%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU546^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n013.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 09:35:12 AM UTC 2026
% Result : Theorem 2.07s 1.45s
% Output : Refutation 2.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 10
% Syntax : Number of formulae : 61 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 1618 ( 507 equ; 0 cnn)
% Maximal formula atoms : 67 ( 26 avg)
% Number of connectives : 980 ( 105 ~; 99 |; 287 &; 208 @)
% ( 12 <=>; 269 =>; 0 <=; 0 <~>)
% Maximal formula depth : 70 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 156 ( 153 usr; 69 con; 0-3 aty)
% Number of variables : 151 ( 33 ^; 83 !; 35 ?; 151 :)
% 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_87,type,
sP0: $i > $i > $o ).
thf(func_def_88,type,
sP1: $i > $o ).
thf(func_def_89,type,
sP2: $i > $i > $o ).
thf(func_def_90,type,
sP3: $i > $i > $o ).
thf(func_def_93,type,
sK6: $i > $i ).
thf(func_def_95,type,
sK8: $i > $i ).
thf(func_def_97,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_98,type,
sK11: $i > $o ).
thf(func_def_99,type,
sK12: $i > $i ).
thf(func_def_101,type,
sK14: $i > $o ).
thf(func_def_104,type,
sK17: $i > ( $i > $o ) > $i ).
thf(func_def_109,type,
sK22: $i > $o ).
thf(func_def_112,type,
sK25: $i > $o ).
thf(func_def_114,type,
sK27: $i > $i ).
thf(func_def_117,type,
sK30: $i > $i ).
thf(func_def_120,type,
sK33: $i > $i ).
thf(func_def_123,type,
sK36: $i > $o ).
thf(func_def_127,type,
sK40: $i > $o ).
thf(func_def_131,type,
sK44: $i > $o ).
thf(func_def_132,type,
sK45: $i > $i ).
thf(func_def_133,type,
sK46: ( $i > $o ) > $i ).
thf(func_def_136,type,
sK49: $i > $i > $i ).
thf(func_def_142,type,
sK55: $i > $i > $i ).
thf(func_def_145,type,
sK58: $i > $o ).
thf(func_def_149,type,
sK62: $o > $i > $i > $i ).
thf(func_def_159,type,
sK72: $i > $o ).
thf(func_def_161,type,
sK74: $i > $o ).
thf(func_def_164,type,
sK77: $i > ( $i > $o ) > $i ).
thf(func_def_167,type,
sK80: $i > ( $i > $o ) > $i ).
thf(func_def_168,type,
sK81: $i > $o ).
thf(func_def_171,type,
sK84: $i > $o ).
thf(func_def_174,type,
sK87: $i > ( $i > $o ) > $i ).
thf(func_def_177,type,
sK90: $i > $i > $i ).
thf(func_def_180,type,
sK93: $i > $o ).
thf(func_def_181,type,
sK94: $i > $i > $i ).
thf(func_def_182,type,
sK95: $i > $i > $i ).
thf(func_def_183,type,
sK96: $i > $i > $i ).
thf(func_def_184,type,
sK97: $i > $i > $i ).
thf(func_def_185,type,
sK98: $i > $i > $i > $i ).
thf(func_def_186,type,
sK99: $i > $i ).
thf(func_def_187,type,
sK100: $i > $i ).
thf(func_def_188,type,
sK101: $i > $i ).
thf(func_def_189,type,
sK102: $i > $i ).
thf(func_def_190,type,
sK103: $i > $i > $i ).
thf(func_def_191,type,
sK104: $i > $i > $i > $i ).
thf(func_def_192,type,
sK105: $i > $i > $i > $i ).
thf(func_def_193,type,
sK106: $i > $i > $i ).
thf(func_def_194,type,
sK107: $i > $i > $i ).
thf(func_def_196,type,
sK109: $i > $i ).
thf(func_def_197,type,
sK110: $i > $i ).
thf(func_def_198,type,
sK111: $i > $i ).
thf(func_def_199,type,
sK112: $i > $i > $i ).
thf(func_def_205,type,
sK118: $i > $o ).
thf(func_def_208,type,
sK121: $i > ( $i > $o ) > $i ).
thf(func_def_214,type,
sK127: $i > $i ).
thf(func_def_216,type,
sK129: $i > $o ).
thf(func_def_218,type,
sK131: ( $i > $o ) > $i ).
thf(func_def_219,type,
sK132: ( $i > $o ) > $i ).
thf(func_def_222,type,
sK135: $i > $i > $i ).
thf(func_def_223,type,
sK136: $i > $i > $i ).
thf(func_def_224,type,
sK137: ( $i > $o ) > $i ).
thf(func_def_225,type,
sK138: $i > $o ).
thf(func_def_227,type,
sK140: $i > $i > $o ).
thf(func_def_228,type,
sK141: $i > $i ).
thf(func_def_229,type,
sK142: $i > $i ).
thf(func_def_230,type,
sK143: ( $i > $i > $o ) > $i > $i ).
thf(func_def_231,type,
sK144: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_232,type,
sK145: ( $i > $i > $o ) > $i > $i ).
thf(func_def_234,type,
sK147: $i > $o ).
thf(func_def_236,type,
sK149: ( $i > $o ) > $i > $i ).
thf(func_def_237,type,
sK150: $i > $i > $i ).
thf(func_def_241,type,
sK154: $i > $o ).
thf(func_def_252,type,
sK165: $i > $i ).
thf(func_def_254,type,
sK167: $i > ( $i > $o ) > $i ).
thf(func_def_255,type,
sK168: $i > $o ).
thf(func_def_269,type,
ph182:
!>[X0: $tType] : X0 ).
thf(f1651,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1600,f1610,f1634,f1650]) ).
thf(f1650,plain,
( spl181_2
| ~ spl181_1
| ~ spl181_3 ),
inference(avatar_split_clause,[status(thm)],[f1649,f1631,f1594,f1598]) ).
thf(f1598,definition,
( spl181_2
<=> ! [X0: $i] :
( ( sK25 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[spl181_2])],[avatar_definition]) ).
thf(f1594,definition,
( spl181_1
<=> ( sK26
= ( sK131 @ sK25 ) ) ),
introduced(definition,[new_symbols(naming,[spl181_1])],[avatar_definition]) ).
thf(f1631,definition,
( spl181_3
<=> ( sK26
= ( sK132 @ sK25 ) ) ),
introduced(definition,[new_symbols(naming,[spl181_3])],[avatar_definition]) ).
thf(f1649,plain,
( ! [X0: $i] :
( ( sK25 @ X0 )
!= $true )
| ~ spl181_1
| ~ spl181_3 ),
inference(subsumption_resolution,[status(thm)],[f1648,f1275]) ).
thf(f1275,plain,
( $true
!= ( exu @ sK25 ) ),
inference(beta_eta_normalization,[status(thm)],[f656]) ).
thf(f656,plain,
( $true
!= ( exu
@ ^ [Y0: $i] : ( sK25 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
thf(f325,plain,
( ( powersetAx = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( notinemptyset = $true )
& ( eqinunit = $true )
& ( subPowSU = $true )
& ( nonemptyImpWitness = $true )
& ( exuE1 = $true )
& ( prop2set2propI = $true )
& ( omega0Ax = $true )
& ( nonemptyE1 = $true )
& ( exuE2 = $true )
& ( setext = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIL = $true )
& ( setadjoinOr = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan4 = $true )
& ( uniqinunit = $true )
& ( emptysetE = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( powersetE = $true )
& ( setunionAx = $true )
& ( exuI1 = $true )
& ( singletonsswitch = $true )
& ( notdexE = $true )
& ( replAx = $true )
& ! [X2: $i] :
( ( ( sK26 = X2 )
| ( ( sK25 @ X2 )
!= $true ) )
& ( ( ( sK25 @ X2 )
= $true )
| ( sK26 != X2 ) ) )
& ( $true
!= ( exu
@ ^ [Y0: $i] : ( sK25 @ Y0 ) ) )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( upairsetE = $true )
& ( upairsetIL = $true )
& ( emptyInPowerset = $true )
& ( upairsetIR = $true )
& ( powersetI = $true )
& ( setadjoinAx = $true )
& ( exuI3 = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( vacuousDall = $true )
& ( setunionI = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( prop2setI = $true )
& ( emptyI = $true )
& ( exuE3e = $true )
& ( notdallE = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f322,f324,f323]) ).
thf(f323,plain,
( ? [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( X1 != X2 ) ) )
& ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( ( sK25 @ X2 )
!= $true ) )
& ( ( ( sK25 @ X2 )
= $true )
| ( X1 != X2 ) ) )
& ( $true
!= ( exu
@ ^ [Y0: $i] : ( sK25 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f324,plain,
( ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( ( sK25 @ X2 )
!= $true ) )
& ( ( ( sK25 @ X2 )
= $true )
| ( X1 != X2 ) ) )
=> ! [X2: $i] :
( ( ( sK26 = X2 )
| ( ( sK25 @ X2 )
!= $true ) )
& ( ( ( sK25 @ X2 )
= $true )
| ( sK26 != X2 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f322,plain,
( ( powersetAx = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( notinemptyset = $true )
& ( eqinunit = $true )
& ( subPowSU = $true )
& ( nonemptyImpWitness = $true )
& ( exuE1 = $true )
& ( prop2set2propI = $true )
& ( omega0Ax = $true )
& ( nonemptyE1 = $true )
& ( exuE2 = $true )
& ( setext = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIL = $true )
& ( setadjoinOr = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan4 = $true )
& ( uniqinunit = $true )
& ( emptysetE = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( powersetE = $true )
& ( setunionAx = $true )
& ( exuI1 = $true )
& ( singletonsswitch = $true )
& ( notdexE = $true )
& ( replAx = $true )
& ? [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( ( X1 = X2 )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( ( X0 @ X2 )
= $true )
| ( X1 != X2 ) ) )
& ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( upairsetE = $true )
& ( upairsetIL = $true )
& ( emptyInPowerset = $true )
& ( upairsetIR = $true )
& ( powersetI = $true )
& ( setadjoinAx = $true )
& ( exuI3 = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( vacuousDall = $true )
& ( setunionI = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( prop2setI = $true )
& ( emptyI = $true )
& ( exuE3e = $true )
& ( notdallE = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true ) ),
inference(nnf_transformation,[status(thm)],[f223]) ).
thf(f223,plain,
( ( powersetAx = $true )
& ( setadjoinE = $true )
& ( setoftrueEq = $true )
& ( notinemptyset = $true )
& ( eqinunit = $true )
& ( subPowSU = $true )
& ( nonemptyImpWitness = $true )
& ( exuE1 = $true )
& ( prop2set2propI = $true )
& ( omega0Ax = $true )
& ( nonemptyE1 = $true )
& ( exuE2 = $true )
& ( setext = $true )
& ( setunionE = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinIL = $true )
& ( setadjoinOr = $true )
& ( omegaSAx = $true )
& ( quantDeMorgan4 = $true )
& ( uniqinunit = $true )
& ( emptysetE = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( notinsingleton = $true )
& ( prop2setE = $true )
& ( emptysetAx = $true )
& ( powersetE = $true )
& ( setunionAx = $true )
& ( exuI1 = $true )
& ( singletonsswitch = $true )
& ( notdexE = $true )
& ( replAx = $true )
& ? [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) )
& ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( setadjoinIR = $true )
& ( noeltsimpempty = $true )
& ( emptyE1 = $true )
& ( wellorderingAx = $true )
& ( upairsetE = $true )
& ( upairsetIL = $true )
& ( emptyInPowerset = $true )
& ( upairsetIR = $true )
& ( powersetI = $true )
& ( setadjoinAx = $true )
& ( exuI3 = $true )
& ( dsetconstrI = $true )
& ( quantDeMorgan2 = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setextAx = $true )
& ( vacuousDall = $true )
& ( setunionI = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan1 = $true )
& ( prop2setI = $true )
& ( emptyI = $true )
& ( exuE3e = $true )
& ( notdallE = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( foundationAx = $true ) ),
inference(flattening,[status(thm)],[f222]) ).
thf(f222,plain,
( ? [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) )
& ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( 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)],[f191]) ).
thf(f191,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 )
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X1 = X2 )
<=> ( ( X0 @ X2 )
= $true ) )
=> ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f190]) ).
thf(f190,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
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) )
=> ( exu
@ ^ [X3: $i] : ( X0 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f66]) ).
thf(f66,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
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f65]) ).
thf(f65,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
=> ! [X0: $i > $o] :
( ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xzwazKCSaL/DTF2THF_12476.p',exuI2) ).
thf(f1648,plain,
( ! [X0: $i] :
( ( $true
= ( exu @ sK25 ) )
| ( ( sK25 @ X0 )
!= $true ) )
| ~ spl181_1
| ~ spl181_3 ),
inference(subsumption_resolution,[status(thm)],[f1647,f1596]) ).
thf(f1596,plain,
( ( sK26
= ( sK131 @ sK25 ) )
| ~ spl181_1 ),
inference(avatar_component_clause,[status(thm)],[f1594]) ).
thf(f1647,plain,
( ! [X0: $i] :
( ( ( sK25 @ X0 )
!= $true )
| ( sK26
!= ( sK131 @ sK25 ) )
| ( $true
= ( exu @ sK25 ) ) )
| ~ spl181_3 ),
inference(superposition,[status(thm)],[f1168,f1633]) ).
thf(f1633,plain,
( ( sK26
= ( sK132 @ sK25 ) )
| ~ spl181_3 ),
inference(avatar_component_clause,[status(thm)],[f1631]) ).
thf(f1168,plain,
! [X4: $i > $o,X5: $i] :
( ( ( sK132 @ X4 )
!= ( sK131 @ X4 ) )
| ( ( X4 @ X5 )
!= $true )
| ( $true
= ( exu @ X4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1167]) ).
thf(f1167,plain,
! [X4: $i > $o,X5: $i] :
( ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ( ( sK132 @ X4 )
!= ( sK131 @ X4 ) )
| ( ( X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1086]) ).
thf(f1086,plain,
! [X4: $i > $o,X5: $i] :
( ( $true != $true )
| ( ( X4 @ X5 )
!= $true )
| ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ( ( sK132 @ X4 )
!= ( sK131 @ X4 ) ) ),
inference(definition_unfolding,[status(thm)],[f846,f645]) ).
thf(f645,plain,
exuI3 = $true,
inference(cnf_transformation,[status(thm)],[f325]) ).
thf(f846,plain,
! [X4: $i > $o,X5: $i] :
( ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ( ( X4 @ X5 )
!= $true )
| ( ( sK132 @ X4 )
!= ( sK131 @ X4 ) )
| ( exuI3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f513]) ).
thf(f513,plain,
( ( ( exuI3 = $true )
| ( ( ( exu
@ ^ [Y0: $i] : ( sK129 @ Y0 ) )
!= $true )
& ( $true
= ( sK129 @ sK130 ) )
& ! [X2: $i,X3: $i] :
( ( ( sK129 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( sK129 @ X3 )
!= $true ) ) ) )
& ( ! [X4: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ! [X5: $i] :
( ( X4 @ X5 )
!= $true )
| ( ( ( X4 @ ( sK131 @ X4 ) )
= $true )
& ( ( sK132 @ X4 )
!= ( sK131 @ X4 ) )
& ( $true
= ( X4 @ ( sK132 @ X4 ) ) ) ) )
| ( exuI3 != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK129,sK130,sK131,sK132])],[f509,f512,f511,f510]) ).
thf(f510,plain,
( ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( X0 @ X3 )
!= $true ) ) )
=> ( ( ( exu
@ ^ [Y0: $i] : ( sK129 @ Y0 ) )
!= $true )
& ? [X1: $i] :
( $true
= ( sK129 @ X1 ) )
& ! [X3: $i,X2: $i] :
( ( ( sK129 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( sK129 @ X3 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f511,plain,
( ? [X1: $i] :
( $true
= ( sK129 @ X1 ) )
=> ( $true
= ( sK129 @ sK130 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f512,plain,
! [X4: $i > $o] :
( ? [X6: $i,X7: $i] :
( ( $true
= ( X4 @ X6 ) )
& ( X6 != X7 )
& ( ( X4 @ X7 )
= $true ) )
=> ( ( ( X4 @ ( sK131 @ X4 ) )
= $true )
& ( ( sK132 @ X4 )
!= ( sK131 @ X4 ) )
& ( $true
= ( X4 @ ( sK132 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f509,plain,
( ( ( exuI3 = $true )
| ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( X0 @ X3 )
!= $true ) ) ) )
& ( ! [X4: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ! [X5: $i] :
( ( X4 @ X5 )
!= $true )
| ? [X6: $i,X7: $i] :
( ( $true
= ( X4 @ X6 ) )
& ( X6 != X7 )
& ( ( X4 @ X7 )
= $true ) ) )
| ( exuI3 != $true ) ) ),
inference(rectify,[status(thm)],[f508]) ).
thf(f508,plain,
( ( ( exuI3 = $true )
| ? [X0: $i > $o] :
( ( $true
!= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
& ? [X1: $i] :
( ( X0 @ X1 )
= $true )
& ! [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
!= $true )
| ( X2 = X3 )
| ( ( X0 @ X3 )
!= $true ) ) ) )
& ( ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ? [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
= $true )
& ( X2 != X3 )
& ( ( X0 @ X3 )
= $true ) ) )
| ( exuI3 != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f268]) ).
thf(f268,plain,
( ( exuI3 = $true )
<=> ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true )
| ? [X2: $i,X3: $i] :
( ( ( X0 @ X2 )
= $true )
& ( X2 != X3 )
& ( ( X0 @ X3 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f267]) ).
thf(f267,plain,
( ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
| ? [X2: $i,X3: $i] :
( ( X2 != X3 )
& ( ( X0 @ X2 )
= $true )
& ( ( X0 @ X3 )
= $true ) )
| ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) )
<=> ( exuI3 = $true ) ),
inference(ennf_transformation,[status(thm)],[f83]) ).
thf(f83,plain,
( ! [X0: $i > $o] :
( ? [X1: $i] :
( ( X0 @ X1 )
= $true )
=> ( ! [X2: $i,X3: $i] :
( ( ( X0 @ X3 )
= $true )
=> ( ( ( X0 @ X2 )
= $true )
=> ( X2 = X3 ) ) )
=> ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) ) )
<=> ( exuI3 = $true ) ),
inference(fool_elimination,[status(thm)],[f82]) ).
thf(f82,plain,
( exuI3
= ( ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X2: $i,X3: $i] :
( ( X0 @ X3 )
=> ( ( X0 @ X2 )
=> ( X2 = X3 ) ) )
=> ( exu
@ ^ [X4: $i] : ( X0 @ X4 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f64]) ).
thf(f64,axiom,
( exuI3
= ( ! [X0: $i > $o] :
( ? [X1: $i] : ( X0 @ X1 )
=> ( ! [X2: $i,X1: $i] :
( ( X0 @ X1 )
=> ( ( X0 @ X2 )
=> ( X1 = X2 ) ) )
=> ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.xzwazKCSaL/DTF2THF_12476.p',exuI3) ).
thf(f1634,plain,
( spl181_3
| spl181_2 ),
inference(avatar_split_clause,[status(thm)],[f1629,f1598,f1631]) ).
thf(f1629,plain,
! [X0: $i] :
( ( ( sK25 @ X0 )
!= $true )
| ( sK26
= ( sK132 @ sK25 ) ) ),
inference(subsumption_resolution,[status(thm)],[f1625,f1275]) ).
thf(f1625,plain,
! [X0: $i] :
( ( $true
= ( exu @ sK25 ) )
| ( sK26
= ( sK132 @ sK25 ) )
| ( ( sK25 @ X0 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1620]) ).
thf(f1620,plain,
! [X0: $i] :
( ( sK26
= ( sK132 @ sK25 ) )
| ( $true != $true )
| ( $true
= ( exu @ sK25 ) )
| ( ( sK25 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f658,f1256]) ).
thf(f1256,plain,
! [X4: $i > $o,X5: $i] :
( ( $true
= ( X4 @ ( sK132 @ X4 ) ) )
| ( ( X4 @ X5 )
!= $true )
| ( $true
= ( exu @ X4 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1255]) ).
thf(f1255,plain,
! [X4: $i > $o,X5: $i] :
( ( ( X4 @ X5 )
!= $true )
| ( $true
= ( X4 @ ( sK132 @ X4 ) ) )
| ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1087]) ).
thf(f1087,plain,
! [X4: $i > $o,X5: $i] :
( ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ( $true
= ( X4 @ ( sK132 @ X4 ) ) )
| ( $true != $true )
| ( ( X4 @ X5 )
!= $true ) ),
inference(definition_unfolding,[status(thm)],[f845,f645]) ).
thf(f845,plain,
! [X4: $i > $o,X5: $i] :
( ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ( ( X4 @ X5 )
!= $true )
| ( $true
= ( X4 @ ( sK132 @ X4 ) ) )
| ( exuI3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f513]) ).
thf(f658,plain,
! [X2: $i] :
( ( ( sK25 @ X2 )
!= $true )
| ( sK26 = X2 ) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
thf(f1610,plain,
~ spl181_2,
inference(avatar_contradiction_clause,[status(thm)],[f1609]) ).
thf(f1609,plain,
( $false
| ~ spl181_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1601]) ).
thf(f1601,plain,
( ( $true != $true )
| ~ spl181_2 ),
inference(superposition,[status(thm)],[f1599,f1155]) ).
thf(f1155,plain,
( $true
= ( sK25 @ sK26 ) ),
inference(equality_resolution,[status(thm)],[f657]) ).
thf(f657,plain,
! [X2: $i] :
( ( ( sK25 @ X2 )
= $true )
| ( sK26 != X2 ) ),
inference(cnf_transformation,[status(thm)],[f325]) ).
thf(f1599,plain,
( ! [X0: $i] :
( ( sK25 @ X0 )
!= $true )
| ~ spl181_2 ),
inference(avatar_component_clause,[status(thm)],[f1598]) ).
thf(f1600,plain,
( spl181_1
| spl181_2 ),
inference(avatar_split_clause,[status(thm)],[f1592,f1598,f1594]) ).
thf(f1592,plain,
! [X0: $i] :
( ( ( sK25 @ X0 )
!= $true )
| ( sK26
= ( sK131 @ sK25 ) ) ),
inference(subsumption_resolution,[status(thm)],[f1590,f1275]) ).
thf(f1590,plain,
! [X0: $i] :
( ( $true
= ( exu @ sK25 ) )
| ( ( sK25 @ X0 )
!= $true )
| ( sK26
= ( sK131 @ sK25 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1583]) ).
thf(f1583,plain,
! [X0: $i] :
( ( ( sK25 @ X0 )
!= $true )
| ( $true
= ( exu @ sK25 ) )
| ( $true != $true )
| ( sK26
= ( sK131 @ sK25 ) ) ),
inference(superposition,[status(thm)],[f658,f1180]) ).
thf(f1180,plain,
! [X4: $i > $o,X5: $i] :
( ( ( X4 @ ( sK131 @ X4 ) )
= $true )
| ( $true
= ( exu @ X4 ) )
| ( ( X4 @ X5 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f1179]) ).
thf(f1179,plain,
! [X4: $i > $o,X5: $i] :
( ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ( ( X4 @ ( sK131 @ X4 ) )
= $true )
| ( ( X4 @ X5 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1085]) ).
thf(f1085,plain,
! [X4: $i > $o,X5: $i] :
( ( ( X4 @ ( sK131 @ X4 ) )
= $true )
| ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ( ( X4 @ X5 )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f847,f645]) ).
thf(f847,plain,
! [X4: $i > $o,X5: $i] :
( ( ( exu
@ ^ [Y0: $i] : ( X4 @ Y0 ) )
= $true )
| ( ( X4 @ X5 )
!= $true )
| ( ( X4 @ ( sK131 @ X4 ) )
= $true )
| ( exuI3 != $true ) ),
inference(cnf_transformation,[status(thm)],[f513]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU546^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.34 % Computer : n013.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Tue Feb 24 12:26:23 EST 2026
% 0.15/0.34 % CPUTime :
% 0.15/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.46 thf(spec,logic,$$dhol).
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 % File : SEU546^1 : TPTP v9.2.1. Released v3.7.0.
% 0.30/0.46 % Domain : Set Theory
% 0.30/0.46 % Problem : Preliminary Notions - Equivalence Laws
% 0.30/0.46 % Version : Especial.
% 0.30/0.46 % English : (! phi:i>o.(? x:i.! y:i.phi y <-> y = x) -> exu (^ x:i.phi x))
% 0.30/0.46
% 0.30/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.30/0.46 % Source : [Bro08]
% 0.30/0.46 % Names : ZFC048g [Bro08]
% 0.30/0.46
% 0.30/0.46 % Status : Theorem
% 0.30/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.60 v5.2.0, 0.80 v5.1.0, 1.00 v5.0.0, 0.80 v4.1.0, 0.67 v3.7.0
% 0.30/0.46 % Syntax : Number of formulae : 139 ( 64 unt; 74 typ; 64 def)
% 0.30/0.46 % Number of atoms : 349 ( 86 equ; 0 cnn)
% 0.30/0.46 % Maximal formula atoms : 64 ( 5 avg)
% 0.30/0.46 % Number of connectives : 585 ( 21 ~; 5 |; 27 &; 368 @)
% 0.30/0.46 % ( 9 <=>; 155 =>; 0 <=; 0 <~>)
% 0.30/0.46 % Maximal formula depth : 69 ( 2 avg)
% 0.30/0.46 % Number of types : 2 ( 0 usr)
% 0.30/0.46 % Number of type conns : 39 ( 39 >; 0 *; 0 +; 0 <<)
% 0.30/0.46 % Number of symbols : 77 ( 74 usr; 66 con; 0-2 aty)
% 0.30/0.46 % Number of variables : 196 ( 18 ^; 150 !; 28 ?; 196 :)
% 0.30/0.46 % SPC : TH0_THM_EQU_NAR
% 0.30/0.46
% 0.30/0.46 % Comments : http://mathgate.info/detsetitem.php?id=409
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 thf(in_type,type,
% 0.30/0.46 in: $i > $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu_type,type,
% 0.30/0.46 exu: ( $i > $o ) > $o ).
% 0.30/0.46
% 0.30/0.46 thf(exu,definition,
% 0.30/0.46 ( exu
% 0.30/0.46 = ( ^ [Xphi: $i > $o] :
% 0.30/0.46 ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx_type,type,
% 0.30/0.46 setextAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setextAx,definition,
% 0.30/0.46 ( setextAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 <=> ( in @ Xx @ B ) )
% 0.30/0.46 => ( A = B ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyset_type,type,
% 0.30/0.46 emptyset: $i ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx_type,type,
% 0.30/0.46 emptysetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetAx,definition,
% 0.30/0.46 ( emptysetAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoin_type,type,
% 0.30/0.46 setadjoin: $i > $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx_type,type,
% 0.30/0.46 setadjoinAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinAx,definition,
% 0.30/0.46 ( setadjoinAx
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 <=> ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powerset_type,type,
% 0.30/0.46 powerset: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx_type,type,
% 0.30/0.46 powersetAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetAx,definition,
% 0.30/0.46 ( powersetAx
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 <=> ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunion_type,type,
% 0.30/0.46 setunion: $i > $i ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx_type,type,
% 0.30/0.46 setunionAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionAx,definition,
% 0.30/0.46 ( setunionAx
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 <=> ? [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omega_type,type,
% 0.30/0.46 omega: $i ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax_type,type,
% 0.30/0.46 omega0Ax: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omega0Ax,definition,
% 0.30/0.46 ( omega0Ax
% 0.30/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx_type,type,
% 0.30/0.46 omegaSAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaSAx,definition,
% 0.30/0.46 ( omegaSAx
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx_type,type,
% 0.30/0.46 omegaIndAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(omegaIndAx,definition,
% 0.30/0.46 ( omegaIndAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( ( in @ emptyset @ A )
% 0.30/0.46 & ! [Xx: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ omega )
% 0.30/0.46 & ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ omega )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(replAx_type,type,
% 0.30/0.46 replAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(replAx,definition,
% 0.30/0.46 ( replAx
% 0.30/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 <=> ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx_type,type,
% 0.30/0.46 foundationAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(foundationAx,definition,
% 0.30/0.46 ( foundationAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ? [B: $i] :
% 0.30/0.46 ( ( in @ B @ A )
% 0.30/0.46 & ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx_type,type,
% 0.30/0.46 wellorderingAx: $o ).
% 0.30/0.46
% 0.30/0.46 thf(wellorderingAx,definition,
% 0.30/0.46 ( wellorderingAx
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ? [B: $i] :
% 0.30/0.46 ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) ) )
% 0.30/0.46 & ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( ( in @ Xx @ A )
% 0.30/0.46 & ( in @ Xy @ A ) )
% 0.30/0.46 => ( ! [C: $i] :
% 0.30/0.46 ( ( in @ C @ B )
% 0.30/0.46 => ( ( in @ Xx @ C )
% 0.30/0.46 <=> ( in @ Xy @ C ) ) )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 & ! [C: $i,D: $i] :
% 0.30/0.46 ( ( ( in @ C @ B )
% 0.30/0.46 & ( in @ D @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ D ) )
% 0.30/0.46 | ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ D )
% 0.30/0.46 => ( in @ Xx @ C ) ) ) )
% 0.30/0.46 & ! [C: $i] :
% 0.30/0.46 ( ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ C )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.30/0.46 => ? [D: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ D @ B )
% 0.30/0.46 & ( in @ Xx @ C )
% 0.30/0.46 & ~ ? [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ D )
% 0.30/0.46 & ( in @ Xy @ C ) )
% 0.30/0.46 & ! [E: $i] :
% 0.30/0.46 ( ( in @ E @ B )
% 0.30/0.46 => ( ! [Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ E )
% 0.30/0.46 => ( in @ Xy @ D ) )
% 0.30/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(descr_type,type,
% 0.30/0.46 descr: ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(descrp_type,type,
% 0.30/0.46 descrp: $o ).
% 0.30/0.46
% 0.30/0.46 thf(descrp,definition,
% 0.30/0.46 ( descrp
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ( Xphi
% 0.30/0.46 @ ( descr
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstr_type,type,
% 0.30/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI_type,type,
% 0.30/0.46 dsetconstrI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrI,definition,
% 0.30/0.46 ( dsetconstrI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL_type,type,
% 0.30/0.46 dsetconstrEL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrEL,definition,
% 0.30/0.46 ( dsetconstrEL
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER_type,type,
% 0.30/0.46 dsetconstrER: $o ).
% 0.30/0.46
% 0.30/0.46 thf(dsetconstrER,definition,
% 0.30/0.46 ( dsetconstrER
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1_type,type,
% 0.30/0.46 exuE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE1,definition,
% 0.30/0.46 ( exuE1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set_type,type,
% 0.30/0.46 prop2set: $o > $i ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE_type,type,
% 0.30/0.46 prop2setE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setE,definition,
% 0.30/0.46 ( prop2setE
% 0.30/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE_type,type,
% 0.30/0.46 emptysetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetE,definition,
% 0.30/0.46 ( emptysetE
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse_type,type,
% 0.30/0.46 emptysetimpfalse: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptysetimpfalse,definition,
% 0.30/0.46 ( emptysetimpfalse
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => $false ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset_type,type,
% 0.30/0.46 notinemptyset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinemptyset,definition,
% 0.30/0.46 ( notinemptyset
% 0.30/0.46 = ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e_type,type,
% 0.30/0.46 exuE3e: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE3e,definition,
% 0.30/0.46 ( exuE3e
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setext_type,type,
% 0.30/0.46 setext: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setext,definition,
% 0.30/0.46 ( setext
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ B ) )
% 0.30/0.46 => ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( A = B ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI_type,type,
% 0.30/0.46 emptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyI,definition,
% 0.30/0.46 ( emptyI
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty_type,type,
% 0.30/0.46 noeltsimpempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(noeltsimpempty,definition,
% 0.30/0.46 ( noeltsimpempty
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ~ ( in @ Xx @ A )
% 0.30/0.46 => ( A = emptyset ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta_type,type,
% 0.30/0.46 setbeta: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setbeta,definition,
% 0.30/0.46 ( setbeta
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( in @ Xx
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.30/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty_type,type,
% 0.30/0.46 nonempty: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonempty,definition,
% 0.30/0.46 ( nonempty
% 0.30/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1_type,type,
% 0.30/0.46 nonemptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyE1,definition,
% 0.30/0.46 ( nonemptyE1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI_type,type,
% 0.30/0.46 nonemptyI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI,definition,
% 0.30/0.46 ( nonemptyI
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( ( Xphi @ Xx )
% 0.30/0.46 => ( nonempty
% 0.30/0.46 @ ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1_type,type,
% 0.30/0.46 nonemptyI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyI1,definition,
% 0.30/0.46 ( nonemptyI1
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.30/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL_type,type,
% 0.30/0.46 setadjoinIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIL,definition,
% 0.30/0.46 ( setadjoinIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty_type,type,
% 0.30/0.46 emptyinunitempty: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinunitempty,definition,
% 0.30/0.46 ( emptyinunitempty
% 0.30/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIR_type,type,
% 0.30/0.46 setadjoinIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinIR,definition,
% 0.30/0.46 ( setadjoinIR
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ A )
% 0.30/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinE_type,type,
% 0.30/0.46 setadjoinE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinE,definition,
% 0.30/0.46 ( setadjoinE
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ( ( Xy = Xx )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => ( ( ( in @ Xy @ A )
% 0.30/0.46 => Xphi )
% 0.30/0.46 => Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinOr_type,type,
% 0.30/0.46 setadjoinOr: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setadjoinOr,definition,
% 0.30/0.46 ( setadjoinOr
% 0.30/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.30/0.46 => ( ( Xy = Xx )
% 0.30/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setoftrueEq_type,type,
% 0.30/0.46 setoftrueEq: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setoftrueEq,definition,
% 0.30/0.46 ( setoftrueEq
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : $true )
% 0.30/0.46 = A ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI_type,type,
% 0.30/0.46 powersetI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetI,definition,
% 0.30/0.46 ( powersetI
% 0.30/0.46 = ( ! [A: $i,B: $i] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) )
% 0.30/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinPowerset_type,type,
% 0.30/0.46 emptyinPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyinPowerset,definition,
% 0.30/0.46 ( emptyinPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyInPowerset_type,type,
% 0.30/0.46 emptyInPowerset: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyInPowerset,definition,
% 0.30/0.46 ( emptyInPowerset
% 0.30/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE_type,type,
% 0.30/0.46 powersetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(powersetE,definition,
% 0.30/0.46 ( powersetE
% 0.30/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.30/0.46 => ( ( in @ Xx @ B )
% 0.30/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionI_type,type,
% 0.30/0.46 setunionI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionI,definition,
% 0.30/0.46 ( setunionI
% 0.30/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( ( in @ B @ A )
% 0.30/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE_type,type,
% 0.30/0.46 setunionE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(setunionE,definition,
% 0.30/0.46 ( setunionE
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.30/0.46 => ! [Xphi: $o] :
% 0.30/0.46 ( ! [B: $i] :
% 0.30/0.46 ( ( in @ Xx @ B )
% 0.30/0.46 => ( ( in @ B @ A )
% 0.30/0.46 => Xphi ) )
% 0.30/0.46 => Xphi ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(subPowSU_type,type,
% 0.30/0.46 subPowSU: $o ).
% 0.30/0.46
% 0.30/0.46 thf(subPowSU,definition,
% 0.30/0.46 ( subPowSU
% 0.30/0.46 = ( ! [A: $i,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuE2_type,type,
% 0.30/0.46 exuE2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuE2,definition,
% 0.30/0.46 ( exuE2
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyImpWitness_type,type,
% 0.30/0.46 nonemptyImpWitness: $o ).
% 0.30/0.46
% 0.30/0.46 thf(nonemptyImpWitness,definition,
% 0.30/0.46 ( nonemptyImpWitness
% 0.30/0.46 = ( ! [A: $i] :
% 0.30/0.46 ( ( nonempty @ A )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & $true ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit_type,type,
% 0.30/0.46 uniqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(uniqinunit,definition,
% 0.30/0.46 ( uniqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notinsingleton_type,type,
% 0.30/0.46 notinsingleton: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notinsingleton,definition,
% 0.30/0.46 ( notinsingleton
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx != Xy )
% 0.30/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit_type,type,
% 0.30/0.46 eqinunit: $o ).
% 0.30/0.46
% 0.30/0.46 thf(eqinunit,definition,
% 0.30/0.46 ( eqinunit
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xx = Xy )
% 0.30/0.46 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsswitch_type,type,
% 0.30/0.46 singletonsswitch: $o ).
% 0.30/0.46
% 0.30/0.46 thf(singletonsswitch,definition,
% 0.30/0.46 ( singletonsswitch
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.30/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetE_type,type,
% 0.30/0.46 upairsetE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetE,definition,
% 0.30/0.46 ( upairsetE
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.30/0.46 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.30/0.46 => ( ( Xz = Xx )
% 0.30/0.46 | ( Xz = Xy ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIL_type,type,
% 0.30/0.46 upairsetIL: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIL,definition,
% 0.30/0.46 ( upairsetIL
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIR_type,type,
% 0.30/0.46 upairsetIR: $o ).
% 0.30/0.46
% 0.30/0.46 thf(upairsetIR,definition,
% 0.30/0.46 ( upairsetIR
% 0.30/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(emptyE1_type,type,
% 0.30/0.46 emptyE1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(emptyE1,definition,
% 0.30/0.46 ( emptyE1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ( ( ( dsetconstr @ A
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.30/0.46 = emptyset )
% 0.30/0.46 => $false ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall_type,type,
% 0.30/0.46 vacuousDall: $o ).
% 0.30/0.46
% 0.30/0.46 thf(vacuousDall,definition,
% 0.30/0.46 ( vacuousDall
% 0.30/0.46 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ emptyset )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan1_type,type,
% 0.30/0.46 quantDeMorgan1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan1,definition,
% 0.30/0.46 ( quantDeMorgan1
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan2_type,type,
% 0.30/0.46 quantDeMorgan2: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan2,definition,
% 0.30/0.46 ( quantDeMorgan2
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) )
% 0.30/0.46 => ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan3_type,type,
% 0.30/0.46 quantDeMorgan3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan3,definition,
% 0.30/0.46 ( quantDeMorgan3
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan4_type,type,
% 0.30/0.46 quantDeMorgan4: $o ).
% 0.30/0.46
% 0.30/0.46 thf(quantDeMorgan4,definition,
% 0.30/0.46 ( quantDeMorgan4
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) )
% 0.30/0.46 => ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setI_type,type,
% 0.30/0.46 prop2setI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2setI,definition,
% 0.30/0.46 ( prop2setI
% 0.30/0.46 = ( ! [Xphi: $o] :
% 0.30/0.46 ( Xphi
% 0.30/0.46 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(set2prop_type,type,
% 0.30/0.46 set2prop: $i > $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set2propI_type,type,
% 0.30/0.46 prop2set2propI: $o ).
% 0.30/0.46
% 0.30/0.46 thf(prop2set2propI,definition,
% 0.30/0.46 ( prop2set2propI
% 0.30/0.46 = ( ! [Xphi: $o] :
% 0.30/0.46 ( Xphi
% 0.30/0.46 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notdexE_type,type,
% 0.30/0.46 notdexE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notdexE,definition,
% 0.30/0.46 ( notdexE
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ( Xphi @ Xx ) )
% 0.30/0.46 => ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(notdallE_type,type,
% 0.30/0.46 notdallE: $o ).
% 0.30/0.46
% 0.30/0.46 thf(notdallE,definition,
% 0.30/0.46 ( notdallE
% 0.30/0.46 = ( ! [A: $i,Xphi: $i > $o] :
% 0.30/0.46 ( ~ ! [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 => ( Xphi @ Xx ) )
% 0.30/0.46 => ? [Xx: $i] :
% 0.30/0.46 ( ( in @ Xx @ A )
% 0.30/0.46 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI1_type,type,
% 0.30/0.46 exuI1: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI1,definition,
% 0.30/0.46 ( exuI1
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 & ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI3_type,type,
% 0.30/0.46 exuI3: $o ).
% 0.30/0.46
% 0.30/0.46 thf(exuI3,definition,
% 0.30/0.46 ( exuI3
% 0.30/0.46 = ( ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] : ( Xphi @ Xx )
% 0.30/0.46 => ( ! [Xx: $i,Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xx )
% 0.30/0.46 => ( ( Xphi @ Xy )
% 0.30/0.46 => ( Xx = Xy ) ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 thf(exuI2,conjecture,
% 0.30/0.46 ( setextAx
% 0.30/0.46 => ( emptysetAx
% 0.30/0.46 => ( setadjoinAx
% 0.30/0.46 => ( powersetAx
% 0.30/0.46 => ( setunionAx
% 0.30/0.46 => ( omega0Ax
% 0.30/0.46 => ( omegaSAx
% 0.30/0.46 => ( omegaIndAx
% 0.30/0.46 => ( replAx
% 0.30/0.46 => ( foundationAx
% 0.30/0.46 => ( wellorderingAx
% 0.30/0.46 => ( descrp
% 0.30/0.46 => ( dsetconstrI
% 0.30/0.46 => ( dsetconstrEL
% 0.30/0.46 => ( dsetconstrER
% 0.30/0.46 => ( exuE1
% 0.30/0.46 => ( prop2setE
% 0.30/0.46 => ( emptysetE
% 0.30/0.46 => ( emptysetimpfalse
% 0.30/0.46 => ( notinemptyset
% 0.30/0.46 => ( exuE3e
% 0.30/0.46 => ( setext
% 0.30/0.46 => ( emptyI
% 0.30/0.46 => ( noeltsimpempty
% 0.30/0.46 => ( setbeta
% 0.30/0.46 => ( nonemptyE1
% 0.30/0.46 => ( nonemptyI
% 0.30/0.46 => ( nonemptyI1
% 0.30/0.46 => ( setadjoinIL
% 0.30/0.46 => ( emptyinunitempty
% 0.30/0.46 => ( setadjoinIR
% 0.30/0.46 => ( setadjoinE
% 0.30/0.46 => ( setadjoinOr
% 0.30/0.46 => ( setoftrueEq
% 0.30/0.46 => ( powersetI
% 0.30/0.46 => ( emptyinPowerset
% 0.30/0.46 => ( emptyInPowerset
% 0.30/0.46 => ( powersetE
% 0.30/0.46 => ( setunionI
% 0.30/0.46 => ( setunionE
% 0.30/0.46 => ( subPowSU
% 0.30/0.46 => ( exuE2
% 0.30/0.46 => ( nonemptyImpWitness
% 0.30/0.46 => ( uniqinunit
% 0.30/0.46 => ( notinsingleton
% 0.30/0.46 => ( eqinunit
% 0.30/0.46 => ( singletonsswitch
% 0.30/0.46 => ( upairsetE
% 0.30/0.46 => ( upairsetIL
% 0.30/0.46 => ( upairsetIR
% 0.30/0.46 => ( emptyE1
% 0.30/0.46 => ( vacuousDall
% 0.30/0.46 => ( quantDeMorgan1
% 0.30/0.46 => ( quantDeMorgan2
% 0.30/0.46 => ( quantDeMorgan3
% 0.30/0.46 => ( quantDeMorgan4
% 0.30/0.46 => ( prop2setI
% 0.30/0.46 => ( prop2set2propI
% 0.30/0.46 => ( notdexE
% 0.30/0.46 => ( notdallE
% 0.30/0.46 => ( exuI1
% 0.30/0.46 => ( exuI3
% 0.30/0.46 => ! [Xphi: $i > $o] :
% 0.30/0.46 ( ? [Xx: $i] :
% 0.30/0.46 ! [Xy: $i] :
% 0.30/0.46 ( ( Xphi @ Xy )
% 0.30/0.46 <=> ( Xy = Xx ) )
% 0.30/0.46 => ( exu
% 0.30/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.30/0.46
% 0.30/0.46 %------------------------------------------------------------------------------
% 0.30/0.46 ------------------------
% 1.89/1.35 ---- Embedded in THF ---
% 1.89/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.89/1.35 %%% Generated on Tue Feb 24 12:26:24 EST 2026
% 1.89/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.89/1.35 %%% Logic specification used:
% 1.89/1.35 %%% thf(spec, logic, $$dhol).
% 1.89/1.35
% 1.89/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.xzwazKCSaL/DTF2DTF12476.p
% See solution above
% 1.89/1.35 ------------------------
% 1.89/1.37 ---- Cleaned THF ---
% 1.89/1.37 thf(in_type,type,
% 1.89/1.37 in: $i > $i > $o ).
% 1.89/1.37
% 1.89/1.37 thf(exu_type,type,
% 1.89/1.37 exu: ( $i > $o ) > $o ).
% 1.89/1.37
% 1.89/1.37 thf(exu,definition,
% 1.89/1.37 ( exu
% 1.89/1.37 = ( ^ [Xphi: $i > $o] :
% 1.89/1.37 ? [Xx: $i] :
% 1.89/1.37 ( ( Xphi @ Xx )
% 1.89/1.37 & ! [Xy: $i] :
% 1.89/1.37 ( ( Xphi @ Xy )
% 1.89/1.37 => ( Xx = Xy ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setextAx_type,type,
% 1.89/1.37 setextAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setextAx,definition,
% 1.89/1.37 ( setextAx
% 1.89/1.37 = ( ! [A: $i,B: $i] :
% 1.89/1.37 ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ A )
% 1.89/1.37 <=> ( in @ Xx @ B ) )
% 1.89/1.37 => ( A = B ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(emptyset_type,type,
% 1.89/1.37 emptyset: $i ).
% 1.89/1.37
% 1.89/1.37 thf(emptysetAx_type,type,
% 1.89/1.37 emptysetAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(emptysetAx,definition,
% 1.89/1.37 ( emptysetAx
% 1.89/1.37 = ( ! [Xx: $i] :
% 1.89/1.37 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoin_type,type,
% 1.89/1.37 setadjoin: $i > $i > $i ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinAx_type,type,
% 1.89/1.37 setadjoinAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinAx,definition,
% 1.89/1.37 ( setadjoinAx
% 1.89/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.89/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.89/1.37 <=> ( ( Xy = Xx )
% 1.89/1.37 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(powerset_type,type,
% 1.89/1.37 powerset: $i > $i ).
% 1.89/1.37
% 1.89/1.37 thf(powersetAx_type,type,
% 1.89/1.37 powersetAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(powersetAx,definition,
% 1.89/1.37 ( powersetAx
% 1.89/1.37 = ( ! [A: $i,B: $i] :
% 1.89/1.37 ( ( in @ B @ ( powerset @ A ) )
% 1.89/1.37 <=> ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ B )
% 1.89/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setunion_type,type,
% 1.89/1.37 setunion: $i > $i ).
% 1.89/1.37
% 1.89/1.37 thf(setunionAx_type,type,
% 1.89/1.37 setunionAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setunionAx,definition,
% 1.89/1.37 ( setunionAx
% 1.89/1.37 = ( ! [A: $i,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ ( setunion @ A ) )
% 1.89/1.37 <=> ? [B: $i] :
% 1.89/1.37 ( ( in @ Xx @ B )
% 1.89/1.37 & ( in @ B @ A ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(omega_type,type,
% 1.89/1.37 omega: $i ).
% 1.89/1.37
% 1.89/1.37 thf(omega0Ax_type,type,
% 1.89/1.37 omega0Ax: $o ).
% 1.89/1.37
% 1.89/1.37 thf(omega0Ax,definition,
% 1.89/1.37 ( omega0Ax
% 1.89/1.37 = ( in @ emptyset @ omega ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(omegaSAx_type,type,
% 1.89/1.37 omegaSAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(omegaSAx,definition,
% 1.89/1.37 ( omegaSAx
% 1.89/1.37 = ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ omega )
% 1.89/1.37 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(omegaIndAx_type,type,
% 1.89/1.37 omegaIndAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(omegaIndAx,definition,
% 1.89/1.37 ( omegaIndAx
% 1.89/1.37 = ( ! [A: $i] :
% 1.89/1.37 ( ( ( in @ emptyset @ A )
% 1.89/1.37 & ! [Xx: $i] :
% 1.89/1.37 ( ( ( in @ Xx @ omega )
% 1.89/1.37 & ( in @ Xx @ A ) )
% 1.89/1.37 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.89/1.37 => ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ omega )
% 1.89/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(replAx_type,type,
% 1.89/1.37 replAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(replAx,definition,
% 1.89/1.37 ( replAx
% 1.89/1.37 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.89/1.37 ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ A )
% 1.89/1.37 => ( exu
% 1.89/1.37 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.89/1.37 => ? [B: $i] :
% 1.89/1.37 ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ B )
% 1.89/1.37 <=> ? [Xy: $i] :
% 1.89/1.37 ( ( in @ Xy @ A )
% 1.89/1.37 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(foundationAx_type,type,
% 1.89/1.37 foundationAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(foundationAx,definition,
% 1.89/1.37 ( foundationAx
% 1.89/1.37 = ( ! [A: $i] :
% 1.89/1.37 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.89/1.37 => ? [B: $i] :
% 1.89/1.37 ( ( in @ B @ A )
% 1.89/1.37 & ~ ? [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ B )
% 1.89/1.37 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(wellorderingAx_type,type,
% 1.89/1.37 wellorderingAx: $o ).
% 1.89/1.37
% 1.89/1.37 thf(wellorderingAx,definition,
% 1.89/1.37 ( wellorderingAx
% 1.89/1.37 = ( ! [A: $i] :
% 1.89/1.37 ? [B: $i] :
% 1.89/1.37 ( ! [C: $i] :
% 1.89/1.37 ( ( in @ C @ B )
% 1.89/1.37 => ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ C )
% 1.89/1.37 => ( in @ Xx @ A ) ) )
% 1.89/1.37 & ! [Xx: $i,Xy: $i] :
% 1.89/1.37 ( ( ( in @ Xx @ A )
% 1.89/1.37 & ( in @ Xy @ A ) )
% 1.89/1.37 => ( ! [C: $i] :
% 1.89/1.37 ( ( in @ C @ B )
% 1.89/1.37 => ( ( in @ Xx @ C )
% 1.89/1.37 <=> ( in @ Xy @ C ) ) )
% 1.89/1.37 => ( Xx = Xy ) ) )
% 1.89/1.37 & ! [C: $i,D: $i] :
% 1.89/1.37 ( ( ( in @ C @ B )
% 1.89/1.37 & ( in @ D @ B ) )
% 1.89/1.37 => ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ C )
% 1.89/1.37 => ( in @ Xx @ D ) )
% 1.89/1.37 | ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ D )
% 1.89/1.37 => ( in @ Xx @ C ) ) ) )
% 1.89/1.37 & ! [C: $i] :
% 1.89/1.37 ( ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ C )
% 1.89/1.37 => ( in @ Xx @ A ) )
% 1.89/1.37 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.89/1.37 => ? [D: $i,Xx: $i] :
% 1.89/1.37 ( ( in @ D @ B )
% 1.89/1.37 & ( in @ Xx @ C )
% 1.89/1.37 & ~ ? [Xy: $i] :
% 1.89/1.37 ( ( in @ Xy @ D )
% 1.89/1.37 & ( in @ Xy @ C ) )
% 1.89/1.37 & ! [E: $i] :
% 1.89/1.37 ( ( in @ E @ B )
% 1.89/1.37 => ( ! [Xy: $i] :
% 1.89/1.37 ( ( in @ Xy @ E )
% 1.89/1.37 => ( in @ Xy @ D ) )
% 1.89/1.37 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(descr_type,type,
% 1.89/1.37 descr: ( $i > $o ) > $i ).
% 1.89/1.37
% 1.89/1.37 thf(descrp_type,type,
% 1.89/1.37 descrp: $o ).
% 1.89/1.37
% 1.89/1.37 thf(descrp,definition,
% 1.89/1.37 ( descrp
% 1.89/1.37 = ( ! [Xphi: $i > $o] :
% 1.89/1.37 ( ( exu
% 1.89/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.89/1.37 => ( Xphi
% 1.89/1.37 @ ( descr
% 1.89/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(dsetconstr_type,type,
% 1.89/1.37 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.89/1.37
% 1.89/1.37 thf(dsetconstrI_type,type,
% 1.89/1.37 dsetconstrI: $o ).
% 1.89/1.37
% 1.89/1.37 thf(dsetconstrI,definition,
% 1.89/1.37 ( dsetconstrI
% 1.89/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ A )
% 1.89/1.37 => ( ( Xphi @ Xx )
% 1.89/1.37 => ( in @ Xx
% 1.89/1.37 @ ( dsetconstr @ A
% 1.89/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(dsetconstrEL_type,type,
% 1.89/1.37 dsetconstrEL: $o ).
% 1.89/1.37
% 1.89/1.37 thf(dsetconstrEL,definition,
% 1.89/1.37 ( dsetconstrEL
% 1.89/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx
% 1.89/1.37 @ ( dsetconstr @ A
% 1.89/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.89/1.37 => ( in @ Xx @ A ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(dsetconstrER_type,type,
% 1.89/1.37 dsetconstrER: $o ).
% 1.89/1.37
% 1.89/1.37 thf(dsetconstrER,definition,
% 1.89/1.37 ( dsetconstrER
% 1.89/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx
% 1.89/1.37 @ ( dsetconstr @ A
% 1.89/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.89/1.37 => ( Xphi @ Xx ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(exuE1_type,type,
% 1.89/1.37 exuE1: $o ).
% 1.89/1.37
% 1.89/1.37 thf(exuE1,definition,
% 1.89/1.37 ( exuE1
% 1.89/1.37 = ( ! [Xphi: $i > $o] :
% 1.89/1.37 ( ( exu
% 1.89/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.89/1.37 => ? [Xx: $i] :
% 1.89/1.37 ( ( Xphi @ Xx )
% 1.89/1.37 & ! [Xy: $i] :
% 1.89/1.37 ( ( Xphi @ Xy )
% 1.89/1.37 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(prop2set_type,type,
% 1.89/1.37 prop2set: $o > $i ).
% 1.89/1.37
% 1.89/1.37 thf(prop2setE_type,type,
% 1.89/1.37 prop2setE: $o ).
% 1.89/1.37
% 1.89/1.37 thf(prop2setE,definition,
% 1.89/1.37 ( prop2setE
% 1.89/1.37 = ( ! [Xphi: $o,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.89/1.37 => Xphi ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(emptysetE_type,type,
% 1.89/1.37 emptysetE: $o ).
% 1.89/1.37
% 1.89/1.37 thf(emptysetE,definition,
% 1.89/1.37 ( emptysetE
% 1.89/1.37 = ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ emptyset )
% 1.89/1.37 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(emptysetimpfalse_type,type,
% 1.89/1.37 emptysetimpfalse: $o ).
% 1.89/1.37
% 1.89/1.37 thf(emptysetimpfalse,definition,
% 1.89/1.37 ( emptysetimpfalse
% 1.89/1.37 = ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ emptyset )
% 1.89/1.37 => $false ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(notinemptyset_type,type,
% 1.89/1.37 notinemptyset: $o ).
% 1.89/1.37
% 1.89/1.37 thf(notinemptyset,definition,
% 1.89/1.37 ( notinemptyset
% 1.89/1.37 = ( ! [Xx: $i] :
% 1.89/1.37 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(exuE3e_type,type,
% 1.89/1.37 exuE3e: $o ).
% 1.89/1.37
% 1.89/1.37 thf(exuE3e,definition,
% 1.89/1.37 ( exuE3e
% 1.89/1.37 = ( ! [Xphi: $i > $o] :
% 1.89/1.37 ( ( exu
% 1.89/1.37 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.89/1.37 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setext_type,type,
% 1.89/1.37 setext: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setext,definition,
% 1.89/1.37 ( setext
% 1.89/1.37 = ( ! [A: $i,B: $i] :
% 1.89/1.37 ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ A )
% 1.89/1.37 => ( in @ Xx @ B ) )
% 1.89/1.37 => ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ B )
% 1.89/1.37 => ( in @ Xx @ A ) )
% 1.89/1.37 => ( A = B ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(emptyI_type,type,
% 1.89/1.37 emptyI: $o ).
% 1.89/1.37
% 1.89/1.37 thf(emptyI,definition,
% 1.89/1.37 ( emptyI
% 1.89/1.37 = ( ! [A: $i] :
% 1.89/1.37 ( ! [Xx: $i] :
% 1.89/1.37 ~ ( in @ Xx @ A )
% 1.89/1.37 => ( A = emptyset ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(noeltsimpempty_type,type,
% 1.89/1.37 noeltsimpempty: $o ).
% 1.89/1.37
% 1.89/1.37 thf(noeltsimpempty,definition,
% 1.89/1.37 ( noeltsimpempty
% 1.89/1.37 = ( ! [A: $i] :
% 1.89/1.37 ( ! [Xx: $i] :
% 1.89/1.37 ~ ( in @ Xx @ A )
% 1.89/1.37 => ( A = emptyset ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setbeta_type,type,
% 1.89/1.37 setbeta: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setbeta,definition,
% 1.89/1.37 ( setbeta
% 1.89/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ A )
% 1.89/1.37 => ( ( in @ Xx
% 1.89/1.37 @ ( dsetconstr @ A
% 1.89/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.89/1.37 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(nonempty_type,type,
% 1.89/1.37 nonempty: $i > $o ).
% 1.89/1.37
% 1.89/1.37 thf(nonempty,definition,
% 1.89/1.37 ( nonempty
% 1.89/1.37 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(nonemptyE1_type,type,
% 1.89/1.37 nonemptyE1: $o ).
% 1.89/1.37
% 1.89/1.37 thf(nonemptyE1,definition,
% 1.89/1.37 ( nonemptyE1
% 1.89/1.37 = ( ! [A: $i] :
% 1.89/1.37 ( ( nonempty @ A )
% 1.89/1.37 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(nonemptyI_type,type,
% 1.89/1.37 nonemptyI: $o ).
% 1.89/1.37
% 1.89/1.37 thf(nonemptyI,definition,
% 1.89/1.37 ( nonemptyI
% 1.89/1.37 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ A )
% 1.89/1.37 => ( ( Xphi @ Xx )
% 1.89/1.37 => ( nonempty
% 1.89/1.37 @ ( dsetconstr @ A
% 1.89/1.37 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(nonemptyI1_type,type,
% 1.89/1.37 nonemptyI1: $o ).
% 1.89/1.37
% 1.89/1.37 thf(nonemptyI1,definition,
% 1.89/1.37 ( nonemptyI1
% 1.89/1.37 = ( ! [A: $i] :
% 1.89/1.37 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.89/1.37 => ( nonempty @ A ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinIL_type,type,
% 1.89/1.37 setadjoinIL: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinIL,definition,
% 1.89/1.37 ( setadjoinIL
% 1.89/1.37 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(emptyinunitempty_type,type,
% 1.89/1.37 emptyinunitempty: $o ).
% 1.89/1.37
% 1.89/1.37 thf(emptyinunitempty,definition,
% 1.89/1.37 ( emptyinunitempty
% 1.89/1.37 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinIR_type,type,
% 1.89/1.37 setadjoinIR: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinIR,definition,
% 1.89/1.37 ( setadjoinIR
% 1.89/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.89/1.37 ( ( in @ Xy @ A )
% 1.89/1.37 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinE_type,type,
% 1.89/1.37 setadjoinE: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinE,definition,
% 1.89/1.37 ( setadjoinE
% 1.89/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.89/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.89/1.37 => ! [Xphi: $o] :
% 1.89/1.37 ( ( ( Xy = Xx )
% 1.89/1.37 => Xphi )
% 1.89/1.37 => ( ( ( in @ Xy @ A )
% 1.89/1.37 => Xphi )
% 1.89/1.37 => Xphi ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinOr_type,type,
% 1.89/1.37 setadjoinOr: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setadjoinOr,definition,
% 1.89/1.37 ( setadjoinOr
% 1.89/1.37 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.89/1.37 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.89/1.37 => ( ( Xy = Xx )
% 1.89/1.37 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setoftrueEq_type,type,
% 1.89/1.37 setoftrueEq: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setoftrueEq,definition,
% 1.89/1.37 ( setoftrueEq
% 1.89/1.37 = ( ! [A: $i] :
% 1.89/1.37 ( ( dsetconstr @ A
% 1.89/1.37 @ ^ [Xx: $i] : $true )
% 1.89/1.37 = A ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(powersetI_type,type,
% 1.89/1.37 powersetI: $o ).
% 1.89/1.37
% 1.89/1.37 thf(powersetI,definition,
% 1.89/1.37 ( powersetI
% 1.89/1.37 = ( ! [A: $i,B: $i] :
% 1.89/1.37 ( ! [Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ B )
% 1.89/1.37 => ( in @ Xx @ A ) )
% 1.89/1.37 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(emptyinPowerset_type,type,
% 1.89/1.37 emptyinPowerset: $o ).
% 1.89/1.37
% 1.89/1.37 thf(emptyinPowerset,definition,
% 1.89/1.37 ( emptyinPowerset
% 1.89/1.37 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(emptyInPowerset_type,type,
% 1.89/1.37 emptyInPowerset: $o ).
% 1.89/1.37
% 1.89/1.37 thf(emptyInPowerset,definition,
% 1.89/1.37 ( emptyInPowerset
% 1.89/1.37 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(powersetE_type,type,
% 1.89/1.37 powersetE: $o ).
% 1.89/1.37
% 1.89/1.37 thf(powersetE,definition,
% 1.89/1.37 ( powersetE
% 1.89/1.37 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.89/1.37 ( ( in @ B @ ( powerset @ A ) )
% 1.89/1.37 => ( ( in @ Xx @ B )
% 1.89/1.37 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setunionI_type,type,
% 1.89/1.37 setunionI: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setunionI,definition,
% 1.89/1.37 ( setunionI
% 1.89/1.37 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.89/1.37 ( ( in @ Xx @ B )
% 1.89/1.37 => ( ( in @ B @ A )
% 1.89/1.37 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(setunionE_type,type,
% 1.89/1.37 setunionE: $o ).
% 1.89/1.37
% 1.89/1.37 thf(setunionE,definition,
% 1.89/1.37 ( setunionE
% 1.89/1.37 = ( ! [A: $i,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ ( setunion @ A ) )
% 1.89/1.37 => ! [Xphi: $o] :
% 1.89/1.37 ( ! [B: $i] :
% 1.89/1.37 ( ( in @ Xx @ B )
% 1.89/1.37 => ( ( in @ B @ A )
% 1.89/1.37 => Xphi ) )
% 1.89/1.37 => Xphi ) ) ) ) ).
% 1.89/1.37
% 1.89/1.37 thf(subPowSU_type,type,
% 1.89/1.37 subPowSU: $o ).
% 1.89/1.37
% 1.89/1.37 thf(subPowSU,definition,
% 1.89/1.37 ( subPowSU
% 1.89/1.37 = ( ! [A: $i,Xx: $i] :
% 1.89/1.37 ( ( in @ Xx @ A )
% 1.89/1.37 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(exuE2_type,type,
% 1.89/1.38 exuE2: $o ).
% 1.89/1.38
% 1.89/1.38 thf(exuE2,definition,
% 1.89/1.38 ( exuE2
% 1.89/1.38 = ( ! [Xphi: $i > $o] :
% 1.89/1.38 ( ( exu
% 1.89/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.89/1.38 => ? [Xx: $i] :
% 1.89/1.38 ! [Xy: $i] :
% 1.89/1.38 ( ( Xphi @ Xy )
% 1.89/1.38 <=> ( Xy = Xx ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(nonemptyImpWitness_type,type,
% 1.89/1.38 nonemptyImpWitness: $o ).
% 1.89/1.38
% 1.89/1.38 thf(nonemptyImpWitness,definition,
% 1.89/1.38 ( nonemptyImpWitness
% 1.89/1.38 = ( ! [A: $i] :
% 1.89/1.38 ( ( nonempty @ A )
% 1.89/1.38 => ? [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 & $true ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(uniqinunit_type,type,
% 1.89/1.38 uniqinunit: $o ).
% 1.89/1.38
% 1.89/1.38 thf(uniqinunit,definition,
% 1.89/1.38 ( uniqinunit
% 1.89/1.38 = ( ! [Xx: $i,Xy: $i] :
% 1.89/1.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.89/1.38 => ( Xx = Xy ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(notinsingleton_type,type,
% 1.89/1.38 notinsingleton: $o ).
% 1.89/1.38
% 1.89/1.38 thf(notinsingleton,definition,
% 1.89/1.38 ( notinsingleton
% 1.89/1.38 = ( ! [Xx: $i,Xy: $i] :
% 1.89/1.38 ( ( Xx != Xy )
% 1.89/1.38 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(eqinunit_type,type,
% 1.89/1.38 eqinunit: $o ).
% 1.89/1.38
% 1.89/1.38 thf(eqinunit,definition,
% 1.89/1.38 ( eqinunit
% 1.89/1.38 = ( ! [Xx: $i,Xy: $i] :
% 1.89/1.38 ( ( Xx = Xy )
% 1.89/1.38 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(singletonsswitch_type,type,
% 1.89/1.38 singletonsswitch: $o ).
% 1.89/1.38
% 1.89/1.38 thf(singletonsswitch,definition,
% 1.89/1.38 ( singletonsswitch
% 1.89/1.38 = ( ! [Xx: $i,Xy: $i] :
% 1.89/1.38 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.89/1.38 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(upairsetE_type,type,
% 1.89/1.38 upairsetE: $o ).
% 1.89/1.38
% 1.89/1.38 thf(upairsetE,definition,
% 1.89/1.38 ( upairsetE
% 1.89/1.38 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.89/1.38 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.89/1.38 => ( ( Xz = Xx )
% 1.89/1.38 | ( Xz = Xy ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(upairsetIL_type,type,
% 1.89/1.38 upairsetIL: $o ).
% 1.89/1.38
% 1.89/1.38 thf(upairsetIL,definition,
% 1.89/1.38 ( upairsetIL
% 1.89/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(upairsetIR_type,type,
% 1.89/1.38 upairsetIR: $o ).
% 1.89/1.38
% 1.89/1.38 thf(upairsetIR,definition,
% 1.89/1.38 ( upairsetIR
% 1.89/1.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(emptyE1_type,type,
% 1.89/1.38 emptyE1: $o ).
% 1.89/1.38
% 1.89/1.38 thf(emptyE1,definition,
% 1.89/1.38 ( emptyE1
% 1.89/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 1.89/1.38 ( ? [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 & ( Xphi @ Xx ) )
% 1.89/1.38 => ( ( ( dsetconstr @ A
% 1.89/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.89/1.38 = emptyset )
% 1.89/1.38 => $false ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(vacuousDall_type,type,
% 1.89/1.38 vacuousDall: $o ).
% 1.89/1.38
% 1.89/1.38 thf(vacuousDall,definition,
% 1.89/1.38 ( vacuousDall
% 1.89/1.38 = ( ! [Xphi: $i > $o,Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ emptyset )
% 1.89/1.38 => ( Xphi @ Xx ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(quantDeMorgan1_type,type,
% 1.89/1.38 quantDeMorgan1: $o ).
% 1.89/1.38
% 1.89/1.38 thf(quantDeMorgan1,definition,
% 1.89/1.38 ( quantDeMorgan1
% 1.89/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 1.89/1.38 ( ~ ! [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 => ( Xphi @ Xx ) )
% 1.89/1.38 => ? [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(quantDeMorgan2_type,type,
% 1.89/1.38 quantDeMorgan2: $o ).
% 1.89/1.38
% 1.89/1.38 thf(quantDeMorgan2,definition,
% 1.89/1.38 ( quantDeMorgan2
% 1.89/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 1.89/1.38 ( ! [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 => ~ ( Xphi @ Xx ) )
% 1.89/1.38 => ~ ? [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 & ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(quantDeMorgan3_type,type,
% 1.89/1.38 quantDeMorgan3: $o ).
% 1.89/1.38
% 1.89/1.38 thf(quantDeMorgan3,definition,
% 1.89/1.38 ( quantDeMorgan3
% 1.89/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 1.89/1.38 ( ~ ? [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 & ( Xphi @ Xx ) )
% 1.89/1.38 => ! [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(quantDeMorgan4_type,type,
% 1.89/1.38 quantDeMorgan4: $o ).
% 1.89/1.38
% 1.89/1.38 thf(quantDeMorgan4,definition,
% 1.89/1.38 ( quantDeMorgan4
% 1.89/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 1.89/1.38 ( ? [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 & ~ ( Xphi @ Xx ) )
% 1.89/1.38 => ~ ! [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 => ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(prop2setI_type,type,
% 1.89/1.38 prop2setI: $o ).
% 1.89/1.38
% 1.89/1.38 thf(prop2setI,definition,
% 1.89/1.38 ( prop2setI
% 1.89/1.38 = ( ! [Xphi: $o] :
% 1.89/1.38 ( Xphi
% 1.89/1.38 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(set2prop_type,type,
% 1.89/1.38 set2prop: $i > $o ).
% 1.89/1.38
% 1.89/1.38 thf(prop2set2propI_type,type,
% 1.89/1.38 prop2set2propI: $o ).
% 1.89/1.38
% 1.89/1.38 thf(prop2set2propI,definition,
% 1.89/1.38 ( prop2set2propI
% 1.89/1.38 = ( ! [Xphi: $o] :
% 1.89/1.38 ( Xphi
% 1.89/1.38 => ( set2prop @ ( prop2set @ Xphi ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(notdexE_type,type,
% 1.89/1.38 notdexE: $o ).
% 1.89/1.38
% 1.89/1.38 thf(notdexE,definition,
% 1.89/1.38 ( notdexE
% 1.89/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 1.89/1.38 ( ~ ? [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 & ( Xphi @ Xx ) )
% 1.89/1.38 => ! [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(notdallE_type,type,
% 1.89/1.38 notdallE: $o ).
% 1.89/1.38
% 1.89/1.38 thf(notdallE,definition,
% 1.89/1.38 ( notdallE
% 1.89/1.38 = ( ! [A: $i,Xphi: $i > $o] :
% 1.89/1.38 ( ~ ! [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 => ( Xphi @ Xx ) )
% 1.89/1.38 => ? [Xx: $i] :
% 1.89/1.38 ( ( in @ Xx @ A )
% 1.89/1.38 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(exuI1_type,type,
% 1.89/1.38 exuI1: $o ).
% 1.89/1.38
% 1.89/1.38 thf(exuI1,definition,
% 1.89/1.38 ( exuI1
% 1.89/1.38 = ( ! [Xphi: $i > $o] :
% 1.89/1.38 ( ? [Xx: $i] :
% 1.89/1.38 ( ( Xphi @ Xx )
% 1.89/1.38 & ! [Xy: $i] :
% 1.89/1.38 ( ( Xphi @ Xy )
% 1.89/1.38 => ( Xx = Xy ) ) )
% 1.89/1.38 => ( exu
% 1.89/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(exuI3_type,type,
% 1.89/1.38 exuI3: $o ).
% 1.89/1.38
% 1.89/1.38 thf(exuI3,definition,
% 1.89/1.38 ( exuI3
% 1.89/1.38 = ( ! [Xphi: $i > $o] :
% 1.89/1.38 ( ? [Xx: $i] : ( Xphi @ Xx )
% 1.89/1.38 => ( ! [Xx: $i,Xy: $i] :
% 1.89/1.38 ( ( Xphi @ Xx )
% 1.89/1.38 => ( ( Xphi @ Xy )
% 1.89/1.38 => ( Xx = Xy ) ) )
% 1.89/1.38 => ( exu
% 1.89/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.89/1.38
% 1.89/1.38 thf(exuI2,conjecture,
% 1.89/1.38 ( setextAx
% 1.89/1.38 => ( emptysetAx
% 1.89/1.38 => ( setadjoinAx
% 1.89/1.38 => ( powersetAx
% 1.89/1.38 => ( setunionAx
% 1.89/1.38 => ( omega0Ax
% 1.89/1.38 => ( omegaSAx
% 1.89/1.38 => ( omegaIndAx
% 1.89/1.38 => ( replAx
% 1.89/1.38 => ( foundationAx
% 1.89/1.38 => ( wellorderingAx
% 1.89/1.38 => ( descrp
% 1.89/1.38 => ( dsetconstrI
% 1.89/1.38 => ( dsetconstrEL
% 1.89/1.38 => ( dsetconstrER
% 1.89/1.38 => ( exuE1
% 1.89/1.38 => ( prop2setE
% 1.89/1.38 => ( emptysetE
% 1.89/1.38 => ( emptysetimpfalse
% 1.89/1.38 => ( notinemptyset
% 1.89/1.38 => ( exuE3e
% 1.89/1.38 => ( setext
% 1.89/1.38 => ( emptyI
% 1.89/1.38 => ( noeltsimpempty
% 1.89/1.38 => ( setbeta
% 1.89/1.38 => ( nonemptyE1
% 1.89/1.38 => ( nonemptyI
% 1.89/1.38 => ( nonemptyI1
% 1.89/1.38 => ( setadjoinIL
% 1.89/1.38 => ( emptyinunitempty
% 1.89/1.38 => ( setadjoinIR
% 1.89/1.38 => ( setadjoinE
% 1.89/1.38 => ( setadjoinOr
% 1.89/1.38 => ( setoftrueEq
% 1.89/1.38 => ( powersetI
% 1.89/1.38 => ( emptyinPowerset
% 1.89/1.38 => ( emptyInPowerset
% 1.89/1.38 => ( powersetE
% 1.89/1.38 => ( setunionI
% 1.89/1.38 => ( setunionE
% 1.89/1.38 => ( subPowSU
% 1.89/1.38 => ( exuE2
% 1.89/1.38 => ( nonemptyImpWitness
% 1.89/1.38 => ( uniqinunit
% 1.89/1.38 => ( notinsingleton
% 1.89/1.38 => ( eqinunit
% 1.89/1.38 => ( singletonsswitch
% 1.89/1.38 => ( upairsetE
% 1.89/1.38 => ( upairsetIL
% 1.89/1.38 => ( upairsetIR
% 1.89/1.38 => ( emptyE1
% 1.89/1.38 => ( vacuousDall
% 1.89/1.38 => ( quantDeMorgan1
% 1.89/1.38 => ( quantDeMorgan2
% 1.89/1.38 => ( quantDeMorgan3
% 1.89/1.38 => ( quantDeMorgan4
% 1.89/1.38 => ( prop2setI
% 1.89/1.38 => ( prop2set2propI
% 1.89/1.38 => ( notdexE
% 1.89/1.38 => ( notdallE
% 1.89/1.38 => ( exuI1
% 1.89/1.38 => ( exuI3
% 1.89/1.38 => ! [Xphi: $i > $o] :
% 1.89/1.38 ( ? [Xx: $i] :
% 1.89/1.38 ! [Xy: $i] :
% 1.89/1.38 ( ( Xphi @ Xy )
% 1.89/1.38 <=> ( Xy = Xx ) )
% 1.89/1.38 => ( exu
% 1.89/1.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.89/1.38 ------------------------
% 1.89/1.39 % (12762)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_12476 for (2999ds/275Mi)
% 1.89/1.39 % (12761)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_12476 for (2999ds/2Mi)
% 1.89/1.39 % (12761)Instruction limit reached!
% 1.89/1.39 % (12761)------------------------------
% 1.89/1.39 % (12761)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.89/1.39 % (12761)Termination reason: Unknown
% 1.89/1.39 % (12761)Termination phase: shuffling
% 1.89/1.39
% 1.89/1.39 % (12761)Memory used [KB]: 1151
% 1.89/1.39 % (12761)Time elapsed: 0.002 s
% 1.89/1.39 % (12761)Instructions burned: 3 (million)
% 1.89/1.39 % (12761)------------------------------
% 1.89/1.39 % (12761)------------------------------
% 2.07/1.40 % (12757)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_12476 for (2999ds/183Mi)
% 2.07/1.40 % (12758)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_12476 for (2999ds/4Mi)
% 2.07/1.40 % (12759)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_12476 for (2999ds/27Mi)
% 2.07/1.40 % (12760)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_12476 for (2999ds/2Mi)
% 2.07/1.40 % (12763)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_12476 for (2999ds/18Mi)
% 2.07/1.40 % (12760)Instruction limit reached!
% 2.07/1.40 % (12760)------------------------------
% 2.07/1.40 % (12760)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.40 % (12760)Termination reason: Unknown
% 2.07/1.40 % (12760)Termination phase: shuffling
% 2.07/1.40
% 2.07/1.40 % (12760)Memory used [KB]: 1151
% 2.07/1.40 % (12760)Time elapsed: 0.004 s
% 2.07/1.40 % (12760)Instructions burned: 3 (million)
% 2.07/1.40 % (12760)------------------------------
% 2.07/1.40 % (12760)------------------------------
% 2.07/1.40 % (12758)Instruction limit reached!
% 2.07/1.40 % (12758)------------------------------
% 2.07/1.40 % (12758)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.40 % (12758)Termination reason: Unknown
% 2.07/1.40 % (12758)Termination phase: shuffling
% 2.07/1.40
% 2.07/1.40 % (12758)Memory used [KB]: 1151
% 2.07/1.40 % (12758)Time elapsed: 0.005 s
% 2.07/1.40 % (12758)Instructions burned: 5 (million)
% 2.07/1.40 % (12758)------------------------------
% 2.07/1.40 % (12758)------------------------------
% 2.07/1.40 % (12764)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_12476 for (2999ds/3Mi)
% 2.07/1.40 % (12764)Instruction limit reached!
% 2.07/1.40 % (12764)------------------------------
% 2.07/1.40 % (12764)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.40 % (12764)Termination reason: Unknown
% 2.07/1.40 % (12764)Termination phase: shuffling
% 2.07/1.40
% 2.07/1.40 % (12764)Memory used [KB]: 1151
% 2.07/1.40 % (12764)Time elapsed: 0.003 s
% 2.07/1.40 % (12764)Instructions burned: 4 (million)
% 2.07/1.40 % (12764)------------------------------
% 2.07/1.40 % (12764)------------------------------
% 2.07/1.41 % (12763)Instruction limit reached!
% 2.07/1.41 % (12763)------------------------------
% 2.07/1.41 % (12763)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.41 % (12763)Termination reason: Unknown
% 2.07/1.41 % (12763)Termination phase: Preprocessing 3
% 2.07/1.41
% 2.07/1.41 % (12763)Memory used [KB]: 1663
% 2.07/1.41 % (12763)Time elapsed: 0.013 s
% 2.07/1.41 % (12763)Instructions burned: 19 (million)
% 2.07/1.41 % (12763)------------------------------
% 2.07/1.41 % (12763)------------------------------
% 2.07/1.41 % (12759)Instruction limit reached!
% 2.07/1.41 % (12759)------------------------------
% 2.07/1.41 % (12759)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.41 % (12759)Termination reason: Unknown
% 2.07/1.41 % (12759)Termination phase: Property scanning
% 2.07/1.41
% 2.07/1.41 % (12759)Memory used [KB]: 1407
% 2.07/1.41 % (12759)Time elapsed: 0.016 s
% 2.07/1.41 % (12759)Instructions burned: 28 (million)
% 2.07/1.41 % (12759)------------------------------
% 2.07/1.41 % (12759)------------------------------
% 2.07/1.41 % (12767)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_12476 for (2999ds/3Mi)
% 2.07/1.42 % (12767)Instruction limit reached!
% 2.07/1.42 % (12767)------------------------------
% 2.07/1.42 % (12767)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.42 % (12767)Termination reason: Unknown
% 2.07/1.42 % (12767)Termination phase: shuffling
% 2.07/1.42
% 2.07/1.42 % (12767)Memory used [KB]: 1151
% 2.07/1.42 % (12767)Time elapsed: 0.003 s
% 2.07/1.42 % (12767)Instructions burned: 5 (million)
% 2.07/1.42 % (12767)------------------------------
% 2.07/1.42 % (12767)------------------------------
% 2.07/1.42 % (12765)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_12476 for (2999ds/37Mi)
% 2.07/1.42 % (12766)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_12476 for (2999ds/15Mi)
% 2.07/1.43 % (12770)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_12476 for (2999ds/16Mi)
% 2.07/1.43 % (12768)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_12476 for (2999ds/1041Mi)
% 2.07/1.43 % (12766)Instruction limit reached!
% 2.07/1.43 % (12766)------------------------------
% 2.07/1.43 % (12766)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.43 % (12766)Termination reason: Unknown
% 2.07/1.43 % (12766)Termination phase: Preprocessing 3
% 2.07/1.43
% 2.07/1.43 % (12766)Memory used [KB]: 1535
% 2.07/1.43 % (12766)Time elapsed: 0.011 s
% 2.07/1.43 % (12766)Instructions burned: 16 (million)
% 2.07/1.43 % (12766)------------------------------
% 2.07/1.43 % (12766)------------------------------
% 2.07/1.43 % (12769)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_12476 for (2999ds/7Mi)
% 2.07/1.43 % (12770)Instruction limit reached!
% 2.07/1.43 % (12770)------------------------------
% 2.07/1.43 % (12770)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.43 % (12770)Termination reason: Unknown
% 2.07/1.43 % (12770)Termination phase: Property scanning
% 2.07/1.43
% 2.07/1.43 % (12770)Memory used [KB]: 1279
% 2.07/1.43 % (12770)Time elapsed: 0.007 s
% 2.07/1.43 % (12770)Instructions burned: 18 (million)
% 2.07/1.43 % (12770)------------------------------
% 2.07/1.43 % (12770)------------------------------
% 2.07/1.43 % (12769)Instruction limit reached!
% 2.07/1.43 % (12769)------------------------------
% 2.07/1.43 % (12769)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.43 % (12769)Termination reason: Unknown
% 2.07/1.43 % (12769)Termination phase: shuffling
% 2.07/1.43
% 2.07/1.43 % (12769)Memory used [KB]: 1151
% 2.07/1.43 % (12769)Time elapsed: 0.005 s
% 2.07/1.43 % (12769)Instructions burned: 7 (million)
% 2.07/1.43 % (12769)------------------------------
% 2.07/1.43 % (12769)------------------------------
% 2.07/1.44 % (12765)Instruction limit reached!
% 2.07/1.44 % (12765)------------------------------
% 2.07/1.44 % (12765)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.44 % (12765)Termination reason: Unknown
% 2.07/1.44 % (12765)Termination phase: Saturation
% 2.07/1.44
% 2.07/1.44 % (12765)Memory used [KB]: 5884
% 2.07/1.44 % (12765)Time elapsed: 0.020 s
% 2.07/1.44 % (12765)Instructions burned: 38 (million)
% 2.07/1.44 % (12765)------------------------------
% 2.07/1.44 % (12765)------------------------------
% 2.07/1.44 % (12772)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_12476 for (2999ds/3Mi)
% 2.07/1.44 % (12772)Instruction limit reached!
% 2.07/1.44 % (12772)------------------------------
% 2.07/1.44 % (12772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.44 % (12772)Termination reason: Unknown
% 2.07/1.44 % (12772)Termination phase: shuffling
% 2.07/1.44
% 2.07/1.44 % (12772)Memory used [KB]: 1151
% 2.07/1.44 % (12772)Time elapsed: 0.003 s
% 2.07/1.44 % (12772)Instructions burned: 5 (million)
% 2.07/1.44 % (12772)------------------------------
% 2.07/1.44 % (12772)------------------------------
% 2.07/1.45 % (12773)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_12476 for (2999ds/7Mi)
% 2.07/1.45 % (12771)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_12476 for (2999ds/3Mi)
% 2.07/1.45 % (12771)Instruction limit reached!
% 2.07/1.45 % (12771)------------------------------
% 2.07/1.45 % (12771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.45 % (12771)Termination reason: Unknown
% 2.07/1.45 % (12771)Termination phase: shuffling
% 2.07/1.45
% 2.07/1.45 % (12771)Memory used [KB]: 1151
% 2.07/1.45 % (12771)Time elapsed: 0.004 s
% 2.07/1.45 % (12771)Instructions burned: 4 (million)
% 2.07/1.45 % (12771)------------------------------
% 2.07/1.45 % (12771)------------------------------
% 2.07/1.45 % (12773)Instruction limit reached!
% 2.07/1.45 % (12773)------------------------------
% 2.07/1.45 % (12773)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.45 % (12773)Termination reason: Unknown
% 2.07/1.45 % (12773)Termination phase: shuffling
% 2.07/1.45
% 2.07/1.45 % (12773)Memory used [KB]: 1279
% 2.07/1.45 % (12773)Time elapsed: 0.004 s
% 2.07/1.45 % (12773)Instructions burned: 9 (million)
% 2.07/1.45 % (12773)------------------------------
% 2.07/1.45 % (12773)------------------------------
% 2.07/1.45 % (12762)First to succeed.
% 2.07/1.45 % (12762)Refutation found. Thanks to Tanya!
% 2.07/1.45 % SZS status Theorem for DTF2THF_12476
% 2.07/1.45 % SZS output start Proof for DTF2THF_12476
% 2.07/1.45 thf(func_def_0, type, in: $i > $i > $o).
% 2.07/1.45 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.07/1.45 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.07/1.45 thf(func_def_8, type, powerset: $i > $i).
% 2.07/1.45 thf(func_def_10, type, setunion: $i > $i).
% 2.07/1.45 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.07/1.45 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.07/1.45 thf(func_def_26, type, prop2set: $o > $i).
% 2.07/1.45 thf(func_def_36, type, nonempty: $i > $o).
% 2.07/1.45 thf(func_def_69, type, set2prop: $i > $o).
% 2.07/1.45 thf(func_def_87, type, sP0: $i > $i > $o).
% 2.07/1.45 thf(func_def_88, type, sP1: $i > $o).
% 2.07/1.45 thf(func_def_89, type, sP2: $i > $i > $o).
% 2.07/1.45 thf(func_def_90, type, sP3: $i > $i > $o).
% 2.07/1.45 thf(func_def_93, type, sK6: $i > $i).
% 2.07/1.45 thf(func_def_95, type, sK8: $i > $i).
% 2.07/1.45 thf(func_def_97, type, sK10: ($i > $o) > $i).
% 2.07/1.45 thf(func_def_98, type, sK11: $i > $o).
% 2.07/1.45 thf(func_def_99, type, sK12: $i > $i).
% 2.07/1.45 thf(func_def_101, type, sK14: $i > $o).
% 2.07/1.45 thf(func_def_104, type, sK17: $i > ($i > $o) > $i).
% 2.07/1.45 thf(func_def_109, type, sK22: $i > $o).
% 2.07/1.45 thf(func_def_112, type, sK25: $i > $o).
% 2.07/1.45 thf(func_def_114, type, sK27: $i > $i).
% 2.07/1.45 thf(func_def_117, type, sK30: $i > $i).
% 2.07/1.45 thf(func_def_120, type, sK33: $i > $i).
% 2.07/1.45 thf(func_def_123, type, sK36: $i > $o).
% 2.07/1.45 thf(func_def_127, type, sK40: $i > $o).
% 2.07/1.45 thf(func_def_131, type, sK44: $i > $o).
% 2.07/1.45 thf(func_def_132, type, sK45: $i > $i).
% 2.07/1.45 thf(func_def_133, type, sK46: ($i > $o) > $i).
% 2.07/1.45 thf(func_def_136, type, sK49: $i > $i > $i).
% 2.07/1.45 thf(func_def_142, type, sK55: $i > $i > $i).
% 2.07/1.45 thf(func_def_145, type, sK58: $i > $o).
% 2.07/1.45 thf(func_def_149, type, sK62: $o > $i > $i > $i).
% 2.07/1.45 thf(func_def_159, type, sK72: $i > $o).
% 2.07/1.45 thf(func_def_161, type, sK74: $i > $o).
% 2.07/1.45 thf(func_def_164, type, sK77: $i > ($i > $o) > $i).
% 2.07/1.45 thf(func_def_167, type, sK80: $i > ($i > $o) > $i).
% 2.07/1.45 thf(func_def_168, type, sK81: $i > $o).
% 2.07/1.45 thf(func_def_171, type, sK84: $i > $o).
% 2.07/1.45 thf(func_def_174, type, sK87: $i > ($i > $o) > $i).
% 2.07/1.45 thf(func_def_177, type, sK90: $i > $i > $i).
% 2.07/1.45 thf(func_def_180, type, sK93: $i > $o).
% 2.07/1.45 thf(func_def_181, type, sK94: $i > $i > $i).
% 2.07/1.45 thf(func_def_182, type, sK95: $i > $i > $i).
% 2.07/1.45 thf(func_def_183, type, sK96: $i > $i > $i).
% 2.07/1.45 thf(func_def_184, type, sK97: $i > $i > $i).
% 2.07/1.45 thf(func_def_185, type, sK98: $i > $i > $i > $i).
% 2.07/1.45 thf(func_def_186, type, sK99: $i > $i).
% 2.07/1.45 thf(func_def_187, type, sK100: $i > $i).
% 2.07/1.45 thf(func_def_188, type, sK101: $i > $i).
% 2.07/1.45 thf(func_def_189, type, sK102: $i > $i).
% 2.07/1.45 thf(func_def_190, type, sK103: $i > $i > $i).
% 2.07/1.45 thf(func_def_191, type, sK104: $i > $i > $i > $i).
% 2.07/1.45 thf(func_def_192, type, sK105: $i > $i > $i > $i).
% 2.07/1.45 thf(func_def_193, type, sK106: $i > $i > $i).
% 2.07/1.45 thf(func_def_194, type, sK107: $i > $i > $i).
% 2.07/1.45 thf(func_def_196, type, sK109: $i > $i).
% 2.07/1.45 thf(func_def_197, type, sK110: $i > $i).
% 2.07/1.45 thf(func_def_198, type, sK111: $i > $i).
% 2.07/1.45 thf(func_def_199, type, sK112: $i > $i > $i).
% 2.07/1.45 thf(func_def_205, type, sK118: $i > $o).
% 2.07/1.45 thf(func_def_208, type, sK121: $i > ($i > $o) > $i).
% 2.07/1.45 thf(func_def_214, type, sK127: $i > $i).
% 2.07/1.45 thf(func_def_216, type, sK129: $i > $o).
% 2.07/1.45 thf(func_def_218, type, sK131: ($i > $o) > $i).
% 2.07/1.45 thf(func_def_219, type, sK132: ($i > $o) > $i).
% 2.07/1.45 thf(func_def_222, type, sK135: $i > $i > $i).
% 2.07/1.45 thf(func_def_223, type, sK136: $i > $i > $i).
% 2.07/1.45 thf(func_def_224, type, sK137: ($i > $o) > $i).
% 2.07/1.45 thf(func_def_225, type, sK138: $i > $o).
% 2.07/1.45 thf(func_def_227, type, sK140: $i > $i > $o).
% 2.07/1.45 thf(func_def_228, type, sK141: $i > $i).
% 2.07/1.45 thf(func_def_229, type, sK142: $i > $i).
% 2.07/1.45 thf(func_def_230, type, sK143: ($i > $i > $o) > $i > $i).
% 2.07/1.45 thf(func_def_231, type, sK144: $i > ($i > $i > $o) > $i > $i).
% 2.07/1.45 thf(func_def_232, type, sK145: ($i > $i > $o) > $i > $i).
% 2.07/1.45 thf(func_def_234, type, sK147: $i > $o).
% 2.07/1.45 thf(func_def_236, type, sK149: ($i > $o) > $i > $i).
% 2.07/1.45 thf(func_def_237, type, sK150: $i > $i > $i).
% 2.07/1.45 thf(func_def_241, type, sK154: $i > $o).
% 2.07/1.45 thf(func_def_252, type, sK165: $i > $i).
% 2.07/1.45 thf(func_def_254, type, sK167: $i > ($i > $o) > $i).
% 2.07/1.45 thf(func_def_255, type, sK168: $i > $o).
% 2.07/1.45 thf(func_def_269, type, ph182: !>[X0: $tType]:(X0)).
% 2.07/1.45 thf(f1651,plain,(
% 2.07/1.45 $false),
% 2.07/1.45 inference(avatar_sat_refutation,[status(thm)],[f1600,f1610,f1634,f1650])).
% 2.07/1.45 thf(f1650,plain,(
% 2.07/1.45 spl181_2 | ~spl181_1 | ~spl181_3),
% 2.07/1.45 inference(avatar_split_clause,[status(thm)],[f1649,f1631,f1594,f1598])).
% 2.07/1.45 thf(f1598,definition,(
% 2.07/1.45 spl181_2 <=> ! [X0 : $i] : ((sK25 @ X0) != $true)),
% 2.07/1.45 introduced(definition,[new_symbols(naming,[spl181_2])],[avatar_definition])).
% 2.07/1.45 thf(f1594,definition,(
% 2.07/1.45 spl181_1 <=> (sK26 = (sK131 @ sK25))),
% 2.07/1.45 introduced(definition,[new_symbols(naming,[spl181_1])],[avatar_definition])).
% 2.07/1.45 thf(f1631,definition,(
% 2.07/1.45 spl181_3 <=> (sK26 = (sK132 @ sK25))),
% 2.07/1.45 introduced(definition,[new_symbols(naming,[spl181_3])],[avatar_definition])).
% 2.07/1.45 thf(f1649,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (((sK25 @ X0) != $true)) ) | (~spl181_1 | ~spl181_3)),
% 2.07/1.45 inference(subsumption_resolution,[status(thm)],[f1648,f1275])).
% 2.07/1.45 thf(f1275,plain,(
% 2.07/1.45 ($true != (exu @ sK25))),
% 2.07/1.45 inference(beta_eta_normalization,[status(thm)],[f656])).
% 2.07/1.45 thf(f656,plain,(
% 2.07/1.45 ($true != (exu @ (^[Y0 : $i]: (sK25 @ Y0))))),
% 2.07/1.45 inference(cnf_transformation,[status(thm)],[f325])).
% 2.07/1.45 thf(f325,plain,(
% 2.07/1.45 (powersetAx = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (notinemptyset = $true) & (eqinunit = $true) & (subPowSU = $true) & (nonemptyImpWitness = $true) & (exuE1 = $true) & (prop2set2propI = $true) & (omega0Ax = $true) & (nonemptyE1 = $true) & (exuE2 = $true) & (setext = $true) & (setunionE = $true) & (emptysetimpfalse = $true) & (setadjoinIL = $true) & (setadjoinOr = $true) & (omegaSAx = $true) & (quantDeMorgan4 = $true) & (uniqinunit = $true) & (emptysetE = $true) & (setbeta = $true) & (omegaIndAx = $true) & (notinsingleton = $true) & (prop2setE = $true) & (emptysetAx = $true) & (powersetE = $true) & (setunionAx = $true) & (exuI1 = $true) & (singletonsswitch = $true) & (notdexE = $true) & (replAx = $true) & (! [X2 : $i] : (((sK26 = X2) | ((sK25 @ X2) != $true)) & (((sK25 @ X2) = $true) | (sK26 != X2))) & ($true != (exu @ (^[Y0 : $i]: (sK25 @ Y0))))) & (setadjoinIR = $true) & (noeltsimpempty = $true) & (emptyE1 = $true) & (wellorderingAx = $true) & (upairsetE = $true) & (upairsetIL = $true) & (emptyInPowerset = $true) & (upairsetIR = $true) & (powersetI = $true) & (setadjoinAx = $true) & (exuI3 = $true) & (dsetconstrI = $true) & (quantDeMorgan2 = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (vacuousDall = $true) & (setunionI = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan1 = $true) & (prop2setI = $true) & (emptyI = $true) & (exuE3e = $true) & (notdallE = $true) & (emptyinunitempty = $true) & (descrp = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (foundationAx = $true)),
% 2.07/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK25,sK26])],[f322,f324,f323])).
% 2.07/1.45 thf(f323,plain,(
% 2.07/1.45 ? [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : (((X1 = X2) | ((X0 @ X2) != $true)) & (((X0 @ X2) = $true) | (X1 != X2))) & ($true != (exu @ (^[Y0 : $i]: (X0 @ Y0))))) => (? [X1 : $i] : ! [X2 : $i] : (((X1 = X2) | ((sK25 @ X2) != $true)) & (((sK25 @ X2) = $true) | (X1 != X2))) & ($true != (exu @ (^[Y0 : $i]: (sK25 @ Y0)))))),
% 2.07/1.45 introduced(definition,[],[choice_axiom])).
% 2.07/1.45 thf(f324,plain,(
% 2.07/1.45 ? [X1 : $i] : ! [X2 : $i] : (((X1 = X2) | ((sK25 @ X2) != $true)) & (((sK25 @ X2) = $true) | (X1 != X2))) => ! [X2 : $i] : (((sK26 = X2) | ((sK25 @ X2) != $true)) & (((sK25 @ X2) = $true) | (sK26 != X2)))),
% 2.07/1.45 introduced(definition,[],[choice_axiom])).
% 2.07/1.45 thf(f322,plain,(
% 2.07/1.45 (powersetAx = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (notinemptyset = $true) & (eqinunit = $true) & (subPowSU = $true) & (nonemptyImpWitness = $true) & (exuE1 = $true) & (prop2set2propI = $true) & (omega0Ax = $true) & (nonemptyE1 = $true) & (exuE2 = $true) & (setext = $true) & (setunionE = $true) & (emptysetimpfalse = $true) & (setadjoinIL = $true) & (setadjoinOr = $true) & (omegaSAx = $true) & (quantDeMorgan4 = $true) & (uniqinunit = $true) & (emptysetE = $true) & (setbeta = $true) & (omegaIndAx = $true) & (notinsingleton = $true) & (prop2setE = $true) & (emptysetAx = $true) & (powersetE = $true) & (setunionAx = $true) & (exuI1 = $true) & (singletonsswitch = $true) & (notdexE = $true) & (replAx = $true) & ? [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : (((X1 = X2) | ((X0 @ X2) != $true)) & (((X0 @ X2) = $true) | (X1 != X2))) & ($true != (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & (setadjoinIR = $true) & (noeltsimpempty = $true) & (emptyE1 = $true) & (wellorderingAx = $true) & (upairsetE = $true) & (upairsetIL = $true) & (emptyInPowerset = $true) & (upairsetIR = $true) & (powersetI = $true) & (setadjoinAx = $true) & (exuI3 = $true) & (dsetconstrI = $true) & (quantDeMorgan2 = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (vacuousDall = $true) & (setunionI = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan1 = $true) & (prop2setI = $true) & (emptyI = $true) & (exuE3e = $true) & (notdallE = $true) & (emptyinunitempty = $true) & (descrp = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (foundationAx = $true)),
% 2.07/1.45 inference(nnf_transformation,[status(thm)],[f223])).
% 2.07/1.45 thf(f223,plain,(
% 2.07/1.45 (powersetAx = $true) & (setadjoinE = $true) & (setoftrueEq = $true) & (notinemptyset = $true) & (eqinunit = $true) & (subPowSU = $true) & (nonemptyImpWitness = $true) & (exuE1 = $true) & (prop2set2propI = $true) & (omega0Ax = $true) & (nonemptyE1 = $true) & (exuE2 = $true) & (setext = $true) & (setunionE = $true) & (emptysetimpfalse = $true) & (setadjoinIL = $true) & (setadjoinOr = $true) & (omegaSAx = $true) & (quantDeMorgan4 = $true) & (uniqinunit = $true) & (emptysetE = $true) & (setbeta = $true) & (omegaIndAx = $true) & (notinsingleton = $true) & (prop2setE = $true) & (emptysetAx = $true) & (powersetE = $true) & (setunionAx = $true) & (exuI1 = $true) & (singletonsswitch = $true) & (notdexE = $true) & (replAx = $true) & ? [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X1 = X2) <=> ((X0 @ X2) = $true)) & ($true != (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & (setadjoinIR = $true) & (noeltsimpempty = $true) & (emptyE1 = $true) & (wellorderingAx = $true) & (upairsetE = $true) & (upairsetIL = $true) & (emptyInPowerset = $true) & (upairsetIR = $true) & (powersetI = $true) & (setadjoinAx = $true) & (exuI3 = $true) & (dsetconstrI = $true) & (quantDeMorgan2 = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setextAx = $true) & (vacuousDall = $true) & (setunionI = $true) & (quantDeMorgan3 = $true) & (quantDeMorgan1 = $true) & (prop2setI = $true) & (emptyI = $true) & (exuE3e = $true) & (notdallE = $true) & (emptyinunitempty = $true) & (descrp = $true) & (dsetconstrER = $true) & (dsetconstrEL = $true) & (foundationAx = $true)),
% 2.07/1.45 inference(flattening,[status(thm)],[f222])).
% 2.07/1.45 thf(f222,plain,(
% 2.07/1.45 (((((((((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X1 = X2) <=> ((X0 @ X2) = $true)) & ($true != (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & (exuI3 = $true)) & (exuI1 = $true)) & (notdallE = $true)) & (notdexE = $true)) & (prop2set2propI = $true)) & (prop2setI = $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.07/1.45 inference(ennf_transformation,[status(thm)],[f191])).
% 2.07/1.45 thf(f191,plain,(
% 2.07/1.45 ~((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) => ! [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X1 = X2) <=> ((X0 @ X2) = $true)) => ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.07/1.45 inference(fool_elimination,[status(thm)],[f190])).
% 2.07/1.45 thf(f190,plain,(
% 2.07/1.45 ~(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 => ! [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X3 : $i] : (X0 @ X3))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.07/1.45 inference(rectify,[status(thm)],[f66])).
% 2.07/1.45 thf(f66,negated_conjecture,(
% 2.07/1.45 ~(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 => ! [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.07/1.45 inference(negated_conjecture,[status(cth)],[f65])).
% 2.07/1.45 thf(f65,conjecture,(
% 2.07/1.45 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 => ! [X0 : $i > $o] : (? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2)) => (exu @ (^[X1 : $i] : (X0 @ X1)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.07/1.45 file('/export/starexec/sandbox/tmp/tmp.xzwazKCSaL/DTF2THF_12476.p',exuI2)).
% 2.07/1.45 thf(f1648,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (($true = (exu @ sK25)) | ((sK25 @ X0) != $true)) ) | (~spl181_1 | ~spl181_3)),
% 2.07/1.45 inference(subsumption_resolution,[status(thm)],[f1647,f1596])).
% 2.07/1.45 thf(f1596,plain,(
% 2.07/1.45 (sK26 = (sK131 @ sK25)) | ~spl181_1),
% 2.07/1.45 inference(avatar_component_clause,[status(thm)],[f1594])).
% 2.07/1.45 thf(f1647,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (((sK25 @ X0) != $true) | (sK26 != (sK131 @ sK25)) | ($true = (exu @ sK25))) ) | ~spl181_3),
% 2.07/1.45 inference(superposition,[status(thm)],[f1168,f1633])).
% 2.07/1.45 thf(f1633,plain,(
% 2.07/1.45 (sK26 = (sK132 @ sK25)) | ~spl181_3),
% 2.07/1.45 inference(avatar_component_clause,[status(thm)],[f1631])).
% 2.07/1.45 thf(f1168,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((sK132 @ X4) != (sK131 @ X4)) | ((X4 @ X5) != $true) | ($true = (exu @ X4))) )),
% 2.07/1.45 inference(beta_eta_normalization,[status(thm)],[f1167])).
% 2.07/1.45 thf(f1167,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ((sK132 @ X4) != (sK131 @ X4)) | ((X4 @ X5) != $true)) )),
% 2.07/1.45 inference(trivial_inequality_removal,[status(thm)],[f1086])).
% 2.07/1.45 thf(f1086,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (($true != $true) | ((X4 @ X5) != $true) | ((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ((sK132 @ X4) != (sK131 @ X4))) )),
% 2.07/1.45 inference(definition_unfolding,[status(thm)],[f846,f645])).
% 2.07/1.45 thf(f645,plain,(
% 2.07/1.45 (exuI3 = $true)),
% 2.07/1.45 inference(cnf_transformation,[status(thm)],[f325])).
% 2.07/1.45 thf(f846,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ((X4 @ X5) != $true) | ((sK132 @ X4) != (sK131 @ X4)) | (exuI3 != $true)) )),
% 2.07/1.45 inference(cnf_transformation,[status(thm)],[f513])).
% 2.07/1.45 thf(f513,plain,(
% 2.07/1.45 ((exuI3 = $true) | (((exu @ (^[Y0 : $i]: (sK129 @ Y0))) != $true) & ($true = (sK129 @ sK130)) & ! [X2 : $i,X3 : $i] : (((sK129 @ X2) != $true) | (X2 = X3) | ((sK129 @ X3) != $true)))) & (! [X4 : $i > $o] : (((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ! [X5 : $i] : ((X4 @ X5) != $true) | (((X4 @ (sK131 @ X4)) = $true) & ((sK132 @ X4) != (sK131 @ X4)) & ($true = (X4 @ (sK132 @ X4))))) | (exuI3 != $true))),
% 2.07/1.45 inference(skolemisation,[status(esa),new_symbols(skolem,[sK129,sK130,sK131,sK132])],[f509,f512,f511,f510])).
% 2.07/1.45 thf(f510,plain,(
% 2.07/1.45 ? [X0 : $i > $o] : (($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ? [X1 : $i] : ((X0 @ X1) = $true) & ! [X2 : $i,X3 : $i] : (((X0 @ X2) != $true) | (X2 = X3) | ((X0 @ X3) != $true))) => (((exu @ (^[Y0 : $i]: (sK129 @ Y0))) != $true) & ? [X1 : $i] : ($true = (sK129 @ X1)) & ! [X3 : $i,X2 : $i] : (((sK129 @ X2) != $true) | (X2 = X3) | ((sK129 @ X3) != $true)))),
% 2.07/1.45 introduced(definition,[],[choice_axiom])).
% 2.07/1.45 thf(f511,plain,(
% 2.07/1.45 ? [X1 : $i] : ($true = (sK129 @ X1)) => ($true = (sK129 @ sK130))),
% 2.07/1.45 introduced(definition,[],[choice_axiom])).
% 2.07/1.45 thf(f512,plain,(
% 2.07/1.45 ! [X4 : $i > $o] : (? [X6 : $i,X7 : $i] : (($true = (X4 @ X6)) & (X6 != X7) & ((X4 @ X7) = $true)) => (((X4 @ (sK131 @ X4)) = $true) & ((sK132 @ X4) != (sK131 @ X4)) & ($true = (X4 @ (sK132 @ X4)))))),
% 2.07/1.45 introduced(definition,[],[choice_axiom])).
% 2.07/1.45 thf(f509,plain,(
% 2.07/1.45 ((exuI3 = $true) | ? [X0 : $i > $o] : (($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ? [X1 : $i] : ((X0 @ X1) = $true) & ! [X2 : $i,X3 : $i] : (((X0 @ X2) != $true) | (X2 = X3) | ((X0 @ X3) != $true)))) & (! [X4 : $i > $o] : (((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ! [X5 : $i] : ((X4 @ X5) != $true) | ? [X6 : $i,X7 : $i] : (($true = (X4 @ X6)) & (X6 != X7) & ((X4 @ X7) = $true))) | (exuI3 != $true))),
% 2.07/1.45 inference(rectify,[status(thm)],[f508])).
% 2.07/1.45 thf(f508,plain,(
% 2.07/1.45 ((exuI3 = $true) | ? [X0 : $i > $o] : (($true != (exu @ (^[Y0 : $i]: (X0 @ Y0)))) & ? [X1 : $i] : ((X0 @ X1) = $true) & ! [X2 : $i,X3 : $i] : (((X0 @ X2) != $true) | (X2 = X3) | ((X0 @ X3) != $true)))) & (! [X0 : $i > $o] : (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) | ! [X1 : $i] : ((X0 @ X1) != $true) | ? [X2 : $i,X3 : $i] : (((X0 @ X2) = $true) & (X2 != X3) & ((X0 @ X3) = $true))) | (exuI3 != $true))),
% 2.07/1.45 inference(nnf_transformation,[status(thm)],[f268])).
% 2.07/1.45 thf(f268,plain,(
% 2.07/1.45 (exuI3 = $true) <=> ! [X0 : $i > $o] : (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) | ! [X1 : $i] : ((X0 @ X1) != $true) | ? [X2 : $i,X3 : $i] : (((X0 @ X2) = $true) & (X2 != X3) & ((X0 @ X3) = $true)))),
% 2.07/1.45 inference(flattening,[status(thm)],[f267])).
% 2.07/1.45 thf(f267,plain,(
% 2.07/1.45 ! [X0 : $i > $o] : ((($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) | ? [X2 : $i,X3 : $i] : (((X2 != X3) & ((X0 @ X2) = $true)) & ((X0 @ X3) = $true))) | ! [X1 : $i] : ((X0 @ X1) != $true)) <=> (exuI3 = $true)),
% 2.07/1.45 inference(ennf_transformation,[status(thm)],[f83])).
% 2.07/1.45 thf(f83,plain,(
% 2.07/1.45 ! [X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) = $true) => (! [X2 : $i,X3 : $i] : (((X0 @ X3) = $true) => (((X0 @ X2) = $true) => (X2 = X3))) => ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))))) <=> (exuI3 = $true)),
% 2.07/1.45 inference(fool_elimination,[status(thm)],[f82])).
% 2.07/1.45 thf(f82,plain,(
% 2.07/1.45 (exuI3 = ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X3 : $i] : ((X0 @ X3) => ((X0 @ X2) => (X2 = X3))) => (exu @ (^[X4 : $i] : (X0 @ X4))))))),
% 2.07/1.45 inference(rectify,[status(thm)],[f64])).
% 2.07/1.45 thf(f64,axiom,(
% 2.07/1.45 (exuI3 = ! [X0 : $i > $o] : (? [X1 : $i] : (X0 @ X1) => (! [X2 : $i,X1 : $i] : ((X0 @ X1) => ((X0 @ X2) => (X1 = X2))) => (exu @ (^[X1 : $i] : (X0 @ X1))))))),
% 2.07/1.45 file('/export/starexec/sandbox/tmp/tmp.xzwazKCSaL/DTF2THF_12476.p',exuI3)).
% 2.07/1.45 thf(f1634,plain,(
% 2.07/1.45 spl181_3 | spl181_2),
% 2.07/1.45 inference(avatar_split_clause,[status(thm)],[f1629,f1598,f1631])).
% 2.07/1.45 thf(f1629,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (((sK25 @ X0) != $true) | (sK26 = (sK132 @ sK25))) )),
% 2.07/1.45 inference(subsumption_resolution,[status(thm)],[f1625,f1275])).
% 2.07/1.45 thf(f1625,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (($true = (exu @ sK25)) | (sK26 = (sK132 @ sK25)) | ((sK25 @ X0) != $true)) )),
% 2.07/1.45 inference(trivial_inequality_removal,[status(thm)],[f1620])).
% 2.07/1.45 thf(f1620,plain,(
% 2.07/1.45 ( ! [X0 : $i] : ((sK26 = (sK132 @ sK25)) | ($true != $true) | ($true = (exu @ sK25)) | ((sK25 @ X0) != $true)) )),
% 2.07/1.45 inference(superposition,[status(thm)],[f658,f1256])).
% 2.07/1.45 thf(f1256,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (($true = (X4 @ (sK132 @ X4))) | ((X4 @ X5) != $true) | ($true = (exu @ X4))) )),
% 2.07/1.45 inference(beta_eta_normalization,[status(thm)],[f1255])).
% 2.07/1.45 thf(f1255,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((X4 @ X5) != $true) | ($true = (X4 @ (sK132 @ X4))) | ((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true)) )),
% 2.07/1.45 inference(trivial_inequality_removal,[status(thm)],[f1087])).
% 2.07/1.45 thf(f1087,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ($true = (X4 @ (sK132 @ X4))) | ($true != $true) | ((X4 @ X5) != $true)) )),
% 2.07/1.45 inference(definition_unfolding,[status(thm)],[f845,f645])).
% 2.07/1.45 thf(f845,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ((X4 @ X5) != $true) | ($true = (X4 @ (sK132 @ X4))) | (exuI3 != $true)) )),
% 2.07/1.45 inference(cnf_transformation,[status(thm)],[f513])).
% 2.07/1.45 thf(f658,plain,(
% 2.07/1.45 ( ! [X2 : $i] : (((sK25 @ X2) != $true) | (sK26 = X2)) )),
% 2.07/1.45 inference(cnf_transformation,[status(thm)],[f325])).
% 2.07/1.45 thf(f1610,plain,(
% 2.07/1.45 ~spl181_2),
% 2.07/1.45 inference(avatar_contradiction_clause,[status(thm)],[f1609])).
% 2.07/1.45 thf(f1609,plain,(
% 2.07/1.45 $false | ~spl181_2),
% 2.07/1.45 inference(trivial_inequality_removal,[status(thm)],[f1601])).
% 2.07/1.45 thf(f1601,plain,(
% 2.07/1.45 ($true != $true) | ~spl181_2),
% 2.07/1.45 inference(superposition,[status(thm)],[f1599,f1155])).
% 2.07/1.45 thf(f1155,plain,(
% 2.07/1.45 ($true = (sK25 @ sK26))),
% 2.07/1.45 inference(equality_resolution,[status(thm)],[f657])).
% 2.07/1.45 thf(f657,plain,(
% 2.07/1.45 ( ! [X2 : $i] : (((sK25 @ X2) = $true) | (sK26 != X2)) )),
% 2.07/1.45 inference(cnf_transformation,[status(thm)],[f325])).
% 2.07/1.45 thf(f1599,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (((sK25 @ X0) != $true)) ) | ~spl181_2),
% 2.07/1.45 inference(avatar_component_clause,[status(thm)],[f1598])).
% 2.07/1.45 thf(f1600,plain,(
% 2.07/1.45 spl181_1 | spl181_2),
% 2.07/1.45 inference(avatar_split_clause,[status(thm)],[f1592,f1598,f1594])).
% 2.07/1.45 thf(f1592,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (((sK25 @ X0) != $true) | (sK26 = (sK131 @ sK25))) )),
% 2.07/1.45 inference(subsumption_resolution,[status(thm)],[f1590,f1275])).
% 2.07/1.45 thf(f1590,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (($true = (exu @ sK25)) | ((sK25 @ X0) != $true) | (sK26 = (sK131 @ sK25))) )),
% 2.07/1.45 inference(trivial_inequality_removal,[status(thm)],[f1583])).
% 2.07/1.45 thf(f1583,plain,(
% 2.07/1.45 ( ! [X0 : $i] : (((sK25 @ X0) != $true) | ($true = (exu @ sK25)) | ($true != $true) | (sK26 = (sK131 @ sK25))) )),
% 2.07/1.45 inference(superposition,[status(thm)],[f658,f1180])).
% 2.07/1.45 thf(f1180,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((X4 @ (sK131 @ X4)) = $true) | ($true = (exu @ X4)) | ((X4 @ X5) != $true)) )),
% 2.07/1.45 inference(beta_eta_normalization,[status(thm)],[f1179])).
% 2.07/1.45 thf(f1179,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ((X4 @ (sK131 @ X4)) = $true) | ((X4 @ X5) != $true)) )),
% 2.07/1.45 inference(trivial_inequality_removal,[status(thm)],[f1085])).
% 2.07/1.45 thf(f1085,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((X4 @ (sK131 @ X4)) = $true) | ((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ((X4 @ X5) != $true) | ($true != $true)) )),
% 2.07/1.45 inference(definition_unfolding,[status(thm)],[f847,f645])).
% 2.07/1.45 thf(f847,plain,(
% 2.07/1.45 ( ! [X4 : $i > $o,X5 : $i] : (((exu @ (^[Y0 : $i]: (X4 @ Y0))) = $true) | ((X4 @ X5) != $true) | ((X4 @ (sK131 @ X4)) = $true) | (exuI3 != $true)) )),
% 2.07/1.45 inference(cnf_transformation,[status(thm)],[f513])).
% 2.07/1.45 % SZS output end Proof for DTF2THF_12476
% 2.07/1.45 % (12762)------------------------------
% 2.07/1.45 % (12762)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.07/1.45 % (12762)Termination reason: Refutation
% 2.07/1.45
% 2.07/1.45 % (12762)Memory used [KB]: 7036
% 2.07/1.45 % (12762)Time elapsed: 0.059 s
% 2.07/1.45 % (12762)Instructions burned: 176 (million)
% 2.07/1.45 % (12762)------------------------------
% 2.07/1.45 % (12762)------------------------------
% 2.07/1.45 % (12756)Success in time 0.065 s
%------------------------------------------------------------------------------