%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU514^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:35:01 AM UTC 2026
% Result : Theorem 1.88s 1.44s
% Output : Refutation 1.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 3
% Syntax : Number of formulae : 29 ( 18 unt; 0 typ; 0 def)
% Number of atoms : 629 ( 177 equ; 0 cnn)
% Maximal formula atoms : 32 ( 21 avg)
% Number of connectives : 444 ( 10 ~; 16 |; 95 &; 181 @)
% ( 2 <=>; 125 =>; 0 <=; 0 <~>)
% Maximal formula depth : 39 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 68 usr; 36 con; 0-3 aty)
% ( 15 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 66 ( 18 ^; 39 !; 9 ?; 66 :)
% 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_62,type,
sK4: $i > $i > $i ).
thf(func_def_63,type,
sK5: $i > $i > $i ).
thf(func_def_64,type,
sK6: $i > $i ).
thf(func_def_65,type,
sK7: $i > $i > $i ).
thf(func_def_66,type,
sK8: $i > $i > $i ).
thf(func_def_67,type,
sK9: $i > $i > $i ).
thf(func_def_68,type,
sK10: $i > $i ).
thf(func_def_69,type,
sK11: $i > $i ).
thf(func_def_70,type,
sK12: $i > $i ).
thf(func_def_71,type,
sK13: ( $i > $o ) > $i ).
thf(func_def_72,type,
sK14: ( $i > $o ) > $i > $i ).
thf(func_def_73,type,
sK15: ( $i > $o ) > $i > $i ).
thf(func_def_74,type,
sK16: $i > ( $i > $i > $o ) > $i ).
thf(func_def_75,type,
sK17: $i > ( $i > $i > $o ) > $i ).
thf(func_def_76,type,
sK18: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_77,type,
sK19: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_78,type,
sK20: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_79,type,
sK21: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_80,type,
sK22: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_81,type,
sK23: $i > $i ).
thf(func_def_82,type,
sK24: $i > $i > $i ).
thf(func_def_83,type,
sK25: $i > $i > $i ).
thf(func_def_84,type,
sK26: $i > $i > $i ).
thf(func_def_85,type,
sK27: $i > $i > $i > $i ).
thf(func_def_86,type,
sK28: $i > $i ).
thf(func_def_87,type,
sK29: $i > $i > $i ).
thf(f661,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f659]) ).
thf(f659,plain,
$false = $true,
inference(superposition,[status(thm)],[f658,f128]) ).
thf(f128,plain,
( $true
= ( in @ sK0 @ sK1 ) ),
inference(cnf_transformation,[status(thm)],[f103]) ).
thf(f103,plain,
( ( foundationAx = $true )
& ( notinemptyset = $true )
& ( setext = $true )
& ( dsetconstrEL = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( powersetAx = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( exuE3e = $true )
& ( dsetconstrER = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( emptysetimpfalse = $true )
& ( setunionAx = $true )
& ( ( in @ sK0 @ ( setadjoin @ sK2 @ sK1 ) )
!= $true )
& ( $true
= ( in @ sK0 @ sK1 ) )
& ( exuE1 = $true )
& ( emptysetAx = $true )
& ( setextAx = $true )
& ( nonemptyI = $true )
& ( emptyI = $true )
& ( omega0Ax = $true )
& ( setadjoinAx = $true )
& ( emptysetE = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI1 = $true )
& ( noeltsimpempty = $true )
& ( prop2setE = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f101,f102]) ).
thf(f102,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
=> ( ( ( in @ sK0 @ ( setadjoin @ sK2 @ sK1 ) )
!= $true )
& ( $true
= ( in @ sK0 @ sK1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f101,plain,
( ( foundationAx = $true )
& ( notinemptyset = $true )
& ( setext = $true )
& ( dsetconstrEL = $true )
& ( setbeta = $true )
& ( omegaIndAx = $true )
& ( powersetAx = $true )
& ( emptyinunitempty = $true )
& ( descrp = $true )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( replAx = $true )
& ( exuE3e = $true )
& ( dsetconstrER = $true )
& ( wellorderingAx = $true )
& ( setadjoinIL = $true )
& ( emptysetimpfalse = $true )
& ( setunionAx = $true )
& ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $true ) )
& ( exuE1 = $true )
& ( emptysetAx = $true )
& ( setextAx = $true )
& ( nonemptyI = $true )
& ( emptyI = $true )
& ( omega0Ax = $true )
& ( setadjoinAx = $true )
& ( emptysetE = $true )
& ( nonemptyE1 = $true )
& ( nonemptyI1 = $true )
& ( noeltsimpempty = $true )
& ( prop2setE = $true ) ),
inference(flattening,[status(thm)],[f100]) ).
thf(f100,plain,
( ? [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
!= $true )
& ( ( in @ X0 @ X1 )
= $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)],[f79]) ).
thf(f79,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 )
=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ X1 )
= $true )
=> ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f78]) ).
thf(f78,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
=> ! [X0: $i,X1: $i,X2: $i] :
( ( in @ X0 @ X1 )
=> ( in @ X0 @ ( setadjoin @ X2 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,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
=> ! [X2: $i,X3: $i,X1: $i] :
( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( setadjoin @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f34]) ).
thf(f34,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
=> ! [X2: $i,X3: $i,X1: $i] :
( ( in @ X2 @ X3 )
=> ( in @ X2 @ ( setadjoin @ X1 @ X3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.etdkTwxwpW/DTF2THF_27557.p',setadjoinIR) ).
thf(f658,plain,
( $false
= ( in @ sK0 @ sK1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f655]) ).
thf(f655,plain,
( ( $true != $true )
| ( $false
= ( in @ sK0 @ sK1 ) ) ),
inference(superposition,[status(thm)],[f129,f353]) ).
thf(f353,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( $false
= ( in @ X3 @ X2 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f348]) ).
thf(f348,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
= $true )
| ( $false
= ( ( in @ X3 @ X2 )
| ( X3 = X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f347]) ).
thf(f347,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
= ( ( in @ X3 @ X2 )
| ( X3 = X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f346]) ).
thf(f346,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X3 @ ( setadjoin @ X1 @ X2 ) )
= ( ( in @ X3 @ X2 )
| ( X3 = X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f345]) ).
thf(f345,plain,
! [X2: $i,X3: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ X2 ) )
= ( ( in @ Y0 @ X2 )
| ( Y0 = X1 ) ) )
@ X3 )
= $true ),
inference(pi_clausification,[status(thm)],[f344]) ).
thf(f344,plain,
! [X2: $i,X1: $i] :
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ ( setadjoin @ X1 @ X2 ) )
= ( ( in @ Y0 @ X2 )
| ( Y0 = X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f343]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ X1 @ Y0 ) )
= ( ( in @ Y1 @ Y0 )
| ( Y1 = X1 ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f342]) ).
thf(f342,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ ( setadjoin @ X1 @ Y0 ) )
= ( ( in @ Y1 @ Y0 )
| ( Y1 = X1 ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f341]) ).
thf(f341,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
= ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
= ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f121,f112]) ).
thf(f112,plain,
( setadjoinAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
= ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f56]) ).
thf(f56,plain,
( setadjoinAx
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ ( setadjoin @ Y0 @ Y1 ) )
= ( ( in @ Y2 @ Y1 )
| ( Y2 = Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f55]) ).
thf(f55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X0 @ ( setadjoin @ X2 @ X1 ) )
<=> ( ( X0 = X2 )
| ( in @ X0 @ X1 ) ) )
= setadjoinAx ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
! [X2: $i,X3: $i,X1: $i] :
( ( ( in @ X2 @ ( setadjoin @ X1 @ X3 ) )
<=> ( ( X1 = X2 )
| ( in @ X2 @ X3 ) ) )
= setadjoinAx ),
file('/export/starexec/sandbox/tmp/tmp.etdkTwxwpW/DTF2THF_27557.p',setadjoinAx) ).
thf(f121,plain,
setadjoinAx = $true,
inference(cnf_transformation,[status(thm)],[f103]) ).
thf(f129,plain,
( ( in @ sK0 @ ( setadjoin @ sK2 @ sK1 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU514^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.09 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n019.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 12:25:09 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.38 ---- Original DTF file ---
% 0.18/0.38 thf(spec,logic,$$dhol).
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 % File : SEU514^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.38 % Domain : Set Theory
% 0.18/0.38 % Problem : Preliminary Notions - Adjoining Elements to Sets
% 0.18/0.38 % Version : Especial.
% 0.18/0.38 % English : (! x:i.! A:i.! y:i.in y A -> in y (setadjoin x A))
% 0.18/0.38
% 0.18/0.38 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.38 % Source : [Bro08]
% 0.18/0.38 % Names : ZFC016g [Bro08]
% 0.18/0.38
% 0.18/0.38 % Status : Theorem
% 0.18/0.38 % 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, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.20 v6.2.0, 0.14 v6.1.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.33 v4.0.0, 0.67 v3.7.0
% 0.18/0.38 % Syntax : Number of formulae : 75 ( 33 unt; 41 typ; 33 def)
% 0.18/0.38 % Number of atoms : 188 ( 42 equ; 0 cnn)
% 0.18/0.38 % Maximal formula atoms : 32 ( 5 avg)
% 0.18/0.38 % Number of connectives : 321 ( 7 ~; 3 |; 18 &; 211 @)
% 0.18/0.38 % ( 7 <=>; 75 =>; 0 <=; 0 <~>)
% 0.18/0.38 % Maximal formula depth : 38 ( 2 avg)
% 0.18/0.38 % Number of types : 2 ( 0 usr)
% 0.18/0.38 % Number of type conns : 26 ( 26 >; 0 *; 0 +; 0 <<)
% 0.18/0.38 % Number of symbols : 43 ( 41 usr; 33 con; 0-2 aty)
% 0.18/0.38 % Number of variables : 106 ( 14 ^; 76 !; 16 ?; 106 :)
% 0.18/0.38 % SPC : TH0_THM_EQU_NAR
% 0.18/0.38
% 0.18/0.38 % Comments : http://mathgate.info/detsetitem.php?id=81
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 thf(in_type,type,
% 0.18/0.38 in: $i > $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(exu_type,type,
% 0.18/0.38 exu: ( $i > $o ) > $o ).
% 0.18/0.38
% 0.18/0.38 thf(exu,definition,
% 0.18/0.38 ( exu
% 0.18/0.38 = ( ^ [Xphi: $i > $o] :
% 0.18/0.38 ? [Xx: $i] :
% 0.18/0.38 ( ( Xphi @ Xx )
% 0.18/0.38 & ! [Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xy )
% 0.18/0.38 => ( Xx = Xy ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setextAx_type,type,
% 0.18/0.38 setextAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setextAx,definition,
% 0.18/0.38 ( setextAx
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 <=> ( in @ Xx @ B ) )
% 0.18/0.38 => ( A = B ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyset_type,type,
% 0.18/0.38 emptyset: $i ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetAx_type,type,
% 0.18/0.38 emptysetAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetAx,definition,
% 0.18/0.38 ( emptysetAx
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoin_type,type,
% 0.18/0.38 setadjoin: $i > $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinAx_type,type,
% 0.18/0.38 setadjoinAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinAx,definition,
% 0.18/0.38 ( setadjoinAx
% 0.18/0.38 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.38 <=> ( ( Xy = Xx )
% 0.18/0.38 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(powerset_type,type,
% 0.18/0.38 powerset: $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(powersetAx_type,type,
% 0.18/0.38 powersetAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(powersetAx,definition,
% 0.18/0.38 ( powersetAx
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.38 <=> ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setunion_type,type,
% 0.18/0.38 setunion: $i > $i ).
% 0.18/0.38
% 0.18/0.38 thf(setunionAx_type,type,
% 0.18/0.38 setunionAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setunionAx,definition,
% 0.18/0.38 ( setunionAx
% 0.18/0.38 = ( ! [A: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.38 <=> ? [B: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 & ( in @ B @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(omega_type,type,
% 0.18/0.38 omega: $i ).
% 0.18/0.38
% 0.18/0.38 thf(omega0Ax_type,type,
% 0.18/0.38 omega0Ax: $o ).
% 0.18/0.38
% 0.18/0.38 thf(omega0Ax,definition,
% 0.18/0.38 ( omega0Ax
% 0.18/0.38 = ( in @ emptyset @ omega ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(omegaSAx_type,type,
% 0.18/0.38 omegaSAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(omegaSAx,definition,
% 0.18/0.38 ( omegaSAx
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ omega )
% 0.18/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(omegaIndAx_type,type,
% 0.18/0.38 omegaIndAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(omegaIndAx,definition,
% 0.18/0.38 ( omegaIndAx
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ( ( in @ emptyset @ A )
% 0.18/0.38 & ! [Xx: $i] :
% 0.18/0.38 ( ( ( in @ Xx @ omega )
% 0.18/0.38 & ( in @ Xx @ A ) )
% 0.18/0.38 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ omega )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(replAx_type,type,
% 0.18/0.38 replAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(replAx,definition,
% 0.18/0.38 ( replAx
% 0.18/0.38 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( exu
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.18/0.38 => ? [B: $i] :
% 0.18/0.38 ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 <=> ? [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ A )
% 0.18/0.38 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(foundationAx_type,type,
% 0.18/0.38 foundationAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(foundationAx,definition,
% 0.18/0.38 ( foundationAx
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.38 => ? [B: $i] :
% 0.18/0.38 ( ( in @ B @ A )
% 0.18/0.38 & ~ ? [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(wellorderingAx_type,type,
% 0.18/0.38 wellorderingAx: $o ).
% 0.18/0.38
% 0.18/0.38 thf(wellorderingAx,definition,
% 0.18/0.38 ( wellorderingAx
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ? [B: $i] :
% 0.18/0.38 ( ! [C: $i] :
% 0.18/0.38 ( ( in @ C @ B )
% 0.18/0.38 => ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ C )
% 0.18/0.38 => ( in @ Xx @ A ) ) )
% 0.18/0.38 & ! [Xx: $i,Xy: $i] :
% 0.18/0.38 ( ( ( in @ Xx @ A )
% 0.18/0.38 & ( in @ Xy @ A ) )
% 0.18/0.38 => ( ! [C: $i] :
% 0.18/0.38 ( ( in @ C @ B )
% 0.18/0.38 => ( ( in @ Xx @ C )
% 0.18/0.38 <=> ( in @ Xy @ C ) ) )
% 0.18/0.38 => ( Xx = Xy ) ) )
% 0.18/0.38 & ! [C: $i,D: $i] :
% 0.18/0.38 ( ( ( in @ C @ B )
% 0.18/0.38 & ( in @ D @ B ) )
% 0.18/0.38 => ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ C )
% 0.18/0.38 => ( in @ Xx @ D ) )
% 0.18/0.38 | ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ D )
% 0.18/0.38 => ( in @ Xx @ C ) ) ) )
% 0.18/0.38 & ! [C: $i] :
% 0.18/0.38 ( ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ C )
% 0.18/0.38 => ( in @ Xx @ A ) )
% 0.18/0.38 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.18/0.38 => ? [D: $i,Xx: $i] :
% 0.18/0.38 ( ( in @ D @ B )
% 0.18/0.38 & ( in @ Xx @ C )
% 0.18/0.38 & ~ ? [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ D )
% 0.18/0.38 & ( in @ Xy @ C ) )
% 0.18/0.38 & ! [E: $i] :
% 0.18/0.38 ( ( in @ E @ B )
% 0.18/0.38 => ( ! [Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ E )
% 0.18/0.38 => ( in @ Xy @ D ) )
% 0.18/0.38 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(descr_type,type,
% 0.18/0.38 descr: ( $i > $o ) > $i ).
% 0.18/0.38
% 0.18/0.38 thf(descrp_type,type,
% 0.18/0.38 descrp: $o ).
% 0.18/0.38
% 0.18/0.38 thf(descrp,definition,
% 0.18/0.38 ( descrp
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ( Xphi
% 0.18/0.38 @ ( descr
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstr_type,type,
% 0.18/0.38 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrI_type,type,
% 0.18/0.38 dsetconstrI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrI,definition,
% 0.18/0.38 ( dsetconstrI
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( Xphi @ Xx )
% 0.18/0.38 => ( in @ Xx
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrEL_type,type,
% 0.18/0.38 dsetconstrEL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrEL,definition,
% 0.18/0.38 ( dsetconstrEL
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.38 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrER_type,type,
% 0.18/0.38 dsetconstrER: $o ).
% 0.18/0.38
% 0.18/0.38 thf(dsetconstrER,definition,
% 0.18/0.38 ( dsetconstrER
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.38 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuE1_type,type,
% 0.18/0.38 exuE1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuE1,definition,
% 0.18/0.38 ( exuE1
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ? [Xx: $i] :
% 0.18/0.38 ( ( Xphi @ Xx )
% 0.18/0.38 & ! [Xy: $i] :
% 0.18/0.38 ( ( Xphi @ Xy )
% 0.18/0.38 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(prop2set_type,type,
% 0.18/0.38 prop2set: $o > $i ).
% 0.18/0.38
% 0.18/0.38 thf(prop2set,definition,
% 0.18/0.38 ( prop2set
% 0.18/0.38 = ( ^ [Xphi: $o] :
% 0.18/0.38 ( dsetconstr @ ( powerset @ emptyset )
% 0.18/0.38 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(prop2setE_type,type,
% 0.18/0.38 prop2setE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(prop2setE,definition,
% 0.18/0.38 ( prop2setE
% 0.18/0.38 = ( ! [Xphi: $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.18/0.38 => Xphi ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetE_type,type,
% 0.18/0.38 emptysetE: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetE,definition,
% 0.18/0.38 ( emptysetE
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ emptyset )
% 0.18/0.38 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetimpfalse_type,type,
% 0.18/0.38 emptysetimpfalse: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptysetimpfalse,definition,
% 0.18/0.38 ( emptysetimpfalse
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ emptyset )
% 0.18/0.38 => $false ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(notinemptyset_type,type,
% 0.18/0.38 notinemptyset: $o ).
% 0.18/0.38
% 0.18/0.38 thf(notinemptyset,definition,
% 0.18/0.38 ( notinemptyset
% 0.18/0.38 = ( ! [Xx: $i] :
% 0.18/0.38 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(exuE3e_type,type,
% 0.18/0.38 exuE3e: $o ).
% 0.18/0.38
% 0.18/0.38 thf(exuE3e,definition,
% 0.18/0.38 ( exuE3e
% 0.18/0.38 = ( ! [Xphi: $i > $o] :
% 0.18/0.38 ( ( exu
% 0.18/0.38 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.38 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setext_type,type,
% 0.18/0.38 setext: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setext,definition,
% 0.18/0.38 ( setext
% 0.18/0.38 = ( ! [A: $i,B: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( in @ Xx @ B ) )
% 0.18/0.38 => ( ! [Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ B )
% 0.18/0.38 => ( in @ Xx @ A ) )
% 0.18/0.38 => ( A = B ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyI_type,type,
% 0.18/0.38 emptyI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptyI,definition,
% 0.18/0.38 ( emptyI
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ~ ( in @ Xx @ A )
% 0.18/0.38 => ( A = emptyset ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(noeltsimpempty_type,type,
% 0.18/0.38 noeltsimpempty: $o ).
% 0.18/0.38
% 0.18/0.38 thf(noeltsimpempty,definition,
% 0.18/0.38 ( noeltsimpempty
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ! [Xx: $i] :
% 0.18/0.38 ~ ( in @ Xx @ A )
% 0.18/0.38 => ( A = emptyset ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setbeta_type,type,
% 0.18/0.38 setbeta: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setbeta,definition,
% 0.18/0.38 ( setbeta
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( in @ Xx
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.38 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonempty_type,type,
% 0.18/0.38 nonempty: $i > $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonempty,definition,
% 0.18/0.38 ( nonempty
% 0.18/0.38 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyE1_type,type,
% 0.18/0.38 nonemptyE1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyE1,definition,
% 0.18/0.38 ( nonemptyE1
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ( nonempty @ A )
% 0.18/0.38 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyI_type,type,
% 0.18/0.38 nonemptyI: $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyI,definition,
% 0.18/0.38 ( nonemptyI
% 0.18/0.38 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.38 ( ( in @ Xx @ A )
% 0.18/0.38 => ( ( Xphi @ Xx )
% 0.18/0.38 => ( nonempty
% 0.18/0.38 @ ( dsetconstr @ A
% 0.18/0.38 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyI1_type,type,
% 0.18/0.38 nonemptyI1: $o ).
% 0.18/0.38
% 0.18/0.38 thf(nonemptyI1,definition,
% 0.18/0.38 ( nonemptyI1
% 0.18/0.38 = ( ! [A: $i] :
% 0.18/0.38 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.38 => ( nonempty @ A ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinIL_type,type,
% 0.18/0.38 setadjoinIL: $o ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinIL,definition,
% 0.18/0.38 ( setadjoinIL
% 0.18/0.38 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(emptyinunitempty_type,type,
% 0.18/0.38 emptyinunitempty: $o ).
% 0.18/0.38
% 0.18/0.38 thf(emptyinunitempty,definition,
% 0.18/0.38 ( emptyinunitempty
% 0.18/0.38 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 0.18/0.38
% 0.18/0.38 thf(setadjoinIR,conjecture,
% 0.18/0.38 ( setextAx
% 0.18/0.38 => ( emptysetAx
% 0.18/0.38 => ( setadjoinAx
% 0.18/0.38 => ( powersetAx
% 0.18/0.38 => ( setunionAx
% 0.18/0.38 => ( omega0Ax
% 0.18/0.38 => ( omegaSAx
% 0.18/0.38 => ( omegaIndAx
% 0.18/0.38 => ( replAx
% 0.18/0.38 => ( foundationAx
% 0.18/0.38 => ( wellorderingAx
% 0.18/0.38 => ( descrp
% 0.18/0.38 => ( dsetconstrI
% 0.18/0.38 => ( dsetconstrEL
% 0.18/0.38 => ( dsetconstrER
% 0.18/0.38 => ( exuE1
% 0.18/0.38 => ( prop2setE
% 0.18/0.38 => ( emptysetE
% 0.18/0.38 => ( emptysetimpfalse
% 0.18/0.38 => ( notinemptyset
% 0.18/0.38 => ( exuE3e
% 0.18/0.38 => ( setext
% 0.18/0.38 => ( emptyI
% 0.18/0.38 => ( noeltsimpempty
% 0.18/0.38 => ( setbeta
% 0.18/0.38 => ( nonemptyE1
% 0.18/0.38 => ( nonemptyI
% 0.18/0.38 => ( nonemptyI1
% 0.18/0.38 => ( setadjoinIL
% 0.18/0.38 => ( emptyinunitempty
% 0.18/0.38 => ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.38 ( ( in @ Xy @ A )
% 0.18/0.38 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.38
% 0.18/0.38 %------------------------------------------------------------------------------
% 0.18/0.38 ------------------------
% 1.72/1.37 ---- Embedded in THF ---
% 1.72/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.72/1.37 %%% Generated on Tue Feb 24 12:25:10 EST 2026
% 1.72/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.72/1.37 %%% Logic specification used:
% 1.72/1.37 %%% thf(spec, logic, $$dhol).
% 1.72/1.37
% 1.72/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.etdkTwxwpW/DTF2DTF27557.p
% See solution above
% 1.72/1.37 ------------------------
% 1.72/1.38 ---- Cleaned THF ---
% 1.72/1.39 thf(in_type,type,
% 1.72/1.39 in: $i > $i > $o ).
% 1.72/1.39
% 1.72/1.39 thf(exu_type,type,
% 1.72/1.39 exu: ( $i > $o ) > $o ).
% 1.72/1.39
% 1.72/1.39 thf(exu,definition,
% 1.72/1.39 ( exu
% 1.72/1.39 = ( ^ [Xphi: $i > $o] :
% 1.72/1.39 ? [Xx: $i] :
% 1.72/1.39 ( ( Xphi @ Xx )
% 1.72/1.39 & ! [Xy: $i] :
% 1.72/1.39 ( ( Xphi @ Xy )
% 1.72/1.39 => ( Xx = Xy ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(setextAx_type,type,
% 1.72/1.39 setextAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(setextAx,definition,
% 1.72/1.39 ( setextAx
% 1.72/1.39 = ( ! [A: $i,B: $i] :
% 1.72/1.39 ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ A )
% 1.72/1.39 <=> ( in @ Xx @ B ) )
% 1.72/1.39 => ( A = B ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(emptyset_type,type,
% 1.72/1.39 emptyset: $i ).
% 1.72/1.39
% 1.72/1.39 thf(emptysetAx_type,type,
% 1.72/1.39 emptysetAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(emptysetAx,definition,
% 1.72/1.39 ( emptysetAx
% 1.72/1.39 = ( ! [Xx: $i] :
% 1.72/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(setadjoin_type,type,
% 1.72/1.39 setadjoin: $i > $i > $i ).
% 1.72/1.39
% 1.72/1.39 thf(setadjoinAx_type,type,
% 1.72/1.39 setadjoinAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(setadjoinAx,definition,
% 1.72/1.39 ( setadjoinAx
% 1.72/1.39 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.72/1.39 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.72/1.39 <=> ( ( Xy = Xx )
% 1.72/1.39 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(powerset_type,type,
% 1.72/1.39 powerset: $i > $i ).
% 1.72/1.39
% 1.72/1.39 thf(powersetAx_type,type,
% 1.72/1.39 powersetAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(powersetAx,definition,
% 1.72/1.39 ( powersetAx
% 1.72/1.39 = ( ! [A: $i,B: $i] :
% 1.72/1.39 ( ( in @ B @ ( powerset @ A ) )
% 1.72/1.39 <=> ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ B )
% 1.72/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(setunion_type,type,
% 1.72/1.39 setunion: $i > $i ).
% 1.72/1.39
% 1.72/1.39 thf(setunionAx_type,type,
% 1.72/1.39 setunionAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(setunionAx,definition,
% 1.72/1.39 ( setunionAx
% 1.72/1.39 = ( ! [A: $i,Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ ( setunion @ A ) )
% 1.72/1.39 <=> ? [B: $i] :
% 1.72/1.39 ( ( in @ Xx @ B )
% 1.72/1.39 & ( in @ B @ A ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(omega_type,type,
% 1.72/1.39 omega: $i ).
% 1.72/1.39
% 1.72/1.39 thf(omega0Ax_type,type,
% 1.72/1.39 omega0Ax: $o ).
% 1.72/1.39
% 1.72/1.39 thf(omega0Ax,definition,
% 1.72/1.39 ( omega0Ax
% 1.72/1.39 = ( in @ emptyset @ omega ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(omegaSAx_type,type,
% 1.72/1.39 omegaSAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(omegaSAx,definition,
% 1.72/1.39 ( omegaSAx
% 1.72/1.39 = ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ omega )
% 1.72/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(omegaIndAx_type,type,
% 1.72/1.39 omegaIndAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(omegaIndAx,definition,
% 1.72/1.39 ( omegaIndAx
% 1.72/1.39 = ( ! [A: $i] :
% 1.72/1.39 ( ( ( in @ emptyset @ A )
% 1.72/1.39 & ! [Xx: $i] :
% 1.72/1.39 ( ( ( in @ Xx @ omega )
% 1.72/1.39 & ( in @ Xx @ A ) )
% 1.72/1.39 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.72/1.39 => ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ omega )
% 1.72/1.39 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(replAx_type,type,
% 1.72/1.39 replAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(replAx,definition,
% 1.72/1.39 ( replAx
% 1.72/1.39 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.72/1.39 ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ A )
% 1.72/1.39 => ( exu
% 1.72/1.39 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.72/1.39 => ? [B: $i] :
% 1.72/1.39 ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ B )
% 1.72/1.39 <=> ? [Xy: $i] :
% 1.72/1.39 ( ( in @ Xy @ A )
% 1.72/1.39 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(foundationAx_type,type,
% 1.72/1.39 foundationAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(foundationAx,definition,
% 1.72/1.39 ( foundationAx
% 1.72/1.39 = ( ! [A: $i] :
% 1.72/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.72/1.39 => ? [B: $i] :
% 1.72/1.39 ( ( in @ B @ A )
% 1.72/1.39 & ~ ? [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ B )
% 1.72/1.39 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(wellorderingAx_type,type,
% 1.72/1.39 wellorderingAx: $o ).
% 1.72/1.39
% 1.72/1.39 thf(wellorderingAx,definition,
% 1.72/1.39 ( wellorderingAx
% 1.72/1.39 = ( ! [A: $i] :
% 1.72/1.39 ? [B: $i] :
% 1.72/1.39 ( ! [C: $i] :
% 1.72/1.39 ( ( in @ C @ B )
% 1.72/1.39 => ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ C )
% 1.72/1.39 => ( in @ Xx @ A ) ) )
% 1.72/1.39 & ! [Xx: $i,Xy: $i] :
% 1.72/1.39 ( ( ( in @ Xx @ A )
% 1.72/1.39 & ( in @ Xy @ A ) )
% 1.72/1.39 => ( ! [C: $i] :
% 1.72/1.39 ( ( in @ C @ B )
% 1.72/1.39 => ( ( in @ Xx @ C )
% 1.72/1.39 <=> ( in @ Xy @ C ) ) )
% 1.72/1.39 => ( Xx = Xy ) ) )
% 1.72/1.39 & ! [C: $i,D: $i] :
% 1.72/1.39 ( ( ( in @ C @ B )
% 1.72/1.39 & ( in @ D @ B ) )
% 1.72/1.39 => ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ C )
% 1.72/1.39 => ( in @ Xx @ D ) )
% 1.72/1.39 | ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ D )
% 1.72/1.39 => ( in @ Xx @ C ) ) ) )
% 1.72/1.39 & ! [C: $i] :
% 1.72/1.39 ( ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ C )
% 1.72/1.39 => ( in @ Xx @ A ) )
% 1.72/1.39 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.72/1.39 => ? [D: $i,Xx: $i] :
% 1.72/1.39 ( ( in @ D @ B )
% 1.72/1.39 & ( in @ Xx @ C )
% 1.72/1.39 & ~ ? [Xy: $i] :
% 1.72/1.39 ( ( in @ Xy @ D )
% 1.72/1.39 & ( in @ Xy @ C ) )
% 1.72/1.39 & ! [E: $i] :
% 1.72/1.39 ( ( in @ E @ B )
% 1.72/1.39 => ( ! [Xy: $i] :
% 1.72/1.39 ( ( in @ Xy @ E )
% 1.72/1.39 => ( in @ Xy @ D ) )
% 1.72/1.39 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(descr_type,type,
% 1.72/1.39 descr: ( $i > $o ) > $i ).
% 1.72/1.39
% 1.72/1.39 thf(descrp_type,type,
% 1.72/1.39 descrp: $o ).
% 1.72/1.39
% 1.72/1.39 thf(descrp,definition,
% 1.72/1.39 ( descrp
% 1.72/1.39 = ( ! [Xphi: $i > $o] :
% 1.72/1.39 ( ( exu
% 1.72/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.72/1.39 => ( Xphi
% 1.72/1.39 @ ( descr
% 1.72/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(dsetconstr_type,type,
% 1.72/1.39 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.72/1.39
% 1.72/1.39 thf(dsetconstrI_type,type,
% 1.72/1.39 dsetconstrI: $o ).
% 1.72/1.39
% 1.72/1.39 thf(dsetconstrI,definition,
% 1.72/1.39 ( dsetconstrI
% 1.72/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ A )
% 1.72/1.39 => ( ( Xphi @ Xx )
% 1.72/1.39 => ( in @ Xx
% 1.72/1.39 @ ( dsetconstr @ A
% 1.72/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(dsetconstrEL_type,type,
% 1.72/1.39 dsetconstrEL: $o ).
% 1.72/1.39
% 1.72/1.39 thf(dsetconstrEL,definition,
% 1.72/1.39 ( dsetconstrEL
% 1.72/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.72/1.39 ( ( in @ Xx
% 1.72/1.39 @ ( dsetconstr @ A
% 1.72/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.72/1.39 => ( in @ Xx @ A ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(dsetconstrER_type,type,
% 1.72/1.39 dsetconstrER: $o ).
% 1.72/1.39
% 1.72/1.39 thf(dsetconstrER,definition,
% 1.72/1.39 ( dsetconstrER
% 1.72/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.72/1.39 ( ( in @ Xx
% 1.72/1.39 @ ( dsetconstr @ A
% 1.72/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.72/1.39 => ( Xphi @ Xx ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(exuE1_type,type,
% 1.72/1.39 exuE1: $o ).
% 1.72/1.39
% 1.72/1.39 thf(exuE1,definition,
% 1.72/1.39 ( exuE1
% 1.72/1.39 = ( ! [Xphi: $i > $o] :
% 1.72/1.39 ( ( exu
% 1.72/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.72/1.39 => ? [Xx: $i] :
% 1.72/1.39 ( ( Xphi @ Xx )
% 1.72/1.39 & ! [Xy: $i] :
% 1.72/1.39 ( ( Xphi @ Xy )
% 1.72/1.39 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(prop2set_type,type,
% 1.72/1.39 prop2set: $o > $i ).
% 1.72/1.39
% 1.72/1.39 thf(prop2set,definition,
% 1.72/1.39 ( prop2set
% 1.72/1.39 = ( ^ [Xphi: $o] :
% 1.72/1.39 ( dsetconstr @ ( powerset @ emptyset )
% 1.72/1.39 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(prop2setE_type,type,
% 1.72/1.39 prop2setE: $o ).
% 1.72/1.39
% 1.72/1.39 thf(prop2setE,definition,
% 1.72/1.39 ( prop2setE
% 1.72/1.39 = ( ! [Xphi: $o,Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.72/1.39 => Xphi ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(emptysetE_type,type,
% 1.72/1.39 emptysetE: $o ).
% 1.72/1.39
% 1.72/1.39 thf(emptysetE,definition,
% 1.72/1.39 ( emptysetE
% 1.72/1.39 = ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ emptyset )
% 1.72/1.39 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(emptysetimpfalse_type,type,
% 1.72/1.39 emptysetimpfalse: $o ).
% 1.72/1.39
% 1.72/1.39 thf(emptysetimpfalse,definition,
% 1.72/1.39 ( emptysetimpfalse
% 1.72/1.39 = ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ emptyset )
% 1.72/1.39 => $false ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(notinemptyset_type,type,
% 1.72/1.39 notinemptyset: $o ).
% 1.72/1.39
% 1.72/1.39 thf(notinemptyset,definition,
% 1.72/1.39 ( notinemptyset
% 1.72/1.39 = ( ! [Xx: $i] :
% 1.72/1.39 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(exuE3e_type,type,
% 1.72/1.39 exuE3e: $o ).
% 1.72/1.39
% 1.72/1.39 thf(exuE3e,definition,
% 1.72/1.39 ( exuE3e
% 1.72/1.39 = ( ! [Xphi: $i > $o] :
% 1.72/1.39 ( ( exu
% 1.72/1.39 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.72/1.39 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(setext_type,type,
% 1.72/1.39 setext: $o ).
% 1.72/1.39
% 1.72/1.39 thf(setext,definition,
% 1.72/1.39 ( setext
% 1.72/1.39 = ( ! [A: $i,B: $i] :
% 1.72/1.39 ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ A )
% 1.72/1.39 => ( in @ Xx @ B ) )
% 1.72/1.39 => ( ! [Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ B )
% 1.72/1.39 => ( in @ Xx @ A ) )
% 1.72/1.39 => ( A = B ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(emptyI_type,type,
% 1.72/1.39 emptyI: $o ).
% 1.72/1.39
% 1.72/1.39 thf(emptyI,definition,
% 1.72/1.39 ( emptyI
% 1.72/1.39 = ( ! [A: $i] :
% 1.72/1.39 ( ! [Xx: $i] :
% 1.72/1.39 ~ ( in @ Xx @ A )
% 1.72/1.39 => ( A = emptyset ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(noeltsimpempty_type,type,
% 1.72/1.39 noeltsimpempty: $o ).
% 1.72/1.39
% 1.72/1.39 thf(noeltsimpempty,definition,
% 1.72/1.39 ( noeltsimpempty
% 1.72/1.39 = ( ! [A: $i] :
% 1.72/1.39 ( ! [Xx: $i] :
% 1.72/1.39 ~ ( in @ Xx @ A )
% 1.72/1.39 => ( A = emptyset ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(setbeta_type,type,
% 1.72/1.39 setbeta: $o ).
% 1.72/1.39
% 1.72/1.39 thf(setbeta,definition,
% 1.72/1.39 ( setbeta
% 1.72/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ A )
% 1.72/1.39 => ( ( in @ Xx
% 1.72/1.39 @ ( dsetconstr @ A
% 1.72/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.72/1.39 <=> ( Xphi @ Xx ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(nonempty_type,type,
% 1.72/1.39 nonempty: $i > $o ).
% 1.72/1.39
% 1.72/1.39 thf(nonempty,definition,
% 1.72/1.39 ( nonempty
% 1.72/1.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(nonemptyE1_type,type,
% 1.72/1.39 nonemptyE1: $o ).
% 1.72/1.39
% 1.72/1.39 thf(nonemptyE1,definition,
% 1.72/1.39 ( nonemptyE1
% 1.72/1.39 = ( ! [A: $i] :
% 1.72/1.39 ( ( nonempty @ A )
% 1.72/1.39 => ? [Xx: $i] : ( in @ Xx @ A ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(nonemptyI_type,type,
% 1.72/1.39 nonemptyI: $o ).
% 1.72/1.39
% 1.72/1.39 thf(nonemptyI,definition,
% 1.72/1.39 ( nonemptyI
% 1.72/1.39 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.72/1.39 ( ( in @ Xx @ A )
% 1.72/1.39 => ( ( Xphi @ Xx )
% 1.72/1.39 => ( nonempty
% 1.72/1.39 @ ( dsetconstr @ A
% 1.72/1.39 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(nonemptyI1_type,type,
% 1.72/1.39 nonemptyI1: $o ).
% 1.72/1.39
% 1.72/1.39 thf(nonemptyI1,definition,
% 1.72/1.39 ( nonemptyI1
% 1.72/1.39 = ( ! [A: $i] :
% 1.72/1.39 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.72/1.39 => ( nonempty @ A ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(setadjoinIL_type,type,
% 1.72/1.39 setadjoinIL: $o ).
% 1.72/1.39
% 1.72/1.39 thf(setadjoinIL,definition,
% 1.72/1.39 ( setadjoinIL
% 1.72/1.39 = ( ! [Xx: $i,Xy: $i] : ( in @ Xx @ ( setadjoin @ Xx @ Xy ) ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(emptyinunitempty_type,type,
% 1.72/1.39 emptyinunitempty: $o ).
% 1.72/1.39
% 1.72/1.39 thf(emptyinunitempty,definition,
% 1.72/1.39 ( emptyinunitempty
% 1.72/1.39 = ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) ) ) ).
% 1.72/1.39
% 1.72/1.39 thf(setadjoinIR,conjecture,
% 1.72/1.39 ( setextAx
% 1.72/1.39 => ( emptysetAx
% 1.72/1.39 => ( setadjoinAx
% 1.72/1.39 => ( powersetAx
% 1.72/1.39 => ( setunionAx
% 1.72/1.39 => ( omega0Ax
% 1.72/1.39 => ( omegaSAx
% 1.72/1.39 => ( omegaIndAx
% 1.72/1.39 => ( replAx
% 1.72/1.39 => ( foundationAx
% 1.72/1.39 => ( wellorderingAx
% 1.72/1.39 => ( descrp
% 1.72/1.39 => ( dsetconstrI
% 1.72/1.39 => ( dsetconstrEL
% 1.72/1.39 => ( dsetconstrER
% 1.72/1.39 => ( exuE1
% 1.72/1.39 => ( prop2setE
% 1.72/1.39 => ( emptysetE
% 1.72/1.39 => ( emptysetimpfalse
% 1.72/1.39 => ( notinemptyset
% 1.72/1.39 => ( exuE3e
% 1.72/1.39 => ( setext
% 1.72/1.39 => ( emptyI
% 1.72/1.39 => ( noeltsimpempty
% 1.72/1.39 => ( setbeta
% 1.72/1.39 => ( nonemptyE1
% 1.72/1.39 => ( nonemptyI
% 1.72/1.39 => ( nonemptyI1
% 1.72/1.39 => ( setadjoinIL
% 1.72/1.39 => ( emptyinunitempty
% 1.72/1.39 => ! [Xx: $i,A: $i,Xy: $i] :
% 1.72/1.39 ( ( in @ Xy @ A )
% 1.72/1.39 => ( in @ Xy @ ( setadjoin @ Xx @ A ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.72/1.39 ------------------------
% 1.88/1.41 % (27657)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_27557 for (2999ds/4Mi)
% 1.88/1.41 % (27659)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_27557 for (2999ds/2Mi)
% 1.88/1.41 % (27656)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_27557 for (2999ds/183Mi)
% 1.88/1.41 % (27660)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_27557 for (2999ds/2Mi)
% 1.88/1.41 % (27661)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_27557 for (2999ds/275Mi)
% 1.88/1.41 % (27662)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_27557 for (2999ds/18Mi)
% 1.88/1.41 % (27658)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_27557 for (2999ds/27Mi)
% 1.88/1.41 % (27659)Instruction limit reached!
% 1.88/1.41 % (27659)------------------------------
% 1.88/1.41 % (27659)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (27659)Termination reason: Unknown
% 1.88/1.41 % (27660)Instruction limit reached!
% 1.88/1.41 % (27660)------------------------------
% 1.88/1.41 % (27660)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (27659)Termination phase: shuffling
% 1.88/1.41
% 1.88/1.41 % (27659)Memory used [KB]: 1023
% 1.88/1.41 % (27659)Time elapsed: 0.003 s
% 1.88/1.41 % (27659)Instructions burned: 3 (million)
% 1.88/1.41 % (27659)------------------------------
% 1.88/1.41 % (27659)------------------------------
% 1.88/1.41 % (27660)Termination reason: Unknown
% 1.88/1.41 % (27660)Termination phase: shuffling
% 1.88/1.41
% 1.88/1.41 % (27660)Memory used [KB]: 1023
% 1.88/1.41 % (27660)Time elapsed: 0.003 s
% 1.88/1.41 % (27660)Instructions burned: 3 (million)
% 1.88/1.41 % (27660)------------------------------
% 1.88/1.41 % (27660)------------------------------
% 1.88/1.41 % (27657)Instruction limit reached!
% 1.88/1.41 % (27657)------------------------------
% 1.88/1.41 % (27657)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.41 % (27657)Termination reason: Unknown
% 1.88/1.41 % (27657)Termination phase: shuffling
% 1.88/1.41
% 1.88/1.41 % (27657)Memory used [KB]: 1151
% 1.88/1.41 % (27657)Time elapsed: 0.004 s
% 1.88/1.41 % (27657)Instructions burned: 5 (million)
% 1.88/1.41 % (27657)------------------------------
% 1.88/1.41 % (27657)------------------------------
% 1.88/1.42 % (27662)Instruction limit reached!
% 1.88/1.42 % (27662)------------------------------
% 1.88/1.42 % (27662)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.42 % (27662)Termination reason: Unknown
% 1.88/1.42 % (27662)Termination phase: Property scanning
% 1.88/1.42
% 1.88/1.42 % (27662)Memory used [KB]: 1407
% 1.88/1.42 % (27662)Time elapsed: 0.010 s
% 1.88/1.42 % (27662)Instructions burned: 18 (million)
% 1.88/1.42 % (27662)------------------------------
% 1.88/1.42 % (27662)------------------------------
% 1.88/1.42 % (27658)Instruction limit reached!
% 1.88/1.42 % (27658)------------------------------
% 1.88/1.42 % (27658)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.42 % (27658)Termination reason: Unknown
% 1.88/1.42 % (27658)Termination phase: Saturation
% 1.88/1.42
% 1.88/1.42 % (27658)Memory used [KB]: 5756
% 1.88/1.42 % (27658)Time elapsed: 0.015 s
% 1.88/1.42 % (27658)Instructions burned: 28 (million)
% 1.88/1.42 % (27658)------------------------------
% 1.88/1.42 % (27658)------------------------------
% 1.88/1.42 % (27663)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_27557 for (2999ds/3Mi)
% 1.88/1.42 % (27664)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_27557 for (2999ds/37Mi)
% 1.88/1.43 % (27665)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_27557 for (2999ds/15Mi)
% 1.88/1.43 % (27663)Instruction limit reached!
% 1.88/1.43 % (27663)------------------------------
% 1.88/1.43 % (27663)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.43 % (27663)Termination reason: Unknown
% 1.88/1.43 % (27663)Termination phase: shuffling
% 1.88/1.43
% 1.88/1.43 % (27663)Memory used [KB]: 1023
% 1.88/1.43 % (27663)Time elapsed: 0.003 s
% 1.88/1.43 % (27663)Instructions burned: 4 (million)
% 1.88/1.43 % (27663)------------------------------
% 1.88/1.43 % (27663)------------------------------
% 1.88/1.43 % (27666)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_27557 for (2999ds/3Mi)
% 1.88/1.43 % (27665)Instruction limit reached!
% 1.88/1.43 % (27665)------------------------------
% 1.88/1.43 % (27665)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.43 % (27665)Termination reason: Unknown
% 1.88/1.43 % (27665)Termination phase: Property scanning
% 1.88/1.43
% 1.88/1.43 % (27665)Memory used [KB]: 1407
% 1.88/1.43 % (27665)Time elapsed: 0.009 s
% 1.88/1.43 % (27665)Instructions burned: 16 (million)
% 1.88/1.43 % (27665)------------------------------
% 1.88/1.43 % (27665)------------------------------
% 1.88/1.43 % (27666)Instruction limit reached!
% 1.88/1.43 % (27666)------------------------------
% 1.88/1.43 % (27666)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.43 % (27666)Termination reason: Unknown
% 1.88/1.43 % (27666)Termination phase: shuffling
% 1.88/1.43
% 1.88/1.43 % (27666)Memory used [KB]: 1023
% 1.88/1.43 % (27666)Time elapsed: 0.003 s
% 1.88/1.43 % (27666)Instructions burned: 4 (million)
% 1.88/1.43 % (27666)------------------------------
% 1.88/1.43 % (27666)------------------------------
% 1.88/1.44 % (27667)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_27557 for (2999ds/1041Mi)
% 1.88/1.44 % (27656)First to succeed.
% 1.88/1.44 % (27656)Refutation found. Thanks to Tanya!
% 1.88/1.44 % SZS status Theorem for DTF2THF_27557
% 1.88/1.44 % SZS output start Proof for DTF2THF_27557
% 1.88/1.44 thf(func_def_0, type, in: $i > $i > $o).
% 1.88/1.44 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.88/1.44 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.88/1.44 thf(func_def_8, type, powerset: $i > $i).
% 1.88/1.44 thf(func_def_10, type, setunion: $i > $i).
% 1.88/1.44 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.88/1.44 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.88/1.44 thf(func_def_26, type, prop2set: $o > $i).
% 1.88/1.44 thf(func_def_36, type, nonempty: $i > $o).
% 1.88/1.44 thf(func_def_62, type, sK4: $i > $i > $i).
% 1.88/1.44 thf(func_def_63, type, sK5: $i > $i > $i).
% 1.88/1.44 thf(func_def_64, type, sK6: $i > $i).
% 1.88/1.44 thf(func_def_65, type, sK7: $i > $i > $i).
% 1.88/1.44 thf(func_def_66, type, sK8: $i > $i > $i).
% 1.88/1.44 thf(func_def_67, type, sK9: $i > $i > $i).
% 1.88/1.44 thf(func_def_68, type, sK10: $i > $i).
% 1.88/1.44 thf(func_def_69, type, sK11: $i > $i).
% 1.88/1.44 thf(func_def_70, type, sK12: $i > $i).
% 1.88/1.44 thf(func_def_71, type, sK13: ($i > $o) > $i).
% 1.88/1.44 thf(func_def_72, type, sK14: ($i > $o) > $i > $i).
% 1.88/1.44 thf(func_def_73, type, sK15: ($i > $o) > $i > $i).
% 1.88/1.44 thf(func_def_74, type, sK16: $i > ($i > $i > $o) > $i).
% 1.88/1.44 thf(func_def_75, type, sK17: $i > ($i > $i > $o) > $i).
% 1.88/1.44 thf(func_def_76, type, sK18: $i > $i > ($i > $i > $o) > $i).
% 1.88/1.44 thf(func_def_77, type, sK19: $i > $i > ($i > $i > $o) > $i).
% 1.88/1.44 thf(func_def_78, type, sK20: $i > $i > ($i > $i > $o) > $i).
% 1.88/1.44 thf(func_def_79, type, sK21: $i > $i > ($i > $i > $o) > $i).
% 1.88/1.44 thf(func_def_80, type, sK22: $i > $i > ($i > $i > $o) > $i).
% 1.88/1.44 thf(func_def_81, type, sK23: $i > $i).
% 1.88/1.44 thf(func_def_82, type, sK24: $i > $i > $i).
% 1.88/1.44 thf(func_def_83, type, sK25: $i > $i > $i).
% 1.88/1.44 thf(func_def_84, type, sK26: $i > $i > $i).
% 1.88/1.44 thf(func_def_85, type, sK27: $i > $i > $i > $i).
% 1.88/1.44 thf(func_def_86, type, sK28: $i > $i).
% 1.88/1.44 thf(func_def_87, type, sK29: $i > $i > $i).
% 1.88/1.44 thf(f661,plain,(
% 1.88/1.44 $false),
% 1.88/1.44 inference(trivial_inequality_removal,[status(thm)],[f659])).
% 1.88/1.44 thf(f659,plain,(
% 1.88/1.44 ($false = $true)),
% 1.88/1.44 inference(superposition,[status(thm)],[f658,f128])).
% 1.88/1.44 thf(f128,plain,(
% 1.88/1.44 ($true = (in @ sK0 @ sK1))),
% 1.88/1.44 inference(cnf_transformation,[status(thm)],[f103])).
% 1.88/1.44 thf(f103,plain,(
% 1.88/1.44 (foundationAx = $true) & (notinemptyset = $true) & (setext = $true) & (dsetconstrEL = $true) & (setbeta = $true) & (omegaIndAx = $true) & (powersetAx = $true) & (emptyinunitempty = $true) & (descrp = $true) & (omegaSAx = $true) & (dsetconstrI = $true) & (replAx = $true) & (exuE3e = $true) & (dsetconstrER = $true) & (wellorderingAx = $true) & (setadjoinIL = $true) & (emptysetimpfalse = $true) & (setunionAx = $true) & (((in @ sK0 @ (setadjoin @ sK2 @ sK1)) != $true) & ($true = (in @ sK0 @ sK1))) & (exuE1 = $true) & (emptysetAx = $true) & (setextAx = $true) & (nonemptyI = $true) & (emptyI = $true) & (omega0Ax = $true) & (setadjoinAx = $true) & (emptysetE = $true) & (nonemptyE1 = $true) & (nonemptyI1 = $true) & (noeltsimpempty = $true) & (prop2setE = $true)),
% 1.88/1.44 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f101,f102])).
% 1.88/1.44 thf(f102,plain,(
% 1.88/1.44 ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setadjoin @ X2 @ X1)) != $true) & ((in @ X0 @ X1) = $true)) => (((in @ sK0 @ (setadjoin @ sK2 @ sK1)) != $true) & ($true = (in @ sK0 @ sK1)))),
% 1.88/1.44 introduced(definition,[],[choice_axiom])).
% 1.88/1.44 thf(f101,plain,(
% 1.88/1.44 (foundationAx = $true) & (notinemptyset = $true) & (setext = $true) & (dsetconstrEL = $true) & (setbeta = $true) & (omegaIndAx = $true) & (powersetAx = $true) & (emptyinunitempty = $true) & (descrp = $true) & (omegaSAx = $true) & (dsetconstrI = $true) & (replAx = $true) & (exuE3e = $true) & (dsetconstrER = $true) & (wellorderingAx = $true) & (setadjoinIL = $true) & (emptysetimpfalse = $true) & (setunionAx = $true) & ? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setadjoin @ X2 @ X1)) != $true) & ((in @ X0 @ X1) = $true)) & (exuE1 = $true) & (emptysetAx = $true) & (setextAx = $true) & (nonemptyI = $true) & (emptyI = $true) & (omega0Ax = $true) & (setadjoinAx = $true) & (emptysetE = $true) & (nonemptyE1 = $true) & (nonemptyI1 = $true) & (noeltsimpempty = $true) & (prop2setE = $true)),
% 1.88/1.44 inference(flattening,[status(thm)],[f100])).
% 1.88/1.44 thf(f100,plain,(
% 1.88/1.44 (((((((((((((((((((((((((((((? [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ (setadjoin @ X2 @ X1)) != $true) & ((in @ X0 @ X1) = $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)),
% 1.88/1.44 inference(ennf_transformation,[status(thm)],[f79])).
% 1.88/1.44 thf(f79,plain,(
% 1.88/1.44 ~((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) => ! [X0 : $i,X1 : $i,X2 : $i] : (((in @ X0 @ X1) = $true) => ((in @ X0 @ (setadjoin @ X2 @ X1)) = $true))))))))))))))))))))))))))))))))),
% 1.88/1.44 inference(fool_elimination,[status(thm)],[f78])).
% 1.88/1.44 thf(f78,plain,(
% 1.88/1.44 ~(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 => ! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ X1) => (in @ X0 @ (setadjoin @ X2 @ X1)))))))))))))))))))))))))))))))))),
% 1.88/1.44 inference(rectify,[status(thm)],[f35])).
% 1.88/1.44 thf(f35,negated_conjecture,(
% 1.88/1.44 ~(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 => ! [X2 : $i,X3 : $i,X1 : $i] : ((in @ X2 @ X3) => (in @ X2 @ (setadjoin @ X1 @ X3)))))))))))))))))))))))))))))))))),
% 1.88/1.44 inference(negated_conjecture,[status(cth)],[f34])).
% 1.88/1.44 thf(f34,conjecture,(
% 1.88/1.44 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 => ! [X2 : $i,X3 : $i,X1 : $i] : ((in @ X2 @ X3) => (in @ X2 @ (setadjoin @ X1 @ X3))))))))))))))))))))))))))))))))),
% 1.88/1.44 file('/export/starexec/sandbox/tmp/tmp.etdkTwxwpW/DTF2THF_27557.p',setadjoinIR)).
% 1.88/1.44 thf(f658,plain,(
% 1.88/1.44 ($false = (in @ sK0 @ sK1))),
% 1.88/1.44 inference(trivial_inequality_removal,[status(thm)],[f655])).
% 1.88/1.44 thf(f655,plain,(
% 1.88/1.44 ($true != $true) | ($false = (in @ sK0 @ sK1))),
% 1.88/1.44 inference(superposition,[status(thm)],[f129,f353])).
% 1.88/1.44 thf(f353,plain,(
% 1.88/1.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (setadjoin @ X1 @ X2)) = $true) | ($false = (in @ X3 @ X2))) )),
% 1.88/1.44 inference(binary_proxy_clausification,[status(thm)],[f348])).
% 1.88/1.44 thf(f348,plain,(
% 1.88/1.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (setadjoin @ X1 @ X2)) = $true) | ($false = ((in @ X3 @ X2) | (X3 = X1)))) )),
% 1.88/1.44 inference(binary_proxy_clausification,[status(thm)],[f347])).
% 1.88/1.44 thf(f347,plain,(
% 1.88/1.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : (((in @ X3 @ (setadjoin @ X1 @ X2)) = ((in @ X3 @ X2) | (X3 = X1)))) )),
% 1.88/1.44 inference(binary_proxy_clausification,[status(thm)],[f346])).
% 1.88/1.44 thf(f346,plain,(
% 1.88/1.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((in @ X3 @ (setadjoin @ X1 @ X2)) = ((in @ X3 @ X2) | (X3 = X1))) = $true)) )),
% 1.88/1.44 inference(beta_eta_normalization,[status(thm)],[f345])).
% 1.88/1.44 thf(f345,plain,(
% 1.88/1.44 ( ! [X2 : $i,X3 : $i,X1 : $i] : ((((^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ X2)) = ((in @ Y0 @ X2) | (Y0 = X1)))) @ X3) = $true)) )),
% 1.88/1.44 inference(pi_clausification,[status(thm)],[f344])).
% 1.88/1.44 thf(f344,plain,(
% 1.88/1.44 ( ! [X2 : $i,X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ (setadjoin @ X1 @ X2)) = ((in @ Y0 @ X2) | (Y0 = X1))))))) )),
% 1.88/1.44 inference(beta_eta_normalization,[status(thm)],[f343])).
% 1.88/1.44 thf(f343,plain,(
% 1.88/1.44 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ X1 @ Y0)) = ((in @ Y1 @ Y0) | (Y1 = X1)))))) @ X2) = $true)) )),
% 1.88/1.44 inference(pi_clausification,[status(thm)],[f342])).
% 1.88/1.44 thf(f342,plain,(
% 1.88/1.44 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ (setadjoin @ X1 @ Y0)) = ((in @ Y1 @ Y0) | (Y1 = X1))))))) = $true)) )),
% 1.88/1.44 inference(beta_eta_normalization,[status(thm)],[f341])).
% 1.88/1.44 thf(f341,plain,(
% 1.88/1.44 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y0 @ Y1)) = ((in @ Y2 @ Y1) | (Y2 = Y0)))))))) @ X1) = $true)) )),
% 1.88/1.44 inference(pi_clausification,[status(thm)],[f179])).
% 1.88/1.44 thf(f179,plain,(
% 1.88/1.44 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y0 @ Y1)) = ((in @ Y2 @ Y1) | (Y2 = Y0))))))))) = $true)),
% 1.88/1.44 inference(definition_unfolding,[status(thm)],[f121,f112])).
% 1.88/1.44 thf(f112,plain,(
% 1.88/1.44 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y0 @ Y1)) = ((in @ Y2 @ Y1) | (Y2 = Y0))))))))))),
% 1.88/1.44 inference(cnf_transformation,[status(thm)],[f56])).
% 1.88/1.44 thf(f56,plain,(
% 1.88/1.44 (setadjoinAx = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ (setadjoin @ Y0 @ Y1)) = ((in @ Y2 @ Y1) | (Y2 = Y0))))))))))),
% 1.88/1.44 inference(fool_elimination,[status(thm)],[f55])).
% 1.88/1.44 thf(f55,plain,(
% 1.88/1.44 (! [X0 : $i,X1 : $i,X2 : $i] : ((in @ X0 @ (setadjoin @ X2 @ X1)) <=> ((X0 = X2) | (in @ X0 @ X1))) = setadjoinAx)),
% 1.88/1.44 inference(rectify,[status(thm)],[f4])).
% 1.88/1.44 thf(f4,axiom,(
% 1.88/1.44 (! [X2 : $i,X3 : $i,X1 : $i] : ((in @ X2 @ (setadjoin @ X1 @ X3)) <=> ((X1 = X2) | (in @ X2 @ X3))) = setadjoinAx)),
% 1.88/1.44 file('/export/starexec/sandbox/tmp/tmp.etdkTwxwpW/DTF2THF_27557.p',setadjoinAx)).
% 1.88/1.44 thf(f121,plain,(
% 1.88/1.44 (setadjoinAx = $true)),
% 1.88/1.44 inference(cnf_transformation,[status(thm)],[f103])).
% 1.88/1.44 thf(f129,plain,(
% 1.88/1.44 ((in @ sK0 @ (setadjoin @ sK2 @ sK1)) != $true)),
% 1.88/1.44 inference(cnf_transformation,[status(thm)],[f103])).
% 1.88/1.44 % SZS output end Proof for DTF2THF_27557
% 1.88/1.44 % (27656)------------------------------
% 1.88/1.44 % (27656)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.88/1.44 % (27656)Termination reason: Refutation
% 1.88/1.44
% 1.88/1.44 % (27656)Memory used [KB]: 6140
% 1.88/1.44 % (27656)Time elapsed: 0.034 s
% 1.88/1.44 % (27656)Instructions burned: 63 (million)
% 1.88/1.44 % (27656)------------------------------
% 1.88/1.44 % (27656)------------------------------
% 1.88/1.44 % (27655)Success in time 0.043 s
%------------------------------------------------------------------------------