%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU525^1 : 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 : n008.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 09:35:05 AM UTC 2026
% Result : Theorem 1.93s 1.49s
% Output : Refutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 14 unt; 0 typ; 0 def)
% Number of atoms : 1067 ( 336 equ; 0 cnn)
% Maximal formula atoms : 46 ( 30 avg)
% Number of connectives : 587 ( 26 ~; 24 |; 184 &; 112 @)
% ( 5 <=>; 223 =>; 0 <=; 2 <~>)
% Maximal formula depth : 49 ( 14 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 81 usr; 46 con; 0-3 aty)
% ( 7 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 78 ( 31 ^; 30 !; 17 ?; 78 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_1,type,
exu: ( $i > $o ) > $o ).
thf(func_def_6,type,
setadjoin: $i > $i > $i ).
thf(func_def_8,type,
powerset: $i > $i ).
thf(func_def_10,type,
setunion: $i > $i ).
thf(func_def_19,type,
descr: ( $i > $o ) > $i ).
thf(func_def_21,type,
dsetconstr: $i > ( $i > $o ) > $i ).
thf(func_def_26,type,
prop2set: $o > $i ).
thf(func_def_36,type,
nonempty: $i > $o ).
thf(func_def_69,type,
sK0: $i > $o ).
thf(func_def_70,type,
sK1: $i > $i ).
thf(func_def_72,type,
sK3: $i > $i ).
thf(func_def_73,type,
sK4: $i > $i > $i ).
thf(func_def_74,type,
sK5: $i > $i > $i ).
thf(func_def_75,type,
sK6: $i > $i > $i ).
thf(func_def_76,type,
sK7: $i > $i > $i > $i ).
thf(func_def_77,type,
sK8: ( $i > $o ) > $i ).
thf(func_def_78,type,
sK9: ( $i > $o ) > $i > $i ).
thf(func_def_79,type,
sK10: $i > $i > $i ).
thf(func_def_80,type,
sK11: $i > $i ).
thf(func_def_82,type,
sK12: ( $i > $i > $o ) > $i > $i ).
thf(func_def_83,type,
sK13: ( $i > $i > $o ) > $i > $i ).
thf(func_def_84,type,
sK14: ( $i > $i > $o ) > $i > $i > $i ).
thf(func_def_85,type,
sK15: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_86,type,
sK16: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_87,type,
sK17: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_88,type,
sK18: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_89,type,
sK19: $i > $i > $i ).
thf(func_def_90,type,
sK20: $i > $i > $i ).
thf(func_def_91,type,
sK21: $i > $i > $i ).
thf(func_def_92,type,
sK22: $i > $i ).
thf(func_def_93,type,
sK23: $i > $i ).
thf(func_def_94,type,
sK24: $o > $i > $i > $i ).
thf(func_def_96,type,
sK26: $i > $i ).
thf(func_def_97,type,
sK27: $i > $i > $i ).
thf(func_def_98,type,
sK28: ( $i > $o ) > $i > $i ).
thf(func_def_99,type,
sK29: $i > $i > $i ).
thf(func_def_100,type,
sK30: $i > $i > $i ).
thf(func_def_101,type,
sK31: $i > $i ).
thf(f798,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f795]) ).
thf(f795,plain,
( ( $true != $true )
| ( sK25 != sK25 ) ),
inference(superposition,[status(thm)],[f794,f634]) ).
thf(f634,plain,
( ( sK0 @ sK25 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f633]) ).
thf(f633,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK25 = Y0 ) ) )
& ( sK0 @ sK25 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f632]) ).
thf(f632,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ sK25 ) ),
inference(sigma_clausification,[status(thm)],[f631]) ).
thf(f631,plain,
( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f239]) ).
thf(f239,plain,
( $true
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(definition_unfolding,[status(thm)],[f177,f149]) ).
thf(f149,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f108]) ).
thf(f108,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f107]) ).
thf(f107,plain,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) )
= exu ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) )
= exu ),
file('/export/starexec/sandbox/tmp/tmp.J0dprC0Sfg/DTF2THF_14868.p',exu) ).
thf(f177,plain,
( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
thf(f139,plain,
( ( subPowSU = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( replAx = $true )
& ( setunionE = $true )
& ( setunionAx = $true )
& ( nonemptyE1 = $true )
& ( setextAx = $true )
& ( prop2setE = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( notinemptyset = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( emptyInPowerset = $true )
& ! [X1: $i] :
( ( ( ( sK1 @ X1 )
!= X1 )
| ( ( sK0 @ ( sK1 @ X1 ) )
!= $true ) )
& ( ( ( sK1 @ X1 )
= X1 )
| ( ( sK0 @ ( sK1 @ X1 ) )
= $true ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) )
& ( setadjoinIL = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ( dsetconstrER = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( emptyinunitempty = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( setunionI = $true )
& ( noeltsimpempty = $true )
& ( setext = $true )
& ( emptysetimpfalse = $true )
& ( exuE1 = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( exuE3e = $true )
& ( powersetI = $true )
& ( setadjoinIR = $true )
& ( dsetconstrI = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f136,f138,f137]) ).
thf(f137,plain,
( ? [X0: $i > $o] :
( ! [X1: $i] :
? [X2: $i] :
( ( ( X1 != X2 )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( X1 = X2 )
| ( ( X0 @ X2 )
= $true ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
=> ( ! [X1: $i] :
? [X2: $i] :
( ( ( X1 != X2 )
| ( $true
!= ( sK0 @ X2 ) ) )
& ( ( X1 = X2 )
| ( $true
= ( sK0 @ X2 ) ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f138,plain,
! [X1: $i] :
( ? [X2: $i] :
( ( ( X1 != X2 )
| ( $true
!= ( sK0 @ X2 ) ) )
& ( ( X1 = X2 )
| ( $true
= ( sK0 @ X2 ) ) ) )
=> ( ( ( ( sK1 @ X1 )
!= X1 )
| ( ( sK0 @ ( sK1 @ X1 ) )
!= $true ) )
& ( ( ( sK1 @ X1 )
= X1 )
| ( ( sK0 @ ( sK1 @ X1 ) )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f136,plain,
( ( subPowSU = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( replAx = $true )
& ( setunionE = $true )
& ( setunionAx = $true )
& ( nonemptyE1 = $true )
& ( setextAx = $true )
& ( prop2setE = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( notinemptyset = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( emptyInPowerset = $true )
& ? [X0: $i > $o] :
( ! [X1: $i] :
? [X2: $i] :
( ( ( X1 != X2 )
| ( ( X0 @ X2 )
!= $true ) )
& ( ( X1 = X2 )
| ( ( X0 @ X2 )
= $true ) ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( setadjoinIL = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ( dsetconstrER = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( emptyinunitempty = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( setunionI = $true )
& ( noeltsimpempty = $true )
& ( setext = $true )
& ( emptysetimpfalse = $true )
& ( exuE1 = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( exuE3e = $true )
& ( powersetI = $true )
& ( setadjoinIR = $true )
& ( dsetconstrI = $true ) ),
inference(nnf_transformation,[status(thm)],[f135]) ).
thf(f135,plain,
( ( subPowSU = $true )
& ( setadjoinE = $true )
& ( omega0Ax = $true )
& ( replAx = $true )
& ( setunionE = $true )
& ( setunionAx = $true )
& ( nonemptyE1 = $true )
& ( setextAx = $true )
& ( prop2setE = $true )
& ( emptyI = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( nonemptyI = $true )
& ( emptyinPowerset = $true )
& ( nonemptyI1 = $true )
& ( setadjoinAx = $true )
& ( notinemptyset = $true )
& ( setadjoinOr = $true )
& ( emptysetAx = $true )
& ( emptyInPowerset = $true )
& ? [X0: $i > $o] :
( ! [X1: $i] :
? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
<~> ( X1 = X2 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( setadjoinIL = $true )
& ( setoftrueEq = $true )
& ( foundationAx = $true )
& ( dsetconstrER = $true )
& ( powersetE = $true )
& ( wellorderingAx = $true )
& ( emptyinunitempty = $true )
& ( powersetAx = $true )
& ( emptysetE = $true )
& ( setunionI = $true )
& ( noeltsimpempty = $true )
& ( setext = $true )
& ( emptysetimpfalse = $true )
& ( exuE1 = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( exuE3e = $true )
& ( powersetI = $true )
& ( setadjoinIR = $true )
& ( dsetconstrI = $true ) ),
inference(flattening,[status(thm)],[f134]) ).
thf(f134,plain,
( ? [X0: $i > $o] :
( ! [X1: $i] :
? [X2: $i] :
( ( ( X0 @ X2 )
= $true )
<~> ( X1 = X2 ) )
& ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) ) )
& ( 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)],[f133]) ).
thf(f133,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 )
=> ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X1: $i] :
! [X2: $i] :
( ( ( X0 @ X2 )
= $true )
<=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f110]) ).
thf(f110,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 )
=> ! [X0: $i > $o] :
( ( $true
= ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( ( X0 @ X3 )
= $true )
<=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f109]) ).
thf(f109,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
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X2: $i] :
! [X3: $i] :
( ( X0 @ X3 )
<=> ( X2 = X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,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
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
thf(f45,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
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] :
! [X2: $i] :
( ( X0 @ X2 )
<=> ( X1 = X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.J0dprC0Sfg/DTF2THF_14868.p',exuE2) ).
thf(f794,plain,
! [X0: $i] :
( ( $true
!= ( sK0 @ X0 ) )
| ( sK25 != X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f790]) ).
thf(f790,plain,
! [X0: $i] :
( ( X0 != X0 )
| ( $true
!= ( sK0 @ X0 ) )
| ( sK25 != X0 ) ),
inference(superposition,[status(thm)],[f179,f786]) ).
thf(f786,plain,
! [X0: $i] :
( ( ( sK1 @ X0 )
= X0 )
| ( sK25 != X0 ) ),
inference(equality_factoring,[status(thm)],[f784]) ).
thf(f784,plain,
! [X0: $i] :
( ( sK25
= ( sK1 @ X0 ) )
| ( ( sK1 @ X0 )
= X0 ) ),
inference(trivial_inequality_removal,[status(thm)],[f782]) ).
thf(f782,plain,
! [X0: $i] :
( ( sK25
= ( sK1 @ X0 ) )
| ( $true = $false )
| ( ( sK1 @ X0 )
= X0 ) ),
inference(superposition,[status(thm)],[f639,f178]) ).
thf(f178,plain,
! [X1: $i] :
( ( ( sK0 @ ( sK1 @ X1 ) )
= $true )
| ( ( sK1 @ X1 )
= X1 ) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
thf(f639,plain,
! [X1: $i] :
( ( $false
= ( sK0 @ X1 ) )
| ( sK25 = X1 ) ),
inference(equality_proxy_clausification,[status(thm)],[f638]) ).
thf(f638,plain,
! [X1: $i] :
( ( $true
= ( sK25 = X1 ) )
| ( $false
= ( sK0 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f637]) ).
thf(f637,plain,
! [X1: $i] :
( $true
= ( ( sK0 @ X1 )
=> ( sK25 = X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f636]) ).
thf(f636,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK25 = Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f635]) ).
thf(f635,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK25 = Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f633]) ).
thf(f179,plain,
! [X1: $i] :
( ( ( sK0 @ ( sK1 @ X1 ) )
!= $true )
| ( ( sK1 @ X1 )
!= X1 ) ),
inference(cnf_transformation,[status(thm)],[f139]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU525^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n008.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:25:39 EST 2026
% 0.12/0.30 % CPUTime :
% 0.12/0.30 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.39 ---- Original DTF file ---
% 0.17/0.39 thf(spec,logic,$$dhol).
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 % File : SEU525^1 : TPTP v9.2.1. Released v3.7.0.
% 0.17/0.39 % Domain : Set Theory
% 0.17/0.39 % Problem : Preliminary Notions - Equality Laws
% 0.17/0.39 % Version : Especial.
% 0.17/0.39 % English : (! phi:i>o.exu (^ x:i.phi x) -> (? x:i.! y:i.phi y <-> y = x))
% 0.17/0.39
% 0.17/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.17/0.39 % Source : [Bro08]
% 0.17/0.39 % Names : ZFC027g [Bro08]
% 0.17/0.39
% 0.17/0.39 % Status : Theorem
% 0.17/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.30 v8.2.0, 0.31 v8.1.0, 0.18 v7.5.0, 0.00 v7.4.0, 0.22 v7.2.0, 0.12 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 v5.2.0, 0.80 v5.1.0, 1.00 v5.0.0, 0.80 v4.1.0, 0.67 v3.7.0
% 0.17/0.39 % Syntax : Number of formulae : 97 ( 44 unt; 52 typ; 44 def)
% 0.17/0.39 % Number of atoms : 247 ( 57 equ; 0 cnn)
% 0.17/0.39 % Maximal formula atoms : 43 ( 5 avg)
% 0.17/0.39 % Number of connectives : 409 ( 7 ~; 4 |; 18 &; 268 @)
% 0.17/0.39 % ( 8 <=>; 104 =>; 0 <=; 0 <~>)
% 0.17/0.39 % Maximal formula depth : 48 ( 2 avg)
% 0.17/0.39 % Number of types : 2 ( 0 usr)
% 0.17/0.39 % Number of type conns : 27 ( 27 >; 0 *; 0 +; 0 <<)
% 0.17/0.39 % Number of symbols : 55 ( 52 usr; 45 con; 0-2 aty)
% 0.17/0.39 % Number of variables : 136 ( 16 ^; 103 !; 17 ?; 136 :)
% 0.17/0.39 % SPC : TH0_THM_EQU_NAR
% 0.17/0.39
% 0.17/0.39 % Comments : http://mathgate.info/detsetitem.php?id=405
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 thf(in_type,type,
% 0.17/0.39 in: $i > $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(exu_type,type,
% 0.17/0.39 exu: ( $i > $o ) > $o ).
% 0.17/0.39
% 0.17/0.39 thf(exu,definition,
% 0.17/0.39 ( exu
% 0.17/0.39 = ( ^ [Xphi: $i > $o] :
% 0.17/0.39 ? [Xx: $i] :
% 0.17/0.39 ( ( Xphi @ Xx )
% 0.17/0.39 & ! [Xy: $i] :
% 0.17/0.39 ( ( Xphi @ Xy )
% 0.17/0.39 => ( Xx = Xy ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setextAx_type,type,
% 0.17/0.39 setextAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setextAx,definition,
% 0.17/0.39 ( setextAx
% 0.17/0.39 = ( ! [A: $i,B: $i] :
% 0.17/0.39 ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 <=> ( in @ Xx @ B ) )
% 0.17/0.39 => ( A = B ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(emptyset_type,type,
% 0.17/0.39 emptyset: $i ).
% 0.17/0.39
% 0.17/0.39 thf(emptysetAx_type,type,
% 0.17/0.39 emptysetAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(emptysetAx,definition,
% 0.17/0.39 ( emptysetAx
% 0.17/0.39 = ( ! [Xx: $i] :
% 0.17/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoin_type,type,
% 0.17/0.39 setadjoin: $i > $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinAx_type,type,
% 0.17/0.39 setadjoinAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinAx,definition,
% 0.17/0.39 ( setadjoinAx
% 0.17/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.39 <=> ( ( Xy = Xx )
% 0.17/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(powerset_type,type,
% 0.17/0.39 powerset: $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(powersetAx_type,type,
% 0.17/0.39 powersetAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(powersetAx,definition,
% 0.17/0.39 ( powersetAx
% 0.17/0.39 = ( ! [A: $i,B: $i] :
% 0.17/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.39 <=> ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ B )
% 0.17/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setunion_type,type,
% 0.17/0.39 setunion: $i > $i ).
% 0.17/0.39
% 0.17/0.39 thf(setunionAx_type,type,
% 0.17/0.39 setunionAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setunionAx,definition,
% 0.17/0.39 ( setunionAx
% 0.17/0.39 = ( ! [A: $i,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.39 <=> ? [B: $i] :
% 0.17/0.39 ( ( in @ Xx @ B )
% 0.17/0.39 & ( in @ B @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(omega_type,type,
% 0.17/0.39 omega: $i ).
% 0.17/0.39
% 0.17/0.39 thf(omega0Ax_type,type,
% 0.17/0.39 omega0Ax: $o ).
% 0.17/0.39
% 0.17/0.39 thf(omega0Ax,definition,
% 0.17/0.39 ( omega0Ax
% 0.17/0.39 = ( in @ emptyset @ omega ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(omegaSAx_type,type,
% 0.17/0.39 omegaSAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(omegaSAx,definition,
% 0.17/0.39 ( omegaSAx
% 0.17/0.39 = ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ omega )
% 0.17/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(omegaIndAx_type,type,
% 0.17/0.39 omegaIndAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(omegaIndAx,definition,
% 0.17/0.39 ( omegaIndAx
% 0.17/0.39 = ( ! [A: $i] :
% 0.17/0.39 ( ( ( in @ emptyset @ A )
% 0.17/0.39 & ! [Xx: $i] :
% 0.17/0.39 ( ( ( in @ Xx @ omega )
% 0.17/0.39 & ( in @ Xx @ A ) )
% 0.17/0.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.17/0.39 => ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ omega )
% 0.17/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(replAx_type,type,
% 0.17/0.39 replAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(replAx,definition,
% 0.17/0.39 ( replAx
% 0.17/0.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.17/0.39 ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( exu
% 0.17/0.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.17/0.39 => ? [B: $i] :
% 0.17/0.39 ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ B )
% 0.17/0.39 <=> ? [Xy: $i] :
% 0.17/0.39 ( ( in @ Xy @ A )
% 0.17/0.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(foundationAx_type,type,
% 0.17/0.39 foundationAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(foundationAx,definition,
% 0.17/0.39 ( foundationAx
% 0.17/0.39 = ( ! [A: $i] :
% 0.17/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.39 => ? [B: $i] :
% 0.17/0.39 ( ( in @ B @ A )
% 0.17/0.39 & ~ ? [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ B )
% 0.17/0.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(wellorderingAx_type,type,
% 0.17/0.39 wellorderingAx: $o ).
% 0.17/0.39
% 0.17/0.39 thf(wellorderingAx,definition,
% 0.17/0.39 ( wellorderingAx
% 0.17/0.39 = ( ! [A: $i] :
% 0.17/0.39 ? [B: $i] :
% 0.17/0.39 ( ! [C: $i] :
% 0.17/0.39 ( ( in @ C @ B )
% 0.17/0.39 => ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ C )
% 0.17/0.39 => ( in @ Xx @ A ) ) )
% 0.17/0.39 & ! [Xx: $i,Xy: $i] :
% 0.17/0.39 ( ( ( in @ Xx @ A )
% 0.17/0.39 & ( in @ Xy @ A ) )
% 0.17/0.39 => ( ! [C: $i] :
% 0.17/0.39 ( ( in @ C @ B )
% 0.17/0.39 => ( ( in @ Xx @ C )
% 0.17/0.39 <=> ( in @ Xy @ C ) ) )
% 0.17/0.39 => ( Xx = Xy ) ) )
% 0.17/0.39 & ! [C: $i,D: $i] :
% 0.17/0.39 ( ( ( in @ C @ B )
% 0.17/0.39 & ( in @ D @ B ) )
% 0.17/0.39 => ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ C )
% 0.17/0.39 => ( in @ Xx @ D ) )
% 0.17/0.39 | ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ D )
% 0.17/0.39 => ( in @ Xx @ C ) ) ) )
% 0.17/0.39 & ! [C: $i] :
% 0.17/0.39 ( ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ C )
% 0.17/0.39 => ( in @ Xx @ A ) )
% 0.17/0.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.17/0.39 => ? [D: $i,Xx: $i] :
% 0.17/0.39 ( ( in @ D @ B )
% 0.17/0.39 & ( in @ Xx @ C )
% 0.17/0.39 & ~ ? [Xy: $i] :
% 0.17/0.39 ( ( in @ Xy @ D )
% 0.17/0.39 & ( in @ Xy @ C ) )
% 0.17/0.39 & ! [E: $i] :
% 0.17/0.39 ( ( in @ E @ B )
% 0.17/0.39 => ( ! [Xy: $i] :
% 0.17/0.39 ( ( in @ Xy @ E )
% 0.17/0.39 => ( in @ Xy @ D ) )
% 0.17/0.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(descr_type,type,
% 0.17/0.39 descr: ( $i > $o ) > $i ).
% 0.17/0.39
% 0.17/0.39 thf(descrp_type,type,
% 0.17/0.39 descrp: $o ).
% 0.17/0.39
% 0.17/0.39 thf(descrp,definition,
% 0.17/0.39 ( descrp
% 0.17/0.39 = ( ! [Xphi: $i > $o] :
% 0.17/0.39 ( ( exu
% 0.17/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.39 => ( Xphi
% 0.17/0.39 @ ( descr
% 0.17/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(dsetconstr_type,type,
% 0.17/0.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.17/0.39
% 0.17/0.39 thf(dsetconstrI_type,type,
% 0.17/0.39 dsetconstrI: $o ).
% 0.17/0.39
% 0.17/0.39 thf(dsetconstrI,definition,
% 0.17/0.39 ( dsetconstrI
% 0.17/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( ( Xphi @ Xx )
% 0.17/0.39 => ( in @ Xx
% 0.17/0.39 @ ( dsetconstr @ A
% 0.17/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(dsetconstrEL_type,type,
% 0.17/0.39 dsetconstrEL: $o ).
% 0.17/0.39
% 0.17/0.39 thf(dsetconstrEL,definition,
% 0.17/0.39 ( dsetconstrEL
% 0.17/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx
% 0.17/0.39 @ ( dsetconstr @ A
% 0.17/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.39 => ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(dsetconstrER_type,type,
% 0.17/0.39 dsetconstrER: $o ).
% 0.17/0.39
% 0.17/0.39 thf(dsetconstrER,definition,
% 0.17/0.39 ( dsetconstrER
% 0.17/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx
% 0.17/0.39 @ ( dsetconstr @ A
% 0.17/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.39 => ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(exuE1_type,type,
% 0.17/0.39 exuE1: $o ).
% 0.17/0.39
% 0.17/0.39 thf(exuE1,definition,
% 0.17/0.39 ( exuE1
% 0.17/0.39 = ( ! [Xphi: $i > $o] :
% 0.17/0.39 ( ( exu
% 0.17/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.39 => ? [Xx: $i] :
% 0.17/0.39 ( ( Xphi @ Xx )
% 0.17/0.39 & ! [Xy: $i] :
% 0.17/0.39 ( ( Xphi @ Xy )
% 0.17/0.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(prop2set_type,type,
% 0.17/0.39 prop2set: $o > $i ).
% 0.17/0.39
% 0.17/0.39 thf(prop2set,definition,
% 0.17/0.39 ( prop2set
% 0.17/0.39 = ( ^ [Xphi: $o] :
% 0.17/0.39 ( dsetconstr @ ( powerset @ emptyset )
% 0.17/0.39 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(prop2setE_type,type,
% 0.17/0.39 prop2setE: $o ).
% 0.17/0.39
% 0.17/0.39 thf(prop2setE,definition,
% 0.17/0.39 ( prop2setE
% 0.17/0.39 = ( ! [Xphi: $o,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.17/0.39 => Xphi ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(emptysetE_type,type,
% 0.17/0.39 emptysetE: $o ).
% 0.17/0.39
% 0.17/0.39 thf(emptysetE,definition,
% 0.17/0.39 ( emptysetE
% 0.17/0.39 = ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ emptyset )
% 0.17/0.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(emptysetimpfalse_type,type,
% 0.17/0.39 emptysetimpfalse: $o ).
% 0.17/0.39
% 0.17/0.39 thf(emptysetimpfalse,definition,
% 0.17/0.39 ( emptysetimpfalse
% 0.17/0.39 = ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ emptyset )
% 0.17/0.39 => $false ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(notinemptyset_type,type,
% 0.17/0.39 notinemptyset: $o ).
% 0.17/0.39
% 0.17/0.39 thf(notinemptyset,definition,
% 0.17/0.39 ( notinemptyset
% 0.17/0.39 = ( ! [Xx: $i] :
% 0.17/0.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(exuE3e_type,type,
% 0.17/0.39 exuE3e: $o ).
% 0.17/0.39
% 0.17/0.39 thf(exuE3e,definition,
% 0.17/0.39 ( exuE3e
% 0.17/0.39 = ( ! [Xphi: $i > $o] :
% 0.17/0.39 ( ( exu
% 0.17/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setext_type,type,
% 0.17/0.39 setext: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setext,definition,
% 0.17/0.39 ( setext
% 0.17/0.39 = ( ! [A: $i,B: $i] :
% 0.17/0.39 ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( in @ Xx @ B ) )
% 0.17/0.39 => ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ B )
% 0.17/0.39 => ( in @ Xx @ A ) )
% 0.17/0.39 => ( A = B ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(emptyI_type,type,
% 0.17/0.39 emptyI: $o ).
% 0.17/0.39
% 0.17/0.39 thf(emptyI,definition,
% 0.17/0.39 ( emptyI
% 0.17/0.39 = ( ! [A: $i] :
% 0.17/0.39 ( ! [Xx: $i] :
% 0.17/0.39 ~ ( in @ Xx @ A )
% 0.17/0.39 => ( A = emptyset ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(noeltsimpempty_type,type,
% 0.17/0.39 noeltsimpempty: $o ).
% 0.17/0.39
% 0.17/0.39 thf(noeltsimpempty,definition,
% 0.17/0.39 ( noeltsimpempty
% 0.17/0.39 = ( ! [A: $i] :
% 0.17/0.39 ( ! [Xx: $i] :
% 0.17/0.39 ~ ( in @ Xx @ A )
% 0.17/0.39 => ( A = emptyset ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setbeta_type,type,
% 0.17/0.39 setbeta: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setbeta,definition,
% 0.17/0.39 ( setbeta
% 0.17/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( ( in @ Xx
% 0.17/0.39 @ ( dsetconstr @ A
% 0.17/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.17/0.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(nonempty_type,type,
% 0.17/0.39 nonempty: $i > $o ).
% 0.17/0.39
% 0.17/0.39 thf(nonempty,definition,
% 0.17/0.39 ( nonempty
% 0.17/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(nonemptyE1_type,type,
% 0.17/0.39 nonemptyE1: $o ).
% 0.17/0.39
% 0.17/0.39 thf(nonemptyE1,definition,
% 0.17/0.39 ( nonemptyE1
% 0.17/0.39 = ( ! [A: $i] :
% 0.17/0.39 ( ( nonempty @ A )
% 0.17/0.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(nonemptyI_type,type,
% 0.17/0.39 nonemptyI: $o ).
% 0.17/0.39
% 0.17/0.39 thf(nonemptyI,definition,
% 0.17/0.39 ( nonemptyI
% 0.17/0.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( ( Xphi @ Xx )
% 0.17/0.39 => ( nonempty
% 0.17/0.39 @ ( dsetconstr @ A
% 0.17/0.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(nonemptyI1_type,type,
% 0.17/0.39 nonemptyI1: $o ).
% 0.17/0.39
% 0.17/0.39 thf(nonemptyI1,definition,
% 0.17/0.39 ( nonemptyI1
% 0.17/0.39 = ( ! [A: $i] :
% 0.17/0.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.17/0.39 => ( nonempty @ A ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinIL_type,type,
% 0.17/0.39 setadjoinIL: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinIL,definition,
% 0.17/0.39 ( setadjoinIL
% 0.17/0.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(emptyinunitempty_type,type,
% 0.17/0.39 emptyinunitempty: $o ).
% 0.17/0.39
% 0.17/0.39 thf(emptyinunitempty,definition,
% 0.17/0.39 ( emptyinunitempty
% 0.17/0.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinIR_type,type,
% 0.17/0.39 setadjoinIR: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinIR,definition,
% 0.17/0.39 ( setadjoinIR
% 0.17/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.39 ( ( in @ Xy @ A )
% 0.17/0.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinE_type,type,
% 0.17/0.39 setadjoinE: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinE,definition,
% 0.17/0.39 ( setadjoinE
% 0.17/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.39 => ! [Xphi: $o] :
% 0.17/0.39 ( ( ( Xy = Xx )
% 0.17/0.39 => Xphi )
% 0.17/0.39 => ( ( ( in @ Xy @ A )
% 0.17/0.39 => Xphi )
% 0.17/0.39 => Xphi ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinOr_type,type,
% 0.17/0.39 setadjoinOr: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setadjoinOr,definition,
% 0.17/0.39 ( setadjoinOr
% 0.17/0.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.17/0.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.17/0.39 => ( ( Xy = Xx )
% 0.17/0.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setoftrueEq_type,type,
% 0.17/0.39 setoftrueEq: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setoftrueEq,definition,
% 0.17/0.39 ( setoftrueEq
% 0.17/0.39 = ( ! [A: $i] :
% 0.17/0.39 ( ( dsetconstr @ A
% 0.17/0.39 @ ^ [Xx: $i] : $true )
% 0.17/0.39 = A ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(powersetI_type,type,
% 0.17/0.39 powersetI: $o ).
% 0.17/0.39
% 0.17/0.39 thf(powersetI,definition,
% 0.17/0.39 ( powersetI
% 0.17/0.39 = ( ! [A: $i,B: $i] :
% 0.17/0.39 ( ! [Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ B )
% 0.17/0.39 => ( in @ Xx @ A ) )
% 0.17/0.39 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(emptyinPowerset_type,type,
% 0.17/0.39 emptyinPowerset: $o ).
% 0.17/0.39
% 0.17/0.39 thf(emptyinPowerset,definition,
% 0.17/0.39 ( emptyinPowerset
% 0.17/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(emptyInPowerset_type,type,
% 0.17/0.39 emptyInPowerset: $o ).
% 0.17/0.39
% 0.17/0.39 thf(emptyInPowerset,definition,
% 0.17/0.39 ( emptyInPowerset
% 0.17/0.39 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(powersetE_type,type,
% 0.17/0.39 powersetE: $o ).
% 0.17/0.39
% 0.17/0.39 thf(powersetE,definition,
% 0.17/0.39 ( powersetE
% 0.17/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.17/0.39 ( ( in @ B @ ( powerset @ A ) )
% 0.17/0.39 => ( ( in @ Xx @ B )
% 0.17/0.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setunionI_type,type,
% 0.17/0.39 setunionI: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setunionI,definition,
% 0.17/0.39 ( setunionI
% 0.17/0.39 = ( ! [A: $i,Xx: $i,B: $i] :
% 0.17/0.39 ( ( in @ Xx @ B )
% 0.17/0.39 => ( ( in @ B @ A )
% 0.17/0.39 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(setunionE_type,type,
% 0.17/0.39 setunionE: $o ).
% 0.17/0.39
% 0.17/0.39 thf(setunionE,definition,
% 0.17/0.39 ( setunionE
% 0.17/0.39 = ( ! [A: $i,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ ( setunion @ A ) )
% 0.17/0.39 => ! [Xphi: $o] :
% 0.17/0.39 ( ! [B: $i] :
% 0.17/0.39 ( ( in @ Xx @ B )
% 0.17/0.39 => ( ( in @ B @ A )
% 0.17/0.39 => Xphi ) )
% 0.17/0.39 => Xphi ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(subPowSU_type,type,
% 0.17/0.39 subPowSU: $o ).
% 0.17/0.39
% 0.17/0.39 thf(subPowSU,definition,
% 0.17/0.39 ( subPowSU
% 0.17/0.39 = ( ! [A: $i,Xx: $i] :
% 0.17/0.39 ( ( in @ Xx @ A )
% 0.17/0.39 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 thf(exuE2,conjecture,
% 0.17/0.39 ( setextAx
% 0.17/0.39 => ( emptysetAx
% 0.17/0.39 => ( setadjoinAx
% 0.17/0.39 => ( powersetAx
% 0.17/0.39 => ( setunionAx
% 0.17/0.39 => ( omega0Ax
% 0.17/0.39 => ( omegaSAx
% 0.17/0.39 => ( omegaIndAx
% 0.17/0.39 => ( replAx
% 0.17/0.39 => ( foundationAx
% 0.17/0.39 => ( wellorderingAx
% 0.17/0.39 => ( descrp
% 0.17/0.39 => ( dsetconstrI
% 0.17/0.39 => ( dsetconstrEL
% 0.17/0.39 => ( dsetconstrER
% 0.17/0.39 => ( exuE1
% 0.17/0.39 => ( prop2setE
% 0.17/0.39 => ( emptysetE
% 0.17/0.39 => ( emptysetimpfalse
% 0.17/0.39 => ( notinemptyset
% 0.17/0.39 => ( exuE3e
% 0.17/0.39 => ( setext
% 0.17/0.39 => ( emptyI
% 0.17/0.39 => ( noeltsimpempty
% 0.17/0.39 => ( setbeta
% 0.17/0.39 => ( nonemptyE1
% 0.17/0.39 => ( nonemptyI
% 0.17/0.39 => ( nonemptyI1
% 0.17/0.39 => ( setadjoinIL
% 0.17/0.39 => ( emptyinunitempty
% 0.17/0.39 => ( setadjoinIR
% 0.17/0.39 => ( setadjoinE
% 0.17/0.39 => ( setadjoinOr
% 0.17/0.39 => ( setoftrueEq
% 0.17/0.39 => ( powersetI
% 0.17/0.39 => ( emptyinPowerset
% 0.17/0.39 => ( emptyInPowerset
% 0.17/0.39 => ( powersetE
% 0.17/0.39 => ( setunionI
% 0.17/0.39 => ( setunionE
% 0.17/0.39 => ( subPowSU
% 0.17/0.39 => ! [Xphi: $i > $o] :
% 0.17/0.39 ( ( exu
% 0.17/0.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.17/0.39 => ? [Xx: $i] :
% 0.17/0.39 ! [Xy: $i] :
% 0.17/0.39 ( ( Xphi @ Xy )
% 0.17/0.39 <=> ( Xy = Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.17/0.39
% 0.17/0.39 %------------------------------------------------------------------------------
% 0.17/0.39 ------------------------
% 1.93/1.42 ---- Embedded in THF ---
% 1.93/1.42 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.93/1.42 %%% Generated on Tue Feb 24 12:25:40 EST 2026
% 1.93/1.42 %%% using '$$dhol' embedding, version 1.3.0.
% 1.93/1.42 %%% Logic specification used:
% 1.93/1.42 %%% thf(spec, logic, $$dhol).
% 1.93/1.42
% 1.93/1.42 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.J0dprC0Sfg/DTF2DTF14868.p
% See solution above
% 1.93/1.42 ------------------------
% 1.93/1.43 ---- Cleaned THF ---
% 1.93/1.43 thf(in_type,type,
% 1.93/1.43 in: $i > $i > $o ).
% 1.93/1.43
% 1.93/1.43 thf(exu_type,type,
% 1.93/1.43 exu: ( $i > $o ) > $o ).
% 1.93/1.43
% 1.93/1.43 thf(exu,definition,
% 1.93/1.43 ( exu
% 1.93/1.43 = ( ^ [Xphi: $i > $o] :
% 1.93/1.43 ? [Xx: $i] :
% 1.93/1.43 ( ( Xphi @ Xx )
% 1.93/1.43 & ! [Xy: $i] :
% 1.93/1.43 ( ( Xphi @ Xy )
% 1.93/1.43 => ( Xx = Xy ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(setextAx_type,type,
% 1.93/1.43 setextAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(setextAx,definition,
% 1.93/1.43 ( setextAx
% 1.93/1.43 = ( ! [A: $i,B: $i] :
% 1.93/1.43 ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ A )
% 1.93/1.43 <=> ( in @ Xx @ B ) )
% 1.93/1.43 => ( A = B ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(emptyset_type,type,
% 1.93/1.43 emptyset: $i ).
% 1.93/1.43
% 1.93/1.43 thf(emptysetAx_type,type,
% 1.93/1.43 emptysetAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(emptysetAx,definition,
% 1.93/1.43 ( emptysetAx
% 1.93/1.43 = ( ! [Xx: $i] :
% 1.93/1.43 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoin_type,type,
% 1.93/1.43 setadjoin: $i > $i > $i ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoinAx_type,type,
% 1.93/1.43 setadjoinAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoinAx,definition,
% 1.93/1.43 ( setadjoinAx
% 1.93/1.43 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.93/1.43 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.93/1.43 <=> ( ( Xy = Xx )
% 1.93/1.43 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(powerset_type,type,
% 1.93/1.43 powerset: $i > $i ).
% 1.93/1.43
% 1.93/1.43 thf(powersetAx_type,type,
% 1.93/1.43 powersetAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(powersetAx,definition,
% 1.93/1.43 ( powersetAx
% 1.93/1.43 = ( ! [A: $i,B: $i] :
% 1.93/1.43 ( ( in @ B @ ( powerset @ A ) )
% 1.93/1.43 <=> ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ B )
% 1.93/1.43 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(setunion_type,type,
% 1.93/1.43 setunion: $i > $i ).
% 1.93/1.43
% 1.93/1.43 thf(setunionAx_type,type,
% 1.93/1.43 setunionAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(setunionAx,definition,
% 1.93/1.43 ( setunionAx
% 1.93/1.43 = ( ! [A: $i,Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ ( setunion @ A ) )
% 1.93/1.43 <=> ? [B: $i] :
% 1.93/1.43 ( ( in @ Xx @ B )
% 1.93/1.43 & ( in @ B @ A ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(omega_type,type,
% 1.93/1.43 omega: $i ).
% 1.93/1.43
% 1.93/1.43 thf(omega0Ax_type,type,
% 1.93/1.43 omega0Ax: $o ).
% 1.93/1.43
% 1.93/1.43 thf(omega0Ax,definition,
% 1.93/1.43 ( omega0Ax
% 1.93/1.43 = ( in @ emptyset @ omega ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(omegaSAx_type,type,
% 1.93/1.43 omegaSAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(omegaSAx,definition,
% 1.93/1.43 ( omegaSAx
% 1.93/1.43 = ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ omega )
% 1.93/1.43 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(omegaIndAx_type,type,
% 1.93/1.43 omegaIndAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(omegaIndAx,definition,
% 1.93/1.43 ( omegaIndAx
% 1.93/1.43 = ( ! [A: $i] :
% 1.93/1.43 ( ( ( in @ emptyset @ A )
% 1.93/1.43 & ! [Xx: $i] :
% 1.93/1.43 ( ( ( in @ Xx @ omega )
% 1.93/1.43 & ( in @ Xx @ A ) )
% 1.93/1.43 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.93/1.43 => ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ omega )
% 1.93/1.43 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(replAx_type,type,
% 1.93/1.43 replAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(replAx,definition,
% 1.93/1.43 ( replAx
% 1.93/1.43 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.93/1.43 ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ A )
% 1.93/1.43 => ( exu
% 1.93/1.43 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.93/1.43 => ? [B: $i] :
% 1.93/1.43 ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ B )
% 1.93/1.43 <=> ? [Xy: $i] :
% 1.93/1.43 ( ( in @ Xy @ A )
% 1.93/1.43 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(foundationAx_type,type,
% 1.93/1.43 foundationAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(foundationAx,definition,
% 1.93/1.43 ( foundationAx
% 1.93/1.43 = ( ! [A: $i] :
% 1.93/1.43 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.93/1.43 => ? [B: $i] :
% 1.93/1.43 ( ( in @ B @ A )
% 1.93/1.43 & ~ ? [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ B )
% 1.93/1.43 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(wellorderingAx_type,type,
% 1.93/1.43 wellorderingAx: $o ).
% 1.93/1.43
% 1.93/1.43 thf(wellorderingAx,definition,
% 1.93/1.43 ( wellorderingAx
% 1.93/1.43 = ( ! [A: $i] :
% 1.93/1.43 ? [B: $i] :
% 1.93/1.43 ( ! [C: $i] :
% 1.93/1.43 ( ( in @ C @ B )
% 1.93/1.43 => ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ C )
% 1.93/1.43 => ( in @ Xx @ A ) ) )
% 1.93/1.43 & ! [Xx: $i,Xy: $i] :
% 1.93/1.43 ( ( ( in @ Xx @ A )
% 1.93/1.43 & ( in @ Xy @ A ) )
% 1.93/1.43 => ( ! [C: $i] :
% 1.93/1.43 ( ( in @ C @ B )
% 1.93/1.43 => ( ( in @ Xx @ C )
% 1.93/1.43 <=> ( in @ Xy @ C ) ) )
% 1.93/1.43 => ( Xx = Xy ) ) )
% 1.93/1.43 & ! [C: $i,D: $i] :
% 1.93/1.43 ( ( ( in @ C @ B )
% 1.93/1.43 & ( in @ D @ B ) )
% 1.93/1.43 => ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ C )
% 1.93/1.43 => ( in @ Xx @ D ) )
% 1.93/1.43 | ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ D )
% 1.93/1.43 => ( in @ Xx @ C ) ) ) )
% 1.93/1.43 & ! [C: $i] :
% 1.93/1.43 ( ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ C )
% 1.93/1.43 => ( in @ Xx @ A ) )
% 1.93/1.43 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.93/1.43 => ? [D: $i,Xx: $i] :
% 1.93/1.43 ( ( in @ D @ B )
% 1.93/1.43 & ( in @ Xx @ C )
% 1.93/1.43 & ~ ? [Xy: $i] :
% 1.93/1.43 ( ( in @ Xy @ D )
% 1.93/1.43 & ( in @ Xy @ C ) )
% 1.93/1.43 & ! [E: $i] :
% 1.93/1.43 ( ( in @ E @ B )
% 1.93/1.43 => ( ! [Xy: $i] :
% 1.93/1.43 ( ( in @ Xy @ E )
% 1.93/1.43 => ( in @ Xy @ D ) )
% 1.93/1.43 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(descr_type,type,
% 1.93/1.43 descr: ( $i > $o ) > $i ).
% 1.93/1.43
% 1.93/1.43 thf(descrp_type,type,
% 1.93/1.43 descrp: $o ).
% 1.93/1.43
% 1.93/1.43 thf(descrp,definition,
% 1.93/1.43 ( descrp
% 1.93/1.43 = ( ! [Xphi: $i > $o] :
% 1.93/1.43 ( ( exu
% 1.93/1.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.93/1.43 => ( Xphi
% 1.93/1.43 @ ( descr
% 1.93/1.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(dsetconstr_type,type,
% 1.93/1.43 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.93/1.43
% 1.93/1.43 thf(dsetconstrI_type,type,
% 1.93/1.43 dsetconstrI: $o ).
% 1.93/1.43
% 1.93/1.43 thf(dsetconstrI,definition,
% 1.93/1.43 ( dsetconstrI
% 1.93/1.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ A )
% 1.93/1.43 => ( ( Xphi @ Xx )
% 1.93/1.43 => ( in @ Xx
% 1.93/1.43 @ ( dsetconstr @ A
% 1.93/1.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(dsetconstrEL_type,type,
% 1.93/1.43 dsetconstrEL: $o ).
% 1.93/1.43
% 1.93/1.43 thf(dsetconstrEL,definition,
% 1.93/1.43 ( dsetconstrEL
% 1.93/1.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.93/1.43 ( ( in @ Xx
% 1.93/1.43 @ ( dsetconstr @ A
% 1.93/1.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.93/1.43 => ( in @ Xx @ A ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(dsetconstrER_type,type,
% 1.93/1.43 dsetconstrER: $o ).
% 1.93/1.43
% 1.93/1.43 thf(dsetconstrER,definition,
% 1.93/1.43 ( dsetconstrER
% 1.93/1.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.93/1.43 ( ( in @ Xx
% 1.93/1.43 @ ( dsetconstr @ A
% 1.93/1.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.93/1.43 => ( Xphi @ Xx ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(exuE1_type,type,
% 1.93/1.43 exuE1: $o ).
% 1.93/1.43
% 1.93/1.43 thf(exuE1,definition,
% 1.93/1.43 ( exuE1
% 1.93/1.43 = ( ! [Xphi: $i > $o] :
% 1.93/1.43 ( ( exu
% 1.93/1.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.93/1.43 => ? [Xx: $i] :
% 1.93/1.43 ( ( Xphi @ Xx )
% 1.93/1.43 & ! [Xy: $i] :
% 1.93/1.43 ( ( Xphi @ Xy )
% 1.93/1.43 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(prop2set_type,type,
% 1.93/1.43 prop2set: $o > $i ).
% 1.93/1.43
% 1.93/1.43 thf(prop2set,definition,
% 1.93/1.43 ( prop2set
% 1.93/1.43 = ( ^ [Xphi: $o] :
% 1.93/1.43 ( dsetconstr @ ( powerset @ emptyset )
% 1.93/1.43 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(prop2setE_type,type,
% 1.93/1.43 prop2setE: $o ).
% 1.93/1.43
% 1.93/1.43 thf(prop2setE,definition,
% 1.93/1.43 ( prop2setE
% 1.93/1.43 = ( ! [Xphi: $o,Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.93/1.43 => Xphi ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(emptysetE_type,type,
% 1.93/1.43 emptysetE: $o ).
% 1.93/1.43
% 1.93/1.43 thf(emptysetE,definition,
% 1.93/1.43 ( emptysetE
% 1.93/1.43 = ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ emptyset )
% 1.93/1.43 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(emptysetimpfalse_type,type,
% 1.93/1.43 emptysetimpfalse: $o ).
% 1.93/1.43
% 1.93/1.43 thf(emptysetimpfalse,definition,
% 1.93/1.43 ( emptysetimpfalse
% 1.93/1.43 = ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ emptyset )
% 1.93/1.43 => $false ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(notinemptyset_type,type,
% 1.93/1.43 notinemptyset: $o ).
% 1.93/1.43
% 1.93/1.43 thf(notinemptyset,definition,
% 1.93/1.43 ( notinemptyset
% 1.93/1.43 = ( ! [Xx: $i] :
% 1.93/1.43 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(exuE3e_type,type,
% 1.93/1.43 exuE3e: $o ).
% 1.93/1.43
% 1.93/1.43 thf(exuE3e,definition,
% 1.93/1.43 ( exuE3e
% 1.93/1.43 = ( ! [Xphi: $i > $o] :
% 1.93/1.43 ( ( exu
% 1.93/1.43 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.93/1.43 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(setext_type,type,
% 1.93/1.43 setext: $o ).
% 1.93/1.43
% 1.93/1.43 thf(setext,definition,
% 1.93/1.43 ( setext
% 1.93/1.43 = ( ! [A: $i,B: $i] :
% 1.93/1.43 ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ A )
% 1.93/1.43 => ( in @ Xx @ B ) )
% 1.93/1.43 => ( ! [Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ B )
% 1.93/1.43 => ( in @ Xx @ A ) )
% 1.93/1.43 => ( A = B ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(emptyI_type,type,
% 1.93/1.43 emptyI: $o ).
% 1.93/1.43
% 1.93/1.43 thf(emptyI,definition,
% 1.93/1.43 ( emptyI
% 1.93/1.43 = ( ! [A: $i] :
% 1.93/1.43 ( ! [Xx: $i] :
% 1.93/1.43 ~ ( in @ Xx @ A )
% 1.93/1.43 => ( A = emptyset ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(noeltsimpempty_type,type,
% 1.93/1.43 noeltsimpempty: $o ).
% 1.93/1.43
% 1.93/1.43 thf(noeltsimpempty,definition,
% 1.93/1.43 ( noeltsimpempty
% 1.93/1.43 = ( ! [A: $i] :
% 1.93/1.43 ( ! [Xx: $i] :
% 1.93/1.43 ~ ( in @ Xx @ A )
% 1.93/1.43 => ( A = emptyset ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(setbeta_type,type,
% 1.93/1.43 setbeta: $o ).
% 1.93/1.43
% 1.93/1.43 thf(setbeta,definition,
% 1.93/1.43 ( setbeta
% 1.93/1.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ A )
% 1.93/1.43 => ( ( in @ Xx
% 1.93/1.43 @ ( dsetconstr @ A
% 1.93/1.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.93/1.43 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(nonempty_type,type,
% 1.93/1.43 nonempty: $i > $o ).
% 1.93/1.43
% 1.93/1.43 thf(nonempty,definition,
% 1.93/1.43 ( nonempty
% 1.93/1.43 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(nonemptyE1_type,type,
% 1.93/1.43 nonemptyE1: $o ).
% 1.93/1.43
% 1.93/1.43 thf(nonemptyE1,definition,
% 1.93/1.43 ( nonemptyE1
% 1.93/1.43 = ( ! [A: $i] :
% 1.93/1.43 ( ( nonempty @ A )
% 1.93/1.43 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(nonemptyI_type,type,
% 1.93/1.43 nonemptyI: $o ).
% 1.93/1.43
% 1.93/1.43 thf(nonemptyI,definition,
% 1.93/1.43 ( nonemptyI
% 1.93/1.43 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.93/1.43 ( ( in @ Xx @ A )
% 1.93/1.43 => ( ( Xphi @ Xx )
% 1.93/1.43 => ( nonempty
% 1.93/1.43 @ ( dsetconstr @ A
% 1.93/1.43 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(nonemptyI1_type,type,
% 1.93/1.43 nonemptyI1: $o ).
% 1.93/1.43
% 1.93/1.43 thf(nonemptyI1,definition,
% 1.93/1.43 ( nonemptyI1
% 1.93/1.43 = ( ! [A: $i] :
% 1.93/1.43 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.93/1.43 => ( nonempty @ A ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoinIL_type,type,
% 1.93/1.43 setadjoinIL: $o ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoinIL,definition,
% 1.93/1.43 ( setadjoinIL
% 1.93/1.43 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(emptyinunitempty_type,type,
% 1.93/1.43 emptyinunitempty: $o ).
% 1.93/1.43
% 1.93/1.43 thf(emptyinunitempty,definition,
% 1.93/1.43 ( emptyinunitempty
% 1.93/1.43 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoinIR_type,type,
% 1.93/1.43 setadjoinIR: $o ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoinIR,definition,
% 1.93/1.43 ( setadjoinIR
% 1.93/1.43 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.93/1.43 ( ( in @ Xy @ A )
% 1.93/1.43 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoinE_type,type,
% 1.93/1.43 setadjoinE: $o ).
% 1.93/1.43
% 1.93/1.43 thf(setadjoinE,definition,
% 1.93/1.43 ( setadjoinE
% 1.93/1.43 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.93/1.43 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.93/1.43 => ! [Xphi: $o] :
% 1.93/1.43 ( ( ( Xy = Xx )
% 1.93/1.43 => Xphi )
% 1.93/1.44 => ( ( ( in @ Xy @ A )
% 1.93/1.44 => Xphi )
% 1.93/1.44 => Xphi ) ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(setadjoinOr_type,type,
% 1.93/1.44 setadjoinOr: $o ).
% 1.93/1.44
% 1.93/1.44 thf(setadjoinOr,definition,
% 1.93/1.44 ( setadjoinOr
% 1.93/1.44 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.93/1.44 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.93/1.44 => ( ( Xy = Xx )
% 1.93/1.44 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(setoftrueEq_type,type,
% 1.93/1.44 setoftrueEq: $o ).
% 1.93/1.44
% 1.93/1.44 thf(setoftrueEq,definition,
% 1.93/1.44 ( setoftrueEq
% 1.93/1.44 = ( ! [A: $i] :
% 1.93/1.44 ( ( dsetconstr @ A
% 1.93/1.44 @ ^ [Xx: $i] : $true )
% 1.93/1.44 = A ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(powersetI_type,type,
% 1.93/1.44 powersetI: $o ).
% 1.93/1.44
% 1.93/1.44 thf(powersetI,definition,
% 1.93/1.44 ( powersetI
% 1.93/1.44 = ( ! [A: $i,B: $i] :
% 1.93/1.44 ( ! [Xx: $i] :
% 1.93/1.44 ( ( in @ Xx @ B )
% 1.93/1.44 => ( in @ Xx @ A ) )
% 1.93/1.44 => ( in @ B @ ( powerset @ A ) ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(emptyinPowerset_type,type,
% 1.93/1.44 emptyinPowerset: $o ).
% 1.93/1.44
% 1.93/1.44 thf(emptyinPowerset,definition,
% 1.93/1.44 ( emptyinPowerset
% 1.93/1.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(emptyInPowerset_type,type,
% 1.93/1.44 emptyInPowerset: $o ).
% 1.93/1.44
% 1.93/1.44 thf(emptyInPowerset,definition,
% 1.93/1.44 ( emptyInPowerset
% 1.93/1.44 = ( ! [A: $i] : ( in @ emptyset @ ( powerset @ A ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(powersetE_type,type,
% 1.93/1.44 powersetE: $o ).
% 1.93/1.44
% 1.93/1.44 thf(powersetE,definition,
% 1.93/1.44 ( powersetE
% 1.93/1.44 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.93/1.44 ( ( in @ B @ ( powerset @ A ) )
% 1.93/1.44 => ( ( in @ Xx @ B )
% 1.93/1.44 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(setunionI_type,type,
% 1.93/1.44 setunionI: $o ).
% 1.93/1.44
% 1.93/1.44 thf(setunionI,definition,
% 1.93/1.44 ( setunionI
% 1.93/1.44 = ( ! [A: $i,Xx: $i,B: $i] :
% 1.93/1.44 ( ( in @ Xx @ B )
% 1.93/1.44 => ( ( in @ B @ A )
% 1.93/1.44 => ( in @ Xx @ ( setunion @ A ) ) ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(setunionE_type,type,
% 1.93/1.44 setunionE: $o ).
% 1.93/1.44
% 1.93/1.44 thf(setunionE,definition,
% 1.93/1.44 ( setunionE
% 1.93/1.44 = ( ! [A: $i,Xx: $i] :
% 1.93/1.44 ( ( in @ Xx @ ( setunion @ A ) )
% 1.93/1.44 => ! [Xphi: $o] :
% 1.93/1.44 ( ! [B: $i] :
% 1.93/1.44 ( ( in @ Xx @ B )
% 1.93/1.44 => ( ( in @ B @ A )
% 1.93/1.44 => Xphi ) )
% 1.93/1.44 => Xphi ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(subPowSU_type,type,
% 1.93/1.44 subPowSU: $o ).
% 1.93/1.44
% 1.93/1.44 thf(subPowSU,definition,
% 1.93/1.44 ( subPowSU
% 1.93/1.44 = ( ! [A: $i,Xx: $i] :
% 1.93/1.44 ( ( in @ Xx @ A )
% 1.93/1.44 => ( in @ Xx @ ( powerset @ ( setunion @ A ) ) ) ) ) ) ).
% 1.93/1.44
% 1.93/1.44 thf(exuE2,conjecture,
% 1.93/1.44 ( setextAx
% 1.93/1.44 => ( emptysetAx
% 1.93/1.44 => ( setadjoinAx
% 1.93/1.44 => ( powersetAx
% 1.93/1.44 => ( setunionAx
% 1.93/1.44 => ( omega0Ax
% 1.93/1.44 => ( omegaSAx
% 1.93/1.44 => ( omegaIndAx
% 1.93/1.44 => ( replAx
% 1.93/1.44 => ( foundationAx
% 1.93/1.44 => ( wellorderingAx
% 1.93/1.44 => ( descrp
% 1.93/1.44 => ( dsetconstrI
% 1.93/1.44 => ( dsetconstrEL
% 1.93/1.44 => ( dsetconstrER
% 1.93/1.44 => ( exuE1
% 1.93/1.44 => ( prop2setE
% 1.93/1.44 => ( emptysetE
% 1.93/1.44 => ( emptysetimpfalse
% 1.93/1.44 => ( notinemptyset
% 1.93/1.44 => ( exuE3e
% 1.93/1.44 => ( setext
% 1.93/1.44 => ( emptyI
% 1.93/1.44 => ( noeltsimpempty
% 1.93/1.44 => ( setbeta
% 1.93/1.44 => ( nonemptyE1
% 1.93/1.44 => ( nonemptyI
% 1.93/1.44 => ( nonemptyI1
% 1.93/1.44 => ( setadjoinIL
% 1.93/1.44 => ( emptyinunitempty
% 1.93/1.44 => ( setadjoinIR
% 1.93/1.44 => ( setadjoinE
% 1.93/1.44 => ( setadjoinOr
% 1.93/1.44 => ( setoftrueEq
% 1.93/1.44 => ( powersetI
% 1.93/1.44 => ( emptyinPowerset
% 1.93/1.44 => ( emptyInPowerset
% 1.93/1.44 => ( powersetE
% 1.93/1.44 => ( setunionI
% 1.93/1.44 => ( setunionE
% 1.93/1.44 => ( subPowSU
% 1.93/1.44 => ! [Xphi: $i > $o] :
% 1.93/1.44 ( ( exu
% 1.93/1.44 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.93/1.44 => ? [Xx: $i] :
% 1.93/1.44 ! [Xy: $i] :
% 1.93/1.44 ( ( Xphi @ Xy )
% 1.93/1.44 <=> ( Xy = Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.93/1.44 ------------------------
% 1.93/1.46 % (14971)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_14868 for (2999ds/275Mi)
% 1.93/1.46 % (14968)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_14868 for (2999ds/27Mi)
% 1.93/1.46 % (14967)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_14868 for (2999ds/4Mi)
% 1.93/1.46 % (14969)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14868 for (2999ds/2Mi)
% 1.93/1.46 % (14970)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_14868 for (2999ds/2Mi)
% 1.93/1.46 % (14966)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14868 for (2999ds/183Mi)
% 1.93/1.46 % (14972)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14868 for (2999ds/18Mi)
% 1.93/1.46 % (14969)Instruction limit reached!
% 1.93/1.46 % (14969)------------------------------
% 1.93/1.46 % (14969)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.46 % (14969)Termination reason: Unknown
% 1.93/1.46 % (14969)Termination phase: shuffling
% 1.93/1.46 % (14970)Instruction limit reached!
% 1.93/1.46 % (14970)------------------------------
% 1.93/1.46 % (14970)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.46 % (14970)Termination reason: Unknown
% 1.93/1.46 % (14970)Termination phase: shuffling
% 1.93/1.46
% 1.93/1.46 % (14970)Memory used [KB]: 1023
% 1.93/1.46 % (14970)Time elapsed: 0.003 s
% 1.93/1.46 % (14970)Instructions burned: 3 (million)
% 1.93/1.46 % (14970)------------------------------
% 1.93/1.46 % (14970)------------------------------
% 1.93/1.46
% 1.93/1.46 % (14969)Memory used [KB]: 1023
% 1.93/1.46 % (14969)Time elapsed: 0.003 s
% 1.93/1.46 % (14969)Instructions burned: 3 (million)
% 1.93/1.46 % (14969)------------------------------
% 1.93/1.46 % (14969)------------------------------
% 1.93/1.46 % (14967)Instruction limit reached!
% 1.93/1.46 % (14967)------------------------------
% 1.93/1.46 % (14967)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.46 % (14967)Termination reason: Unknown
% 1.93/1.46 % (14967)Termination phase: shuffling
% 1.93/1.46
% 1.93/1.46 % (14967)Memory used [KB]: 1151
% 1.93/1.46 % (14967)Time elapsed: 0.004 s
% 1.93/1.46 % (14967)Instructions burned: 5 (million)
% 1.93/1.46 % (14967)------------------------------
% 1.93/1.46 % (14967)------------------------------
% 1.93/1.47 % (14972)Instruction limit reached!
% 1.93/1.47 % (14972)------------------------------
% 1.93/1.47 % (14972)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.47 % (14972)Termination reason: Unknown
% 1.93/1.47 % (14972)Termination phase: Property scanning
% 1.93/1.47
% 1.93/1.47 % (14972)Memory used [KB]: 1535
% 1.93/1.47 % (14972)Time elapsed: 0.011 s
% 1.93/1.47 % (14972)Instructions burned: 19 (million)
% 1.93/1.47 % (14972)------------------------------
% 1.93/1.47 % (14972)------------------------------
% 1.93/1.47 % (14968)Instruction limit reached!
% 1.93/1.47 % (14968)------------------------------
% 1.93/1.47 % (14968)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.47 % (14968)Termination reason: Unknown
% 1.93/1.47 % (14968)Termination phase: Saturation
% 1.93/1.47
% 1.93/1.47 % (14968)Memory used [KB]: 5756
% 1.93/1.47 % (14968)Time elapsed: 0.013 s
% 1.93/1.47 % (14968)Instructions burned: 27 (million)
% 1.93/1.47 % (14968)------------------------------
% 1.93/1.47 % (14968)------------------------------
% 1.93/1.47 % (14973)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14868 for (2999ds/3Mi)
% 1.93/1.47 % (14975)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_14868 for (2999ds/15Mi)
% 1.93/1.48 % (14974)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_14868 for (2999ds/37Mi)
% 1.93/1.48 % (14973)Instruction limit reached!
% 1.93/1.48 % (14973)------------------------------
% 1.93/1.48 % (14973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.48 % (14973)Termination reason: Unknown
% 1.93/1.48 % (14973)Termination phase: shuffling
% 1.93/1.48
% 1.93/1.48 % (14973)Memory used [KB]: 1023
% 1.93/1.48 % (14973)Time elapsed: 0.003 s
% 1.93/1.48 % (14973)Instructions burned: 3 (million)
% 1.93/1.48 % (14973)------------------------------
% 1.93/1.48 % (14973)------------------------------
% 1.93/1.48 % (14975)Instruction limit reached!
% 1.93/1.48 % (14975)------------------------------
% 1.93/1.48 % (14975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.48 % (14975)Termination reason: Unknown
% 1.93/1.48 % (14975)Termination phase: Preprocessing 3
% 1.93/1.48
% 1.93/1.48 % (14975)Memory used [KB]: 1407
% 1.93/1.48 % (14975)Time elapsed: 0.008 s
% 1.93/1.48 % (14975)Instructions burned: 15 (million)
% 1.93/1.48 % (14975)------------------------------
% 1.93/1.48 % (14975)------------------------------
% 1.93/1.48 % (14976)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_14868 for (2999ds/3Mi)
% 1.93/1.48 % (14977)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_14868 for (2999ds/1041Mi)
% 1.93/1.48 % (14976)Instruction limit reached!
% 1.93/1.48 % (14976)------------------------------
% 1.93/1.48 % (14976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.48 % (14976)Termination reason: Unknown
% 1.93/1.48 % (14976)Termination phase: shuffling
% 1.93/1.48
% 1.93/1.48 % (14976)Memory used [KB]: 1023
% 1.93/1.48 % (14976)Time elapsed: 0.003 s
% 1.93/1.48 % (14976)Instructions burned: 4 (million)
% 1.93/1.48 % (14976)------------------------------
% 1.93/1.48 % (14976)------------------------------
% 1.93/1.49 % (14974)Instruction limit reached!
% 1.93/1.49 % (14974)------------------------------
% 1.93/1.49 % (14974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.49 % (14974)Termination reason: Unknown
% 1.93/1.49 % (14974)Termination phase: Saturation
% 1.93/1.49
% 1.93/1.49 % (14974)Memory used [KB]: 5884
% 1.93/1.49 % (14974)Time elapsed: 0.018 s
% 1.93/1.49 % (14974)Instructions burned: 37 (million)
% 1.93/1.49 % (14974)------------------------------
% 1.93/1.49 % (14974)------------------------------
% 1.93/1.49 % (14978)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14868 for (2999ds/7Mi)
% 1.93/1.49 % (14966)First to succeed.
% 1.93/1.49 % (14966)Refutation found. Thanks to Tanya!
% 1.93/1.49 % SZS status Theorem for DTF2THF_14868
% 1.93/1.49 % SZS output start Proof for DTF2THF_14868
% 1.93/1.49 thf(func_def_0, type, in: $i > $i > $o).
% 1.93/1.49 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.93/1.49 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.93/1.49 thf(func_def_8, type, powerset: $i > $i).
% 1.93/1.49 thf(func_def_10, type, setunion: $i > $i).
% 1.93/1.49 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.93/1.49 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.93/1.49 thf(func_def_26, type, prop2set: $o > $i).
% 1.93/1.49 thf(func_def_36, type, nonempty: $i > $o).
% 1.93/1.49 thf(func_def_69, type, sK0: $i > $o).
% 1.93/1.49 thf(func_def_70, type, sK1: $i > $i).
% 1.93/1.49 thf(func_def_72, type, sK3: $i > $i).
% 1.93/1.49 thf(func_def_73, type, sK4: $i > $i > $i).
% 1.93/1.49 thf(func_def_74, type, sK5: $i > $i > $i).
% 1.93/1.49 thf(func_def_75, type, sK6: $i > $i > $i).
% 1.93/1.49 thf(func_def_76, type, sK7: $i > $i > $i > $i).
% 1.93/1.49 thf(func_def_77, type, sK8: ($i > $o) > $i).
% 1.93/1.49 thf(func_def_78, type, sK9: ($i > $o) > $i > $i).
% 1.93/1.49 thf(func_def_79, type, sK10: $i > $i > $i).
% 1.93/1.49 thf(func_def_80, type, sK11: $i > $i).
% 1.93/1.49 thf(func_def_82, type, sK12: ($i > $i > $o) > $i > $i).
% 1.93/1.49 thf(func_def_83, type, sK13: ($i > $i > $o) > $i > $i).
% 1.93/1.49 thf(func_def_84, type, sK14: ($i > $i > $o) > $i > $i > $i).
% 1.93/1.49 thf(func_def_85, type, sK15: $i > ($i > $i > $o) > $i > $i).
% 1.93/1.49 thf(func_def_86, type, sK16: $i > ($i > $i > $o) > $i > $i).
% 1.93/1.49 thf(func_def_87, type, sK17: $i > ($i > $i > $o) > $i > $i).
% 1.93/1.49 thf(func_def_88, type, sK18: $i > ($i > $i > $o) > $i > $i).
% 1.93/1.49 thf(func_def_89, type, sK19: $i > $i > $i).
% 1.93/1.49 thf(func_def_90, type, sK20: $i > $i > $i).
% 1.93/1.49 thf(func_def_91, type, sK21: $i > $i > $i).
% 1.93/1.49 thf(func_def_92, type, sK22: $i > $i).
% 1.93/1.49 thf(func_def_93, type, sK23: $i > $i).
% 1.93/1.49 thf(func_def_94, type, sK24: $o > $i > $i > $i).
% 1.93/1.49 thf(func_def_96, type, sK26: $i > $i).
% 1.93/1.49 thf(func_def_97, type, sK27: $i > $i > $i).
% 1.93/1.49 thf(func_def_98, type, sK28: ($i > $o) > $i > $i).
% 1.93/1.49 thf(func_def_99, type, sK29: $i > $i > $i).
% 1.93/1.49 thf(func_def_100, type, sK30: $i > $i > $i).
% 1.93/1.49 thf(func_def_101, type, sK31: $i > $i).
% 1.93/1.49 thf(f798,plain,(
% 1.93/1.49 $false),
% 1.93/1.49 inference(trivial_inequality_removal,[status(thm)],[f795])).
% 1.93/1.49 thf(f795,plain,(
% 1.93/1.49 ($true != $true) | (sK25 != sK25)),
% 1.93/1.49 inference(superposition,[status(thm)],[f794,f634])).
% 1.93/1.49 thf(f634,plain,(
% 1.93/1.49 ((sK0 @ sK25) = $true)),
% 1.93/1.49 inference(binary_proxy_clausification,[status(thm)],[f633])).
% 1.93/1.49 thf(f633,plain,(
% 1.93/1.49 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK25 = Y0)))) & (sK0 @ sK25)))),
% 1.93/1.49 inference(beta_eta_normalization,[status(thm)],[f632])).
% 1.93/1.49 thf(f632,plain,(
% 1.93/1.49 ($true = ((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))) @ sK25))),
% 1.93/1.49 inference(sigma_clausification,[status(thm)],[f631])).
% 1.93/1.49 thf(f631,plain,(
% 1.93/1.49 ($true = (?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))))),
% 1.93/1.49 inference(beta_eta_normalization,[status(thm)],[f239])).
% 1.93/1.49 thf(f239,plain,(
% 1.93/1.49 ($true = ((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))) @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.93/1.49 inference(definition_unfolding,[status(thm)],[f177,f149])).
% 1.93/1.49 thf(f149,plain,(
% 1.93/1.49 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.93/1.49 inference(cnf_transformation,[status(thm)],[f108])).
% 1.93/1.49 thf(f108,plain,(
% 1.93/1.49 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.93/1.49 inference(fool_elimination,[status(thm)],[f107])).
% 1.93/1.49 thf(f107,plain,(
% 1.93/1.49 ((^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 1.93/1.49 inference(rectify,[status(thm)],[f1])).
% 1.93/1.49 thf(f1,axiom,(
% 1.93/1.49 ((^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))) = exu)),
% 1.93/1.49 file('/export/starexec/sandbox/tmp/tmp.J0dprC0Sfg/DTF2THF_14868.p',exu)).
% 1.93/1.49 thf(f177,plain,(
% 1.93/1.49 ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))),
% 1.93/1.49 inference(cnf_transformation,[status(thm)],[f139])).
% 1.93/1.49 thf(f139,plain,(
% 1.93/1.49 (subPowSU = $true) & (setadjoinE = $true) & (omega0Ax = $true) & (replAx = $true) & (setunionE = $true) & (setunionAx = $true) & (nonemptyE1 = $true) & (setextAx = $true) & (prop2setE = $true) & (emptyI = $true) & (setbeta = $true) & (omegaIndAx = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (notinemptyset = $true) & (setadjoinOr = $true) & (emptysetAx = $true) & (emptyInPowerset = $true) & (! [X1 : $i] : ((((sK1 @ X1) != X1) | ((sK0 @ (sK1 @ X1)) != $true)) & (((sK1 @ X1) = X1) | ((sK0 @ (sK1 @ X1)) = $true))) & ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0))))) & (setadjoinIL = $true) & (setoftrueEq = $true) & (foundationAx = $true) & (dsetconstrER = $true) & (powersetE = $true) & (wellorderingAx = $true) & (emptyinunitempty = $true) & (powersetAx = $true) & (emptysetE = $true) & (setunionI = $true) & (noeltsimpempty = $true) & (setext = $true) & (emptysetimpfalse = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (descrp = $true) & (omegaSAx = $true) & (exuE3e = $true) & (powersetI = $true) & (setadjoinIR = $true) & (dsetconstrI = $true)),
% 1.93/1.50 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f136,f138,f137])).
% 1.93/1.50 thf(f137,plain,(
% 1.93/1.50 ? [X0 : $i > $o] : (! [X1 : $i] : ? [X2 : $i] : (((X1 != X2) | ((X0 @ X2) != $true)) & ((X1 = X2) | ((X0 @ X2) = $true))) & ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0))))) => (! [X1 : $i] : ? [X2 : $i] : (((X1 != X2) | ($true != (sK0 @ X2))) & ((X1 = X2) | ($true = (sK0 @ X2)))) & ($true = (exu @ (^[Y0 : $i]: (sK0 @ Y0)))))),
% 1.93/1.50 introduced(definition,[],[choice_axiom])).
% 1.93/1.50 thf(f138,plain,(
% 1.93/1.50 ! [X1 : $i] : (? [X2 : $i] : (((X1 != X2) | ($true != (sK0 @ X2))) & ((X1 = X2) | ($true = (sK0 @ X2)))) => ((((sK1 @ X1) != X1) | ((sK0 @ (sK1 @ X1)) != $true)) & (((sK1 @ X1) = X1) | ((sK0 @ (sK1 @ X1)) = $true))))),
% 1.93/1.50 introduced(definition,[],[choice_axiom])).
% 1.93/1.50 thf(f136,plain,(
% 1.93/1.50 (subPowSU = $true) & (setadjoinE = $true) & (omega0Ax = $true) & (replAx = $true) & (setunionE = $true) & (setunionAx = $true) & (nonemptyE1 = $true) & (setextAx = $true) & (prop2setE = $true) & (emptyI = $true) & (setbeta = $true) & (omegaIndAx = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (notinemptyset = $true) & (setadjoinOr = $true) & (emptysetAx = $true) & (emptyInPowerset = $true) & ? [X0 : $i > $o] : (! [X1 : $i] : ? [X2 : $i] : (((X1 != X2) | ((X0 @ X2) != $true)) & ((X1 = X2) | ((X0 @ X2) = $true))) & ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & (setadjoinIL = $true) & (setoftrueEq = $true) & (foundationAx = $true) & (dsetconstrER = $true) & (powersetE = $true) & (wellorderingAx = $true) & (emptyinunitempty = $true) & (powersetAx = $true) & (emptysetE = $true) & (setunionI = $true) & (noeltsimpempty = $true) & (setext = $true) & (emptysetimpfalse = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (descrp = $true) & (omegaSAx = $true) & (exuE3e = $true) & (powersetI = $true) & (setadjoinIR = $true) & (dsetconstrI = $true)),
% 1.93/1.50 inference(nnf_transformation,[status(thm)],[f135])).
% 1.93/1.50 thf(f135,plain,(
% 1.93/1.50 (subPowSU = $true) & (setadjoinE = $true) & (omega0Ax = $true) & (replAx = $true) & (setunionE = $true) & (setunionAx = $true) & (nonemptyE1 = $true) & (setextAx = $true) & (prop2setE = $true) & (emptyI = $true) & (setbeta = $true) & (omegaIndAx = $true) & (nonemptyI = $true) & (emptyinPowerset = $true) & (nonemptyI1 = $true) & (setadjoinAx = $true) & (notinemptyset = $true) & (setadjoinOr = $true) & (emptysetAx = $true) & (emptyInPowerset = $true) & ? [X0 : $i > $o] : (! [X1 : $i] : ? [X2 : $i] : (((X0 @ X2) = $true) <~> (X1 = X2)) & ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & (setadjoinIL = $true) & (setoftrueEq = $true) & (foundationAx = $true) & (dsetconstrER = $true) & (powersetE = $true) & (wellorderingAx = $true) & (emptyinunitempty = $true) & (powersetAx = $true) & (emptysetE = $true) & (setunionI = $true) & (noeltsimpempty = $true) & (setext = $true) & (emptysetimpfalse = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (descrp = $true) & (omegaSAx = $true) & (exuE3e = $true) & (powersetI = $true) & (setadjoinIR = $true) & (dsetconstrI = $true)),
% 1.93/1.50 inference(flattening,[status(thm)],[f134])).
% 1.93/1.50 thf(f134,plain,(
% 1.93/1.50 ((((((((((((((((((((((((((((((((((((((((? [X0 : $i > $o] : (! [X1 : $i] : ? [X2 : $i] : (((X0 @ X2) = $true) <~> (X1 = X2)) & ($true = (exu @ (^[Y0 : $i]: (X0 @ Y0))))) & (subPowSU = $true)) & (setunionE = $true)) & (setunionI = $true)) & (powersetE = $true)) & (emptyInPowerset = $true)) & (emptyinPowerset = $true)) & (powersetI = $true)) & (setoftrueEq = $true)) & (setadjoinOr = $true)) & (setadjoinE = $true)) & (setadjoinIR = $true)) & (emptyinunitempty = $true)) & (setadjoinIL = $true)) & (nonemptyI1 = $true)) & (nonemptyI = $true)) & (nonemptyE1 = $true)) & (setbeta = $true)) & (noeltsimpempty = $true)) & (emptyI = $true)) & (setext = $true)) & (exuE3e = $true)) & (notinemptyset = $true)) & (emptysetimpfalse = $true)) & (emptysetE = $true)) & (prop2setE = $true)) & (exuE1 = $true)) & (dsetconstrER = $true)) & (dsetconstrEL = $true)) & (dsetconstrI = $true)) & (descrp = $true)) & (wellorderingAx = $true)) & (foundationAx = $true)) & (replAx = $true)) & (omegaIndAx = $true)) & (omegaSAx = $true)) & (omega0Ax = $true)) & (setunionAx = $true)) & (powersetAx = $true)) & (setadjoinAx = $true)) & (emptysetAx = $true)) & (setextAx = $true)),
% 1.93/1.50 inference(ennf_transformation,[status(thm)],[f133])).
% 1.93/1.50 thf(f133,plain,(
% 1.93/1.50 ~((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) => ! [X0 : $i > $o] : (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) => ? [X1 : $i] : ! [X2 : $i] : (((X0 @ X2) = $true) <=> (X1 = X2))))))))))))))))))))))))))))))))))))))))))))),
% 1.93/1.50 inference(rectify,[status(thm)],[f110])).
% 1.93/1.50 thf(f110,plain,(
% 1.93/1.50 ~((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) => ! [X0 : $i > $o] : (($true = (exu @ (^[Y0 : $i]: (X0 @ Y0)))) => ? [X2 : $i] : ! [X3 : $i] : (((X0 @ X3) = $true) <=> (X2 = X3))))))))))))))))))))))))))))))))))))))))))))),
% 1.93/1.50 inference(fool_elimination,[status(thm)],[f109])).
% 1.93/1.50 thf(f109,plain,(
% 1.93/1.50 ~(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 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2 : $i] : ! [X3 : $i] : ((X0 @ X3) <=> (X2 = X3))))))))))))))))))))))))))))))))))))))))))))),
% 1.93/1.50 inference(rectify,[status(thm)],[f46])).
% 1.93/1.50 thf(f46,negated_conjecture,(
% 1.93/1.50 ~(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 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2))))))))))))))))))))))))))))))))))))))))))))),
% 1.93/1.50 inference(negated_conjecture,[status(cth)],[f45])).
% 1.93/1.50 thf(f45,conjecture,(
% 1.93/1.50 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 => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : ! [X2 : $i] : ((X0 @ X2) <=> (X1 = X2)))))))))))))))))))))))))))))))))))))))))))),
% 1.93/1.50 file('/export/starexec/sandbox/tmp/tmp.J0dprC0Sfg/DTF2THF_14868.p',exuE2)).
% 1.93/1.50 thf(f794,plain,(
% 1.93/1.50 ( ! [X0 : $i] : (($true != (sK0 @ X0)) | (sK25 != X0)) )),
% 1.93/1.50 inference(trivial_inequality_removal,[status(thm)],[f790])).
% 1.93/1.50 thf(f790,plain,(
% 1.93/1.50 ( ! [X0 : $i] : ((X0 != X0) | ($true != (sK0 @ X0)) | (sK25 != X0)) )),
% 1.93/1.50 inference(superposition,[status(thm)],[f179,f786])).
% 1.93/1.50 thf(f786,plain,(
% 1.93/1.50 ( ! [X0 : $i] : (((sK1 @ X0) = X0) | (sK25 != X0)) )),
% 1.93/1.50 inference(equality_factoring,[status(thm)],[f784])).
% 1.93/1.50 thf(f784,plain,(
% 1.93/1.50 ( ! [X0 : $i] : ((sK25 = (sK1 @ X0)) | ((sK1 @ X0) = X0)) )),
% 1.93/1.50 inference(trivial_inequality_removal,[status(thm)],[f782])).
% 1.93/1.50 thf(f782,plain,(
% 1.93/1.50 ( ! [X0 : $i] : ((sK25 = (sK1 @ X0)) | ($true = $false) | ((sK1 @ X0) = X0)) )),
% 1.93/1.50 inference(superposition,[status(thm)],[f639,f178])).
% 1.93/1.50 thf(f178,plain,(
% 1.93/1.50 ( ! [X1 : $i] : (((sK0 @ (sK1 @ X1)) = $true) | ((sK1 @ X1) = X1)) )),
% 1.93/1.50 inference(cnf_transformation,[status(thm)],[f139])).
% 1.93/1.50 thf(f639,plain,(
% 1.93/1.50 ( ! [X1 : $i] : (($false = (sK0 @ X1)) | (sK25 = X1)) )),
% 1.93/1.50 inference(equality_proxy_clausification,[status(thm)],[f638])).
% 1.93/1.50 thf(f638,plain,(
% 1.93/1.50 ( ! [X1 : $i] : (($true = (sK25 = X1)) | ($false = (sK0 @ X1))) )),
% 1.93/1.50 inference(binary_proxy_clausification,[status(thm)],[f637])).
% 1.93/1.50 thf(f637,plain,(
% 1.93/1.50 ( ! [X1 : $i] : (($true = ((sK0 @ X1) => (sK25 = X1)))) )),
% 1.93/1.50 inference(beta_eta_normalization,[status(thm)],[f636])).
% 1.93/1.50 thf(f636,plain,(
% 1.93/1.50 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((sK0 @ Y0) => (sK25 = Y0))) @ X1))) )),
% 1.93/1.50 inference(pi_clausification,[status(thm)],[f635])).
% 1.93/1.50 thf(f635,plain,(
% 1.93/1.50 ($true = (!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK25 = Y0)))))),
% 1.93/1.50 inference(binary_proxy_clausification,[status(thm)],[f633])).
% 1.93/1.50 thf(f179,plain,(
% 1.93/1.50 ( ! [X1 : $i] : (((sK0 @ (sK1 @ X1)) != $true) | ((sK1 @ X1) != X1)) )),
% 1.93/1.50 inference(cnf_transformation,[status(thm)],[f139])).
% 1.93/1.50 % SZS output end Proof for DTF2THF_14868
% 1.93/1.50 % (14966)------------------------------
% 1.93/1.50 % (14966)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.93/1.50 % (14966)Termination reason: Refutation
% 1.93/1.50
% 1.93/1.50 % (14966)Memory used [KB]: 6140
% 1.93/1.50 % (14966)Time elapsed: 0.038 s
% 1.93/1.50 % (14966)Instructions burned: 73 (million)
% 1.93/1.50 % (14966)------------------------------
% 1.93/1.50 % (14966)------------------------------
% 1.93/1.50 % (14965)Success in time 0.052 s
%------------------------------------------------------------------------------