%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU540^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:35:10 AM UTC 2026
% Result : Theorem 2.21s 1.66s
% Output : Refutation 2.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 34 ( 26 unt; 0 typ; 0 def)
% Number of atoms : 988 ( 268 equ; 0 cnn)
% Maximal formula atoms : 58 ( 29 avg)
% Number of connectives : 524 ( 12 ~; 0 |; 173 &; 104 @)
% ( 0 <=>; 229 =>; 0 <=; 0 <~>)
% Maximal formula depth : 62 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 110 ( 106 usr; 61 con; 0-3 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 41 ( 25 ^; 13 !; 3 ?; 41 :)
% 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_87,type,
sK2: ( $i > $i > $o ) > $i > $i ).
thf(func_def_88,type,
sK3: ( $i > $i > $o ) > $i > $i ).
thf(func_def_89,type,
sK4: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_90,type,
sK5: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_91,type,
sK6: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_92,type,
sK7: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_93,type,
sK8: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_94,type,
sK9: $i > ( $i > $o ) > $i ).
thf(func_def_95,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_96,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_97,type,
sK12: ( $i > $o ) > $i > $i ).
thf(func_def_98,type,
sK13: $i > $i ).
thf(func_def_99,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_100,type,
sK15: $i > ( $i > $o ) > $i ).
thf(func_def_101,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_102,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_103,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_104,type,
sK19: $i > $i ).
thf(func_def_105,type,
sK20: ( $i > $o ) > $i > $i ).
thf(func_def_106,type,
sK21: $i > $i ).
thf(func_def_107,type,
sK22: $i > $i > $i > $i ).
thf(func_def_108,type,
sK23: $i > $i > $i ).
thf(func_def_109,type,
sK24: $i > $i > $i ).
thf(func_def_110,type,
sK25: $i > $i > $i ).
thf(func_def_111,type,
sK26: $i > $i > $i ).
thf(func_def_112,type,
sK27: $i > $i > $i ).
thf(func_def_113,type,
sK28: $i > ( $i > $o ) > $i ).
thf(func_def_114,type,
sK29: ( $i > $o ) > $i > $i ).
thf(func_def_115,type,
sK30: $i > $i > $i ).
thf(func_def_116,type,
sK31: $i > $i > $i ).
thf(func_def_117,type,
sK32: $i > $i > $i ).
thf(func_def_118,type,
sK33: $i > $i > $i ).
thf(func_def_119,type,
sK34: $i > $i > $i ).
thf(func_def_120,type,
sK35: $i > $i ).
thf(func_def_121,type,
sK36: $i > $i ).
thf(func_def_122,type,
sK37: $i > $i ).
thf(func_def_123,type,
sK38: $o > $i > $i > $i ).
thf(func_def_124,type,
sK39: $i > $i ).
thf(func_def_125,type,
ph40:
!>[X0: $tType] : X0 ).
thf(f1394,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f1388,f1004]) ).
thf(f1004,plain,
! [X1: $i] :
( $true
= ( in @ emptyset @ ( powerset @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f1003]) ).
thf(f1003,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] : ( in @ emptyset @ ( powerset @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f315]) ).
thf(f315,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ emptyset @ ( powerset @ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f254,f230]) ).
thf(f230,plain,
emptyinPowerset = $true,
inference(cnf_transformation,[status(thm)],[f181]) ).
thf(f181,plain,
( ( emptysetimpfalse = $true )
& ( quantDeMorgan4 = $true )
& ( omegaSAx = $true )
& ( nonemptyImpWitness = $true )
& ( foundationAx = $true )
& ( $true = sK0 )
& ( $true
!= ( in @ emptyset @ ( prop2set @ sK0 ) ) )
& ( prop2setE = $true )
& ( exuE3e = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( setunionE = $true )
& ( uniqinunit = $true )
& ( singletonsswitch = $true )
& ( setadjoinOr = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( omegaIndAx = $true )
& ( powersetAx = $true )
& ( notinemptyset = $true )
& ( powersetE = $true )
& ( setunionI = $true )
& ( noeltsimpempty = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinIL = $true )
& ( quantDeMorgan3 = $true )
& ( setoftrueEq = $true )
& ( dsetconstrER = $true )
& ( exuE2 = $true )
& ( setunionAx = $true )
& ( emptysetAx = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( subPowSU = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( upairsetIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( nonemptyI1 = $true )
& ( upairsetIL = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( emptysetE = $true )
& ( powersetI = $true )
& ( replAx = $true )
& ( nonemptyE1 = $true )
& ( setext = $true )
& ( dsetconstrI = $true )
& ( wellorderingAx = $true )
& ( nonemptyI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f179,f180]) ).
thf(f180,plain,
( ? [X0: $o] :
( ( $true = X0 )
& ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true ) )
=> ( ( $true = sK0 )
& ( $true
!= ( in @ emptyset @ ( prop2set @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f179,plain,
( ( emptysetimpfalse = $true )
& ( quantDeMorgan4 = $true )
& ( omegaSAx = $true )
& ( nonemptyImpWitness = $true )
& ( foundationAx = $true )
& ? [X0: $o] :
( ( $true = X0 )
& ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true ) )
& ( prop2setE = $true )
& ( exuE3e = $true )
& ( upairsetE = $true )
& ( quantDeMorgan2 = $true )
& ( setadjoinIR = $true )
& ( setunionE = $true )
& ( uniqinunit = $true )
& ( singletonsswitch = $true )
& ( setadjoinOr = $true )
& ( emptyInPowerset = $true )
& ( setbeta = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( emptyinPowerset = $true )
& ( emptyI = $true )
& ( omegaIndAx = $true )
& ( powersetAx = $true )
& ( notinemptyset = $true )
& ( powersetE = $true )
& ( setunionI = $true )
& ( noeltsimpempty = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( quantDeMorgan1 = $true )
& ( setadjoinIL = $true )
& ( quantDeMorgan3 = $true )
& ( setoftrueEq = $true )
& ( dsetconstrER = $true )
& ( exuE2 = $true )
& ( setunionAx = $true )
& ( emptysetAx = $true )
& ( dsetconstrEL = $true )
& ( setadjoinE = $true )
& ( subPowSU = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( upairsetIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinAx = $true )
& ( nonemptyI1 = $true )
& ( upairsetIL = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( emptysetE = $true )
& ( powersetI = $true )
& ( replAx = $true )
& ( nonemptyE1 = $true )
& ( setext = $true )
& ( dsetconstrI = $true )
& ( wellorderingAx = $true )
& ( nonemptyI = $true ) ),
inference(flattening,[status(thm)],[f178]) ).
thf(f178,plain,
( ? [X0: $o] :
( ( $true = X0 )
& ( ( in @ emptyset @ ( prop2set @ X0 ) )
!= $true ) )
& ( quantDeMorgan4 = $true )
& ( quantDeMorgan3 = $true )
& ( quantDeMorgan2 = $true )
& ( quantDeMorgan1 = $true )
& ( vacuousDall = $true )
& ( emptyE1 = $true )
& ( upairsetIR = $true )
& ( upairsetIL = $true )
& ( upairsetE = $true )
& ( singletonsswitch = $true )
& ( eqinunit = $true )
& ( notinsingleton = $true )
& ( uniqinunit = $true )
& ( nonemptyImpWitness = $true )
& ( exuE2 = $true )
& ( subPowSU = $true )
& ( setunionE = $true )
& ( setunionI = $true )
& ( powersetE = $true )
& ( emptyInPowerset = $true )
& ( emptyinPowerset = $true )
& ( powersetI = $true )
& ( setoftrueEq = $true )
& ( setadjoinOr = $true )
& ( setadjoinE = $true )
& ( setadjoinIR = $true )
& ( emptyinunitempty = $true )
& ( setadjoinIL = $true )
& ( nonemptyI1 = $true )
& ( nonemptyI = $true )
& ( nonemptyE1 = $true )
& ( setbeta = $true )
& ( noeltsimpempty = $true )
& ( emptyI = $true )
& ( setext = $true )
& ( exuE3e = $true )
& ( notinemptyset = $true )
& ( emptysetimpfalse = $true )
& ( emptysetE = $true )
& ( prop2setE = $true )
& ( exuE1 = $true )
& ( dsetconstrER = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( descrp = $true )
& ( wellorderingAx = $true )
& ( foundationAx = $true )
& ( replAx = $true )
& ( omegaIndAx = $true )
& ( omegaSAx = $true )
& ( omega0Ax = $true )
& ( setunionAx = $true )
& ( powersetAx = $true )
& ( setadjoinAx = $true )
& ( emptysetAx = $true )
& ( setextAx = $true ) ),
inference(ennf_transformation,[status(thm)],[f72]) ).
thf(f72,plain,
~ ( ( setextAx = $true )
=> ( ( emptysetAx = $true )
=> ( ( setadjoinAx = $true )
=> ( ( powersetAx = $true )
=> ( ( setunionAx = $true )
=> ( ( omega0Ax = $true )
=> ( ( omegaSAx = $true )
=> ( ( omegaIndAx = $true )
=> ( ( replAx = $true )
=> ( ( foundationAx = $true )
=> ( ( wellorderingAx = $true )
=> ( ( descrp = $true )
=> ( ( dsetconstrI = $true )
=> ( ( dsetconstrEL = $true )
=> ( ( dsetconstrER = $true )
=> ( ( exuE1 = $true )
=> ( ( prop2setE = $true )
=> ( ( emptysetE = $true )
=> ( ( emptysetimpfalse = $true )
=> ( ( notinemptyset = $true )
=> ( ( exuE3e = $true )
=> ( ( setext = $true )
=> ( ( emptyI = $true )
=> ( ( noeltsimpempty = $true )
=> ( ( setbeta = $true )
=> ( ( nonemptyE1 = $true )
=> ( ( nonemptyI = $true )
=> ( ( nonemptyI1 = $true )
=> ( ( setadjoinIL = $true )
=> ( ( emptyinunitempty = $true )
=> ( ( setadjoinIR = $true )
=> ( ( setadjoinE = $true )
=> ( ( setadjoinOr = $true )
=> ( ( setoftrueEq = $true )
=> ( ( powersetI = $true )
=> ( ( emptyinPowerset = $true )
=> ( ( emptyInPowerset = $true )
=> ( ( powersetE = $true )
=> ( ( setunionI = $true )
=> ( ( setunionE = $true )
=> ( ( subPowSU = $true )
=> ( ( exuE2 = $true )
=> ( ( nonemptyImpWitness = $true )
=> ( ( uniqinunit = $true )
=> ( ( notinsingleton = $true )
=> ( ( eqinunit = $true )
=> ( ( singletonsswitch = $true )
=> ( ( upairsetE = $true )
=> ( ( upairsetIL = $true )
=> ( ( upairsetIR = $true )
=> ( ( emptyE1 = $true )
=> ( ( vacuousDall = $true )
=> ( ( quantDeMorgan1 = $true )
=> ( ( quantDeMorgan2 = $true )
=> ( ( quantDeMorgan3 = $true )
=> ( ( quantDeMorgan4 = $true )
=> ! [X0: $o] :
( ( $true = X0 )
=> ( ( in @ emptyset @ ( prop2set @ X0 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f71]) ).
thf(f71,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f61]) ).
thf(f61,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f60]) ).
thf(f60,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ( exuE3e
=> ( setext
=> ( emptyI
=> ( noeltsimpempty
=> ( setbeta
=> ( nonemptyE1
=> ( nonemptyI
=> ( nonemptyI1
=> ( setadjoinIL
=> ( emptyinunitempty
=> ( setadjoinIR
=> ( setadjoinE
=> ( setadjoinOr
=> ( setoftrueEq
=> ( powersetI
=> ( emptyinPowerset
=> ( emptyInPowerset
=> ( powersetE
=> ( setunionI
=> ( setunionE
=> ( subPowSU
=> ( exuE2
=> ( nonemptyImpWitness
=> ( uniqinunit
=> ( notinsingleton
=> ( eqinunit
=> ( singletonsswitch
=> ( upairsetE
=> ( upairsetIL
=> ( upairsetIR
=> ( emptyE1
=> ( vacuousDall
=> ( quantDeMorgan1
=> ( quantDeMorgan2
=> ( quantDeMorgan3
=> ( quantDeMorgan4
=> ! [X0: $o] :
( X0
=> ( in @ emptyset @ ( prop2set @ X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2THF_32072.p',prop2setI) ).
thf(f254,plain,
( emptyinPowerset
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ emptyset @ ( powerset @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
thf(f82,plain,
( emptyinPowerset
= ( !! @ $i
@ ^ [Y0: $i] : ( in @ emptyset @ ( powerset @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f81]) ).
thf(f81,plain,
( emptyinPowerset
= ( ! [X0: $i] : ( in @ emptyset @ ( powerset @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,axiom,
( emptyinPowerset
= ( ! [X3: $i] : ( in @ emptyset @ ( powerset @ X3 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2THF_32072.p',emptyinPowerset) ).
thf(f1388,plain,
( $true
!= ( in @ emptyset @ ( powerset @ emptyset ) ) ),
inference(superposition,[status(thm)],[f930,f718]) ).
thf(f718,plain,
! [X1: $i] :
( ( dsetconstr @ X1
@ ^ [Y0: $i] : $true )
= X1 ),
inference(equality_proxy_clausification,[status(thm)],[f717]) ).
thf(f717,plain,
! [X1: $i] :
( $true
= ( X1
= ( dsetconstr @ X1
@ ^ [Y0: $i] : $true ) ) ),
inference(beta_eta_normalization,[status(thm)],[f716]) ).
thf(f716,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( Y0
= ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f350]) ).
thf(f350,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( Y0
= ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true ) ) ) ),
inference(definition_unfolding,[status(thm)],[f291,f217]) ).
thf(f217,plain,
setoftrueEq = $true,
inference(cnf_transformation,[status(thm)],[f181]) ).
thf(f291,plain,
( setoftrueEq
= ( !! @ $i
@ ^ [Y0: $i] :
( Y0
= ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true ) ) ) ),
inference(cnf_transformation,[status(thm)],[f171]) ).
thf(f171,plain,
( setoftrueEq
= ( !! @ $i
@ ^ [Y0: $i] :
( Y0
= ( dsetconstr @ Y0
@ ^ [Y1: $i] : $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f170]) ).
thf(f170,plain,
( setoftrueEq
= ( ! [X0: $i] :
( X0
= ( dsetconstr @ X0
@ ^ [X1: $i] : $true ) ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,axiom,
( setoftrueEq
= ( ! [X3: $i] :
( X3
= ( dsetconstr @ X3
@ ^ [X1: $i] : $true ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2THF_32072.p',setoftrueEq) ).
thf(f930,plain,
( $true
!= ( in @ emptyset
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y0: $i] : $true ) ) ),
inference(beta_eta_normalization,[status(thm)],[f300]) ).
thf(f300,plain,
( $true
!= ( in @ emptyset
@ ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 )
@ $true ) ) ),
inference(definition_unfolding,[status(thm)],[f244,f259,f245]) ).
thf(f245,plain,
$true = sK0,
inference(cnf_transformation,[status(thm)],[f181]) ).
thf(f259,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
thf(f87,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,axiom,
( prop2set
= ( ^ [X0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : X0 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2THF_32072.p',prop2set) ).
thf(f244,plain,
( $true
!= ( in @ emptyset @ ( prop2set @ sK0 ) ) ),
inference(cnf_transformation,[status(thm)],[f181]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SEU540^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.11 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.14/0.31 % Computer : n019.cluster.edu
% 0.14/0.31 % Model : x86_64 x86_64
% 0.14/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.31 % Memory : 8042.1875MB
% 0.14/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.31 % CPULimit : 300
% 0.14/0.31 % WCLimit : 300
% 0.14/0.31 % DateTime : Tue Feb 24 12:26:09 EST 2026
% 0.14/0.31 % CPUTime :
% 0.14/0.31 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : SEU540^1 : TPTP v9.2.1. Released v3.7.0.
% 0.16/0.44 % Domain : Set Theory
% 0.16/0.44 % Problem : Preliminary Notions - Dependent Connective Laws
% 0.16/0.44 % Version : Especial.
% 0.16/0.44 % English : (! phi:o.phi -> in emptyset (prop2set phi))
% 0.16/0.44
% 0.16/0.44 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.16/0.44 % Source : [Bro08]
% 0.16/0.44 % Names : ZFC042g [Bro08]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.23 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.50 v5.4.0, 0.60 v4.1.0, 1.00 v3.7.0
% 0.16/0.44 % Syntax : Number of formulae : 127 ( 59 unt; 67 typ; 59 def)
% 0.16/0.44 % Number of atoms : 321 ( 78 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 57 ( 5 avg)
% 0.16/0.44 % Number of connectives : 536 ( 17 ~; 5 |; 24 &; 345 @)
% 0.16/0.44 % ( 8 <=>; 137 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 61 ( 2 avg)
% 0.16/0.44 % Number of types : 2 ( 0 usr)
% 0.16/0.44 % Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 70 ( 67 usr; 60 con; 0-2 aty)
% 0.16/0.44 % Number of variables : 176 ( 17 ^; 136 !; 23 ?; 176 :)
% 0.16/0.44 % SPC : TH0_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : http://mathgate.info/detsetitem.php?id=101
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 thf(in_type,type,
% 0.16/0.44 in: $i > $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(exu_type,type,
% 0.16/0.44 exu: ( $i > $o ) > $o ).
% 0.16/0.44
% 0.16/0.44 thf(exu,definition,
% 0.16/0.44 ( exu
% 0.16/0.44 = ( ^ [Xphi: $i > $o] :
% 0.16/0.44 ? [Xx: $i] :
% 0.16/0.44 ( ( Xphi @ Xx )
% 0.16/0.44 & ! [Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xy )
% 0.16/0.44 => ( Xx = Xy ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setextAx_type,type,
% 0.16/0.44 setextAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setextAx,definition,
% 0.16/0.44 ( setextAx
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 <=> ( in @ Xx @ B ) )
% 0.16/0.44 => ( A = B ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyset_type,type,
% 0.16/0.44 emptyset: $i ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetAx_type,type,
% 0.16/0.44 emptysetAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetAx,definition,
% 0.16/0.44 ( emptysetAx
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoin_type,type,
% 0.16/0.44 setadjoin: $i > $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinAx_type,type,
% 0.16/0.44 setadjoinAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinAx,definition,
% 0.16/0.44 ( setadjoinAx
% 0.16/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.44 <=> ( ( Xy = Xx )
% 0.16/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powerset_type,type,
% 0.16/0.44 powerset: $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(powersetAx_type,type,
% 0.16/0.44 powersetAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetAx,definition,
% 0.16/0.44 ( powersetAx
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.44 <=> ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setunion_type,type,
% 0.16/0.44 setunion: $i > $i ).
% 0.16/0.44
% 0.16/0.44 thf(setunionAx_type,type,
% 0.16/0.44 setunionAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setunionAx,definition,
% 0.16/0.44 ( setunionAx
% 0.16/0.44 = ( ! [A: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.44 <=> ? [B: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 & ( in @ B @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(omega_type,type,
% 0.16/0.44 omega: $i ).
% 0.16/0.44
% 0.16/0.44 thf(omega0Ax_type,type,
% 0.16/0.44 omega0Ax: $o ).
% 0.16/0.44
% 0.16/0.44 thf(omega0Ax,definition,
% 0.16/0.44 ( omega0Ax
% 0.16/0.44 = ( in @ emptyset @ omega ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(omegaSAx_type,type,
% 0.16/0.44 omegaSAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(omegaSAx,definition,
% 0.16/0.44 ( omegaSAx
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ omega )
% 0.16/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(omegaIndAx_type,type,
% 0.16/0.44 omegaIndAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(omegaIndAx,definition,
% 0.16/0.44 ( omegaIndAx
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( ( in @ emptyset @ A )
% 0.16/0.44 & ! [Xx: $i] :
% 0.16/0.44 ( ( ( in @ Xx @ omega )
% 0.16/0.44 & ( in @ Xx @ A ) )
% 0.16/0.44 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.16/0.44 => ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ omega )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(replAx_type,type,
% 0.16/0.44 replAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(replAx,definition,
% 0.16/0.44 ( replAx
% 0.16/0.44 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( exu
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.16/0.44 => ? [B: $i] :
% 0.16/0.44 ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 <=> ? [Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ A )
% 0.16/0.44 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(foundationAx_type,type,
% 0.16/0.44 foundationAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(foundationAx,definition,
% 0.16/0.44 ( foundationAx
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.44 => ? [B: $i] :
% 0.16/0.44 ( ( in @ B @ A )
% 0.16/0.44 & ~ ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(wellorderingAx_type,type,
% 0.16/0.44 wellorderingAx: $o ).
% 0.16/0.44
% 0.16/0.44 thf(wellorderingAx,definition,
% 0.16/0.44 ( wellorderingAx
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ? [B: $i] :
% 0.16/0.44 ( ! [C: $i] :
% 0.16/0.44 ( ( in @ C @ B )
% 0.16/0.44 => ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ C )
% 0.16/0.44 => ( in @ Xx @ A ) ) )
% 0.16/0.44 & ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( ( in @ Xx @ A )
% 0.16/0.44 & ( in @ Xy @ A ) )
% 0.16/0.44 => ( ! [C: $i] :
% 0.16/0.44 ( ( in @ C @ B )
% 0.16/0.44 => ( ( in @ Xx @ C )
% 0.16/0.44 <=> ( in @ Xy @ C ) ) )
% 0.16/0.44 => ( Xx = Xy ) ) )
% 0.16/0.44 & ! [C: $i,D: $i] :
% 0.16/0.44 ( ( ( in @ C @ B )
% 0.16/0.44 & ( in @ D @ B ) )
% 0.16/0.44 => ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ C )
% 0.16/0.44 => ( in @ Xx @ D ) )
% 0.16/0.44 | ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ D )
% 0.16/0.44 => ( in @ Xx @ C ) ) ) )
% 0.16/0.44 & ! [C: $i] :
% 0.16/0.44 ( ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ C )
% 0.16/0.44 => ( in @ Xx @ A ) )
% 0.16/0.44 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.16/0.44 => ? [D: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ D @ B )
% 0.16/0.44 & ( in @ Xx @ C )
% 0.16/0.44 & ~ ? [Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ D )
% 0.16/0.44 & ( in @ Xy @ C ) )
% 0.16/0.44 & ! [E: $i] :
% 0.16/0.44 ( ( in @ E @ B )
% 0.16/0.44 => ( ! [Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ E )
% 0.16/0.44 => ( in @ Xy @ D ) )
% 0.16/0.44 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(descr_type,type,
% 0.16/0.44 descr: ( $i > $o ) > $i ).
% 0.16/0.44
% 0.16/0.44 thf(descrp_type,type,
% 0.16/0.44 descrp: $o ).
% 0.16/0.44
% 0.16/0.44 thf(descrp,definition,
% 0.16/0.44 ( descrp
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ( Xphi
% 0.16/0.44 @ ( descr
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstr_type,type,
% 0.16/0.44 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrI_type,type,
% 0.16/0.44 dsetconstrI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrI,definition,
% 0.16/0.44 ( dsetconstrI
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ( Xphi @ Xx )
% 0.16/0.44 => ( in @ Xx
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrEL_type,type,
% 0.16/0.44 dsetconstrEL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrEL,definition,
% 0.16/0.44 ( dsetconstrEL
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrER_type,type,
% 0.16/0.44 dsetconstrER: $o ).
% 0.16/0.44
% 0.16/0.44 thf(dsetconstrER,definition,
% 0.16/0.44 ( dsetconstrER
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuE1_type,type,
% 0.16/0.44 exuE1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuE1,definition,
% 0.16/0.44 ( exuE1
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ( ( Xphi @ Xx )
% 0.16/0.44 & ! [Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xy )
% 0.16/0.44 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(prop2set_type,type,
% 0.16/0.44 prop2set: $o > $i ).
% 0.16/0.44
% 0.16/0.44 thf(prop2set,definition,
% 0.16/0.44 ( prop2set
% 0.16/0.44 = ( ^ [Xphi: $o] :
% 0.16/0.44 ( dsetconstr @ ( powerset @ emptyset )
% 0.16/0.44 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(prop2setE_type,type,
% 0.16/0.44 prop2setE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(prop2setE,definition,
% 0.16/0.44 ( prop2setE
% 0.16/0.44 = ( ! [Xphi: $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.16/0.44 => Xphi ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetE_type,type,
% 0.16/0.44 emptysetE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetE,definition,
% 0.16/0.44 ( emptysetE
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ emptyset )
% 0.16/0.44 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetimpfalse_type,type,
% 0.16/0.44 emptysetimpfalse: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptysetimpfalse,definition,
% 0.16/0.44 ( emptysetimpfalse
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ emptyset )
% 0.16/0.44 => $false ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notinemptyset_type,type,
% 0.16/0.44 notinemptyset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notinemptyset,definition,
% 0.16/0.44 ( notinemptyset
% 0.16/0.44 = ( ! [Xx: $i] :
% 0.16/0.44 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuE3e_type,type,
% 0.16/0.44 exuE3e: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuE3e,definition,
% 0.16/0.44 ( exuE3e
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setext_type,type,
% 0.16/0.44 setext: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setext,definition,
% 0.16/0.44 ( setext
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ B ) )
% 0.16/0.44 => ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ A ) )
% 0.16/0.44 => ( A = B ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyI_type,type,
% 0.16/0.44 emptyI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyI,definition,
% 0.16/0.44 ( emptyI
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ~ ( in @ Xx @ A )
% 0.16/0.44 => ( A = emptyset ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(noeltsimpempty_type,type,
% 0.16/0.44 noeltsimpempty: $o ).
% 0.16/0.44
% 0.16/0.44 thf(noeltsimpempty,definition,
% 0.16/0.44 ( noeltsimpempty
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ~ ( in @ Xx @ A )
% 0.16/0.44 => ( A = emptyset ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setbeta_type,type,
% 0.16/0.44 setbeta: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setbeta,definition,
% 0.16/0.44 ( setbeta
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ( in @ Xx
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.16/0.44 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonempty_type,type,
% 0.16/0.44 nonempty: $i > $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonempty,definition,
% 0.16/0.44 ( nonempty
% 0.16/0.44 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyE1_type,type,
% 0.16/0.44 nonemptyE1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyE1,definition,
% 0.16/0.44 ( nonemptyE1
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( nonempty @ A )
% 0.16/0.44 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyI_type,type,
% 0.16/0.44 nonemptyI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyI,definition,
% 0.16/0.44 ( nonemptyI
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( ( Xphi @ Xx )
% 0.16/0.44 => ( nonempty
% 0.16/0.44 @ ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyI1_type,type,
% 0.16/0.44 nonemptyI1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyI1,definition,
% 0.16/0.44 ( nonemptyI1
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.16/0.44 => ( nonempty @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinIL_type,type,
% 0.16/0.44 setadjoinIL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinIL,definition,
% 0.16/0.44 ( setadjoinIL
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyinunitempty_type,type,
% 0.16/0.44 emptyinunitempty: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyinunitempty,definition,
% 0.16/0.44 ( emptyinunitempty
% 0.16/0.44 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinIR_type,type,
% 0.16/0.44 setadjoinIR: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinIR,definition,
% 0.16/0.44 ( setadjoinIR
% 0.16/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ A )
% 0.16/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinE_type,type,
% 0.16/0.44 setadjoinE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinE,definition,
% 0.16/0.44 ( setadjoinE
% 0.16/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.44 => ! [Xphi: $o] :
% 0.16/0.44 ( ( ( Xy = Xx )
% 0.16/0.44 => Xphi )
% 0.16/0.44 => ( ( ( in @ Xy @ A )
% 0.16/0.44 => Xphi )
% 0.16/0.44 => Xphi ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinOr_type,type,
% 0.16/0.44 setadjoinOr: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setadjoinOr,definition,
% 0.16/0.44 ( setadjoinOr
% 0.16/0.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.16/0.44 => ( ( Xy = Xx )
% 0.16/0.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setoftrueEq_type,type,
% 0.16/0.44 setoftrueEq: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setoftrueEq,definition,
% 0.16/0.44 ( setoftrueEq
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xx: $i] : $true )
% 0.16/0.44 = A ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powersetI_type,type,
% 0.16/0.44 powersetI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetI,definition,
% 0.16/0.44 ( powersetI
% 0.16/0.44 = ( ! [A: $i,B: $i] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ A ) )
% 0.16/0.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyinPowerset_type,type,
% 0.16/0.44 emptyinPowerset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyinPowerset,definition,
% 0.16/0.44 ( emptyinPowerset
% 0.16/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyInPowerset_type,type,
% 0.16/0.44 emptyInPowerset: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyInPowerset,definition,
% 0.16/0.44 ( emptyInPowerset
% 0.16/0.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(powersetE_type,type,
% 0.16/0.44 powersetE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(powersetE,definition,
% 0.16/0.44 ( powersetE
% 0.16/0.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ B @ ( powerset @ A ) )
% 0.16/0.44 => ( ( in @ Xx @ B )
% 0.16/0.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setunionI_type,type,
% 0.16/0.44 setunionI: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setunionI,definition,
% 0.16/0.44 ( setunionI
% 0.16/0.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( ( in @ B @ A )
% 0.16/0.44 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(setunionE_type,type,
% 0.16/0.44 setunionE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(setunionE,definition,
% 0.16/0.44 ( setunionE
% 0.16/0.44 = ( ! [A: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setunion @ A ) )
% 0.16/0.44 => ! [Xphi: $o] :
% 0.16/0.44 ( ! [B: $i] :
% 0.16/0.44 ( ( in @ Xx @ B )
% 0.16/0.44 => ( ( in @ B @ A )
% 0.16/0.44 => Xphi ) )
% 0.16/0.44 => Xphi ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(subPowSU_type,type,
% 0.16/0.44 subPowSU: $o ).
% 0.16/0.44
% 0.16/0.44 thf(subPowSU,definition,
% 0.16/0.44 ( subPowSU
% 0.16/0.44 = ( ! [A: $i,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(exuE2_type,type,
% 0.16/0.44 exuE2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(exuE2,definition,
% 0.16/0.44 ( exuE2
% 0.16/0.44 = ( ! [Xphi: $i > $o] :
% 0.16/0.44 ( ( exu
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ! [Xy: $i] :
% 0.16/0.44 ( ( Xphi @ Xy )
% 0.16/0.44 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyImpWitness_type,type,
% 0.16/0.44 nonemptyImpWitness: $o ).
% 0.16/0.44
% 0.16/0.44 thf(nonemptyImpWitness,definition,
% 0.16/0.44 ( nonemptyImpWitness
% 0.16/0.44 = ( ! [A: $i] :
% 0.16/0.44 ( ( nonempty @ A )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & $true ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(uniqinunit_type,type,
% 0.16/0.44 uniqinunit: $o ).
% 0.16/0.44
% 0.16/0.44 thf(uniqinunit,definition,
% 0.16/0.44 ( uniqinunit
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.44 => ( Xx = Xy ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(notinsingleton_type,type,
% 0.16/0.44 notinsingleton: $o ).
% 0.16/0.44
% 0.16/0.44 thf(notinsingleton,definition,
% 0.16/0.44 ( notinsingleton
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx != Xy )
% 0.16/0.44 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(eqinunit_type,type,
% 0.16/0.44 eqinunit: $o ).
% 0.16/0.44
% 0.16/0.44 thf(eqinunit,definition,
% 0.16/0.44 ( eqinunit
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( Xx = Xy )
% 0.16/0.44 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(singletonsswitch_type,type,
% 0.16/0.44 singletonsswitch: $o ).
% 0.16/0.44
% 0.16/0.44 thf(singletonsswitch,definition,
% 0.16/0.44 ( singletonsswitch
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] :
% 0.16/0.44 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.16/0.44 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetE_type,type,
% 0.16/0.44 upairsetE: $o ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetE,definition,
% 0.16/0.44 ( upairsetE
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 0.16/0.44 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 0.16/0.44 => ( ( Xz = Xx )
% 0.16/0.44 | ( Xz = Xy ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetIL_type,type,
% 0.16/0.44 upairsetIL: $o ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetIL,definition,
% 0.16/0.44 ( upairsetIL
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetIR_type,type,
% 0.16/0.44 upairsetIR: $o ).
% 0.16/0.44
% 0.16/0.44 thf(upairsetIR,definition,
% 0.16/0.44 ( upairsetIR
% 0.16/0.44 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(emptyE1_type,type,
% 0.16/0.44 emptyE1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(emptyE1,definition,
% 0.16/0.44 ( emptyE1
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ( Xphi @ Xx ) )
% 0.16/0.44 => ( ( ( dsetconstr @ A
% 0.16/0.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.16/0.44 = emptyset )
% 0.16/0.44 => $false ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(vacuousDall_type,type,
% 0.16/0.44 vacuousDall: $o ).
% 0.16/0.44
% 0.16/0.44 thf(vacuousDall,definition,
% 0.16/0.44 ( vacuousDall
% 0.16/0.44 = ( ! [Xphi: $i > $o,Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ emptyset )
% 0.16/0.44 => ( Xphi @ Xx ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan1_type,type,
% 0.16/0.44 quantDeMorgan1: $o ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan1,definition,
% 0.16/0.44 ( quantDeMorgan1
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ~ ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( Xphi @ Xx ) )
% 0.16/0.44 => ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan2_type,type,
% 0.16/0.44 quantDeMorgan2: $o ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan2,definition,
% 0.16/0.44 ( quantDeMorgan2
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ~ ( Xphi @ Xx ) )
% 0.16/0.44 => ~ ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan3_type,type,
% 0.16/0.44 quantDeMorgan3: $o ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan3,definition,
% 0.16/0.44 ( quantDeMorgan3
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ~ ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ( Xphi @ Xx ) )
% 0.16/0.44 => ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan4_type,type,
% 0.16/0.44 quantDeMorgan4: $o ).
% 0.16/0.44
% 0.16/0.44 thf(quantDeMorgan4,definition,
% 0.16/0.44 ( quantDeMorgan4
% 0.16/0.44 = ( ! [A: $i,Xphi: $i > $o] :
% 0.16/0.44 ( ? [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 & ~ ( Xphi @ Xx ) )
% 0.16/0.44 => ~ ! [Xx: $i] :
% 0.16/0.44 ( ( in @ Xx @ A )
% 0.16/0.44 => ( Xphi @ Xx ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 thf(prop2setI,conjecture,
% 0.16/0.44 ( setextAx
% 0.16/0.44 => ( emptysetAx
% 0.16/0.44 => ( setadjoinAx
% 0.16/0.44 => ( powersetAx
% 0.16/0.44 => ( setunionAx
% 0.16/0.44 => ( omega0Ax
% 0.16/0.44 => ( omegaSAx
% 0.16/0.44 => ( omegaIndAx
% 0.16/0.44 => ( replAx
% 0.16/0.44 => ( foundationAx
% 0.16/0.44 => ( wellorderingAx
% 0.16/0.44 => ( descrp
% 0.16/0.44 => ( dsetconstrI
% 0.16/0.44 => ( dsetconstrEL
% 0.16/0.44 => ( dsetconstrER
% 0.16/0.44 => ( exuE1
% 0.16/0.44 => ( prop2setE
% 0.16/0.44 => ( emptysetE
% 0.16/0.44 => ( emptysetimpfalse
% 0.16/0.44 => ( notinemptyset
% 0.16/0.44 => ( exuE3e
% 0.16/0.44 => ( setext
% 0.16/0.44 => ( emptyI
% 0.16/0.44 => ( noeltsimpempty
% 0.16/0.44 => ( setbeta
% 0.16/0.44 => ( nonemptyE1
% 0.16/0.44 => ( nonemptyI
% 0.16/0.44 => ( nonemptyI1
% 0.16/0.44 => ( setadjoinIL
% 0.16/0.44 => ( emptyinunitempty
% 0.16/0.44 => ( setadjoinIR
% 0.16/0.44 => ( setadjoinE
% 0.16/0.44 => ( setadjoinOr
% 0.16/0.44 => ( setoftrueEq
% 0.16/0.44 => ( powersetI
% 0.16/0.44 => ( emptyinPowerset
% 0.16/0.44 => ( emptyInPowerset
% 0.16/0.44 => ( powersetE
% 0.16/0.44 => ( setunionI
% 0.16/0.44 => ( setunionE
% 0.16/0.44 => ( subPowSU
% 0.16/0.44 => ( exuE2
% 0.16/0.44 => ( nonemptyImpWitness
% 0.16/0.44 => ( uniqinunit
% 0.16/0.44 => ( notinsingleton
% 0.16/0.44 => ( eqinunit
% 0.16/0.44 => ( singletonsswitch
% 0.16/0.44 => ( upairsetE
% 0.16/0.44 => ( upairsetIL
% 0.16/0.44 => ( upairsetIR
% 0.16/0.44 => ( emptyE1
% 0.16/0.44 => ( vacuousDall
% 0.16/0.44 => ( quantDeMorgan1
% 0.16/0.44 => ( quantDeMorgan2
% 0.16/0.44 => ( quantDeMorgan3
% 0.16/0.44 => ( quantDeMorgan4
% 0.16/0.44 => ! [Xphi: $o] :
% 0.16/0.44 ( Xphi
% 0.16/0.44 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 2.04/1.56 ---- Embedded in THF ---
% 2.04/1.56 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.04/1.56 %%% Generated on Tue Feb 24 12:26:10 EST 2026
% 2.04/1.56 %%% using '$$dhol' embedding, version 1.3.0.
% 2.04/1.56 %%% Logic specification used:
% 2.04/1.56 %%% thf(spec, logic, $$dhol).
% 2.04/1.56
% 2.04/1.56 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2DTF32072.p
% See solution above
% 2.04/1.56 ------------------------
% 2.04/1.57 ---- Cleaned THF ---
% 2.04/1.57 thf(in_type,type,
% 2.04/1.57 in: $i > $i > $o ).
% 2.04/1.57
% 2.04/1.57 thf(exu_type,type,
% 2.04/1.57 exu: ( $i > $o ) > $o ).
% 2.04/1.57
% 2.04/1.57 thf(exu,definition,
% 2.04/1.57 ( exu
% 2.04/1.57 = ( ^ [Xphi: $i > $o] :
% 2.04/1.57 ? [Xx: $i] :
% 2.04/1.57 ( ( Xphi @ Xx )
% 2.04/1.57 & ! [Xy: $i] :
% 2.04/1.57 ( ( Xphi @ Xy )
% 2.04/1.57 => ( Xx = Xy ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setextAx_type,type,
% 2.04/1.57 setextAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setextAx,definition,
% 2.04/1.57 ( setextAx
% 2.04/1.57 = ( ! [A: $i,B: $i] :
% 2.04/1.57 ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ A )
% 2.04/1.57 <=> ( in @ Xx @ B ) )
% 2.04/1.57 => ( A = B ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(emptyset_type,type,
% 2.04/1.57 emptyset: $i ).
% 2.04/1.57
% 2.04/1.57 thf(emptysetAx_type,type,
% 2.04/1.57 emptysetAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(emptysetAx,definition,
% 2.04/1.57 ( emptysetAx
% 2.04/1.57 = ( ! [Xx: $i] :
% 2.04/1.57 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoin_type,type,
% 2.04/1.57 setadjoin: $i > $i > $i ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinAx_type,type,
% 2.04/1.57 setadjoinAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinAx,definition,
% 2.04/1.57 ( setadjoinAx
% 2.04/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.04/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.04/1.57 <=> ( ( Xy = Xx )
% 2.04/1.57 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(powerset_type,type,
% 2.04/1.57 powerset: $i > $i ).
% 2.04/1.57
% 2.04/1.57 thf(powersetAx_type,type,
% 2.04/1.57 powersetAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(powersetAx,definition,
% 2.04/1.57 ( powersetAx
% 2.04/1.57 = ( ! [A: $i,B: $i] :
% 2.04/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.04/1.57 <=> ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ B )
% 2.04/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setunion_type,type,
% 2.04/1.57 setunion: $i > $i ).
% 2.04/1.57
% 2.04/1.57 thf(setunionAx_type,type,
% 2.04/1.57 setunionAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setunionAx,definition,
% 2.04/1.57 ( setunionAx
% 2.04/1.57 = ( ! [A: $i,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.04/1.57 <=> ? [B: $i] :
% 2.04/1.57 ( ( in @ Xx @ B )
% 2.04/1.57 & ( in @ B @ A ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(omega_type,type,
% 2.04/1.57 omega: $i ).
% 2.04/1.57
% 2.04/1.57 thf(omega0Ax_type,type,
% 2.04/1.57 omega0Ax: $o ).
% 2.04/1.57
% 2.04/1.57 thf(omega0Ax,definition,
% 2.04/1.57 ( omega0Ax
% 2.04/1.57 = ( in @ emptyset @ omega ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(omegaSAx_type,type,
% 2.04/1.57 omegaSAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(omegaSAx,definition,
% 2.04/1.57 ( omegaSAx
% 2.04/1.57 = ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ omega )
% 2.04/1.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(omegaIndAx_type,type,
% 2.04/1.57 omegaIndAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(omegaIndAx,definition,
% 2.04/1.57 ( omegaIndAx
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ( ( ( in @ emptyset @ A )
% 2.04/1.57 & ! [Xx: $i] :
% 2.04/1.57 ( ( ( in @ Xx @ omega )
% 2.04/1.57 & ( in @ Xx @ A ) )
% 2.04/1.57 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.04/1.57 => ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ omega )
% 2.04/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(replAx_type,type,
% 2.04/1.57 replAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(replAx,definition,
% 2.04/1.57 ( replAx
% 2.04/1.57 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.04/1.57 ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ A )
% 2.04/1.57 => ( exu
% 2.04/1.57 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.04/1.57 => ? [B: $i] :
% 2.04/1.57 ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ B )
% 2.04/1.57 <=> ? [Xy: $i] :
% 2.04/1.57 ( ( in @ Xy @ A )
% 2.04/1.57 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(foundationAx_type,type,
% 2.04/1.57 foundationAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(foundationAx,definition,
% 2.04/1.57 ( foundationAx
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.04/1.57 => ? [B: $i] :
% 2.04/1.57 ( ( in @ B @ A )
% 2.04/1.57 & ~ ? [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ B )
% 2.04/1.57 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(wellorderingAx_type,type,
% 2.04/1.57 wellorderingAx: $o ).
% 2.04/1.57
% 2.04/1.57 thf(wellorderingAx,definition,
% 2.04/1.57 ( wellorderingAx
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ? [B: $i] :
% 2.04/1.57 ( ! [C: $i] :
% 2.04/1.57 ( ( in @ C @ B )
% 2.04/1.57 => ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ C )
% 2.04/1.57 => ( in @ Xx @ A ) ) )
% 2.04/1.57 & ! [Xx: $i,Xy: $i] :
% 2.04/1.57 ( ( ( in @ Xx @ A )
% 2.04/1.57 & ( in @ Xy @ A ) )
% 2.04/1.57 => ( ! [C: $i] :
% 2.04/1.57 ( ( in @ C @ B )
% 2.04/1.57 => ( ( in @ Xx @ C )
% 2.04/1.57 <=> ( in @ Xy @ C ) ) )
% 2.04/1.57 => ( Xx = Xy ) ) )
% 2.04/1.57 & ! [C: $i,D: $i] :
% 2.04/1.57 ( ( ( in @ C @ B )
% 2.04/1.57 & ( in @ D @ B ) )
% 2.04/1.57 => ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ C )
% 2.04/1.57 => ( in @ Xx @ D ) )
% 2.04/1.57 | ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ D )
% 2.04/1.57 => ( in @ Xx @ C ) ) ) )
% 2.04/1.57 & ! [C: $i] :
% 2.04/1.57 ( ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ C )
% 2.04/1.57 => ( in @ Xx @ A ) )
% 2.04/1.57 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.04/1.57 => ? [D: $i,Xx: $i] :
% 2.04/1.57 ( ( in @ D @ B )
% 2.04/1.57 & ( in @ Xx @ C )
% 2.04/1.57 & ~ ? [Xy: $i] :
% 2.04/1.57 ( ( in @ Xy @ D )
% 2.04/1.57 & ( in @ Xy @ C ) )
% 2.04/1.57 & ! [E: $i] :
% 2.04/1.57 ( ( in @ E @ B )
% 2.04/1.57 => ( ! [Xy: $i] :
% 2.04/1.57 ( ( in @ Xy @ E )
% 2.04/1.57 => ( in @ Xy @ D ) )
% 2.04/1.57 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(descr_type,type,
% 2.04/1.57 descr: ( $i > $o ) > $i ).
% 2.04/1.57
% 2.04/1.57 thf(descrp_type,type,
% 2.04/1.57 descrp: $o ).
% 2.04/1.57
% 2.04/1.57 thf(descrp,definition,
% 2.04/1.57 ( descrp
% 2.04/1.57 = ( ! [Xphi: $i > $o] :
% 2.04/1.57 ( ( exu
% 2.04/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.04/1.57 => ( Xphi
% 2.04/1.57 @ ( descr
% 2.04/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(dsetconstr_type,type,
% 2.04/1.57 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.04/1.57
% 2.04/1.57 thf(dsetconstrI_type,type,
% 2.04/1.57 dsetconstrI: $o ).
% 2.04/1.57
% 2.04/1.57 thf(dsetconstrI,definition,
% 2.04/1.57 ( dsetconstrI
% 2.04/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ A )
% 2.04/1.57 => ( ( Xphi @ Xx )
% 2.04/1.57 => ( in @ Xx
% 2.04/1.57 @ ( dsetconstr @ A
% 2.04/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(dsetconstrEL_type,type,
% 2.04/1.57 dsetconstrEL: $o ).
% 2.04/1.57
% 2.04/1.57 thf(dsetconstrEL,definition,
% 2.04/1.57 ( dsetconstrEL
% 2.04/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx
% 2.04/1.57 @ ( dsetconstr @ A
% 2.04/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.04/1.57 => ( in @ Xx @ A ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(dsetconstrER_type,type,
% 2.04/1.57 dsetconstrER: $o ).
% 2.04/1.57
% 2.04/1.57 thf(dsetconstrER,definition,
% 2.04/1.57 ( dsetconstrER
% 2.04/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx
% 2.04/1.57 @ ( dsetconstr @ A
% 2.04/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.04/1.57 => ( Xphi @ Xx ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(exuE1_type,type,
% 2.04/1.57 exuE1: $o ).
% 2.04/1.57
% 2.04/1.57 thf(exuE1,definition,
% 2.04/1.57 ( exuE1
% 2.04/1.57 = ( ! [Xphi: $i > $o] :
% 2.04/1.57 ( ( exu
% 2.04/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.04/1.57 => ? [Xx: $i] :
% 2.04/1.57 ( ( Xphi @ Xx )
% 2.04/1.57 & ! [Xy: $i] :
% 2.04/1.57 ( ( Xphi @ Xy )
% 2.04/1.57 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(prop2set_type,type,
% 2.04/1.57 prop2set: $o > $i ).
% 2.04/1.57
% 2.04/1.57 thf(prop2set,definition,
% 2.04/1.57 ( prop2set
% 2.04/1.57 = ( ^ [Xphi: $o] :
% 2.04/1.57 ( dsetconstr @ ( powerset @ emptyset )
% 2.04/1.57 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(prop2setE_type,type,
% 2.04/1.57 prop2setE: $o ).
% 2.04/1.57
% 2.04/1.57 thf(prop2setE,definition,
% 2.04/1.57 ( prop2setE
% 2.04/1.57 = ( ! [Xphi: $o,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.04/1.57 => Xphi ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(emptysetE_type,type,
% 2.04/1.57 emptysetE: $o ).
% 2.04/1.57
% 2.04/1.57 thf(emptysetE,definition,
% 2.04/1.57 ( emptysetE
% 2.04/1.57 = ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ emptyset )
% 2.04/1.57 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(emptysetimpfalse_type,type,
% 2.04/1.57 emptysetimpfalse: $o ).
% 2.04/1.57
% 2.04/1.57 thf(emptysetimpfalse,definition,
% 2.04/1.57 ( emptysetimpfalse
% 2.04/1.57 = ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ emptyset )
% 2.04/1.57 => $false ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(notinemptyset_type,type,
% 2.04/1.57 notinemptyset: $o ).
% 2.04/1.57
% 2.04/1.57 thf(notinemptyset,definition,
% 2.04/1.57 ( notinemptyset
% 2.04/1.57 = ( ! [Xx: $i] :
% 2.04/1.57 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(exuE3e_type,type,
% 2.04/1.57 exuE3e: $o ).
% 2.04/1.57
% 2.04/1.57 thf(exuE3e,definition,
% 2.04/1.57 ( exuE3e
% 2.04/1.57 = ( ! [Xphi: $i > $o] :
% 2.04/1.57 ( ( exu
% 2.04/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.04/1.57 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setext_type,type,
% 2.04/1.57 setext: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setext,definition,
% 2.04/1.57 ( setext
% 2.04/1.57 = ( ! [A: $i,B: $i] :
% 2.04/1.57 ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ A )
% 2.04/1.57 => ( in @ Xx @ B ) )
% 2.04/1.57 => ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ B )
% 2.04/1.57 => ( in @ Xx @ A ) )
% 2.04/1.57 => ( A = B ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(emptyI_type,type,
% 2.04/1.57 emptyI: $o ).
% 2.04/1.57
% 2.04/1.57 thf(emptyI,definition,
% 2.04/1.57 ( emptyI
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ( ! [Xx: $i] :
% 2.04/1.57 ~ ( in @ Xx @ A )
% 2.04/1.57 => ( A = emptyset ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(noeltsimpempty_type,type,
% 2.04/1.57 noeltsimpempty: $o ).
% 2.04/1.57
% 2.04/1.57 thf(noeltsimpempty,definition,
% 2.04/1.57 ( noeltsimpempty
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ( ! [Xx: $i] :
% 2.04/1.57 ~ ( in @ Xx @ A )
% 2.04/1.57 => ( A = emptyset ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setbeta_type,type,
% 2.04/1.57 setbeta: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setbeta,definition,
% 2.04/1.57 ( setbeta
% 2.04/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ A )
% 2.04/1.57 => ( ( in @ Xx
% 2.04/1.57 @ ( dsetconstr @ A
% 2.04/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.04/1.57 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(nonempty_type,type,
% 2.04/1.57 nonempty: $i > $o ).
% 2.04/1.57
% 2.04/1.57 thf(nonempty,definition,
% 2.04/1.57 ( nonempty
% 2.04/1.57 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(nonemptyE1_type,type,
% 2.04/1.57 nonemptyE1: $o ).
% 2.04/1.57
% 2.04/1.57 thf(nonemptyE1,definition,
% 2.04/1.57 ( nonemptyE1
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ( ( nonempty @ A )
% 2.04/1.57 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(nonemptyI_type,type,
% 2.04/1.57 nonemptyI: $o ).
% 2.04/1.57
% 2.04/1.57 thf(nonemptyI,definition,
% 2.04/1.57 ( nonemptyI
% 2.04/1.57 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ A )
% 2.04/1.57 => ( ( Xphi @ Xx )
% 2.04/1.57 => ( nonempty
% 2.04/1.57 @ ( dsetconstr @ A
% 2.04/1.57 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(nonemptyI1_type,type,
% 2.04/1.57 nonemptyI1: $o ).
% 2.04/1.57
% 2.04/1.57 thf(nonemptyI1,definition,
% 2.04/1.57 ( nonemptyI1
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.04/1.57 => ( nonempty @ A ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinIL_type,type,
% 2.04/1.57 setadjoinIL: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinIL,definition,
% 2.04/1.57 ( setadjoinIL
% 2.04/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(emptyinunitempty_type,type,
% 2.04/1.57 emptyinunitempty: $o ).
% 2.04/1.57
% 2.04/1.57 thf(emptyinunitempty,definition,
% 2.04/1.57 ( emptyinunitempty
% 2.04/1.57 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinIR_type,type,
% 2.04/1.57 setadjoinIR: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinIR,definition,
% 2.04/1.57 ( setadjoinIR
% 2.04/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.04/1.57 ( ( in @ Xy @ A )
% 2.04/1.57 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinE_type,type,
% 2.04/1.57 setadjoinE: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinE,definition,
% 2.04/1.57 ( setadjoinE
% 2.04/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.04/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.04/1.57 => ! [Xphi: $o] :
% 2.04/1.57 ( ( ( Xy = Xx )
% 2.04/1.57 => Xphi )
% 2.04/1.57 => ( ( ( in @ Xy @ A )
% 2.04/1.57 => Xphi )
% 2.04/1.57 => Xphi ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinOr_type,type,
% 2.04/1.57 setadjoinOr: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setadjoinOr,definition,
% 2.04/1.57 ( setadjoinOr
% 2.04/1.57 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.04/1.57 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.04/1.57 => ( ( Xy = Xx )
% 2.04/1.57 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setoftrueEq_type,type,
% 2.04/1.57 setoftrueEq: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setoftrueEq,definition,
% 2.04/1.57 ( setoftrueEq
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ( ( dsetconstr @ A
% 2.04/1.57 @ ^ [Xx: $i] : $true )
% 2.04/1.57 = A ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(powersetI_type,type,
% 2.04/1.57 powersetI: $o ).
% 2.04/1.57
% 2.04/1.57 thf(powersetI,definition,
% 2.04/1.57 ( powersetI
% 2.04/1.57 = ( ! [A: $i,B: $i] :
% 2.04/1.57 ( ! [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ B )
% 2.04/1.57 => ( in @ Xx @ A ) )
% 2.04/1.57 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(emptyinPowerset_type,type,
% 2.04/1.57 emptyinPowerset: $o ).
% 2.04/1.57
% 2.04/1.57 thf(emptyinPowerset,definition,
% 2.04/1.57 ( emptyinPowerset
% 2.04/1.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(emptyInPowerset_type,type,
% 2.04/1.57 emptyInPowerset: $o ).
% 2.04/1.57
% 2.04/1.57 thf(emptyInPowerset,definition,
% 2.04/1.57 ( emptyInPowerset
% 2.04/1.57 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(powersetE_type,type,
% 2.04/1.57 powersetE: $o ).
% 2.04/1.57
% 2.04/1.57 thf(powersetE,definition,
% 2.04/1.57 ( powersetE
% 2.04/1.57 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.04/1.57 ( ( in @ B @ ( powerset @ A ) )
% 2.04/1.57 => ( ( in @ Xx @ B )
% 2.04/1.57 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setunionI_type,type,
% 2.04/1.57 setunionI: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setunionI,definition,
% 2.04/1.57 ( setunionI
% 2.04/1.57 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.04/1.57 ( ( in @ Xx @ B )
% 2.04/1.57 => ( ( in @ B @ A )
% 2.04/1.57 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(setunionE_type,type,
% 2.04/1.57 setunionE: $o ).
% 2.04/1.57
% 2.04/1.57 thf(setunionE,definition,
% 2.04/1.57 ( setunionE
% 2.04/1.57 = ( ! [A: $i,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ ( setunion @ A ) )
% 2.04/1.57 => ! [Xphi: $o] :
% 2.04/1.57 ( ! [B: $i] :
% 2.04/1.57 ( ( in @ Xx @ B )
% 2.04/1.57 => ( ( in @ B @ A )
% 2.04/1.57 => Xphi ) )
% 2.04/1.57 => Xphi ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(subPowSU_type,type,
% 2.04/1.57 subPowSU: $o ).
% 2.04/1.57
% 2.04/1.57 thf(subPowSU,definition,
% 2.04/1.57 ( subPowSU
% 2.04/1.57 = ( ! [A: $i,Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ A )
% 2.04/1.57 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(exuE2_type,type,
% 2.04/1.57 exuE2: $o ).
% 2.04/1.57
% 2.04/1.57 thf(exuE2,definition,
% 2.04/1.57 ( exuE2
% 2.04/1.57 = ( ! [Xphi: $i > $o] :
% 2.04/1.57 ( ( exu
% 2.04/1.57 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.04/1.57 => ? [Xx: $i] :
% 2.04/1.57 ! [Xy: $i] :
% 2.04/1.57 ( ( Xphi @ Xy )
% 2.04/1.57 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(nonemptyImpWitness_type,type,
% 2.04/1.57 nonemptyImpWitness: $o ).
% 2.04/1.57
% 2.04/1.57 thf(nonemptyImpWitness,definition,
% 2.04/1.57 ( nonemptyImpWitness
% 2.04/1.57 = ( ! [A: $i] :
% 2.04/1.57 ( ( nonempty @ A )
% 2.04/1.57 => ? [Xx: $i] :
% 2.04/1.57 ( ( in @ Xx @ A )
% 2.04/1.57 & $true ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(uniqinunit_type,type,
% 2.04/1.57 uniqinunit: $o ).
% 2.04/1.57
% 2.04/1.57 thf(uniqinunit,definition,
% 2.04/1.57 ( uniqinunit
% 2.04/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.04/1.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.04/1.57 => ( Xx = Xy ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(notinsingleton_type,type,
% 2.04/1.57 notinsingleton: $o ).
% 2.04/1.57
% 2.04/1.57 thf(notinsingleton,definition,
% 2.04/1.57 ( notinsingleton
% 2.04/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.04/1.57 ( ( Xx != Xy )
% 2.04/1.57 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(eqinunit_type,type,
% 2.04/1.57 eqinunit: $o ).
% 2.04/1.57
% 2.04/1.57 thf(eqinunit,definition,
% 2.04/1.57 ( eqinunit
% 2.04/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.04/1.57 ( ( Xx = Xy )
% 2.04/1.57 => ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(singletonsswitch_type,type,
% 2.04/1.57 singletonsswitch: $o ).
% 2.04/1.57
% 2.04/1.57 thf(singletonsswitch,definition,
% 2.04/1.57 ( singletonsswitch
% 2.04/1.57 = ( ! [Xx: $i,Xy: $i] :
% 2.04/1.57 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.04/1.57 => ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(upairsetE_type,type,
% 2.04/1.57 upairsetE: $o ).
% 2.04/1.57
% 2.04/1.57 thf(upairsetE,definition,
% 2.04/1.57 ( upairsetE
% 2.04/1.57 = ( ! [Xx: $i,Xy: $i,Xz: $i] :
% 2.04/1.57 ( ( in @ Xz @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) )
% 2.04/1.57 => ( ( Xz = Xx )
% 2.04/1.57 | ( Xz = Xy ) ) ) ) ) ).
% 2.04/1.57
% 2.04/1.57 thf(upairsetIL_type,type,
% 2.04/1.57 upairsetIL: $o ).
% 2.04/1.57
% 2.04/1.57 thf(upairsetIL,definition,
% 2.04/1.57 ( upairsetIL
% 2.04/1.57 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.04/1.58
% 2.04/1.58 thf(upairsetIR_type,type,
% 2.04/1.58 upairsetIR: $o ).
% 2.04/1.58
% 2.04/1.58 thf(upairsetIR,definition,
% 2.04/1.58 ( upairsetIR
% 2.04/1.58 = ( ! [Xx: $i,Xy: $i] : ( in @ Xy @ ( setadjoin @ Xx @ ( setadjoin @ Xy @ emptyset ) ) ) ) ) ).
% 2.04/1.58
% 2.04/1.58 thf(emptyE1_type,type,
% 2.04/1.58 emptyE1: $o ).
% 2.04/1.58
% 2.04/1.58 thf(emptyE1,definition,
% 2.04/1.58 ( emptyE1
% 2.04/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.04/1.58 ( ? [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 & ( Xphi @ Xx ) )
% 2.04/1.58 => ( ( ( dsetconstr @ A
% 2.04/1.58 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.04/1.58 = emptyset )
% 2.04/1.58 => $false ) ) ) ) ).
% 2.04/1.58
% 2.04/1.58 thf(vacuousDall_type,type,
% 2.04/1.58 vacuousDall: $o ).
% 2.04/1.58
% 2.04/1.58 thf(vacuousDall,definition,
% 2.04/1.58 ( vacuousDall
% 2.04/1.58 = ( ! [Xphi: $i > $o,Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ emptyset )
% 2.04/1.58 => ( Xphi @ Xx ) ) ) ) ).
% 2.04/1.58
% 2.04/1.58 thf(quantDeMorgan1_type,type,
% 2.04/1.58 quantDeMorgan1: $o ).
% 2.04/1.58
% 2.04/1.58 thf(quantDeMorgan1,definition,
% 2.04/1.58 ( quantDeMorgan1
% 2.04/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.04/1.58 ( ~ ! [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 => ( Xphi @ Xx ) )
% 2.04/1.58 => ? [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 & ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.04/1.58
% 2.04/1.58 thf(quantDeMorgan2_type,type,
% 2.04/1.58 quantDeMorgan2: $o ).
% 2.04/1.58
% 2.04/1.58 thf(quantDeMorgan2,definition,
% 2.04/1.58 ( quantDeMorgan2
% 2.04/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.04/1.58 ( ! [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 => ~ ( Xphi @ Xx ) )
% 2.04/1.58 => ~ ? [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 & ( Xphi @ Xx ) ) ) ) ) ).
% 2.04/1.58
% 2.04/1.58 thf(quantDeMorgan3_type,type,
% 2.04/1.58 quantDeMorgan3: $o ).
% 2.04/1.58
% 2.04/1.58 thf(quantDeMorgan3,definition,
% 2.04/1.58 ( quantDeMorgan3
% 2.04/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.04/1.58 ( ~ ? [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 & ( Xphi @ Xx ) )
% 2.04/1.58 => ! [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 => ~ ( Xphi @ Xx ) ) ) ) ) ).
% 2.04/1.58
% 2.04/1.58 thf(quantDeMorgan4_type,type,
% 2.04/1.58 quantDeMorgan4: $o ).
% 2.04/1.58
% 2.04/1.58 thf(quantDeMorgan4,definition,
% 2.04/1.58 ( quantDeMorgan4
% 2.04/1.58 = ( ! [A: $i,Xphi: $i > $o] :
% 2.04/1.58 ( ? [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 & ~ ( Xphi @ Xx ) )
% 2.04/1.58 => ~ ! [Xx: $i] :
% 2.04/1.58 ( ( in @ Xx @ A )
% 2.04/1.58 => ( Xphi @ Xx ) ) ) ) ) ).
% 2.04/1.58
% 2.04/1.58 thf(prop2setI,conjecture,
% 2.04/1.58 ( setextAx
% 2.04/1.58 => ( emptysetAx
% 2.04/1.58 => ( setadjoinAx
% 2.04/1.58 => ( powersetAx
% 2.04/1.58 => ( setunionAx
% 2.04/1.58 => ( omega0Ax
% 2.04/1.58 => ( omegaSAx
% 2.04/1.58 => ( omegaIndAx
% 2.04/1.58 => ( replAx
% 2.04/1.58 => ( foundationAx
% 2.04/1.58 => ( wellorderingAx
% 2.04/1.58 => ( descrp
% 2.04/1.58 => ( dsetconstrI
% 2.04/1.58 => ( dsetconstrEL
% 2.04/1.58 => ( dsetconstrER
% 2.04/1.58 => ( exuE1
% 2.04/1.58 => ( prop2setE
% 2.04/1.58 => ( emptysetE
% 2.04/1.58 => ( emptysetimpfalse
% 2.04/1.58 => ( notinemptyset
% 2.04/1.58 => ( exuE3e
% 2.04/1.58 => ( setext
% 2.04/1.58 => ( emptyI
% 2.04/1.58 => ( noeltsimpempty
% 2.04/1.58 => ( setbeta
% 2.04/1.58 => ( nonemptyE1
% 2.04/1.58 => ( nonemptyI
% 2.04/1.58 => ( nonemptyI1
% 2.04/1.58 => ( setadjoinIL
% 2.04/1.58 => ( emptyinunitempty
% 2.04/1.58 => ( setadjoinIR
% 2.04/1.58 => ( setadjoinE
% 2.04/1.58 => ( setadjoinOr
% 2.04/1.58 => ( setoftrueEq
% 2.04/1.58 => ( powersetI
% 2.04/1.58 => ( emptyinPowerset
% 2.04/1.58 => ( emptyInPowerset
% 2.04/1.58 => ( powersetE
% 2.04/1.58 => ( setunionI
% 2.04/1.58 => ( setunionE
% 2.04/1.58 => ( subPowSU
% 2.04/1.58 => ( exuE2
% 2.04/1.58 => ( nonemptyImpWitness
% 2.04/1.58 => ( uniqinunit
% 2.04/1.58 => ( notinsingleton
% 2.04/1.58 => ( eqinunit
% 2.04/1.58 => ( singletonsswitch
% 2.04/1.58 => ( upairsetE
% 2.04/1.58 => ( upairsetIL
% 2.04/1.58 => ( upairsetIR
% 2.04/1.58 => ( emptyE1
% 2.04/1.58 => ( vacuousDall
% 2.04/1.58 => ( quantDeMorgan1
% 2.04/1.58 => ( quantDeMorgan2
% 2.04/1.58 => ( quantDeMorgan3
% 2.04/1.58 => ( quantDeMorgan4
% 2.04/1.58 => ! [Xphi: $o] :
% 2.04/1.58 ( Xphi
% 2.04/1.58 => ( in @ emptyset @ ( prop2set @ Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.04/1.58 ------------------------
% 2.21/1.60 % (32232)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/2Mi)
% 2.21/1.60 % (32231)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_32072 for (2999ds/27Mi)
% 2.21/1.60 % (32233)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_32072 for (2999ds/2Mi)
% 2.21/1.60 % (32234)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_32072 for (2999ds/275Mi)
% 2.21/1.60 % (32235)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/18Mi)
% 2.21/1.60 % (32230)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_32072 for (2999ds/4Mi)
% 2.21/1.60 % (32229)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/183Mi)
% 2.21/1.60 % (32232)Instruction limit reached!
% 2.21/1.60 % (32232)------------------------------
% 2.21/1.60 % (32232)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.60 % (32232)Termination reason: Unknown
% 2.21/1.60 % (32232)Termination phase: shuffling
% 2.21/1.60
% 2.21/1.60 % (32233)Instruction limit reached!
% 2.21/1.60 % (32233)------------------------------
% 2.21/1.60 % (32233)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.60 % (32232)Memory used [KB]: 1023
% 2.21/1.60 % (32232)Time elapsed: 0.003 s
% 2.21/1.60 % (32232)Instructions burned: 2 (million)
% 2.21/1.60 % (32232)------------------------------
% 2.21/1.60 % (32232)------------------------------
% 2.21/1.60 % (32233)Termination reason: Unknown
% 2.21/1.60 % (32233)Termination phase: shuffling
% 2.21/1.60
% 2.21/1.60 % (32233)Memory used [KB]: 1023
% 2.21/1.60 % (32233)Time elapsed: 0.003 s
% 2.21/1.60 % (32233)Instructions burned: 2 (million)
% 2.21/1.60 % (32233)------------------------------
% 2.21/1.60 % (32233)------------------------------
% 2.21/1.60 % (32230)Instruction limit reached!
% 2.21/1.60 % (32230)------------------------------
% 2.21/1.60 % (32230)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.60 % (32230)Termination reason: Unknown
% 2.21/1.60 % (32230)Termination phase: shuffling
% 2.21/1.60
% 2.21/1.60 % (32230)Memory used [KB]: 1151
% 2.21/1.60 % (32230)Time elapsed: 0.003 s
% 2.21/1.60 % (32230)Instructions burned: 4 (million)
% 2.21/1.60 % (32230)------------------------------
% 2.21/1.60 % (32230)------------------------------
% 2.21/1.61 % (32235)Instruction limit reached!
% 2.21/1.61 % (32235)------------------------------
% 2.21/1.61 % (32235)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.61 % (32235)Termination reason: Unknown
% 2.21/1.61 % (32235)Termination phase: Preprocessing 3
% 2.21/1.61
% 2.21/1.61 % (32235)Memory used [KB]: 1535
% 2.21/1.61 % (32235)Time elapsed: 0.011 s
% 2.21/1.61 % (32235)Instructions burned: 18 (million)
% 2.21/1.61 % (32235)------------------------------
% 2.21/1.61 % (32235)------------------------------
% 2.21/1.61 % (32231)Instruction limit reached!
% 2.21/1.61 % (32231)------------------------------
% 2.21/1.61 % (32231)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.61 % (32231)Termination reason: Unknown
% 2.21/1.61 % (32231)Termination phase: Property scanning
% 2.21/1.61
% 2.21/1.61 % (32231)Memory used [KB]: 1279
% 2.21/1.61 % (32231)Time elapsed: 0.014 s
% 2.21/1.61 % (32231)Instructions burned: 27 (million)
% 2.21/1.61 % (32231)------------------------------
% 2.21/1.61 % (32231)------------------------------
% 2.21/1.61 % (32237)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_32072 for (2999ds/37Mi)
% 2.21/1.61 % (32236)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/3Mi)
% 2.21/1.62 % (32238)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_32072 for (2999ds/15Mi)
% 2.21/1.62 % (32236)Instruction limit reached!
% 2.21/1.62 % (32236)------------------------------
% 2.21/1.62 % (32236)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.62 % (32236)Termination reason: Unknown
% 2.21/1.62 % (32236)Termination phase: shuffling
% 2.21/1.62
% 2.21/1.62 % (32236)Memory used [KB]: 1023
% 2.21/1.62 % (32236)Time elapsed: 0.003 s
% 2.21/1.62 % (32236)Instructions burned: 3 (million)
% 2.21/1.62 % (32236)------------------------------
% 2.21/1.62 % (32236)------------------------------
% 2.21/1.62 % (32238)Instruction limit reached!
% 2.21/1.62 % (32238)------------------------------
% 2.21/1.62 % (32238)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.62 % (32238)Termination reason: Unknown
% 2.21/1.62 % (32238)Termination phase: Preprocessing 3
% 2.21/1.62
% 2.21/1.62 % (32238)Memory used [KB]: 1407
% 2.21/1.62 % (32238)Time elapsed: 0.009 s
% 2.21/1.62 % (32238)Instructions burned: 16 (million)
% 2.21/1.62 % (32238)------------------------------
% 2.21/1.62 % (32238)------------------------------
% 2.21/1.62 % (32239)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_32072 for (2999ds/3Mi)
% 2.21/1.62 % (32239)Instruction limit reached!
% 2.21/1.62 % (32239)------------------------------
% 2.21/1.62 % (32239)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.62 % (32239)Termination reason: Unknown
% 2.21/1.62 % (32239)Termination phase: shuffling
% 2.21/1.62
% 2.21/1.62 % (32239)Memory used [KB]: 1023
% 2.21/1.62 % (32239)Time elapsed: 0.003 s
% 2.21/1.62 % (32239)Instructions burned: 3 (million)
% 2.21/1.62 % (32239)------------------------------
% 2.21/1.62 % (32239)------------------------------
% 2.21/1.63 % (32240)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_32072 for (2999ds/1041Mi)
% 2.21/1.63 % (32237)Instruction limit reached!
% 2.21/1.63 % (32237)------------------------------
% 2.21/1.63 % (32237)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.63 % (32237)Termination reason: Unknown
% 2.21/1.63 % (32237)Termination phase: Saturation
% 2.21/1.63
% 2.21/1.63 % (32237)Memory used [KB]: 5756
% 2.21/1.63 % (32237)Time elapsed: 0.018 s
% 2.21/1.63 % (32237)Instructions burned: 39 (million)
% 2.21/1.63 % (32237)------------------------------
% 2.21/1.63 % (32237)------------------------------
% 2.21/1.63 % (32241)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/7Mi)
% 2.21/1.64 % (32241)Instruction limit reached!
% 2.21/1.64 % (32241)------------------------------
% 2.21/1.64 % (32241)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.64 % (32241)Termination reason: Unknown
% 2.21/1.64 % (32241)Termination phase: shuffling
% 2.21/1.64
% 2.21/1.64 % (32241)Memory used [KB]: 1151
% 2.21/1.64 % (32241)Time elapsed: 0.005 s
% 2.21/1.64 % (32241)Instructions burned: 8 (million)
% 2.21/1.64 % (32241)------------------------------
% 2.21/1.64 % (32241)------------------------------
% 2.21/1.64 % (32242)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/16Mi)
% 2.21/1.64 % (32243)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_32072 for (2999ds/3Mi)
% 2.21/1.64 % (32243)Instruction limit reached!
% 2.21/1.64 % (32243)------------------------------
% 2.21/1.64 % (32243)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.64 % (32243)Termination reason: Unknown
% 2.21/1.64 % (32243)Termination phase: shuffling
% 2.21/1.64
% 2.21/1.64 % (32243)Memory used [KB]: 1023
% 2.21/1.64 % (32243)Time elapsed: 0.003 s
% 2.21/1.64 % (32243)Instructions burned: 3 (million)
% 2.21/1.64 % (32243)------------------------------
% 2.21/1.64 % (32243)------------------------------
% 2.21/1.65 % (32242)Instruction limit reached!
% 2.21/1.65 % (32242)------------------------------
% 2.21/1.65 % (32242)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.65 % (32242)Termination reason: Unknown
% 2.21/1.65 % (32242)Termination phase: Property scanning
% 2.21/1.65
% 2.21/1.65 % (32242)Memory used [KB]: 1279
% 2.21/1.65 % (32242)Time elapsed: 0.009 s
% 2.21/1.65 % (32242)Instructions burned: 17 (million)
% 2.21/1.65 % (32242)------------------------------
% 2.21/1.65 % (32242)------------------------------
% 2.21/1.65 % (32244)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_32072 for (2999ds/3Mi)
% 2.21/1.65 % (32244)Instruction limit reached!
% 2.21/1.65 % (32244)------------------------------
% 2.21/1.65 % (32244)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.65 % (32244)Termination reason: Unknown
% 2.21/1.65 % (32244)Termination phase: shuffling
% 2.21/1.65
% 2.21/1.65 % (32244)Memory used [KB]: 1023
% 2.21/1.65 % (32244)Time elapsed: 0.003 s
% 2.21/1.65 % (32244)Instructions burned: 4 (million)
% 2.21/1.65 % (32244)------------------------------
% 2.21/1.65 % (32244)------------------------------
% 2.21/1.65 % (32245)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/7Mi)
% 2.21/1.65 % (32245)Instruction limit reached!
% 2.21/1.65 % (32245)------------------------------
% 2.21/1.65 % (32245)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.65 % (32245)Termination reason: Unknown
% 2.21/1.66 % (32245)Termination phase: shuffling
% 2.21/1.66
% 2.21/1.66 % (32245)Memory used [KB]: 1151
% 2.21/1.66 % (32245)Time elapsed: 0.005 s
% 2.21/1.66 % (32245)Instructions burned: 8 (million)
% 2.21/1.66 % (32245)------------------------------
% 2.21/1.66 % (32245)------------------------------
% 2.21/1.66 % (32246)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/3Mi)
% 2.21/1.66 % (32246)Instruction limit reached!
% 2.21/1.66 % (32246)------------------------------
% 2.21/1.66 % (32246)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.66 % (32246)Termination reason: Unknown
% 2.21/1.66 % (32246)Termination phase: shuffling
% 2.21/1.66
% 2.21/1.66 % (32246)Memory used [KB]: 1151
% 2.21/1.66 % (32246)Time elapsed: 0.003 s
% 2.21/1.66 % (32246)Instructions burned: 3 (million)
% 2.21/1.66 % (32246)------------------------------
% 2.21/1.66 % (32246)------------------------------
% 2.21/1.66 % (32229)First to succeed.
% 2.21/1.66 % (32247)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_32072 for (2999ds/4Mi)
% 2.21/1.66 % (32229)Refutation found. Thanks to Tanya!
% 2.21/1.66 % SZS status Theorem for DTF2THF_32072
% 2.21/1.66 % SZS output start Proof for DTF2THF_32072
% 2.21/1.66 thf(func_def_0, type, in: $i > $i > $o).
% 2.21/1.66 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.21/1.66 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.21/1.66 thf(func_def_8, type, powerset: $i > $i).
% 2.21/1.66 thf(func_def_10, type, setunion: $i > $i).
% 2.21/1.66 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.21/1.66 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.21/1.66 thf(func_def_26, type, prop2set: $o > $i).
% 2.21/1.66 thf(func_def_36, type, nonempty: $i > $o).
% 2.21/1.66 thf(func_def_87, type, sK2: ($i > $i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_88, type, sK3: ($i > $i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_89, type, sK4: $i > ($i > $i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_90, type, sK5: $i > ($i > $i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_91, type, sK6: $i > ($i > $i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_92, type, sK7: $i > ($i > $i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_93, type, sK8: $i > ($i > $i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_94, type, sK9: $i > ($i > $o) > $i).
% 2.21/1.66 thf(func_def_95, type, sK10: ($i > $o) > $i).
% 2.21/1.66 thf(func_def_96, type, sK11: ($i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_97, type, sK12: ($i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_98, type, sK13: $i > $i).
% 2.21/1.66 thf(func_def_99, type, sK14: ($i > $o) > $i).
% 2.21/1.66 thf(func_def_100, type, sK15: $i > ($i > $o) > $i).
% 2.21/1.66 thf(func_def_101, type, sK16: ($i > $o) > $i).
% 2.21/1.66 thf(func_def_102, type, sK17: ($i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_103, type, sK18: ($i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_104, type, sK19: $i > $i).
% 2.21/1.66 thf(func_def_105, type, sK20: ($i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_106, type, sK21: $i > $i).
% 2.21/1.66 thf(func_def_107, type, sK22: $i > $i > $i > $i).
% 2.21/1.66 thf(func_def_108, type, sK23: $i > $i > $i).
% 2.21/1.66 thf(func_def_109, type, sK24: $i > $i > $i).
% 2.21/1.66 thf(func_def_110, type, sK25: $i > $i > $i).
% 2.21/1.66 thf(func_def_111, type, sK26: $i > $i > $i).
% 2.21/1.66 thf(func_def_112, type, sK27: $i > $i > $i).
% 2.21/1.66 thf(func_def_113, type, sK28: $i > ($i > $o) > $i).
% 2.21/1.66 thf(func_def_114, type, sK29: ($i > $o) > $i > $i).
% 2.21/1.66 thf(func_def_115, type, sK30: $i > $i > $i).
% 2.21/1.66 thf(func_def_116, type, sK31: $i > $i > $i).
% 2.21/1.66 thf(func_def_117, type, sK32: $i > $i > $i).
% 2.21/1.66 thf(func_def_118, type, sK33: $i > $i > $i).
% 2.21/1.66 thf(func_def_119, type, sK34: $i > $i > $i).
% 2.21/1.66 thf(func_def_120, type, sK35: $i > $i).
% 2.21/1.66 thf(func_def_121, type, sK36: $i > $i).
% 2.21/1.66 thf(func_def_122, type, sK37: $i > $i).
% 2.21/1.66 thf(func_def_123, type, sK38: $o > $i > $i > $i).
% 2.21/1.66 thf(func_def_124, type, sK39: $i > $i).
% 2.21/1.66 thf(func_def_125, type, ph40: !>[X0: $tType]:(X0)).
% 2.21/1.66 thf(f1394,plain,(
% 2.21/1.66 $false),
% 2.21/1.66 inference(subsumption_resolution,[status(thm)],[f1388,f1004])).
% 2.21/1.66 thf(f1004,plain,(
% 2.21/1.66 ( ! [X1 : $i] : (($true = (in @ emptyset @ (powerset @ X1)))) )),
% 2.21/1.66 inference(beta_eta_normalization,[status(thm)],[f1003])).
% 2.21/1.66 thf(f1003,plain,(
% 2.21/1.66 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0))) @ X1))) )),
% 2.21/1.66 inference(pi_clausification,[status(thm)],[f315])).
% 2.21/1.66 thf(f315,plain,(
% 2.21/1.66 ($true = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))),
% 2.21/1.66 inference(definition_unfolding,[status(thm)],[f254,f230])).
% 2.21/1.66 thf(f230,plain,(
% 2.21/1.66 (emptyinPowerset = $true)),
% 2.21/1.66 inference(cnf_transformation,[status(thm)],[f181])).
% 2.21/1.66 thf(f181,plain,(
% 2.21/1.66 (emptysetimpfalse = $true) & (quantDeMorgan4 = $true) & (omegaSAx = $true) & (nonemptyImpWitness = $true) & (foundationAx = $true) & (($true = sK0) & ($true != (in @ emptyset @ (prop2set @ sK0)))) & (prop2setE = $true) & (exuE3e = $true) & (upairsetE = $true) & (quantDeMorgan2 = $true) & (setadjoinIR = $true) & (setunionE = $true) & (uniqinunit = $true) & (singletonsswitch = $true) & (setadjoinOr = $true) & (emptyInPowerset = $true) & (setbeta = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (emptyinPowerset = $true) & (emptyI = $true) & (omegaIndAx = $true) & (powersetAx = $true) & (notinemptyset = $true) & (powersetE = $true) & (setunionI = $true) & (noeltsimpempty = $true) & (exuE1 = $true) & (omega0Ax = $true) & (quantDeMorgan1 = $true) & (setadjoinIL = $true) & (quantDeMorgan3 = $true) & (setoftrueEq = $true) & (dsetconstrER = $true) & (exuE2 = $true) & (setunionAx = $true) & (emptysetAx = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (subPowSU = $true) & (descrp = $true) & (setextAx = $true) & (upairsetIR = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (upairsetIL = $true) & (eqinunit = $true) & (notinsingleton = $true) & (emptysetE = $true) & (powersetI = $true) & (replAx = $true) & (nonemptyE1 = $true) & (setext = $true) & (dsetconstrI = $true) & (wellorderingAx = $true) & (nonemptyI = $true)),
% 2.21/1.66 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f179,f180])).
% 2.21/1.66 thf(f180,plain,(
% 2.21/1.66 ? [X0 : $o] : (($true = X0) & ((in @ emptyset @ (prop2set @ X0)) != $true)) => (($true = sK0) & ($true != (in @ emptyset @ (prop2set @ sK0))))),
% 2.21/1.66 introduced(definition,[],[choice_axiom])).
% 2.21/1.66 thf(f179,plain,(
% 2.21/1.66 (emptysetimpfalse = $true) & (quantDeMorgan4 = $true) & (omegaSAx = $true) & (nonemptyImpWitness = $true) & (foundationAx = $true) & ? [X0 : $o] : (($true = X0) & ((in @ emptyset @ (prop2set @ X0)) != $true)) & (prop2setE = $true) & (exuE3e = $true) & (upairsetE = $true) & (quantDeMorgan2 = $true) & (setadjoinIR = $true) & (setunionE = $true) & (uniqinunit = $true) & (singletonsswitch = $true) & (setadjoinOr = $true) & (emptyInPowerset = $true) & (setbeta = $true) & (vacuousDall = $true) & (emptyE1 = $true) & (emptyinPowerset = $true) & (emptyI = $true) & (omegaIndAx = $true) & (powersetAx = $true) & (notinemptyset = $true) & (powersetE = $true) & (setunionI = $true) & (noeltsimpempty = $true) & (exuE1 = $true) & (omega0Ax = $true) & (quantDeMorgan1 = $true) & (setadjoinIL = $true) & (quantDeMorgan3 = $true) & (setoftrueEq = $true) & (dsetconstrER = $true) & (exuE2 = $true) & (setunionAx = $true) & (emptysetAx = $true) & (dsetconstrEL = $true) & (setadjoinE = $true) & (subPowSU = $true) & (descrp = $true) & (setextAx = $true) & (upairsetIR = $true) & (emptyinunitempty = $true) & (setadjoinAx = $true) & (nonemptyI1 = $true) & (upairsetIL = $true) & (eqinunit = $true) & (notinsingleton = $true) & (emptysetE = $true) & (powersetI = $true) & (replAx = $true) & (nonemptyE1 = $true) & (setext = $true) & (dsetconstrI = $true) & (wellorderingAx = $true) & (nonemptyI = $true)),
% 2.21/1.66 inference(flattening,[status(thm)],[f178])).
% 2.21/1.66 thf(f178,plain,(
% 2.21/1.66 (((((((((((((((((((((((((((((((((((((((((((((((((((((((? [X0 : $o] : (($true = X0) & ((in @ emptyset @ (prop2set @ X0)) != $true)) & (quantDeMorgan4 = $true)) & (quantDeMorgan3 = $true)) & (quantDeMorgan2 = $true)) & (quantDeMorgan1 = $true)) & (vacuousDall = $true)) & (emptyE1 = $true)) & (upairsetIR = $true)) & (upairsetIL = $true)) & (upairsetE = $true)) & (singletonsswitch = $true)) & (eqinunit = $true)) & (notinsingleton = $true)) & (uniqinunit = $true)) & (nonemptyImpWitness = $true)) & (exuE2 = $true)) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 2.21/1.66 inference(ennf_transformation,[status(thm)],[f72])).
% 2.21/1.66 thf(f72,plain,(
% 2.21/1.66 ~((setextAx = $true) => ((emptysetAx = $true) => ((setadjoinAx = $true) => ((powersetAx = $true) => ((setunionAx = $true) => ((omega0Ax = $true) => ((omegaSAx = $true) => ((omegaIndAx = $true) => ((replAx = $true) => ((foundationAx = $true) => ((wellorderingAx = $true) => ((descrp = $true) => ((dsetconstrI = $true) => ((dsetconstrEL = $true) => ((dsetconstrER = $true) => ((exuE1 = $true) => ((prop2setE = $true) => ((emptysetE = $true) => ((emptysetimpfalse = $true) => ((notinemptyset = $true) => ((exuE3e = $true) => ((setext = $true) => ((emptyI = $true) => ((noeltsimpempty = $true) => ((setbeta = $true) => ((nonemptyE1 = $true) => ((nonemptyI = $true) => ((nonemptyI1 = $true) => ((setadjoinIL = $true) => ((emptyinunitempty = $true) => ((setadjoinIR = $true) => ((setadjoinE = $true) => ((setadjoinOr = $true) => ((setoftrueEq = $true) => ((powersetI = $true) => ((emptyinPowerset = $true) => ((emptyInPowerset = $true) => ((powersetE = $true) => ((setunionI = $true) => ((setunionE = $true) => ((subPowSU = $true) => ((exuE2 = $true) => ((nonemptyImpWitness = $true) => ((uniqinunit = $true) => ((notinsingleton = $true) => ((eqinunit = $true) => ((singletonsswitch = $true) => ((upairsetE = $true) => ((upairsetIL = $true) => ((upairsetIR = $true) => ((emptyE1 = $true) => ((vacuousDall = $true) => ((quantDeMorgan1 = $true) => ((quantDeMorgan2 = $true) => ((quantDeMorgan3 = $true) => ((quantDeMorgan4 = $true) => ! [X0 : $o] : (($true = X0) => ((in @ emptyset @ (prop2set @ X0)) = $true))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.21/1.66 inference(fool_elimination,[status(thm)],[f71])).
% 2.21/1.66 thf(f71,plain,(
% 2.21/1.66 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.21/1.66 inference(rectify,[status(thm)],[f61])).
% 2.21/1.66 thf(f61,negated_conjecture,(
% 2.21/1.66 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0)))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.21/1.66 inference(negated_conjecture,[status(cth)],[f60])).
% 2.21/1.66 thf(f60,conjecture,(
% 2.21/1.66 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => (exuE3e => (setext => (emptyI => (noeltsimpempty => (setbeta => (nonemptyE1 => (nonemptyI => (nonemptyI1 => (setadjoinIL => (emptyinunitempty => (setadjoinIR => (setadjoinE => (setadjoinOr => (setoftrueEq => (powersetI => (emptyinPowerset => (emptyInPowerset => (powersetE => (setunionI => (setunionE => (subPowSU => (exuE2 => (nonemptyImpWitness => (uniqinunit => (notinsingleton => (eqinunit => (singletonsswitch => (upairsetE => (upairsetIL => (upairsetIR => (emptyE1 => (vacuousDall => (quantDeMorgan1 => (quantDeMorgan2 => (quantDeMorgan3 => (quantDeMorgan4 => ! [X0 : $o] : (X0 => (in @ emptyset @ (prop2set @ X0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.21/1.66 file('/export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2THF_32072.p',prop2setI)).
% 2.21/1.66 thf(f254,plain,(
% 2.21/1.66 (emptyinPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))),
% 2.21/1.66 inference(cnf_transformation,[status(thm)],[f82])).
% 2.21/1.66 thf(f82,plain,(
% 2.21/1.66 (emptyinPowerset = (!! @ $i @ (^[Y0 : $i]: (in @ emptyset @ (powerset @ Y0)))))),
% 2.21/1.66 inference(fool_elimination,[status(thm)],[f81])).
% 2.21/1.66 thf(f81,plain,(
% 2.21/1.66 (emptyinPowerset = ! [X0 : $i] : (in @ emptyset @ (powerset @ X0)))),
% 2.21/1.66 inference(rectify,[status(thm)],[f39])).
% 2.21/1.66 thf(f39,axiom,(
% 2.21/1.66 (emptyinPowerset = ! [X3 : $i] : (in @ emptyset @ (powerset @ X3)))),
% 2.21/1.66 file('/export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2THF_32072.p',emptyinPowerset)).
% 2.21/1.66 thf(f1388,plain,(
% 2.21/1.66 ($true != (in @ emptyset @ (powerset @ emptyset)))),
% 2.21/1.66 inference(superposition,[status(thm)],[f930,f718])).
% 2.21/1.66 thf(f718,plain,(
% 2.21/1.66 ( ! [X1 : $i] : (((dsetconstr @ X1 @ (^[Y0 : $i]: ($true))) = X1)) )),
% 2.21/1.66 inference(equality_proxy_clausification,[status(thm)],[f717])).
% 2.21/1.66 thf(f717,plain,(
% 2.21/1.66 ( ! [X1 : $i] : (($true = (X1 = (dsetconstr @ X1 @ (^[Y0 : $i]: ($true)))))) )),
% 2.21/1.66 inference(beta_eta_normalization,[status(thm)],[f716])).
% 2.21/1.66 thf(f716,plain,(
% 2.21/1.66 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true))))) @ X1))) )),
% 2.21/1.66 inference(pi_clausification,[status(thm)],[f350])).
% 2.21/1.66 thf(f350,plain,(
% 2.21/1.66 ($true = (!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))))),
% 2.21/1.66 inference(definition_unfolding,[status(thm)],[f291,f217])).
% 2.21/1.66 thf(f217,plain,(
% 2.21/1.66 (setoftrueEq = $true)),
% 2.21/1.66 inference(cnf_transformation,[status(thm)],[f181])).
% 2.21/1.66 thf(f291,plain,(
% 2.21/1.66 (setoftrueEq = (!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))))),
% 2.21/1.66 inference(cnf_transformation,[status(thm)],[f171])).
% 2.21/1.66 thf(f171,plain,(
% 2.21/1.66 (setoftrueEq = (!! @ $i @ (^[Y0 : $i]: (Y0 = (dsetconstr @ Y0 @ (^[Y1 : $i]: ($true)))))))),
% 2.21/1.66 inference(fool_elimination,[status(thm)],[f170])).
% 2.21/1.66 thf(f170,plain,(
% 2.21/1.66 (setoftrueEq = ! [X0 : $i] : (X0 = (dsetconstr @ X0 @ (^[X1 : $i] : ($true)))))),
% 2.21/1.66 inference(rectify,[status(thm)],[f37])).
% 2.21/1.66 thf(f37,axiom,(
% 2.21/1.66 (setoftrueEq = ! [X3 : $i] : (X3 = (dsetconstr @ X3 @ (^[X1 : $i] : ($true)))))),
% 2.21/1.66 file('/export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2THF_32072.p',setoftrueEq)).
% 2.21/1.66 thf(f930,plain,(
% 2.21/1.66 ($true != (in @ emptyset @ (dsetconstr @ (powerset @ emptyset) @ (^[Y0 : $i]: ($true)))))),
% 2.21/1.66 inference(beta_eta_normalization,[status(thm)],[f300])).
% 2.21/1.66 thf(f300,plain,(
% 2.21/1.66 ($true != (in @ emptyset @ ((^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))) @ $true)))),
% 2.21/1.66 inference(definition_unfolding,[status(thm)],[f244,f259,f245])).
% 2.21/1.66 thf(f245,plain,(
% 2.21/1.66 ($true = sK0)),
% 2.21/1.66 inference(cnf_transformation,[status(thm)],[f181])).
% 2.21/1.66 thf(f259,plain,(
% 2.21/1.66 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 2.21/1.66 inference(cnf_transformation,[status(thm)],[f87])).
% 2.21/1.66 thf(f87,plain,(
% 2.21/1.66 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 2.21/1.66 inference(fool_elimination,[status(thm)],[f18])).
% 2.21/1.66 thf(f18,axiom,(
% 2.21/1.66 (prop2set = (^[X0 : $o] : (dsetconstr @ (powerset @ emptyset) @ (^[X1 : $i] : (X0)))))),
% 2.21/1.66 file('/export/starexec/sandbox/tmp/tmp.2yhNlamfaV/DTF2THF_32072.p',prop2set)).
% 2.21/1.66 thf(f244,plain,(
% 2.21/1.66 ($true != (in @ emptyset @ (prop2set @ sK0)))),
% 2.21/1.66 inference(cnf_transformation,[status(thm)],[f181])).
% 2.21/1.66 % SZS output end Proof for DTF2THF_32072
% 2.21/1.66 % (32229)------------------------------
% 2.21/1.66 % (32229)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.21/1.66 % (32229)Termination reason: Refutation
% 2.21/1.66
% 2.21/1.66 % (32229)Memory used [KB]: 6780
% 2.21/1.66 % (32229)Time elapsed: 0.065 s
% 2.21/1.66 % (32229)Instructions burned: 129 (million)
% 2.21/1.66 % (32229)------------------------------
% 2.21/1.66 % (32229)------------------------------
% 2.21/1.66 % (32228)Success in time 0.077 s
%------------------------------------------------------------------------------