%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU534^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n012.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 09:35:08 AM UTC 2026
% Result : Theorem 1.43s 1.09s
% Output : Refutation 1.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 13 unt; 0 typ; 1 def)
% Number of atoms : 1535 ( 444 equ; 0 cnn)
% Maximal formula atoms : 54 ( 28 avg)
% Number of connectives : 904 ( 75 ~; 53 |; 184 &; 262 @)
% ( 7 <=>; 323 =>; 0 <=; 0 <~>)
% Maximal formula depth : 59 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% Number of symbols : 127 ( 124 usr; 59 con; 0-3 aty)
% Number of variables : 115 ( 26 ^; 60 !; 29 ?; 115 :)
% 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_74,type,
sP0: $i > $i > $o ).
thf(func_def_75,type,
sP1: $i > $o ).
thf(func_def_76,type,
sP2: $i > $i > $o ).
thf(func_def_77,type,
sP3: $i > $i > $o ).
thf(func_def_81,type,
sK7: $i > $i ).
thf(func_def_83,type,
sK9: $i > $i ).
thf(func_def_91,type,
sK17: $i > $o ).
thf(func_def_94,type,
sK20: $i > $i ).
thf(func_def_97,type,
sK23: $i > $o ).
thf(func_def_102,type,
sK28: $i > $i > $i ).
thf(func_def_107,type,
sK33: $i > $o ).
thf(func_def_109,type,
sK35: $i > $i > $i ).
thf(func_def_110,type,
sK36: $i > $i > $i ).
thf(func_def_111,type,
sK37: $i > $i > $i ).
thf(func_def_112,type,
sK38: $i > $i > $i ).
thf(func_def_113,type,
sK39: $i > $i > $i > $i ).
thf(func_def_114,type,
sK40: $i > $i ).
thf(func_def_115,type,
sK41: $i > $i ).
thf(func_def_116,type,
sK42: $i > $i ).
thf(func_def_117,type,
sK43: $i > $i ).
thf(func_def_118,type,
sK44: $i > $i > $i > $i ).
thf(func_def_119,type,
sK45: $i > $i > $i > $i ).
thf(func_def_120,type,
sK46: $i > $i > $i ).
thf(func_def_121,type,
sK47: $i > $i > $i ).
thf(func_def_122,type,
sK48: $i > $i > $i ).
thf(func_def_124,type,
sK50: $i > $i ).
thf(func_def_125,type,
sK51: $i > $i ).
thf(func_def_126,type,
sK52: $i > $i ).
thf(func_def_127,type,
sK53: $i > $i > $i ).
thf(func_def_129,type,
sK55: $i > $i ).
thf(func_def_131,type,
sK57: $i > $i ).
thf(func_def_132,type,
sK58: $i > $o ).
thf(func_def_138,type,
sK64: $o > $i > $i > $i ).
thf(func_def_141,type,
sK67: $i > $i > $i ).
thf(func_def_146,type,
sK72: $i > $o ).
thf(func_def_152,type,
sK78: $i > $i > $i ).
thf(func_def_158,type,
sK84: $i > $i > $i ).
thf(func_def_159,type,
sK85: $i > $i > $i ).
thf(func_def_162,type,
sK88: $i > $i ).
thf(func_def_167,type,
sK93: ( $i > $o ) > $i ).
thf(func_def_168,type,
sK94: $i > $o ).
thf(func_def_169,type,
sK95: $i > $o ).
thf(func_def_173,type,
sK99: $i > $i > $o ).
thf(func_def_174,type,
sK100: $i > $i ).
thf(func_def_175,type,
sK101: $i > $i ).
thf(func_def_176,type,
sK102: ( $i > $i > $o ) > $i > $i ).
thf(func_def_177,type,
sK103: ( $i > $i > $o ) > $i > $i ).
thf(func_def_178,type,
sK104: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_192,type,
sK118: $i > $i > $i ).
thf(func_def_197,type,
sK123: $i > $i ).
thf(func_def_203,type,
sK129: $i > $o ).
thf(func_def_211,type,
sK137: ( $i > $o ) > $i ).
thf(func_def_212,type,
sK138: $i > $o ).
thf(func_def_213,type,
sK139: $i > $i ).
thf(func_def_214,type,
sK140: ( $i > $o ) > $i ).
thf(func_def_215,type,
sK141: $i > $o ).
thf(func_def_216,type,
sK142: $i > $i ).
thf(func_def_221,type,
ph147:
!>[X0: $tType] : X0 ).
thf(f1408,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f1259,f1407]) ).
thf(f1407,plain,
~ spl146_2,
inference(avatar_contradiction_clause,[status(thm)],[f1406]) ).
thf(f1406,plain,
( $false
| ~ spl146_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1405]) ).
thf(f1405,plain,
( ( $true != $true )
| ~ spl146_2 ),
inference(superposition,[status(thm)],[f1351,f546]) ).
thf(f546,plain,
( ( sK23 @ sK24 )
= $true ),
inference(cnf_transformation,[status(thm)],[f270]) ).
thf(f270,plain,
( ( emptyInPowerset = $true )
& ( replAx = $true )
& ( setbeta = $true )
& ( setadjoinIR = $true )
& ( emptyI = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( foundationAx = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( singletonsswitch = $true )
& ( setunionI = $true )
& ( omegaIndAx = $true )
& ( eqinunit = $true )
& ( upairsetIL = $true )
& ( setadjoinOr = $true )
& ( dsetconstrI = $true )
& ( notinemptyset = $true )
& ( upairsetIR = $true )
& ( uniqinunit = $true )
& ( ( in @ sK24 @ sK22 )
= $true )
& ( ( sK23 @ sK24 )
= $true )
& ( emptyset
= ( dsetconstr @ sK22
@ ^ [Y0: $i] : ( sK23 @ Y0 ) ) )
& ( setoftrueEq = $true )
& ( powersetAx = $true )
& ( nonemptyE1 = $true )
& ( prop2setE = $true )
& ( emptyinunitempty = $true )
& ( notinsingleton = $true )
& ( emptysetAx = $true )
& ( emptysetE = $true )
& ( setextAx = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinIL = $true )
& ( powersetE = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinAx = $true )
& ( exuE2 = $true )
& ( setext = $true )
& ( subPowSU = $true )
& ( upairsetE = $true )
& ( powersetI = $true )
& ( exuE3e = $true )
& ( dsetconstrER = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24])],[f201,f269,f268]) ).
thf(f268,plain,
( ? [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
& ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
=> ( ? [X2: $i] :
( ( ( in @ X2 @ sK22 )
= $true )
& ( ( sK23 @ X2 )
= $true ) )
& ( emptyset
= ( dsetconstr @ sK22
@ ^ [Y0: $i] : ( sK23 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f269,plain,
( ? [X2: $i] :
( ( ( in @ X2 @ sK22 )
= $true )
& ( ( sK23 @ X2 )
= $true ) )
=> ( ( ( in @ sK24 @ sK22 )
= $true )
& ( ( sK23 @ sK24 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f201,plain,
( ( emptyInPowerset = $true )
& ( replAx = $true )
& ( setbeta = $true )
& ( setadjoinIR = $true )
& ( emptyI = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI = $true )
& ( noeltsimpempty = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( descrp = $true )
& ( setunionE = $true )
& ( foundationAx = $true )
& ( wellorderingAx = $true )
& ( nonemptyI1 = $true )
& ( singletonsswitch = $true )
& ( setunionI = $true )
& ( omegaIndAx = $true )
& ( eqinunit = $true )
& ( upairsetIL = $true )
& ( setadjoinOr = $true )
& ( dsetconstrI = $true )
& ( notinemptyset = $true )
& ( upairsetIR = $true )
& ( uniqinunit = $true )
& ? [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
& ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( setoftrueEq = $true )
& ( powersetAx = $true )
& ( nonemptyE1 = $true )
& ( prop2setE = $true )
& ( emptyinunitempty = $true )
& ( notinsingleton = $true )
& ( emptysetAx = $true )
& ( emptysetE = $true )
& ( setextAx = $true )
& ( nonemptyImpWitness = $true )
& ( setadjoinIL = $true )
& ( powersetE = $true )
& ( emptysetimpfalse = $true )
& ( setadjoinAx = $true )
& ( exuE2 = $true )
& ( setext = $true )
& ( subPowSU = $true )
& ( upairsetE = $true )
& ( powersetI = $true )
& ( exuE3e = $true )
& ( dsetconstrER = $true )
& ( setunionAx = $true )
& ( omegaSAx = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true ) ),
inference(flattening,[status(thm)],[f200]) ).
thf(f200,plain,
( ? [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
& ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
& ( 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)],[f165]) ).
thf(f165,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 )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
=> ( emptyset
!= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f164]) ).
thf(f164,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 )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
=> ( emptyset
!= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(true_and_false_elimination,[status(thm)],[f75]) ).
thf(f75,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 )
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( ( in @ X2 @ X0 )
= $true )
& ( ( X1 @ X2 )
= $true ) )
=> ( ( emptyset
= ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f74]) ).
thf(f74,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
=> ! [X0: $i,X1: $i > $o] :
( ? [X2: $i] :
( ( in @ X2 @ X0 )
& ( X1 @ X2 ) )
=> ( ( ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) )
= emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f55]) ).
thf(f55,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
=> ! [X3: $i,X0: $i > $o] :
( ? [X1: $i] :
( ( in @ X1 @ X3 )
& ( X0 @ X1 ) )
=> ( ( ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
= emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f54]) ).
thf(f54,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
=> ! [X3: $i,X0: $i > $o] :
( ? [X1: $i] :
( ( in @ X1 @ X3 )
& ( X0 @ X1 ) )
=> ( ( ( dsetconstr @ X3
@ ^ [X1: $i] : ( X0 @ X1 ) )
= emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rxuSLvj59h/DTF2THF_29102.p',emptyE1) ).
thf(f1351,plain,
( ( ( sK23 @ sK24 )
!= $true )
| ~ spl146_2 ),
inference(trivial_inequality_removal,[status(thm)],[f1290]) ).
thf(f1290,plain,
( ( ( sK23 @ sK24 )
!= $true )
| ( $true != $true )
| ~ spl146_2 ),
inference(superposition,[status(thm)],[f815,f547]) ).
thf(f547,plain,
( ( in @ sK24 @ sK22 )
= $true ),
inference(cnf_transformation,[status(thm)],[f270]) ).
thf(f815,plain,
( ! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK22 ) )
| ( ( sK23 @ X0 )
!= $true ) )
| ~ spl146_2 ),
inference(avatar_component_clause,[status(thm)],[f814]) ).
thf(f814,definition,
( spl146_2
<=> ! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK22 ) )
| ( ( sK23 @ X0 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl146_2])],[avatar_definition]) ).
thf(f1259,plain,
spl146_2,
inference(avatar_split_clause,[status(thm)],[f1258,f814]) ).
thf(f1258,plain,
! [X0: $i] :
( ( ( sK23 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ sK22 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f1257]) ).
thf(f1257,plain,
! [X0: $i] :
( ( $true
!= ( in @ X0 @ sK22 ) )
| ( $true != $true )
| ( ( sK23 @ X0 )
!= $true ) ),
inference(forward_demodulation,[status(thm)],[f1238,f532]) ).
thf(f532,plain,
emptysetimpfalse = $true,
inference(cnf_transformation,[status(thm)],[f270]) ).
thf(f1238,plain,
! [X0: $i] :
( ( ( sK23 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ sK22 ) )
| ( emptysetimpfalse != $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1216]) ).
thf(f1216,plain,
! [X0: $i] :
( ( ( sK23 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ sK22 ) )
| ( emptysetimpfalse != $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f740,f818]) ).
thf(f818,plain,
! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
| ( ( sK23 @ X0 )
!= $true )
| ( $true
!= ( in @ X0 @ sK22 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f817]) ).
thf(f817,plain,
! [X0: $i] :
( ( $true != $true )
| ( ( sK23 @ X0 )
!= $true )
| ( ( in @ X0 @ emptyset )
= $true )
| ( $true
!= ( in @ X0 @ sK22 ) ) ),
inference(forward_demodulation,[status(thm)],[f801,f551]) ).
thf(f551,plain,
dsetconstrI = $true,
inference(cnf_transformation,[status(thm)],[f270]) ).
thf(f801,plain,
! [X0: $i] :
( ( ( sK23 @ X0 )
!= $true )
| ( ( in @ X0 @ emptyset )
= $true )
| ( dsetconstrI != $true )
| ( $true
!= ( in @ X0 @ sK22 ) ) ),
inference(superposition,[status(thm)],[f776,f793]) ).
thf(f793,plain,
( emptyset
= ( dsetconstr @ sK22 @ sK23 ) ),
inference(beta_eta_normalization,[status(thm)],[f545]) ).
thf(f545,plain,
( emptyset
= ( dsetconstr @ sK22
@ ^ [Y0: $i] : ( sK23 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f270]) ).
thf(f776,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X3 @ ( dsetconstr @ X4 @ X5 ) )
= $true )
| ( ( X5 @ X3 )
!= $true )
| ( dsetconstrI != $true )
| ( ( in @ X3 @ X4 )
!= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f508]) ).
thf(f508,plain,
! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true )
| ( ( X5 @ X3 )
!= $true )
| ( dsetconstrI != $true )
| ( ( in @ X3 @ X4 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f254]) ).
thf(f254,plain,
( ( ( dsetconstrI = $true )
| ( ( ( sK17 @ sK15 )
= $true )
& ( ( in @ sK15
@ ( dsetconstr @ sK16
@ ^ [Y0: $i] : ( sK17 @ Y0 ) ) )
!= $true )
& ( ( in @ sK15 @ sK16 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X3 )
!= $true )
| ( ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( dsetconstrI != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f252,f253]) ).
thf(f253,plain,
( ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
= $true )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
=> ( ( ( sK17 @ sK15 )
= $true )
& ( ( in @ sK15
@ ( dsetconstr @ sK16
@ ^ [Y0: $i] : ( sK17 @ Y0 ) ) )
!= $true )
& ( ( in @ sK15 @ sK16 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f252,plain,
( ( ( dsetconstrI = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
= $true )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X3: $i,X4: $i,X5: $i > $o] :
( ( ( X5 @ X3 )
!= $true )
| ( ( in @ X3
@ ( dsetconstr @ X4
@ ^ [Y0: $i] : ( X5 @ Y0 ) ) )
= $true )
| ( ( in @ X3 @ X4 )
!= $true ) )
| ( dsetconstrI != $true ) ) ),
inference(rectify,[status(thm)],[f251]) ).
thf(f251,plain,
( ( ( dsetconstrI = $true )
| ? [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
= $true )
& ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) ) )
& ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) )
| ( dsetconstrI != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f188]) ).
thf(f188,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( X2 @ X0 )
!= $true )
| ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f187]) ).
thf(f187,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true )
| ( ( X2 @ X0 )
!= $true )
| ( ( in @ X0 @ X1 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f109]) ).
thf(f109,plain,
( ( dsetconstrI = $true )
<=> ! [X0: $i,X1: $i,X2: $i > $o] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( ( X2 @ X0 )
= $true )
=> ( ( in @ X0
@ ( dsetconstr @ X1
@ ^ [Y0: $i] : ( X2 @ Y0 ) ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f108]) ).
thf(f108,plain,
( dsetconstrI
= ( ! [X0: $i,X1: $i,X2: $i > $o] :
( ( in @ X0 @ X1 )
=> ( ( X2 @ X0 )
=> ( in @ X0
@ ( dsetconstr @ X1
@ ^ [X3: $i] : ( X2 @ X3 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( dsetconstrI
= ( ! [X1: $i,X3: $i,X0: $i > $o] :
( ( in @ X1 @ X3 )
=> ( ( X0 @ X1 )
=> ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rxuSLvj59h/DTF2THF_29102.p',dsetconstrI) ).
thf(f740,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ),
inference(cnf_transformation,[status(thm)],[f466]) ).
thf(f466,plain,
( ( ( emptysetimpfalse = $true )
| ( ( in @ sK133 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK133])],[f464,f465]) ).
thf(f465,plain,
( ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true )
=> ( ( in @ sK133 @ emptyset )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f464,plain,
( ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(rectify,[status(thm)],[f463]) ).
thf(f463,plain,
( ( ( emptysetimpfalse = $true )
| ? [X0: $i] :
( ( in @ X0 @ emptyset )
= $true ) )
& ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true )
| ( emptysetimpfalse != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f169]) ).
thf(f169,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(flattening,[status(thm)],[f168]) ).
thf(f168,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
!= $true ) ),
inference(true_and_false_elimination,[status(thm)],[f89]) ).
thf(f89,plain,
( ( emptysetimpfalse = $true )
<=> ! [X0: $i] :
( ( ( in @ X0 @ emptyset )
= $true )
=> $false ) ),
inference(fool_elimination,[status(thm)],[f88]) ).
thf(f88,plain,
( emptysetimpfalse
= ( ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
( emptysetimpfalse
= ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> $false ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.rxuSLvj59h/DTF2THF_29102.p',emptysetimpfalse) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU534^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.07 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:26:00 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.07/0.31 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEU534^1 : TPTP v9.2.1. Released v3.7.0.
% 0.07/0.32 % Domain : Set Theory
% 0.07/0.32 % Problem : Preliminary Notions - Bounded Quantifier Laws
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English : (! A:i.! phi:i>o.(? x:i.in x A & phi x) -> dsetconstr A
% 0.07/0.32 % (^ x:i.phi x) = emptyset -> false)
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.07/0.32 % Source : [Bro08]
% 0.07/0.32 % Names : ZFC036g [Bro08]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.38 v8.1.0, 0.27 v7.5.0, 0.14 v7.4.0, 0.33 v7.2.0, 0.25 v7.1.0, 0.50 v7.0.0, 0.43 v6.4.0, 0.50 v6.3.0, 0.40 v6.2.0, 0.29 v6.1.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.07/0.32 % Syntax : Number of formulae : 115 ( 53 unt; 61 typ; 53 def)
% 0.07/0.32 % Number of atoms : 293 ( 72 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 53 ( 5 avg)
% 0.07/0.32 % Number of connectives : 478 ( 9 ~; 5 |; 20 &; 315 @)
% 0.07/0.32 % ( 8 <=>; 121 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 58 ( 2 avg)
% 0.07/0.32 % Number of types : 2 ( 0 usr)
% 0.07/0.32 % Number of type conns : 28 ( 28 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 64 ( 61 usr; 54 con; 0-2 aty)
% 0.07/0.32 % Number of variables : 157 ( 17 ^; 121 !; 19 ?; 157 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : http://mathgate.info/detsetitem.php?id=385
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(in_type,type,
% 0.07/0.32 in: $i > $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(exu_type,type,
% 0.07/0.32 exu: ( $i > $o ) > $o ).
% 0.07/0.32
% 0.07/0.32 thf(exu,definition,
% 0.07/0.32 ( exu
% 0.07/0.32 = ( ^ [Xphi: $i > $o] :
% 0.07/0.32 ? [Xx: $i] :
% 0.07/0.32 ( ( Xphi @ Xx )
% 0.07/0.32 & ! [Xy: $i] :
% 0.07/0.32 ( ( Xphi @ Xy )
% 0.07/0.32 => ( Xx = Xy ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setextAx_type,type,
% 0.07/0.32 setextAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setextAx,definition,
% 0.07/0.32 ( setextAx
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 <=> ( in @ Xx @ B ) )
% 0.07/0.32 => ( A = B ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyset_type,type,
% 0.07/0.32 emptyset: $i ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetAx_type,type,
% 0.07/0.32 emptysetAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetAx,definition,
% 0.07/0.32 ( emptysetAx
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoin_type,type,
% 0.07/0.32 setadjoin: $i > $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinAx_type,type,
% 0.07/0.32 setadjoinAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinAx,definition,
% 0.07/0.32 ( setadjoinAx
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.07/0.32 <=> ( ( Xy = Xx )
% 0.07/0.32 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(powerset_type,type,
% 0.07/0.32 powerset: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(powersetAx_type,type,
% 0.07/0.32 powersetAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(powersetAx,definition,
% 0.07/0.32 ( powersetAx
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.07/0.32 <=> ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setunion_type,type,
% 0.07/0.32 setunion: $i > $i ).
% 0.07/0.32
% 0.07/0.32 thf(setunionAx_type,type,
% 0.07/0.32 setunionAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setunionAx,definition,
% 0.07/0.32 ( setunionAx
% 0.07/0.32 = ( ! [A: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.07/0.32 <=> ? [B: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 & ( in @ B @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(omega_type,type,
% 0.07/0.32 omega: $i ).
% 0.07/0.32
% 0.07/0.32 thf(omega0Ax_type,type,
% 0.07/0.32 omega0Ax: $o ).
% 0.07/0.32
% 0.07/0.32 thf(omega0Ax,definition,
% 0.07/0.32 ( omega0Ax
% 0.07/0.32 = ( in @ emptyset @ omega ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(omegaSAx_type,type,
% 0.07/0.32 omegaSAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(omegaSAx,definition,
% 0.07/0.32 ( omegaSAx
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ omega )
% 0.07/0.32 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(omegaIndAx_type,type,
% 0.07/0.32 omegaIndAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(omegaIndAx,definition,
% 0.07/0.32 ( omegaIndAx
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ( ( in @ emptyset @ A )
% 0.07/0.32 & ! [Xx: $i] :
% 0.07/0.32 ( ( ( in @ Xx @ omega )
% 0.07/0.32 & ( in @ Xx @ A ) )
% 0.07/0.32 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.07/0.32 => ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ omega )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(replAx_type,type,
% 0.07/0.32 replAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(replAx,definition,
% 0.07/0.32 ( replAx
% 0.07/0.32 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( exu
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.07/0.32 => ? [B: $i] :
% 0.07/0.32 ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 <=> ? [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ A )
% 0.07/0.32 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(foundationAx_type,type,
% 0.07/0.32 foundationAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(foundationAx,definition,
% 0.07/0.32 ( foundationAx
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.07/0.32 => ? [B: $i] :
% 0.07/0.32 ( ( in @ B @ A )
% 0.07/0.32 & ~ ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(wellorderingAx_type,type,
% 0.07/0.32 wellorderingAx: $o ).
% 0.07/0.32
% 0.07/0.32 thf(wellorderingAx,definition,
% 0.07/0.32 ( wellorderingAx
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ? [B: $i] :
% 0.07/0.32 ( ! [C: $i] :
% 0.07/0.32 ( ( in @ C @ B )
% 0.07/0.32 => ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ C )
% 0.07/0.32 => ( in @ Xx @ A ) ) )
% 0.07/0.32 & ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( ( in @ Xx @ A )
% 0.07/0.32 & ( in @ Xy @ A ) )
% 0.07/0.32 => ( ! [C: $i] :
% 0.07/0.32 ( ( in @ C @ B )
% 0.07/0.32 => ( ( in @ Xx @ C )
% 0.07/0.32 <=> ( in @ Xy @ C ) ) )
% 0.07/0.32 => ( Xx = Xy ) ) )
% 0.07/0.32 & ! [C: $i,D: $i] :
% 0.07/0.32 ( ( ( in @ C @ B )
% 0.07/0.32 & ( in @ D @ B ) )
% 0.07/0.32 => ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ C )
% 0.07/0.32 => ( in @ Xx @ D ) )
% 0.07/0.32 | ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ D )
% 0.07/0.32 => ( in @ Xx @ C ) ) ) )
% 0.07/0.32 & ! [C: $i] :
% 0.07/0.32 ( ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ C )
% 0.07/0.32 => ( in @ Xx @ A ) )
% 0.07/0.32 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.07/0.32 => ? [D: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ D @ B )
% 0.07/0.32 & ( in @ Xx @ C )
% 0.07/0.32 & ~ ? [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ D )
% 0.07/0.32 & ( in @ Xy @ C ) )
% 0.07/0.32 & ! [E: $i] :
% 0.07/0.32 ( ( in @ E @ B )
% 0.07/0.32 => ( ! [Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ E )
% 0.07/0.32 => ( in @ Xy @ D ) )
% 0.07/0.32 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(descr_type,type,
% 0.07/0.32 descr: ( $i > $o ) > $i ).
% 0.07/0.32
% 0.07/0.32 thf(descrp_type,type,
% 0.07/0.32 descrp: $o ).
% 0.07/0.32
% 0.07/0.32 thf(descrp,definition,
% 0.07/0.32 ( descrp
% 0.07/0.32 = ( ! [Xphi: $i > $o] :
% 0.07/0.32 ( ( exu
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.07/0.32 => ( Xphi
% 0.07/0.32 @ ( descr
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstr_type,type,
% 0.07/0.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrI_type,type,
% 0.07/0.32 dsetconstrI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrI,definition,
% 0.07/0.32 ( dsetconstrI
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( ( Xphi @ Xx )
% 0.07/0.32 => ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrEL_type,type,
% 0.07/0.32 dsetconstrEL: $o ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrEL,definition,
% 0.07/0.32 ( dsetconstrEL
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrER_type,type,
% 0.07/0.32 dsetconstrER: $o ).
% 0.07/0.32
% 0.07/0.32 thf(dsetconstrER,definition,
% 0.07/0.32 ( dsetconstrER
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.07/0.32 => ( Xphi @ Xx ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(exuE1_type,type,
% 0.07/0.32 exuE1: $o ).
% 0.07/0.32
% 0.07/0.32 thf(exuE1,definition,
% 0.07/0.32 ( exuE1
% 0.07/0.32 = ( ! [Xphi: $i > $o] :
% 0.07/0.32 ( ( exu
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.07/0.32 => ? [Xx: $i] :
% 0.07/0.32 ( ( Xphi @ Xx )
% 0.07/0.32 & ! [Xy: $i] :
% 0.07/0.32 ( ( Xphi @ Xy )
% 0.07/0.32 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(prop2set_type,type,
% 0.07/0.32 prop2set: $o > $i ).
% 0.07/0.32
% 0.07/0.32 thf(prop2set,definition,
% 0.07/0.32 ( prop2set
% 0.07/0.32 = ( ^ [Xphi: $o] :
% 0.07/0.32 ( dsetconstr @ ( powerset @ emptyset )
% 0.07/0.32 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(prop2setE_type,type,
% 0.07/0.32 prop2setE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(prop2setE,definition,
% 0.07/0.32 ( prop2setE
% 0.07/0.32 = ( ! [Xphi: $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.07/0.32 => Xphi ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetE_type,type,
% 0.07/0.32 emptysetE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetE,definition,
% 0.07/0.32 ( emptysetE
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ emptyset )
% 0.07/0.32 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetimpfalse_type,type,
% 0.07/0.32 emptysetimpfalse: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptysetimpfalse,definition,
% 0.07/0.32 ( emptysetimpfalse
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ emptyset )
% 0.07/0.32 => $false ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(notinemptyset_type,type,
% 0.07/0.32 notinemptyset: $o ).
% 0.07/0.32
% 0.07/0.32 thf(notinemptyset,definition,
% 0.07/0.32 ( notinemptyset
% 0.07/0.32 = ( ! [Xx: $i] :
% 0.07/0.32 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(exuE3e_type,type,
% 0.07/0.32 exuE3e: $o ).
% 0.07/0.32
% 0.07/0.32 thf(exuE3e,definition,
% 0.07/0.32 ( exuE3e
% 0.07/0.32 = ( ! [Xphi: $i > $o] :
% 0.07/0.32 ( ( exu
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.07/0.32 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setext_type,type,
% 0.07/0.32 setext: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setext,definition,
% 0.07/0.32 ( setext
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( in @ Xx @ B ) )
% 0.07/0.32 => ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) )
% 0.07/0.32 => ( A = B ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyI_type,type,
% 0.07/0.32 emptyI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyI,definition,
% 0.07/0.32 ( emptyI
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ~ ( in @ Xx @ A )
% 0.07/0.32 => ( A = emptyset ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(noeltsimpempty_type,type,
% 0.07/0.32 noeltsimpempty: $o ).
% 0.07/0.32
% 0.07/0.32 thf(noeltsimpempty,definition,
% 0.07/0.32 ( noeltsimpempty
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ~ ( in @ Xx @ A )
% 0.07/0.32 => ( A = emptyset ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setbeta_type,type,
% 0.07/0.32 setbeta: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setbeta,definition,
% 0.07/0.32 ( setbeta
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( ( in @ Xx
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.07/0.32 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonempty_type,type,
% 0.07/0.32 nonempty: $i > $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonempty,definition,
% 0.07/0.32 ( nonempty
% 0.07/0.32 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyE1_type,type,
% 0.07/0.32 nonemptyE1: $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyE1,definition,
% 0.07/0.32 ( nonemptyE1
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ( nonempty @ A )
% 0.07/0.32 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyI_type,type,
% 0.07/0.32 nonemptyI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyI,definition,
% 0.07/0.32 ( nonemptyI
% 0.07/0.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( ( Xphi @ Xx )
% 0.07/0.32 => ( nonempty
% 0.07/0.32 @ ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyI1_type,type,
% 0.07/0.32 nonemptyI1: $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyI1,definition,
% 0.07/0.32 ( nonemptyI1
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.07/0.32 => ( nonempty @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIL_type,type,
% 0.07/0.32 setadjoinIL: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIL,definition,
% 0.07/0.32 ( setadjoinIL
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyinunitempty_type,type,
% 0.07/0.32 emptyinunitempty: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyinunitempty,definition,
% 0.07/0.32 ( emptyinunitempty
% 0.07/0.32 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIR_type,type,
% 0.07/0.32 setadjoinIR: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinIR,definition,
% 0.07/0.32 ( setadjoinIR
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ A )
% 0.07/0.32 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinE_type,type,
% 0.07/0.32 setadjoinE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinE,definition,
% 0.07/0.32 ( setadjoinE
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.07/0.32 => ! [Xphi: $o] :
% 0.07/0.32 ( ( ( Xy = Xx )
% 0.07/0.32 => Xphi )
% 0.07/0.32 => ( ( ( in @ Xy @ A )
% 0.07/0.32 => Xphi )
% 0.07/0.32 => Xphi ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinOr_type,type,
% 0.07/0.32 setadjoinOr: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setadjoinOr,definition,
% 0.07/0.32 ( setadjoinOr
% 0.07/0.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.07/0.32 => ( ( Xy = Xx )
% 0.07/0.32 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setoftrueEq_type,type,
% 0.07/0.32 setoftrueEq: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setoftrueEq,definition,
% 0.07/0.32 ( setoftrueEq
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xx: $i] : $true )
% 0.07/0.32 = A ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(powersetI_type,type,
% 0.07/0.32 powersetI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(powersetI,definition,
% 0.07/0.32 ( powersetI
% 0.07/0.32 = ( ! [A: $i,B: $i] :
% 0.07/0.32 ( ! [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) )
% 0.07/0.32 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyinPowerset_type,type,
% 0.07/0.32 emptyinPowerset: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyinPowerset,definition,
% 0.07/0.32 ( emptyinPowerset
% 0.07/0.32 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyInPowerset_type,type,
% 0.07/0.32 emptyInPowerset: $o ).
% 0.07/0.32
% 0.07/0.32 thf(emptyInPowerset,definition,
% 0.07/0.32 ( emptyInPowerset
% 0.07/0.32 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(powersetE_type,type,
% 0.07/0.32 powersetE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(powersetE,definition,
% 0.07/0.32 ( powersetE
% 0.07/0.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ B @ ( powerset @ A ) )
% 0.07/0.32 => ( ( in @ Xx @ B )
% 0.07/0.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setunionI_type,type,
% 0.07/0.32 setunionI: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setunionI,definition,
% 0.07/0.32 ( setunionI
% 0.07/0.32 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( ( in @ B @ A )
% 0.07/0.32 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(setunionE_type,type,
% 0.07/0.32 setunionE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(setunionE,definition,
% 0.07/0.32 ( setunionE
% 0.07/0.32 = ( ! [A: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.07/0.32 => ! [Xphi: $o] :
% 0.07/0.32 ( ! [B: $i] :
% 0.07/0.32 ( ( in @ Xx @ B )
% 0.07/0.32 => ( ( in @ B @ A )
% 0.07/0.32 => Xphi ) )
% 0.07/0.32 => Xphi ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(subPowSU_type,type,
% 0.07/0.32 subPowSU: $o ).
% 0.07/0.32
% 0.07/0.32 thf(subPowSU,definition,
% 0.07/0.32 ( subPowSU
% 0.07/0.32 = ( ! [A: $i,Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(exuE2_type,type,
% 0.07/0.32 exuE2: $o ).
% 0.07/0.32
% 0.07/0.32 thf(exuE2,definition,
% 0.07/0.32 ( exuE2
% 0.07/0.32 = ( ! [Xphi: $i > $o] :
% 0.07/0.32 ( ( exu
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.07/0.32 => ? [Xx: $i] :
% 0.07/0.32 ! [Xy: $i] :
% 0.07/0.32 ( ( Xphi @ Xy )
% 0.07/0.32 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyImpWitness_type,type,
% 0.07/0.32 nonemptyImpWitness: $o ).
% 0.07/0.32
% 0.07/0.32 thf(nonemptyImpWitness,definition,
% 0.07/0.32 ( nonemptyImpWitness
% 0.07/0.32 = ( ! [A: $i] :
% 0.07/0.32 ( ( nonempty @ A )
% 0.07/0.32 => ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 & $true ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(uniqinunit_type,type,
% 0.07/0.32 uniqinunit: $o ).
% 0.07/0.32
% 0.07/0.32 thf(uniqinunit,definition,
% 0.07/0.32 ( uniqinunit
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.07/0.32 => ( Xx = Xy ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(notinsingleton_type,type,
% 0.07/0.32 notinsingleton: $o ).
% 0.07/0.32
% 0.07/0.32 thf(notinsingleton,definition,
% 0.07/0.32 ( notinsingleton
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( Xx != Xy )
% 0.07/0.32 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(eqinunit_type,type,
% 0.07/0.32 eqinunit: $o ).
% 0.07/0.32
% 0.07/0.32 thf(eqinunit,definition,
% 0.07/0.32 ( eqinunit
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( Xx = Xy )
% 0.07/0.32 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(singletonsswitch_type,type,
% 0.07/0.32 singletonsswitch: $o ).
% 0.07/0.32
% 0.07/0.32 thf(singletonsswitch,definition,
% 0.07/0.32 ( singletonsswitch
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] :
% 0.07/0.32 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.07/0.32 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(upairsetE_type,type,
% 0.07/0.32 upairsetE: $o ).
% 0.07/0.32
% 0.07/0.32 thf(upairsetE,definition,
% 0.07/0.32 ( upairsetE
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.07/0.32 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.07/0.32 => ( ( Xz = Xx )
% 0.07/0.32 | ( Xz = Xy ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(upairsetIL_type,type,
% 0.07/0.32 upairsetIL: $o ).
% 0.07/0.32
% 0.07/0.32 thf(upairsetIL,definition,
% 0.07/0.32 ( upairsetIL
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(upairsetIR_type,type,
% 0.07/0.32 upairsetIR: $o ).
% 0.07/0.32
% 0.07/0.32 thf(upairsetIR,definition,
% 0.07/0.32 ( upairsetIR
% 0.07/0.32 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 thf(emptyE1,conjecture,
% 0.07/0.32 ( setextAx
% 0.07/0.32 => ( emptysetAx
% 0.07/0.32 => ( setadjoinAx
% 0.07/0.32 => ( powersetAx
% 0.07/0.32 => ( setunionAx
% 0.07/0.32 => ( omega0Ax
% 0.07/0.32 => ( omegaSAx
% 0.07/0.32 => ( omegaIndAx
% 0.07/0.32 => ( replAx
% 0.07/0.32 => ( foundationAx
% 0.07/0.32 => ( wellorderingAx
% 0.07/0.32 => ( descrp
% 0.07/0.32 => ( dsetconstrI
% 0.07/0.32 => ( dsetconstrEL
% 0.07/0.32 => ( dsetconstrER
% 0.07/0.32 => ( exuE1
% 0.07/0.32 => ( prop2setE
% 0.07/0.32 => ( emptysetE
% 0.07/0.32 => ( emptysetimpfalse
% 0.07/0.32 => ( notinemptyset
% 0.07/0.32 => ( exuE3e
% 0.07/0.32 => ( setext
% 0.07/0.32 => ( emptyI
% 0.07/0.32 => ( noeltsimpempty
% 0.07/0.32 => ( setbeta
% 0.07/0.32 => ( nonemptyE1
% 0.07/0.32 => ( nonemptyI
% 0.07/0.32 => ( nonemptyI1
% 0.07/0.32 => ( setadjoinIL
% 0.07/0.32 => ( emptyinunitempty
% 0.07/0.32 => ( setadjoinIR
% 0.07/0.32 => ( setadjoinE
% 0.07/0.32 => ( setadjoinOr
% 0.07/0.32 => ( setoftrueEq
% 0.07/0.32 => ( powersetI
% 0.07/0.32 => ( emptyinPowerset
% 0.07/0.32 => ( emptyInPowerset
% 0.07/0.32 => ( powersetE
% 0.07/0.32 => ( setunionI
% 0.07/0.32 => ( setunionE
% 0.07/0.32 => ( subPowSU
% 0.07/0.32 => ( exuE2
% 0.07/0.32 => ( nonemptyImpWitness
% 0.07/0.32 => ( uniqinunit
% 0.07/0.32 => ( notinsingleton
% 0.07/0.32 => ( eqinunit
% 0.07/0.32 => ( singletonsswitch
% 0.07/0.32 => ( upairsetE
% 0.07/0.32 => ( upairsetIL
% 0.07/0.32 => ( upairsetIR
% 0.07/0.32 => ! [A: $i,Xphi: $i > $o] :
% 0.07/0.32 ( ? [Xx: $i] :
% 0.07/0.32 ( ( in @ Xx @ A )
% 0.07/0.32 & ( Xphi @ Xx ) )
% 0.07/0.32 => ( ( ( dsetconstr @ A
% 0.07/0.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.07/0.32 = emptyset )
% 0.07/0.32 => $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.12/0.97 ---- Embedded in THF ---
% 1.12/0.97 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.12/0.97 %%% Generated on Tue Feb 24 12:26:01 EST 2026
% 1.12/0.97 %%% using '$$dhol' embedding, version 1.3.0.
% 1.12/0.97 %%% Logic specification used:
% 1.12/0.97 %%% thf(spec, logic, $$dhol).
% 1.12/0.97
% 1.12/0.97 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.rxuSLvj59h/DTF2DTF29102.p
% See solution above
% 1.12/0.97 ------------------------
% 1.12/0.98 ---- Cleaned THF ---
% 1.12/0.98 thf(in_type,type,
% 1.12/0.98 in: $i > $i > $o ).
% 1.12/0.98
% 1.12/0.98 thf(exu_type,type,
% 1.12/0.98 exu: ( $i > $o ) > $o ).
% 1.12/0.98
% 1.12/0.98 thf(exu,definition,
% 1.12/0.98 ( exu
% 1.12/0.98 = ( ^ [Xphi: $i > $o] :
% 1.12/0.98 ? [Xx: $i] :
% 1.12/0.98 ( ( Xphi @ Xx )
% 1.12/0.98 & ! [Xy: $i] :
% 1.12/0.98 ( ( Xphi @ Xy )
% 1.12/0.98 => ( Xx = Xy ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setextAx_type,type,
% 1.12/0.98 setextAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setextAx,definition,
% 1.12/0.98 ( setextAx
% 1.12/0.98 = ( ! [A: $i,B: $i] :
% 1.12/0.98 ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 <=> ( in @ Xx @ B ) )
% 1.12/0.98 => ( A = B ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(emptyset_type,type,
% 1.12/0.98 emptyset: $i ).
% 1.12/0.98
% 1.12/0.98 thf(emptysetAx_type,type,
% 1.12/0.98 emptysetAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(emptysetAx,definition,
% 1.12/0.98 ( emptysetAx
% 1.12/0.98 = ( ! [Xx: $i] :
% 1.12/0.98 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoin_type,type,
% 1.12/0.98 setadjoin: $i > $i > $i ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinAx_type,type,
% 1.12/0.98 setadjoinAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinAx,definition,
% 1.12/0.98 ( setadjoinAx
% 1.12/0.98 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.12/0.98 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.12/0.98 <=> ( ( Xy = Xx )
% 1.12/0.98 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(powerset_type,type,
% 1.12/0.98 powerset: $i > $i ).
% 1.12/0.98
% 1.12/0.98 thf(powersetAx_type,type,
% 1.12/0.98 powersetAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(powersetAx,definition,
% 1.12/0.98 ( powersetAx
% 1.12/0.98 = ( ! [A: $i,B: $i] :
% 1.12/0.98 ( ( in @ B @ ( powerset @ A ) )
% 1.12/0.98 <=> ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ B )
% 1.12/0.98 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setunion_type,type,
% 1.12/0.98 setunion: $i > $i ).
% 1.12/0.98
% 1.12/0.98 thf(setunionAx_type,type,
% 1.12/0.98 setunionAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setunionAx,definition,
% 1.12/0.98 ( setunionAx
% 1.12/0.98 = ( ! [A: $i,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ ( setunion @ A ) )
% 1.12/0.98 <=> ? [B: $i] :
% 1.12/0.98 ( ( in @ Xx @ B )
% 1.12/0.98 & ( in @ B @ A ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(omega_type,type,
% 1.12/0.98 omega: $i ).
% 1.12/0.98
% 1.12/0.98 thf(omega0Ax_type,type,
% 1.12/0.98 omega0Ax: $o ).
% 1.12/0.98
% 1.12/0.98 thf(omega0Ax,definition,
% 1.12/0.98 ( omega0Ax
% 1.12/0.98 = ( in @ emptyset @ omega ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(omegaSAx_type,type,
% 1.12/0.98 omegaSAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(omegaSAx,definition,
% 1.12/0.98 ( omegaSAx
% 1.12/0.98 = ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ omega )
% 1.12/0.98 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(omegaIndAx_type,type,
% 1.12/0.98 omegaIndAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(omegaIndAx,definition,
% 1.12/0.98 ( omegaIndAx
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ( ( ( in @ emptyset @ A )
% 1.12/0.98 & ! [Xx: $i] :
% 1.12/0.98 ( ( ( in @ Xx @ omega )
% 1.12/0.98 & ( in @ Xx @ A ) )
% 1.12/0.98 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.12/0.98 => ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ omega )
% 1.12/0.98 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(replAx_type,type,
% 1.12/0.98 replAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(replAx,definition,
% 1.12/0.98 ( replAx
% 1.12/0.98 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.12/0.98 ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 => ( exu
% 1.12/0.98 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.12/0.98 => ? [B: $i] :
% 1.12/0.98 ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ B )
% 1.12/0.98 <=> ? [Xy: $i] :
% 1.12/0.98 ( ( in @ Xy @ A )
% 1.12/0.98 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(foundationAx_type,type,
% 1.12/0.98 foundationAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(foundationAx,definition,
% 1.12/0.98 ( foundationAx
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.12/0.98 => ? [B: $i] :
% 1.12/0.98 ( ( in @ B @ A )
% 1.12/0.98 & ~ ? [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ B )
% 1.12/0.98 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(wellorderingAx_type,type,
% 1.12/0.98 wellorderingAx: $o ).
% 1.12/0.98
% 1.12/0.98 thf(wellorderingAx,definition,
% 1.12/0.98 ( wellorderingAx
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ? [B: $i] :
% 1.12/0.98 ( ! [C: $i] :
% 1.12/0.98 ( ( in @ C @ B )
% 1.12/0.98 => ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ C )
% 1.12/0.98 => ( in @ Xx @ A ) ) )
% 1.12/0.98 & ! [Xx: $i,Xy: $i] :
% 1.12/0.98 ( ( ( in @ Xx @ A )
% 1.12/0.98 & ( in @ Xy @ A ) )
% 1.12/0.98 => ( ! [C: $i] :
% 1.12/0.98 ( ( in @ C @ B )
% 1.12/0.98 => ( ( in @ Xx @ C )
% 1.12/0.98 <=> ( in @ Xy @ C ) ) )
% 1.12/0.98 => ( Xx = Xy ) ) )
% 1.12/0.98 & ! [C: $i,D: $i] :
% 1.12/0.98 ( ( ( in @ C @ B )
% 1.12/0.98 & ( in @ D @ B ) )
% 1.12/0.98 => ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ C )
% 1.12/0.98 => ( in @ Xx @ D ) )
% 1.12/0.98 | ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ D )
% 1.12/0.98 => ( in @ Xx @ C ) ) ) )
% 1.12/0.98 & ! [C: $i] :
% 1.12/0.98 ( ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ C )
% 1.12/0.98 => ( in @ Xx @ A ) )
% 1.12/0.98 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.12/0.98 => ? [D: $i,Xx: $i] :
% 1.12/0.98 ( ( in @ D @ B )
% 1.12/0.98 & ( in @ Xx @ C )
% 1.12/0.98 & ~ ? [Xy: $i] :
% 1.12/0.98 ( ( in @ Xy @ D )
% 1.12/0.98 & ( in @ Xy @ C ) )
% 1.12/0.98 & ! [E: $i] :
% 1.12/0.98 ( ( in @ E @ B )
% 1.12/0.98 => ( ! [Xy: $i] :
% 1.12/0.98 ( ( in @ Xy @ E )
% 1.12/0.98 => ( in @ Xy @ D ) )
% 1.12/0.98 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(descr_type,type,
% 1.12/0.98 descr: ( $i > $o ) > $i ).
% 1.12/0.98
% 1.12/0.98 thf(descrp_type,type,
% 1.12/0.98 descrp: $o ).
% 1.12/0.98
% 1.12/0.98 thf(descrp,definition,
% 1.12/0.98 ( descrp
% 1.12/0.98 = ( ! [Xphi: $i > $o] :
% 1.12/0.98 ( ( exu
% 1.12/0.98 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.12/0.98 => ( Xphi
% 1.12/0.98 @ ( descr
% 1.12/0.98 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(dsetconstr_type,type,
% 1.12/0.98 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.12/0.98
% 1.12/0.98 thf(dsetconstrI_type,type,
% 1.12/0.98 dsetconstrI: $o ).
% 1.12/0.98
% 1.12/0.98 thf(dsetconstrI,definition,
% 1.12/0.98 ( dsetconstrI
% 1.12/0.98 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 => ( ( Xphi @ Xx )
% 1.12/0.98 => ( in @ Xx
% 1.12/0.98 @ ( dsetconstr @ A
% 1.12/0.98 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(dsetconstrEL_type,type,
% 1.12/0.98 dsetconstrEL: $o ).
% 1.12/0.98
% 1.12/0.98 thf(dsetconstrEL,definition,
% 1.12/0.98 ( dsetconstrEL
% 1.12/0.98 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx
% 1.12/0.98 @ ( dsetconstr @ A
% 1.12/0.98 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.12/0.98 => ( in @ Xx @ A ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(dsetconstrER_type,type,
% 1.12/0.98 dsetconstrER: $o ).
% 1.12/0.98
% 1.12/0.98 thf(dsetconstrER,definition,
% 1.12/0.98 ( dsetconstrER
% 1.12/0.98 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx
% 1.12/0.98 @ ( dsetconstr @ A
% 1.12/0.98 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.12/0.98 => ( Xphi @ Xx ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(exuE1_type,type,
% 1.12/0.98 exuE1: $o ).
% 1.12/0.98
% 1.12/0.98 thf(exuE1,definition,
% 1.12/0.98 ( exuE1
% 1.12/0.98 = ( ! [Xphi: $i > $o] :
% 1.12/0.98 ( ( exu
% 1.12/0.98 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.12/0.98 => ? [Xx: $i] :
% 1.12/0.98 ( ( Xphi @ Xx )
% 1.12/0.98 & ! [Xy: $i] :
% 1.12/0.98 ( ( Xphi @ Xy )
% 1.12/0.98 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(prop2set_type,type,
% 1.12/0.98 prop2set: $o > $i ).
% 1.12/0.98
% 1.12/0.98 thf(prop2set,definition,
% 1.12/0.98 ( prop2set
% 1.12/0.98 = ( ^ [Xphi: $o] :
% 1.12/0.98 ( dsetconstr @ ( powerset @ emptyset )
% 1.12/0.98 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(prop2setE_type,type,
% 1.12/0.98 prop2setE: $o ).
% 1.12/0.98
% 1.12/0.98 thf(prop2setE,definition,
% 1.12/0.98 ( prop2setE
% 1.12/0.98 = ( ! [Xphi: $o,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.12/0.98 => Xphi ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(emptysetE_type,type,
% 1.12/0.98 emptysetE: $o ).
% 1.12/0.98
% 1.12/0.98 thf(emptysetE,definition,
% 1.12/0.98 ( emptysetE
% 1.12/0.98 = ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ emptyset )
% 1.12/0.98 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(emptysetimpfalse_type,type,
% 1.12/0.98 emptysetimpfalse: $o ).
% 1.12/0.98
% 1.12/0.98 thf(emptysetimpfalse,definition,
% 1.12/0.98 ( emptysetimpfalse
% 1.12/0.98 = ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ emptyset )
% 1.12/0.98 => $false ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(notinemptyset_type,type,
% 1.12/0.98 notinemptyset: $o ).
% 1.12/0.98
% 1.12/0.98 thf(notinemptyset,definition,
% 1.12/0.98 ( notinemptyset
% 1.12/0.98 = ( ! [Xx: $i] :
% 1.12/0.98 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(exuE3e_type,type,
% 1.12/0.98 exuE3e: $o ).
% 1.12/0.98
% 1.12/0.98 thf(exuE3e,definition,
% 1.12/0.98 ( exuE3e
% 1.12/0.98 = ( ! [Xphi: $i > $o] :
% 1.12/0.98 ( ( exu
% 1.12/0.98 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.12/0.98 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setext_type,type,
% 1.12/0.98 setext: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setext,definition,
% 1.12/0.98 ( setext
% 1.12/0.98 = ( ! [A: $i,B: $i] :
% 1.12/0.98 ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 => ( in @ Xx @ B ) )
% 1.12/0.98 => ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ B )
% 1.12/0.98 => ( in @ Xx @ A ) )
% 1.12/0.98 => ( A = B ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(emptyI_type,type,
% 1.12/0.98 emptyI: $o ).
% 1.12/0.98
% 1.12/0.98 thf(emptyI,definition,
% 1.12/0.98 ( emptyI
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ( ! [Xx: $i] :
% 1.12/0.98 ~ ( in @ Xx @ A )
% 1.12/0.98 => ( A = emptyset ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(noeltsimpempty_type,type,
% 1.12/0.98 noeltsimpempty: $o ).
% 1.12/0.98
% 1.12/0.98 thf(noeltsimpempty,definition,
% 1.12/0.98 ( noeltsimpempty
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ( ! [Xx: $i] :
% 1.12/0.98 ~ ( in @ Xx @ A )
% 1.12/0.98 => ( A = emptyset ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setbeta_type,type,
% 1.12/0.98 setbeta: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setbeta,definition,
% 1.12/0.98 ( setbeta
% 1.12/0.98 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 => ( ( in @ Xx
% 1.12/0.98 @ ( dsetconstr @ A
% 1.12/0.98 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.12/0.98 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(nonempty_type,type,
% 1.12/0.98 nonempty: $i > $o ).
% 1.12/0.98
% 1.12/0.98 thf(nonempty,definition,
% 1.12/0.98 ( nonempty
% 1.12/0.98 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(nonemptyE1_type,type,
% 1.12/0.98 nonemptyE1: $o ).
% 1.12/0.98
% 1.12/0.98 thf(nonemptyE1,definition,
% 1.12/0.98 ( nonemptyE1
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ( ( nonempty @ A )
% 1.12/0.98 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(nonemptyI_type,type,
% 1.12/0.98 nonemptyI: $o ).
% 1.12/0.98
% 1.12/0.98 thf(nonemptyI,definition,
% 1.12/0.98 ( nonemptyI
% 1.12/0.98 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 => ( ( Xphi @ Xx )
% 1.12/0.98 => ( nonempty
% 1.12/0.98 @ ( dsetconstr @ A
% 1.12/0.98 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(nonemptyI1_type,type,
% 1.12/0.98 nonemptyI1: $o ).
% 1.12/0.98
% 1.12/0.98 thf(nonemptyI1,definition,
% 1.12/0.98 ( nonemptyI1
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.12/0.98 => ( nonempty @ A ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinIL_type,type,
% 1.12/0.98 setadjoinIL: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinIL,definition,
% 1.12/0.98 ( setadjoinIL
% 1.12/0.98 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(emptyinunitempty_type,type,
% 1.12/0.98 emptyinunitempty: $o ).
% 1.12/0.98
% 1.12/0.98 thf(emptyinunitempty,definition,
% 1.12/0.98 ( emptyinunitempty
% 1.12/0.98 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinIR_type,type,
% 1.12/0.98 setadjoinIR: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinIR,definition,
% 1.12/0.98 ( setadjoinIR
% 1.12/0.98 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.12/0.98 ( ( in @ Xy @ A )
% 1.12/0.98 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinE_type,type,
% 1.12/0.98 setadjoinE: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinE,definition,
% 1.12/0.98 ( setadjoinE
% 1.12/0.98 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.12/0.98 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.12/0.98 => ! [Xphi: $o] :
% 1.12/0.98 ( ( ( Xy = Xx )
% 1.12/0.98 => Xphi )
% 1.12/0.98 => ( ( ( in @ Xy @ A )
% 1.12/0.98 => Xphi )
% 1.12/0.98 => Xphi ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinOr_type,type,
% 1.12/0.98 setadjoinOr: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setadjoinOr,definition,
% 1.12/0.98 ( setadjoinOr
% 1.12/0.98 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.12/0.98 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.12/0.98 => ( ( Xy = Xx )
% 1.12/0.98 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setoftrueEq_type,type,
% 1.12/0.98 setoftrueEq: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setoftrueEq,definition,
% 1.12/0.98 ( setoftrueEq
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ( ( dsetconstr @ A
% 1.12/0.98 @ ^ [Xx: $i] : $true )
% 1.12/0.98 = A ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(powersetI_type,type,
% 1.12/0.98 powersetI: $o ).
% 1.12/0.98
% 1.12/0.98 thf(powersetI,definition,
% 1.12/0.98 ( powersetI
% 1.12/0.98 = ( ! [A: $i,B: $i] :
% 1.12/0.98 ( ! [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ B )
% 1.12/0.98 => ( in @ Xx @ A ) )
% 1.12/0.98 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(emptyinPowerset_type,type,
% 1.12/0.98 emptyinPowerset: $o ).
% 1.12/0.98
% 1.12/0.98 thf(emptyinPowerset,definition,
% 1.12/0.98 ( emptyinPowerset
% 1.12/0.98 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(emptyInPowerset_type,type,
% 1.12/0.98 emptyInPowerset: $o ).
% 1.12/0.98
% 1.12/0.98 thf(emptyInPowerset,definition,
% 1.12/0.98 ( emptyInPowerset
% 1.12/0.98 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(powersetE_type,type,
% 1.12/0.98 powersetE: $o ).
% 1.12/0.98
% 1.12/0.98 thf(powersetE,definition,
% 1.12/0.98 ( powersetE
% 1.12/0.98 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.12/0.98 ( ( in @ B @ ( powerset @ A ) )
% 1.12/0.98 => ( ( in @ Xx @ B )
% 1.12/0.98 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setunionI_type,type,
% 1.12/0.98 setunionI: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setunionI,definition,
% 1.12/0.98 ( setunionI
% 1.12/0.98 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.12/0.98 ( ( in @ Xx @ B )
% 1.12/0.98 => ( ( in @ B @ A )
% 1.12/0.98 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(setunionE_type,type,
% 1.12/0.98 setunionE: $o ).
% 1.12/0.98
% 1.12/0.98 thf(setunionE,definition,
% 1.12/0.98 ( setunionE
% 1.12/0.98 = ( ! [A: $i,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ ( setunion @ A ) )
% 1.12/0.98 => ! [Xphi: $o] :
% 1.12/0.98 ( ! [B: $i] :
% 1.12/0.98 ( ( in @ Xx @ B )
% 1.12/0.98 => ( ( in @ B @ A )
% 1.12/0.98 => Xphi ) )
% 1.12/0.98 => Xphi ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(subPowSU_type,type,
% 1.12/0.98 subPowSU: $o ).
% 1.12/0.98
% 1.12/0.98 thf(subPowSU,definition,
% 1.12/0.98 ( subPowSU
% 1.12/0.98 = ( ! [A: $i,Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(exuE2_type,type,
% 1.12/0.98 exuE2: $o ).
% 1.12/0.98
% 1.12/0.98 thf(exuE2,definition,
% 1.12/0.98 ( exuE2
% 1.12/0.98 = ( ! [Xphi: $i > $o] :
% 1.12/0.98 ( ( exu
% 1.12/0.98 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.12/0.98 => ? [Xx: $i] :
% 1.12/0.98 ! [Xy: $i] :
% 1.12/0.98 ( ( Xphi @ Xy )
% 1.12/0.98 <=> ( Xy = Xx ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(nonemptyImpWitness_type,type,
% 1.12/0.98 nonemptyImpWitness: $o ).
% 1.12/0.98
% 1.12/0.98 thf(nonemptyImpWitness,definition,
% 1.12/0.98 ( nonemptyImpWitness
% 1.12/0.98 = ( ! [A: $i] :
% 1.12/0.98 ( ( nonempty @ A )
% 1.12/0.98 => ? [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 & $true ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(uniqinunit_type,type,
% 1.12/0.98 uniqinunit: $o ).
% 1.12/0.98
% 1.12/0.98 thf(uniqinunit,definition,
% 1.12/0.98 ( uniqinunit
% 1.12/0.98 = ( ! [Xx: $i,Xy: $i] :
% 1.12/0.98 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.12/0.98 => ( Xx = Xy ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(notinsingleton_type,type,
% 1.12/0.98 notinsingleton: $o ).
% 1.12/0.98
% 1.12/0.98 thf(notinsingleton,definition,
% 1.12/0.98 ( notinsingleton
% 1.12/0.98 = ( ! [Xx: $i,Xy: $i] :
% 1.12/0.98 ( ( Xx != Xy )
% 1.12/0.98 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(eqinunit_type,type,
% 1.12/0.98 eqinunit: $o ).
% 1.12/0.98
% 1.12/0.98 thf(eqinunit,definition,
% 1.12/0.98 ( eqinunit
% 1.12/0.98 = ( ! [Xx: $i,Xy: $i] :
% 1.12/0.98 ( ( Xx = Xy )
% 1.12/0.98 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(singletonsswitch_type,type,
% 1.12/0.98 singletonsswitch: $o ).
% 1.12/0.98
% 1.12/0.98 thf(singletonsswitch,definition,
% 1.12/0.98 ( singletonsswitch
% 1.12/0.98 = ( ! [Xx: $i,Xy: $i] :
% 1.12/0.98 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 1.12/0.98 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(upairsetE_type,type,
% 1.12/0.98 upairsetE: $o ).
% 1.12/0.98
% 1.12/0.98 thf(upairsetE,definition,
% 1.12/0.98 ( upairsetE
% 1.12/0.98 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 1.12/0.98 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 1.12/0.98 => ( ( Xz = Xx )
% 1.12/0.98 | ( Xz = Xy ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(upairsetIL_type,type,
% 1.12/0.98 upairsetIL: $o ).
% 1.12/0.98
% 1.12/0.98 thf(upairsetIL,definition,
% 1.12/0.98 ( upairsetIL
% 1.12/0.98 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(upairsetIR_type,type,
% 1.12/0.98 upairsetIR: $o ).
% 1.12/0.98
% 1.12/0.98 thf(upairsetIR,definition,
% 1.12/0.98 ( upairsetIR
% 1.12/0.98 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 1.12/0.98
% 1.12/0.98 thf(emptyE1,conjecture,
% 1.12/0.98 ( setextAx
% 1.12/0.98 => ( emptysetAx
% 1.12/0.98 => ( setadjoinAx
% 1.12/0.98 => ( powersetAx
% 1.12/0.98 => ( setunionAx
% 1.12/0.98 => ( omega0Ax
% 1.12/0.98 => ( omegaSAx
% 1.12/0.98 => ( omegaIndAx
% 1.12/0.98 => ( replAx
% 1.12/0.98 => ( foundationAx
% 1.12/0.98 => ( wellorderingAx
% 1.12/0.98 => ( descrp
% 1.12/0.98 => ( dsetconstrI
% 1.12/0.98 => ( dsetconstrEL
% 1.12/0.98 => ( dsetconstrER
% 1.12/0.98 => ( exuE1
% 1.12/0.98 => ( prop2setE
% 1.12/0.98 => ( emptysetE
% 1.12/0.98 => ( emptysetimpfalse
% 1.12/0.98 => ( notinemptyset
% 1.12/0.98 => ( exuE3e
% 1.12/0.98 => ( setext
% 1.12/0.98 => ( emptyI
% 1.12/0.98 => ( noeltsimpempty
% 1.12/0.98 => ( setbeta
% 1.12/0.98 => ( nonemptyE1
% 1.12/0.98 => ( nonemptyI
% 1.12/0.98 => ( nonemptyI1
% 1.12/0.98 => ( setadjoinIL
% 1.12/0.98 => ( emptyinunitempty
% 1.12/0.98 => ( setadjoinIR
% 1.12/0.98 => ( setadjoinE
% 1.12/0.98 => ( setadjoinOr
% 1.12/0.98 => ( setoftrueEq
% 1.12/0.98 => ( powersetI
% 1.12/0.98 => ( emptyinPowerset
% 1.12/0.98 => ( emptyInPowerset
% 1.12/0.98 => ( powersetE
% 1.12/0.98 => ( setunionI
% 1.12/0.98 => ( setunionE
% 1.12/0.98 => ( subPowSU
% 1.12/0.98 => ( exuE2
% 1.12/0.98 => ( nonemptyImpWitness
% 1.12/0.98 => ( uniqinunit
% 1.12/0.98 => ( notinsingleton
% 1.12/0.98 => ( eqinunit
% 1.12/0.98 => ( singletonsswitch
% 1.12/0.98 => ( upairsetE
% 1.12/0.98 => ( upairsetIL
% 1.12/0.98 => ( upairsetIR
% 1.12/0.98 => ! [A: $i,Xphi: $i > $o] :
% 1.12/0.98 ( ? [Xx: $i] :
% 1.12/0.98 ( ( in @ Xx @ A )
% 1.12/0.98 & ( Xphi @ Xx ) )
% 1.12/0.98 => ( ( ( dsetconstr @ A
% 1.12/0.98 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.12/0.98 = emptyset )
% 1.12/0.98 => $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.12/0.98 ------------------------
% 1.12/1.00 % (29200)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/183Mi)
% 1.12/1.00 % (29205)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_29102 for (2999ds/275Mi)
% 1.12/1.00 % (29203)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/2Mi)
% 1.12/1.00 % (29206)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/18Mi)
% 1.12/1.00 % (29202)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_29102 for (2999ds/27Mi)
% 1.12/1.00 % (29203)Instruction limit reached!
% 1.12/1.00 % (29203)------------------------------
% 1.12/1.00 % (29203)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.00 % (29203)Termination reason: Unknown
% 1.12/1.00 % (29203)Termination phase: shuffling
% 1.12/1.00
% 1.12/1.00 % (29203)Memory used [KB]: 1151
% 1.12/1.00 % (29203)Time elapsed: 0.003 s
% 1.12/1.00 % (29203)Instructions burned: 4 (million)
% 1.12/1.00 % (29203)------------------------------
% 1.12/1.00 % (29203)------------------------------
% 1.12/1.00 % (29201)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_29102 for (2999ds/4Mi)
% 1.12/1.00 % (29201)Instruction limit reached!
% 1.12/1.00 % (29201)------------------------------
% 1.12/1.00 % (29201)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.00 % (29201)Termination reason: Unknown
% 1.12/1.00 % (29201)Termination phase: shuffling
% 1.12/1.00
% 1.12/1.00 % (29201)Memory used [KB]: 1151
% 1.12/1.00 % (29201)Time elapsed: 0.002 s
% 1.12/1.00 % (29201)Instructions burned: 4 (million)
% 1.12/1.00 % (29201)------------------------------
% 1.12/1.00 % (29201)------------------------------
% 1.12/1.00 % (29204)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_29102 for (2999ds/2Mi)
% 1.12/1.00 % (29204)Instruction limit reached!
% 1.12/1.00 % (29204)------------------------------
% 1.12/1.00 % (29204)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.00 % (29204)Termination reason: Unknown
% 1.12/1.00 % (29204)Termination phase: shuffling
% 1.12/1.00
% 1.12/1.00 % (29204)Memory used [KB]: 1023
% 1.12/1.00 % (29204)Time elapsed: 0.003 s
% 1.12/1.00 % (29204)Instructions burned: 3 (million)
% 1.12/1.00 % (29204)------------------------------
% 1.12/1.00 % (29204)------------------------------
% 1.12/1.00 % (29206)Instruction limit reached!
% 1.12/1.00 % (29206)------------------------------
% 1.12/1.00 % (29206)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.00 % (29206)Termination reason: Unknown
% 1.12/1.00 % (29206)Termination phase: Preprocessing 3
% 1.12/1.00
% 1.12/1.00 % (29206)Memory used [KB]: 1535
% 1.12/1.00 % (29206)Time elapsed: 0.007 s
% 1.12/1.00 % (29206)Instructions burned: 18 (million)
% 1.12/1.00 % (29206)------------------------------
% 1.12/1.00 % (29206)------------------------------
% 1.12/1.00 % (29202)Instruction limit reached!
% 1.12/1.00 % (29202)------------------------------
% 1.12/1.00 % (29202)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.00 % (29202)Termination reason: Unknown
% 1.12/1.00 % (29202)Termination phase: Saturation
% 1.12/1.00
% 1.12/1.00 % (29202)Memory used [KB]: 5756
% 1.12/1.00 % (29202)Time elapsed: 0.009 s
% 1.12/1.00 % (29202)Instructions burned: 27 (million)
% 1.12/1.00 % (29202)------------------------------
% 1.12/1.00 % (29202)------------------------------
% 1.12/1.01 % (29211)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_29102 for (2999ds/37Mi)
% 1.12/1.01 % (29212)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_29102 for (2999ds/15Mi)
% 1.12/1.01 % (29213)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_29102 for (2999ds/3Mi)
% 1.12/1.01 % (29213)Instruction limit reached!
% 1.12/1.01 % (29213)------------------------------
% 1.12/1.01 % (29213)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.01 % (29213)Termination reason: Unknown
% 1.12/1.01 % (29213)Termination phase: shuffling
% 1.12/1.01
% 1.12/1.01 % (29213)Memory used [KB]: 1023
% 1.12/1.01 % (29213)Time elapsed: 0.002 s
% 1.12/1.01 % (29213)Instructions burned: 3 (million)
% 1.12/1.01 % (29213)------------------------------
% 1.12/1.01 % (29213)------------------------------
% 1.12/1.02 % (29212)Instruction limit reached!
% 1.12/1.02 % (29212)------------------------------
% 1.12/1.02 % (29212)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.12/1.02 % (29212)Termination reason: Unknown
% 1.12/1.02 % (29212)Termination phase: Preprocessing 3
% 1.12/1.02
% 1.12/1.02 % (29212)Memory used [KB]: 1407
% 1.12/1.02 % (29212)Time elapsed: 0.006 s
% 1.12/1.02 % (29212)Instructions burned: 16 (million)
% 1.12/1.02 % (29212)------------------------------
% 1.12/1.02 % (29212)------------------------------
% 1.12/1.02 % (29214)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_29102 for (2999ds/1041Mi)
% 1.43/1.02 % (29211)Instruction limit reached!
% 1.43/1.02 % (29211)------------------------------
% 1.43/1.02 % (29211)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.02 % (29211)Termination reason: Unknown
% 1.43/1.02 % (29211)Termination phase: Saturation
% 1.43/1.02
% 1.43/1.02 % (29211)Memory used [KB]: 5756
% 1.43/1.02 % (29211)Time elapsed: 0.012 s
% 1.43/1.02 % (29211)Instructions burned: 39 (million)
% 1.43/1.02 % (29211)------------------------------
% 1.43/1.02 % (29211)------------------------------
% 1.43/1.02 % (29210)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/3Mi)
% 1.43/1.02 % (29210)Instruction limit reached!
% 1.43/1.02 % (29210)------------------------------
% 1.43/1.02 % (29210)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.02 % (29210)Termination reason: Unknown
% 1.43/1.02 % (29210)Termination phase: shuffling
% 1.43/1.02
% 1.43/1.02 % (29210)Memory used [KB]: 1151
% 1.43/1.02 % (29210)Time elapsed: 0.003 s
% 1.43/1.02 % (29210)Instructions burned: 5 (million)
% 1.43/1.02 % (29210)------------------------------
% 1.43/1.02 % (29210)------------------------------
% 1.43/1.03 % (29224)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/16Mi)
% 1.43/1.03 % (29224)Instruction limit reached!
% 1.43/1.03 % (29224)------------------------------
% 1.43/1.03 % (29224)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.03 % (29224)Termination reason: Unknown
% 1.43/1.03 % (29224)Termination phase: Property scanning
% 1.43/1.03
% 1.43/1.03 % (29224)Memory used [KB]: 1279
% 1.43/1.03 % (29224)Time elapsed: 0.006 s
% 1.43/1.03 % (29224)Instructions burned: 17 (million)
% 1.43/1.03 % (29224)------------------------------
% 1.43/1.03 % (29224)------------------------------
% 1.43/1.03 % (29231)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_29102 for (2999ds/3Mi)
% 1.43/1.03 % (29219)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/7Mi)
% 1.43/1.03 % (29231)Instruction limit reached!
% 1.43/1.03 % (29231)------------------------------
% 1.43/1.03 % (29231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.03 % (29231)Termination reason: Unknown
% 1.43/1.03 % (29231)Termination phase: shuffling
% 1.43/1.03
% 1.43/1.03 % (29231)Memory used [KB]: 1151
% 1.43/1.03 % (29231)Time elapsed: 0.003 s
% 1.43/1.03 % (29231)Instructions burned: 6 (million)
% 1.43/1.03 % (29231)------------------------------
% 1.43/1.03 % (29231)------------------------------
% 1.43/1.03 % (29232)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_29102 for (2999ds/3Mi)
% 1.43/1.03 % (29232)Instruction limit reached!
% 1.43/1.03 % (29232)------------------------------
% 1.43/1.03 % (29232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.03 % (29232)Termination reason: Unknown
% 1.43/1.03 % (29232)Termination phase: shuffling
% 1.43/1.03
% 1.43/1.03 % (29232)Memory used [KB]: 1023
% 1.43/1.03 % (29232)Time elapsed: 0.002 s
% 1.43/1.03 % (29232)Instructions burned: 3 (million)
% 1.43/1.03 % (29232)------------------------------
% 1.43/1.03 % (29232)------------------------------
% 1.43/1.03 % (29219)Instruction limit reached!
% 1.43/1.03 % (29219)------------------------------
% 1.43/1.03 % (29219)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.03 % (29219)Termination reason: Unknown
% 1.43/1.03 % (29219)Termination phase: shuffling
% 1.43/1.03
% 1.43/1.03 % (29219)Memory used [KB]: 1151
% 1.43/1.03 % (29219)Time elapsed: 0.005 s
% 1.43/1.03 % (29219)Instructions burned: 7 (million)
% 1.43/1.03 % (29219)------------------------------
% 1.43/1.03 % (29219)------------------------------
% 1.43/1.04 % (29233)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/7Mi)
% 1.43/1.04 % (29234)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/3Mi)
% 1.43/1.04 % (29233)Instruction limit reached!
% 1.43/1.04 % (29233)------------------------------
% 1.43/1.04 % (29233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.04 % (29233)Termination reason: Unknown
% 1.43/1.04 % (29233)Termination phase: shuffling
% 1.43/1.04
% 1.43/1.04 % (29233)Memory used [KB]: 1151
% 1.43/1.04 % (29233)Time elapsed: 0.003 s
% 1.43/1.04 % (29233)Instructions burned: 7 (million)
% 1.43/1.04 % (29233)------------------------------
% 1.43/1.04 % (29233)------------------------------
% 1.43/1.04 % (29234)Instruction limit reached!
% 1.43/1.04 % (29234)------------------------------
% 1.43/1.04 % (29234)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.04 % (29234)Termination reason: Unknown
% 1.43/1.04 % (29234)Termination phase: shuffling
% 1.43/1.04
% 1.43/1.04 % (29234)Memory used [KB]: 1151
% 1.43/1.04 % (29234)Time elapsed: 0.002 s
% 1.43/1.04 % (29234)Instructions burned: 4 (million)
% 1.43/1.04 % (29234)------------------------------
% 1.43/1.04 % (29234)------------------------------
% 1.43/1.04 % (29235)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/4Mi)
% 1.43/1.04 % (29236)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/18Mi)
% 1.43/1.04 % (29235)Instruction limit reached!
% 1.43/1.04 % (29235)------------------------------
% 1.43/1.04 % (29235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.04 % (29235)Termination reason: Unknown
% 1.43/1.04 % (29235)Termination phase: shuffling
% 1.43/1.04
% 1.43/1.04 % (29235)Memory used [KB]: 1151
% 1.43/1.04 % (29235)Time elapsed: 0.002 s
% 1.43/1.04 % (29235)Instructions burned: 4 (million)
% 1.43/1.04 % (29235)------------------------------
% 1.43/1.04 % (29235)------------------------------
% 1.43/1.05 % (29236)Instruction limit reached!
% 1.43/1.05 % (29236)------------------------------
% 1.43/1.05 % (29236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.05 % (29236)Termination reason: Unknown
% 1.43/1.05 % (29236)Termination phase: Saturation
% 1.43/1.05
% 1.43/1.05 % (29236)Memory used [KB]: 1279
% 1.43/1.05 % (29236)Time elapsed: 0.006 s
% 1.43/1.05 % (29236)Instructions burned: 19 (million)
% 1.43/1.05 % (29236)------------------------------
% 1.43/1.05 % (29236)------------------------------
% 1.43/1.05 % (29237)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/710Mi)
% 1.43/1.05 % (29238)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/6Mi)
% 1.43/1.05 % (29239)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/902Mi)
% 1.43/1.05 % (29238)Instruction limit reached!
% 1.43/1.05 % (29238)------------------------------
% 1.43/1.05 % (29238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.05 % (29238)Termination reason: Unknown
% 1.43/1.05 % (29238)Termination phase: shuffling
% 1.43/1.05
% 1.43/1.05 % (29238)Memory used [KB]: 1151
% 1.43/1.05 % (29238)Time elapsed: 0.003 s
% 1.43/1.05 % (29238)Instructions burned: 8 (million)
% 1.43/1.05 % (29238)------------------------------
% 1.43/1.05 % (29238)------------------------------
% 1.43/1.05 % (29200)Instruction limit reached!
% 1.43/1.05 % (29200)------------------------------
% 1.43/1.05 % (29200)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.05 % (29200)Termination reason: Unknown
% 1.43/1.05 % (29200)Termination phase: Saturation
% 1.43/1.05
% 1.43/1.05 % (29200)Memory used [KB]: 6652
% 1.43/1.05 % (29200)Time elapsed: 0.059 s
% 1.43/1.05 % (29200)Instructions burned: 185 (million)
% 1.43/1.05 % (29200)------------------------------
% 1.43/1.05 % (29200)------------------------------
% 1.43/1.06 % (29240)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/21Mi)
% 1.43/1.06 % (29241)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/5Mi)
% 1.43/1.06 % (29242)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/6Mi)
% 1.43/1.06 % (29240)Instruction limit reached!
% 1.43/1.06 % (29240)------------------------------
% 1.43/1.06 % (29240)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.06 % (29240)Termination reason: Unknown
% 1.43/1.06 % (29240)Termination phase: Function definition elimination
% 1.43/1.06
% 1.43/1.06 % (29240)Memory used [KB]: 1279
% 1.43/1.06 % (29240)Time elapsed: 0.007 s
% 1.43/1.06 % (29240)Instructions burned: 23 (million)
% 1.43/1.06 % (29240)------------------------------
% 1.43/1.06 % (29240)------------------------------
% 1.43/1.06 % (29241)Instruction limit reached!
% 1.43/1.06 % (29241)------------------------------
% 1.43/1.06 % (29241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.06 % (29241)Termination reason: Unknown
% 1.43/1.06 % (29241)Termination phase: shuffling
% 1.43/1.06
% 1.43/1.06 % (29241)Memory used [KB]: 1151
% 1.43/1.06 % (29241)Time elapsed: 0.003 s
% 1.43/1.06 % (29241)Instructions burned: 7 (million)
% 1.43/1.06 % (29241)------------------------------
% 1.43/1.06 % (29241)------------------------------
% 1.43/1.07 % (29242)Instruction limit reached!
% 1.43/1.07 % (29242)------------------------------
% 1.43/1.07 % (29242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.07 % (29242)Termination reason: Unknown
% 1.43/1.07 % (29242)Termination phase: shuffling
% 1.43/1.07
% 1.43/1.07 % (29242)Memory used [KB]: 1151
% 1.43/1.07 % (29242)Time elapsed: 0.003 s
% 1.43/1.07 % (29242)Instructions burned: 7 (million)
% 1.43/1.07 % (29242)------------------------------
% 1.43/1.07 % (29242)------------------------------
% 1.43/1.07 % (29243)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/377Mi)
% 1.43/1.07 % (29244)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/779Mi)
% 1.43/1.08 % (29245)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_29102 for (2999ds/19Mi)
% 1.43/1.08 % (29245)Instruction limit reached!
% 1.43/1.08 % (29245)------------------------------
% 1.43/1.08 % (29245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.08 % (29245)Termination reason: Unknown
% 1.43/1.08 % (29245)Termination phase: Property scanning
% 1.43/1.08
% 1.43/1.08 % (29245)Memory used [KB]: 1279
% 1.43/1.08 % (29245)Time elapsed: 0.006 s
% 1.43/1.08 % (29245)Instructions burned: 19 (million)
% 1.43/1.08 % (29245)------------------------------
% 1.43/1.08 % (29245)------------------------------
% 1.43/1.08 % (29205)Instruction limit reached!
% 1.43/1.08 % (29205)------------------------------
% 1.43/1.08 % (29205)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.08 % (29239)First to succeed.
% 1.43/1.08 % (29205)Termination reason: Unknown
% 1.43/1.08 % (29205)Termination phase: Saturation
% 1.43/1.08
% 1.43/1.08 % (29205)Memory used [KB]: 7036
% 1.43/1.08 % (29205)Time elapsed: 0.089 s
% 1.43/1.08 % (29205)Instructions burned: 278 (million)
% 1.43/1.08 % (29205)------------------------------
% 1.43/1.08 % (29205)------------------------------
% 1.43/1.09 % (29239)Refutation found. Thanks to Tanya!
% 1.43/1.09 % SZS status Theorem for DTF2THF_29102
% 1.43/1.09 % SZS output start Proof for DTF2THF_29102
% 1.43/1.09 thf(func_def_0, type, in: $i > $i > $o).
% 1.43/1.09 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.43/1.09 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.43/1.09 thf(func_def_8, type, powerset: $i > $i).
% 1.43/1.09 thf(func_def_10, type, setunion: $i > $i).
% 1.43/1.09 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.43/1.09 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.43/1.09 thf(func_def_26, type, prop2set: $o > $i).
% 1.43/1.09 thf(func_def_36, type, nonempty: $i > $o).
% 1.43/1.09 thf(func_def_74, type, sP0: $i > $i > $o).
% 1.43/1.09 thf(func_def_75, type, sP1: $i > $o).
% 1.43/1.09 thf(func_def_76, type, sP2: $i > $i > $o).
% 1.43/1.09 thf(func_def_77, type, sP3: $i > $i > $o).
% 1.43/1.09 thf(func_def_81, type, sK7: $i > $i).
% 1.43/1.09 thf(func_def_83, type, sK9: $i > $i).
% 1.43/1.09 thf(func_def_91, type, sK17: $i > $o).
% 1.43/1.09 thf(func_def_94, type, sK20: $i > $i).
% 1.43/1.09 thf(func_def_97, type, sK23: $i > $o).
% 1.43/1.09 thf(func_def_102, type, sK28: $i > $i > $i).
% 1.43/1.09 thf(func_def_107, type, sK33: $i > $o).
% 1.43/1.09 thf(func_def_109, type, sK35: $i > $i > $i).
% 1.43/1.09 thf(func_def_110, type, sK36: $i > $i > $i).
% 1.43/1.09 thf(func_def_111, type, sK37: $i > $i > $i).
% 1.43/1.09 thf(func_def_112, type, sK38: $i > $i > $i).
% 1.43/1.09 thf(func_def_113, type, sK39: $i > $i > $i > $i).
% 1.43/1.09 thf(func_def_114, type, sK40: $i > $i).
% 1.43/1.09 thf(func_def_115, type, sK41: $i > $i).
% 1.43/1.09 thf(func_def_116, type, sK42: $i > $i).
% 1.43/1.09 thf(func_def_117, type, sK43: $i > $i).
% 1.43/1.09 thf(func_def_118, type, sK44: $i > $i > $i > $i).
% 1.43/1.09 thf(func_def_119, type, sK45: $i > $i > $i > $i).
% 1.43/1.09 thf(func_def_120, type, sK46: $i > $i > $i).
% 1.43/1.09 thf(func_def_121, type, sK47: $i > $i > $i).
% 1.43/1.09 thf(func_def_122, type, sK48: $i > $i > $i).
% 1.43/1.09 thf(func_def_124, type, sK50: $i > $i).
% 1.43/1.09 thf(func_def_125, type, sK51: $i > $i).
% 1.43/1.09 thf(func_def_126, type, sK52: $i > $i).
% 1.43/1.09 thf(func_def_127, type, sK53: $i > $i > $i).
% 1.43/1.09 thf(func_def_129, type, sK55: $i > $i).
% 1.43/1.09 thf(func_def_131, type, sK57: $i > $i).
% 1.43/1.09 thf(func_def_132, type, sK58: $i > $o).
% 1.43/1.09 thf(func_def_138, type, sK64: $o > $i > $i > $i).
% 1.43/1.09 thf(func_def_141, type, sK67: $i > $i > $i).
% 1.43/1.09 thf(func_def_146, type, sK72: $i > $o).
% 1.43/1.09 thf(func_def_152, type, sK78: $i > $i > $i).
% 1.43/1.09 thf(func_def_158, type, sK84: $i > $i > $i).
% 1.43/1.09 thf(func_def_159, type, sK85: $i > $i > $i).
% 1.43/1.09 thf(func_def_162, type, sK88: $i > $i).
% 1.43/1.09 thf(func_def_167, type, sK93: ($i > $o) > $i).
% 1.43/1.09 thf(func_def_168, type, sK94: $i > $o).
% 1.43/1.09 thf(func_def_169, type, sK95: $i > $o).
% 1.43/1.09 thf(func_def_173, type, sK99: $i > $i > $o).
% 1.43/1.09 thf(func_def_174, type, sK100: $i > $i).
% 1.43/1.09 thf(func_def_175, type, sK101: $i > $i).
% 1.43/1.09 thf(func_def_176, type, sK102: ($i > $i > $o) > $i > $i).
% 1.43/1.09 thf(func_def_177, type, sK103: ($i > $i > $o) > $i > $i).
% 1.43/1.09 thf(func_def_178, type, sK104: $i > ($i > $i > $o) > $i > $i).
% 1.43/1.09 thf(func_def_192, type, sK118: $i > $i > $i).
% 1.43/1.09 thf(func_def_197, type, sK123: $i > $i).
% 1.43/1.09 thf(func_def_203, type, sK129: $i > $o).
% 1.43/1.09 thf(func_def_211, type, sK137: ($i > $o) > $i).
% 1.43/1.09 thf(func_def_212, type, sK138: $i > $o).
% 1.43/1.09 thf(func_def_213, type, sK139: $i > $i).
% 1.43/1.09 thf(func_def_214, type, sK140: ($i > $o) > $i).
% 1.43/1.09 thf(func_def_215, type, sK141: $i > $o).
% 1.43/1.09 thf(func_def_216, type, sK142: $i > $i).
% 1.43/1.09 thf(func_def_221, type, ph147: !>[X0: $tType]:(X0)).
% 1.43/1.09 thf(f1408,plain,(
% 1.43/1.09 $false),
% 1.43/1.09 inference(avatar_sat_refutation,[status(thm)],[f1259,f1407])).
% 1.43/1.09 thf(f1407,plain,(
% 1.43/1.09 ~spl146_2),
% 1.43/1.09 inference(avatar_contradiction_clause,[status(thm)],[f1406])).
% 1.43/1.09 thf(f1406,plain,(
% 1.43/1.09 $false | ~spl146_2),
% 1.43/1.09 inference(trivial_inequality_removal,[status(thm)],[f1405])).
% 1.43/1.09 thf(f1405,plain,(
% 1.43/1.09 ($true != $true) | ~spl146_2),
% 1.43/1.09 inference(superposition,[status(thm)],[f1351,f546])).
% 1.43/1.09 thf(f546,plain,(
% 1.43/1.09 ((sK23 @ sK24) = $true)),
% 1.43/1.09 inference(cnf_transformation,[status(thm)],[f270])).
% 1.43/1.09 thf(f270,plain,(
% 1.43/1.09 (emptyInPowerset = $true) & (replAx = $true) & (setbeta = $true) & (setadjoinIR = $true) & (emptyI = $true) & (emptyinPowerset = $true) & (nonemptyI = $true) & (noeltsimpempty = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (descrp = $true) & (setunionE = $true) & (foundationAx = $true) & (wellorderingAx = $true) & (nonemptyI1 = $true) & (singletonsswitch = $true) & (setunionI = $true) & (omegaIndAx = $true) & (eqinunit = $true) & (upairsetIL = $true) & (setadjoinOr = $true) & (dsetconstrI = $true) & (notinemptyset = $true) & (upairsetIR = $true) & (uniqinunit = $true) & ((((in @ sK24 @ sK22) = $true) & ((sK23 @ sK24) = $true)) & (emptyset = (dsetconstr @ sK22 @ (^[Y0 : $i]: (sK23 @ Y0))))) & (setoftrueEq = $true) & (powersetAx = $true) & (nonemptyE1 = $true) & (prop2setE = $true) & (emptyinunitempty = $true) & (notinsingleton = $true) & (emptysetAx = $true) & (emptysetE = $true) & (setextAx = $true) & (nonemptyImpWitness = $true) & (setadjoinIL = $true) & (powersetE = $true) & (emptysetimpfalse = $true) & (setadjoinAx = $true) & (exuE2 = $true) & (setext = $true) & (subPowSU = $true) & (upairsetE = $true) & (powersetI = $true) & (exuE3e = $true) & (dsetconstrER = $true) & (setunionAx = $true) & (omegaSAx = $true) & (exuE1 = $true) & (omega0Ax = $true)),
% 1.43/1.09 inference(skolemisation,[status(esa),new_symbols(skolem,[sK22,sK23,sK24])],[f201,f269,f268])).
% 1.43/1.09 thf(f268,plain,(
% 1.43/1.09 ? [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) = $true)) & (emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) => (? [X2 : $i] : (((in @ X2 @ sK22) = $true) & ((sK23 @ X2) = $true)) & (emptyset = (dsetconstr @ sK22 @ (^[Y0 : $i]: (sK23 @ Y0)))))),
% 1.43/1.09 introduced(definition,[],[choice_axiom])).
% 1.43/1.09 thf(f269,plain,(
% 1.43/1.09 ? [X2 : $i] : (((in @ X2 @ sK22) = $true) & ((sK23 @ X2) = $true)) => (((in @ sK24 @ sK22) = $true) & ((sK23 @ sK24) = $true))),
% 1.43/1.09 introduced(definition,[],[choice_axiom])).
% 1.43/1.09 thf(f201,plain,(
% 1.43/1.09 (emptyInPowerset = $true) & (replAx = $true) & (setbeta = $true) & (setadjoinIR = $true) & (emptyI = $true) & (emptyinPowerset = $true) & (nonemptyI = $true) & (noeltsimpempty = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (descrp = $true) & (setunionE = $true) & (foundationAx = $true) & (wellorderingAx = $true) & (nonemptyI1 = $true) & (singletonsswitch = $true) & (setunionI = $true) & (omegaIndAx = $true) & (eqinunit = $true) & (upairsetIL = $true) & (setadjoinOr = $true) & (dsetconstrI = $true) & (notinemptyset = $true) & (upairsetIR = $true) & (uniqinunit = $true) & ? [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) = $true)) & (emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) & (setoftrueEq = $true) & (powersetAx = $true) & (nonemptyE1 = $true) & (prop2setE = $true) & (emptyinunitempty = $true) & (notinsingleton = $true) & (emptysetAx = $true) & (emptysetE = $true) & (setextAx = $true) & (nonemptyImpWitness = $true) & (setadjoinIL = $true) & (powersetE = $true) & (emptysetimpfalse = $true) & (setadjoinAx = $true) & (exuE2 = $true) & (setext = $true) & (subPowSU = $true) & (upairsetE = $true) & (powersetI = $true) & (exuE3e = $true) & (dsetconstrER = $true) & (setunionAx = $true) & (omegaSAx = $true) & (exuE1 = $true) & (omega0Ax = $true)),
% 1.43/1.09 inference(flattening,[status(thm)],[f200])).
% 1.43/1.09 thf(f200,plain,(
% 1.43/1.09 (((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) = $true)) & (emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) & (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)),
% 1.43/1.09 inference(ennf_transformation,[status(thm)],[f165])).
% 1.43/1.09 thf(f165,plain,(
% 1.43/1.09 ~((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) => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) = $true)) => (emptyset != (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.43/1.09 inference(flattening,[status(thm)],[f164])).
% 1.43/1.09 thf(f164,plain,(
% 1.43/1.09 ~((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) => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) = $true)) => ~(emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.43/1.09 inference(true_and_false_elimination,[status(thm)],[f75])).
% 1.43/1.09 thf(f75,plain,(
% 1.43/1.09 ~((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) => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : (((in @ X2 @ X0) = $true) & ((X1 @ X2) = $true)) => ((emptyset = (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))) => $false))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.43/1.09 inference(fool_elimination,[status(thm)],[f74])).
% 1.43/1.09 thf(f74,plain,(
% 1.43/1.09 ~(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 => ! [X0 : $i,X1 : $i > $o] : (? [X2 : $i] : ((in @ X2 @ X0) & (X1 @ X2)) => (((dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3))) = emptyset) => $false))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.43/1.09 inference(rectify,[status(thm)],[f55])).
% 1.43/1.09 thf(f55,negated_conjecture,(
% 1.43/1.09 ~(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 => ! [X3 : $i,X0 : $i > $o] : (? [X1 : $i] : ((in @ X1 @ X3) & (X0 @ X1)) => (((dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) = emptyset) => $false))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.43/1.09 inference(negated_conjecture,[status(cth)],[f54])).
% 1.43/1.09 thf(f54,conjecture,(
% 1.43/1.09 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 => ! [X3 : $i,X0 : $i > $o] : (? [X1 : $i] : ((in @ X1 @ X3) & (X0 @ X1)) => (((dsetconstr @ X3 @ (^[X1 : $i] : (X0 @ X1))) = emptyset) => $false)))))))))))))))))))))))))))))))))))))))))))))))))))),
% 1.43/1.09 file('/export/starexec/sandbox2/tmp/tmp.rxuSLvj59h/DTF2THF_29102.p',emptyE1)).
% 1.43/1.09 thf(f1351,plain,(
% 1.43/1.09 ((sK23 @ sK24) != $true) | ~spl146_2),
% 1.43/1.09 inference(trivial_inequality_removal,[status(thm)],[f1290])).
% 1.43/1.09 thf(f1290,plain,(
% 1.43/1.09 ((sK23 @ sK24) != $true) | ($true != $true) | ~spl146_2),
% 1.43/1.09 inference(superposition,[status(thm)],[f815,f547])).
% 1.43/1.09 thf(f547,plain,(
% 1.43/1.09 ((in @ sK24 @ sK22) = $true)),
% 1.43/1.09 inference(cnf_transformation,[status(thm)],[f270])).
% 1.43/1.09 thf(f815,plain,(
% 1.43/1.09 ( ! [X0 : $i] : (($true != (in @ X0 @ sK22)) | ((sK23 @ X0) != $true)) ) | ~spl146_2),
% 1.43/1.09 inference(avatar_component_clause,[status(thm)],[f814])).
% 1.43/1.09 thf(f814,definition,(
% 1.43/1.09 spl146_2 <=> ! [X0 : $i] : (($true != (in @ X0 @ sK22)) | ((sK23 @ X0) != $true))),
% 1.43/1.09 introduced(definition,[new_symbols(naming,[spl146_2])],[avatar_definition])).
% 1.43/1.09 thf(f1259,plain,(
% 1.43/1.09 spl146_2),
% 1.43/1.09 inference(avatar_split_clause,[status(thm)],[f1258,f814])).
% 1.43/1.09 thf(f1258,plain,(
% 1.43/1.09 ( ! [X0 : $i] : (((sK23 @ X0) != $true) | ($true != (in @ X0 @ sK22))) )),
% 1.43/1.09 inference(trivial_inequality_removal,[status(thm)],[f1257])).
% 1.43/1.09 thf(f1257,plain,(
% 1.43/1.09 ( ! [X0 : $i] : (($true != (in @ X0 @ sK22)) | ($true != $true) | ((sK23 @ X0) != $true)) )),
% 1.43/1.09 inference(forward_demodulation,[status(thm)],[f1238,f532])).
% 1.43/1.09 thf(f532,plain,(
% 1.43/1.09 (emptysetimpfalse = $true)),
% 1.43/1.09 inference(cnf_transformation,[status(thm)],[f270])).
% 1.43/1.09 thf(f1238,plain,(
% 1.43/1.09 ( ! [X0 : $i] : (((sK23 @ X0) != $true) | ($true != (in @ X0 @ sK22)) | (emptysetimpfalse != $true)) )),
% 1.43/1.09 inference(trivial_inequality_removal,[status(thm)],[f1216])).
% 1.43/1.09 thf(f1216,plain,(
% 1.43/1.09 ( ! [X0 : $i] : (((sK23 @ X0) != $true) | ($true != (in @ X0 @ sK22)) | (emptysetimpfalse != $true) | ($true != $true)) )),
% 1.43/1.09 inference(superposition,[status(thm)],[f740,f818])).
% 1.43/1.09 thf(f818,plain,(
% 1.43/1.09 ( ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) | ((sK23 @ X0) != $true) | ($true != (in @ X0 @ sK22))) )),
% 1.43/1.09 inference(trivial_inequality_removal,[status(thm)],[f817])).
% 1.43/1.09 thf(f817,plain,(
% 1.43/1.09 ( ! [X0 : $i] : (($true != $true) | ((sK23 @ X0) != $true) | ((in @ X0 @ emptyset) = $true) | ($true != (in @ X0 @ sK22))) )),
% 1.43/1.09 inference(forward_demodulation,[status(thm)],[f801,f551])).
% 1.43/1.09 thf(f551,plain,(
% 1.43/1.09 (dsetconstrI = $true)),
% 1.43/1.09 inference(cnf_transformation,[status(thm)],[f270])).
% 1.43/1.09 thf(f801,plain,(
% 1.43/1.09 ( ! [X0 : $i] : (((sK23 @ X0) != $true) | ((in @ X0 @ emptyset) = $true) | (dsetconstrI != $true) | ($true != (in @ X0 @ sK22))) )),
% 1.43/1.09 inference(superposition,[status(thm)],[f776,f793])).
% 1.43/1.09 thf(f793,plain,(
% 1.43/1.09 (emptyset = (dsetconstr @ sK22 @ sK23))),
% 1.43/1.09 inference(beta_eta_normalization,[status(thm)],[f545])).
% 1.43/1.09 thf(f545,plain,(
% 1.43/1.09 (emptyset = (dsetconstr @ sK22 @ (^[Y0 : $i]: (sK23 @ Y0))))),
% 1.43/1.09 inference(cnf_transformation,[status(thm)],[f270])).
% 1.43/1.09 thf(f776,plain,(
% 1.43/1.09 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X3 @ (dsetconstr @ X4 @ X5)) = $true) | ((X5 @ X3) != $true) | (dsetconstrI != $true) | ((in @ X3 @ X4) != $true)) )),
% 1.43/1.09 inference(beta_eta_normalization,[status(thm)],[f508])).
% 1.43/1.09 thf(f508,plain,(
% 1.43/1.09 ( ! [X3 : $i,X4 : $i,X5 : $i > $o] : (((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true) | ((X5 @ X3) != $true) | (dsetconstrI != $true) | ((in @ X3 @ X4) != $true)) )),
% 1.43/1.09 inference(cnf_transformation,[status(thm)],[f254])).
% 1.43/1.09 thf(f254,plain,(
% 1.43/1.09 ((dsetconstrI = $true) | (((sK17 @ sK15) = $true) & ((in @ sK15 @ (dsetconstr @ sK16 @ (^[Y0 : $i]: (sK17 @ Y0)))) != $true) & ((in @ sK15 @ sK16) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X3) != $true) | ((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true) | ((in @ X3 @ X4) != $true)) | (dsetconstrI != $true))),
% 1.43/1.09 inference(skolemisation,[status(esa),new_symbols(skolem,[sK15,sK16,sK17])],[f252,f253])).
% 1.43/1.09 thf(f253,plain,(
% 1.43/1.09 ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) = $true) & ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) & ((in @ X0 @ X1) = $true)) => (((sK17 @ sK15) = $true) & ((in @ sK15 @ (dsetconstr @ sK16 @ (^[Y0 : $i]: (sK17 @ Y0)))) != $true) & ((in @ sK15 @ sK16) = $true))),
% 1.43/1.09 introduced(definition,[],[choice_axiom])).
% 1.43/1.09 thf(f252,plain,(
% 1.43/1.09 ((dsetconstrI = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) = $true) & ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) & ((in @ X0 @ X1) = $true))) & (! [X3 : $i,X4 : $i,X5 : $i > $o] : (((X5 @ X3) != $true) | ((in @ X3 @ (dsetconstr @ X4 @ (^[Y0 : $i]: (X5 @ Y0)))) = $true) | ((in @ X3 @ X4) != $true)) | (dsetconstrI != $true))),
% 1.43/1.09 inference(rectify,[status(thm)],[f251])).
% 1.43/1.09 thf(f251,plain,(
% 1.43/1.09 ((dsetconstrI = $true) | ? [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) = $true) & ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) != $true) & ((in @ X0 @ X1) = $true))) & (! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) != $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((in @ X0 @ X1) != $true)) | (dsetconstrI != $true))),
% 1.43/1.09 inference(nnf_transformation,[status(thm)],[f188])).
% 1.43/1.09 thf(f188,plain,(
% 1.43/1.09 (dsetconstrI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((X2 @ X0) != $true) | ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((in @ X0 @ X1) != $true))),
% 1.43/1.09 inference(flattening,[status(thm)],[f187])).
% 1.43/1.09 thf(f187,plain,(
% 1.43/1.09 (dsetconstrI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true) | ((X2 @ X0) != $true)) | ((in @ X0 @ X1) != $true))),
% 1.43/1.09 inference(ennf_transformation,[status(thm)],[f109])).
% 1.43/1.09 thf(f109,plain,(
% 1.43/1.09 (dsetconstrI = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i > $o] : (((in @ X0 @ X1) = $true) => (((X2 @ X0) = $true) => ((in @ X0 @ (dsetconstr @ X1 @ (^[Y0 : $i]: (X2 @ Y0)))) = $true)))),
% 1.43/1.09 inference(fool_elimination,[status(thm)],[f108])).
% 1.43/1.09 thf(f108,plain,(
% 1.43/1.09 (dsetconstrI = ! [X0 : $i,X1 : $i,X2 : $i > $o] : ((in @ X0 @ X1) => ((X2 @ X0) => (in @ X0 @ (dsetconstr @ X1 @ (^[X3 : $i] : (X2 @ X3)))))))),
% 1.43/1.09 inference(rectify,[status(thm)],[f14])).
% 1.43/1.09 thf(f14,axiom,(
% 1.43/1.09 (dsetconstrI = ! [X1 : $i,X3 : $i,X0 : $i > $o] : ((in @ X1 @ X3) => ((X0 @ X1) => (in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))))))),
% 1.43/1.09 file('/export/starexec/sandbox2/tmp/tmp.rxuSLvj59h/DTF2THF_29102.p',dsetconstrI)).
% 1.43/1.09 thf(f740,plain,(
% 1.43/1.09 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true)) )),
% 1.43/1.09 inference(cnf_transformation,[status(thm)],[f466])).
% 1.43/1.09 thf(f466,plain,(
% 1.43/1.09 ((emptysetimpfalse = $true) | ((in @ sK133 @ emptyset) = $true)) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.43/1.09 inference(skolemisation,[status(esa),new_symbols(skolem,[sK133])],[f464,f465])).
% 1.43/1.09 thf(f465,plain,(
% 1.43/1.09 ? [X0 : $i] : ((in @ X0 @ emptyset) = $true) => ((in @ sK133 @ emptyset) = $true)),
% 1.43/1.09 introduced(definition,[],[choice_axiom])).
% 1.43/1.09 thf(f464,plain,(
% 1.43/1.09 ((emptysetimpfalse = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.43/1.09 inference(rectify,[status(thm)],[f463])).
% 1.43/1.09 thf(f463,plain,(
% 1.43/1.09 ((emptysetimpfalse = $true) | ? [X0 : $i] : ((in @ X0 @ emptyset) = $true)) & (! [X0 : $i] : ((in @ X0 @ emptyset) != $true) | (emptysetimpfalse != $true))),
% 1.43/1.09 inference(nnf_transformation,[status(thm)],[f169])).
% 1.43/1.09 thf(f169,plain,(
% 1.43/1.09 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ((in @ X0 @ emptyset) != $true)),
% 1.43/1.09 inference(flattening,[status(thm)],[f168])).
% 1.43/1.09 thf(f168,plain,(
% 1.43/1.09 (emptysetimpfalse = $true) <=> ! [X0 : $i] : ~((in @ X0 @ emptyset) = $true)),
% 1.43/1.09 inference(true_and_false_elimination,[status(thm)],[f89])).
% 1.43/1.09 thf(f89,plain,(
% 1.43/1.09 (emptysetimpfalse = $true) <=> ! [X0 : $i] : (((in @ X0 @ emptyset) = $true) => $false)),
% 1.43/1.09 inference(fool_elimination,[status(thm)],[f88])).
% 1.43/1.09 thf(f88,plain,(
% 1.43/1.09 (emptysetimpfalse = ! [X0 : $i] : ((in @ X0 @ emptyset) => $false))),
% 1.43/1.09 inference(rectify,[status(thm)],[f21])).
% 1.43/1.09 thf(f21,axiom,(
% 1.43/1.09 (emptysetimpfalse = ! [X1 : $i] : ((in @ X1 @ emptyset) => $false))),
% 1.43/1.09 file('/export/starexec/sandbox2/tmp/tmp.rxuSLvj59h/DTF2THF_29102.p',emptysetimpfalse)).
% 1.43/1.09 % SZS output end Proof for DTF2THF_29102
% 1.43/1.09 % (29239)------------------------------
% 1.43/1.09 % (29239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.43/1.09 % (29239)Termination reason: Refutation
% 1.43/1.09
% 1.43/1.09 % (29239)Memory used [KB]: 6652
% 1.43/1.09 % (29239)Time elapsed: 0.054 s
% 1.43/1.09 % (29239)Instructions burned: 100 (million)
% 1.43/1.09 % (29239)------------------------------
% 1.43/1.09 % (29239)------------------------------
% 1.43/1.09 % (29199)Success in time 0.099 s
%------------------------------------------------------------------------------