%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU504^1 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n024.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 09:34:58 AM UTC 2026
% Result : Theorem 1.09s 0.99s
% Output : Refutation 1.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 22 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 461 ( 134 equ; 0 cnn)
% Maximal formula atoms : 22 ( 20 avg)
% Number of connectives : 281 ( 11 ~; 0 |; 73 &; 73 @)
% ( 0 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 13 >; 0 *; 0 +; 0 <<)
% Number of symbols : 55 ( 50 usr; 25 con; 0-3 aty)
% ( 6 !!; 4 ??; 0 @@+; 0 @@-)
% Number of variables : 51 ( 28 ^; 13 !; 10 ?; 51 :)
% 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_47,type,
sK0: $i > $o ).
thf(func_def_49,type,
sK2: $i > ( $i > $i > $o ) > $i ).
thf(func_def_50,type,
sK3: $i > ( $i > $i > $o ) > $i ).
thf(func_def_51,type,
sK4: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_52,type,
sK5: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_53,type,
sK6: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_54,type,
sK7: $i > $i > ( $i > $i > $o ) > $i ).
thf(func_def_55,type,
sK8: $i > $i ).
thf(func_def_56,type,
sK9: $i > $i > $i > $i ).
thf(func_def_57,type,
sK10: $i > $i > $i ).
thf(func_def_58,type,
sK11: $i > $i > $i ).
thf(func_def_59,type,
sK12: $i > $i > $i ).
thf(func_def_60,type,
sK13: ( $i > $o ) > $i > $i ).
thf(func_def_61,type,
sK14: $i > $i > $i ).
thf(func_def_62,type,
sK15: $i > $i > $i ).
thf(func_def_63,type,
sK16: ( $i > $o ) > $i ).
thf(func_def_64,type,
sK17: ( $i > $o ) > $i > $i ).
thf(func_def_65,type,
sK18: ( $i > $o ) > $i > $i ).
thf(func_def_67,type,
sK20: $i > $i ).
thf(func_def_68,type,
sK21: $i > $i > $i ).
thf(func_def_69,type,
sK22: $i > $i ).
thf(f463,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f462]) ).
thf(f462,plain,
$true != $true,
inference(superposition,[status(thm)],[f94,f403]) ).
thf(f403,plain,
( ( sK0 @ sK19 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f402]) ).
thf(f402,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK0 @ Y0 )
=> ( sK19 = Y0 ) ) )
& ( sK0 @ sK19 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f401]) ).
thf(f401,plain,
( ( ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) )
@ sK19 )
= $true ),
inference(sigma_clausification,[status(thm)],[f400]) ).
thf(f400,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ $i
@ ^ [Y1: $i] :
( ( sK0 @ Y1 )
=> ( Y0 = Y1 ) ) )
& ( sK0 @ Y0 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
( ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) )
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f95,f76]) ).
thf(f76,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( exu
= ( ^ [Y0: $i > $o] :
( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 )
=> ( Y1 = Y2 ) ) )
& ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
inference(rectify,[status(thm)],[f1]) ).
thf(f1,axiom,
( exu
= ( ^ [X0: $i > $o] :
? [X1: $i] :
( ( X0 @ X1 )
& ! [X2: $i] :
( ( X0 @ X2 )
=> ( X1 = X2 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LXgTTamYWB/DTF2THF_9734.p',exu) ).
thf(f95,plain,
( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f73]) ).
thf(f73,plain,
( ( emptysetimpfalse = $true )
& ( exuE1 = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true )
& ! [X1: $i] :
( ( sK0 @ X1 )
!= $true )
& ( descrp = $true )
& ( powersetAx = $true )
& ( setunionAx = $true )
& ( omega0Ax = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( dsetconstrER = $true )
& ( emptysetAx = $true )
& ( foundationAx = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( omegaIndAx = $true )
& ( prop2setE = $true )
& ( replAx = $true )
& ( wellorderingAx = $true )
& ( omegaSAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f71,f72]) ).
thf(f72,plain,
( ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) )
=> ( ( ( exu
@ ^ [Y0: $i] : ( sK0 @ Y0 ) )
= $true )
& ! [X1: $i] :
( ( sK0 @ X1 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f71,plain,
( ( emptysetimpfalse = $true )
& ( exuE1 = $true )
& ( dsetconstrEL = $true )
& ( dsetconstrI = $true )
& ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X1: $i] :
( ( X0 @ X1 )
!= $true ) )
& ( descrp = $true )
& ( powersetAx = $true )
& ( setunionAx = $true )
& ( omega0Ax = $true )
& ( emptysetE = $true )
& ( notinemptyset = $true )
& ( dsetconstrER = $true )
& ( emptysetAx = $true )
& ( foundationAx = $true )
& ( setextAx = $true )
& ( setadjoinAx = $true )
& ( omegaIndAx = $true )
& ( prop2setE = $true )
& ( replAx = $true )
& ( wellorderingAx = $true )
& ( omegaSAx = $true ) ),
inference(flattening,[status(thm)],[f70]) ).
thf(f70,plain,
( ? [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
& ! [X1: $i] :
( ( X0 @ X1 )
!= $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)],[f69]) ).
thf(f69,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 )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X1: $i] :
( ( X0 @ X1 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f33]) ).
thf(f33,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 )
=> ! [X0: $i > $o] :
( ( ( exu
@ ^ [Y0: $i] : ( X0 @ Y0 ) )
= $true )
=> ? [X2: $i] :
( ( X0 @ X2 )
= $true ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X2: $i] : ( X0 @ X2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
thf(f23,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ( emptysetimpfalse
=> ( notinemptyset
=> ! [X0: $i > $o] :
( ( exu
@ ^ [X1: $i] : ( X0 @ X1 ) )
=> ? [X1: $i] : ( X0 @ X1 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.LXgTTamYWB/DTF2THF_9734.p',exuE3e) ).
thf(f94,plain,
! [X1: $i] :
( ( sK0 @ X1 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f73]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEU504^1 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.06 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.25 % Computer : n024.cluster.edu
% 0.08/0.25 % Model : x86_64 x86_64
% 0.08/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.25 % Memory : 8042.1875MB
% 0.08/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.25 % CPULimit : 300
% 0.08/0.25 % WCLimit : 300
% 0.08/0.25 % DateTime : Tue Feb 24 07:24:40 EST 2026
% 0.08/0.25 % CPUTime :
% 0.08/0.25 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.08/0.31 ---- Original DTF file ---
% 0.08/0.31 thf(spec,logic,$$dhol).
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 % File : SEU504^1 : TPTP v9.2.1. Released v3.7.0.
% 0.08/0.31 % Domain : Set Theory
% 0.08/0.31 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.08/0.31 % Version : Especial.
% 0.08/0.31 % English : (! phi:i>o.exu (^ x:i.phi x) -> (? x:i.phi x))
% 0.08/0.31
% 0.08/0.31 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.08/0.31 % Source : [Bro08]
% 0.08/0.31 % Names : ZFC006g [Bro08]
% 0.08/0.31
% 0.08/0.31 % Status : Theorem
% 0.08/0.31 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0, 0.09 v7.5.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.00 v6.2.0, 0.14 v6.0.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v4.1.0, 0.33 v4.0.0, 0.00 v3.7.0
% 0.08/0.31 % Syntax : Number of formulae : 53 ( 22 unt; 30 typ; 22 def)
% 0.08/0.31 % Number of atoms : 134 ( 27 equ; 0 cnn)
% 0.08/0.31 % Maximal formula atoms : 21 ( 5 avg)
% 0.08/0.31 % Number of connectives : 248 ( 4 ~; 3 |; 18 &; 164 @)
% 0.08/0.31 % ( 6 <=>; 53 =>; 0 <=; 0 <~>)
% 0.08/0.31 % Maximal formula depth : 26 ( 2 avg)
% 0.08/0.31 % Number of types : 2 ( 0 usr)
% 0.08/0.31 % Number of type conns : 23 ( 23 >; 0 *; 0 +; 0 <<)
% 0.08/0.31 % Number of symbols : 32 ( 30 usr; 23 con; 0-2 aty)
% 0.08/0.31 % Number of variables : 80 ( 11 ^; 55 !; 14 ?; 80 :)
% 0.08/0.31 % SPC : TH0_THM_EQU_NAR
% 0.08/0.31
% 0.08/0.31 % Comments : http://mathgate.info/detsetitem.php?id=406
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 thf(in_type,type,
% 0.08/0.31 in: $i > $i > $o ).
% 0.08/0.31
% 0.08/0.31 thf(exu_type,type,
% 0.08/0.31 exu: ( $i > $o ) > $o ).
% 0.08/0.31
% 0.08/0.31 thf(exu,definition,
% 0.08/0.31 ( exu
% 0.08/0.31 = ( ^ [Xphi: $i > $o] :
% 0.08/0.31 ? [Xx: $i] :
% 0.08/0.31 ( ( Xphi @ Xx )
% 0.08/0.31 & ! [Xy: $i] :
% 0.08/0.31 ( ( Xphi @ Xy )
% 0.08/0.31 => ( Xx = Xy ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(setextAx_type,type,
% 0.08/0.31 setextAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(setextAx,definition,
% 0.08/0.31 ( setextAx
% 0.08/0.31 = ( ! [A: $i,B: $i] :
% 0.08/0.31 ( ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ A )
% 0.08/0.31 <=> ( in @ Xx @ B ) )
% 0.08/0.31 => ( A = B ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(emptyset_type,type,
% 0.08/0.31 emptyset: $i ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetAx_type,type,
% 0.08/0.31 emptysetAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetAx,definition,
% 0.08/0.31 ( emptysetAx
% 0.08/0.31 = ( ! [Xx: $i] :
% 0.08/0.31 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(setadjoin_type,type,
% 0.08/0.31 setadjoin: $i > $i > $i ).
% 0.08/0.31
% 0.08/0.31 thf(setadjoinAx_type,type,
% 0.08/0.31 setadjoinAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(setadjoinAx,definition,
% 0.08/0.31 ( setadjoinAx
% 0.08/0.31 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.08/0.31 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.08/0.31 <=> ( ( Xy = Xx )
% 0.08/0.31 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(powerset_type,type,
% 0.08/0.31 powerset: $i > $i ).
% 0.08/0.31
% 0.08/0.31 thf(powersetAx_type,type,
% 0.08/0.31 powersetAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(powersetAx,definition,
% 0.08/0.31 ( powersetAx
% 0.08/0.31 = ( ! [A: $i,B: $i] :
% 0.08/0.31 ( ( in @ B @ ( powerset @ A ) )
% 0.08/0.31 <=> ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ B )
% 0.08/0.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(setunion_type,type,
% 0.08/0.31 setunion: $i > $i ).
% 0.08/0.31
% 0.08/0.31 thf(setunionAx_type,type,
% 0.08/0.31 setunionAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(setunionAx,definition,
% 0.08/0.31 ( setunionAx
% 0.08/0.31 = ( ! [A: $i,Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ ( setunion @ A ) )
% 0.08/0.31 <=> ? [B: $i] :
% 0.08/0.31 ( ( in @ Xx @ B )
% 0.08/0.31 & ( in @ B @ A ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(omega_type,type,
% 0.08/0.31 omega: $i ).
% 0.08/0.31
% 0.08/0.31 thf(omega0Ax_type,type,
% 0.08/0.31 omega0Ax: $o ).
% 0.08/0.31
% 0.08/0.31 thf(omega0Ax,definition,
% 0.08/0.31 ( omega0Ax
% 0.08/0.31 = ( in @ emptyset @ omega ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(omegaSAx_type,type,
% 0.08/0.31 omegaSAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(omegaSAx,definition,
% 0.08/0.31 ( omegaSAx
% 0.08/0.31 = ( ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ omega )
% 0.08/0.31 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(omegaIndAx_type,type,
% 0.08/0.31 omegaIndAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(omegaIndAx,definition,
% 0.08/0.31 ( omegaIndAx
% 0.08/0.31 = ( ! [A: $i] :
% 0.08/0.31 ( ( ( in @ emptyset @ A )
% 0.08/0.31 & ! [Xx: $i] :
% 0.08/0.31 ( ( ( in @ Xx @ omega )
% 0.08/0.31 & ( in @ Xx @ A ) )
% 0.08/0.31 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.08/0.31 => ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ omega )
% 0.08/0.31 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(replAx_type,type,
% 0.08/0.31 replAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(replAx,definition,
% 0.08/0.31 ( replAx
% 0.08/0.31 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.08/0.31 ( ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ A )
% 0.08/0.31 => ( exu
% 0.08/0.31 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.08/0.31 => ? [B: $i] :
% 0.08/0.31 ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ B )
% 0.08/0.31 <=> ? [Xy: $i] :
% 0.08/0.31 ( ( in @ Xy @ A )
% 0.08/0.31 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(foundationAx_type,type,
% 0.08/0.31 foundationAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(foundationAx,definition,
% 0.08/0.31 ( foundationAx
% 0.08/0.31 = ( ! [A: $i] :
% 0.08/0.31 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.08/0.31 => ? [B: $i] :
% 0.08/0.31 ( ( in @ B @ A )
% 0.08/0.31 & ~ ? [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ B )
% 0.08/0.31 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(wellorderingAx_type,type,
% 0.08/0.31 wellorderingAx: $o ).
% 0.08/0.31
% 0.08/0.31 thf(wellorderingAx,definition,
% 0.08/0.31 ( wellorderingAx
% 0.08/0.31 = ( ! [A: $i] :
% 0.08/0.31 ? [B: $i] :
% 0.08/0.31 ( ! [C: $i] :
% 0.08/0.31 ( ( in @ C @ B )
% 0.08/0.31 => ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ C )
% 0.08/0.31 => ( in @ Xx @ A ) ) )
% 0.08/0.31 & ! [Xx: $i,Xy: $i] :
% 0.08/0.31 ( ( ( in @ Xx @ A )
% 0.08/0.31 & ( in @ Xy @ A ) )
% 0.08/0.31 => ( ! [C: $i] :
% 0.08/0.31 ( ( in @ C @ B )
% 0.08/0.31 => ( ( in @ Xx @ C )
% 0.08/0.31 <=> ( in @ Xy @ C ) ) )
% 0.08/0.31 => ( Xx = Xy ) ) )
% 0.08/0.31 & ! [C: $i,D: $i] :
% 0.08/0.31 ( ( ( in @ C @ B )
% 0.08/0.31 & ( in @ D @ B ) )
% 0.08/0.31 => ( ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ C )
% 0.08/0.31 => ( in @ Xx @ D ) )
% 0.08/0.31 | ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ D )
% 0.08/0.31 => ( in @ Xx @ C ) ) ) )
% 0.08/0.31 & ! [C: $i] :
% 0.08/0.31 ( ( ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ C )
% 0.08/0.31 => ( in @ Xx @ A ) )
% 0.08/0.31 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.08/0.31 => ? [D: $i,Xx: $i] :
% 0.08/0.31 ( ( in @ D @ B )
% 0.08/0.31 & ( in @ Xx @ C )
% 0.08/0.31 & ~ ? [Xy: $i] :
% 0.08/0.31 ( ( in @ Xy @ D )
% 0.08/0.31 & ( in @ Xy @ C ) )
% 0.08/0.31 & ! [E: $i] :
% 0.08/0.31 ( ( in @ E @ B )
% 0.08/0.31 => ( ! [Xy: $i] :
% 0.08/0.31 ( ( in @ Xy @ E )
% 0.08/0.31 => ( in @ Xy @ D ) )
% 0.08/0.31 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(descr_type,type,
% 0.08/0.31 descr: ( $i > $o ) > $i ).
% 0.08/0.31
% 0.08/0.31 thf(descrp_type,type,
% 0.08/0.31 descrp: $o ).
% 0.08/0.31
% 0.08/0.31 thf(descrp,definition,
% 0.08/0.31 ( descrp
% 0.08/0.31 = ( ! [Xphi: $i > $o] :
% 0.08/0.31 ( ( exu
% 0.08/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.31 => ( Xphi
% 0.08/0.31 @ ( descr
% 0.08/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(dsetconstr_type,type,
% 0.08/0.31 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.08/0.31
% 0.08/0.31 thf(dsetconstrI_type,type,
% 0.08/0.31 dsetconstrI: $o ).
% 0.08/0.31
% 0.08/0.31 thf(dsetconstrI,definition,
% 0.08/0.31 ( dsetconstrI
% 0.08/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ A )
% 0.08/0.31 => ( ( Xphi @ Xx )
% 0.08/0.31 => ( in @ Xx
% 0.08/0.31 @ ( dsetconstr @ A
% 0.08/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(dsetconstrEL_type,type,
% 0.08/0.31 dsetconstrEL: $o ).
% 0.08/0.31
% 0.08/0.31 thf(dsetconstrEL,definition,
% 0.08/0.31 ( dsetconstrEL
% 0.08/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.31 ( ( in @ Xx
% 0.08/0.31 @ ( dsetconstr @ A
% 0.08/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.08/0.31 => ( in @ Xx @ A ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(dsetconstrER_type,type,
% 0.08/0.31 dsetconstrER: $o ).
% 0.08/0.31
% 0.08/0.31 thf(dsetconstrER,definition,
% 0.08/0.31 ( dsetconstrER
% 0.08/0.31 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.08/0.31 ( ( in @ Xx
% 0.08/0.31 @ ( dsetconstr @ A
% 0.08/0.31 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.08/0.31 => ( Xphi @ Xx ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(exuE1_type,type,
% 0.08/0.31 exuE1: $o ).
% 0.08/0.31
% 0.08/0.31 thf(exuE1,definition,
% 0.08/0.31 ( exuE1
% 0.08/0.31 = ( ! [Xphi: $i > $o] :
% 0.08/0.31 ( ( exu
% 0.08/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.31 => ? [Xx: $i] :
% 0.08/0.31 ( ( Xphi @ Xx )
% 0.08/0.31 & ! [Xy: $i] :
% 0.08/0.31 ( ( Xphi @ Xy )
% 0.08/0.31 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(prop2set_type,type,
% 0.08/0.31 prop2set: $o > $i ).
% 0.08/0.31
% 0.08/0.31 thf(prop2set,definition,
% 0.08/0.31 ( prop2set
% 0.08/0.31 = ( ^ [Xphi: $o] :
% 0.08/0.31 ( dsetconstr @ ( powerset @ emptyset )
% 0.08/0.31 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(prop2setE_type,type,
% 0.08/0.31 prop2setE: $o ).
% 0.08/0.31
% 0.08/0.31 thf(prop2setE,definition,
% 0.08/0.31 ( prop2setE
% 0.08/0.31 = ( ! [Xphi: $o,Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.08/0.31 => Xphi ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetE_type,type,
% 0.08/0.31 emptysetE: $o ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetE,definition,
% 0.08/0.31 ( emptysetE
% 0.08/0.31 = ( ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ emptyset )
% 0.08/0.31 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetimpfalse_type,type,
% 0.08/0.31 emptysetimpfalse: $o ).
% 0.08/0.31
% 0.08/0.31 thf(emptysetimpfalse,definition,
% 0.08/0.31 ( emptysetimpfalse
% 0.08/0.31 = ( ! [Xx: $i] :
% 0.08/0.31 ( ( in @ Xx @ emptyset )
% 0.08/0.31 => $false ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(notinemptyset_type,type,
% 0.08/0.31 notinemptyset: $o ).
% 0.08/0.31
% 0.08/0.31 thf(notinemptyset,definition,
% 0.08/0.31 ( notinemptyset
% 0.08/0.31 = ( ! [Xx: $i] :
% 0.08/0.31 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.08/0.31
% 0.08/0.31 thf(exuE3e,conjecture,
% 0.08/0.31 ( setextAx
% 0.08/0.31 => ( emptysetAx
% 0.08/0.31 => ( setadjoinAx
% 0.08/0.31 => ( powersetAx
% 0.08/0.31 => ( setunionAx
% 0.08/0.31 => ( omega0Ax
% 0.08/0.31 => ( omegaSAx
% 0.08/0.31 => ( omegaIndAx
% 0.08/0.31 => ( replAx
% 0.08/0.31 => ( foundationAx
% 0.08/0.31 => ( wellorderingAx
% 0.08/0.31 => ( descrp
% 0.08/0.31 => ( dsetconstrI
% 0.08/0.31 => ( dsetconstrEL
% 0.08/0.31 => ( dsetconstrER
% 0.08/0.31 => ( exuE1
% 0.08/0.31 => ( prop2setE
% 0.08/0.31 => ( emptysetE
% 0.08/0.31 => ( emptysetimpfalse
% 0.08/0.31 => ( notinemptyset
% 0.08/0.31 => ! [Xphi: $i > $o] :
% 0.08/0.31 ( ( exu
% 0.08/0.31 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.08/0.31 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.08/0.31
% 0.08/0.31 %------------------------------------------------------------------------------
% 0.08/0.31 ------------------------
% 1.09/0.95 ---- Embedded in THF ---
% 1.09/0.95 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.09/0.95 %%% Generated on Tue Feb 24 07:24:41 EST 2026
% 1.09/0.95 %%% using '$$dhol' embedding, version 1.3.0.
% 1.09/0.95 %%% Logic specification used:
% 1.09/0.95 %%% thf(spec, logic, $$dhol).
% 1.09/0.95
% 1.09/0.95 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.LXgTTamYWB/DTF2DTF9734.p
% See solution above
% 1.09/0.95 ------------------------
% 1.09/0.96 ---- Cleaned THF ---
% 1.09/0.96 thf(in_type,type,
% 1.09/0.96 in: $i > $i > $o ).
% 1.09/0.96
% 1.09/0.96 thf(exu_type,type,
% 1.09/0.96 exu: ( $i > $o ) > $o ).
% 1.09/0.96
% 1.09/0.96 thf(exu,definition,
% 1.09/0.96 ( exu
% 1.09/0.96 = ( ^ [Xphi: $i > $o] :
% 1.09/0.96 ? [Xx: $i] :
% 1.09/0.96 ( ( Xphi @ Xx )
% 1.09/0.96 & ! [Xy: $i] :
% 1.09/0.96 ( ( Xphi @ Xy )
% 1.09/0.96 => ( Xx = Xy ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(setextAx_type,type,
% 1.09/0.96 setextAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(setextAx,definition,
% 1.09/0.96 ( setextAx
% 1.09/0.96 = ( ! [A: $i,B: $i] :
% 1.09/0.96 ( ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ A )
% 1.09/0.96 <=> ( in @ Xx @ B ) )
% 1.09/0.96 => ( A = B ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(emptyset_type,type,
% 1.09/0.96 emptyset: $i ).
% 1.09/0.96
% 1.09/0.96 thf(emptysetAx_type,type,
% 1.09/0.96 emptysetAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(emptysetAx,definition,
% 1.09/0.96 ( emptysetAx
% 1.09/0.96 = ( ! [Xx: $i] :
% 1.09/0.96 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(setadjoin_type,type,
% 1.09/0.96 setadjoin: $i > $i > $i ).
% 1.09/0.96
% 1.09/0.96 thf(setadjoinAx_type,type,
% 1.09/0.96 setadjoinAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(setadjoinAx,definition,
% 1.09/0.96 ( setadjoinAx
% 1.09/0.96 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.09/0.96 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.09/0.96 <=> ( ( Xy = Xx )
% 1.09/0.96 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(powerset_type,type,
% 1.09/0.96 powerset: $i > $i ).
% 1.09/0.96
% 1.09/0.96 thf(powersetAx_type,type,
% 1.09/0.96 powersetAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(powersetAx,definition,
% 1.09/0.96 ( powersetAx
% 1.09/0.96 = ( ! [A: $i,B: $i] :
% 1.09/0.96 ( ( in @ B @ ( powerset @ A ) )
% 1.09/0.96 <=> ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ B )
% 1.09/0.96 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(setunion_type,type,
% 1.09/0.96 setunion: $i > $i ).
% 1.09/0.96
% 1.09/0.96 thf(setunionAx_type,type,
% 1.09/0.96 setunionAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(setunionAx,definition,
% 1.09/0.96 ( setunionAx
% 1.09/0.96 = ( ! [A: $i,Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ ( setunion @ A ) )
% 1.09/0.96 <=> ? [B: $i] :
% 1.09/0.96 ( ( in @ Xx @ B )
% 1.09/0.96 & ( in @ B @ A ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(omega_type,type,
% 1.09/0.96 omega: $i ).
% 1.09/0.96
% 1.09/0.96 thf(omega0Ax_type,type,
% 1.09/0.96 omega0Ax: $o ).
% 1.09/0.96
% 1.09/0.96 thf(omega0Ax,definition,
% 1.09/0.96 ( omega0Ax
% 1.09/0.96 = ( in @ emptyset @ omega ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(omegaSAx_type,type,
% 1.09/0.96 omegaSAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(omegaSAx,definition,
% 1.09/0.96 ( omegaSAx
% 1.09/0.96 = ( ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ omega )
% 1.09/0.96 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(omegaIndAx_type,type,
% 1.09/0.96 omegaIndAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(omegaIndAx,definition,
% 1.09/0.96 ( omegaIndAx
% 1.09/0.96 = ( ! [A: $i] :
% 1.09/0.96 ( ( ( in @ emptyset @ A )
% 1.09/0.96 & ! [Xx: $i] :
% 1.09/0.96 ( ( ( in @ Xx @ omega )
% 1.09/0.96 & ( in @ Xx @ A ) )
% 1.09/0.96 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.09/0.96 => ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ omega )
% 1.09/0.96 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(replAx_type,type,
% 1.09/0.96 replAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(replAx,definition,
% 1.09/0.96 ( replAx
% 1.09/0.96 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.09/0.96 ( ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ A )
% 1.09/0.96 => ( exu
% 1.09/0.96 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.09/0.96 => ? [B: $i] :
% 1.09/0.96 ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ B )
% 1.09/0.96 <=> ? [Xy: $i] :
% 1.09/0.96 ( ( in @ Xy @ A )
% 1.09/0.96 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(foundationAx_type,type,
% 1.09/0.96 foundationAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(foundationAx,definition,
% 1.09/0.96 ( foundationAx
% 1.09/0.96 = ( ! [A: $i] :
% 1.09/0.96 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.09/0.96 => ? [B: $i] :
% 1.09/0.96 ( ( in @ B @ A )
% 1.09/0.96 & ~ ? [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ B )
% 1.09/0.96 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(wellorderingAx_type,type,
% 1.09/0.96 wellorderingAx: $o ).
% 1.09/0.96
% 1.09/0.96 thf(wellorderingAx,definition,
% 1.09/0.96 ( wellorderingAx
% 1.09/0.96 = ( ! [A: $i] :
% 1.09/0.96 ? [B: $i] :
% 1.09/0.96 ( ! [C: $i] :
% 1.09/0.96 ( ( in @ C @ B )
% 1.09/0.96 => ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ C )
% 1.09/0.96 => ( in @ Xx @ A ) ) )
% 1.09/0.96 & ! [Xx: $i,Xy: $i] :
% 1.09/0.96 ( ( ( in @ Xx @ A )
% 1.09/0.96 & ( in @ Xy @ A ) )
% 1.09/0.96 => ( ! [C: $i] :
% 1.09/0.96 ( ( in @ C @ B )
% 1.09/0.96 => ( ( in @ Xx @ C )
% 1.09/0.96 <=> ( in @ Xy @ C ) ) )
% 1.09/0.96 => ( Xx = Xy ) ) )
% 1.09/0.96 & ! [C: $i,D: $i] :
% 1.09/0.96 ( ( ( in @ C @ B )
% 1.09/0.96 & ( in @ D @ B ) )
% 1.09/0.96 => ( ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ C )
% 1.09/0.96 => ( in @ Xx @ D ) )
% 1.09/0.96 | ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ D )
% 1.09/0.96 => ( in @ Xx @ C ) ) ) )
% 1.09/0.96 & ! [C: $i] :
% 1.09/0.96 ( ( ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ C )
% 1.09/0.96 => ( in @ Xx @ A ) )
% 1.09/0.96 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.09/0.96 => ? [D: $i,Xx: $i] :
% 1.09/0.96 ( ( in @ D @ B )
% 1.09/0.96 & ( in @ Xx @ C )
% 1.09/0.96 & ~ ? [Xy: $i] :
% 1.09/0.96 ( ( in @ Xy @ D )
% 1.09/0.96 & ( in @ Xy @ C ) )
% 1.09/0.96 & ! [E: $i] :
% 1.09/0.96 ( ( in @ E @ B )
% 1.09/0.96 => ( ! [Xy: $i] :
% 1.09/0.96 ( ( in @ Xy @ E )
% 1.09/0.96 => ( in @ Xy @ D ) )
% 1.09/0.96 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(descr_type,type,
% 1.09/0.96 descr: ( $i > $o ) > $i ).
% 1.09/0.96
% 1.09/0.96 thf(descrp_type,type,
% 1.09/0.96 descrp: $o ).
% 1.09/0.96
% 1.09/0.96 thf(descrp,definition,
% 1.09/0.96 ( descrp
% 1.09/0.96 = ( ! [Xphi: $i > $o] :
% 1.09/0.96 ( ( exu
% 1.09/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.09/0.96 => ( Xphi
% 1.09/0.96 @ ( descr
% 1.09/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(dsetconstr_type,type,
% 1.09/0.96 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.09/0.96
% 1.09/0.96 thf(dsetconstrI_type,type,
% 1.09/0.96 dsetconstrI: $o ).
% 1.09/0.96
% 1.09/0.96 thf(dsetconstrI,definition,
% 1.09/0.96 ( dsetconstrI
% 1.09/0.96 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ A )
% 1.09/0.96 => ( ( Xphi @ Xx )
% 1.09/0.96 => ( in @ Xx
% 1.09/0.96 @ ( dsetconstr @ A
% 1.09/0.96 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(dsetconstrEL_type,type,
% 1.09/0.96 dsetconstrEL: $o ).
% 1.09/0.96
% 1.09/0.96 thf(dsetconstrEL,definition,
% 1.09/0.96 ( dsetconstrEL
% 1.09/0.96 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.09/0.96 ( ( in @ Xx
% 1.09/0.96 @ ( dsetconstr @ A
% 1.09/0.96 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.09/0.96 => ( in @ Xx @ A ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(dsetconstrER_type,type,
% 1.09/0.96 dsetconstrER: $o ).
% 1.09/0.96
% 1.09/0.96 thf(dsetconstrER,definition,
% 1.09/0.96 ( dsetconstrER
% 1.09/0.96 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.09/0.96 ( ( in @ Xx
% 1.09/0.96 @ ( dsetconstr @ A
% 1.09/0.96 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.09/0.96 => ( Xphi @ Xx ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(exuE1_type,type,
% 1.09/0.96 exuE1: $o ).
% 1.09/0.96
% 1.09/0.96 thf(exuE1,definition,
% 1.09/0.96 ( exuE1
% 1.09/0.96 = ( ! [Xphi: $i > $o] :
% 1.09/0.96 ( ( exu
% 1.09/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.09/0.96 => ? [Xx: $i] :
% 1.09/0.96 ( ( Xphi @ Xx )
% 1.09/0.96 & ! [Xy: $i] :
% 1.09/0.96 ( ( Xphi @ Xy )
% 1.09/0.96 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(prop2set_type,type,
% 1.09/0.96 prop2set: $o > $i ).
% 1.09/0.96
% 1.09/0.96 thf(prop2set,definition,
% 1.09/0.96 ( prop2set
% 1.09/0.96 = ( ^ [Xphi: $o] :
% 1.09/0.96 ( dsetconstr @ ( powerset @ emptyset )
% 1.09/0.96 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(prop2setE_type,type,
% 1.09/0.96 prop2setE: $o ).
% 1.09/0.96
% 1.09/0.96 thf(prop2setE,definition,
% 1.09/0.96 ( prop2setE
% 1.09/0.96 = ( ! [Xphi: $o,Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.09/0.96 => Xphi ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(emptysetE_type,type,
% 1.09/0.96 emptysetE: $o ).
% 1.09/0.96
% 1.09/0.96 thf(emptysetE,definition,
% 1.09/0.96 ( emptysetE
% 1.09/0.96 = ( ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ emptyset )
% 1.09/0.96 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(emptysetimpfalse_type,type,
% 1.09/0.96 emptysetimpfalse: $o ).
% 1.09/0.96
% 1.09/0.96 thf(emptysetimpfalse,definition,
% 1.09/0.96 ( emptysetimpfalse
% 1.09/0.96 = ( ! [Xx: $i] :
% 1.09/0.96 ( ( in @ Xx @ emptyset )
% 1.09/0.96 => $false ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(notinemptyset_type,type,
% 1.09/0.96 notinemptyset: $o ).
% 1.09/0.96
% 1.09/0.96 thf(notinemptyset,definition,
% 1.09/0.96 ( notinemptyset
% 1.09/0.96 = ( ! [Xx: $i] :
% 1.09/0.96 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.09/0.96
% 1.09/0.96 thf(exuE3e,conjecture,
% 1.09/0.96 ( setextAx
% 1.09/0.96 => ( emptysetAx
% 1.09/0.96 => ( setadjoinAx
% 1.09/0.96 => ( powersetAx
% 1.09/0.96 => ( setunionAx
% 1.09/0.96 => ( omega0Ax
% 1.09/0.96 => ( omegaSAx
% 1.09/0.96 => ( omegaIndAx
% 1.09/0.96 => ( replAx
% 1.09/0.96 => ( foundationAx
% 1.09/0.96 => ( wellorderingAx
% 1.09/0.96 => ( descrp
% 1.09/0.96 => ( dsetconstrI
% 1.09/0.96 => ( dsetconstrEL
% 1.09/0.96 => ( dsetconstrER
% 1.09/0.96 => ( exuE1
% 1.09/0.96 => ( prop2setE
% 1.09/0.96 => ( emptysetE
% 1.09/0.96 => ( emptysetimpfalse
% 1.09/0.96 => ( notinemptyset
% 1.09/0.96 => ! [Xphi: $i > $o] :
% 1.09/0.96 ( ( exu
% 1.09/0.96 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.09/0.96 => ? [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.09/0.96 ------------------------
% 1.09/0.97 % (9849)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9734 for (2999ds/183Mi)
% 1.09/0.97 % (9851)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_9734 for (2999ds/27Mi)
% 1.09/0.97 % (9854)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_9734 for (2999ds/275Mi)
% 1.09/0.97 % (9850)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_9734 for (2999ds/4Mi)
% 1.09/0.97 % (9852)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9734 for (2999ds/2Mi)
% 1.09/0.97 % (9853)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_9734 for (2999ds/2Mi)
% 1.09/0.97 % (9852)Instruction limit reached!
% 1.09/0.97 % (9852)------------------------------
% 1.09/0.97 % (9852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/0.97 % (9853)Instruction limit reached!
% 1.09/0.97 % (9853)------------------------------
% 1.09/0.97 % (9853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/0.97 % (9852)Termination reason: Unknown
% 1.09/0.97 % (9852)Termination phase: shuffling
% 1.09/0.97
% 1.09/0.97 % (9852)Memory used [KB]: 1023
% 1.09/0.97 % (9852)Time elapsed: 0.002 s
% 1.09/0.97 % (9852)Instructions burned: 2 (million)
% 1.09/0.97 % (9852)------------------------------
% 1.09/0.97 % (9852)------------------------------
% 1.09/0.97 % (9853)Termination reason: Unknown
% 1.09/0.97 % (9853)Termination phase: shuffling
% 1.09/0.97
% 1.09/0.97 % (9853)Memory used [KB]: 1023
% 1.09/0.97 % (9853)Time elapsed: 0.002 s
% 1.09/0.97 % (9853)Instructions burned: 3 (million)
% 1.09/0.97 % (9853)------------------------------
% 1.09/0.97 % (9853)------------------------------
% 1.09/0.97 % (9855)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9734 for (2999ds/18Mi)
% 1.09/0.97 % (9850)Instruction limit reached!
% 1.09/0.97 % (9850)------------------------------
% 1.09/0.97 % (9850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/0.97 % (9850)Termination reason: Unknown
% 1.09/0.97 % (9850)Termination phase: Property scanning
% 1.09/0.97
% 1.09/0.97 % (9850)Memory used [KB]: 1023
% 1.09/0.97 % (9850)Time elapsed: 0.003 s
% 1.09/0.97 % (9850)Instructions burned: 6 (million)
% 1.09/0.97 % (9850)------------------------------
% 1.09/0.97 % (9850)------------------------------
% 1.09/0.98 % (9855)Instruction limit reached!
% 1.09/0.98 % (9855)------------------------------
% 1.09/0.98 % (9855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/0.98 % (9855)Termination reason: Unknown
% 1.09/0.98 % (9855)Termination phase: Property scanning
% 1.09/0.98
% 1.09/0.98 % (9855)Memory used [KB]: 1279
% 1.09/0.98 % (9855)Time elapsed: 0.006 s
% 1.09/0.98 % (9855)Instructions burned: 18 (million)
% 1.09/0.98 % (9855)------------------------------
% 1.09/0.98 % (9855)------------------------------
% 1.09/0.98 % (9851)Instruction limit reached!
% 1.09/0.98 % (9851)------------------------------
% 1.09/0.98 % (9851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/0.98 % (9851)Termination reason: Unknown
% 1.09/0.98 % (9851)Termination phase: Saturation
% 1.09/0.98
% 1.09/0.98 % (9851)Memory used [KB]: 5756
% 1.09/0.98 % (9851)Time elapsed: 0.009 s
% 1.09/0.98 % (9851)Instructions burned: 28 (million)
% 1.09/0.98 % (9851)------------------------------
% 1.09/0.98 % (9851)------------------------------
% 1.09/0.98 % (9857)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_9734 for (2999ds/37Mi)
% 1.09/0.98 % (9856)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9734 for (2999ds/3Mi)
% 1.09/0.98 % (9858)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_9734 for (2999ds/15Mi)
% 1.09/0.98 % (9856)Instruction limit reached!
% 1.09/0.98 % (9856)------------------------------
% 1.09/0.98 % (9856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/0.98 % (9856)Termination reason: Unknown
% 1.09/0.98 % (9856)Termination phase: shuffling
% 1.09/0.98
% 1.09/0.98 % (9856)Memory used [KB]: 1023
% 1.09/0.98 % (9856)Time elapsed: 0.002 s
% 1.09/0.98 % (9856)Instructions burned: 3 (million)
% 1.09/0.98 % (9856)------------------------------
% 1.09/0.98 % (9856)------------------------------
% 1.09/0.98 % (9849)First to succeed.
% 1.09/0.99 % (9854)Also succeeded, but the first one will report.
% 1.09/0.99 % (9849)Refutation found. Thanks to Tanya!
% 1.09/0.99 % SZS status Theorem for DTF2THF_9734
% 1.09/0.99 % SZS output start Proof for DTF2THF_9734
% 1.09/0.99 thf(func_def_0, type, in: $i > $i > $o).
% 1.09/0.99 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.09/0.99 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.09/0.99 thf(func_def_8, type, powerset: $i > $i).
% 1.09/0.99 thf(func_def_10, type, setunion: $i > $i).
% 1.09/0.99 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.09/0.99 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.09/0.99 thf(func_def_26, type, prop2set: $o > $i).
% 1.09/0.99 thf(func_def_47, type, sK0: $i > $o).
% 1.09/0.99 thf(func_def_49, type, sK2: $i > ($i > $i > $o) > $i).
% 1.09/0.99 thf(func_def_50, type, sK3: $i > ($i > $i > $o) > $i).
% 1.09/0.99 thf(func_def_51, type, sK4: $i > $i > ($i > $i > $o) > $i).
% 1.09/0.99 thf(func_def_52, type, sK5: $i > $i > ($i > $i > $o) > $i).
% 1.09/0.99 thf(func_def_53, type, sK6: $i > $i > ($i > $i > $o) > $i).
% 1.09/0.99 thf(func_def_54, type, sK7: $i > $i > ($i > $i > $o) > $i).
% 1.09/0.99 thf(func_def_55, type, sK8: $i > $i).
% 1.09/0.99 thf(func_def_56, type, sK9: $i > $i > $i > $i).
% 1.09/0.99 thf(func_def_57, type, sK10: $i > $i > $i).
% 1.09/0.99 thf(func_def_58, type, sK11: $i > $i > $i).
% 1.09/0.99 thf(func_def_59, type, sK12: $i > $i > $i).
% 1.09/0.99 thf(func_def_60, type, sK13: ($i > $o) > $i > $i).
% 1.09/0.99 thf(func_def_61, type, sK14: $i > $i > $i).
% 1.09/0.99 thf(func_def_62, type, sK15: $i > $i > $i).
% 1.09/0.99 thf(func_def_63, type, sK16: ($i > $o) > $i).
% 1.09/0.99 thf(func_def_64, type, sK17: ($i > $o) > $i > $i).
% 1.09/0.99 thf(func_def_65, type, sK18: ($i > $o) > $i > $i).
% 1.09/0.99 thf(func_def_67, type, sK20: $i > $i).
% 1.09/0.99 thf(func_def_68, type, sK21: $i > $i > $i).
% 1.09/0.99 thf(func_def_69, type, sK22: $i > $i).
% 1.09/0.99 thf(f463,plain,(
% 1.09/0.99 $false),
% 1.09/0.99 inference(trivial_inequality_removal,[status(thm)],[f462])).
% 1.09/0.99 thf(f462,plain,(
% 1.09/0.99 ($true != $true)),
% 1.09/0.99 inference(superposition,[status(thm)],[f94,f403])).
% 1.09/0.99 thf(f403,plain,(
% 1.09/0.99 ((sK0 @ sK19) = $true)),
% 1.09/0.99 inference(binary_proxy_clausification,[status(thm)],[f402])).
% 1.09/0.99 thf(f402,plain,(
% 1.09/0.99 ($true = ((!! @ $i @ (^[Y0 : $i]: ((sK0 @ Y0) => (sK19 = Y0)))) & (sK0 @ sK19)))),
% 1.09/0.99 inference(beta_eta_normalization,[status(thm)],[f401])).
% 1.09/0.99 thf(f401,plain,(
% 1.09/0.99 (((^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0))) @ sK19) = $true)),
% 1.09/0.99 inference(sigma_clausification,[status(thm)],[f400])).
% 1.09/0.99 thf(f400,plain,(
% 1.09/0.99 ((?? @ $i @ (^[Y0 : $i]: ((!! @ $i @ (^[Y1 : $i]: ((sK0 @ Y1) => (Y0 = Y1)))) & (sK0 @ Y0)))) = $true)),
% 1.09/0.99 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.09/0.99 thf(f120,plain,(
% 1.09/0.99 (((^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))) @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 1.09/0.99 inference(definition_unfolding,[status(thm)],[f95,f76])).
% 1.09/0.99 thf(f76,plain,(
% 1.09/0.99 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.09/0.99 inference(cnf_transformation,[status(thm)],[f41])).
% 1.09/0.99 thf(f41,plain,(
% 1.09/0.99 (exu = (^[Y0 : $i > $o]: (?? @ $i @ (^[Y1 : $i]: ((!! @ $i @ (^[Y2 : $i]: ((Y0 @ Y2) => (Y1 = Y2)))) & (Y0 @ Y1))))))),
% 1.09/0.99 inference(fool_elimination,[status(thm)],[f40])).
% 1.09/0.99 thf(f40,plain,(
% 1.09/0.99 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))))),
% 1.09/0.99 inference(rectify,[status(thm)],[f1])).
% 1.09/0.99 thf(f1,axiom,(
% 1.09/0.99 (exu = (^[X0 : $i > $o] : (? [X1 : $i] : ((X0 @ X1) & ! [X2 : $i] : ((X0 @ X2) => (X1 = X2))))))),
% 1.09/0.99 file('/export/starexec/sandbox2/tmp/tmp.LXgTTamYWB/DTF2THF_9734.p',exu)).
% 1.09/0.99 thf(f95,plain,(
% 1.09/0.99 ((exu @ (^[Y0 : $i]: (sK0 @ Y0))) = $true)),
% 1.09/0.99 inference(cnf_transformation,[status(thm)],[f73])).
% 1.09/0.99 thf(f73,plain,(
% 1.09/0.99 (emptysetimpfalse = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & (((exu @ (^[Y0 : $i]: (sK0 @ Y0))) = $true) & ! [X1 : $i] : ((sK0 @ X1) != $true)) & (descrp = $true) & (powersetAx = $true) & (setunionAx = $true) & (omega0Ax = $true) & (emptysetE = $true) & (notinemptyset = $true) & (dsetconstrER = $true) & (emptysetAx = $true) & (foundationAx = $true) & (setextAx = $true) & (setadjoinAx = $true) & (omegaIndAx = $true) & (prop2setE = $true) & (replAx = $true) & (wellorderingAx = $true) & (omegaSAx = $true)),
% 1.09/0.99 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f71,f72])).
% 1.09/0.99 thf(f72,plain,(
% 1.09/0.99 ? [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X1 : $i] : ((X0 @ X1) != $true)) => (((exu @ (^[Y0 : $i]: (sK0 @ Y0))) = $true) & ! [X1 : $i] : ((sK0 @ X1) != $true))),
% 1.09/0.99 introduced(definition,[],[choice_axiom])).
% 1.09/0.99 thf(f71,plain,(
% 1.09/0.99 (emptysetimpfalse = $true) & (exuE1 = $true) & (dsetconstrEL = $true) & (dsetconstrI = $true) & ? [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X1 : $i] : ((X0 @ X1) != $true)) & (descrp = $true) & (powersetAx = $true) & (setunionAx = $true) & (omega0Ax = $true) & (emptysetE = $true) & (notinemptyset = $true) & (dsetconstrER = $true) & (emptysetAx = $true) & (foundationAx = $true) & (setextAx = $true) & (setadjoinAx = $true) & (omegaIndAx = $true) & (prop2setE = $true) & (replAx = $true) & (wellorderingAx = $true) & (omegaSAx = $true)),
% 1.09/0.99 inference(flattening,[status(thm)],[f70])).
% 1.09/0.99 thf(f70,plain,(
% 1.09/0.99 (((((((((((((((((((? [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) & ! [X1 : $i] : ((X0 @ X1) != $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)),
% 1.09/0.99 inference(ennf_transformation,[status(thm)],[f69])).
% 1.09/0.99 thf(f69,plain,(
% 1.09/0.99 ~((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) => ! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X1 : $i] : ((X0 @ X1) = $true))))))))))))))))))))))),
% 1.09/0.99 inference(rectify,[status(thm)],[f33])).
% 1.09/0.99 thf(f33,plain,(
% 1.09/0.99 ~((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) => ! [X0 : $i > $o] : (((exu @ (^[Y0 : $i]: (X0 @ Y0))) = $true) => ? [X2 : $i] : ((X0 @ X2) = $true))))))))))))))))))))))),
% 1.09/0.99 inference(fool_elimination,[status(thm)],[f32])).
% 1.09/0.99 thf(f32,plain,(
% 1.09/0.99 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X2 : $i] : (X0 @ X2))))))))))))))))))))))),
% 1.09/0.99 inference(rectify,[status(thm)],[f24])).
% 1.09/0.99 thf(f24,negated_conjecture,(
% 1.09/0.99 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : (X0 @ X1))))))))))))))))))))))),
% 1.09/0.99 inference(negated_conjecture,[status(cth)],[f23])).
% 1.09/0.99 thf(f23,conjecture,(
% 1.09/0.99 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => (emptysetimpfalse => (notinemptyset => ! [X0 : $i > $o] : ((exu @ (^[X1 : $i] : (X0 @ X1))) => ? [X1 : $i] : (X0 @ X1)))))))))))))))))))))),
% 1.09/0.99 file('/export/starexec/sandbox2/tmp/tmp.LXgTTamYWB/DTF2THF_9734.p',exuE3e)).
% 1.09/0.99 thf(f94,plain,(
% 1.09/0.99 ( ! [X1 : $i] : (((sK0 @ X1) != $true)) )),
% 1.09/0.99 inference(cnf_transformation,[status(thm)],[f73])).
% 1.09/0.99 % SZS output end Proof for DTF2THF_9734
% 1.09/0.99 % (9849)------------------------------
% 1.09/0.99 % (9849)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.09/0.99 % (9849)Termination reason: Refutation
% 1.09/0.99
% 1.09/0.99 % (9849)Memory used [KB]: 5884
% 1.09/0.99 % (9849)Time elapsed: 0.015 s
% 1.09/0.99 % (9849)Instructions burned: 47 (million)
% 1.09/0.99 % (9849)------------------------------
% 1.09/0.99 % (9849)------------------------------
% 1.09/0.99 % (9848)Success in time 0.016 s
%------------------------------------------------------------------------------