%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU528^1 : 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 : n003.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 09:35:06 AM UTC 2026
% Result : Theorem 2.06s 1.58s
% Output : Refutation 2.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 3
% Syntax : Number of formulae : 26 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 931 ( 266 equ; 0 cnn)
% Maximal formula atoms : 47 ( 35 avg)
% Number of connectives : 509 ( 20 ~; 3 |; 137 &; 106 @)
% ( 0 <=>; 235 =>; 0 <=; 0 <~>)
% Maximal formula depth : 53 ( 17 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 93 ( 89 usr; 50 con; 0-3 aty)
% ( 8 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 40 ( 10 ^; 24 !; 6 ?; 40 :)
% 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_75,type,
sK3: $i > $i ).
thf(func_def_76,type,
sK4: $i > $i > $i ).
thf(func_def_77,type,
sK5: $i > $i > $i ).
thf(func_def_78,type,
sK6: $i > $i ).
thf(func_def_79,type,
sK7: ( $i > $o ) > $i > $i ).
thf(func_def_80,type,
sK8: $i > $i ).
thf(func_def_81,type,
sK9: $i > $i ).
thf(func_def_82,type,
sK10: ( $i > $o ) > $i ).
thf(func_def_83,type,
sK11: ( $i > $o ) > $i > $i ).
thf(func_def_84,type,
sK12: $o > $i > $i > $i ).
thf(func_def_85,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_86,type,
sK14: ( $i > $o ) > $i ).
thf(func_def_87,type,
sK15: ( $i > $o ) > $i ).
thf(func_def_88,type,
sK16: $i > $i > $i ).
thf(func_def_89,type,
sK17: $i > $i > $i ).
thf(func_def_90,type,
sK18: $i > $i > $i ).
thf(func_def_91,type,
sK19: $i > ( $i > $i > $o ) > $i ).
thf(func_def_92,type,
sK20: $i > ( $i > $i > $o ) > $i ).
thf(func_def_93,type,
sK21: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_94,type,
sK22: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_95,type,
sK23: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_96,type,
sK24: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_97,type,
sK25: $i > $i ).
thf(func_def_98,type,
sK26: $i > $i ).
thf(func_def_99,type,
sK27: $i > $i ).
thf(func_def_100,type,
sK28: $i > $i > $i ).
thf(func_def_101,type,
sK29: $i > $i > $i ).
thf(func_def_102,type,
sK30: $i > $i > $i ).
thf(func_def_103,type,
sK31: $i > $i > $i ).
thf(func_def_104,type,
sK32: $i > $i > $i > $i ).
thf(func_def_105,type,
sK33: $i > $i > $i ).
thf(func_def_106,type,
sK34: $i > $i > $i ).
thf(func_def_107,type,
ph35:
!>[X0: $tType] : X0 ).
thf(f898,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f895,f194]) ).
thf(f194,plain,
sK1 != sK0,
inference(cnf_transformation,[status(thm)],[f146]) ).
thf(f146,plain,
( ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( setextAx = $true )
& ( powersetE = $true )
& ( descrp = $true )
& ( noeltsimpempty = $true )
& ( powersetAx = $true )
& ( prop2setE = $true )
& ( exuE2 = $true )
& ( omegaSAx = $true )
& ( dsetconstrEL = $true )
& ( setadjoinOr = $true )
& ( dsetconstrI = $true )
& ( setunionE = $true )
& ( powersetI = $true )
& ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK1 != sK0 )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ( replAx = $true )
& ( nonemptyI1 = $true )
& ( uniqinunit = $true )
& ( emptyinPowerset = $true )
& ( nonemptyE1 = $true )
& ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( setext = $true )
& ( emptysetAx = $true )
& ( setbeta = $true )
& ( setadjoinE = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ( setadjoinAx = $true )
& ( emptyInPowerset = $true )
& ( setunionAx = $true )
& ( emptyI = $true )
& ( setunionI = $true )
& ( subPowSU = $true )
& ( nonemptyImpWitness = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f144,f145]) ).
thf(f145,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 != X1 ) )
=> ( ( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) )
& ( sK1 != sK0 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f144,plain,
( ( notinemptyset = $true )
& ( wellorderingAx = $true )
& ( setextAx = $true )
& ( powersetE = $true )
& ( descrp = $true )
& ( noeltsimpempty = $true )
& ( powersetAx = $true )
& ( prop2setE = $true )
& ( exuE2 = $true )
& ( omegaSAx = $true )
& ( dsetconstrEL = $true )
& ( setadjoinOr = $true )
& ( dsetconstrI = $true )
& ( setunionE = $true )
& ( powersetI = $true )
& ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 != X1 ) )
& ( omegaIndAx = $true )
& ( exuE3e = $true )
& ( emptyinunitempty = $true )
& ( omega0Ax = $true )
& ( replAx = $true )
& ( nonemptyI1 = $true )
& ( uniqinunit = $true )
& ( emptyinPowerset = $true )
& ( nonemptyE1 = $true )
& ( setadjoinIR = $true )
& ( setadjoinIL = $true )
& ( emptysetE = $true )
& ( emptysetimpfalse = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( setext = $true )
& ( emptysetAx = $true )
& ( setbeta = $true )
& ( setadjoinE = $true )
& ( nonemptyI = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ( setadjoinAx = $true )
& ( emptyInPowerset = $true )
& ( setunionAx = $true )
& ( emptyI = $true )
& ( setunionI = $true )
& ( subPowSU = $true )
& ( nonemptyImpWitness = $true ) ),
inference(flattening,[status(thm)],[f143]) ).
thf(f143,plain,
( ? [X0: $i,X1: $i] :
( ( $true
= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) )
& ( X0 != X1 ) )
& ( 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)],[f142]) ).
thf(f142,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 )
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f129]) ).
thf(f129,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 )
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ( $true
!= ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f128]) ).
thf(f128,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
=> ! [X0: $i,X1: $i] :
( ( X0 != X1 )
=> ~ ( in @ X1 @ ( setadjoin @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f49]) ).
thf(f49,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
=> ! [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f48]) ).
thf(f48,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
=> ! [X1: $i,X2: $i] :
( ( X1 != X2 )
=> ~ ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LPAaOweVIv/DTF2THF_6365.p',notinsingleton) ).
thf(f895,plain,
sK1 = sK0,
inference(trivial_inequality_removal,[status(thm)],[f886]) ).
thf(f886,plain,
( ( sK1 = sK0 )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f195,f455]) ).
thf(f455,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false )
| ( X1 = X2 ) ),
inference(equality_proxy_clausification,[status(thm)],[f454]) ).
thf(f454,plain,
! [X2: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
= $false )
| ( ( X2 = X1 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f453]) ).
thf(f453,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( in @ X2 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X2 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f452]) ).
thf(f452,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f451]) ).
thf(f451,plain,
! [X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( Y0 = X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f450]) ).
thf(f450,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f282]) ).
thf(f282,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f231,f187]) ).
thf(f187,plain,
uniqinunit = $true,
inference(cnf_transformation,[status(thm)],[f146]) ).
thf(f231,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f87]) ).
thf(f87,plain,
( uniqinunit
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ Y0 @ emptyset ) )
=> ( Y1 = Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f86]) ).
thf(f86,plain,
( uniqinunit
= ( ! [X0: $i,X1: $i] :
( ( in @ X0 @ ( setadjoin @ X1 @ emptyset ) )
=> ( X0 = X1 ) ) ) ),
inference(rectify,[status(thm)],[f47]) ).
thf(f47,axiom,
( uniqinunit
= ( ! [X1: $i,X2: $i] :
( ( in @ X1 @ ( setadjoin @ X2 @ emptyset ) )
=> ( X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.LPAaOweVIv/DTF2THF_6365.p',uniqinunit) ).
thf(f195,plain,
( $true
= ( in @ sK1 @ ( setadjoin @ sK0 @ emptyset ) ) ),
inference(cnf_transformation,[status(thm)],[f146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU528^1 : TPTP v9.2.1. Released v3.7.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n003.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:25:40 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SEU528^1 : TPTP v9.2.1. Released v3.7.0.
% 0.20/0.46 % Domain : Set Theory
% 0.20/0.46 % Problem : Preliminary Notions - Equality Laws
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English : (! x:i.! y:i.~(x = y) -> ~(in y (setadjoin x emptyset)))
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.20/0.46 % Source : [Bro08]
% 0.20/0.46 % Names : ZFC030g [Bro08]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.67 v3.7.0
% 0.20/0.46 % Syntax : Number of formulae : 103 ( 47 unt; 55 typ; 47 def)
% 0.20/0.46 % Number of atoms : 263 ( 62 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 46 ( 5 avg)
% 0.20/0.46 % Number of connectives : 429 ( 9 ~; 4 |; 19 &; 279 @)
% 0.20/0.46 % ( 8 <=>; 110 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 52 ( 2 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 58 ( 55 usr; 48 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 142 ( 16 ^; 108 !; 18 ?; 142 :)
% 0.20/0.46 % SPC : TH0_THM_EQU_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : http://mathgate.info/detsetitem.php?id=437
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(in_type,type,
% 0.20/0.46 in: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu_type,type,
% 0.20/0.46 exu: ( $i > $o ) > $o ).
% 0.20/0.46
% 0.20/0.46 thf(exu,definition,
% 0.20/0.46 ( exu
% 0.20/0.46 = ( ^ [Xphi: $i > $o] :
% 0.20/0.46 ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setextAx_type,type,
% 0.20/0.46 setextAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setextAx,definition,
% 0.20/0.46 ( setextAx
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 <=> ( in @ Xx @ B ) )
% 0.20/0.46 => ( A = B ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyset_type,type,
% 0.20/0.46 emptyset: $i ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetAx_type,type,
% 0.20/0.46 emptysetAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetAx,definition,
% 0.20/0.46 ( emptysetAx
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoin_type,type,
% 0.20/0.46 setadjoin: $i > $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinAx_type,type,
% 0.20/0.46 setadjoinAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinAx,definition,
% 0.20/0.46 ( setadjoinAx
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 <=> ( ( Xy = Xx )
% 0.20/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powerset_type,type,
% 0.20/0.46 powerset: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(powersetAx_type,type,
% 0.20/0.46 powersetAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetAx,definition,
% 0.20/0.46 ( powersetAx
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 <=> ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunion_type,type,
% 0.20/0.46 setunion: $i > $i ).
% 0.20/0.46
% 0.20/0.46 thf(setunionAx_type,type,
% 0.20/0.46 setunionAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionAx,definition,
% 0.20/0.46 ( setunionAx
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 <=> ? [B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omega_type,type,
% 0.20/0.46 omega: $i ).
% 0.20/0.46
% 0.20/0.46 thf(omega0Ax_type,type,
% 0.20/0.46 omega0Ax: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omega0Ax,definition,
% 0.20/0.46 ( omega0Ax
% 0.20/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omegaSAx_type,type,
% 0.20/0.46 omegaSAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omegaSAx,definition,
% 0.20/0.46 ( omegaSAx
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ omega )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(omegaIndAx_type,type,
% 0.20/0.46 omegaIndAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(omegaIndAx,definition,
% 0.20/0.46 ( omegaIndAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( ( in @ emptyset @ A )
% 0.20/0.46 & ! [Xx: $i] :
% 0.20/0.46 ( ( ( in @ Xx @ omega )
% 0.20/0.46 & ( in @ Xx @ A ) )
% 0.20/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ omega )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(replAx_type,type,
% 0.20/0.46 replAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(replAx,definition,
% 0.20/0.46 ( replAx
% 0.20/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( exu
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.20/0.46 => ? [B: $i] :
% 0.20/0.46 ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 <=> ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(foundationAx_type,type,
% 0.20/0.46 foundationAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(foundationAx,definition,
% 0.20/0.46 ( foundationAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.46 => ? [B: $i] :
% 0.20/0.46 ( ( in @ B @ A )
% 0.20/0.46 & ~ ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(wellorderingAx_type,type,
% 0.20/0.46 wellorderingAx: $o ).
% 0.20/0.46
% 0.20/0.46 thf(wellorderingAx,definition,
% 0.20/0.46 ( wellorderingAx
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ? [B: $i] :
% 0.20/0.46 ( ! [C: $i] :
% 0.20/0.46 ( ( in @ C @ B )
% 0.20/0.46 => ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ A ) ) )
% 0.20/0.46 & ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( ( in @ Xx @ A )
% 0.20/0.46 & ( in @ Xy @ A ) )
% 0.20/0.46 => ( ! [C: $i] :
% 0.20/0.46 ( ( in @ C @ B )
% 0.20/0.46 => ( ( in @ Xx @ C )
% 0.20/0.46 <=> ( in @ Xy @ C ) ) )
% 0.20/0.46 => ( Xx = Xy ) ) )
% 0.20/0.46 & ! [C: $i,D: $i] :
% 0.20/0.46 ( ( ( in @ C @ B )
% 0.20/0.46 & ( in @ D @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ D ) )
% 0.20/0.46 | ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ D )
% 0.20/0.46 => ( in @ Xx @ C ) ) ) )
% 0.20/0.46 & ! [C: $i] :
% 0.20/0.46 ( ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ C )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.20/0.46 => ? [D: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ D @ B )
% 0.20/0.46 & ( in @ Xx @ C )
% 0.20/0.46 & ~ ? [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ D )
% 0.20/0.46 & ( in @ Xy @ C ) )
% 0.20/0.46 & ! [E: $i] :
% 0.20/0.46 ( ( in @ E @ B )
% 0.20/0.46 => ( ! [Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ E )
% 0.20/0.46 => ( in @ Xy @ D ) )
% 0.20/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(descr_type,type,
% 0.20/0.46 descr: ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(descrp_type,type,
% 0.20/0.46 descrp: $o ).
% 0.20/0.46
% 0.20/0.46 thf(descrp,definition,
% 0.20/0.46 ( descrp
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ( Xphi
% 0.20/0.46 @ ( descr
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstr_type,type,
% 0.20/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrI_type,type,
% 0.20/0.46 dsetconstrI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrI,definition,
% 0.20/0.46 ( dsetconstrI
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrEL_type,type,
% 0.20/0.46 dsetconstrEL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrEL,definition,
% 0.20/0.46 ( dsetconstrEL
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrER_type,type,
% 0.20/0.46 dsetconstrER: $o ).
% 0.20/0.46
% 0.20/0.46 thf(dsetconstrER,definition,
% 0.20/0.46 ( dsetconstrER
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE1_type,type,
% 0.20/0.46 exuE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE1,definition,
% 0.20/0.46 ( exuE1
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( Xphi @ Xx )
% 0.20/0.46 & ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set_type,type,
% 0.20/0.46 prop2set: $o > $i ).
% 0.20/0.46
% 0.20/0.46 thf(prop2set,definition,
% 0.20/0.46 ( prop2set
% 0.20/0.46 = ( ^ [Xphi: $o] :
% 0.20/0.46 ( dsetconstr @ ( powerset @ emptyset )
% 0.20/0.46 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setE_type,type,
% 0.20/0.46 prop2setE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(prop2setE,definition,
% 0.20/0.46 ( prop2setE
% 0.20/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetE_type,type,
% 0.20/0.46 emptysetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetE,definition,
% 0.20/0.46 ( emptysetE
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetimpfalse_type,type,
% 0.20/0.46 emptysetimpfalse: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptysetimpfalse,definition,
% 0.20/0.46 ( emptysetimpfalse
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ emptyset )
% 0.20/0.46 => $false ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notinemptyset_type,type,
% 0.20/0.46 notinemptyset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(notinemptyset,definition,
% 0.20/0.46 ( notinemptyset
% 0.20/0.46 = ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3e_type,type,
% 0.20/0.46 exuE3e: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE3e,definition,
% 0.20/0.46 ( exuE3e
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setext_type,type,
% 0.20/0.46 setext: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setext,definition,
% 0.20/0.46 ( setext
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ B ) )
% 0.20/0.46 => ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 => ( A = B ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyI_type,type,
% 0.20/0.46 emptyI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyI,definition,
% 0.20/0.46 ( emptyI
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ A )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(noeltsimpempty_type,type,
% 0.20/0.46 noeltsimpempty: $o ).
% 0.20/0.46
% 0.20/0.46 thf(noeltsimpempty,definition,
% 0.20/0.46 ( noeltsimpempty
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ~ ( in @ Xx @ A )
% 0.20/0.46 => ( A = emptyset ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setbeta_type,type,
% 0.20/0.46 setbeta: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setbeta,definition,
% 0.20/0.46 ( setbeta
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( in @ Xx
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.20/0.46 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonempty_type,type,
% 0.20/0.46 nonempty: $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonempty,definition,
% 0.20/0.46 ( nonempty
% 0.20/0.46 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyE1_type,type,
% 0.20/0.46 nonemptyE1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyE1,definition,
% 0.20/0.46 ( nonemptyE1
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( nonempty @ A )
% 0.20/0.46 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI_type,type,
% 0.20/0.46 nonemptyI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI,definition,
% 0.20/0.46 ( nonemptyI
% 0.20/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( ( Xphi @ Xx )
% 0.20/0.46 => ( nonempty
% 0.20/0.46 @ ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI1_type,type,
% 0.20/0.46 nonemptyI1: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyI1,definition,
% 0.20/0.46 ( nonemptyI1
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.20/0.46 => ( nonempty @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL_type,type,
% 0.20/0.46 setadjoinIL: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIL,definition,
% 0.20/0.46 ( setadjoinIL
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinunitempty_type,type,
% 0.20/0.46 emptyinunitempty: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinunitempty,definition,
% 0.20/0.46 ( emptyinunitempty
% 0.20/0.46 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIR_type,type,
% 0.20/0.46 setadjoinIR: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinIR,definition,
% 0.20/0.46 ( setadjoinIR
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ A )
% 0.20/0.46 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinE_type,type,
% 0.20/0.46 setadjoinE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinE,definition,
% 0.20/0.46 ( setadjoinE
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ( ( Xy = Xx )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => ( ( ( in @ Xy @ A )
% 0.20/0.46 => Xphi )
% 0.20/0.46 => Xphi ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinOr_type,type,
% 0.20/0.46 setadjoinOr: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setadjoinOr,definition,
% 0.20/0.46 ( setadjoinOr
% 0.20/0.46 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.20/0.46 => ( ( Xy = Xx )
% 0.20/0.46 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setoftrueEq_type,type,
% 0.20/0.46 setoftrueEq: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setoftrueEq,definition,
% 0.20/0.46 ( setoftrueEq
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( dsetconstr @ A
% 0.20/0.46 @ ^ [Xx: $i] : $true )
% 0.20/0.46 = A ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI_type,type,
% 0.20/0.46 powersetI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetI,definition,
% 0.20/0.46 ( powersetI
% 0.20/0.46 = ( ! [A: $i,B: $i] :
% 0.20/0.46 ( ! [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) )
% 0.20/0.46 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinPowerset_type,type,
% 0.20/0.46 emptyinPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyinPowerset,definition,
% 0.20/0.46 ( emptyinPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(emptyInPowerset_type,type,
% 0.20/0.46 emptyInPowerset: $o ).
% 0.20/0.46
% 0.20/0.46 thf(emptyInPowerset,definition,
% 0.20/0.46 ( emptyInPowerset
% 0.20/0.46 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE_type,type,
% 0.20/0.46 powersetE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(powersetE,definition,
% 0.20/0.46 ( powersetE
% 0.20/0.46 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ B @ ( powerset @ A ) )
% 0.20/0.46 => ( ( in @ Xx @ B )
% 0.20/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionI_type,type,
% 0.20/0.46 setunionI: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionI,definition,
% 0.20/0.46 ( setunionI
% 0.20/0.46 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( ( in @ B @ A )
% 0.20/0.46 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE_type,type,
% 0.20/0.46 setunionE: $o ).
% 0.20/0.46
% 0.20/0.46 thf(setunionE,definition,
% 0.20/0.46 ( setunionE
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setunion @ A ) )
% 0.20/0.46 => ! [Xphi: $o] :
% 0.20/0.46 ( ! [B: $i] :
% 0.20/0.46 ( ( in @ Xx @ B )
% 0.20/0.46 => ( ( in @ B @ A )
% 0.20/0.46 => Xphi ) )
% 0.20/0.46 => Xphi ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(subPowSU_type,type,
% 0.20/0.46 subPowSU: $o ).
% 0.20/0.46
% 0.20/0.46 thf(subPowSU,definition,
% 0.20/0.46 ( subPowSU
% 0.20/0.46 = ( ! [A: $i,Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(exuE2_type,type,
% 0.20/0.46 exuE2: $o ).
% 0.20/0.46
% 0.20/0.46 thf(exuE2,definition,
% 0.20/0.46 ( exuE2
% 0.20/0.46 = ( ! [Xphi: $i > $o] :
% 0.20/0.46 ( ( exu
% 0.20/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ! [Xy: $i] :
% 0.20/0.46 ( ( Xphi @ Xy )
% 0.20/0.46 <=> ( Xy = Xx ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyImpWitness_type,type,
% 0.20/0.46 nonemptyImpWitness: $o ).
% 0.20/0.46
% 0.20/0.46 thf(nonemptyImpWitness,definition,
% 0.20/0.46 ( nonemptyImpWitness
% 0.20/0.46 = ( ! [A: $i] :
% 0.20/0.46 ( ( nonempty @ A )
% 0.20/0.46 => ? [Xx: $i] :
% 0.20/0.46 ( ( in @ Xx @ A )
% 0.20/0.46 & $true ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit_type,type,
% 0.20/0.46 uniqinunit: $o ).
% 0.20/0.46
% 0.20/0.46 thf(uniqinunit,definition,
% 0.20/0.46 ( uniqinunit
% 0.20/0.46 = ( ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 0.20/0.46 => ( Xx = Xy ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 thf(notinsingleton,conjecture,
% 0.20/0.46 ( setextAx
% 0.20/0.46 => ( emptysetAx
% 0.20/0.46 => ( setadjoinAx
% 0.20/0.46 => ( powersetAx
% 0.20/0.46 => ( setunionAx
% 0.20/0.46 => ( omega0Ax
% 0.20/0.46 => ( omegaSAx
% 0.20/0.46 => ( omegaIndAx
% 0.20/0.46 => ( replAx
% 0.20/0.46 => ( foundationAx
% 0.20/0.46 => ( wellorderingAx
% 0.20/0.46 => ( descrp
% 0.20/0.46 => ( dsetconstrI
% 0.20/0.46 => ( dsetconstrEL
% 0.20/0.46 => ( dsetconstrER
% 0.20/0.46 => ( exuE1
% 0.20/0.46 => ( prop2setE
% 0.20/0.46 => ( emptysetE
% 0.20/0.46 => ( emptysetimpfalse
% 0.20/0.46 => ( notinemptyset
% 0.20/0.46 => ( exuE3e
% 0.20/0.46 => ( setext
% 0.20/0.46 => ( emptyI
% 0.20/0.46 => ( noeltsimpempty
% 0.20/0.46 => ( setbeta
% 0.20/0.46 => ( nonemptyE1
% 0.20/0.46 => ( nonemptyI
% 0.20/0.46 => ( nonemptyI1
% 0.20/0.46 => ( setadjoinIL
% 0.20/0.46 => ( emptyinunitempty
% 0.20/0.46 => ( setadjoinIR
% 0.20/0.46 => ( setadjoinE
% 0.20/0.46 => ( setadjoinOr
% 0.20/0.46 => ( setoftrueEq
% 0.20/0.46 => ( powersetI
% 0.20/0.46 => ( emptyinPowerset
% 0.20/0.46 => ( emptyInPowerset
% 0.20/0.46 => ( powersetE
% 0.20/0.46 => ( setunionI
% 0.20/0.46 => ( setunionE
% 0.20/0.46 => ( subPowSU
% 0.20/0.46 => ( exuE2
% 0.20/0.46 => ( nonemptyImpWitness
% 0.20/0.46 => ( uniqinunit
% 0.20/0.46 => ! [Xx: $i,Xy: $i] :
% 0.20/0.46 ( ( Xx != Xy )
% 0.20/0.46 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 2.06/1.51 ---- Embedded in THF ---
% 2.06/1.51 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 2.06/1.51 %%% Generated on Tue Feb 24 12:25:41 EST 2026
% 2.06/1.51 %%% using '$$dhol' embedding, version 1.3.0.
% 2.06/1.51 %%% Logic specification used:
% 2.06/1.51 %%% thf(spec, logic, $$dhol).
% 2.06/1.51
% 2.06/1.51 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.LPAaOweVIv/DTF2DTF6365.p
% See solution above
% 2.06/1.51 ------------------------
% 2.06/1.52 ---- Cleaned THF ---
% 2.06/1.52 thf(in_type,type,
% 2.06/1.52 in: $i > $i > $o ).
% 2.06/1.52
% 2.06/1.52 thf(exu_type,type,
% 2.06/1.52 exu: ( $i > $o ) > $o ).
% 2.06/1.52
% 2.06/1.52 thf(exu,definition,
% 2.06/1.52 ( exu
% 2.06/1.52 = ( ^ [Xphi: $i > $o] :
% 2.06/1.52 ? [Xx: $i] :
% 2.06/1.52 ( ( Xphi @ Xx )
% 2.06/1.52 & ! [Xy: $i] :
% 2.06/1.52 ( ( Xphi @ Xy )
% 2.06/1.52 => ( Xx = Xy ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setextAx_type,type,
% 2.06/1.52 setextAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setextAx,definition,
% 2.06/1.52 ( setextAx
% 2.06/1.52 = ( ! [A: $i,B: $i] :
% 2.06/1.52 ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ A )
% 2.06/1.52 <=> ( in @ Xx @ B ) )
% 2.06/1.52 => ( A = B ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(emptyset_type,type,
% 2.06/1.52 emptyset: $i ).
% 2.06/1.52
% 2.06/1.52 thf(emptysetAx_type,type,
% 2.06/1.52 emptysetAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(emptysetAx,definition,
% 2.06/1.52 ( emptysetAx
% 2.06/1.52 = ( ! [Xx: $i] :
% 2.06/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoin_type,type,
% 2.06/1.52 setadjoin: $i > $i > $i ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinAx_type,type,
% 2.06/1.52 setadjoinAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinAx,definition,
% 2.06/1.52 ( setadjoinAx
% 2.06/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.06/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.06/1.52 <=> ( ( Xy = Xx )
% 2.06/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(powerset_type,type,
% 2.06/1.52 powerset: $i > $i ).
% 2.06/1.52
% 2.06/1.52 thf(powersetAx_type,type,
% 2.06/1.52 powersetAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(powersetAx,definition,
% 2.06/1.52 ( powersetAx
% 2.06/1.52 = ( ! [A: $i,B: $i] :
% 2.06/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.06/1.52 <=> ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ B )
% 2.06/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setunion_type,type,
% 2.06/1.52 setunion: $i > $i ).
% 2.06/1.52
% 2.06/1.52 thf(setunionAx_type,type,
% 2.06/1.52 setunionAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setunionAx,definition,
% 2.06/1.52 ( setunionAx
% 2.06/1.52 = ( ! [A: $i,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.06/1.52 <=> ? [B: $i] :
% 2.06/1.52 ( ( in @ Xx @ B )
% 2.06/1.52 & ( in @ B @ A ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(omega_type,type,
% 2.06/1.52 omega: $i ).
% 2.06/1.52
% 2.06/1.52 thf(omega0Ax_type,type,
% 2.06/1.52 omega0Ax: $o ).
% 2.06/1.52
% 2.06/1.52 thf(omega0Ax,definition,
% 2.06/1.52 ( omega0Ax
% 2.06/1.52 = ( in @ emptyset @ omega ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(omegaSAx_type,type,
% 2.06/1.52 omegaSAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(omegaSAx,definition,
% 2.06/1.52 ( omegaSAx
% 2.06/1.52 = ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ omega )
% 2.06/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(omegaIndAx_type,type,
% 2.06/1.52 omegaIndAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(omegaIndAx,definition,
% 2.06/1.52 ( omegaIndAx
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ( ( ( in @ emptyset @ A )
% 2.06/1.52 & ! [Xx: $i] :
% 2.06/1.52 ( ( ( in @ Xx @ omega )
% 2.06/1.52 & ( in @ Xx @ A ) )
% 2.06/1.52 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 2.06/1.52 => ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ omega )
% 2.06/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(replAx_type,type,
% 2.06/1.52 replAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(replAx,definition,
% 2.06/1.52 ( replAx
% 2.06/1.52 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 2.06/1.52 ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ A )
% 2.06/1.52 => ( exu
% 2.06/1.52 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 2.06/1.52 => ? [B: $i] :
% 2.06/1.52 ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ B )
% 2.06/1.52 <=> ? [Xy: $i] :
% 2.06/1.52 ( ( in @ Xy @ A )
% 2.06/1.52 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(foundationAx_type,type,
% 2.06/1.52 foundationAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(foundationAx,definition,
% 2.06/1.52 ( foundationAx
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.06/1.52 => ? [B: $i] :
% 2.06/1.52 ( ( in @ B @ A )
% 2.06/1.52 & ~ ? [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ B )
% 2.06/1.52 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(wellorderingAx_type,type,
% 2.06/1.52 wellorderingAx: $o ).
% 2.06/1.52
% 2.06/1.52 thf(wellorderingAx,definition,
% 2.06/1.52 ( wellorderingAx
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ? [B: $i] :
% 2.06/1.52 ( ! [C: $i] :
% 2.06/1.52 ( ( in @ C @ B )
% 2.06/1.52 => ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ C )
% 2.06/1.52 => ( in @ Xx @ A ) ) )
% 2.06/1.52 & ! [Xx: $i,Xy: $i] :
% 2.06/1.52 ( ( ( in @ Xx @ A )
% 2.06/1.52 & ( in @ Xy @ A ) )
% 2.06/1.52 => ( ! [C: $i] :
% 2.06/1.52 ( ( in @ C @ B )
% 2.06/1.52 => ( ( in @ Xx @ C )
% 2.06/1.52 <=> ( in @ Xy @ C ) ) )
% 2.06/1.52 => ( Xx = Xy ) ) )
% 2.06/1.52 & ! [C: $i,D: $i] :
% 2.06/1.52 ( ( ( in @ C @ B )
% 2.06/1.52 & ( in @ D @ B ) )
% 2.06/1.52 => ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ C )
% 2.06/1.52 => ( in @ Xx @ D ) )
% 2.06/1.52 | ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ D )
% 2.06/1.52 => ( in @ Xx @ C ) ) ) )
% 2.06/1.52 & ! [C: $i] :
% 2.06/1.52 ( ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ C )
% 2.06/1.52 => ( in @ Xx @ A ) )
% 2.06/1.52 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 2.06/1.52 => ? [D: $i,Xx: $i] :
% 2.06/1.52 ( ( in @ D @ B )
% 2.06/1.52 & ( in @ Xx @ C )
% 2.06/1.52 & ~ ? [Xy: $i] :
% 2.06/1.52 ( ( in @ Xy @ D )
% 2.06/1.52 & ( in @ Xy @ C ) )
% 2.06/1.52 & ! [E: $i] :
% 2.06/1.52 ( ( in @ E @ B )
% 2.06/1.52 => ( ! [Xy: $i] :
% 2.06/1.52 ( ( in @ Xy @ E )
% 2.06/1.52 => ( in @ Xy @ D ) )
% 2.06/1.52 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(descr_type,type,
% 2.06/1.52 descr: ( $i > $o ) > $i ).
% 2.06/1.52
% 2.06/1.52 thf(descrp_type,type,
% 2.06/1.52 descrp: $o ).
% 2.06/1.52
% 2.06/1.52 thf(descrp,definition,
% 2.06/1.52 ( descrp
% 2.06/1.52 = ( ! [Xphi: $i > $o] :
% 2.06/1.52 ( ( exu
% 2.06/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.52 => ( Xphi
% 2.06/1.52 @ ( descr
% 2.06/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(dsetconstr_type,type,
% 2.06/1.52 dsetconstr: $i > ( $i > $o ) > $i ).
% 2.06/1.52
% 2.06/1.52 thf(dsetconstrI_type,type,
% 2.06/1.52 dsetconstrI: $o ).
% 2.06/1.52
% 2.06/1.52 thf(dsetconstrI,definition,
% 2.06/1.52 ( dsetconstrI
% 2.06/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ A )
% 2.06/1.52 => ( ( Xphi @ Xx )
% 2.06/1.52 => ( in @ Xx
% 2.06/1.52 @ ( dsetconstr @ A
% 2.06/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(dsetconstrEL_type,type,
% 2.06/1.52 dsetconstrEL: $o ).
% 2.06/1.52
% 2.06/1.52 thf(dsetconstrEL,definition,
% 2.06/1.52 ( dsetconstrEL
% 2.06/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx
% 2.06/1.52 @ ( dsetconstr @ A
% 2.06/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.06/1.52 => ( in @ Xx @ A ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(dsetconstrER_type,type,
% 2.06/1.52 dsetconstrER: $o ).
% 2.06/1.52
% 2.06/1.52 thf(dsetconstrER,definition,
% 2.06/1.52 ( dsetconstrER
% 2.06/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx
% 2.06/1.52 @ ( dsetconstr @ A
% 2.06/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.06/1.52 => ( Xphi @ Xx ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(exuE1_type,type,
% 2.06/1.52 exuE1: $o ).
% 2.06/1.52
% 2.06/1.52 thf(exuE1,definition,
% 2.06/1.52 ( exuE1
% 2.06/1.52 = ( ! [Xphi: $i > $o] :
% 2.06/1.52 ( ( exu
% 2.06/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.52 => ? [Xx: $i] :
% 2.06/1.52 ( ( Xphi @ Xx )
% 2.06/1.52 & ! [Xy: $i] :
% 2.06/1.52 ( ( Xphi @ Xy )
% 2.06/1.52 => ( Xx = Xy ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(prop2set_type,type,
% 2.06/1.52 prop2set: $o > $i ).
% 2.06/1.52
% 2.06/1.52 thf(prop2set,definition,
% 2.06/1.52 ( prop2set
% 2.06/1.52 = ( ^ [Xphi: $o] :
% 2.06/1.52 ( dsetconstr @ ( powerset @ emptyset )
% 2.06/1.52 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(prop2setE_type,type,
% 2.06/1.52 prop2setE: $o ).
% 2.06/1.52
% 2.06/1.52 thf(prop2setE,definition,
% 2.06/1.52 ( prop2setE
% 2.06/1.52 = ( ! [Xphi: $o,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 2.06/1.52 => Xphi ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(emptysetE_type,type,
% 2.06/1.52 emptysetE: $o ).
% 2.06/1.52
% 2.06/1.52 thf(emptysetE,definition,
% 2.06/1.52 ( emptysetE
% 2.06/1.52 = ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ emptyset )
% 2.06/1.52 => ! [Xphi: $o] : Xphi ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(emptysetimpfalse_type,type,
% 2.06/1.52 emptysetimpfalse: $o ).
% 2.06/1.52
% 2.06/1.52 thf(emptysetimpfalse,definition,
% 2.06/1.52 ( emptysetimpfalse
% 2.06/1.52 = ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ emptyset )
% 2.06/1.52 => $false ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(notinemptyset_type,type,
% 2.06/1.52 notinemptyset: $o ).
% 2.06/1.52
% 2.06/1.52 thf(notinemptyset,definition,
% 2.06/1.52 ( notinemptyset
% 2.06/1.52 = ( ! [Xx: $i] :
% 2.06/1.52 ~ ( in @ Xx @ emptyset ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(exuE3e_type,type,
% 2.06/1.52 exuE3e: $o ).
% 2.06/1.52
% 2.06/1.52 thf(exuE3e,definition,
% 2.06/1.52 ( exuE3e
% 2.06/1.52 = ( ! [Xphi: $i > $o] :
% 2.06/1.52 ( ( exu
% 2.06/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.52 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setext_type,type,
% 2.06/1.52 setext: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setext,definition,
% 2.06/1.52 ( setext
% 2.06/1.52 = ( ! [A: $i,B: $i] :
% 2.06/1.52 ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ A )
% 2.06/1.52 => ( in @ Xx @ B ) )
% 2.06/1.52 => ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ B )
% 2.06/1.52 => ( in @ Xx @ A ) )
% 2.06/1.52 => ( A = B ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(emptyI_type,type,
% 2.06/1.52 emptyI: $o ).
% 2.06/1.52
% 2.06/1.52 thf(emptyI,definition,
% 2.06/1.52 ( emptyI
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ( ! [Xx: $i] :
% 2.06/1.52 ~ ( in @ Xx @ A )
% 2.06/1.52 => ( A = emptyset ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(noeltsimpempty_type,type,
% 2.06/1.52 noeltsimpempty: $o ).
% 2.06/1.52
% 2.06/1.52 thf(noeltsimpempty,definition,
% 2.06/1.52 ( noeltsimpempty
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ( ! [Xx: $i] :
% 2.06/1.52 ~ ( in @ Xx @ A )
% 2.06/1.52 => ( A = emptyset ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setbeta_type,type,
% 2.06/1.52 setbeta: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setbeta,definition,
% 2.06/1.52 ( setbeta
% 2.06/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ A )
% 2.06/1.52 => ( ( in @ Xx
% 2.06/1.52 @ ( dsetconstr @ A
% 2.06/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 2.06/1.52 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(nonempty_type,type,
% 2.06/1.52 nonempty: $i > $o ).
% 2.06/1.52
% 2.06/1.52 thf(nonempty,definition,
% 2.06/1.52 ( nonempty
% 2.06/1.52 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(nonemptyE1_type,type,
% 2.06/1.52 nonemptyE1: $o ).
% 2.06/1.52
% 2.06/1.52 thf(nonemptyE1,definition,
% 2.06/1.52 ( nonemptyE1
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ( ( nonempty @ A )
% 2.06/1.52 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(nonemptyI_type,type,
% 2.06/1.52 nonemptyI: $o ).
% 2.06/1.52
% 2.06/1.52 thf(nonemptyI,definition,
% 2.06/1.52 ( nonemptyI
% 2.06/1.52 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ A )
% 2.06/1.52 => ( ( Xphi @ Xx )
% 2.06/1.52 => ( nonempty
% 2.06/1.52 @ ( dsetconstr @ A
% 2.06/1.52 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(nonemptyI1_type,type,
% 2.06/1.52 nonemptyI1: $o ).
% 2.06/1.52
% 2.06/1.52 thf(nonemptyI1,definition,
% 2.06/1.52 ( nonemptyI1
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ( ? [Xx: $i] : ( in @ Xx @ A )
% 2.06/1.52 => ( nonempty @ A ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinIL_type,type,
% 2.06/1.52 setadjoinIL: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinIL,definition,
% 2.06/1.52 ( setadjoinIL
% 2.06/1.52 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(emptyinunitempty_type,type,
% 2.06/1.52 emptyinunitempty: $o ).
% 2.06/1.52
% 2.06/1.52 thf(emptyinunitempty,definition,
% 2.06/1.52 ( emptyinunitempty
% 2.06/1.52 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinIR_type,type,
% 2.06/1.52 setadjoinIR: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinIR,definition,
% 2.06/1.52 ( setadjoinIR
% 2.06/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.06/1.52 ( ( in @ Xy @ A )
% 2.06/1.52 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinE_type,type,
% 2.06/1.52 setadjoinE: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinE,definition,
% 2.06/1.52 ( setadjoinE
% 2.06/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.06/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.06/1.52 => ! [Xphi: $o] :
% 2.06/1.52 ( ( ( Xy = Xx )
% 2.06/1.52 => Xphi )
% 2.06/1.52 => ( ( ( in @ Xy @ A )
% 2.06/1.52 => Xphi )
% 2.06/1.52 => Xphi ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinOr_type,type,
% 2.06/1.52 setadjoinOr: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setadjoinOr,definition,
% 2.06/1.52 ( setadjoinOr
% 2.06/1.52 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 2.06/1.52 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 2.06/1.52 => ( ( Xy = Xx )
% 2.06/1.52 | ( in @ Xy @ A ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setoftrueEq_type,type,
% 2.06/1.52 setoftrueEq: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setoftrueEq,definition,
% 2.06/1.52 ( setoftrueEq
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ( ( dsetconstr @ A
% 2.06/1.52 @ ^ [Xx: $i] : $true )
% 2.06/1.52 = A ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(powersetI_type,type,
% 2.06/1.52 powersetI: $o ).
% 2.06/1.52
% 2.06/1.52 thf(powersetI,definition,
% 2.06/1.52 ( powersetI
% 2.06/1.52 = ( ! [A: $i,B: $i] :
% 2.06/1.52 ( ! [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ B )
% 2.06/1.52 => ( in @ Xx @ A ) )
% 2.06/1.52 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(emptyinPowerset_type,type,
% 2.06/1.52 emptyinPowerset: $o ).
% 2.06/1.52
% 2.06/1.52 thf(emptyinPowerset,definition,
% 2.06/1.52 ( emptyinPowerset
% 2.06/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(emptyInPowerset_type,type,
% 2.06/1.52 emptyInPowerset: $o ).
% 2.06/1.52
% 2.06/1.52 thf(emptyInPowerset,definition,
% 2.06/1.52 ( emptyInPowerset
% 2.06/1.52 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(powersetE_type,type,
% 2.06/1.52 powersetE: $o ).
% 2.06/1.52
% 2.06/1.52 thf(powersetE,definition,
% 2.06/1.52 ( powersetE
% 2.06/1.52 = ( ! [A: $i,B: $i,Xx: $i] :
% 2.06/1.52 ( ( in @ B @ ( powerset @ A ) )
% 2.06/1.52 => ( ( in @ Xx @ B )
% 2.06/1.52 => ( in @ Xx @ A ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setunionI_type,type,
% 2.06/1.52 setunionI: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setunionI,definition,
% 2.06/1.52 ( setunionI
% 2.06/1.52 = ( ! [A: $i,Xx: $i,B: $i] :
% 2.06/1.52 ( ( in @ Xx @ B )
% 2.06/1.52 => ( ( in @ B @ A )
% 2.06/1.52 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(setunionE_type,type,
% 2.06/1.52 setunionE: $o ).
% 2.06/1.52
% 2.06/1.52 thf(setunionE,definition,
% 2.06/1.52 ( setunionE
% 2.06/1.52 = ( ! [A: $i,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ ( setunion @ A ) )
% 2.06/1.52 => ! [Xphi: $o] :
% 2.06/1.52 ( ! [B: $i] :
% 2.06/1.52 ( ( in @ Xx @ B )
% 2.06/1.52 => ( ( in @ B @ A )
% 2.06/1.52 => Xphi ) )
% 2.06/1.52 => Xphi ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(subPowSU_type,type,
% 2.06/1.52 subPowSU: $o ).
% 2.06/1.52
% 2.06/1.52 thf(subPowSU,definition,
% 2.06/1.52 ( subPowSU
% 2.06/1.52 = ( ! [A: $i,Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ A )
% 2.06/1.52 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(exuE2_type,type,
% 2.06/1.52 exuE2: $o ).
% 2.06/1.52
% 2.06/1.52 thf(exuE2,definition,
% 2.06/1.52 ( exuE2
% 2.06/1.52 = ( ! [Xphi: $i > $o] :
% 2.06/1.52 ( ( exu
% 2.06/1.52 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 2.06/1.52 => ? [Xx: $i] :
% 2.06/1.52 ! [Xy: $i] :
% 2.06/1.52 ( ( Xphi @ Xy )
% 2.06/1.52 <=> ( Xy = Xx ) ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(nonemptyImpWitness_type,type,
% 2.06/1.52 nonemptyImpWitness: $o ).
% 2.06/1.52
% 2.06/1.52 thf(nonemptyImpWitness,definition,
% 2.06/1.52 ( nonemptyImpWitness
% 2.06/1.52 = ( ! [A: $i] :
% 2.06/1.52 ( ( nonempty @ A )
% 2.06/1.52 => ? [Xx: $i] :
% 2.06/1.52 ( ( in @ Xx @ A )
% 2.06/1.52 & $true ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(uniqinunit_type,type,
% 2.06/1.52 uniqinunit: $o ).
% 2.06/1.52
% 2.06/1.52 thf(uniqinunit,definition,
% 2.06/1.52 ( uniqinunit
% 2.06/1.52 = ( ! [Xx: $i,Xy: $i] :
% 2.06/1.52 ( ( in @ Xx @ ( setadjoin @ Xy @ emptyset ) )
% 2.06/1.52 => ( Xx = Xy ) ) ) ) ).
% 2.06/1.52
% 2.06/1.52 thf(notinsingleton,conjecture,
% 2.06/1.52 ( setextAx
% 2.06/1.52 => ( emptysetAx
% 2.06/1.52 => ( setadjoinAx
% 2.06/1.52 => ( powersetAx
% 2.06/1.53 => ( setunionAx
% 2.06/1.53 => ( omega0Ax
% 2.06/1.53 => ( omegaSAx
% 2.06/1.53 => ( omegaIndAx
% 2.06/1.53 => ( replAx
% 2.06/1.53 => ( foundationAx
% 2.06/1.53 => ( wellorderingAx
% 2.06/1.53 => ( descrp
% 2.06/1.53 => ( dsetconstrI
% 2.06/1.53 => ( dsetconstrEL
% 2.06/1.53 => ( dsetconstrER
% 2.06/1.53 => ( exuE1
% 2.06/1.53 => ( prop2setE
% 2.06/1.53 => ( emptysetE
% 2.06/1.53 => ( emptysetimpfalse
% 2.06/1.53 => ( notinemptyset
% 2.06/1.53 => ( exuE3e
% 2.06/1.53 => ( setext
% 2.06/1.53 => ( emptyI
% 2.06/1.53 => ( noeltsimpempty
% 2.06/1.53 => ( setbeta
% 2.06/1.53 => ( nonemptyE1
% 2.06/1.53 => ( nonemptyI
% 2.06/1.53 => ( nonemptyI1
% 2.06/1.53 => ( setadjoinIL
% 2.06/1.53 => ( emptyinunitempty
% 2.06/1.53 => ( setadjoinIR
% 2.06/1.53 => ( setadjoinE
% 2.06/1.53 => ( setadjoinOr
% 2.06/1.53 => ( setoftrueEq
% 2.06/1.53 => ( powersetI
% 2.06/1.53 => ( emptyinPowerset
% 2.06/1.53 => ( emptyInPowerset
% 2.06/1.53 => ( powersetE
% 2.06/1.53 => ( setunionI
% 2.06/1.53 => ( setunionE
% 2.06/1.53 => ( subPowSU
% 2.06/1.53 => ( exuE2
% 2.06/1.53 => ( nonemptyImpWitness
% 2.06/1.53 => ( uniqinunit
% 2.06/1.53 => ! [Xx: $i,Xy: $i] :
% 2.06/1.53 ( ( Xx != Xy )
% 2.06/1.53 => ~ ( in @ Xy @ ( setadjoin @ Xx @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 2.06/1.53 ------------------------
% 2.06/1.55 % (6464)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_6365 for (2999ds/4Mi)
% 2.06/1.55 % (6463)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_6365 for (2999ds/183Mi)
% 2.06/1.55 % (6465)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_6365 for (2999ds/27Mi)
% 2.06/1.55 % (6466)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_6365 for (2999ds/2Mi)
% 2.06/1.55 % (6467)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_6365 for (2999ds/2Mi)
% 2.06/1.55 % (6468)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_6365 for (2999ds/275Mi)
% 2.06/1.55 % (6469)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_6365 for (2999ds/18Mi)
% 2.06/1.55 % (6466)Instruction limit reached!
% 2.06/1.55 % (6466)------------------------------
% 2.06/1.55 % (6466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.55 % (6466)Termination reason: Unknown
% 2.06/1.55 % (6466)Termination phase: shuffling
% 2.06/1.55 % (6467)Instruction limit reached!
% 2.06/1.55 % (6467)------------------------------
% 2.06/1.55 % (6467)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.55 % (6467)Termination reason: Unknown
% 2.06/1.55 % (6467)Termination phase: shuffling
% 2.06/1.55
% 2.06/1.55 % (6467)Memory used [KB]: 1023
% 2.06/1.55 % (6467)Time elapsed: 0.003 s
% 2.06/1.55 % (6467)Instructions burned: 3 (million)
% 2.06/1.55 % (6467)------------------------------
% 2.06/1.55 % (6467)------------------------------
% 2.06/1.55
% 2.06/1.55 % (6466)Memory used [KB]: 1023
% 2.06/1.55 % (6466)Time elapsed: 0.003 s
% 2.06/1.55 % (6466)Instructions burned: 3 (million)
% 2.06/1.55 % (6466)------------------------------
% 2.06/1.55 % (6466)------------------------------
% 2.06/1.55 % (6464)Instruction limit reached!
% 2.06/1.55 % (6464)------------------------------
% 2.06/1.55 % (6464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.55 % (6464)Termination reason: Unknown
% 2.06/1.55 % (6464)Termination phase: shuffling
% 2.06/1.55
% 2.06/1.55 % (6464)Memory used [KB]: 1151
% 2.06/1.55 % (6464)Time elapsed: 0.004 s
% 2.06/1.55 % (6464)Instructions burned: 5 (million)
% 2.06/1.55 % (6464)------------------------------
% 2.06/1.55 % (6464)------------------------------
% 2.06/1.56 % (6469)Instruction limit reached!
% 2.06/1.56 % (6469)------------------------------
% 2.06/1.56 % (6469)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.56 % (6469)Termination reason: Unknown
% 2.06/1.56 % (6469)Termination phase: Property scanning
% 2.06/1.56
% 2.06/1.56 % (6469)Memory used [KB]: 1535
% 2.06/1.56 % (6469)Time elapsed: 0.011 s
% 2.06/1.56 % (6469)Instructions burned: 20 (million)
% 2.06/1.56 % (6469)------------------------------
% 2.06/1.56 % (6469)------------------------------
% 2.06/1.56 % (6465)Instruction limit reached!
% 2.06/1.56 % (6465)------------------------------
% 2.06/1.56 % (6465)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.56 % (6465)Termination reason: Unknown
% 2.06/1.56 % (6465)Termination phase: Saturation
% 2.06/1.56
% 2.06/1.56 % (6465)Memory used [KB]: 5756
% 2.06/1.56 % (6465)Time elapsed: 0.014 s
% 2.06/1.56 % (6465)Instructions burned: 27 (million)
% 2.06/1.56 % (6465)------------------------------
% 2.06/1.56 % (6465)------------------------------
% 2.06/1.56 % (6470)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_6365 for (2999ds/3Mi)
% 2.06/1.56 % (6471)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_6365 for (2999ds/37Mi)
% 2.06/1.56 % (6472)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_6365 for (2999ds/15Mi)
% 2.06/1.56 % (6470)Instruction limit reached!
% 2.06/1.56 % (6470)------------------------------
% 2.06/1.56 % (6470)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.56 % (6470)Termination reason: Unknown
% 2.06/1.56 % (6470)Termination phase: shuffling
% 2.06/1.56
% 2.06/1.56 % (6470)Memory used [KB]: 1023
% 2.06/1.56 % (6470)Time elapsed: 0.003 s
% 2.06/1.56 % (6470)Instructions burned: 4 (million)
% 2.06/1.56 % (6470)------------------------------
% 2.06/1.56 % (6470)------------------------------
% 2.06/1.57 % (6473)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_6365 for (2999ds/3Mi)
% 2.06/1.57 % (6472)Instruction limit reached!
% 2.06/1.57 % (6472)------------------------------
% 2.06/1.57 % (6472)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.57 % (6472)Termination reason: Unknown
% 2.06/1.57 % (6472)Termination phase: Preprocessing 3
% 2.06/1.57
% 2.06/1.57 % (6472)Memory used [KB]: 1407
% 2.06/1.57 % (6472)Time elapsed: 0.009 s
% 2.06/1.57 % (6472)Instructions burned: 16 (million)
% 2.06/1.57 % (6472)------------------------------
% 2.06/1.57 % (6472)------------------------------
% 2.06/1.57 % (6473)Instruction limit reached!
% 2.06/1.57 % (6473)------------------------------
% 2.06/1.57 % (6473)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.57 % (6473)Termination reason: Unknown
% 2.06/1.57 % (6473)Termination phase: shuffling
% 2.06/1.57
% 2.06/1.57 % (6473)Memory used [KB]: 1023
% 2.06/1.57 % (6473)Time elapsed: 0.003 s
% 2.06/1.57 % (6473)Instructions burned: 4 (million)
% 2.06/1.57 % (6473)------------------------------
% 2.06/1.57 % (6473)------------------------------
% 2.06/1.57 % (6474)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_6365 for (2999ds/1041Mi)
% 2.06/1.58 % (6471)Instruction limit reached!
% 2.06/1.58 % (6471)------------------------------
% 2.06/1.58 % (6471)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.58 % (6471)Termination reason: Unknown
% 2.06/1.58 % (6471)Termination phase: Saturation
% 2.06/1.58
% 2.06/1.58 % (6471)Memory used [KB]: 5884
% 2.06/1.58 % (6471)Time elapsed: 0.017 s
% 2.06/1.58 % (6471)Instructions burned: 37 (million)
% 2.06/1.58 % (6471)------------------------------
% 2.06/1.58 % (6471)------------------------------
% 2.06/1.58 % (6475)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_6365 for (2999ds/7Mi)
% 2.06/1.58 % (6463)First to succeed.
% 2.06/1.58 % (6475)Instruction limit reached!
% 2.06/1.58 % (6475)------------------------------
% 2.06/1.58 % (6475)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.58 % (6475)Termination reason: Unknown
% 2.06/1.58 % (6475)Termination phase: Property scanning
% 2.06/1.58
% 2.06/1.58 % (6475)Memory used [KB]: 1151
% 2.06/1.58 % (6475)Time elapsed: 0.005 s
% 2.06/1.58 % (6475)Instructions burned: 8 (million)
% 2.06/1.58 % (6475)------------------------------
% 2.06/1.58 % (6475)------------------------------
% 2.06/1.58 % (6463)Refutation found. Thanks to Tanya!
% 2.06/1.58 % SZS status Theorem for DTF2THF_6365
% 2.06/1.58 % SZS output start Proof for DTF2THF_6365
% 2.06/1.58 thf(func_def_0, type, in: $i > $i > $o).
% 2.06/1.58 thf(func_def_1, type, exu: ($i > $o) > $o).
% 2.06/1.58 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 2.06/1.58 thf(func_def_8, type, powerset: $i > $i).
% 2.06/1.58 thf(func_def_10, type, setunion: $i > $i).
% 2.06/1.58 thf(func_def_19, type, descr: ($i > $o) > $i).
% 2.06/1.58 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 2.06/1.58 thf(func_def_26, type, prop2set: $o > $i).
% 2.06/1.58 thf(func_def_36, type, nonempty: $i > $o).
% 2.06/1.58 thf(func_def_75, type, sK3: $i > $i).
% 2.06/1.58 thf(func_def_76, type, sK4: $i > $i > $i).
% 2.06/1.58 thf(func_def_77, type, sK5: $i > $i > $i).
% 2.06/1.58 thf(func_def_78, type, sK6: $i > $i).
% 2.06/1.58 thf(func_def_79, type, sK7: ($i > $o) > $i > $i).
% 2.06/1.58 thf(func_def_80, type, sK8: $i > $i).
% 2.06/1.58 thf(func_def_81, type, sK9: $i > $i).
% 2.06/1.58 thf(func_def_82, type, sK10: ($i > $o) > $i).
% 2.06/1.58 thf(func_def_83, type, sK11: ($i > $o) > $i > $i).
% 2.06/1.58 thf(func_def_84, type, sK12: $o > $i > $i > $i).
% 2.06/1.58 thf(func_def_85, type, sK13: ($i > $o) > $i > $i).
% 2.06/1.58 thf(func_def_86, type, sK14: ($i > $o) > $i).
% 2.06/1.58 thf(func_def_87, type, sK15: ($i > $o) > $i).
% 2.06/1.58 thf(func_def_88, type, sK16: $i > $i > $i).
% 2.06/1.58 thf(func_def_89, type, sK17: $i > $i > $i).
% 2.06/1.58 thf(func_def_90, type, sK18: $i > $i > $i).
% 2.06/1.58 thf(func_def_91, type, sK19: $i > ($i > $i > $o) > $i).
% 2.06/1.58 thf(func_def_92, type, sK20: $i > ($i > $i > $o) > $i).
% 2.06/1.58 thf(func_def_93, type, sK21: $i > $i > ($i > $i > $o) > $i).
% 2.06/1.58 thf(func_def_94, type, sK22: $i > $i > ($i > $i > $o) > $i).
% 2.06/1.58 thf(func_def_95, type, sK23: $i > $i > ($i > $i > $o) > $i).
% 2.06/1.58 thf(func_def_96, type, sK24: $i > $i > ($i > $i > $o) > $i).
% 2.06/1.58 thf(func_def_97, type, sK25: $i > $i).
% 2.06/1.58 thf(func_def_98, type, sK26: $i > $i).
% 2.06/1.58 thf(func_def_99, type, sK27: $i > $i).
% 2.06/1.58 thf(func_def_100, type, sK28: $i > $i > $i).
% 2.06/1.58 thf(func_def_101, type, sK29: $i > $i > $i).
% 2.06/1.58 thf(func_def_102, type, sK30: $i > $i > $i).
% 2.06/1.58 thf(func_def_103, type, sK31: $i > $i > $i).
% 2.06/1.58 thf(func_def_104, type, sK32: $i > $i > $i > $i).
% 2.06/1.58 thf(func_def_105, type, sK33: $i > $i > $i).
% 2.06/1.58 thf(func_def_106, type, sK34: $i > $i > $i).
% 2.06/1.58 thf(func_def_107, type, ph35: !>[X0: $tType]:(X0)).
% 2.06/1.59 thf(f898,plain,(
% 2.06/1.59 $false),
% 2.06/1.59 inference(subsumption_resolution,[status(thm)],[f895,f194])).
% 2.06/1.59 thf(f194,plain,(
% 2.06/1.59 (sK1 != sK0)),
% 2.06/1.59 inference(cnf_transformation,[status(thm)],[f146])).
% 2.06/1.59 thf(f146,plain,(
% 2.06/1.59 (notinemptyset = $true) & (wellorderingAx = $true) & (setextAx = $true) & (powersetE = $true) & (descrp = $true) & (noeltsimpempty = $true) & (powersetAx = $true) & (prop2setE = $true) & (exuE2 = $true) & (omegaSAx = $true) & (dsetconstrEL = $true) & (setadjoinOr = $true) & (dsetconstrI = $true) & (setunionE = $true) & (powersetI = $true) & (($true = (in @ sK1 @ (setadjoin @ sK0 @ emptyset))) & (sK1 != sK0)) & (omegaIndAx = $true) & (exuE3e = $true) & (emptyinunitempty = $true) & (omega0Ax = $true) & (replAx = $true) & (nonemptyI1 = $true) & (uniqinunit = $true) & (emptyinPowerset = $true) & (nonemptyE1 = $true) & (setadjoinIR = $true) & (setadjoinIL = $true) & (emptysetE = $true) & (emptysetimpfalse = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (setext = $true) & (emptysetAx = $true) & (setbeta = $true) & (setadjoinE = $true) & (nonemptyI = $true) & (setoftrueEq = $true) & (foundationAx = $true) & (setadjoinAx = $true) & (emptyInPowerset = $true) & (setunionAx = $true) & (emptyI = $true) & (setunionI = $true) & (subPowSU = $true) & (nonemptyImpWitness = $true)),
% 2.06/1.59 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f144,f145])).
% 2.06/1.59 thf(f145,plain,(
% 2.06/1.59 ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))) & (X0 != X1)) => (($true = (in @ sK1 @ (setadjoin @ sK0 @ emptyset))) & (sK1 != sK0))),
% 2.06/1.59 introduced(definition,[],[choice_axiom])).
% 2.06/1.59 thf(f144,plain,(
% 2.06/1.59 (notinemptyset = $true) & (wellorderingAx = $true) & (setextAx = $true) & (powersetE = $true) & (descrp = $true) & (noeltsimpempty = $true) & (powersetAx = $true) & (prop2setE = $true) & (exuE2 = $true) & (omegaSAx = $true) & (dsetconstrEL = $true) & (setadjoinOr = $true) & (dsetconstrI = $true) & (setunionE = $true) & (powersetI = $true) & ? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))) & (X0 != X1)) & (omegaIndAx = $true) & (exuE3e = $true) & (emptyinunitempty = $true) & (omega0Ax = $true) & (replAx = $true) & (nonemptyI1 = $true) & (uniqinunit = $true) & (emptyinPowerset = $true) & (nonemptyE1 = $true) & (setadjoinIR = $true) & (setadjoinIL = $true) & (emptysetE = $true) & (emptysetimpfalse = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (setext = $true) & (emptysetAx = $true) & (setbeta = $true) & (setadjoinE = $true) & (nonemptyI = $true) & (setoftrueEq = $true) & (foundationAx = $true) & (setadjoinAx = $true) & (emptyInPowerset = $true) & (setunionAx = $true) & (emptyI = $true) & (setunionI = $true) & (subPowSU = $true) & (nonemptyImpWitness = $true)),
% 2.06/1.59 inference(flattening,[status(thm)],[f143])).
% 2.06/1.59 thf(f143,plain,(
% 2.06/1.59 (((((((((((((((((((((((((((((((((((((((((((? [X0 : $i,X1 : $i] : (($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))) & (X0 != X1)) & (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)),
% 2.06/1.59 inference(ennf_transformation,[status(thm)],[f142])).
% 2.06/1.59 thf(f142,plain,(
% 2.06/1.59 ~((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) => ! [X0 : $i,X1 : $i] : ((X0 != X1) => ($true != (in @ X1 @ (setadjoin @ X0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.06/1.59 inference(flattening,[status(thm)],[f129])).
% 2.06/1.59 thf(f129,plain,(
% 2.06/1.59 ~((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) => ! [X0 : $i,X1 : $i] : ((X0 != X1) => ~($true = (in @ X1 @ (setadjoin @ X0 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))))),
% 2.06/1.59 inference(fool_elimination,[status(thm)],[f128])).
% 2.06/1.59 thf(f128,plain,(
% 2.06/1.59 ~(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 => ! [X0 : $i,X1 : $i] : ((X0 != X1) => ~(in @ X1 @ (setadjoin @ X0 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))),
% 2.06/1.59 inference(rectify,[status(thm)],[f49])).
% 2.06/1.59 thf(f49,negated_conjecture,(
% 2.06/1.59 ~(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 => ! [X1 : $i,X2 : $i] : ((X1 != X2) => ~(in @ X2 @ (setadjoin @ X1 @ emptyset)))))))))))))))))))))))))))))))))))))))))))))))),
% 2.06/1.59 inference(negated_conjecture,[status(cth)],[f48])).
% 2.06/1.59 thf(f48,conjecture,(
% 2.06/1.59 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 => ! [X1 : $i,X2 : $i] : ((X1 != X2) => ~(in @ X2 @ (setadjoin @ X1 @ emptyset))))))))))))))))))))))))))))))))))))))))))))))),
% 2.06/1.59 file('/export/starexec/sandbox/tmp/tmp.LPAaOweVIv/DTF2THF_6365.p',notinsingleton)).
% 2.06/1.59 thf(f895,plain,(
% 2.06/1.59 (sK1 = sK0)),
% 2.06/1.59 inference(trivial_inequality_removal,[status(thm)],[f886])).
% 2.06/1.59 thf(f886,plain,(
% 2.06/1.59 (sK1 = sK0) | ($true = $false)),
% 2.06/1.59 inference(superposition,[status(thm)],[f195,f455])).
% 2.06/1.59 thf(f455,plain,(
% 2.06/1.59 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false) | (X1 = X2)) )),
% 2.06/1.59 inference(equality_proxy_clausification,[status(thm)],[f454])).
% 2.06/1.59 thf(f454,plain,(
% 2.06/1.59 ( ! [X2 : $i,X1 : $i] : (((in @ X2 @ (setadjoin @ X1 @ emptyset)) = $false) | ((X2 = X1) = $true)) )),
% 2.06/1.59 inference(binary_proxy_clausification,[status(thm)],[f453])).
% 2.06/1.59 thf(f453,plain,(
% 2.06/1.59 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X2 @ (setadjoin @ X1 @ emptyset)) => (X2 = X1)))) )),
% 2.06/1.59 inference(beta_eta_normalization,[status(thm)],[f452])).
% 2.06/1.59 thf(f452,plain,(
% 2.06/1.59 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1))) @ X2))) )),
% 2.06/1.59 inference(pi_clausification,[status(thm)],[f451])).
% 2.06/1.59 thf(f451,plain,(
% 2.06/1.59 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ emptyset)) => (Y0 = X1)))))) )),
% 2.06/1.59 inference(beta_eta_normalization,[status(thm)],[f450])).
% 2.06/1.59 thf(f450,plain,(
% 2.06/1.59 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0))))) @ X1))) )),
% 2.06/1.59 inference(pi_clausification,[status(thm)],[f282])).
% 2.06/1.59 thf(f282,plain,(
% 2.06/1.59 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 2.06/1.59 inference(definition_unfolding,[status(thm)],[f231,f187])).
% 2.06/1.59 thf(f187,plain,(
% 2.06/1.59 (uniqinunit = $true)),
% 2.06/1.59 inference(cnf_transformation,[status(thm)],[f146])).
% 2.06/1.59 thf(f231,plain,(
% 2.06/1.59 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 2.06/1.59 inference(cnf_transformation,[status(thm)],[f87])).
% 2.06/1.59 thf(f87,plain,(
% 2.06/1.59 (uniqinunit = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ Y0 @ emptyset)) => (Y1 = Y0)))))))),
% 2.06/1.59 inference(fool_elimination,[status(thm)],[f86])).
% 2.06/1.59 thf(f86,plain,(
% 2.06/1.59 (uniqinunit = ! [X0 : $i,X1 : $i] : ((in @ X0 @ (setadjoin @ X1 @ emptyset)) => (X0 = X1)))),
% 2.06/1.59 inference(rectify,[status(thm)],[f47])).
% 2.06/1.59 thf(f47,axiom,(
% 2.06/1.59 (uniqinunit = ! [X1 : $i,X2 : $i] : ((in @ X1 @ (setadjoin @ X2 @ emptyset)) => (X1 = X2)))),
% 2.06/1.59 file('/export/starexec/sandbox/tmp/tmp.LPAaOweVIv/DTF2THF_6365.p',uniqinunit)).
% 2.06/1.59 thf(f195,plain,(
% 2.06/1.59 ($true = (in @ sK1 @ (setadjoin @ sK0 @ emptyset)))),
% 2.06/1.59 inference(cnf_transformation,[status(thm)],[f146])).
% 2.06/1.59 % SZS output end Proof for DTF2THF_6365
% 2.06/1.59 % (6463)------------------------------
% 2.06/1.59 % (6463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.06/1.59 % (6463)Termination reason: Refutation
% 2.06/1.59
% 2.06/1.59 % (6463)Memory used [KB]: 6268
% 2.06/1.59 % (6463)Time elapsed: 0.040 s
% 2.06/1.59 % (6463)Instructions burned: 76 (million)
% 2.06/1.59 % (6463)------------------------------
% 2.06/1.59 % (6463)------------------------------
% 2.06/1.59 % (6462)Success in time 0.052 s
%------------------------------------------------------------------------------