 aty)
% 0.29/0.46 % Number of variables : 308 ( 32 ^; 248 !; 28 ?; 308 :)
% 0.29/0.46 % SPC : TH0_THM_EQU_NAR
% 0.29/0.46
% 0.29/0.46 % Comments : http://mathgate.info/detsetitem.php?id=161
% 0.29/0.46 %------------------------------------------------------------------------------
% 0.29/0.46 thf(in_type,type,
% 0.29/0.46 in: $i > $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu_type,type,
% 0.29/0.46 exu: ( $i > $o ) > $o ).
% 0.29/0.46
% 0.29/0.46 thf(exu,definition,
% 0.29/0.46 ( exu
% 0.29/0.46 = ( ^ [Xphi: $i > $o] :
% 0.29/0.46 ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx_type,type,
% 0.29/0.46 setextAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setextAx,definition,
% 0.29/0.46 ( setextAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 <=> ( in @ Xx @ B ) )
% 0.29/0.46 => ( A = B ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyset_type,type,
% 0.29/0.46 emptyset: $i ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx_type,type,
% 0.29/0.46 emptysetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetAx,definition,
% 0.29/0.46 ( emptysetAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoin_type,type,
% 0.29/0.46 setadjoin: $i > $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx_type,type,
% 0.29/0.46 setadjoinAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinAx,definition,
% 0.29/0.46 ( setadjoinAx
% 0.29/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.46 <=> ( ( Xy = Xx )
% 0.29/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(powerset_type,type,
% 0.29/0.46 powerset: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx_type,type,
% 0.29/0.46 powersetAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(powersetAx,definition,
% 0.29/0.46 ( powersetAx
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.46 <=> ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setunion_type,type,
% 0.29/0.46 setunion: $i > $i ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx_type,type,
% 0.29/0.46 setunionAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setunionAx,definition,
% 0.29/0.46 ( setunionAx
% 0.29/0.46 = ( ! [A: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.46 <=> ? [B: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omega_type,type,
% 0.29/0.46 omega: $i ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax_type,type,
% 0.29/0.46 omega0Ax: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omega0Ax,definition,
% 0.29/0.46 ( omega0Ax
% 0.29/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx_type,type,
% 0.29/0.46 omegaSAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaSAx,definition,
% 0.29/0.46 ( omegaSAx
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx_type,type,
% 0.29/0.46 omegaIndAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(omegaIndAx,definition,
% 0.29/0.46 ( omegaIndAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( ( in @ emptyset @ A )
% 0.29/0.46 & ! [Xx: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ omega )
% 0.29/0.46 & ( in @ Xx @ A ) )
% 0.29/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ omega )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(replAx_type,type,
% 0.29/0.46 replAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(replAx,definition,
% 0.29/0.46 ( replAx
% 0.29/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( exu
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 <=> ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ A )
% 0.29/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx_type,type,
% 0.29/0.46 foundationAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(foundationAx,definition,
% 0.29/0.46 ( foundationAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ? [B: $i] :
% 0.29/0.46 ( ( in @ B @ A )
% 0.29/0.46 & ~ ? [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx_type,type,
% 0.29/0.46 wellorderingAx: $o ).
% 0.29/0.46
% 0.29/0.46 thf(wellorderingAx,definition,
% 0.29/0.46 ( wellorderingAx
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ? [B: $i] :
% 0.29/0.46 ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) ) )
% 0.29/0.46 & ! [Xx: $i,Xy: $i] :
% 0.29/0.46 ( ( ( in @ Xx @ A )
% 0.29/0.46 & ( in @ Xy @ A ) )
% 0.29/0.46 => ( ! [C: $i] :
% 0.29/0.46 ( ( in @ C @ B )
% 0.29/0.46 => ( ( in @ Xx @ C )
% 0.29/0.46 <=> ( in @ Xy @ C ) ) )
% 0.29/0.46 => ( Xx = Xy ) ) )
% 0.29/0.46 & ! [C: $i,D: $i] :
% 0.29/0.46 ( ( ( in @ C @ B )
% 0.29/0.46 & ( in @ D @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ D ) )
% 0.29/0.46 | ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ D )
% 0.29/0.46 => ( in @ Xx @ C ) ) ) )
% 0.29/0.46 & ! [C: $i] :
% 0.29/0.46 ( ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ C )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.46 => ? [D: $i,Xx: $i] :
% 0.29/0.46 ( ( in @ D @ B )
% 0.29/0.46 & ( in @ Xx @ C )
% 0.29/0.46 & ~ ? [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ D )
% 0.29/0.46 & ( in @ Xy @ C ) )
% 0.29/0.46 & ! [E: $i] :
% 0.29/0.46 ( ( in @ E @ B )
% 0.29/0.46 => ( ! [Xy: $i] :
% 0.29/0.46 ( ( in @ Xy @ E )
% 0.29/0.46 => ( in @ Xy @ D ) )
% 0.29/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(descr_type,type,
% 0.29/0.46 descr: ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(descrp_type,type,
% 0.29/0.46 descrp: $o ).
% 0.29/0.46
% 0.29/0.46 thf(descrp,definition,
% 0.29/0.46 ( descrp
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ( Xphi
% 0.29/0.46 @ ( descr
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstr_type,type,
% 0.29/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI_type,type,
% 0.29/0.46 dsetconstrI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrI,definition,
% 0.29/0.46 ( dsetconstrI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL_type,type,
% 0.29/0.46 dsetconstrEL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrEL,definition,
% 0.29/0.46 ( dsetconstrEL
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER_type,type,
% 0.29/0.46 dsetconstrER: $o ).
% 0.29/0.46
% 0.29/0.46 thf(dsetconstrER,definition,
% 0.29/0.46 ( dsetconstrER
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1_type,type,
% 0.29/0.46 exuE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE1,definition,
% 0.29/0.46 ( exuE1
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] :
% 0.29/0.46 ( ( Xphi @ Xx )
% 0.29/0.46 & ! [Xy: $i] :
% 0.29/0.46 ( ( Xphi @ Xy )
% 0.29/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(prop2set_type,type,
% 0.29/0.46 prop2set: $o > $i ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE_type,type,
% 0.29/0.46 prop2setE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(prop2setE,definition,
% 0.29/0.46 ( prop2setE
% 0.29/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.46 => Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE_type,type,
% 0.29/0.46 emptysetE: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetE,definition,
% 0.29/0.46 ( emptysetE
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse_type,type,
% 0.29/0.46 emptysetimpfalse: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptysetimpfalse,definition,
% 0.29/0.46 ( emptysetimpfalse
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ emptyset )
% 0.29/0.46 => $false ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset_type,type,
% 0.29/0.46 notinemptyset: $o ).
% 0.29/0.46
% 0.29/0.46 thf(notinemptyset,definition,
% 0.29/0.46 ( notinemptyset
% 0.29/0.46 = ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e_type,type,
% 0.29/0.46 exuE3e: $o ).
% 0.29/0.46
% 0.29/0.46 thf(exuE3e,definition,
% 0.29/0.46 ( exuE3e
% 0.29/0.46 = ( ! [Xphi: $i > $o] :
% 0.29/0.46 ( ( exu
% 0.29/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setext_type,type,
% 0.29/0.46 setext: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setext,definition,
% 0.29/0.46 ( setext
% 0.29/0.46 = ( ! [A: $i,B: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( in @ Xx @ B ) )
% 0.29/0.46 => ( ! [Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ B )
% 0.29/0.46 => ( in @ Xx @ A ) )
% 0.29/0.46 => ( A = B ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI_type,type,
% 0.29/0.46 emptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyI,definition,
% 0.29/0.46 ( emptyI
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty_type,type,
% 0.29/0.46 noeltsimpempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(noeltsimpempty,definition,
% 0.29/0.46 ( noeltsimpempty
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ! [Xx: $i] :
% 0.29/0.46 ~ ( in @ Xx @ A )
% 0.29/0.46 => ( A = emptyset ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta_type,type,
% 0.29/0.46 setbeta: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setbeta,definition,
% 0.29/0.46 ( setbeta
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( in @ Xx
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty_type,type,
% 0.29/0.46 nonempty: $i > $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonempty,definition,
% 0.29/0.46 ( nonempty
% 0.29/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1_type,type,
% 0.29/0.46 nonemptyE1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyE1,definition,
% 0.29/0.46 ( nonemptyE1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ( nonempty @ A )
% 0.29/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI_type,type,
% 0.29/0.46 nonemptyI: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI,definition,
% 0.29/0.46 ( nonemptyI
% 0.29/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.46 ( ( in @ Xx @ A )
% 0.29/0.46 => ( ( Xphi @ Xx )
% 0.29/0.46 => ( nonempty
% 0.29/0.46 @ ( dsetconstr @ A
% 0.29/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1_type,type,
% 0.29/0.46 nonemptyI1: $o ).
% 0.29/0.46
% 0.29/0.46 thf(nonemptyI1,definition,
% 0.29/0.46 ( nonemptyI1
% 0.29/0.46 = ( ! [A: $i] :
% 0.29/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL_type,type,
% 0.29/0.46 setadjoinIL: $o ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIL,definition,
% 0.29/0.46 ( setadjoinIL
% 0.29/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty_type,type,
% 0.29/0.46 emptyinunitempty: $o ).
% 0.29/0.46
% 0.29/0.46 thf(emptyinunitempty,definition,
% 0.29/0.46 ( emptyinunitempty
% 0.29/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.29/0.46
% 0.29/0.46 thf(setadjoinIR_type,type,
% 0.29/0.47 setadjoinIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinIR,definition,
% 0.29/0.47 ( setadjoinIR
% 0.29/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinE_type,type,
% 0.29/0.47 setadjoinE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinE,definition,
% 0.29/0.47 ( setadjoinE
% 0.29/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ( ( Xy = Xx )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => ( ( ( in @ Xy @ A )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinOr_type,type,
% 0.29/0.47 setadjoinOr: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinOr,definition,
% 0.29/0.47 ( setadjoinOr
% 0.29/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.47 => ( ( Xy = Xx )
% 0.29/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setoftrueEq_type,type,
% 0.29/0.47 setoftrueEq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setoftrueEq,definition,
% 0.29/0.47 ( setoftrueEq
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : $true )
% 0.29/0.47 = A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI_type,type,
% 0.29/0.47 powersetI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI,definition,
% 0.29/0.47 ( powersetI
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) )
% 0.29/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyinPowerset_type,type,
% 0.29/0.47 emptyinPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyinPowerset,definition,
% 0.29/0.47 ( emptyinPowerset
% 0.29/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyInPowerset_type,type,
% 0.29/0.47 emptyInPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyInPowerset,definition,
% 0.29/0.47 ( emptyInPowerset
% 0.29/0.47 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE_type,type,
% 0.29/0.47 powersetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE,definition,
% 0.29/0.47 ( powersetE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.47 => ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionI_type,type,
% 0.29/0.47 setunionI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionI,definition,
% 0.29/0.47 ( setunionI
% 0.29/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( ( in @ B @ A )
% 0.29/0.47 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE_type,type,
% 0.29/0.47 setunionE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionE,definition,
% 0.29/0.47 ( setunionE
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.47 => ! [Xphi: $o] :
% 0.29/0.47 ( ! [B: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( ( in @ B @ A )
% 0.29/0.47 => Xphi ) )
% 0.29/0.47 => Xphi ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subPowSU_type,type,
% 0.29/0.47 subPowSU: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subPowSU,definition,
% 0.29/0.47 ( subPowSU
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE2_type,type,
% 0.29/0.47 exuE2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE2,definition,
% 0.29/0.47 ( exuE2
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyImpWitness_type,type,
% 0.29/0.47 nonemptyImpWitness: $o ).
% 0.29/0.47
% 0.29/0.47 thf(nonemptyImpWitness,definition,
% 0.29/0.47 ( nonemptyImpWitness
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( nonempty @ A )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & $true ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(uniqinunit_type,type,
% 0.29/0.47 uniqinunit: $o ).
% 0.29/0.47
% 0.29/0.47 thf(uniqinunit,definition,
% 0.29/0.47 ( uniqinunit
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notinsingleton_type,type,
% 0.29/0.47 notinsingleton: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notinsingleton,definition,
% 0.29/0.47 ( notinsingleton
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx != Xy )
% 0.29/0.47 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqinunit_type,type,
% 0.29/0.47 eqinunit: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqinunit,definition,
% 0.29/0.47 ( eqinunit
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsswitch_type,type,
% 0.29/0.47 singletonsswitch: $o ).
% 0.29/0.47
% 0.29/0.47 thf(singletonsswitch,definition,
% 0.29/0.47 ( singletonsswitch
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.29/0.47 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetE_type,type,
% 0.29/0.47 upairsetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetE,definition,
% 0.29/0.47 ( upairsetE
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.29/0.47 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.29/0.47 => ( ( Xz = Xx )
% 0.29/0.47 | ( Xz = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIL_type,type,
% 0.29/0.47 upairsetIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIL,definition,
% 0.29/0.47 ( upairsetIL
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIR_type,type,
% 0.29/0.47 upairsetIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairsetIR,definition,
% 0.29/0.47 ( upairsetIR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyE1_type,type,
% 0.29/0.47 emptyE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyE1,definition,
% 0.29/0.47 ( emptyE1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ( ( ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = emptyset )
% 0.29/0.47 => $false ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(vacuousDall_type,type,
% 0.29/0.47 vacuousDall: $o ).
% 0.29/0.47
% 0.29/0.47 thf(vacuousDall,definition,
% 0.29/0.47 ( vacuousDall
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ emptyset )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan1_type,type,
% 0.29/0.47 quantDeMorgan1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan1,definition,
% 0.29/0.47 ( quantDeMorgan1
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan2_type,type,
% 0.29/0.47 quantDeMorgan2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan2,definition,
% 0.29/0.47 ( quantDeMorgan2
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) )
% 0.29/0.47 => ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan3_type,type,
% 0.29/0.47 quantDeMorgan3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan3,definition,
% 0.29/0.47 ( quantDeMorgan3
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan4_type,type,
% 0.29/0.47 quantDeMorgan4: $o ).
% 0.29/0.47
% 0.29/0.47 thf(quantDeMorgan4,definition,
% 0.29/0.47 ( quantDeMorgan4
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) )
% 0.29/0.47 => ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setI_type,type,
% 0.29/0.47 prop2setI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setI,definition,
% 0.29/0.47 ( prop2setI
% 0.29/0.47 = ( ! [Xphi: $o] :
% 0.29/0.47 ( Xphi
% 0.29/0.47 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(set2prop_type,type,
% 0.29/0.47 set2prop: $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set2propI_type,type,
% 0.29/0.47 prop2set2propI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set2propI,definition,
% 0.29/0.47 ( prop2set2propI
% 0.29/0.47 = ( ! [Xphi: $o] :
% 0.29/0.47 ( Xphi
% 0.29/0.47 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notdexE_type,type,
% 0.29/0.47 notdexE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notdexE,definition,
% 0.29/0.47 ( notdexE
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notdallE_type,type,
% 0.29/0.47 notdallE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notdallE,definition,
% 0.29/0.47 ( notdallE
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( ~ ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI1_type,type,
% 0.29/0.47 exuI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI1,definition,
% 0.29/0.47 ( exuI1
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI3_type,type,
% 0.29/0.47 exuI3: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI3,definition,
% 0.29/0.47 ( exuI3
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.29/0.47 => ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuI2_type,type,
% 0.29/0.47 exuI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuI2,definition,
% 0.29/0.47 ( exuI2
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ? [Xx: $i] :
% 0.29/0.47 ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 <=> ( Xy = Xx ) )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(inCongP_type,type,
% 0.29/0.47 inCongP: $o ).
% 0.29/0.47
% 0.29/0.47 thf(inCongP,definition,
% 0.29/0.47 ( inCongP
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(in__Cong_type,type,
% 0.29/0.47 in__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(in__Cong,definition,
% 0.29/0.47 ( in__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE3u_type,type,
% 0.29/0.47 exuE3u: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE3u,definition,
% 0.29/0.47 ( exuE3u
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exu__Cong_type,type,
% 0.29/0.47 exu__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exu__Cong,definition,
% 0.29/0.47 ( exu__Cong
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 <=> ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset__Cong_type,type,
% 0.29/0.47 emptyset__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset__Cong,definition,
% 0.29/0.47 ( emptyset__Cong
% 0.29/0.47 = ( emptyset = emptyset ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoin__Cong_type,type,
% 0.29/0.47 setadjoin__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoin__Cong,definition,
% 0.29/0.47 ( setadjoin__Cong
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ! [Xz: $i,Xu: $i] :
% 0.29/0.47 ( ( Xz = Xu )
% 0.29/0.47 => ( ( setadjoin @ Xx @ Xz )
% 0.29/0.47 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powerset__Cong_type,type,
% 0.29/0.47 powerset__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powerset__Cong,definition,
% 0.29/0.47 ( powerset__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( powerset @ A )
% 0.29/0.47 = ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunion__Cong_type,type,
% 0.29/0.47 setunion__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunion__Cong,definition,
% 0.29/0.47 ( setunion__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( ( setunion @ A )
% 0.29/0.47 = ( setunion @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omega__Cong_type,type,
% 0.29/0.47 omega__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omega__Cong,definition,
% 0.29/0.47 ( omega__Cong
% 0.29/0.47 = ( omega = omega ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuEu_type,type,
% 0.29/0.47 exuEu: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuEu,definition,
% 0.29/0.47 ( exuEu
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 => ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(descr__Cong_type,type,
% 0.29/0.47 descr__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(descr__Cong,definition,
% 0.29/0.47 ( descr__Cong
% 0.29/0.47 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 0.29/0.47 => ( ( descr
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = ( descr
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr__Cong_type,type,
% 0.29/0.47 dsetconstr__Cong: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr__Cong,definition,
% 0.29/0.47 ( dsetconstr__Cong
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ B )
% 0.29/0.47 => ( ( Xx = Xy )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 <=> ( Xpsi @ Xy ) ) ) ) )
% 0.29/0.47 => ( ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 = ( dsetconstr @ B
% 0.29/0.47 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subset_type,type,
% 0.29/0.47 subset: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(disjoint_type,type,
% 0.29/0.47 disjoint: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(setsmeet_type,type,
% 0.29/0.47 setsmeet: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI1_type,type,
% 0.29/0.47 subsetI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI1,definition,
% 0.29/0.47 ( subsetI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset2_type,type,
% 0.29/0.47 eqimpsubset2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset2,definition,
% 0.29/0.47 ( eqimpsubset2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset1_type,type,
% 0.29/0.47 eqimpsubset1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(eqimpsubset1,definition,
% 0.29/0.47 ( eqimpsubset1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( A = B )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI2_type,type,
% 0.29/0.47 subsetI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetI2,definition,
% 0.29/0.47 ( subsetI2
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) )
% 0.29/0.47 => ( subset @ A @ B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetsubset_type,type,
% 0.29/0.47 emptysetsubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetsubset,definition,
% 0.29/0.47 ( emptysetsubset
% 0.29/0.47 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE_type,type,
% 0.29/0.47 subsetE: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE,definition,
% 0.29/0.47 ( subsetE
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE2_type,type,
% 0.29/0.47 subsetE2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetE2,definition,
% 0.29/0.47 ( subsetE2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notsubsetI_type,type,
% 0.29/0.47 notsubsetI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notsubsetI,definition,
% 0.29/0.47 ( notsubsetI
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI1_type,type,
% 0.29/0.47 notequalI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI1,definition,
% 0.29/0.47 ( notequalI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ~ ( subset @ A @ B )
% 0.29/0.47 => ( A != B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI2_type,type,
% 0.29/0.47 notequalI2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(notequalI2,definition,
% 0.29/0.47 ( notequalI2
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ~ ( in @ Xx @ B )
% 0.29/0.47 => ( A != B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetRefl_type,type,
% 0.29/0.47 subsetRefl: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetRefl,definition,
% 0.29/0.47 ( subsetRefl
% 0.29/0.47 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetTrans_type,type,
% 0.29/0.47 subsetTrans: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetTrans,definition,
% 0.29/0.47 ( subsetTrans
% 0.29/0.47 = ( ! [A: $i,B: $i,C: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( subset @ B @ C )
% 0.29/0.47 => ( subset @ A @ C ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub_type,type,
% 0.29/0.47 setadjoinSub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub,definition,
% 0.29/0.47 ( setadjoinSub
% 0.29/0.47 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub2_type,type,
% 0.29/0.47 setadjoinSub2: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinSub2,definition,
% 0.29/0.47 ( setadjoinSub2
% 0.29/0.47 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subset2powerset_type,type,
% 0.29/0.47 subset2powerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subset2powerset,definition,
% 0.29/0.47 ( subset2powerset
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setextsub_type,type,
% 0.29/0.47 setextsub: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setextsub,definition,
% 0.29/0.47 ( setextsub
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( ( subset @ B @ A )
% 0.29/0.47 => ( A = B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(subsetemptysetimpeq_type,type,
% 0.29/0.47 subsetemptysetimpeq: $o ).
% 0.29/0.47
% 0.29/0.47 thf(subsetemptysetimpeq,definition,
% 0.29/0.47 ( subsetemptysetimpeq
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( subset @ A @ emptyset )
% 0.29/0.47 => ( A = emptyset ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI1_type,type,
% 0.29/0.47 powersetI1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetI1,definition,
% 0.29/0.47 ( powersetI1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ B @ A )
% 0.29/0.47 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE1_type,type,
% 0.29/0.47 powersetE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetE1,definition,
% 0.29/0.47 ( powersetE1
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.47 => ( subset @ B @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(inPowerset_type,type,
% 0.29/0.47 inPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(inPowerset,definition,
% 0.29/0.47 ( inPowerset
% 0.29/0.47 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powersetsubset_type,type,
% 0.29/0.47 powersetsubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetsubset,definition,
% 0.29/0.47 ( powersetsubset
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( subset @ A @ B )
% 0.29/0.47 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(sepInPowerset_type,type,
% 0.29/0.47 sepInPowerset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(sepInPowerset,definition,
% 0.29/0.47 ( sepInPowerset
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( in
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 @ ( powerset @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(sepSubset_type,type,
% 0.29/0.47 sepSubset: $o ).
% 0.29/0.47
% 0.29/0.47 thf(sepSubset,definition,
% 0.29/0.47 ( sepSubset
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o] :
% 0.29/0.47 ( subset
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 @ A ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunion_type,type,
% 0.29/0.47 binunion: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(binunion,definition,
% 0.29/0.47 ( binunion
% 0.29/0.47 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIL_type,type,
% 0.29/0.47 binunionIL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIL,definition,
% 0.29/0.47 ( binunionIL
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2IR_type,type,
% 0.29/0.47 upairset2IR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(upairset2IR,definition,
% 0.29/0.47 ( upairset2IR
% 0.29/0.47 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIR_type,type,
% 0.29/0.47 binunionIR: $o ).
% 0.29/0.47
% 0.29/0.47 thf(binunionIR,definition,
% 0.29/0.47 ( binunionIR
% 0.29/0.47 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(binunionEcases,conjecture,
% 0.29/0.47 ( setextAx
% 0.29/0.47 => ( emptysetAx
% 0.29/0.47 => ( setadjoinAx
% 0.29/0.47 => ( powersetAx
% 0.29/0.47 => ( setunionAx
% 0.29/0.47 => ( omega0Ax
% 0.29/0.47 => ( omegaSAx
% 0.29/0.47 => ( omegaIndAx
% 0.29/0.47 => ( replAx
% 0.29/0.47 => ( foundationAx
% 0.29/0.47 => ( wellorderingAx
% 0.29/0.47 => ( descrp
% 0.29/0.47 => ( dsetconstrI
% 0.29/0.47 => ( dsetconstrEL
% 0.29/0.47 => ( dsetconstrER
% 0.29/0.47 => ( exuE1
% 0.29/0.47 => ( prop2setE
% 0.29/0.47 => ( emptysetE
% 0.29/0.47 => ( emptysetimpfalse
% 0.29/0.47 => ( notinemptyset
% 0.29/0.47 => ( exuE3e
% 0.29/0.47 => ( setext
% 0.29/0.47 => ( emptyI
% 0.29/0.47 => ( noeltsimpempty
% 0.29/0.47 => ( setbeta
% 0.29/0.47 => ( nonemptyE1
% 0.29/0.47 => ( nonemptyI
% 0.29/0.47 => ( nonemptyI1
% 0.29/0.47 => ( setadjoinIL
% 0.29/0.47 => ( emptyinunitempty
% 0.29/0.47 => ( setadjoinIR
% 0.29/0.47 => ( setadjoinE
% 0.29/0.47 => ( setadjoinOr
% 0.29/0.47 => ( setoftrueEq
% 0.29/0.47 => ( powersetI
% 0.29/0.47 => ( emptyinPowerset
% 0.29/0.47 => ( emptyInPowerset
% 0.29/0.47 => ( powersetE
% 0.29/0.47 => ( setunionI
% 0.29/0.47 => ( setunionE
% 0.29/0.47 => ( subPowSU
% 0.29/0.47 => ( exuE2
% 0.29/0.47 => ( nonemptyImpWitness
% 0.29/0.47 => ( uniqinunit
% 0.29/0.47 => ( notinsingleton
% 0.29/0.47 => ( eqinunit
% 0.29/0.47 => ( singletonsswitch
% 0.29/0.47 => ( upairsetE
% 0.29/0.47 => ( upairsetIL
% 0.29/0.47 => ( upairsetIR
% 0.29/0.47 => ( emptyE1
% 0.29/0.47 => ( vacuousDall
% 0.29/0.47 => ( quantDeMorgan1
% 0.29/0.47 => ( quantDeMorgan2
% 0.29/0.47 => ( quantDeMorgan3
% 0.29/0.47 => ( quantDeMorgan4
% 0.29/0.47 => ( prop2setI
% 0.29/0.47 => ( prop2set2propI
% 0.29/0.47 => ( notdexE
% 0.29/0.47 => ( notdallE
% 0.29/0.47 => ( exuI1
% 0.29/0.47 => ( exuI3
% 0.29/0.47 => ( exuI2
% 0.29/0.47 => ( inCongP
% 0.29/0.47 => ( in__Cong
% 0.29/0.47 => ( exuE3u
% 0.29/0.47 => ( exu__Cong
% 0.29/0.47 => ( emptyset__Cong
% 0.29/0.47 => ( setadjoin__Cong
% 0.29/0.47 => ( powerset__Cong
% 0.29/0.47 => ( setunion__Cong
% 0.29/0.47 => ( omega__Cong
% 0.29/0.47 => ( exuEu
% 0.29/0.47 => ( descr__Cong
% 0.29/0.47 => ( dsetconstr__Cong
% 0.29/0.47 => ( subsetI1
% 0.29/0.47 => ( eqimpsubset2
% 0.29/0.47 => ( eqimpsubset1
% 0.29/0.47 => ( subsetI2
% 0.29/0.47 => ( emptysetsubset
% 0.29/0.47 => ( subsetE
% 0.29/0.47 => ( subsetE2
% 0.29/0.47 => ( notsubsetI
% 0.29/0.47 => ( notequalI1
% 0.29/0.47 => ( notequalI2
% 0.29/0.47 => ( subsetRefl
% 0.29/0.47 => ( subsetTrans
% 0.29/0.47 => ( setadjoinSub
% 0.29/0.47 => ( setadjoinSub2
% 0.29/0.47 => ( subset2powerset
% 0.29/0.47 => ( setextsub
% 0.29/0.47 => ( subsetemptysetimpeq
% 0.29/0.47 => ( powersetI1
% 0.29/0.47 => ( powersetE1
% 0.29/0.47 => ( inPowerset
% 0.29/0.47 => ( powersetsubset
% 0.29/0.47 => ( sepInPowerset
% 0.29/0.47 => ( sepSubset
% 0.29/0.47 => ( binunionIL
% 0.29/0.47 => ( upairset2IR
% 0.29/0.47 => ( binunionIR
% 0.29/0.47 => ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 0.29/0.47 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 0.29/0.47 => ( ( ( in @ Xx @ A )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => ( ( ( in @ Xx @ B )
% 0.29/0.47 => Xphi )
% 0.29/0.47 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 2.39/1.41 ---- Embedded in THF ---
% 2.39/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.39/1.41 %%% Generated on Tue Feb 24 12:28:04 EST 2026
% 2.39/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 2.39/1.41 %%% Logic specification used:
% 2.39/1.41 %%% thf(spec, logic, $$dhol).
% 2.39/1.41
% 2.39/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2DTF27107.p
% See solution above
% 2.39/1.41 ------------------------
% 2.39/1.43 ---- Cleaned THF ---
% 2.39/1.44 thf(in_type,type,
% 2.39/1.44 in: $i > $i > $o ).
% 2.39/1.44
% 2.39/1.44 thf(exu_type,type,
% 2.39/1.44 exu: ( $i > $o ) > $o ).
% 2.39/1.44
% 2.39/1.44 thf(exu,definition,
% 2.39/1.44 ( exu
% 2.39/1.44 = ( ^ [Xphi: $i > $o] :
% 2.39/1.44 ? [Xx: $i] :
% 2.39/1.44 ( ( Xphi @ Xx )
% 2.39/1.44 & ! [Xy: $i] :
% 2.39/1.44 ( ( Xphi @ Xy )
% 2.39/1.44 => ( Xx = Xy ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setextAx_type,type,
% 2.39/1.44 setextAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setextAx,definition,
% 2.39/1.44 ( setextAx
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 <=> ( in @ Xx @ B ) )
% 2.39/1.44 => ( A = B ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptyset_type,type,
% 2.39/1.44 emptyset: $i ).
% 2.39/1.44
% 2.39/1.44 thf(emptysetAx_type,type,
% 2.39/1.44 emptysetAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptysetAx,definition,
% 2.39/1.44 ( emptysetAx
% 2.39/1.44 = ( ! [Xx: $i] :
% 2.39/1.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoin_type,type,
% 2.39/1.44 setadjoin: $i > $i > $i ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinAx_type,type,
% 2.39/1.44 setadjoinAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinAx,definition,
% 2.39/1.44 ( setadjoinAx
% 2.39/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.39/1.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.39/1.44 <=> ( ( Xy = Xx )
% 2.39/1.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(powerset_type,type,
% 2.39/1.44 powerset: $i > $i ).
% 2.39/1.44
% 2.39/1.44 thf(powersetAx_type,type,
% 2.39/1.44 powersetAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(powersetAx,definition,
% 2.39/1.44 ( powersetAx
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( in @ B @ ( powerset @ A ) )
% 2.39/1.44 <=> ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setunion_type,type,
% 2.39/1.44 setunion: $i > $i ).
% 2.39/1.44
% 2.39/1.44 thf(setunionAx_type,type,
% 2.39/1.44 setunionAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setunionAx,definition,
% 2.39/1.44 ( setunionAx
% 2.39/1.44 = ( ! [A: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ ( setunion @ A ) )
% 2.39/1.44 <=> ? [B: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 & ( in @ B @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(omega_type,type,
% 2.39/1.44 omega: $i ).
% 2.39/1.44
% 2.39/1.44 thf(omega0Ax_type,type,
% 2.39/1.44 omega0Ax: $o ).
% 2.39/1.44
% 2.39/1.44 thf(omega0Ax,definition,
% 2.39/1.44 ( omega0Ax
% 2.39/1.44 = ( in @ emptyset @ omega ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(omegaSAx_type,type,
% 2.39/1.44 omegaSAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(omegaSAx,definition,
% 2.39/1.44 ( omegaSAx
% 2.39/1.44 = ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ omega )
% 2.39/1.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(omegaIndAx_type,type,
% 2.39/1.44 omegaIndAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(omegaIndAx,definition,
% 2.39/1.44 ( omegaIndAx
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ( ( in @ emptyset @ A )
% 2.39/1.44 & ! [Xx: $i] :
% 2.39/1.44 ( ( ( in @ Xx @ omega )
% 2.39/1.44 & ( in @ Xx @ A ) )
% 2.39/1.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.39/1.44 => ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ omega )
% 2.39/1.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(replAx_type,type,
% 2.39/1.44 replAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(replAx,definition,
% 2.39/1.44 ( replAx
% 2.39/1.44 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( exu
% 2.39/1.44 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.39/1.44 => ? [B: $i] :
% 2.39/1.44 ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 <=> ? [Xy: $i] :
% 2.39/1.44 ( ( in @ Xy @ A )
% 2.39/1.44 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(foundationAx_type,type,
% 2.39/1.44 foundationAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(foundationAx,definition,
% 2.39/1.44 ( foundationAx
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.39/1.44 => ? [B: $i] :
% 2.39/1.44 ( ( in @ B @ A )
% 2.39/1.44 & ~ ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(wellorderingAx_type,type,
% 2.39/1.44 wellorderingAx: $o ).
% 2.39/1.44
% 2.39/1.44 thf(wellorderingAx,definition,
% 2.39/1.44 ( wellorderingAx
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ? [B: $i] :
% 2.39/1.44 ( ! [C: $i] :
% 2.39/1.44 ( ( in @ C @ B )
% 2.39/1.44 => ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ C )
% 2.39/1.44 => ( in @ Xx @ A ) ) )
% 2.39/1.44 & ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( ( in @ Xx @ A )
% 2.39/1.44 & ( in @ Xy @ A ) )
% 2.39/1.44 => ( ! [C: $i] :
% 2.39/1.44 ( ( in @ C @ B )
% 2.39/1.44 => ( ( in @ Xx @ C )
% 2.39/1.44 <=> ( in @ Xy @ C ) ) )
% 2.39/1.44 => ( Xx = Xy ) ) )
% 2.39/1.44 & ! [C: $i,D: $i] :
% 2.39/1.44 ( ( ( in @ C @ B )
% 2.39/1.44 & ( in @ D @ B ) )
% 2.39/1.44 => ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ C )
% 2.39/1.44 => ( in @ Xx @ D ) )
% 2.39/1.44 | ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ D )
% 2.39/1.44 => ( in @ Xx @ C ) ) ) )
% 2.39/1.44 & ! [C: $i] :
% 2.39/1.44 ( ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ C )
% 2.39/1.44 => ( in @ Xx @ A ) )
% 2.39/1.44 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.39/1.44 => ? [D: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ D @ B )
% 2.39/1.44 & ( in @ Xx @ C )
% 2.39/1.44 & ~ ? [Xy: $i] :
% 2.39/1.44 ( ( in @ Xy @ D )
% 2.39/1.44 & ( in @ Xy @ C ) )
% 2.39/1.44 & ! [E: $i] :
% 2.39/1.44 ( ( in @ E @ B )
% 2.39/1.44 => ( ! [Xy: $i] :
% 2.39/1.44 ( ( in @ Xy @ E )
% 2.39/1.44 => ( in @ Xy @ D ) )
% 2.39/1.44 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(descr_type,type,
% 2.39/1.44 descr: ( $i > $o ) > $i ).
% 2.39/1.44
% 2.39/1.44 thf(descrp_type,type,
% 2.39/1.44 descrp: $o ).
% 2.39/1.44
% 2.39/1.44 thf(descrp,definition,
% 2.39/1.44 ( descrp
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 => ( Xphi
% 2.39/1.44 @ ( descr
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstr_type,type,
% 2.39/1.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstrI_type,type,
% 2.39/1.44 dsetconstrI: $o ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstrI,definition,
% 2.39/1.44 ( dsetconstrI
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( ( Xphi @ Xx )
% 2.39/1.44 => ( in @ Xx
% 2.39/1.44 @ ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstrEL_type,type,
% 2.39/1.44 dsetconstrEL: $o ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstrEL,definition,
% 2.39/1.44 ( dsetconstrEL
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx
% 2.39/1.44 @ ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.39/1.44 => ( in @ Xx @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstrER_type,type,
% 2.39/1.44 dsetconstrER: $o ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstrER,definition,
% 2.39/1.44 ( dsetconstrER
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx
% 2.39/1.44 @ ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.39/1.44 => ( Xphi @ Xx ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exuE1_type,type,
% 2.39/1.44 exuE1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exuE1,definition,
% 2.39/1.44 ( exuE1
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 => ? [Xx: $i] :
% 2.39/1.44 ( ( Xphi @ Xx )
% 2.39/1.44 & ! [Xy: $i] :
% 2.39/1.44 ( ( Xphi @ Xy )
% 2.39/1.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(prop2set_type,type,
% 2.39/1.44 prop2set: $o > $i ).
% 2.39/1.44
% 2.39/1.44 thf(prop2setE_type,type,
% 2.39/1.44 prop2setE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(prop2setE,definition,
% 2.39/1.44 ( prop2setE
% 2.39/1.44 = ( ! [Xphi: $o,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.39/1.44 => Xphi ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptysetE_type,type,
% 2.39/1.44 emptysetE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptysetE,definition,
% 2.39/1.44 ( emptysetE
% 2.39/1.44 = ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ emptyset )
% 2.39/1.44 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptysetimpfalse_type,type,
% 2.39/1.44 emptysetimpfalse: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptysetimpfalse,definition,
% 2.39/1.44 ( emptysetimpfalse
% 2.39/1.44 = ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ emptyset )
% 2.39/1.44 => $false ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(notinemptyset_type,type,
% 2.39/1.44 notinemptyset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(notinemptyset,definition,
% 2.39/1.44 ( notinemptyset
% 2.39/1.44 = ( ! [Xx: $i] :
% 2.39/1.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exuE3e_type,type,
% 2.39/1.44 exuE3e: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exuE3e,definition,
% 2.39/1.44 ( exuE3e
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setext_type,type,
% 2.39/1.44 setext: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setext,definition,
% 2.39/1.44 ( setext
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( in @ Xx @ B ) )
% 2.39/1.44 => ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 => ( in @ Xx @ A ) )
% 2.39/1.44 => ( A = B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptyI_type,type,
% 2.39/1.44 emptyI: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptyI,definition,
% 2.39/1.44 ( emptyI
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ~ ( in @ Xx @ A )
% 2.39/1.44 => ( A = emptyset ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(noeltsimpempty_type,type,
% 2.39/1.44 noeltsimpempty: $o ).
% 2.39/1.44
% 2.39/1.44 thf(noeltsimpempty,definition,
% 2.39/1.44 ( noeltsimpempty
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ~ ( in @ Xx @ A )
% 2.39/1.44 => ( A = emptyset ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setbeta_type,type,
% 2.39/1.44 setbeta: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setbeta,definition,
% 2.39/1.44 ( setbeta
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( ( in @ Xx
% 2.39/1.44 @ ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.39/1.44 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(nonempty_type,type,
% 2.39/1.44 nonempty: $i > $o ).
% 2.39/1.44
% 2.39/1.44 thf(nonempty,definition,
% 2.39/1.44 ( nonempty
% 2.39/1.44 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(nonemptyE1_type,type,
% 2.39/1.44 nonemptyE1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(nonemptyE1,definition,
% 2.39/1.44 ( nonemptyE1
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ( nonempty @ A )
% 2.39/1.44 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(nonemptyI_type,type,
% 2.39/1.44 nonemptyI: $o ).
% 2.39/1.44
% 2.39/1.44 thf(nonemptyI,definition,
% 2.39/1.44 ( nonemptyI
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( ( Xphi @ Xx )
% 2.39/1.44 => ( nonempty
% 2.39/1.44 @ ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(nonemptyI1_type,type,
% 2.39/1.44 nonemptyI1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(nonemptyI1,definition,
% 2.39/1.44 ( nonemptyI1
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.39/1.44 => ( nonempty @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinIL_type,type,
% 2.39/1.44 setadjoinIL: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinIL,definition,
% 2.39/1.44 ( setadjoinIL
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptyinunitempty_type,type,
% 2.39/1.44 emptyinunitempty: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptyinunitempty,definition,
% 2.39/1.44 ( emptyinunitempty
% 2.39/1.44 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinIR_type,type,
% 2.39/1.44 setadjoinIR: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinIR,definition,
% 2.39/1.44 ( setadjoinIR
% 2.39/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.39/1.44 ( ( in @ Xy @ A )
% 2.39/1.44 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinE_type,type,
% 2.39/1.44 setadjoinE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinE,definition,
% 2.39/1.44 ( setadjoinE
% 2.39/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.39/1.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.39/1.44 => ! [Xphi: $o] :
% 2.39/1.44 ( ( ( Xy = Xx )
% 2.39/1.44 => Xphi )
% 2.39/1.44 => ( ( ( in @ Xy @ A )
% 2.39/1.44 => Xphi )
% 2.39/1.44 => Xphi ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinOr_type,type,
% 2.39/1.44 setadjoinOr: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinOr,definition,
% 2.39/1.44 ( setadjoinOr
% 2.39/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.39/1.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.39/1.44 => ( ( Xy = Xx )
% 2.39/1.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setoftrueEq_type,type,
% 2.39/1.44 setoftrueEq: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setoftrueEq,definition,
% 2.39/1.44 ( setoftrueEq
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xx: $i] : $true )
% 2.39/1.44 = A ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(powersetI_type,type,
% 2.39/1.44 powersetI: $o ).
% 2.39/1.44
% 2.39/1.44 thf(powersetI,definition,
% 2.39/1.44 ( powersetI
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 => ( in @ Xx @ A ) )
% 2.39/1.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptyinPowerset_type,type,
% 2.39/1.44 emptyinPowerset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptyinPowerset,definition,
% 2.39/1.44 ( emptyinPowerset
% 2.39/1.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptyInPowerset_type,type,
% 2.39/1.44 emptyInPowerset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptyInPowerset,definition,
% 2.39/1.44 ( emptyInPowerset
% 2.39/1.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(powersetE_type,type,
% 2.39/1.44 powersetE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(powersetE,definition,
% 2.39/1.44 ( powersetE
% 2.39/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ B @ ( powerset @ A ) )
% 2.39/1.44 => ( ( in @ Xx @ B )
% 2.39/1.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setunionI_type,type,
% 2.39/1.44 setunionI: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setunionI,definition,
% 2.39/1.44 ( setunionI
% 2.39/1.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 => ( ( in @ B @ A )
% 2.39/1.44 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setunionE_type,type,
% 2.39/1.44 setunionE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setunionE,definition,
% 2.39/1.44 ( setunionE
% 2.39/1.44 = ( ! [A: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ ( setunion @ A ) )
% 2.39/1.44 => ! [Xphi: $o] :
% 2.39/1.44 ( ! [B: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 => ( ( in @ B @ A )
% 2.39/1.44 => Xphi ) )
% 2.39/1.44 => Xphi ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subPowSU_type,type,
% 2.39/1.44 subPowSU: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subPowSU,definition,
% 2.39/1.44 ( subPowSU
% 2.39/1.44 = ( ! [A: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exuE2_type,type,
% 2.39/1.44 exuE2: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exuE2,definition,
% 2.39/1.44 ( exuE2
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 => ? [Xx: $i] :
% 2.39/1.44 ! [Xy: $i] :
% 2.39/1.44 ( ( Xphi @ Xy )
% 2.39/1.44 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(nonemptyImpWitness_type,type,
% 2.39/1.44 nonemptyImpWitness: $o ).
% 2.39/1.44
% 2.39/1.44 thf(nonemptyImpWitness,definition,
% 2.39/1.44 ( nonemptyImpWitness
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ( nonempty @ A )
% 2.39/1.44 => ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 & $true ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(uniqinunit_type,type,
% 2.39/1.44 uniqinunit: $o ).
% 2.39/1.44
% 2.39/1.44 thf(uniqinunit,definition,
% 2.39/1.44 ( uniqinunit
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.39/1.44 => ( Xx = Xy ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(notinsingleton_type,type,
% 2.39/1.44 notinsingleton: $o ).
% 2.39/1.44
% 2.39/1.44 thf(notinsingleton,definition,
% 2.39/1.44 ( notinsingleton
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xx != Xy )
% 2.39/1.44 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(eqinunit_type,type,
% 2.39/1.44 eqinunit: $o ).
% 2.39/1.44
% 2.39/1.44 thf(eqinunit,definition,
% 2.39/1.44 ( eqinunit
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xx = Xy )
% 2.39/1.44 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(singletonsswitch_type,type,
% 2.39/1.44 singletonsswitch: $o ).
% 2.39/1.44
% 2.39/1.44 thf(singletonsswitch,definition,
% 2.39/1.44 ( singletonsswitch
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.39/1.44 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(upairsetE_type,type,
% 2.39/1.44 upairsetE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(upairsetE,definition,
% 2.39/1.44 ( upairsetE
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.39/1.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.39/1.44 => ( ( Xz = Xx )
% 2.39/1.44 | ( Xz = Xy ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(upairsetIL_type,type,
% 2.39/1.44 upairsetIL: $o ).
% 2.39/1.44
% 2.39/1.44 thf(upairsetIL,definition,
% 2.39/1.44 ( upairsetIL
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(upairsetIR_type,type,
% 2.39/1.44 upairsetIR: $o ).
% 2.39/1.44
% 2.39/1.44 thf(upairsetIR,definition,
% 2.39/1.44 ( upairsetIR
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptyE1_type,type,
% 2.39/1.44 emptyE1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptyE1,definition,
% 2.39/1.44 ( emptyE1
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 & ( Xphi @ Xx ) )
% 2.39/1.44 => ( ( ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 = emptyset )
% 2.39/1.44 => $false ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(vacuousDall_type,type,
% 2.39/1.44 vacuousDall: $o ).
% 2.39/1.44
% 2.39/1.44 thf(vacuousDall,definition,
% 2.39/1.44 ( vacuousDall
% 2.39/1.44 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ emptyset )
% 2.39/1.44 => ( Xphi @ Xx ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(quantDeMorgan1_type,type,
% 2.39/1.44 quantDeMorgan1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(quantDeMorgan1,definition,
% 2.39/1.44 ( quantDeMorgan1
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( ~ ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( Xphi @ Xx ) )
% 2.39/1.44 => ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(quantDeMorgan2_type,type,
% 2.39/1.44 quantDeMorgan2: $o ).
% 2.39/1.44
% 2.39/1.44 thf(quantDeMorgan2,definition,
% 2.39/1.44 ( quantDeMorgan2
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ~ ( Xphi @ Xx ) )
% 2.39/1.44 => ~ ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(quantDeMorgan3_type,type,
% 2.39/1.44 quantDeMorgan3: $o ).
% 2.39/1.44
% 2.39/1.44 thf(quantDeMorgan3,definition,
% 2.39/1.44 ( quantDeMorgan3
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( ~ ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 & ( Xphi @ Xx ) )
% 2.39/1.44 => ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(quantDeMorgan4_type,type,
% 2.39/1.44 quantDeMorgan4: $o ).
% 2.39/1.44
% 2.39/1.44 thf(quantDeMorgan4,definition,
% 2.39/1.44 ( quantDeMorgan4
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 & ~ ( Xphi @ Xx ) )
% 2.39/1.44 => ~ ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(prop2setI_type,type,
% 2.39/1.44 prop2setI: $o ).
% 2.39/1.44
% 2.39/1.44 thf(prop2setI,definition,
% 2.39/1.44 ( prop2setI
% 2.39/1.44 = ( ! [Xphi: $o] :
% 2.39/1.44 ( Xphi
% 2.39/1.44 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(set2prop_type,type,
% 2.39/1.44 set2prop: $i > $o ).
% 2.39/1.44
% 2.39/1.44 thf(prop2set2propI_type,type,
% 2.39/1.44 prop2set2propI: $o ).
% 2.39/1.44
% 2.39/1.44 thf(prop2set2propI,definition,
% 2.39/1.44 ( prop2set2propI
% 2.39/1.44 = ( ! [Xphi: $o] :
% 2.39/1.44 ( Xphi
% 2.39/1.44 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(notdexE_type,type,
% 2.39/1.44 notdexE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(notdexE,definition,
% 2.39/1.44 ( notdexE
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( ~ ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 & ( Xphi @ Xx ) )
% 2.39/1.44 => ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(notdallE_type,type,
% 2.39/1.44 notdallE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(notdallE,definition,
% 2.39/1.44 ( notdallE
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( ~ ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( Xphi @ Xx ) )
% 2.39/1.44 => ? [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exuI1_type,type,
% 2.39/1.44 exuI1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exuI1,definition,
% 2.39/1.44 ( exuI1
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ? [Xx: $i] :
% 2.39/1.44 ( ( Xphi @ Xx )
% 2.39/1.44 & ! [Xy: $i] :
% 2.39/1.44 ( ( Xphi @ Xy )
% 2.39/1.44 => ( Xx = Xy ) ) )
% 2.39/1.44 => ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exuI3_type,type,
% 2.39/1.44 exuI3: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exuI3,definition,
% 2.39/1.44 ( exuI3
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ? [Xx: $i] : ( Xphi @ Xx )
% 2.39/1.44 => ( ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xphi @ Xx )
% 2.39/1.44 => ( ( Xphi @ Xy )
% 2.39/1.44 => ( Xx = Xy ) ) )
% 2.39/1.44 => ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exuI2_type,type,
% 2.39/1.44 exuI2: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exuI2,definition,
% 2.39/1.44 ( exuI2
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ? [Xx: $i] :
% 2.39/1.44 ! [Xy: $i] :
% 2.39/1.44 ( ( Xphi @ Xy )
% 2.39/1.44 <=> ( Xy = Xx ) )
% 2.39/1.44 => ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(inCongP_type,type,
% 2.39/1.44 inCongP: $o ).
% 2.39/1.44
% 2.39/1.44 thf(inCongP,definition,
% 2.39/1.44 ( inCongP
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( A = B )
% 2.39/1.44 => ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xx = Xy )
% 2.39/1.44 => ( ( in @ Xx @ A )
% 2.39/1.44 => ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(in__Cong_type,type,
% 2.39/1.44 in__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(in__Cong,definition,
% 2.39/1.44 ( in__Cong
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( A = B )
% 2.39/1.44 => ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xx = Xy )
% 2.39/1.44 => ( ( in @ Xx @ A )
% 2.39/1.44 <=> ( in @ Xy @ B ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exuE3u_type,type,
% 2.39/1.44 exuE3u: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exuE3u,definition,
% 2.39/1.44 ( exuE3u
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 => ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xphi @ Xx )
% 2.39/1.44 => ( ( Xphi @ Xy )
% 2.39/1.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exu__Cong_type,type,
% 2.39/1.44 exu__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exu__Cong,definition,
% 2.39/1.44 ( exu__Cong
% 2.39/1.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.39/1.44 ( ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xx = Xy )
% 2.39/1.44 => ( ( Xphi @ Xx )
% 2.39/1.44 <=> ( Xpsi @ Xy ) ) )
% 2.39/1.44 => ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 <=> ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptyset__Cong_type,type,
% 2.39/1.44 emptyset__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptyset__Cong,definition,
% 2.39/1.44 ( emptyset__Cong
% 2.39/1.44 = ( emptyset = emptyset ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoin__Cong_type,type,
% 2.39/1.44 setadjoin__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoin__Cong,definition,
% 2.39/1.44 ( setadjoin__Cong
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xx = Xy )
% 2.39/1.44 => ! [Xz: $i,Xu: $i] :
% 2.39/1.44 ( ( Xz = Xu )
% 2.39/1.44 => ( ( setadjoin @ Xx @ Xz )
% 2.39/1.44 = ( setadjoin @ Xy @ Xu ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(powerset__Cong_type,type,
% 2.39/1.44 powerset__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(powerset__Cong,definition,
% 2.39/1.44 ( powerset__Cong
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( A = B )
% 2.39/1.44 => ( ( powerset @ A )
% 2.39/1.44 = ( powerset @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setunion__Cong_type,type,
% 2.39/1.44 setunion__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setunion__Cong,definition,
% 2.39/1.44 ( setunion__Cong
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( A = B )
% 2.39/1.44 => ( ( setunion @ A )
% 2.39/1.44 = ( setunion @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(omega__Cong_type,type,
% 2.39/1.44 omega__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(omega__Cong,definition,
% 2.39/1.44 ( omega__Cong
% 2.39/1.44 = ( omega = omega ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(exuEu_type,type,
% 2.39/1.44 exuEu: $o ).
% 2.39/1.44
% 2.39/1.44 thf(exuEu,definition,
% 2.39/1.44 ( exuEu
% 2.39/1.44 = ( ! [Xphi: $i > $o] :
% 2.39/1.44 ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 => ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xphi @ Xx )
% 2.39/1.44 => ( ( Xphi @ Xy )
% 2.39/1.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(descr__Cong_type,type,
% 2.39/1.44 descr__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(descr__Cong,definition,
% 2.39/1.44 ( descr__Cong
% 2.39/1.44 = ( ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.39/1.44 ( ! [Xx: $i,Xy: $i] :
% 2.39/1.44 ( ( Xx = Xy )
% 2.39/1.44 => ( ( Xphi @ Xx )
% 2.39/1.44 <=> ( Xpsi @ Xy ) ) )
% 2.39/1.44 => ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 => ( ( exu
% 2.39/1.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) )
% 2.39/1.44 => ( ( descr
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 = ( descr
% 2.39/1.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstr__Cong_type,type,
% 2.39/1.44 dsetconstr__Cong: $o ).
% 2.39/1.44
% 2.39/1.44 thf(dsetconstr__Cong,definition,
% 2.39/1.44 ( dsetconstr__Cong
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( A = B )
% 2.39/1.44 => ! [Xphi: $i > $o,Xpsi: $i > $o] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ! [Xy: $i] :
% 2.39/1.44 ( ( in @ Xy @ B )
% 2.39/1.44 => ( ( Xx = Xy )
% 2.39/1.44 => ( ( Xphi @ Xx )
% 2.39/1.44 <=> ( Xpsi @ Xy ) ) ) ) )
% 2.39/1.44 => ( ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 = ( dsetconstr @ B
% 2.39/1.44 @ ^ [Xx: $i] : ( Xpsi @ Xx ) ) ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subset_type,type,
% 2.39/1.44 subset: $i > $i > $o ).
% 2.39/1.44
% 2.39/1.44 thf(disjoint_type,type,
% 2.39/1.44 disjoint: $i > $i > $o ).
% 2.39/1.44
% 2.39/1.44 thf(setsmeet_type,type,
% 2.39/1.44 setsmeet: $i > $i > $o ).
% 2.39/1.44
% 2.39/1.44 thf(subsetI1_type,type,
% 2.39/1.44 subsetI1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subsetI1,definition,
% 2.39/1.44 ( subsetI1
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( in @ Xx @ B ) )
% 2.39/1.44 => ( subset @ A @ B ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(eqimpsubset2_type,type,
% 2.39/1.44 eqimpsubset2: $o ).
% 2.39/1.44
% 2.39/1.44 thf(eqimpsubset2,definition,
% 2.39/1.44 ( eqimpsubset2
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( A = B )
% 2.39/1.44 => ( subset @ B @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(eqimpsubset1_type,type,
% 2.39/1.44 eqimpsubset1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(eqimpsubset1,definition,
% 2.39/1.44 ( eqimpsubset1
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( A = B )
% 2.39/1.44 => ( subset @ A @ B ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subsetI2_type,type,
% 2.39/1.44 subsetI2: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subsetI2,definition,
% 2.39/1.44 ( subsetI2
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ! [Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( in @ Xx @ B ) )
% 2.39/1.44 => ( subset @ A @ B ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(emptysetsubset_type,type,
% 2.39/1.44 emptysetsubset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(emptysetsubset,definition,
% 2.39/1.44 ( emptysetsubset
% 2.39/1.44 = ( ! [A: $i] : ( subset @ emptyset @ A ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subsetE_type,type,
% 2.39/1.44 subsetE: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subsetE,definition,
% 2.39/1.44 ( subsetE
% 2.39/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.39/1.44 ( ( subset @ A @ B )
% 2.39/1.44 => ( ( in @ Xx @ A )
% 2.39/1.44 => ( in @ Xx @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subsetE2_type,type,
% 2.39/1.44 subsetE2: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subsetE2,definition,
% 2.39/1.44 ( subsetE2
% 2.39/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.39/1.44 ( ( subset @ A @ B )
% 2.39/1.44 => ( ~ ( in @ Xx @ B )
% 2.39/1.44 => ~ ( in @ Xx @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(notsubsetI_type,type,
% 2.39/1.44 notsubsetI: $o ).
% 2.39/1.44
% 2.39/1.44 thf(notsubsetI,definition,
% 2.39/1.44 ( notsubsetI
% 2.39/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( ~ ( in @ Xx @ B )
% 2.39/1.44 => ~ ( subset @ A @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(notequalI1_type,type,
% 2.39/1.44 notequalI1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(notequalI1,definition,
% 2.39/1.44 ( notequalI1
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ~ ( subset @ A @ B )
% 2.39/1.44 => ( A != B ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(notequalI2_type,type,
% 2.39/1.44 notequalI2: $o ).
% 2.39/1.44
% 2.39/1.44 thf(notequalI2,definition,
% 2.39/1.44 ( notequalI2
% 2.39/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( ~ ( in @ Xx @ B )
% 2.39/1.44 => ( A != B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subsetRefl_type,type,
% 2.39/1.44 subsetRefl: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subsetRefl,definition,
% 2.39/1.44 ( subsetRefl
% 2.39/1.44 = ( ! [A: $i] : ( subset @ A @ A ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subsetTrans_type,type,
% 2.39/1.44 subsetTrans: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subsetTrans,definition,
% 2.39/1.44 ( subsetTrans
% 2.39/1.44 = ( ! [A: $i,B: $i,C: $i] :
% 2.39/1.44 ( ( subset @ A @ B )
% 2.39/1.44 => ( ( subset @ B @ C )
% 2.39/1.44 => ( subset @ A @ C ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinSub_type,type,
% 2.39/1.44 setadjoinSub: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinSub,definition,
% 2.39/1.44 ( setadjoinSub
% 2.39/1.44 = ( ! [Xx: $i,A: $i] : ( subset @ A @ ( setadjoin @ Xx @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinSub2_type,type,
% 2.39/1.44 setadjoinSub2: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setadjoinSub2,definition,
% 2.39/1.44 ( setadjoinSub2
% 2.39/1.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.39/1.44 ( ( subset @ A @ B )
% 2.39/1.44 => ( subset @ A @ ( setadjoin @ Xx @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subset2powerset_type,type,
% 2.39/1.44 subset2powerset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subset2powerset,definition,
% 2.39/1.44 ( subset2powerset
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( subset @ A @ B )
% 2.39/1.44 => ( in @ A @ ( powerset @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(setextsub_type,type,
% 2.39/1.44 setextsub: $o ).
% 2.39/1.44
% 2.39/1.44 thf(setextsub,definition,
% 2.39/1.44 ( setextsub
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( subset @ A @ B )
% 2.39/1.44 => ( ( subset @ B @ A )
% 2.39/1.44 => ( A = B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(subsetemptysetimpeq_type,type,
% 2.39/1.44 subsetemptysetimpeq: $o ).
% 2.39/1.44
% 2.39/1.44 thf(subsetemptysetimpeq,definition,
% 2.39/1.44 ( subsetemptysetimpeq
% 2.39/1.44 = ( ! [A: $i] :
% 2.39/1.44 ( ( subset @ A @ emptyset )
% 2.39/1.44 => ( A = emptyset ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(powersetI1_type,type,
% 2.39/1.44 powersetI1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(powersetI1,definition,
% 2.39/1.44 ( powersetI1
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( subset @ B @ A )
% 2.39/1.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(powersetE1_type,type,
% 2.39/1.44 powersetE1: $o ).
% 2.39/1.44
% 2.39/1.44 thf(powersetE1,definition,
% 2.39/1.44 ( powersetE1
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( in @ B @ ( powerset @ A ) )
% 2.39/1.44 => ( subset @ B @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(inPowerset_type,type,
% 2.39/1.44 inPowerset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(inPowerset,definition,
% 2.39/1.44 ( inPowerset
% 2.39/1.44 = ( ! [A: $i] : ( in @ A @ ( powerset @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(powersetsubset_type,type,
% 2.39/1.44 powersetsubset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(powersetsubset,definition,
% 2.39/1.44 ( powersetsubset
% 2.39/1.44 = ( ! [A: $i,B: $i] :
% 2.39/1.44 ( ( subset @ A @ B )
% 2.39/1.44 => ( subset @ ( powerset @ A ) @ ( powerset @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(sepInPowerset_type,type,
% 2.39/1.44 sepInPowerset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(sepInPowerset,definition,
% 2.39/1.44 ( sepInPowerset
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( in
% 2.39/1.44 @ ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 @ ( powerset @ A ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(sepSubset_type,type,
% 2.39/1.44 sepSubset: $o ).
% 2.39/1.44
% 2.39/1.44 thf(sepSubset,definition,
% 2.39/1.44 ( sepSubset
% 2.39/1.44 = ( ! [A: $i,Xphi: $i > $o] :
% 2.39/1.44 ( subset
% 2.39/1.44 @ ( dsetconstr @ A
% 2.39/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.39/1.44 @ A ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(binunion_type,type,
% 2.39/1.44 binunion: $i > $i > $i ).
% 2.39/1.44
% 2.39/1.44 thf(binunion,definition,
% 2.39/1.44 ( binunion
% 2.39/1.44 = ( ^ [Xx: $i,Xy: $i] : ( setunion @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(binunionIL_type,type,
% 2.39/1.44 binunionIL: $o ).
% 2.39/1.44
% 2.39/1.44 thf(binunionIL,definition,
% 2.39/1.44 ( binunionIL
% 2.39/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ A )
% 2.39/1.44 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(upairset2IR_type,type,
% 2.39/1.44 upairset2IR: $o ).
% 2.39/1.44
% 2.39/1.44 thf(upairset2IR,definition,
% 2.39/1.44 ( upairset2IR
% 2.39/1.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(binunionIR_type,type,
% 2.39/1.44 binunionIR: $o ).
% 2.39/1.44
% 2.39/1.44 thf(binunionIR,definition,
% 2.39/1.44 ( binunionIR
% 2.39/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.39/1.44 ( ( in @ Xx @ B )
% 2.39/1.44 => ( in @ Xx @ ( binunion @ A @ B ) ) ) ) ) ).
% 2.39/1.44
% 2.39/1.44 thf(binunionEcases,conjecture,
% 2.39/1.44 ( setextAx
% 2.39/1.44 => ( emptysetAx
% 2.39/1.44 => ( setadjoinAx
% 2.39/1.44 => ( powersetAx
% 2.39/1.44 => ( setunionAx
% 2.39/1.44 => ( omega0Ax
% 2.39/1.44 => ( omegaSAx
% 2.39/1.44 => ( omegaIndAx
% 2.39/1.44 => ( replAx
% 2.39/1.44 => ( foundationAx
% 2.39/1.44 => ( wellorderingAx
% 2.39/1.44 => ( descrp
% 2.39/1.44 => ( dsetconstrI
% 2.39/1.44 => ( dsetconstrEL
% 2.39/1.44 => ( dsetconstrER
% 2.39/1.44 => ( exuE1
% 2.39/1.44 => ( prop2setE
% 2.39/1.44 => ( emptysetE
% 2.39/1.44 => ( emptysetimpfalse
% 2.39/1.44 => ( notinemptyset
% 2.39/1.44 => ( exuE3e
% 2.39/1.44 => ( setext
% 2.39/1.44 => ( emptyI
% 2.39/1.44 => ( noeltsimpempty
% 2.39/1.44 => ( setbeta
% 2.39/1.44 => ( nonemptyE1
% 2.39/1.44 => ( nonemptyI
% 2.39/1.44 => ( nonemptyI1
% 2.39/1.44 => ( setadjoinIL
% 2.39/1.44 => ( emptyinunitempty
% 2.39/1.44 => ( setadjoinIR
% 2.39/1.44 => ( setadjoinE
% 2.39/1.44 => ( setadjoinOr
% 2.39/1.44 => ( setoftrueEq
% 2.39/1.44 => ( powersetI
% 2.39/1.44 => ( emptyinPowerset
% 2.39/1.44 => ( emptyInPowerset
% 2.39/1.44 => ( powersetE
% 2.39/1.44 => ( setunionI
% 2.39/1.44 => ( setunionE
% 2.39/1.44 => ( subPowSU
% 2.39/1.44 => ( exuE2
% 2.39/1.44 => ( nonemptyImpWitness
% 2.39/1.44 => ( uniqinunit
% 2.39/1.44 => ( notinsingleton
% 2.39/1.44 => ( eqinunit
% 2.39/1.44 => ( singletonsswitch
% 2.39/1.44 => ( upairsetE
% 2.39/1.44 => ( upairsetIL
% 2.39/1.44 => ( upairsetIR
% 2.39/1.44 => ( emptyE1
% 2.39/1.44 => ( vacuousDall
% 2.39/1.44 => ( quantDeMorgan1
% 2.39/1.44 => ( quantDeMorgan2
% 2.39/1.44 => ( quantDeMorgan3
% 2.39/1.44 => ( quantDeMorgan4
% 2.39/1.44 => ( prop2setI
% 2.39/1.44 => ( prop2set2propI
% 2.39/1.44 => ( notdexE
% 2.39/1.44 => ( notdallE
% 2.39/1.44 => ( exuI1
% 2.39/1.44 => ( exuI3
% 2.39/1.44 => ( exuI2
% 2.39/1.44 => ( inCongP
% 2.39/1.44 => ( in__Cong
% 2.39/1.44 => ( exuE3u
% 2.39/1.44 => ( exu__Cong
% 2.39/1.44 => ( emptyset__Cong
% 2.39/1.44 => ( setadjoin__Cong
% 2.39/1.44 => ( powerset__Cong
% 2.39/1.44 => ( setunion__Cong
% 2.39/1.44 => ( omega__Cong
% 2.39/1.44 => ( exuEu
% 2.39/1.44 => ( descr__Cong
% 2.39/1.44 => ( dsetconstr__Cong
% 2.39/1.44 => ( subsetI1
% 2.39/1.44 => ( eqimpsubset2
% 2.39/1.44 => ( eqimpsubset1
% 2.39/1.44 => ( subsetI2
% 2.39/1.44 => ( emptysetsubset
% 2.39/1.44 => ( subsetE
% 2.39/1.44 => ( subsetE2
% 2.39/1.44 => ( notsubsetI
% 2.39/1.44 => ( notequalI1
% 2.39/1.44 => ( notequalI2
% 2.39/1.44 => ( subsetRefl
% 2.39/1.44 => ( subsetTrans
% 2.39/1.44 => ( setadjoinSub
% 2.39/1.44 => ( setadjoinSub2
% 2.39/1.44 => ( subset2powerset
% 2.39/1.44 => ( setextsub
% 2.39/1.44 => ( subsetemptysetimpeq
% 2.39/1.44 => ( powersetI1
% 2.39/1.44 => ( powersetE1
% 2.39/1.44 => ( inPowerset
% 2.39/1.44 => ( powersetsubset
% 2.39/1.44 => ( sepInPowerset
% 2.39/1.44 => ( sepSubset
% 2.39/1.44 => ( binunionIL
% 2.39/1.44 => ( upairset2IR
% 2.39/1.44 => ( binunionIR
% 2.39/1.44 => ! [A: $i,B: $i,Xx: $i,Xphi: $o] :
% 2.39/1.44 ( ( in @ Xx @ ( binunion @ A @ B ) )
% 2.39/1.44 => ( ( ( in @ Xx @ A )
% 2.39/1.44 => Xphi )
% 2.39/1.44 => ( ( ( in @ Xx @ B )
% 2.39/1.44 => Xphi )
% 2.39/1.44 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.39/1.44 ------------------------
% 2.39/1.46 % (27315)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_27107 for (2999ds/2Mi)
% 2.39/1.46 % (27314)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/2Mi)
% 2.39/1.46 % (27313)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_27107 for (2999ds/27Mi)
% 2.39/1.46 % (27314)Instruction limit reached!
% 2.39/1.46 % (27314)------------------------------
% 2.39/1.46 % (27314)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.46 % (27314)Termination reason: Unknown
% 2.39/1.46 % (27314)Termination phase: shuffling
% 2.39/1.46
% 2.39/1.46 % (27314)Memory used [KB]: 1151
% 2.39/1.46 % (27314)Time elapsed: 0.002 s
% 2.39/1.46 % (27314)Instructions burned: 2 (million)
% 2.39/1.46 % (27314)------------------------------
% 2.39/1.46 % (27314)------------------------------
% 2.39/1.46 % (27315)Instruction limit reached!
% 2.39/1.46 % (27315)------------------------------
% 2.39/1.46 % (27315)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.46 % (27315)Termination reason: Unknown
% 2.39/1.46 % (27315)Termination phase: shuffling
% 2.39/1.46
% 2.39/1.46 % (27315)Memory used [KB]: 1279
% 2.39/1.46 % (27315)Time elapsed: 0.003 s
% 2.39/1.46 % (27315)Instructions burned: 5 (million)
% 2.39/1.46 % (27315)------------------------------
% 2.39/1.46 % (27315)------------------------------
% 2.39/1.46 % (27311)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/183Mi)
% 2.39/1.46 % (27312)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_27107 for (2999ds/4Mi)
% 2.39/1.46 % (27316)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_27107 for (2999ds/275Mi)
% 2.39/1.46 % (27317)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/18Mi)
% 2.39/1.47 % (27313)Instruction limit reached!
% 2.39/1.47 % (27313)------------------------------
% 2.39/1.47 % (27313)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.47 % (27313)Termination reason: Unknown
% 2.39/1.47 % (27313)Termination phase: Property scanning
% 2.39/1.47
% 2.39/1.47 % (27313)Memory used [KB]: 1535
% 2.39/1.47 % (27313)Time elapsed: 0.010 s
% 2.39/1.47 % (27313)Instructions burned: 30 (million)
% 2.39/1.47 % (27313)------------------------------
% 2.39/1.47 % (27313)------------------------------
% 2.39/1.47 % (27312)Instruction limit reached!
% 2.39/1.47 % (27312)------------------------------
% 2.39/1.47 % (27312)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.47 % (27312)Termination reason: Unknown
% 2.39/1.47 % (27312)Termination phase: shuffling
% 2.39/1.47
% 2.39/1.47 % (27312)Memory used [KB]: 1279
% 2.39/1.47 % (27312)Time elapsed: 0.005 s
% 2.39/1.47 % (27312)Instructions burned: 5 (million)
% 2.39/1.47 % (27312)------------------------------
% 2.39/1.47 % (27312)------------------------------
% 2.39/1.47 % (27319)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_27107 for (2999ds/37Mi)
% 2.39/1.47 % (27318)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/3Mi)
% 2.39/1.47 % (27318)Instruction limit reached!
% 2.39/1.47 % (27318)------------------------------
% 2.39/1.47 % (27318)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.47 % (27318)Termination reason: Unknown
% 2.39/1.47 % (27318)Termination phase: shuffling
% 2.39/1.47
% 2.39/1.47 % (27318)Memory used [KB]: 1151
% 2.39/1.47 % (27318)Time elapsed: 0.002 s
% 2.39/1.47 % (27318)Instructions burned: 4 (million)
% 2.39/1.47 % (27318)------------------------------
% 2.39/1.47 % (27318)------------------------------
% 2.39/1.47 % (27317)Instruction limit reached!
% 2.39/1.47 % (27317)------------------------------
% 2.39/1.47 % (27317)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.47 % (27317)Termination reason: Unknown
% 2.39/1.47 % (27317)Termination phase: Preprocessing 3
% 2.39/1.47
% 2.39/1.47 % (27317)Memory used [KB]: 1535
% 2.39/1.47 % (27317)Time elapsed: 0.013 s
% 2.39/1.48 % (27317)Instructions burned: 19 (million)
% 2.39/1.48 % (27317)------------------------------
% 2.39/1.48 % (27317)------------------------------
% 2.39/1.48 % (27320)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_27107 for (2999ds/15Mi)
% 2.39/1.48 % (27319)Instruction limit reached!
% 2.39/1.48 % (27319)------------------------------
% 2.39/1.48 % (27319)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.48 % (27319)Termination reason: Unknown
% 2.39/1.48 % (27319)Termination phase: Function definition elimination
% 2.39/1.48
% 2.39/1.48 % (27319)Memory used [KB]: 1535
% 2.39/1.48 % (27319)Time elapsed: 0.011 s
% 2.39/1.48 % (27319)Instructions burned: 38 (million)
% 2.39/1.48 % (27319)------------------------------
% 2.39/1.48 % (27319)------------------------------
% 2.39/1.48 % (27322)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_27107 for (2999ds/1041Mi)
% 2.39/1.48 % (27320)Instruction limit reached!
% 2.39/1.48 % (27320)------------------------------
% 2.39/1.48 % (27320)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.48 % (27320)Termination reason: Unknown
% 2.39/1.48 % (27320)Termination phase: Naming
% 2.39/1.48
% 2.39/1.48 % (27320)Memory used [KB]: 1535
% 2.39/1.48 % (27320)Time elapsed: 0.007 s
% 2.39/1.48 % (27320)Instructions burned: 16 (million)
% 2.39/1.48 % (27320)------------------------------
% 2.39/1.48 % (27320)------------------------------
% 2.39/1.48 % (27321)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_27107 for (2999ds/3Mi)
% 2.39/1.49 % (27321)Instruction limit reached!
% 2.39/1.49 % (27321)------------------------------
% 2.39/1.49 % (27321)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.49 % (27321)Termination reason: Unknown
% 2.39/1.49 % (27321)Termination phase: shuffling
% 2.39/1.49
% 2.39/1.49 % (27321)Memory used [KB]: 1279
% 2.39/1.49 % (27321)Time elapsed: 0.004 s
% 2.39/1.49 % (27321)Instructions burned: 5 (million)
% 2.39/1.49 % (27321)------------------------------
% 2.39/1.49 % (27321)------------------------------
% 2.39/1.49 % (27324)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/16Mi)
% 2.39/1.49 % (27325)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_27107 for (2999ds/3Mi)
% 2.39/1.49 % (27324)Instruction limit reached!
% 2.39/1.49 % (27324)------------------------------
% 2.39/1.49 % (27324)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.49 % (27324)Termination reason: Unknown
% 2.39/1.49 % (27324)Termination phase: Property scanning
% 2.39/1.49
% 2.39/1.49 % (27324)Memory used [KB]: 1407
% 2.39/1.49 % (27324)Time elapsed: 0.006 s
% 2.39/1.49 % (27324)Instructions burned: 18 (million)
% 2.39/1.49 % (27324)------------------------------
% 2.39/1.49 % (27324)------------------------------
% 2.39/1.49 % (27325)Instruction limit reached!
% 2.39/1.49 % (27325)------------------------------
% 2.39/1.49 % (27325)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.39/1.49 % (27325)Termination reason: Unknown
% 2.39/1.49 % (27325)Termination phase: shuffling
% 2.39/1.49
% 2.39/1.49 % (27325)Memory used [KB]: 1151
% 2.39/1.49 % (27325)Time elapsed: 0.003 s
% 2.39/1.49 % (27325)Instructions burned: 4 (million)
% 2.39/1.49 % (27325)------------------------------
% 2.39/1.49 % (27325)------------------------------
% 2.39/1.49 % (27323)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/7Mi)
% 2.45/1.50 % (27323)Instruction limit reached!
% 2.45/1.50 % (27323)------------------------------
% 2.45/1.50 % (27323)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (27323)Termination reason: Unknown
% 2.45/1.50 % (27323)Termination phase: shuffling
% 2.45/1.50
% 2.45/1.50 % (27323)Memory used [KB]: 1279
% 2.45/1.50 % (27323)Time elapsed: 0.006 s
% 2.45/1.50 % (27323)Instructions burned: 7 (million)
% 2.45/1.50 % (27323)------------------------------
% 2.45/1.50 % (27323)------------------------------
% 2.45/1.50 % (27326)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_27107 for (2999ds/3Mi)
% 2.45/1.50 % (27326)Instruction limit reached!
% 2.45/1.50 % (27326)------------------------------
% 2.45/1.50 % (27326)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (27326)Termination reason: Unknown
% 2.45/1.50 % (27326)Termination phase: shuffling
% 2.45/1.50
% 2.45/1.50 % (27326)Memory used [KB]: 1279
% 2.45/1.50 % (27326)Time elapsed: 0.003 s
% 2.45/1.50 % (27326)Instructions burned: 4 (million)
% 2.45/1.50 % (27326)------------------------------
% 2.45/1.50 % (27326)------------------------------
% 2.45/1.50 % (27327)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/7Mi)
% 2.45/1.50 % (27328)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/3Mi)
% 2.45/1.50 % (27327)Instruction limit reached!
% 2.45/1.50 % (27327)------------------------------
% 2.45/1.50 % (27327)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (27327)Termination reason: Unknown
% 2.45/1.50 % (27327)Termination phase: shuffling
% 2.45/1.50
% 2.45/1.50 % (27327)Memory used [KB]: 1279
% 2.45/1.50 % (27327)Time elapsed: 0.003 s
% 2.45/1.50 % (27327)Instructions burned: 7 (million)
% 2.45/1.50 % (27327)------------------------------
% 2.45/1.50 % (27327)------------------------------
% 2.45/1.50 % (27328)Instruction limit reached!
% 2.45/1.50 % (27328)------------------------------
% 2.45/1.50 % (27328)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.50 % (27328)Termination reason: Unknown
% 2.45/1.50 % (27328)Termination phase: shuffling
% 2.45/1.50
% 2.45/1.50 % (27328)Memory used [KB]: 1279
% 2.45/1.50 % (27328)Time elapsed: 0.003 s
% 2.45/1.50 % (27328)Instructions burned: 4 (million)
% 2.45/1.50 % (27328)------------------------------
% 2.45/1.50 % (27328)------------------------------
% 2.45/1.51 % (27330)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/18Mi)
% 2.45/1.51 % (27331)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/710Mi)
% 2.45/1.51 % (27332)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/6Mi)
% 2.45/1.51 % (27329)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/4Mi)
% 2.45/1.52 % (27330)Instruction limit reached!
% 2.45/1.52 % (27330)------------------------------
% 2.45/1.52 % (27330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.52 % (27330)Termination reason: Unknown
% 2.45/1.52 % (27330)Termination phase: Property scanning
% 2.45/1.52
% 2.45/1.52 % (27330)Memory used [KB]: 1407
% 2.45/1.52 % (27330)Time elapsed: 0.007 s
% 2.45/1.52 % (27330)Instructions burned: 18 (million)
% 2.45/1.52 % (27330)------------------------------
% 2.45/1.52 % (27330)------------------------------
% 2.45/1.52 % (27329)Instruction limit reached!
% 2.45/1.52 % (27329)------------------------------
% 2.45/1.52 % (27329)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.52 % (27332)Instruction limit reached!
% 2.45/1.52 % (27332)------------------------------
% 2.45/1.52 % (27332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.52 % (27332)Termination reason: Unknown
% 2.45/1.52 % (27329)Termination reason: Unknown
% 2.45/1.52 % (27332)Termination phase: shuffling
% 2.45/1.52
% 2.45/1.52 % (27332)Memory used [KB]: 1279
% 2.45/1.52 % (27332)Time elapsed: 0.004 s
% 2.45/1.52 % (27329)Termination phase: shuffling
% 2.45/1.52
% 2.45/1.52 % (27332)Instructions burned: 9 (million)
% 2.45/1.52 % (27332)------------------------------
% 2.45/1.52 % (27332)------------------------------
% 2.45/1.52 % (27329)Memory used [KB]: 1151
% 2.45/1.52 % (27329)Time elapsed: 0.004 s
% 2.45/1.52 % (27329)Instructions burned: 4 (million)
% 2.45/1.52 % (27329)------------------------------
% 2.45/1.52 % (27329)------------------------------
% 2.45/1.53 % (27334)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_27107 for (2999ds/21Mi)
% 2.45/1.53 % (27333)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_27107 for (2999ds/902Mi)
% 2.45/1.53 % (27334)Instruction limit reached!
% 2.45/1.53 % (27334)------------------------------
% 2.45/1.53 % (27334)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.53 % (27334)Termination reason: Unknown
% 2.45/1.53 % (27334)Termination phase: Property scanning
% 2.45/1.53
% 2.45/1.53 % (27334)Memory used [KB]: 1407
% 2.45/1.53 % (27334)Time elapsed: 0.007 s
% 2.45/1.53 % (27334)Instructions burned: 23 (million)
% 2.45/1.53 % (27334)------------------------------
% 2.45/1.53 % (27334)------------------------------
% 2.45/1.53 % (27335)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/5Mi)
% 2.45/1.54 % (27335)Instruction limit reached!
% 2.45/1.54 % (27335)------------------------------
% 2.45/1.54 % (27335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.54 % (27335)Termination reason: Unknown
% 2.45/1.54 % (27335)Termination phase: shuffling
% 2.45/1.54
% 2.45/1.54 % (27335)Memory used [KB]: 1279
% 2.45/1.54 % (27335)Time elapsed: 0.005 s
% 2.45/1.54 % (27335)Instructions burned: 6 (million)
% 2.45/1.54 % (27335)------------------------------
% 2.45/1.54 % (27335)------------------------------
% 2.45/1.54 % (27336)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_27107 for (2999ds/6Mi)
% 2.45/1.54 % (27336)Instruction limit reached!
% 2.45/1.54 % (27336)------------------------------
% 2.45/1.54 % (27336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.54 % (27336)Termination reason: Unknown
% 2.45/1.54 % (27336)Termination phase: shuffling
% 2.45/1.54
% 2.45/1.54 % (27336)Memory used [KB]: 1279
% 2.45/1.54 % (27336)Time elapsed: 0.003 s
% 2.45/1.54 % (27336)Instructions burned: 8 (million)
% 2.45/1.54 % (27336)------------------------------
% 2.45/1.54 % (27336)------------------------------
% 2.45/1.55 % (27338)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_27107 for (2999ds/779Mi)
% 2.45/1.55 % (27337)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_27107 for (2999ds/377Mi)
% 2.45/1.56 % (27311)Instruction limit reached!
% 2.45/1.56 % (27311)------------------------------
% 2.45/1.56 % (27311)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.56 % (27311)Termination reason: Unknown
% 2.45/1.56 % (27311)Termination phase: Saturation
% 2.45/1.56
% 2.45/1.56 % (27311)Memory used [KB]: 6908
% 2.45/1.56 % (27311)Time elapsed: 0.102 s
% 2.45/1.56 % (27311)Instructions burned: 184 (million)
% 2.45/1.56 % (27311)------------------------------
% 2.45/1.56 % (27311)------------------------------
% 2.45/1.58 % (27339)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_27107 for (2998ds/19Mi)
% 2.45/1.58 % (27339)Instruction limit reached!
% 2.45/1.58 % (27339)------------------------------
% 2.45/1.58 % (27339)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.58 % (27339)Termination reason: Unknown
% 2.45/1.58 % (27339)Termination phase: Property scanning
% 2.45/1.58
% 2.45/1.58 % (27339)Memory used [KB]: 1407
% 2.45/1.58 % (27339)Time elapsed: 0.008 s
% 2.45/1.58 % (27339)Instructions burned: 22 (million)
% 2.45/1.58 % (27339)------------------------------
% 2.45/1.58 % (27339)------------------------------
% 2.45/1.58 % (27316)Instruction limit reached!
% 2.45/1.58 % (27316)------------------------------
% 2.45/1.58 % (27316)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.58 % (27316)Termination reason: Unknown
% 2.45/1.58 % (27316)Termination phase: Saturation
% 2.45/1.58
% 2.45/1.58 % (27316)Memory used [KB]: 7547
% 2.45/1.58 % (27316)Time elapsed: 0.121 s
% 2.45/1.58 % (27316)Instructions burned: 275 (million)
% 2.45/1.58 % (27316)------------------------------
% 2.45/1.58 % (27316)------------------------------
% 2.45/1.59 % (27340)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_27107 for (2998ds/879Mi)
% 2.45/1.59 % (27341)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_27107 for (2998ds/17Mi)
% 2.45/1.60 % (27341)Instruction limit reached!
% 2.45/1.60 % (27341)------------------------------
% 2.45/1.60 % (27341)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.60 % (27341)Termination reason: Unknown
% 2.45/1.60 % (27341)Termination phase: Property scanning
% 2.45/1.60
% 2.45/1.60 % (27341)Memory used [KB]: 1407
% 2.45/1.60 % (27341)Time elapsed: 0.007 s
% 2.45/1.60 % (27341)Instructions burned: 18 (million)
% 2.45/1.60 % (27341)------------------------------
% 2.45/1.60 % (27341)------------------------------
% 2.45/1.61 % (27342)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_27107 for (2998ds/3Mi)
% 2.45/1.61 % (27342)Instruction limit reached!
% 2.45/1.61 % (27342)------------------------------
% 2.45/1.61 % (27342)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.61 % (27342)Termination reason: Unknown
% 2.45/1.61 % (27342)Termination phase: shuffling
% 2.45/1.61
% 2.45/1.61 % (27342)Memory used [KB]: 1279
% 2.45/1.61 % (27342)Time elapsed: 0.003 s
% 2.45/1.61 % (27342)Instructions burned: 4 (million)
% 2.45/1.61 % (27342)------------------------------
% 2.45/1.61 % (27342)------------------------------
% 2.45/1.62 % (27343)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_27107 for (2998ds/30Mi)
% 2.45/1.63 % (27343)Instruction limit reached!
% 2.45/1.63 % (27343)------------------------------
% 2.45/1.63 % (27343)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.63 % (27343)Termination reason: Unknown
% 2.45/1.63 % (27343)Termination phase: Property scanning
% 2.45/1.63
% 2.45/1.63 % (27343)Memory used [KB]: 1535
% 2.45/1.63 % (27343)Time elapsed: 0.011 s
% 2.45/1.63 % (27343)Instructions burned: 33 (million)
% 2.45/1.63 % (27343)------------------------------
% 2.45/1.63 % (27343)------------------------------
% 2.45/1.64 % (27344)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_27107 for (2998ds/127Mi)
% 2.45/1.68 % (27344)Instruction limit reached!
% 2.45/1.68 % (27344)------------------------------
% 2.45/1.68 % (27344)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.68 % (27344)Termination reason: Unknown
% 2.45/1.68 % (27344)Termination phase: Saturation
% 2.45/1.68
% 2.45/1.68 % (27344)Memory used [KB]: 6780
% 2.45/1.68 % (27344)Time elapsed: 0.041 s
% 2.45/1.68 % (27344)Instructions burned: 128 (million)
% 2.45/1.68 % (27344)------------------------------
% 2.45/1.68 % (27344)------------------------------
% 2.45/1.68 % (27337)Instruction limit reached!
% 2.45/1.68 % (27337)------------------------------
% 2.45/1.68 % (27337)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.68 % (27337)Termination reason: Unknown
% 2.45/1.68 % (27337)Termination phase: Saturation
% 2.45/1.68
% 2.45/1.68 % (27337)Memory used [KB]: 7164
% 2.45/1.68 % (27337)Time elapsed: 0.129 s
% 2.45/1.68 % (27337)Instructions burned: 379 (million)
% 2.45/1.68 % (27337)------------------------------
% 2.45/1.68 % (27337)------------------------------
% 2.45/1.69 % (27345)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_27107 for (2997ds/100Mi)
% 2.45/1.69 % (27346)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_27107 for (2997ds/3Mi)
% 2.45/1.69 % (27346)Instruction limit reached!
% 2.45/1.69 % (27346)------------------------------
% 2.45/1.69 % (27346)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.69 % (27346)Termination reason: Unknown
% 2.45/1.69 % (27346)Termination phase: shuffling
% 2.45/1.69
% 2.45/1.69 % (27346)Memory used [KB]: 1279
% 2.45/1.69 % (27346)Time elapsed: 0.003 s
% 2.45/1.69 % (27346)Instructions burned: 4 (million)
% 2.45/1.69 % (27346)------------------------------
% 2.45/1.69 % (27346)------------------------------
% 2.45/1.70 % (27347)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_27107 for (2997ds/20Mi)
% 2.45/1.71 % (27347)Instruction limit reached!
% 2.45/1.71 % (27347)------------------------------
% 2.45/1.71 % (27347)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.71 % (27347)Termination reason: Unknown
% 2.45/1.71 % (27347)Termination phase: Preprocessing 2
% 2.45/1.71
% 2.45/1.71 % (27347)Memory used [KB]: 1407
% 2.45/1.71 % (27347)Time elapsed: 0.007 s
% 2.45/1.71 % (27347)Instructions burned: 20 (million)
% 2.45/1.71 % (27347)------------------------------
% 2.45/1.71 % (27347)------------------------------
% 2.45/1.72 % (27348)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_27107 for (2997ds/86Mi)
% 2.45/1.72 % (27345)Instruction limit reached!
% 2.45/1.72 % (27345)------------------------------
% 2.45/1.72 % (27345)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.72 % (27345)Termination reason: Unknown
% 2.45/1.72 % (27345)Termination phase: Saturation
% 2.45/1.72
% 2.45/1.72 % (27345)Memory used [KB]: 6396
% 2.45/1.72 % (27345)Time elapsed: 0.032 s
% 2.45/1.72 % (27345)Instructions burned: 101 (million)
% 2.45/1.72 % (27345)------------------------------
% 2.45/1.72 % (27345)------------------------------
% 2.45/1.73 % (27349)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_27107 for (2997ds/107Mi)
% 2.45/1.74 % (27331)Instruction limit reached!
% 2.45/1.74 % (27331)------------------------------
% 2.45/1.74 % (27331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.74 % (27331)Termination reason: Unknown
% 2.45/1.74 % (27331)Termination phase: Saturation
% 2.45/1.74
% 2.45/1.74 % (27331)Memory used [KB]: 8827
% 2.45/1.74 % (27331)Time elapsed: 0.225 s
% 2.45/1.74 % (27331)Instructions burned: 711 (million)
% 2.45/1.74 % (27331)------------------------------
% 2.45/1.74 % (27331)------------------------------
% 2.45/1.74 % (27322)Instruction limit reached!
% 2.45/1.74 % (27322)------------------------------
% 2.45/1.74 % (27322)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.74 % (27322)Termination reason: Unknown
% 2.45/1.74 % (27322)Termination phase: Saturation
% 2.45/1.74
% 2.45/1.74 % (27322)Memory used [KB]: 7803
% 2.45/1.74 % (27322)Time elapsed: 0.260 s
% 2.45/1.74 % (27322)Instructions burned: 1045 (million)
% 2.45/1.74 % (27322)------------------------------
% 2.45/1.74 % (27322)------------------------------
% 2.45/1.74 % (27338)Instruction limit reached!
% 2.45/1.74 % (27338)------------------------------
% 2.45/1.74 % (27338)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.74 % (27338)Termination reason: Unknown
% 2.45/1.74 % (27338)Termination phase: Saturation
% 2.45/1.74
% 2.45/1.74 % (27338)Memory used [KB]: 6780
% 2.45/1.74 % (27338)Time elapsed: 0.188 s
% 2.45/1.74 % (27338)Instructions burned: 780 (million)
% 2.45/1.74 % (27338)------------------------------
% 2.45/1.74 % (27338)------------------------------
% 2.45/1.74 % (27348)Instruction limit reached!
% 2.45/1.74 % (27348)------------------------------
% 2.45/1.74 % (27348)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.74 % (27348)Termination reason: Unknown
% 2.45/1.74 % (27348)Termination phase: Saturation
% 2.45/1.74
% 2.45/1.74 % (27348)Memory used [KB]: 6396
% 2.45/1.74 % (27348)Time elapsed: 0.027 s
% 2.45/1.74 % (27348)Instructions burned: 88 (million)
% 2.45/1.74 % (27348)------------------------------
% 2.45/1.74 % (27348)------------------------------
% 2.45/1.75 % (27350)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_27107 for (2997ds/39Mi)
% 2.45/1.75 % (27351)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_27107 for (2997ds/448Mi)
% 2.45/1.75 % (27352)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_27107 for (2997ds/46Mi)
% 2.45/1.75 % (27353)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_27107 for (2997ds/98Mi)
% 2.45/1.76 % (27350)Instruction limit reached!
% 2.45/1.76 % (27350)------------------------------
% 2.45/1.76 % (27350)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.76 % (27350)Termination reason: Unknown
% 2.45/1.76 % (27350)Termination phase: Property scanning
% 2.45/1.76
% 2.45/1.76 % (27350)Memory used [KB]: 1535
% 2.45/1.76 % (27350)Time elapsed: 0.011 s
% 2.45/1.76 % (27350)Instructions burned: 40 (million)
% 2.45/1.76 % (27350)------------------------------
% 2.45/1.76 % (27350)------------------------------
% 2.45/1.76 % (27349)Instruction limit reached!
% 2.45/1.76 % (27349)------------------------------
% 2.45/1.76 % (27349)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.76 % (27349)Termination reason: Unknown
% 2.45/1.76 % (27349)Termination phase: Saturation
% 2.45/1.76
% 2.45/1.76 % (27349)Memory used [KB]: 6652
% 2.45/1.76 % (27349)Time elapsed: 0.033 s
% 2.45/1.76 % (27349)Instructions burned: 109 (million)
% 2.45/1.76 % (27349)------------------------------
% 2.45/1.76 % (27349)------------------------------
% 2.45/1.76 % (27352)Instruction limit reached!
% 2.45/1.76 % (27352)------------------------------
% 2.45/1.76 % (27352)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.76 % (27352)Termination reason: Unknown
% 2.45/1.76 % (27352)Termination phase: Twee Goal Transformation
% 2.45/1.76
% 2.45/1.76 % (27352)Memory used [KB]: 1535
% 2.45/1.76 % (27352)Time elapsed: 0.013 s
% 2.45/1.76 % (27352)Instructions burned: 47 (million)
% 2.45/1.76 % (27352)------------------------------
% 2.45/1.76 % (27352)------------------------------
% 2.45/1.77 % (27354)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_27107 for (2996ds/507Mi)
% 2.45/1.77 % (27355)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_27107 for (2996ds/149Mi)
% 2.45/1.77 % (27356)lrs+21_1:16_au=on:bd=off:piset=and:i=39:si=on:rtra=on_0 on DTF2THF_27107 for (2996ds/39Mi)
% 2.45/1.78 % (27353)Instruction limit reached!
% 2.45/1.78 % (27353)------------------------------
% 2.45/1.78 % (27353)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.78 % (27353)Termination reason: Unknown
% 2.45/1.78 % (27353)Termination phase: Saturation
% 2.45/1.78
% 2.45/1.78 % (27353)Memory used [KB]: 1663
% 2.45/1.78 % (27353)Time elapsed: 0.029 s
% 2.45/1.78 % (27353)Instructions burned: 102 (million)
% 2.45/1.78 % (27353)------------------------------
% 2.45/1.78 % (27353)------------------------------
% 2.45/1.78 % (27356)Instruction limit reached!
% 2.45/1.78 % (27356)------------------------------
% 2.45/1.78 % (27356)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.78 % (27356)Termination reason: Unknown
% 2.45/1.78 % (27356)Termination phase: Property scanning
% 2.45/1.78
% 2.45/1.78 % (27356)Memory used [KB]: 1535
% 2.45/1.78 % (27356)Time elapsed: 0.013 s
% 2.45/1.78 % (27356)Instructions burned: 41 (million)
% 2.45/1.78 % (27356)------------------------------
% 2.45/1.78 % (27356)------------------------------
% 2.45/1.79 % (27357)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_27107 for (2996ds/6Mi)
% 2.45/1.79 % (27358)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_27107 for (2996ds/1087Mi)
% 2.45/1.79 % (27357)Instruction limit reached!
% 2.45/1.79 % (27357)------------------------------
% 2.45/1.79 % (27357)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.79 % (27357)Termination reason: Unknown
% 2.45/1.79 % (27357)Termination phase: shuffling
% 2.45/1.79
% 2.45/1.79 % (27357)Memory used [KB]: 1279
% 2.45/1.79 % (27357)Time elapsed: 0.004 s
% 2.45/1.79 % (27357)Instructions burned: 8 (million)
% 2.45/1.79 % (27357)------------------------------
% 2.45/1.79 % (27357)------------------------------
% 2.45/1.80 % (27359)dis+10_1:1_aac=none:cs=on:i=47:si=on:rtra=on_0 on DTF2THF_27107 for (2996ds/47Mi)
% 2.45/1.81 % (27355)Instruction limit reached!
% 2.45/1.81 % (27355)------------------------------
% 2.45/1.81 % (27355)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.81 % (27355)Termination reason: Unknown
% 2.45/1.81 % (27355)Termination phase: Saturation
% 2.45/1.81
% 2.45/1.81 % (27355)Memory used [KB]: 6652
% 2.45/1.81 % (27355)Time elapsed: 0.046 s
% 2.45/1.81 % (27355)Instructions burned: 150 (million)
% 2.45/1.81 % (27355)------------------------------
% 2.45/1.81 % (27355)------------------------------
% 2.45/1.82 % (27359)Instruction limit reached!
% 2.45/1.82 % (27359)------------------------------
% 2.45/1.82 % (27359)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.82 % (27359)Termination reason: Unknown
% 2.45/1.82 % (27359)Termination phase: Saturation
% 2.45/1.82
% 2.45/1.82 % (27359)Memory used [KB]: 6012
% 2.45/1.82 % (27359)Time elapsed: 0.014 s
% 2.45/1.82 % (27359)Instructions burned: 47 (million)
% 2.45/1.82 % (27359)------------------------------
% 2.45/1.82 % (27359)------------------------------
% 2.45/1.82 % (27360)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_27107 for (2996ds/44Mi)
% 2.45/1.83 % (27361)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_27107 for (2996ds/432Mi)
% 2.45/1.83 % (27333)Instruction limit reached!
% 2.45/1.83 % (27333)------------------------------
% 2.45/1.83 % (27333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.83 % (27333)Termination reason: Unknown
% 2.45/1.83 % (27333)Termination phase: Saturation
% 2.45/1.83
% 2.45/1.83 % (27333)Memory used [KB]: 10234
% 2.45/1.83 % (27333)Time elapsed: 0.304 s
% 2.45/1.83 % (27333)Instructions burned: 905 (million)
% 2.45/1.83 % (27333)------------------------------
% 2.45/1.83 % (27333)------------------------------
% 2.45/1.84 % (27360)Instruction limit reached!
% 2.45/1.84 % (27360)------------------------------
% 2.45/1.84 % (27360)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.84 % (27360)Termination reason: Unknown
% 2.45/1.84 % (27360)Termination phase: Function definition elimination
% 2.45/1.84
% 2.45/1.84 % (27360)Memory used [KB]: 1535
% 2.45/1.84 % (27360)Time elapsed: 0.012 s
% 2.45/1.84 % (27360)Instructions burned: 44 (million)
% 2.45/1.84 % (27360)------------------------------
% 2.45/1.84 % (27360)------------------------------
% 2.45/1.84 % (27362)lrs+10_7:1_cnfonf=lazy_gen:fe=off:nwc=5.0:plsq=on:i=62:si=on:rtra=on_0 on DTF2THF_27107 for (2996ds/62Mi)
% 2.45/1.84 % (27363)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_27107 for (2996ds/31Mi)
% 2.45/1.85 % (27351)Instruction limit reached!
% 2.45/1.85 % (27351)------------------------------
% 2.45/1.85 % (27351)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.85 % (27351)Termination reason: Unknown
% 2.45/1.85 % (27351)Termination phase: Saturation
% 2.45/1.85
% 2.45/1.85 % (27351)Memory used [KB]: 6396
% 2.45/1.85 % (27351)Time elapsed: 0.105 s
% 2.45/1.85 % (27351)Instructions burned: 449 (million)
% 2.45/1.85 % (27351)------------------------------
% 2.45/1.85 % (27351)------------------------------
% 2.45/1.85 % (27363)Instruction limit reached!
% 2.45/1.85 % (27363)------------------------------
% 2.45/1.85 % (27363)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.85 % (27363)Termination reason: Unknown
% 2.45/1.85 % (27363)Termination phase: Property scanning
% 2.45/1.85
% 2.45/1.85 % (27363)Memory used [KB]: 1535
% 2.45/1.85 % (27363)Time elapsed: 0.009 s
% 2.45/1.85 % (27363)Instructions burned: 31 (million)
% 2.45/1.85 % (27363)------------------------------
% 2.45/1.85 % (27363)------------------------------
% 2.45/1.86 % (27362)Instruction limit reached!
% 2.45/1.86 % (27362)------------------------------
% 2.45/1.86 % (27362)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.86 % (27362)Termination reason: Unknown
% 2.45/1.86 % (27362)Termination phase: Saturation
% 2.45/1.86
% 2.45/1.86 % (27362)Memory used [KB]: 6140
% 2.45/1.86 % (27362)Time elapsed: 0.018 s
% 2.45/1.86 % (27362)Instructions burned: 64 (million)
% 2.45/1.86 % (27362)------------------------------
% 2.45/1.86 % (27362)------------------------------
% 2.45/1.86 % (27364)dis+10_1:128_hud=1:i=96:si=on:rtra=on_0 on DTF2THF_27107 for (2995ds/96Mi)
% 2.45/1.86 % (27365)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_27107 for (2995ds/453Mi)
% 2.45/1.86 % (27366)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_27107 for (2995ds/71Mi)
% 2.45/1.88 % (27366)Instruction limit reached!
% 2.45/1.88 % (27366)------------------------------
% 2.45/1.88 % (27366)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.88 % (27366)Termination reason: Unknown
% 2.45/1.88 % (27366)Termination phase: Saturation
% 2.45/1.88
% 2.45/1.88 % (27366)Memory used [KB]: 6268
% 2.45/1.88 % (27366)Time elapsed: 0.021 s
% 2.45/1.88 % (27366)Instructions burned: 73 (million)
% 2.45/1.88 % (27366)------------------------------
% 2.45/1.88 % (27366)------------------------------
% 2.45/1.89 % (27364)Instruction limit reached!
% 2.45/1.89 % (27364)------------------------------
% 2.45/1.89 % (27364)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.89 % (27364)Termination reason: Unknown
% 2.45/1.89 % (27364)Termination phase: Saturation
% 2.45/1.89
% 2.45/1.89 % (27364)Memory used [KB]: 6524
% 2.45/1.89 % (27364)Time elapsed: 0.027 s
% 2.45/1.89 % (27364)Instructions burned: 96 (million)
% 2.45/1.89 % (27364)------------------------------
% 2.45/1.89 % (27364)------------------------------
% 2.45/1.89 % (27340)Instruction limit reached!
% 2.45/1.89 % (27340)------------------------------
% 2.45/1.89 % (27340)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.89 % (27340)Termination reason: Unknown
% 2.45/1.89 % (27340)Termination phase: Saturation
% 2.45/1.89
% 2.45/1.89 % (27340)Memory used [KB]: 7419
% 2.45/1.89 % (27340)Time elapsed: 0.299 s
% 2.45/1.89 % (27340)Instructions burned: 882 (million)
% 2.45/1.89 % (27340)------------------------------
% 2.45/1.89 % (27340)------------------------------
% 2.45/1.89 % (27367)dis+1002_1:1_bd=off:fsr=off:ntd=on:s2a=on:ss=axioms:i=83:si=on:rtra=on_0 on DTF2THF_27107 for (2995ds/83Mi)
% 2.45/1.90 % (27368)lrs+10_1:128_cnfonf=lazy_not_gen_be_off:hud=1:ins=1:i=11:si=on:rtra=on_0 on DTF2THF_27107 for (2995ds/11Mi)
% 2.45/1.90 % (27368)Instruction limit reached!
% 2.45/1.90 % (27368)------------------------------
% 2.45/1.90 % (27368)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.90 % (27368)Termination reason: Unknown
% 2.45/1.90 % (27368)Termination phase: shuffling
% 2.45/1.90
% 2.45/1.90 % (27368)Memory used [KB]: 1407
% 2.45/1.90 % (27368)Time elapsed: 0.004 s
% 2.45/1.90 % (27368)Instructions burned: 11 (million)
% 2.45/1.90 % (27368)------------------------------
% 2.45/1.90 % (27368)------------------------------
% 2.45/1.90 % (27369)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_27107 for (2995ds/41Mi)
% 2.45/1.91 % (27370)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_27107 for (2995ds/6Mi)
% 2.45/1.91 % (27370)Instruction limit reached!
% 2.45/1.91 % (27370)------------------------------
% 2.45/1.91 % (27370)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.91 % (27370)Termination reason: Unknown
% 2.45/1.91 % (27370)Termination phase: shuffling
% 2.45/1.91
% 2.45/1.91 % (27370)Memory used [KB]: 1279
% 2.45/1.91 % (27370)Time elapsed: 0.003 s
% 2.45/1.91 % (27370)Instructions burned: 6 (million)
% 2.45/1.91 % (27370)------------------------------
% 2.45/1.91 % (27370)------------------------------
% 2.45/1.91 % (27369)Instruction limit reached!
% 2.45/1.91 % (27369)------------------------------
% 2.45/1.91 % (27369)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.91 % (27369)Termination reason: Unknown
% 2.45/1.91 % (27369)Termination phase: Property scanning
% 2.45/1.91
% 2.45/1.91 % (27369)Memory used [KB]: 1535
% 2.45/1.91 % (27369)Time elapsed: 0.013 s
% 2.45/1.91 % (27369)Instructions burned: 41 (million)
% 2.45/1.91 % (27369)------------------------------
% 2.45/1.91 % (27369)------------------------------
% 2.45/1.92 % (27367)Instruction limit reached!
% 2.45/1.92 % (27367)------------------------------
% 2.45/1.92 % (27367)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.92 % (27367)Termination reason: Unknown
% 2.45/1.92 % (27367)Termination phase: Saturation
% 2.45/1.92
% 2.45/1.92 % (27367)Memory used [KB]: 6268
% 2.45/1.92 % (27367)Time elapsed: 0.024 s
% 2.45/1.92 % (27367)Instructions burned: 86 (million)
% 2.45/1.92 % (27367)------------------------------
% 2.45/1.92 % (27367)------------------------------
% 2.45/1.92 % (27354)Instruction limit reached!
% 2.45/1.92 % (27354)------------------------------
% 2.45/1.92 % (27354)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.92 % (27354)Termination reason: Unknown
% 2.45/1.92 % (27354)Termination phase: Saturation
% 2.45/1.92
% 2.45/1.92 % (27354)Memory used [KB]: 7164
% 2.45/1.92 % (27354)Time elapsed: 0.154 s
% 2.45/1.92 % (27354)Instructions burned: 507 (million)
% 2.45/1.92 % (27354)------------------------------
% 2.45/1.92 % (27354)------------------------------
% 2.45/1.92 % (27371)dis+10_1:1_avsq=on:cnfonf=off:e2e=on:nm=32:i=150:si=on:rtra=on_0 on DTF2THF_27107 for (2995ds/150Mi)
% 2.45/1.92 % (27372)ott+1010_1:1_au=on:s2a=on:sd=7:ss=axioms:st=1.5:i=343:si=on:rtra=on_0 on DTF2THF_27107 for (2995ds/343Mi)
% 2.45/1.93 % (27373)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_27107 for (2995ds/109Mi)
% 2.45/1.93 % (27374)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_27107 for (2995ds/253Mi)
% 2.45/1.94 % (27361)Instruction limit reached!
% 2.45/1.94 % (27361)------------------------------
% 2.45/1.94 % (27361)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.94 % (27361)Termination reason: Unknown
% 2.45/1.94 % (27361)Termination phase: Saturation
% 2.45/1.94
% 2.45/1.94 % (27361)Memory used [KB]: 2558
% 2.45/1.94 % (27361)Time elapsed: 0.117 s
% 2.45/1.94 % (27361)Instructions burned: 435 (million)
% 2.45/1.94 % (27361)------------------------------
% 2.45/1.94 % (27361)------------------------------
% 2.45/1.95 % (27375)lrs+10_1:1_au=on:cnfonf=off:sd=1:sgt=16:ss=axioms:i=140:si=on:rtra=on_0 on DTF2THF_27107 for (2995ds/140Mi)
% 2.45/1.96 % (27373)Instruction limit reached!
% 2.45/1.96 % (27373)------------------------------
% 2.45/1.96 % (27373)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.96 % (27373)Termination reason: Unknown
% 2.45/1.96 % (27373)Termination phase: Saturation
% 2.45/1.96
% 2.45/1.96 % (27373)Memory used [KB]: 6652
% 2.45/1.96 % (27373)Time elapsed: 0.031 s
% 2.45/1.96 % (27373)Instructions burned: 112 (million)
% 2.45/1.96 % (27373)------------------------------
% 2.45/1.96 % (27373)------------------------------
% 2.45/1.97 % (27376)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_27107 for (2994ds/614Mi)
% 2.45/1.97 % (27371)Instruction limit reached!
% 2.45/1.97 % (27371)------------------------------
% 2.45/1.97 % (27371)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.97 % (27371)Termination reason: Unknown
% 2.45/1.97 % (27371)Termination phase: Saturation
% 2.45/1.97
% 2.45/1.97 % (27371)Memory used [KB]: 7291
% 2.45/1.97 % (27371)Time elapsed: 0.047 s
% 2.45/1.97 % (27371)Instructions burned: 150 (million)
% 2.45/1.97 % (27371)------------------------------
% 2.45/1.97 % (27371)------------------------------
% 2.45/1.97 % (27365)Instruction limit reached!
% 2.45/1.97 % (27365)------------------------------
% 2.45/1.97 % (27365)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.97 % (27365)Termination reason: Unknown
% 2.45/1.97 % (27365)Termination phase: Saturation
% 2.45/1.97
% 2.45/1.97 % (27365)Memory used [KB]: 6268
% 2.45/1.97 % (27365)Time elapsed: 0.111 s
% 2.45/1.97 % (27365)Instructions burned: 456 (million)
% 2.45/1.97 % (27365)------------------------------
% 2.45/1.97 % (27365)------------------------------
% 2.45/1.98 % (27377)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_27107 for (2994ds/202Mi)
% 2.45/1.98 % (27378)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_27107 for (2994ds/339Mi)
% 2.45/1.99 % (27375)Refutation not found, incomplete strategy
% 2.45/1.99 % (27375)------------------------------
% 2.45/1.99 % (27375)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/1.99 % (27375)Termination reason: Refutation not found, incomplete strategy
% 2.45/1.99
% 2.45/1.99
% 2.45/1.99 % (27375)Memory used [KB]: 6268
% 2.45/1.99 % (27375)Time elapsed: 0.035 s
% 2.45/1.99 % (27375)Instructions burned: 125 (million)
% 2.45/1.99 % (27375)------------------------------
% 2.45/1.99 % (27375)------------------------------
% 2.45/2.00 % (27379)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_27107 for (2994ds/283Mi)
% 2.45/2.00 % (27374)Instruction limit reached!
% 2.45/2.00 % (27374)------------------------------
% 2.45/2.00 % (27374)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.45/2.00 % (27374)Termination reason: Unknown
% 2.45/2.00 % (27374)Termination phase: Saturation
% 2.45/2.00
% 2.45/2.00 % (27374)Memory used [KB]: 7803
% 2.45/2.00 % (27374)Time elapsed: 0.078 s
% 2.45/2.00 % (27374)Instructions burned: 253 (million)
% 2.45/2.00 % (27374)------------------------------
% 2.45/2.00 % (27374)------------------------------
% 6.35/2.01 % (27380)dis+2_1:1_cha=on:hud=7:nwc=3.0:prag=on:tnu=2:i=134:si=on:rtra=on_0 on DTF2THF_27107 for (2994ds/134Mi)
% 6.35/2.03 % (27372)Instruction limit reached!
% 6.35/2.03 % (27372)------------------------------
% 6.35/2.03 % (27372)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.03 % (27372)Termination reason: Unknown
% 6.35/2.03 % (27372)Termination phase: Saturation
% 6.35/2.03
% 6.35/2.03 % (27372)Memory used [KB]: 7164
% 6.35/2.03 % (27372)Time elapsed: 0.108 s
% 6.35/2.03 % (27372)Instructions burned: 345 (million)
% 6.35/2.03 % (27372)------------------------------
% 6.35/2.03 % (27372)------------------------------
% 6.35/2.04 % (27381)dis+1010_1:64_cnfonf=lazy_simp:fd=off:i=298:si=on:rtra=on_0 on DTF2THF_27107 for (2994ds/298Mi)
% 6.35/2.04 % (27377)Instruction limit reached!
% 6.35/2.04 % (27377)------------------------------
% 6.35/2.04 % (27377)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.04 % (27377)Termination reason: Unknown
% 6.35/2.04 % (27377)Termination phase: Saturation
% 6.35/2.04
% 6.35/2.04 % (27377)Memory used [KB]: 7547
% 6.35/2.04 % (27377)Time elapsed: 0.064 s
% 6.35/2.04 % (27377)Instructions burned: 202 (million)
% 6.35/2.04 % (27377)------------------------------
% 6.35/2.04 % (27377)------------------------------
% 6.35/2.05 % (27382)lrs+2_1:8_erd=off:plsq=on:plsqr=32,1:sos=on:i=192:si=on:rtra=on_0 on DTF2THF_27107 for (2994ds/192Mi)
% 6.35/2.05 % (27380)Instruction limit reached!
% 6.35/2.05 % (27380)------------------------------
% 6.35/2.05 % (27380)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.05 % (27380)Termination reason: Unknown
% 6.35/2.05 % (27380)Termination phase: Saturation
% 6.35/2.05
% 6.35/2.05 % (27380)Memory used [KB]: 6780
% 6.35/2.05 % (27380)Time elapsed: 0.040 s
% 6.35/2.05 % (27380)Instructions burned: 136 (million)
% 6.35/2.05 % (27380)------------------------------
% 6.35/2.05 % (27380)------------------------------
% 6.35/2.06 % (27383)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_27107 for (2994ds/258Mi)
% 6.35/2.08 % (27378)Instruction limit reached!
% 6.35/2.08 % (27378)------------------------------
% 6.35/2.08 % (27378)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.08 % (27378)Termination reason: Unknown
% 6.35/2.08 % (27378)Termination phase: Saturation
% 6.35/2.08
% 6.35/2.08 % (27378)Memory used [KB]: 7291
% 6.35/2.08 % (27378)Time elapsed: 0.100 s
% 6.35/2.08 % (27378)Instructions burned: 341 (million)
% 6.35/2.08 % (27378)------------------------------
% 6.35/2.08 % (27378)------------------------------
% 6.35/2.09 % (27384)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_27107 for (2993ds/90Mi)
% 6.35/2.10 % (27382)Instruction limit reached!
% 6.35/2.10 % (27382)------------------------------
% 6.35/2.10 % (27382)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.35/2.10 % (27382)Termination reason: Unknown
% 6.35/2.10 % (27382)Termination phase: Saturation
% 6.35/2.10
% 6.35/2.10 % (27382)Memory used [KB]: 7036
% 6.35/2.10 % (27382)Time elapsed: 0.056 s
% 6.35/2.10 % (27382)Instructions burned: 193 (million)
% 6.35/2.10 % (27382)------------------------------
% 6.35/2.10 % (27382)------------------------------
% 6.90/2.11 % (27385)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_27107 for (2993ds/231Mi)
% 6.90/2.11 % (27381)Instruction limit reached!
% 6.90/2.11 % (27381)------------------------------
% 6.90/2.11 % (27381)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.11 % (27381)Termination reason: Unknown
% 6.90/2.11 % (27381)Termination phase: Saturation
% 6.90/2.11
% 6.90/2.11 % (27381)Memory used [KB]: 6396
% 6.90/2.11 % (27381)Time elapsed: 0.077 s
% 6.90/2.11 % (27381)Instructions burned: 299 (million)
% 6.90/2.11 % (27381)------------------------------
% 6.90/2.11 % (27381)------------------------------
% 6.90/2.11 % (27384)Instruction limit reached!
% 6.90/2.11 % (27384)------------------------------
% 6.90/2.11 % (27384)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.11 % (27384)Termination reason: Unknown
% 6.90/2.11 % (27384)Termination phase: Saturation
% 6.90/2.11
% 6.90/2.11 % (27384)Memory used [KB]: 6524
% 6.90/2.11 % (27384)Time elapsed: 0.026 s
% 6.90/2.11 % (27384)Instructions burned: 91 (million)
% 6.90/2.11 % (27384)------------------------------
% 6.90/2.11 % (27384)------------------------------
% 6.90/2.12 % (27386)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_27107 for (2993ds/458Mi)
% 6.90/2.12 % (27387)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_27107 for (2993ds/31Mi)
% 6.90/2.13 % (27379)Instruction limit reached!
% 6.90/2.13 % (27379)------------------------------
% 6.90/2.13 % (27379)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.13 % (27379)Termination reason: Unknown
% 6.90/2.13 % (27379)Termination phase: Saturation
% 6.90/2.13
% 6.90/2.13 % (27379)Memory used [KB]: 8059
% 6.90/2.13 % (27379)Time elapsed: 0.133 s
% 6.90/2.13 % (27379)Instructions burned: 284 (million)
% 6.90/2.13 % (27379)------------------------------
% 6.90/2.13 % (27379)------------------------------
% 6.90/2.13 % (27387)Instruction limit reached!
% 6.90/2.13 % (27387)------------------------------
% 6.90/2.13 % (27387)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.13 % (27387)Termination reason: Unknown
% 6.90/2.13 % (27387)Termination phase: Property scanning
% 6.90/2.13
% 6.90/2.13 % (27387)Memory used [KB]: 1535
% 6.90/2.13 % (27387)Time elapsed: 0.010 s
% 6.90/2.13 % (27387)Instructions burned: 32 (million)
% 6.90/2.13 % (27387)------------------------------
% 6.90/2.13 % (27387)------------------------------
% 6.90/2.14 % (27388)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_27107 for (2993ds/297Mi)
% 6.90/2.14 % (27383)Instruction limit reached!
% 6.90/2.14 % (27383)------------------------------
% 6.90/2.14 % (27383)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.14 % (27383)Termination reason: Unknown
% 6.90/2.14 % (27383)Termination phase: Saturation
% 6.90/2.14
% 6.90/2.14 % (27383)Memory used [KB]: 7036
% 6.90/2.14 % (27383)Time elapsed: 0.100 s
% 6.90/2.14 % (27383)Instructions burned: 260 (million)
% 6.90/2.14 % (27383)------------------------------
% 6.90/2.14 % (27383)------------------------------
% 6.90/2.14 % (27389)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_27107 for (2993ds/987Mi)
% 6.90/2.14 % (27358)Instruction limit reached!
% 6.90/2.14 % (27358)------------------------------
% 6.90/2.14 % (27358)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.14 % (27358)Termination reason: Unknown
% 6.90/2.14 % (27358)Termination phase: Saturation
% 6.90/2.14
% 6.90/2.14 % (27358)Memory used [KB]: 9850
% 6.90/2.14 % (27358)Time elapsed: 0.353 s
% 6.90/2.14 % (27358)Instructions burned: 1089 (million)
% 6.90/2.14 % (27358)------------------------------
% 6.90/2.14 % (27358)------------------------------
% 6.90/2.15 % (27390)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_27107 for (2993ds/182Mi)
% 6.90/2.15 % (27391)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_27107 for (2993ds/182Mi)
% 6.90/2.16 % (27376)Instruction limit reached!
% 6.90/2.16 % (27376)------------------------------
% 6.90/2.16 % (27376)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.16 % (27376)Termination reason: Unknown
% 6.90/2.16 % (27376)Termination phase: Saturation
% 6.90/2.16
% 6.90/2.16 % (27376)Memory used [KB]: 7931
% 6.90/2.16 % (27376)Time elapsed: 0.192 s
% 6.90/2.16 % (27376)Instructions burned: 616 (million)
% 6.90/2.16 % (27376)------------------------------
% 6.90/2.16 % (27376)------------------------------
% 6.90/2.17 % (27392)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_27107 for (2992ds/154Mi)
% 6.90/2.18 % (27385)Instruction limit reached!
% 6.90/2.18 % (27385)------------------------------
% 6.90/2.18 % (27385)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 6.90/2.18 % (27385)Termination reason: Unknown
% 6.90/2.18 % (27385)Termination phase: Saturation
% 6.90/2.18
% 6.90/2.18 % (27385)Memory used [KB]: 9338
% 6.90/2.18 % (27385)Time elapsed: 0.093 s
% 6.90/2.18 % (27385)Instructions burned: 232 (million)
% 6.90/2.18 % (27385)------------------------------
% 6.90/2.18 % (27385)------------------------------
% 6.90/2.19 % (27393)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_27107 for (2992ds/79Mi)
% 7.33/2.20 % (27390)Instruction limit reached!
% 7.33/2.20 % (27390)------------------------------
% 7.33/2.20 % (27390)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.20 % (27390)Termination reason: Unknown
% 7.33/2.20 % (27390)Termination phase: Saturation
% 7.33/2.20
% 7.33/2.20 % (27390)Memory used [KB]: 6908
% 7.33/2.20 % (27390)Time elapsed: 0.055 s
% 7.33/2.20 % (27390)Instructions burned: 182 (million)
% 7.33/2.20 % (27390)------------------------------
% 7.33/2.20 % (27390)------------------------------
% 7.33/2.21 % (27392)Instruction limit reached!
% 7.33/2.21 % (27392)------------------------------
% 7.33/2.21 % (27392)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.21 % (27392)Termination reason: Unknown
% 7.33/2.21 % (27392)Termination phase: Saturation
% 7.33/2.21
% 7.33/2.21 % (27392)Memory used [KB]: 6140
% 7.33/2.21 % (27392)Time elapsed: 0.040 s
% 7.33/2.21 % (27392)Instructions burned: 158 (million)
% 7.33/2.21 % (27392)------------------------------
% 7.33/2.21 % (27392)------------------------------
% 7.33/2.21 % (27391)Instruction limit reached!
% 7.33/2.21 % (27391)------------------------------
% 7.33/2.21 % (27391)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.21 % (27391)Termination reason: Unknown
% 7.33/2.21 % (27391)Termination phase: Saturation
% 7.33/2.21
% 7.33/2.21 % (27391)Memory used [KB]: 8699
% 7.33/2.21 % (27391)Time elapsed: 0.086 s
% 7.33/2.21 % (27391)Instructions burned: 184 (million)
% 7.33/2.21 % (27391)------------------------------
% 7.33/2.21 % (27391)------------------------------
% 7.33/2.21 % (27393)Instruction limit reached!
% 7.33/2.21 % (27393)------------------------------
% 7.33/2.21 % (27393)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.21 % (27393)Termination reason: Unknown
% 7.33/2.21 % (27393)Termination phase: Saturation
% 7.33/2.21
% 7.33/2.21 % (27393)Memory used [KB]: 6268
% 7.33/2.21 % (27393)Time elapsed: 0.022 s
% 7.33/2.21 % (27393)Instructions burned: 79 (million)
% 7.33/2.21 % (27393)------------------------------
% 7.33/2.21 % (27393)------------------------------
% 7.33/2.21 % (27394)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_27107 for (2992ds/216Mi)
% 7.33/2.21 % (27395)lrs+1002_1:1_fe=off:hud=10:ins=2:sac=on:sp=const_frequency:i=114:si=on:rtra=on_0 on DTF2THF_27107 for (2992ds/114Mi)
% 7.33/2.22 % (27388)Instruction limit reached!
% 7.33/2.22 % (27388)------------------------------
% 7.33/2.22 % (27388)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.22 % (27388)Termination reason: Unknown
% 7.33/2.22 % (27388)Termination phase: Saturation
% 7.33/2.22
% 7.33/2.22 % (27388)Memory used [KB]: 7291
% 7.33/2.22 % (27388)Time elapsed: 0.104 s
% 7.33/2.22 % (27388)Instructions burned: 299 (million)
% 7.33/2.22 % (27388)------------------------------
% 7.33/2.22 % (27388)------------------------------
% 7.33/2.22 % (27396)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_27107 for (2992ds/922Mi)
% 7.33/2.22 % (27397)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_27107 for (2992ds/182Mi)
% 7.33/2.23 % (27398)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_27107 for (2992ds/164Mi)
% 7.33/2.25 % (27395)Instruction limit reached!
% 7.33/2.25 % (27395)------------------------------
% 7.33/2.25 % (27395)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.25 % (27395)Termination reason: Unknown
% 7.33/2.25 % (27395)Termination phase: Saturation
% 7.33/2.25
% 7.33/2.25 % (27395)Memory used [KB]: 6780
% 7.33/2.25 % (27395)Time elapsed: 0.033 s
% 7.33/2.25 % (27395)Instructions burned: 117 (million)
% 7.33/2.25 % (27395)------------------------------
% 7.33/2.25 % (27395)------------------------------
% 7.33/2.26 % (27399)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_27107 for (2991ds/50Mi)
% 7.33/2.26 % (27386)Instruction limit reached!
% 7.33/2.26 % (27386)------------------------------
% 7.33/2.26 % (27386)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.26 % (27386)Termination reason: Unknown
% 7.33/2.26 % (27386)Termination phase: Saturation
% 7.33/2.26
% 7.33/2.26 % (27386)Memory used [KB]: 7419
% 7.33/2.26 % (27386)Time elapsed: 0.165 s
% 7.33/2.26 % (27386)Instructions burned: 458 (million)
% 7.33/2.26 % (27386)------------------------------
% 7.33/2.26 % (27386)------------------------------
% 7.33/2.27 % (27394)Instruction limit reached!
% 7.33/2.27 % (27394)------------------------------
% 7.33/2.27 % (27394)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.27 % (27394)Termination reason: Unknown
% 7.33/2.27 % (27394)Termination phase: Saturation
% 7.33/2.27
% 7.33/2.27 % (27394)Memory used [KB]: 7036
% 7.33/2.27 % (27394)Time elapsed: 0.054 s
% 7.33/2.27 % (27394)Instructions burned: 217 (million)
% 7.33/2.27 % (27394)------------------------------
% 7.33/2.27 % (27394)------------------------------
% 7.33/2.27 % (27397)Instruction limit reached!
% 7.33/2.27 % (27397)------------------------------
% 7.33/2.27 % (27397)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.27 % (27397)Termination reason: Unknown
% 7.33/2.27 % (27397)Termination phase: Saturation
% 7.33/2.27
% 7.33/2.27 % (27397)Memory used [KB]: 6268
% 7.33/2.27 % (27397)Time elapsed: 0.046 s
% 7.33/2.27 % (27397)Instructions burned: 183 (million)
% 7.33/2.27 % (27397)------------------------------
% 7.33/2.27 % (27397)------------------------------
% 7.33/2.27 % (27399)Instruction limit reached!
% 7.33/2.27 % (27399)------------------------------
% 7.33/2.27 % (27399)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.27 % (27399)Termination reason: Unknown
% 7.33/2.27 % (27399)Termination phase: Saturation
% 7.33/2.27
% 7.33/2.27 % (27399)Memory used [KB]: 10618
% 7.33/2.27 % (27399)Time elapsed: 0.014 s
% 7.33/2.27 % (27399)Instructions burned: 50 (million)
% 7.33/2.27 % (27399)------------------------------
% 7.33/2.27 % (27399)------------------------------
% 7.33/2.27 % (27400)dis-30_1:1_acc=on:bd=off:fsr=off:plsq=on:plsqr=32,1:i=368:si=on:rtra=on_0 on DTF2THF_27107 for (2991ds/368Mi)
% 7.33/2.28 % (27402)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_27107 for (2991ds/267Mi)
% 7.33/2.28 % (27403)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_27107 for (2991ds/204Mi)
% 7.33/2.28 % (27398)Instruction limit reached!
% 7.33/2.28 % (27398)------------------------------
% 7.33/2.28 % (27398)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 7.33/2.28 % (27398)Termination reason: Unknown
% 7.33/2.28 % (27398)Termination phase: Saturation
% 7.33/2.28
% 7.33/2.28 % (27398)Memory used [KB]: 2046
% 7.33/2.28 % (27398)Time elapsed: 0.053 s
% 7.33/2.28 % (27398)Instructions burned: 164 (million)
% 7.33/2.28 % (27398)------------------------------
% 7.33/2.28 % (27398)------------------------------
% 7.33/2.28 % (27401)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_27107 for (2991ds/1021Mi)
% 7.33/2.29 % (27404)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_27107 for (2991ds/26Mi)
% 8.03/2.30 % (27404)Instruction limit reached!
% 8.03/2.30 % (27404)------------------------------
% 8.03/2.30 % (27404)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.30 % (27404)Termination reason: Unknown
% 8.03/2.30 % (27404)Termination phase: Property scanning
% 8.03/2.30
% 8.03/2.30 % (27404)Memory used [KB]: 1535
% 8.03/2.30 % (27404)Time elapsed: 0.009 s
% 8.03/2.30 % (27404)Instructions burned: 29 (million)
% 8.03/2.30 % (27404)------------------------------
% 8.03/2.30 % (27404)------------------------------
% 8.03/2.31 % (27405)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_27107 for (2991ds/53Mi)
% 8.03/2.33 % (27405)Instruction limit reached!
% 8.03/2.33 % (27405)------------------------------
% 8.03/2.33 % (27405)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.33 % (27405)Termination reason: Unknown
% 8.03/2.33 % (27405)Termination phase: Saturation
% 8.03/2.33
% 8.03/2.33 % (27405)Memory used [KB]: 6140
% 8.03/2.33 % (27405)Time elapsed: 0.017 s
% 8.03/2.33 % (27405)Instructions burned: 56 (million)
% 8.03/2.33 % (27405)------------------------------
% 8.03/2.33 % (27405)------------------------------
% 8.03/2.34 % (27406)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_27107 for (2991ds/4436Mi)
% 8.03/2.34 % (27403)Instruction limit reached!
% 8.03/2.34 % (27403)------------------------------
% 8.03/2.34 % (27403)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.34 % (27403)Termination reason: Unknown
% 8.03/2.34 % (27403)Termination phase: Saturation
% 8.03/2.34
% 8.03/2.34 % (27403)Memory used [KB]: 6908
% 8.03/2.34 % (27403)Time elapsed: 0.062 s
% 8.03/2.34 % (27403)Instructions burned: 204 (million)
% 8.03/2.34 % (27403)------------------------------
% 8.03/2.34 % (27403)------------------------------
% 8.03/2.34 % (27402)Instruction limit reached!
% 8.03/2.34 % (27402)------------------------------
% 8.03/2.34 % (27402)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.34 % (27402)Termination reason: Unknown
% 8.03/2.34 % (27402)Termination phase: Saturation
% 8.03/2.34
% 8.03/2.34 % (27402)Memory used [KB]: 8059
% 8.03/2.34 % (27402)Time elapsed: 0.069 s
% 8.03/2.34 % (27402)Instructions burned: 270 (million)
% 8.03/2.34 % (27402)------------------------------
% 8.03/2.34 % (27402)------------------------------
% 8.03/2.35 % (27407)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_27107 for (2991ds/1539Mi)
% 8.03/2.35 % (27408)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_27107 for (2991ds/408Mi)
% 8.03/2.38 % (27389)Instruction limit reached!
% 8.03/2.38 % (27389)------------------------------
% 8.03/2.38 % (27389)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.38 % (27389)Termination reason: Unknown
% 8.03/2.38 % (27389)Termination phase: Saturation
% 8.03/2.38
% 8.03/2.38 % (27389)Memory used [KB]: 7803
% 8.03/2.38 % (27389)Time elapsed: 0.260 s
% 8.03/2.38 % (27389)Instructions burned: 989 (million)
% 8.03/2.38 % (27389)------------------------------
% 8.03/2.38 % (27389)------------------------------
% 8.03/2.39 % (27400)Instruction limit reached!
% 8.03/2.39 % (27400)------------------------------
% 8.03/2.39 % (27400)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.03/2.39 % (27400)Termination reason: Unknown
% 8.03/2.39 % (27400)Termination phase: Saturation
% 8.03/2.39
% 8.03/2.39 % (27400)Memory used [KB]: 7291
% 8.03/2.39 % (27400)Time elapsed: 0.114 s
% 8.03/2.39 % (27400)Instructions burned: 369 (million)
% 8.03/2.39 % (27400)------------------------------
% 8.03/2.39 % (27400)------------------------------
% 8.03/2.39 % (27409)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_27107 for (2990ds/5205Mi)
% 8.59/2.40 % (27410)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_27107 for (2990ds/1913Mi)
% 8.59/2.49 % (27408)Instruction limit reached!
% 8.59/2.49 % (27408)------------------------------
% 8.59/2.49 % (27408)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.59/2.49 % (27408)Termination reason: Unknown
% 8.59/2.49 % (27408)Termination phase: Saturation
% 8.59/2.49
% 8.59/2.49 % (27408)Memory used [KB]: 8443
% 8.59/2.49 % (27408)Time elapsed: 0.133 s
% 8.59/2.49 % (27408)Instructions burned: 410 (million)
% 8.59/2.49 % (27408)------------------------------
% 8.59/2.49 % (27408)------------------------------
% 8.59/2.50 % (27411)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_27107 for (2989ds/4350Mi)
% 8.73/2.51 % (27396)Instruction limit reached!
% 8.73/2.51 % (27396)------------------------------
% 8.73/2.51 % (27396)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.51 % (27396)Termination reason: Unknown
% 8.73/2.51 % (27396)Termination phase: Saturation
% 8.73/2.51
% 8.73/2.51 % (27396)Memory used [KB]: 9083
% 8.73/2.51 % (27396)Time elapsed: 0.287 s
% 8.73/2.51 % (27396)Instructions burned: 922 (million)
% 8.73/2.51 % (27396)------------------------------
% 8.73/2.51 % (27396)------------------------------
% 8.73/2.52 % (27412)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_27107 for (2989ds/68Mi)
% 8.73/2.54 % (27412)Instruction limit reached!
% 8.73/2.54 % (27412)------------------------------
% 8.73/2.54 % (27412)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 8.73/2.54 % (27412)Termination reason: Unknown
% 8.73/2.54 % (27412)Termination phase: Saturation
% 8.73/2.54
% 8.73/2.54 % (27412)Memory used [KB]: 6268
% 8.73/2.54 % (27412)Time elapsed: 0.019 s
% 8.73/2.54 % (27412)Instructions burned: 69 (million)
% 8.73/2.54 % (27412)------------------------------
% 8.73/2.54 % (27412)------------------------------
% 8.73/2.54 % (27413)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_27107 for (2989ds/358Mi)
% 9.05/2.62 % (27401)Instruction limit reached!
% 9.05/2.62 % (27401)------------------------------
% 9.05/2.62 % (27401)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.62 % (27401)Termination reason: Unknown
% 9.05/2.62 % (27401)Termination phase: Saturation
% 9.05/2.62
% 9.05/2.62 % (27401)Memory used [KB]: 9594
% 9.05/2.62 % (27401)Time elapsed: 0.341 s
% 9.05/2.62 % (27401)Instructions burned: 1024 (million)
% 9.05/2.62 % (27401)------------------------------
% 9.05/2.62 % (27401)------------------------------
% 9.05/2.63 % (27414)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_27107 for (2988ds/31Mi)
% 9.05/2.64 % (27414)Instruction limit reached!
% 9.05/2.64 % (27414)------------------------------
% 9.05/2.64 % (27414)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.64 % (27414)Termination reason: Unknown
% 9.05/2.64 % (27414)Termination phase: Property scanning
% 9.05/2.64
% 9.05/2.64 % (27414)Memory used [KB]: 1535
% 9.05/2.64 % (27414)Time elapsed: 0.010 s
% 9.05/2.64 % (27414)Instructions burned: 33 (million)
% 9.05/2.64 % (27414)------------------------------
% 9.05/2.64 % (27414)------------------------------
% 9.05/2.65 % (27413)Instruction limit reached!
% 9.05/2.65 % (27413)------------------------------
% 9.05/2.65 % (27413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.05/2.65 % (27413)Termination reason: Unknown
% 9.05/2.65 % (27413)Termination phase: Saturation
% 9.05/2.65
% 9.05/2.65 % (27413)Memory used [KB]: 7164
% 9.05/2.65 % (27413)Time elapsed: 0.107 s
% 9.05/2.65 % (27413)Instructions burned: 359 (million)
% 9.05/2.65 % (27413)------------------------------
% 9.05/2.65 % (27413)------------------------------
% 9.05/2.65 % (27415)lrs+10_1:1_cnfonf=lazy_simp:sgt=5:sos=on:ss=axioms:i=279:si=on:rtra=on_0 on DTF2THF_27107 for (2988ds/279Mi)
% 9.05/2.66 % (27416)lrs+10_8:1_au=on:fde=none:slsq=on:i=258:si=on:rtra=on_0 on DTF2THF_27107 for (2987ds/258Mi)
% 9.54/2.72 % (27415)Instruction limit reached!
% 9.54/2.72 % (27415)------------------------------
% 9.54/2.72 % (27415)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.72 % (27415)Termination reason: Unknown
% 9.54/2.72 % (27415)Termination phase: Saturation
% 9.54/2.72
% 9.54/2.72 % (27415)Memory used [KB]: 6396
% 9.54/2.72 % (27415)Time elapsed: 0.072 s
% 9.54/2.72 % (27415)Instructions burned: 279 (million)
% 9.54/2.72 % (27415)------------------------------
% 9.54/2.72 % (27415)------------------------------
% 9.54/2.72 % (27407)First to succeed.
% 9.54/2.73 % (27407)Refutation found. Thanks to Tanya!
% 9.54/2.73 % SZS status Theorem for DTF2THF_27107
% 9.54/2.73 % SZS output start Proof for DTF2THF_27107
% 9.54/2.73 thf(func_def_0, type, in: $i > $i > $o).
% 9.54/2.73 thf(func_def_1, type, exu: ($i > $o) > $o).
% 9.54/2.73 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 9.54/2.73 thf(func_def_8, type, powerset: $i > $i).
% 9.54/2.73 thf(func_def_10, type, setunion: $i > $i).
% 9.54/2.73 thf(func_def_19, type, descr: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_26, type, prop2set: $o > $i).
% 9.54/2.73 thf(func_def_36, type, nonempty: $i > $o).
% 9.54/2.73 thf(func_def_69, type, set2prop: $i > $o).
% 9.54/2.73 thf(func_def_88, type, subset: $i > $i > $o).
% 9.54/2.73 thf(func_def_89, type, disjoint: $i > $i > $o).
% 9.54/2.73 thf(func_def_90, type, setsmeet: $i > $i > $o).
% 9.54/2.73 thf(func_def_114, type, binunion: $i > $i > $i).
% 9.54/2.73 thf(func_def_139, type, sK5: $i > $i).
% 9.54/2.73 thf(func_def_140, type, sK6: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_141, type, sK7: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_142, type, sK8: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_143, type, sK9: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_144, type, sK10: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_145, type, sK11: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_146, type, sK12: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_147, type, sK13: ($i > $o) > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_148, type, sK14: ($i > $o) > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_149, type, sK15: $i > $i).
% 9.54/2.73 thf(func_def_150, type, sK16: $i > $i).
% 9.54/2.73 thf(func_def_151, type, sK17: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_152, type, sK18: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_153, type, sK19: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_154, type, sK20: $i > $i > $i).
% 9.54/2.73 thf(func_def_155, type, sK21: ($i > $o) > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_156, type, sK22: ($i > $o) > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_157, type, sK23: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_158, type, sK24: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_159, type, sK25: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_160, type, sK26: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_161, type, sK27: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_162, type, sK28: $i > $i > $i).
% 9.54/2.73 thf(func_def_163, type, sK29: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_164, type, sK30: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_165, type, sK31: $i > $i > $i).
% 9.54/2.73 thf(func_def_166, type, sK32: $i > $i > $i).
% 9.54/2.73 thf(func_def_167, type, sK33: $i > $i > $i).
% 9.54/2.73 thf(func_def_168, type, sK34: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_169, type, sK35: $i > $i > $i).
% 9.54/2.73 thf(func_def_170, type, sK36: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_171, type, sK37: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_172, type, sK38: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_173, type, sK39: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_174, type, sK40: $o > $i > $i > $i).
% 9.54/2.73 thf(func_def_175, type, sK41: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_176, type, sK42: $i > $i).
% 9.54/2.73 thf(func_def_177, type, sK43: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_178, type, sK44: $i > ($i > $i > $o) > $i).
% 9.54/2.73 thf(func_def_179, type, sK45: $i > ($i > $i > $o) > $i).
% 9.54/2.73 thf(func_def_180, type, sK46: $i > $i > ($i > $i > $o) > $i).
% 9.54/2.73 thf(func_def_181, type, sK47: ($i > $o) > $i > ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_182, type, sK48: $i > $i > ($i > $o) > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_183, type, sK49: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_184, type, sK50: $i > $i > $i).
% 9.54/2.73 thf(func_def_185, type, sK51: $i > $i).
% 9.54/2.73 thf(func_def_186, type, sK52: $i > $i > $i > $i).
% 9.54/2.73 thf(func_def_187, type, sK53: $i > $i > $i).
% 9.54/2.73 thf(func_def_188, type, sK54: $i > $i > $i).
% 9.54/2.73 thf(func_def_189, type, sK55: $i > $i > $i).
% 9.54/2.73 thf(func_def_190, type, sK56: $i > $i > $i).
% 9.54/2.73 thf(func_def_191, type, sK57: $i > $i > $i).
% 9.54/2.73 thf(func_def_192, type, sK58: $i > $i > $i).
% 9.54/2.73 thf(func_def_193, type, sK59: $i > $i).
% 9.54/2.73 thf(func_def_194, type, sK60: ($i > $o) > $i).
% 9.54/2.73 thf(func_def_195, type, sK61: ($i > $o) > $i > $i).
% 9.54/2.73 thf(func_def_196, type, sK62: $i > $i).
% 9.54/2.73 thf(func_def_197, type, sK63: $i > ($i > $o) > $i).
% 9.54/2.73 thf(func_def_198, type, ph64: !>[X0: $tType]:(X0)).
% 9.54/2.73 thf(func_def_200, type, sK66: $i > $i > $i > $i).
% 9.54/2.73 thf(func_def_201, type, sK67: $i > $i > $i).
% 9.54/2.73 thf(func_def_202, type, sK68: $i > $i > $i).
% 9.54/2.73 thf(func_def_203, type, sK69: $i > $i > $i).
% 9.54/2.73 thf(func_def_204, type, sK70: $i > $i).
% 9.54/2.73 thf(func_def_205, type, sK71: $i > $i > $i).
% 9.54/2.73 thf(func_def_206, type, sK72: $i > $i > $i).
% 9.54/2.73 thf(func_def_207, type, sK73: $i > $i).
% 9.54/2.73 thf(func_def_208, type, sK74: $i > $i).
% 9.54/2.73 thf(func_def_209, type, sK75: $i > $i > $i).
% 9.54/2.73 thf(func_def_211, type, sK77: $i > $i > $i > $i).
% 9.54/2.73 thf(func_def_212, type, sK78: $i > $i).
% 9.54/2.73 thf(func_def_213, type, sK79: $i > $i > $i).
% 9.54/2.73 thf(func_def_214, type, sK80: $i > $i > $i).
% 9.54/2.73 thf(func_def_215, type, sK81: $i > $i > $i).
% 9.54/2.73 thf(func_def_216, type, sK82: $i > $i > $i).
% 9.54/2.73 thf(func_def_217, type, sK83: $i > $i > $i).
% 9.54/2.73 thf(func_def_218, type, sK84: $i > $i > $i).
% 9.54/2.73 thf(func_def_219, type, sK85: $i > $i > $i).
% 9.54/2.73 thf(func_def_220, type, sK86: $i > $i > $i).
% 9.54/2.73 thf(f4395,plain,(
% 9.54/2.73 $false),
% 9.54/2.73 inference(avatar_sat_refutation,[status(thm)],[f1643,f1667,f1673,f2189,f3634,f4283,f4384,f4386,f4392])).
% 9.54/2.73 thf(f4392,plain,(
% 9.54/2.73 (sK0 != sK76) | ((in @ sK3 @ sK76) != $true) | ((in @ sK3 @ sK0) = $true)),
% 9.54/2.73 introduced(definition,[],[theory_tautology_sat_conflict])).
% 9.54/2.73 thf(f4386,plain,(
% 9.54/2.73 (sK2 != sK76) | ((in @ sK3 @ sK76) != $true) | ((in @ sK3 @ sK2) = $true)),
% 9.54/2.73 introduced(definition,[],[theory_tautology_sat_conflict])).
% 9.54/2.73 thf(f4384,plain,(
% 9.54/2.73 spl4_15 | spl4_16 | ~spl4_14),
% 9.54/2.73 inference(avatar_split_clause,[status(thm)],[f4371,f4280,f4381,f4377])).
% 9.54/2.73 thf(f4377,definition,(
% 9.54/2.73 spl4_15 <=> (sK2 = sK76)),
% 9.54/2.73 introduced(definition,[new_symbols(naming,[spl4_15])],[avatar_definition])).
% 9.54/2.73 thf(f4381,definition,(
% 9.54/2.73 spl4_16 <=> (sK0 = sK76)),
% 9.54/2.73 introduced(definition,[new_symbols(naming,[spl4_16])],[avatar_definition])).
% 9.54/2.73 thf(f4280,definition,(
% 9.54/2.73 spl4_14 <=> ($true = (in @ sK76 @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset))))),
% 9.54/2.73 introduced(definition,[new_symbols(naming,[spl4_14])],[avatar_definition])).
% 9.54/2.73 thf(f4371,plain,(
% 9.54/2.73 (sK2 = sK76) | (sK0 = sK76) | ~spl4_14),
% 9.54/2.73 inference(trivial_inequality_removal,[status(thm)],[f4356])).
% 9.54/2.73 thf(f4356,plain,(
% 9.54/2.73 (sK2 = sK76) | (sK0 = sK76) | ($false = $true) | ~spl4_14),
% 9.54/2.73 inference(superposition,[status(thm)],[f1075,f4282])).
% 9.54/2.73 thf(f4282,plain,(
% 9.54/2.73 ($true = (in @ sK76 @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset)))) | ~spl4_14),
% 9.54/2.73 inference(avatar_component_clause,[status(thm)],[f4280])).
% 9.54/2.73 thf(f1075,plain,(
% 9.54/2.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))) | (X1 = X2) | (X1 = X3)) )),
% 9.54/2.73 inference(equality_proxy_clausification,[status(thm)],[f1074])).
% 9.54/2.73 thf(f1074,plain,(
% 9.54/2.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))) | ((X3 = X1) = $true) | (X1 = X2)) )),
% 9.54/2.73 inference(equality_proxy_clausification,[status(thm)],[f1073])).
% 9.54/2.73 thf(f1073,plain,(
% 9.54/2.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($false = (in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset)))) | ((X2 = X1) = $true) | ((X3 = X1) = $true)) )),
% 9.54/2.73 inference(binary_proxy_clausification,[status(thm)],[f1072])).
% 9.54/2.73 thf(f1072,plain,(
% 9.54/2.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((X2 = X1) | (X3 = X1)) = $true) | ($false = (in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))))) )),
% 9.54/2.73 inference(binary_proxy_clausification,[status(thm)],[f1071])).
% 9.54/2.73 thf(f1071,plain,(
% 9.54/2.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ X3 @ emptyset))) => ((X2 = X1) | (X3 = X1))) = $true)) )),
% 9.54/2.73 inference(beta_eta_normalization,[status(thm)],[f1070])).
% 9.54/2.73 thf(f1070,plain,(
% 9.54/2.73 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset))) => ((X2 = X1) | (Y0 = X1)))) @ X3) = $true)) )),
% 9.54/2.73 inference(pi_clausification,[status(thm)],[f1069])).
% 9.54/2.73 thf(f1069,plain,(
% 9.54/2.73 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ X1 @ (setadjoin @ X2 @ (setadjoin @ Y0 @ emptyset))) => ((X2 = X1) | (Y0 = X1))))) = $true)) )),
% 9.54/2.73 inference(beta_eta_normalization,[status(thm)],[f1068])).
% 9.54/2.73 thf(f1068,plain,(
% 9.54/2.73 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => ((Y0 = X1) | (Y1 = X1)))))) @ X2) = $true)) )),
% 9.54/2.73 inference(pi_clausification,[status(thm)],[f1067])).
% 9.54/2.73 thf(f1067,plain,(
% 9.54/2.73 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ X1 @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset))) => ((Y0 = X1) | (Y1 = X1))))))))) )),
% 9.54/2.73 inference(beta_eta_normalization,[status(thm)],[f1066])).
% 9.54/2.73 thf(f1066,plain,(
% 9.54/2.73 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y0)))))))) @ X1))) )),
% 9.54/2.73 inference(pi_clausification,[status(thm)],[f627])).
% 9.54/2.73 thf(f627,plain,(
% 9.54/2.73 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y0))))))))) = $true)),
% 9.54/2.73 inference(definition_unfolding,[status(thm)],[f522,f358])).
% 9.54/2.73 thf(f358,plain,(
% 9.54/2.73 (upairsetE = $true)),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f315])).
% 9.54/2.73 thf(f315,plain,(
% 9.54/2.73 (setextsub = $true) & (powerset__Cong = $true) & (omegaIndAx = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (notdallE = $true) & (exuE1 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan1 = $true) & (exuI3 = $true) & (subsetI2 = $true) & (foundationAx = $true) & (exuI2 = $true) & (prop2set2propI = $true) & (setadjoinSub2 = $true) & (in__Cong = $true) & (descrp = $true) & (dsetconstrI = $true) & (eqimpsubset2 = $true) & (subsetE = $true) & (powersetsubset = $true) & (wellorderingAx = $true) & (((in @ sK3 @ (binunion @ sK0 @ sK2)) = $true) & ((sK1 = $true) | ((in @ sK3 @ sK2) != $true)) & (sK1 != $true) & ((sK1 = $true) | ((in @ sK3 @ sK0) != $true))) & (nonemptyI1 = $true) & (setunion__Cong = $true) & (dsetconstrER = $true) & (eqimpsubset1 = $true) & (sepSubset = $true) & (upairset2IR = $true) & (inCongP = $true) & (subsetRefl = $true) & (exuE3u = $true) & (setadjoinIL = $true) & (emptyset__Cong = $true) & (subPowSU = $true) & (quantDeMorgan2 = $true) & (subset2powerset = $true) & (exuE3e = $true) & (omega0Ax = $true) & (binunionIL = $true) & (vacuousDall = $true) & (nonemptyE1 = $true) & (setadjoinE = $true) & (prop2setI = $true) & (powersetI1 = $true) & (sepInPowerset = $true) & (notequalI1 = $true) & (setext = $true) & (setadjoinAx = $true) & (omega__Cong = $true) & (setextAx = $true) & (replAx = $true) & (powersetI = $true) & (powersetAx = $true) & (exuE2 = $true) & (setadjoin__Cong = $true) & (setadjoinOr = $true) & (notequalI2 = $true) & (prop2setE = $true) & (quantDeMorgan4 = $true) & (setadjoinIR = $true) & (subsetI1 = $true) & (emptyinPowerset = $true) & (emptysetE = $true) & (upairsetE = $true) & (emptyInPowerset = $true) & (exu__Cong = $true) & (subsetemptysetimpeq = $true) & (exuI1 = $true) & (subsetE2 = $true) & (exuEu = $true) & (upairsetIL = $true) & (inPowerset = $true) & (binunionIR = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (subsetTrans = $true) & (setunionAx = $true) & (notinemptyset = $true) & (powersetE = $true) & (setunionI = $true) & (upairsetIR = $true) & (dsetconstrEL = $true) & (nonemptyImpWitness = $true) & (emptysetAx = $true) & (emptysetsubset = $true) & (emptyinunitempty = $true) & (notsubsetI = $true) & (setadjoinSub = $true) & (setunionE = $true) & (notdexE = $true) & (emptyE1 = $true) & (eqinunit = $true) & (notinsingleton = $true) & (nonemptyI = $true) & (setoftrueEq = $true) & (emptysetimpfalse = $true) & (uniqinunit = $true) & (setbeta = $true) & (singletonsswitch = $true) & (emptyI = $true) & (powersetE1 = $true)),
% 9.54/2.73 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3])],[f313,f314])).
% 9.54/2.73 thf(f314,plain,(
% 9.54/2.73 ? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) & (($true = X1) | ((in @ X3 @ X2) != $true)) & ($true != X1) & (($true = X1) | ((in @ X3 @ X0) != $true))) => (((in @ sK3 @ (binunion @ sK0 @ sK2)) = $true) & ((sK1 = $true) | ((in @ sK3 @ sK2) != $true)) & (sK1 != $true) & ((sK1 = $true) | ((in @ sK3 @ sK0) != $true)))),
% 9.54/2.73 introduced(definition,[],[choice_axiom])).
% 9.54/2.73 thf(f313,plain,(
% 9.54/2.73 (setextsub = $true) & (powerset__Cong = $true) & (omegaIndAx = $true) & (noeltsimpempty = $true) & (omegaSAx = $true) & (notdallE = $true) & (exuE1 = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan1 = $true) & (exuI3 = $true) & (subsetI2 = $true) & (foundationAx = $true) & (exuI2 = $true) & (prop2set2propI = $true) & (setadjoinSub2 = $true) & (in__Cong = $true) & (descrp = $true) & (dsetconstrI = $true) & (eqimpsubset2 = $true) & (subsetE = $true) & (powersetsubset = $true) & (wellorderingAx = $true) & ? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) & (($true = X1) | ((in @ X3 @ X2) != $true)) & ($true != X1) & (($true = X1) | ((in @ X3 @ X0) != $true))) & (nonemptyI1 = $true) & (setunion__Cong = $true) & (dsetconstrER = $true) & (eqimpsubset1 = $true) & (sepSubset = $true) & (upairset2IR = $true) & (inCongP = $true) & (subsetRefl = $true) & (exuE3u = $true) & (setadjoinIL = $true) & (emptyset__Cong = $true) & (subPowSU = $true) & (quantDeMorgan2 = $true) & (subset2powerset = $true) & (exuE3e = $true) & (omega0Ax = $true) & (binunionIL = $true) & (vacuousDall = $true) & (nonemptyE1 = $true) & (setadjoinE = $true) & (prop2setI = $true) & (powersetI1 = $true) & (sepInPowerset = $true) & (notequalI1 = $true) & (setext = $true) & (setadjoinAx = $true) & (omega__Cong = $true) & (setextAx = $true) & (replAx = $true) & (powersetI = $true) & (powersetAx = $true) & (exuE2 = $true) & (setadjoin__Cong = $true) & (setadjoinOr = $true) & (notequalI2 = $true) & (prop2setE = $true) & (quantDeMorgan4 = $true) & (setadjoinIR = $true) & (subsetI1 = $true) & (emptyinPowerset = $true) & (emptysetE = $true) & (upairsetE = $true) & (emptyInPowerset = $true) & (exu__Cong = $true) & (subsetemptysetimpeq = $true) & (exuI1 = $true) & (subsetE2 = $true) & (exuEu = $true) & (upairsetIL = $true) & (inPowerset = $true) & (binunionIR = $true) & (dsetconstr__Cong = $true) & (descr__Cong = $true) & (subsetTrans = $true) & (setunionAx = $true) & (notinemptyset = $true) & (powersetE = $true) & (setunionI = $true) & (upairsetIR = $true) & (dsetconstrEL = $true) & (nonemptyImpWitness = $true) & (emptysetAx = $true) & (emptysetsubset = $true) & (emptyinunitempty = $true) & (notsubsetI = $true) & (setadjoinSub = $true) & (setunionE = $true) & (notdexE = $true) & (emptyE1 = $true) & (eqinunit = $true) & (notinsingleton = $true) & (nonemptyI = $true) & (setoftrueEq = $true) & (emptysetimpfalse = $true) & (uniqinunit = $true) & (setbeta = $true) & (singletonsswitch = $true) & (emptyI = $true) & (powersetE1 = $true)),
% 9.54/2.73 inference(flattening,[status(thm)],[f312])).
% 9.54/2.73 thf(f312,plain,(
% 9.54/2.73 ((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (((($true != X1) & (($true = X1) | ((in @ X3 @ X2) != $true))) & (($true = X1) | ((in @ X3 @ X0) != $true))) & ((in @ X3 @ (binunion @ X0 @ X2)) = $true)) & (binunionIR = $true)) & (upairset2IR = $true)) & (binunionIL = $true)) & (sepSubset = $true)) & (sepInPowerset = $true)) & (powersetsubset = $true)) & (inPowerset = $true)) & (powersetE1 = $true)) & (powersetI1 = $true)) & (subsetemptysetimpeq = $true)) & (setextsub = $true)) & (subset2powerset = $true)) & (setadjoinSub2 = $true)) & (setadjoinSub = $true)) & (subsetTrans = $true)) & (subsetRefl = $true)) & (notequalI2 = $true)) & (notequalI1 = $true)) & (notsubsetI = $true)) & (subsetE2 = $true)) & (subsetE = $true)) & (emptysetsubset = $true)) & (subsetI2 = $true)) & (eqimpsubset1 = $true)) & (eqimpsubset2 = $true)) & (subsetI1 = $true)) & (dsetconstr__Cong = $true)) & (descr__Cong = $true)) & (exuEu = $true)) & (omega__Cong = $true)) & (setunion__Cong = $true)) & (powerset__Cong = $true)) & (setadjoin__Cong = $true)) & (emptyset__Cong = $true)) & (exu__Cong = $true)) & (exuE3u = $true)) & (in__Cong = $true)) & (inCongP = $true)) & (exuI2 = $true)) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 9.54/2.73 inference(ennf_transformation,[status(thm)],[f201])).
% 9.54/2.73 thf(f201,plain,(
% 9.54/2.73 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ((prop2setI = $true) => ((prop2set2propI = $true) => ((notdexE = $true) => ((notdallE = $true) => ((exuI1 = $true) => ((exuI3 = $true) => ((exuI2 = $true) => ((inCongP = $true) => ((in__Cong = $true) => ((exuE3u = $true) => ((exu__Cong = $true) => ((emptyset__Cong = $true) => ((setadjoin__Cong = $true) => ((powerset__Cong = $true) => ((setunion__Cong = $true) => ((omega__Cong = $true) => ((exuEu = $true) => ((descr__Cong = $true) => ((dsetconstr__Cong = $true) => ((subsetI1 = $true) => ((eqimpsubset2 = $true) => ((eqimpsubset1 = $true) => ((subsetI2 = $true) => ((emptysetsubset = $true) => ((subsetE = $true) => ((subsetE2 = $true) => ((notsubsetI = $true) => ((notequalI1 = $true) => ((notequalI2 = $true) => ((subsetRefl = $true) => ((subsetTrans = $true) => ((setadjoinSub = $true) => ((setadjoinSub2 = $true) => ((subset2powerset = $true) => ((setextsub = $true) => ((subsetemptysetimpeq = $true) => ((powersetI1 = $true) => ((powersetE1 = $true) => ((inPowerset = $true) => ((powersetsubset = $true) => ((sepInPowerset = $true) => ((sepSubset = $true) => ((binunionIL = $true) => ((upairset2IR = $true) => ((binunionIR = $true) => ! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : (((in @ X3 @ (binunion @ X0 @ X2)) = $true) => ((((in @ X3 @ X0) = $true) => ($true = X1)) => ((((in @ X3 @ X2) = $true) => ($true = X1)) => ($true = X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.54/2.73 inference(fool_elimination,[status(thm)],[f200])).
% 9.54/2.73 thf(f200,plain,(
% 9.54/2.73 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => ! [X0 : $i,X1 : $o,X2 : $i,X3 : $i] : ((in @ X3 @ (binunion @ X0 @ X2)) => (((in @ X3 @ X0) => X1) => (((in @ X3 @ X2) => X1) => X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.54/2.73 inference(rectify,[status(thm)],[f106])).
% 9.54/2.73 thf(f106,negated_conjecture,(
% 9.54/2.73 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => ! [X3 : $i,X0 : $o,X4 : $i,X1 : $i] : ((in @ X1 @ (binunion @ X3 @ X4)) => (((in @ X1 @ X3) => X0) => (((in @ X1 @ X4) => X0) => X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.54/2.73 inference(negated_conjecture,[status(cth)],[f105])).
% 9.54/2.73 thf(f105,conjecture,(
% 9.54/2.73 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => (prop2setI => (prop2set2propI => (notdexE => (notdallE => (exuI1 => (exuI3 => (exuI2 => (inCongP => (in__Cong => (exuE3u => (exu__Cong => (emptyset__Cong => (setadjoin__Cong => (powerset__Cong => (setunion__Cong => (omega__Cong => (exuEu => (descr__Cong => (dsetconstr__Cong => (subsetI1 => (eqimpsubset2 => (eqimpsubset1 => (subsetI2 => (emptysetsubset => (subsetE => (subsetE2 => (notsubsetI => (notequalI1 => (notequalI2 => (subsetRefl => (subsetTrans => (setadjoinSub => (setadjoinSub2 => (subset2powerset => (setextsub => (subsetemptysetimpeq => (powersetI1 => (powersetE1 => (inPowerset => (powersetsubset => (sepInPowerset => (sepSubset => (binunionIL => (upairset2IR => (binunionIR => ! [X3 : $i,X0 : $o,X4 : $i,X1 : $i] : ((in @ X1 @ (binunion @ X3 @ X4)) => (((in @ X1 @ X3) => X0) => (((in @ X1 @ X4) => X0) => X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 9.54/2.73 file('/export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2THF_27107.p',binunionEcases)).
% 9.54/2.73 thf(f522,plain,(
% 9.54/2.73 (upairsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y0))))))))))),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f203])).
% 9.54/2.73 thf(f203,plain,(
% 9.54/2.73 (upairsetE = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y0 @ (setadjoin @ Y1 @ (setadjoin @ Y2 @ emptyset))) => ((Y1 = Y0) | (Y2 = Y0))))))))))),
% 9.54/2.73 inference(fool_elimination,[status(thm)],[f202])).
% 9.54/2.73 thf(f202,plain,(
% 9.54/2.73 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X2 @ (setadjoin @ X1 @ (setadjoin @ X0 @ emptyset))) => ((X0 = X2) | (X1 = X2))) = upairsetE)),
% 9.54/2.73 inference(rectify,[status(thm)],[f50])).
% 9.54/2.73 thf(f50,axiom,(
% 9.54/2.73 (! [X2 : $i,X1 : $i,X8 : $i] : ((in @ X8 @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset))) => ((X2 = X8) | (X1 = X8))) = upairsetE)),
% 9.54/2.73 file('/export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2THF_27107.p',upairsetE)).
% 9.54/2.73 thf(f4283,plain,(
% 9.54/2.73 spl4_14 | ~spl4_10),
% 9.54/2.73 inference(avatar_split_clause,[status(thm)],[f3546,f2186,f4280])).
% 9.54/2.73 thf(f2186,definition,(
% 9.54/2.73 spl4_10 <=> ((in @ sK3 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset)))) = $true)),
% 9.54/2.73 introduced(definition,[new_symbols(naming,[spl4_10])],[avatar_definition])).
% 9.54/2.73 thf(f3546,plain,(
% 9.54/2.73 ($true = (in @ sK76 @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset)))) | ~spl4_10),
% 9.54/2.73 inference(binary_proxy_clausification,[status(thm)],[f3544])).
% 9.54/2.73 thf(f3544,plain,(
% 9.54/2.73 (((in @ sK76 @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset))) & (in @ sK3 @ sK76)) = $true) | ~spl4_10),
% 9.54/2.73 inference(beta_eta_normalization,[status(thm)],[f3543])).
% 9.54/2.73 thf(f3543,plain,(
% 9.54/2.73 (((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset))) & (in @ sK3 @ Y0))) @ sK76) = $true) | ~spl4_10),
% 9.54/2.73 inference(sigma_clausification,[status(thm)],[f3542])).
% 9.54/2.73 thf(f3542,plain,(
% 9.54/2.73 ((?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset))) & (in @ sK3 @ Y0)))) = $true) | ~spl4_10),
% 9.54/2.73 inference(boolean_simplification,[status(thm)],[f3460])).
% 9.54/2.73 thf(f3460,plain,(
% 9.54/2.73 (($true = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset))) & (in @ sK3 @ Y0))))) = $true) | ~spl4_10),
% 9.54/2.73 inference(superposition,[status(thm)],[f812,f2188])).
% 9.54/2.73 thf(f2188,plain,(
% 9.54/2.73 ((in @ sK3 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset)))) = $true) | ~spl4_10),
% 9.54/2.73 inference(avatar_component_clause,[status(thm)],[f2186])).
% 9.54/2.73 thf(f812,plain,(
% 9.54/2.73 ( ! [X2 : $i,X1 : $i] : ((((in @ X2 @ (setunion @ X1)) = (?? @ $i @ (^[Y0 : $i]: ((in @ Y0 @ X1) & (in @ X2 @ Y0))))) = $true)) )),
% 9.54/2.73 inference(beta_eta_normalization,[status(thm)],[f811])).
% 9.54/2.73 thf(f811,plain,(
% 9.54/2.73 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (setunion @ X1)) = (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) & (in @ Y0 @ Y1)))))) @ X2) = $true)) )),
% 9.54/2.73 inference(pi_clausification,[status(thm)],[f810])).
% 9.54/2.73 thf(f810,plain,(
% 9.54/2.73 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setunion @ X1)) = (?? @ $i @ (^[Y1 : $i]: ((in @ Y1 @ X1) & (in @ Y0 @ Y1))))))) = $true)) )),
% 9.54/2.73 inference(beta_eta_normalization,[status(thm)],[f809])).
% 9.54/2.73 thf(f809,plain,(
% 9.54/2.73 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2)))))))) @ X1) = $true)) )),
% 9.54/2.73 inference(pi_clausification,[status(thm)],[f592])).
% 9.54/2.73 thf(f592,plain,(
% 9.54/2.73 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))) = $true)),
% 9.54/2.73 inference(definition_unfolding,[status(thm)],[f486,f345])).
% 9.54/2.73 thf(f345,plain,(
% 9.54/2.73 (setunionAx = $true)),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f315])).
% 9.54/2.73 thf(f486,plain,(
% 9.54/2.73 (setunionAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))))),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f169])).
% 9.54/2.73 thf(f169,plain,(
% 9.54/2.73 (setunionAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setunion @ Y0)) = (?? @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y0) & (in @ Y1 @ Y2))))))))))),
% 9.54/2.73 inference(fool_elimination,[status(thm)],[f168])).
% 9.54/2.73 thf(f168,plain,(
% 9.54/2.73 (! [X0 : $i,X1 : $i] : ((in @ X0 @ (setunion @ X1)) <=> ? [X2 : $i] : ((in @ X0 @ X2) & (in @ X2 @ X1))) = setunionAx)),
% 9.54/2.73 inference(rectify,[status(thm)],[f6])).
% 9.54/2.73 thf(f6,axiom,(
% 9.54/2.73 (! [X1 : $i,X3 : $i] : ((in @ X1 @ (setunion @ X3)) <=> ? [X4 : $i] : ((in @ X1 @ X4) & (in @ X4 @ X3))) = setunionAx)),
% 9.54/2.73 file('/export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2THF_27107.p',setunionAx)).
% 9.54/2.73 thf(f3634,plain,(
% 9.54/2.73 spl4_13 | ~spl4_10),
% 9.54/2.73 inference(avatar_split_clause,[status(thm)],[f3545,f2186,f3631])).
% 9.54/2.73 thf(f3631,definition,(
% 9.54/2.73 spl4_13 <=> ((in @ sK3 @ sK76) = $true)),
% 9.54/2.73 introduced(definition,[new_symbols(naming,[spl4_13])],[avatar_definition])).
% 9.54/2.73 thf(f3545,plain,(
% 9.54/2.73 ((in @ sK3 @ sK76) = $true) | ~spl4_10),
% 9.54/2.73 inference(binary_proxy_clausification,[status(thm)],[f3544])).
% 9.54/2.73 thf(f2189,plain,(
% 9.54/2.73 spl4_10),
% 9.54/2.73 inference(avatar_split_clause,[status(thm)],[f984,f2186])).
% 9.54/2.73 thf(f984,plain,(
% 9.54/2.73 ((in @ sK3 @ (setunion @ (setadjoin @ sK0 @ (setadjoin @ sK2 @ emptyset)))) = $true)),
% 9.54/2.73 inference(beta_eta_normalization,[status(thm)],[f530])).
% 9.54/2.73 thf(f530,plain,(
% 9.54/2.73 ((in @ sK3 @ ((^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))) @ sK0 @ sK2)) = $true)),
% 9.54/2.73 inference(definition_unfolding,[status(thm)],[f403,f436])).
% 9.54/2.73 thf(f436,plain,(
% 9.54/2.73 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f181])).
% 9.54/2.73 thf(f181,plain,(
% 9.54/2.73 (binunion = (^[Y0 : $i]: ((^[Y1 : $i]: (setunion @ (setadjoin @ Y0 @ (setadjoin @ Y1 @ emptyset)))))))),
% 9.54/2.73 inference(fool_elimination,[status(thm)],[f180])).
% 9.54/2.73 thf(f180,plain,(
% 9.54/2.73 (binunion = (^[X0 : $i, X1 : $i] : (setunion @ (setadjoin @ X0 @ (setadjoin @ X1 @ emptyset)))))),
% 9.54/2.73 inference(rectify,[status(thm)],[f101])).
% 9.54/2.73 thf(f101,axiom,(
% 9.54/2.73 (binunion = (^[X1 : $i, X2 : $i] : (setunion @ (setadjoin @ X1 @ (setadjoin @ X2 @ emptyset)))))),
% 9.54/2.73 file('/export/starexec/sandbox2/tmp/tmp.S7lkPFCtoZ/DTF2THF_27107.p',binunion)).
% 9.54/2.73 thf(f403,plain,(
% 9.54/2.73 ((in @ sK3 @ (binunion @ sK0 @ sK2)) = $true)),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f315])).
% 9.54/2.73 thf(f1673,plain,(
% 9.54/2.73 ~spl4_5 | spl4_1),
% 9.54/2.73 inference(avatar_split_clause,[status(thm)],[f1668,f1640,f1670])).
% 9.54/2.73 thf(f1670,definition,(
% 9.54/2.73 spl4_5 <=> ((in @ sK3 @ sK2) = $true)),
% 9.54/2.73 introduced(definition,[new_symbols(naming,[spl4_5])],[avatar_definition])).
% 9.54/2.73 thf(f1640,definition,(
% 9.54/2.73 spl4_1 <=> (sK1 = $true)),
% 9.54/2.73 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 9.54/2.73 thf(f1668,plain,(
% 9.54/2.73 ((in @ sK3 @ sK2) != $true) | spl4_1),
% 9.54/2.73 inference(subsumption_resolution,[status(thm)],[f402,f1642])).
% 9.54/2.73 thf(f1642,plain,(
% 9.54/2.73 (sK1 != $true) | spl4_1),
% 9.54/2.73 inference(avatar_component_clause,[status(thm)],[f1640])).
% 9.54/2.73 thf(f402,plain,(
% 9.54/2.73 ((in @ sK3 @ sK2) != $true) | (sK1 = $true)),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f315])).
% 9.54/2.73 thf(f1667,plain,(
% 9.54/2.73 ~spl4_4 | spl4_1),
% 9.54/2.73 inference(avatar_split_clause,[status(thm)],[f1662,f1640,f1664])).
% 9.54/2.73 thf(f1664,definition,(
% 9.54/2.73 spl4_4 <=> ((in @ sK3 @ sK0) = $true)),
% 9.54/2.73 introduced(definition,[new_symbols(naming,[spl4_4])],[avatar_definition])).
% 9.54/2.73 thf(f1662,plain,(
% 9.54/2.73 ((in @ sK3 @ sK0) != $true) | spl4_1),
% 9.54/2.73 inference(subsumption_resolution,[status(thm)],[f400,f1642])).
% 9.54/2.73 thf(f400,plain,(
% 9.54/2.73 (sK1 = $true) | ((in @ sK3 @ sK0) != $true)),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f315])).
% 9.54/2.73 thf(f1643,plain,(
% 9.54/2.73 ~spl4_1),
% 9.54/2.73 inference(avatar_split_clause,[status(thm)],[f401,f1640])).
% 9.54/2.73 thf(f401,plain,(
% 9.54/2.73 (sK1 != $true)),
% 9.54/2.73 inference(cnf_transformation,[status(thm)],[f315])).
% 9.54/2.73 % SZS output end Proof for DTF2THF_27107
% 9.54/2.73 % (27407)------------------------------
% 9.54/2.73 % (27407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 9.54/2.73 % (27407)Termination reason: Refutation
% 9.54/2.73
% 9.54/2.73 % (27407)Memory used [KB]: 8315
% 9.54/2.73 % (27407)Time elapsed: 0.378 s
% 9.54/2.73 % (27407)Instructions burned: 1203 (million)
% 9.54/2.73 % (27407)------------------------------
% 9.54/2.73 % (27407)------------------------------
% 9.54/2.73 % (27310)Success in time 1.278 s
%------------------------------------------------------------------------------