%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU502^1 : 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 : n010.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 09:34:57 AM UTC 2026
% Result : Theorem 1.95s 1.51s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 4
% Syntax : Number of formulae : 24 ( 6 unt; 0 typ; 0 def)
% Number of atoms : 523 ( 143 equ; 0 cnn)
% Maximal formula atoms : 21 ( 21 avg)
% Number of connectives : 257 ( 22 ~; 8 |; 57 &; 54 @)
% ( 2 <=>; 114 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 69 usr; 23 con; 0-3 aty)
% Number of variables : 22 ( 0 ^; 16 !; 6 ?; 22 :)
% 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_40,type,
sP0: $i > $i > $o ).
thf(func_def_41,type,
sP1: $i > $o ).
thf(func_def_42,type,
sP2: $i > $i > $o ).
thf(func_def_43,type,
sP3: $i > $i > $o ).
thf(func_def_45,type,
sK5: $i > $i ).
thf(func_def_48,type,
sK8: $i > $i > $i ).
thf(func_def_49,type,
sK9: $i > $i > $i ).
thf(func_def_50,type,
sK10: $i > $i > $i ).
thf(func_def_51,type,
sK11: $i > $i > $i ).
thf(func_def_52,type,
sK12: $i > $i > $i ).
thf(func_def_53,type,
sK13: $i > $i > $i > $i ).
thf(func_def_54,type,
sK14: $i > $i ).
thf(func_def_55,type,
sK15: $i > $i ).
thf(func_def_56,type,
sK16: $i > $i ).
thf(func_def_57,type,
sK17: $i > $i ).
thf(func_def_58,type,
sK18: $i > $i > $i ).
thf(func_def_59,type,
sK19: $i > $i > $i > $i ).
thf(func_def_60,type,
sK20: $i > $i > $i > $i ).
thf(func_def_61,type,
sK21: $i > $i > $i ).
thf(func_def_62,type,
sK22: $i > $i > $i ).
thf(func_def_63,type,
sK23: $i > $i ).
thf(func_def_65,type,
sK25: $i > $i ).
thf(func_def_66,type,
sK26: $i > $i ).
thf(func_def_67,type,
sK27: $i > $i > $i ).
thf(func_def_71,type,
sK31: $i > $i > $o ).
thf(func_def_72,type,
sK32: $i > $i ).
thf(func_def_73,type,
sK33: $i > $i ).
thf(func_def_74,type,
sK34: ( $i > $i > $o ) > $i > $i ).
thf(func_def_75,type,
sK35: ( $i > $i > $o ) > $i > $i ).
thf(func_def_76,type,
sK36: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_78,type,
sK38: $i > $i > $i ).
thf(func_def_85,type,
sK45: ( $i > $o ) > $i ).
thf(func_def_86,type,
sK46: $i > $o ).
thf(func_def_87,type,
sK47: $i > $i ).
thf(func_def_90,type,
sK50: $i > $o ).
thf(func_def_92,type,
sK52: $i > $o ).
thf(func_def_100,type,
sK60: $i > $o ).
thf(func_def_101,type,
sK61: $i > $i ).
thf(func_def_103,type,
sK63: $i > $i ).
thf(func_def_108,type,
ph68:
!>[X0: $tType] : X0 ).
thf(f425,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f300,f414]) ).
thf(f414,plain,
! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f343]) ).
thf(f343,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f259,f293]) ).
thf(f293,plain,
emptysetAx = $true,
inference(cnf_transformation,[status(thm)],[f183]) ).
thf(f183,plain,
( ( replAx = $true )
& ( setunionAx = $true )
& ( wellorderingAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( omegaIndAx = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( exuE1 = $true )
& ( $true
= ( in @ sK57 @ emptyset ) )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( emptysetE = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( omega0Ax = $true )
& ( emptysetAx = $true )
& ( foundationAx = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f71,f182]) ).
thf(f182,plain,
( ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) )
=> ( $true
= ( in @ sK57 @ emptyset ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f71,plain,
( ( replAx = $true )
& ( setunionAx = $true )
& ( wellorderingAx = $true )
& ( prop2setE = $true )
& ( dsetconstrER = $true )
& ( omegaIndAx = $true )
& ( dsetconstrEL = $true )
& ( descrp = $true )
& ( setextAx = $true )
& ( exuE1 = $true )
& ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( emptysetE = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( omega0Ax = $true )
& ( emptysetAx = $true )
& ( foundationAx = $true ) ),
inference(flattening,[status(thm)],[f70]) ).
thf(f70,plain,
( ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) )
& ( 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)],[f64]) ).
thf(f64,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 )
=> ! [X0: $i] :
( $true
!= ( in @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f63]) ).
thf(f63,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 )
=> ! [X0: $i] :
( $true
!= ( in @ X0 @ emptyset ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(true_and_false_elimination,[status(thm)],[f60]) ).
thf(f60,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 )
=> ! [X0: $i] :
( ( $true
= ( in @ X0 @ emptyset ) )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f59]) ).
thf(f59,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ! [X0: $i] :
( ( in @ X0 @ emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f22]) ).
thf(f22,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f21]) ).
thf(f21,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ( prop2setE
=> ( emptysetE
=> ! [X1: $i] :
( ( in @ X1 @ emptyset )
=> $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.U6moXOrfhg/DTF2THF_19517.p',emptysetimpfalse) ).
thf(f259,plain,
! [X1: $i] :
( ( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetAx != $true ) ),
inference(cnf_transformation,[status(thm)],[f148]) ).
thf(f148,plain,
( ( ( emptysetAx = $true )
| ( $true
= ( in @ sK37 @ emptyset ) ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetAx != $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f146,f147]) ).
thf(f147,plain,
( ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) )
=> ( $true
= ( in @ sK37 @ emptyset ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f146,plain,
( ( ( emptysetAx = $true )
| ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) ) )
& ( ! [X1: $i] :
( ( in @ X1 @ emptyset )
!= $true )
| ( emptysetAx != $true ) ) ),
inference(rectify,[status(thm)],[f145]) ).
thf(f145,plain,
( ( ( emptysetAx = $true )
| ? [X0: $i] :
( $true
= ( in @ X0 @ emptyset ) ) )
& ( ! [X0: $i] :
( $true
!= ( in @ X0 @ emptyset ) )
| ( emptysetAx != $true ) ) ),
inference(nnf_transformation,[status(thm)],[f65]) ).
thf(f65,plain,
( ( emptysetAx = $true )
<=> ! [X0: $i] :
( $true
!= ( in @ X0 @ emptyset ) ) ),
inference(flattening,[status(thm)],[f36]) ).
thf(f36,plain,
( ( emptysetAx = $true )
<=> ! [X0: $i] :
( $true
!= ( in @ X0 @ emptyset ) ) ),
inference(fool_elimination,[status(thm)],[f35]) ).
thf(f35,plain,
( emptysetAx
= ( ! [X0: $i] :
~ ( in @ X0 @ emptyset ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( emptysetAx
= ( ! [X1: $i] :
~ ( in @ X1 @ emptyset ) ) ),
file('/export/starexec/sandbox/tmp/tmp.U6moXOrfhg/DTF2THF_19517.p',emptysetAx) ).
thf(f300,plain,
( $true
= ( in @ sK57 @ emptyset ) ),
inference(cnf_transformation,[status(thm)],[f183]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU502^1 : TPTP v9.2.1. Released v3.7.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n010.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.33 % DateTime : Tue Feb 24 12:24:18 EST 2026
% 0.17/0.33 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.18/0.45 ---- Original DTF file ---
% 0.18/0.45 thf(spec,logic,$$dhol).
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 % File : SEU502^1 : TPTP v9.2.1. Released v3.7.0.
% 0.18/0.45 % Domain : Set Theory
% 0.18/0.45 % Problem : Preliminary Notions - Basic Laws of Logic
% 0.18/0.45 % Version : Especial.
% 0.18/0.45 % English : (! x:i.in x emptyset -> false)
% 0.18/0.45
% 0.18/0.45 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.18/0.45 % Source : [Bro08]
% 0.18/0.45 % Names : ZFC004g [Bro08]
% 0.18/0.45
% 0.18/0.45 % Status : Theorem
% 0.18/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0, 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, 0.00 v4.0.1, 0.33 v3.7.0
% 0.18/0.45 % Syntax : Number of formulae : 49 ( 20 unt; 28 typ; 20 def)
% 0.18/0.45 % Number of atoms : 126 ( 25 equ; 0 cnn)
% 0.18/0.45 % Maximal formula atoms : 20 ( 6 avg)
% 0.18/0.45 % Number of connectives : 239 ( 3 ~; 3 |; 18 &; 159 @)
% 0.18/0.45 % ( 6 <=>; 50 =>; 0 <=; 0 <~>)
% 0.18/0.45 % Maximal formula depth : 23 ( 2 avg)
% 0.18/0.45 % Number of types : 2 ( 0 usr)
% 0.18/0.45 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.18/0.45 % Number of symbols : 30 ( 28 usr; 21 con; 0-2 aty)
% 0.18/0.45 % Number of variables : 76 ( 10 ^; 53 !; 13 ?; 76 :)
% 0.18/0.45 % SPC : TH0_THM_EQU_NAR
% 0.18/0.45
% 0.18/0.45 % Comments : http://mathgate.info/detsetitem.php?id=391
% 0.18/0.45 %------------------------------------------------------------------------------
% 0.18/0.45 thf(in_type,type,
% 0.18/0.45 in: $i > $i > $o ).
% 0.18/0.45
% 0.18/0.45 thf(exu_type,type,
% 0.18/0.45 exu: ( $i > $o ) > $o ).
% 0.18/0.45
% 0.18/0.45 thf(exu,definition,
% 0.18/0.45 ( exu
% 0.18/0.45 = ( ^ [Xphi: $i > $o] :
% 0.18/0.45 ? [Xx: $i] :
% 0.18/0.45 ( ( Xphi @ Xx )
% 0.18/0.45 & ! [Xy: $i] :
% 0.18/0.45 ( ( Xphi @ Xy )
% 0.18/0.45 => ( Xx = Xy ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setextAx_type,type,
% 0.18/0.45 setextAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setextAx,definition,
% 0.18/0.45 ( setextAx
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ A )
% 0.18/0.45 <=> ( in @ Xx @ B ) )
% 0.18/0.45 => ( A = B ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(emptyset_type,type,
% 0.18/0.45 emptyset: $i ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetAx_type,type,
% 0.18/0.45 emptysetAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(emptysetAx,definition,
% 0.18/0.45 ( emptysetAx
% 0.18/0.45 = ( ! [Xx: $i] :
% 0.18/0.45 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoin_type,type,
% 0.18/0.45 setadjoin: $i > $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinAx_type,type,
% 0.18/0.45 setadjoinAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setadjoinAx,definition,
% 0.18/0.45 ( setadjoinAx
% 0.18/0.45 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.18/0.45 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.18/0.45 <=> ( ( Xy = Xx )
% 0.18/0.45 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(powerset_type,type,
% 0.18/0.45 powerset: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(powersetAx_type,type,
% 0.18/0.45 powersetAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(powersetAx,definition,
% 0.18/0.45 ( powersetAx
% 0.18/0.45 = ( ! [A: $i,B: $i] :
% 0.18/0.45 ( ( in @ B @ ( powerset @ A ) )
% 0.18/0.45 <=> ! [Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ B )
% 0.18/0.45 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.45
% 0.18/0.45 thf(setunion_type,type,
% 0.18/0.45 setunion: $i > $i ).
% 0.18/0.45
% 0.18/0.45 thf(setunionAx_type,type,
% 0.18/0.45 setunionAx: $o ).
% 0.18/0.45
% 0.18/0.45 thf(setunionAx,definition,
% 0.18/0.45 ( setunionAx
% 0.18/0.45 = ( ! [A: $i,Xx: $i] :
% 0.18/0.45 ( ( in @ Xx @ ( setunion @ A ) )
% 0.18/0.45 <=> ? [B: $i] :
% 0.18/0.46 ( ( in @ Xx @ B )
% 0.18/0.46 & ( in @ B @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(omega_type,type,
% 0.18/0.46 omega: $i ).
% 0.18/0.46
% 0.18/0.46 thf(omega0Ax_type,type,
% 0.18/0.46 omega0Ax: $o ).
% 0.18/0.46
% 0.18/0.46 thf(omega0Ax,definition,
% 0.18/0.46 ( omega0Ax
% 0.18/0.46 = ( in @ emptyset @ omega ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(omegaSAx_type,type,
% 0.18/0.46 omegaSAx: $o ).
% 0.18/0.46
% 0.18/0.46 thf(omegaSAx,definition,
% 0.18/0.46 ( omegaSAx
% 0.18/0.46 = ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ omega )
% 0.18/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(omegaIndAx_type,type,
% 0.18/0.46 omegaIndAx: $o ).
% 0.18/0.46
% 0.18/0.46 thf(omegaIndAx,definition,
% 0.18/0.46 ( omegaIndAx
% 0.18/0.46 = ( ! [A: $i] :
% 0.18/0.46 ( ( ( in @ emptyset @ A )
% 0.18/0.46 & ! [Xx: $i] :
% 0.18/0.46 ( ( ( in @ Xx @ omega )
% 0.18/0.46 & ( in @ Xx @ A ) )
% 0.18/0.46 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.18/0.46 => ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ omega )
% 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(replAx_type,type,
% 0.18/0.46 replAx: $o ).
% 0.18/0.46
% 0.18/0.46 thf(replAx,definition,
% 0.18/0.46 ( replAx
% 0.18/0.46 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.18/0.46 ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( exu
% 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.18/0.46 => ? [B: $i] :
% 0.18/0.46 ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ B )
% 0.18/0.46 <=> ? [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ A )
% 0.18/0.46 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(foundationAx_type,type,
% 0.18/0.46 foundationAx: $o ).
% 0.18/0.46
% 0.18/0.46 thf(foundationAx,definition,
% 0.18/0.46 ( foundationAx
% 0.18/0.46 = ( ! [A: $i] :
% 0.18/0.46 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.18/0.46 => ? [B: $i] :
% 0.18/0.46 ( ( in @ B @ A )
% 0.18/0.46 & ~ ? [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ B )
% 0.18/0.46 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(wellorderingAx_type,type,
% 0.18/0.46 wellorderingAx: $o ).
% 0.18/0.46
% 0.18/0.46 thf(wellorderingAx,definition,
% 0.18/0.46 ( wellorderingAx
% 0.18/0.46 = ( ! [A: $i] :
% 0.18/0.46 ? [B: $i] :
% 0.18/0.46 ( ! [C: $i] :
% 0.18/0.46 ( ( in @ C @ B )
% 0.18/0.46 => ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ C )
% 0.18/0.46 => ( in @ Xx @ A ) ) )
% 0.18/0.46 & ! [Xx: $i,Xy: $i] :
% 0.18/0.46 ( ( ( in @ Xx @ A )
% 0.18/0.46 & ( in @ Xy @ A ) )
% 0.18/0.46 => ( ! [C: $i] :
% 0.18/0.46 ( ( in @ C @ B )
% 0.18/0.46 => ( ( in @ Xx @ C )
% 0.18/0.46 <=> ( in @ Xy @ C ) ) )
% 0.18/0.46 => ( Xx = Xy ) ) )
% 0.18/0.46 & ! [C: $i,D: $i] :
% 0.18/0.46 ( ( ( in @ C @ B )
% 0.18/0.46 & ( in @ D @ B ) )
% 0.18/0.46 => ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ C )
% 0.18/0.46 => ( in @ Xx @ D ) )
% 0.18/0.46 | ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ D )
% 0.18/0.46 => ( in @ Xx @ C ) ) ) )
% 0.18/0.46 & ! [C: $i] :
% 0.18/0.46 ( ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ C )
% 0.18/0.46 => ( in @ Xx @ A ) )
% 0.18/0.46 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.18/0.46 => ? [D: $i,Xx: $i] :
% 0.18/0.46 ( ( in @ D @ B )
% 0.18/0.46 & ( in @ Xx @ C )
% 0.18/0.46 & ~ ? [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ D )
% 0.18/0.46 & ( in @ Xy @ C ) )
% 0.18/0.46 & ! [E: $i] :
% 0.18/0.46 ( ( in @ E @ B )
% 0.18/0.46 => ( ! [Xy: $i] :
% 0.18/0.46 ( ( in @ Xy @ E )
% 0.18/0.46 => ( in @ Xy @ D ) )
% 0.18/0.46 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(descr_type,type,
% 0.18/0.46 descr: ( $i > $o ) > $i ).
% 0.18/0.46
% 0.18/0.46 thf(descrp_type,type,
% 0.18/0.46 descrp: $o ).
% 0.18/0.46
% 0.18/0.46 thf(descrp,definition,
% 0.18/0.46 ( descrp
% 0.18/0.46 = ( ! [Xphi: $i > $o] :
% 0.18/0.46 ( ( exu
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 => ( Xphi
% 0.18/0.46 @ ( descr
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstr_type,type,
% 0.18/0.46 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstrI_type,type,
% 0.18/0.46 dsetconstrI: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstrI,definition,
% 0.18/0.46 ( dsetconstrI
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ A )
% 0.18/0.46 => ( ( Xphi @ Xx )
% 0.18/0.46 => ( in @ Xx
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstrEL_type,type,
% 0.18/0.46 dsetconstrEL: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstrEL,definition,
% 0.18/0.46 ( dsetconstrEL
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.46 => ( in @ Xx @ A ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstrER_type,type,
% 0.18/0.46 dsetconstrER: $o ).
% 0.18/0.46
% 0.18/0.46 thf(dsetconstrER,definition,
% 0.18/0.46 ( dsetconstrER
% 0.18/0.46 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx
% 0.18/0.46 @ ( dsetconstr @ A
% 0.18/0.46 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.18/0.46 => ( Xphi @ Xx ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(exuE1_type,type,
% 0.18/0.46 exuE1: $o ).
% 0.18/0.46
% 0.18/0.46 thf(exuE1,definition,
% 0.18/0.46 ( exuE1
% 0.18/0.46 = ( ! [Xphi: $i > $o] :
% 0.18/0.46 ( ( exu
% 0.18/0.46 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.18/0.46 => ? [Xx: $i] :
% 0.18/0.46 ( ( Xphi @ Xx )
% 0.18/0.46 & ! [Xy: $i] :
% 0.18/0.46 ( ( Xphi @ Xy )
% 0.18/0.46 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(prop2set_type,type,
% 0.18/0.46 prop2set: $o > $i ).
% 0.18/0.46
% 0.18/0.46 thf(prop2set,definition,
% 0.18/0.46 ( prop2set
% 0.18/0.46 = ( ^ [Xphi: $o] :
% 0.18/0.46 ( dsetconstr @ ( powerset @ emptyset )
% 0.18/0.46 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(prop2setE_type,type,
% 0.18/0.46 prop2setE: $o ).
% 0.18/0.46
% 0.18/0.46 thf(prop2setE,definition,
% 0.18/0.46 ( prop2setE
% 0.18/0.46 = ( ! [Xphi: $o,Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.18/0.46 => Xphi ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(emptysetE_type,type,
% 0.18/0.46 emptysetE: $o ).
% 0.18/0.46
% 0.18/0.46 thf(emptysetE,definition,
% 0.18/0.46 ( emptysetE
% 0.18/0.46 = ( ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ emptyset )
% 0.18/0.46 => ! [Xphi: $o] : Xphi ) ) ) ).
% 0.18/0.46
% 0.18/0.46 thf(emptysetimpfalse,conjecture,
% 0.18/0.46 ( setextAx
% 0.18/0.46 => ( emptysetAx
% 0.18/0.46 => ( setadjoinAx
% 0.18/0.46 => ( powersetAx
% 0.18/0.46 => ( setunionAx
% 0.18/0.46 => ( omega0Ax
% 0.18/0.46 => ( omegaSAx
% 0.18/0.46 => ( omegaIndAx
% 0.18/0.46 => ( replAx
% 0.18/0.46 => ( foundationAx
% 0.18/0.46 => ( wellorderingAx
% 0.18/0.46 => ( descrp
% 0.18/0.46 => ( dsetconstrI
% 0.18/0.46 => ( dsetconstrEL
% 0.18/0.46 => ( dsetconstrER
% 0.18/0.46 => ( exuE1
% 0.18/0.46 => ( prop2setE
% 0.18/0.46 => ( emptysetE
% 0.18/0.46 => ! [Xx: $i] :
% 0.18/0.46 ( ( in @ Xx @ emptyset )
% 0.18/0.46 => $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.18/0.46
% 0.18/0.46 %------------------------------------------------------------------------------
% 0.18/0.46 ------------------------
% 1.81/1.46 ---- Embedded in THF ---
% 1.81/1.46 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.81/1.46 %%% Generated on Tue Feb 24 12:24:19 EST 2026
% 1.81/1.46 %%% using '$$dhol' embedding, version 1.3.0.
% 1.81/1.46 %%% Logic specification used:
% 1.81/1.46 %%% thf(spec, logic, $$dhol).
% 1.81/1.46
% 1.81/1.46 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.U6moXOrfhg/DTF2DTF19517.p
% See solution above
% 1.81/1.46 ------------------------
% 1.81/1.48 ---- Cleaned THF ---
% 1.81/1.48 thf(in_type,type,
% 1.81/1.48 in: $i > $i > $o ).
% 1.81/1.48
% 1.81/1.48 thf(exu_type,type,
% 1.81/1.48 exu: ( $i > $o ) > $o ).
% 1.81/1.48
% 1.81/1.48 thf(exu,definition,
% 1.81/1.48 ( exu
% 1.81/1.48 = ( ^ [Xphi: $i > $o] :
% 1.81/1.48 ? [Xx: $i] :
% 1.81/1.48 ( ( Xphi @ Xx )
% 1.81/1.48 & ! [Xy: $i] :
% 1.81/1.48 ( ( Xphi @ Xy )
% 1.81/1.48 => ( Xx = Xy ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(setextAx_type,type,
% 1.81/1.48 setextAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(setextAx,definition,
% 1.81/1.48 ( setextAx
% 1.81/1.48 = ( ! [A: $i,B: $i] :
% 1.81/1.48 ( ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ A )
% 1.81/1.48 <=> ( in @ Xx @ B ) )
% 1.81/1.48 => ( A = B ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(emptyset_type,type,
% 1.81/1.48 emptyset: $i ).
% 1.81/1.48
% 1.81/1.48 thf(emptysetAx_type,type,
% 1.81/1.48 emptysetAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(emptysetAx,definition,
% 1.81/1.48 ( emptysetAx
% 1.81/1.48 = ( ! [Xx: $i] :
% 1.81/1.48 ~ ( in @ Xx @ emptyset ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(setadjoin_type,type,
% 1.81/1.48 setadjoin: $i > $i > $i ).
% 1.81/1.48
% 1.81/1.48 thf(setadjoinAx_type,type,
% 1.81/1.48 setadjoinAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(setadjoinAx,definition,
% 1.81/1.48 ( setadjoinAx
% 1.81/1.48 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 1.81/1.48 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 1.81/1.48 <=> ( ( Xy = Xx )
% 1.81/1.48 | ( in @ Xy @ A ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(powerset_type,type,
% 1.81/1.48 powerset: $i > $i ).
% 1.81/1.48
% 1.81/1.48 thf(powersetAx_type,type,
% 1.81/1.48 powersetAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(powersetAx,definition,
% 1.81/1.48 ( powersetAx
% 1.81/1.48 = ( ! [A: $i,B: $i] :
% 1.81/1.48 ( ( in @ B @ ( powerset @ A ) )
% 1.81/1.48 <=> ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ B )
% 1.81/1.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(setunion_type,type,
% 1.81/1.48 setunion: $i > $i ).
% 1.81/1.48
% 1.81/1.48 thf(setunionAx_type,type,
% 1.81/1.48 setunionAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(setunionAx,definition,
% 1.81/1.48 ( setunionAx
% 1.81/1.48 = ( ! [A: $i,Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ ( setunion @ A ) )
% 1.81/1.48 <=> ? [B: $i] :
% 1.81/1.48 ( ( in @ Xx @ B )
% 1.81/1.48 & ( in @ B @ A ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(omega_type,type,
% 1.81/1.48 omega: $i ).
% 1.81/1.48
% 1.81/1.48 thf(omega0Ax_type,type,
% 1.81/1.48 omega0Ax: $o ).
% 1.81/1.48
% 1.81/1.48 thf(omega0Ax,definition,
% 1.81/1.48 ( omega0Ax
% 1.81/1.48 = ( in @ emptyset @ omega ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(omegaSAx_type,type,
% 1.81/1.48 omegaSAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(omegaSAx,definition,
% 1.81/1.48 ( omegaSAx
% 1.81/1.48 = ( ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ omega )
% 1.81/1.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(omegaIndAx_type,type,
% 1.81/1.48 omegaIndAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(omegaIndAx,definition,
% 1.81/1.48 ( omegaIndAx
% 1.81/1.48 = ( ! [A: $i] :
% 1.81/1.48 ( ( ( in @ emptyset @ A )
% 1.81/1.48 & ! [Xx: $i] :
% 1.81/1.48 ( ( ( in @ Xx @ omega )
% 1.81/1.48 & ( in @ Xx @ A ) )
% 1.81/1.48 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 1.81/1.48 => ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ omega )
% 1.81/1.48 => ( in @ Xx @ A ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(replAx_type,type,
% 1.81/1.48 replAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(replAx,definition,
% 1.81/1.48 ( replAx
% 1.81/1.48 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 1.81/1.48 ( ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ A )
% 1.81/1.48 => ( exu
% 1.81/1.48 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 1.81/1.48 => ? [B: $i] :
% 1.81/1.48 ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ B )
% 1.81/1.48 <=> ? [Xy: $i] :
% 1.81/1.48 ( ( in @ Xy @ A )
% 1.81/1.48 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(foundationAx_type,type,
% 1.81/1.48 foundationAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(foundationAx,definition,
% 1.81/1.48 ( foundationAx
% 1.81/1.48 = ( ! [A: $i] :
% 1.81/1.48 ( ? [Xx: $i] : ( in @ Xx @ A )
% 1.81/1.48 => ? [B: $i] :
% 1.81/1.48 ( ( in @ B @ A )
% 1.81/1.48 & ~ ? [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ B )
% 1.81/1.48 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(wellorderingAx_type,type,
% 1.81/1.48 wellorderingAx: $o ).
% 1.81/1.48
% 1.81/1.48 thf(wellorderingAx,definition,
% 1.81/1.48 ( wellorderingAx
% 1.81/1.48 = ( ! [A: $i] :
% 1.81/1.48 ? [B: $i] :
% 1.81/1.48 ( ! [C: $i] :
% 1.81/1.48 ( ( in @ C @ B )
% 1.81/1.48 => ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ C )
% 1.81/1.48 => ( in @ Xx @ A ) ) )
% 1.81/1.48 & ! [Xx: $i,Xy: $i] :
% 1.81/1.48 ( ( ( in @ Xx @ A )
% 1.81/1.48 & ( in @ Xy @ A ) )
% 1.81/1.48 => ( ! [C: $i] :
% 1.81/1.48 ( ( in @ C @ B )
% 1.81/1.48 => ( ( in @ Xx @ C )
% 1.81/1.48 <=> ( in @ Xy @ C ) ) )
% 1.81/1.48 => ( Xx = Xy ) ) )
% 1.81/1.48 & ! [C: $i,D: $i] :
% 1.81/1.48 ( ( ( in @ C @ B )
% 1.81/1.48 & ( in @ D @ B ) )
% 1.81/1.48 => ( ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ C )
% 1.81/1.48 => ( in @ Xx @ D ) )
% 1.81/1.48 | ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ D )
% 1.81/1.48 => ( in @ Xx @ C ) ) ) )
% 1.81/1.48 & ! [C: $i] :
% 1.81/1.48 ( ( ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ C )
% 1.81/1.48 => ( in @ Xx @ A ) )
% 1.81/1.48 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 1.81/1.48 => ? [D: $i,Xx: $i] :
% 1.81/1.48 ( ( in @ D @ B )
% 1.81/1.48 & ( in @ Xx @ C )
% 1.81/1.48 & ~ ? [Xy: $i] :
% 1.81/1.48 ( ( in @ Xy @ D )
% 1.81/1.48 & ( in @ Xy @ C ) )
% 1.81/1.48 & ! [E: $i] :
% 1.81/1.48 ( ( in @ E @ B )
% 1.81/1.48 => ( ! [Xy: $i] :
% 1.81/1.48 ( ( in @ Xy @ E )
% 1.81/1.48 => ( in @ Xy @ D ) )
% 1.81/1.48 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(descr_type,type,
% 1.81/1.48 descr: ( $i > $o ) > $i ).
% 1.81/1.48
% 1.81/1.48 thf(descrp_type,type,
% 1.81/1.48 descrp: $o ).
% 1.81/1.48
% 1.81/1.48 thf(descrp,definition,
% 1.81/1.48 ( descrp
% 1.81/1.48 = ( ! [Xphi: $i > $o] :
% 1.81/1.48 ( ( exu
% 1.81/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.81/1.48 => ( Xphi
% 1.81/1.48 @ ( descr
% 1.81/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(dsetconstr_type,type,
% 1.81/1.48 dsetconstr: $i > ( $i > $o ) > $i ).
% 1.81/1.48
% 1.81/1.48 thf(dsetconstrI_type,type,
% 1.81/1.48 dsetconstrI: $o ).
% 1.81/1.48
% 1.81/1.48 thf(dsetconstrI,definition,
% 1.81/1.48 ( dsetconstrI
% 1.81/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ A )
% 1.81/1.48 => ( ( Xphi @ Xx )
% 1.81/1.48 => ( in @ Xx
% 1.81/1.48 @ ( dsetconstr @ A
% 1.81/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(dsetconstrEL_type,type,
% 1.81/1.48 dsetconstrEL: $o ).
% 1.81/1.48
% 1.81/1.48 thf(dsetconstrEL,definition,
% 1.81/1.48 ( dsetconstrEL
% 1.81/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.81/1.48 ( ( in @ Xx
% 1.81/1.48 @ ( dsetconstr @ A
% 1.81/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.81/1.48 => ( in @ Xx @ A ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(dsetconstrER_type,type,
% 1.81/1.48 dsetconstrER: $o ).
% 1.81/1.48
% 1.81/1.48 thf(dsetconstrER,definition,
% 1.81/1.48 ( dsetconstrER
% 1.81/1.48 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 1.81/1.48 ( ( in @ Xx
% 1.81/1.48 @ ( dsetconstr @ A
% 1.81/1.48 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 1.81/1.48 => ( Xphi @ Xx ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(exuE1_type,type,
% 1.81/1.48 exuE1: $o ).
% 1.81/1.48
% 1.81/1.48 thf(exuE1,definition,
% 1.81/1.48 ( exuE1
% 1.81/1.48 = ( ! [Xphi: $i > $o] :
% 1.81/1.48 ( ( exu
% 1.81/1.48 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 1.81/1.48 => ? [Xx: $i] :
% 1.81/1.48 ( ( Xphi @ Xx )
% 1.81/1.48 & ! [Xy: $i] :
% 1.81/1.48 ( ( Xphi @ Xy )
% 1.81/1.48 => ( Xx = Xy ) ) ) ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(prop2set_type,type,
% 1.81/1.48 prop2set: $o > $i ).
% 1.81/1.48
% 1.81/1.48 thf(prop2set,definition,
% 1.81/1.48 ( prop2set
% 1.81/1.48 = ( ^ [Xphi: $o] :
% 1.81/1.48 ( dsetconstr @ ( powerset @ emptyset )
% 1.81/1.48 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(prop2setE_type,type,
% 1.81/1.48 prop2setE: $o ).
% 1.81/1.48
% 1.81/1.48 thf(prop2setE,definition,
% 1.81/1.48 ( prop2setE
% 1.81/1.48 = ( ! [Xphi: $o,Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 1.81/1.48 => Xphi ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(emptysetE_type,type,
% 1.81/1.48 emptysetE: $o ).
% 1.81/1.48
% 1.81/1.48 thf(emptysetE,definition,
% 1.81/1.48 ( emptysetE
% 1.81/1.48 = ( ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ emptyset )
% 1.81/1.48 => ! [Xphi: $o] : Xphi ) ) ) ).
% 1.81/1.48
% 1.81/1.48 thf(emptysetimpfalse,conjecture,
% 1.81/1.48 ( setextAx
% 1.81/1.48 => ( emptysetAx
% 1.81/1.48 => ( setadjoinAx
% 1.81/1.48 => ( powersetAx
% 1.81/1.48 => ( setunionAx
% 1.81/1.48 => ( omega0Ax
% 1.81/1.48 => ( omegaSAx
% 1.81/1.48 => ( omegaIndAx
% 1.81/1.48 => ( replAx
% 1.81/1.48 => ( foundationAx
% 1.81/1.48 => ( wellorderingAx
% 1.81/1.48 => ( descrp
% 1.81/1.48 => ( dsetconstrI
% 1.81/1.48 => ( dsetconstrEL
% 1.81/1.48 => ( dsetconstrER
% 1.81/1.48 => ( exuE1
% 1.81/1.48 => ( prop2setE
% 1.81/1.48 => ( emptysetE
% 1.81/1.48 => ! [Xx: $i] :
% 1.81/1.48 ( ( in @ Xx @ emptyset )
% 1.81/1.48 => $false ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 1.81/1.48 ------------------------
% 1.95/1.50 % (19615)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19517 for (2999ds/183Mi)
% 1.95/1.50 % (19618)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19517 for (2999ds/2Mi)
% 1.95/1.50 % (19616)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_19517 for (2999ds/4Mi)
% 1.95/1.50 % (19619)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_19517 for (2999ds/2Mi)
% 1.95/1.50 % (19620)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_19517 for (2999ds/275Mi)
% 1.95/1.50 % (19617)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_19517 for (2999ds/27Mi)
% 1.95/1.50 % (19621)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19517 for (2999ds/18Mi)
% 1.95/1.50 % (19618)Instruction limit reached!
% 1.95/1.50 % (19618)------------------------------
% 1.95/1.50 % (19618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.50 % (19618)Termination reason: Unknown
% 1.95/1.50 % (19618)Termination phase: shuffling
% 1.95/1.50 % (19619)Instruction limit reached!
% 1.95/1.50 % (19619)------------------------------
% 1.95/1.50 % (19619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.50 % (19619)Termination reason: Unknown
% 1.95/1.50 % (19619)Termination phase: shuffling
% 1.95/1.50
% 1.95/1.50 % (19619)Memory used [KB]: 1023
% 1.95/1.50 % (19619)Time elapsed: 0.003 s
% 1.95/1.50 % (19619)Instructions burned: 3 (million)
% 1.95/1.50 % (19619)------------------------------
% 1.95/1.50 % (19619)------------------------------
% 1.95/1.50
% 1.95/1.50 % (19618)Memory used [KB]: 1023
% 1.95/1.50 % (19618)Time elapsed: 0.003 s
% 1.95/1.50 % (19618)Instructions burned: 3 (million)
% 1.95/1.50 % (19618)------------------------------
% 1.95/1.50 % (19618)------------------------------
% 1.95/1.50 % (19616)Instruction limit reached!
% 1.95/1.50 % (19616)------------------------------
% 1.95/1.50 % (19616)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.50 % (19616)Termination reason: Unknown
% 1.95/1.50 % (19616)Termination phase: Property scanning
% 1.95/1.50
% 1.95/1.50 % (19616)Memory used [KB]: 1023
% 1.95/1.50 % (19616)Time elapsed: 0.004 s
% 1.95/1.50 % (19616)Instructions burned: 5 (million)
% 1.95/1.50 % (19616)------------------------------
% 1.95/1.50 % (19616)------------------------------
% 1.95/1.51 % (19621)Instruction limit reached!
% 1.95/1.51 % (19621)------------------------------
% 1.95/1.51 % (19621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.51 % (19621)Termination reason: Unknown
% 1.95/1.51 % (19621)Termination phase: Property scanning
% 1.95/1.51
% 1.95/1.51 % (19621)Memory used [KB]: 1279
% 1.95/1.51 % (19621)Time elapsed: 0.011 s
% 1.95/1.51 % (19621)Instructions burned: 20 (million)
% 1.95/1.51 % (19621)------------------------------
% 1.95/1.51 % (19621)------------------------------
% 1.95/1.51 % (19617)Instruction limit reached!
% 1.95/1.51 % (19617)------------------------------
% 1.95/1.51 % (19617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.51 % (19617)Termination reason: Unknown
% 1.95/1.51 % (19617)Termination phase: Saturation
% 1.95/1.51
% 1.95/1.51 % (19617)Memory used [KB]: 5756
% 1.95/1.51 % (19617)Time elapsed: 0.014 s
% 1.95/1.51 % (19617)Instructions burned: 27 (million)
% 1.95/1.51 % (19617)------------------------------
% 1.95/1.51 % (19617)------------------------------
% 1.95/1.51 % (19620)First to succeed.
% 1.95/1.51 % (19620)Refutation found. Thanks to Tanya!
% 1.95/1.51 % SZS status Theorem for DTF2THF_19517
% 1.95/1.51 % SZS output start Proof for DTF2THF_19517
% 1.95/1.51 thf(func_def_0, type, in: $i > $i > $o).
% 1.95/1.51 thf(func_def_1, type, exu: ($i > $o) > $o).
% 1.95/1.51 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 1.95/1.51 thf(func_def_8, type, powerset: $i > $i).
% 1.95/1.51 thf(func_def_10, type, setunion: $i > $i).
% 1.95/1.51 thf(func_def_19, type, descr: ($i > $o) > $i).
% 1.95/1.51 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 1.95/1.51 thf(func_def_26, type, prop2set: $o > $i).
% 1.95/1.51 thf(func_def_40, type, sP0: $i > $i > $o).
% 1.95/1.51 thf(func_def_41, type, sP1: $i > $o).
% 1.95/1.51 thf(func_def_42, type, sP2: $i > $i > $o).
% 1.95/1.51 thf(func_def_43, type, sP3: $i > $i > $o).
% 1.95/1.51 thf(func_def_45, type, sK5: $i > $i).
% 1.95/1.51 thf(func_def_48, type, sK8: $i > $i > $i).
% 1.95/1.51 thf(func_def_49, type, sK9: $i > $i > $i).
% 1.95/1.51 thf(func_def_50, type, sK10: $i > $i > $i).
% 1.95/1.51 thf(func_def_51, type, sK11: $i > $i > $i).
% 1.95/1.51 thf(func_def_52, type, sK12: $i > $i > $i).
% 1.95/1.51 thf(func_def_53, type, sK13: $i > $i > $i > $i).
% 1.95/1.51 thf(func_def_54, type, sK14: $i > $i).
% 1.95/1.51 thf(func_def_55, type, sK15: $i > $i).
% 1.95/1.51 thf(func_def_56, type, sK16: $i > $i).
% 1.95/1.51 thf(func_def_57, type, sK17: $i > $i).
% 1.95/1.51 thf(func_def_58, type, sK18: $i > $i > $i).
% 1.95/1.51 thf(func_def_59, type, sK19: $i > $i > $i > $i).
% 1.95/1.51 thf(func_def_60, type, sK20: $i > $i > $i > $i).
% 1.95/1.51 thf(func_def_61, type, sK21: $i > $i > $i).
% 1.95/1.51 thf(func_def_62, type, sK22: $i > $i > $i).
% 1.95/1.51 thf(func_def_63, type, sK23: $i > $i).
% 1.95/1.51 thf(func_def_65, type, sK25: $i > $i).
% 1.95/1.51 thf(func_def_66, type, sK26: $i > $i).
% 1.95/1.51 thf(func_def_67, type, sK27: $i > $i > $i).
% 1.95/1.51 thf(func_def_71, type, sK31: $i > $i > $o).
% 1.95/1.51 thf(func_def_72, type, sK32: $i > $i).
% 1.95/1.51 thf(func_def_73, type, sK33: $i > $i).
% 1.95/1.51 thf(func_def_74, type, sK34: ($i > $i > $o) > $i > $i).
% 1.95/1.51 thf(func_def_75, type, sK35: ($i > $i > $o) > $i > $i).
% 1.95/1.51 thf(func_def_76, type, sK36: $i > ($i > $i > $o) > $i > $i).
% 1.95/1.51 thf(func_def_78, type, sK38: $i > $i > $i).
% 1.95/1.51 thf(func_def_85, type, sK45: ($i > $o) > $i).
% 1.95/1.51 thf(func_def_86, type, sK46: $i > $o).
% 1.95/1.51 thf(func_def_87, type, sK47: $i > $i).
% 1.95/1.51 thf(func_def_90, type, sK50: $i > $o).
% 1.95/1.51 thf(func_def_92, type, sK52: $i > $o).
% 1.95/1.51 thf(func_def_100, type, sK60: $i > $o).
% 1.95/1.51 thf(func_def_101, type, sK61: $i > $i).
% 1.95/1.51 thf(func_def_103, type, sK63: $i > $i).
% 1.95/1.51 thf(func_def_108, type, ph68: !>[X0: $tType]:(X0)).
% 1.95/1.51 thf(f425,plain,(
% 1.95/1.51 $false),
% 1.95/1.51 inference(subsumption_resolution,[status(thm)],[f300,f414])).
% 1.95/1.51 thf(f414,plain,(
% 1.95/1.51 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true)) )),
% 1.95/1.51 inference(trivial_inequality_removal,[status(thm)],[f343])).
% 1.95/1.51 thf(f343,plain,(
% 1.95/1.51 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true) | ($true != $true)) )),
% 1.95/1.51 inference(definition_unfolding,[status(thm)],[f259,f293])).
% 1.95/1.51 thf(f293,plain,(
% 1.95/1.51 (emptysetAx = $true)),
% 1.95/1.51 inference(cnf_transformation,[status(thm)],[f183])).
% 1.95/1.51 thf(f183,plain,(
% 1.95/1.51 (replAx = $true) & (setunionAx = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (omegaIndAx = $true) & (dsetconstrEL = $true) & (descrp = $true) & (setextAx = $true) & (exuE1 = $true) & ($true = (in @ sK57 @ emptyset)) & (omegaSAx = $true) & (dsetconstrI = $true) & (emptysetE = $true) & (setadjoinAx = $true) & (powersetAx = $true) & (omega0Ax = $true) & (emptysetAx = $true) & (foundationAx = $true)),
% 1.95/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK57])],[f71,f182])).
% 1.95/1.51 thf(f182,plain,(
% 1.95/1.51 ? [X0 : $i] : ($true = (in @ X0 @ emptyset)) => ($true = (in @ sK57 @ emptyset))),
% 1.95/1.51 introduced(definition,[],[choice_axiom])).
% 1.95/1.51 thf(f71,plain,(
% 1.95/1.51 (replAx = $true) & (setunionAx = $true) & (wellorderingAx = $true) & (prop2setE = $true) & (dsetconstrER = $true) & (omegaIndAx = $true) & (dsetconstrEL = $true) & (descrp = $true) & (setextAx = $true) & (exuE1 = $true) & ? [X0 : $i] : ($true = (in @ X0 @ emptyset)) & (omegaSAx = $true) & (dsetconstrI = $true) & (emptysetE = $true) & (setadjoinAx = $true) & (powersetAx = $true) & (omega0Ax = $true) & (emptysetAx = $true) & (foundationAx = $true)),
% 1.95/1.51 inference(flattening,[status(thm)],[f70])).
% 1.95/1.51 thf(f70,plain,(
% 1.95/1.51 (((((((((((((((((? [X0 : $i] : ($true = (in @ X0 @ emptyset)) & (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)),
% 1.95/1.51 inference(ennf_transformation,[status(thm)],[f64])).
% 1.95/1.51 thf(f64,plain,(
% 1.95/1.51 ~((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) => ! [X0 : $i] : ($true != (in @ X0 @ emptyset))))))))))))))))))))),
% 1.95/1.51 inference(flattening,[status(thm)],[f63])).
% 1.95/1.51 thf(f63,plain,(
% 1.95/1.51 ~((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) => ! [X0 : $i] : ~($true = (in @ X0 @ emptyset))))))))))))))))))))),
% 1.95/1.51 inference(true_and_false_elimination,[status(thm)],[f60])).
% 1.95/1.51 thf(f60,plain,(
% 1.95/1.51 ~((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) => ! [X0 : $i] : (($true = (in @ X0 @ emptyset)) => $false)))))))))))))))))))),
% 1.95/1.51 inference(fool_elimination,[status(thm)],[f59])).
% 1.95/1.51 thf(f59,plain,(
% 1.95/1.51 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => ! [X0 : $i] : ((in @ X0 @ emptyset) => $false)))))))))))))))))))),
% 1.95/1.51 inference(rectify,[status(thm)],[f22])).
% 1.95/1.51 thf(f22,negated_conjecture,(
% 1.95/1.51 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => ! [X1 : $i] : ((in @ X1 @ emptyset) => $false)))))))))))))))))))),
% 1.95/1.51 inference(negated_conjecture,[status(cth)],[f21])).
% 1.95/1.51 thf(f21,conjecture,(
% 1.95/1.51 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => (prop2setE => (emptysetE => ! [X1 : $i] : ((in @ X1 @ emptyset) => $false))))))))))))))))))),
% 1.95/1.51 file('/export/starexec/sandbox/tmp/tmp.U6moXOrfhg/DTF2THF_19517.p',emptysetimpfalse)).
% 1.95/1.51 thf(f259,plain,(
% 1.95/1.51 ( ! [X1 : $i] : (((in @ X1 @ emptyset) != $true) | (emptysetAx != $true)) )),
% 1.95/1.51 inference(cnf_transformation,[status(thm)],[f148])).
% 1.95/1.51 thf(f148,plain,(
% 1.95/1.51 ((emptysetAx = $true) | ($true = (in @ sK37 @ emptyset))) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetAx != $true))),
% 1.95/1.51 inference(skolemisation,[status(esa),new_symbols(skolem,[sK37])],[f146,f147])).
% 1.95/1.51 thf(f147,plain,(
% 1.95/1.51 ? [X0 : $i] : ($true = (in @ X0 @ emptyset)) => ($true = (in @ sK37 @ emptyset))),
% 1.95/1.51 introduced(definition,[],[choice_axiom])).
% 1.95/1.51 thf(f146,plain,(
% 1.95/1.51 ((emptysetAx = $true) | ? [X0 : $i] : ($true = (in @ X0 @ emptyset))) & (! [X1 : $i] : ((in @ X1 @ emptyset) != $true) | (emptysetAx != $true))),
% 1.95/1.51 inference(rectify,[status(thm)],[f145])).
% 1.95/1.51 thf(f145,plain,(
% 1.95/1.51 ((emptysetAx = $true) | ? [X0 : $i] : ($true = (in @ X0 @ emptyset))) & (! [X0 : $i] : ($true != (in @ X0 @ emptyset)) | (emptysetAx != $true))),
% 1.95/1.51 inference(nnf_transformation,[status(thm)],[f65])).
% 1.95/1.51 thf(f65,plain,(
% 1.95/1.51 (emptysetAx = $true) <=> ! [X0 : $i] : ($true != (in @ X0 @ emptyset))),
% 1.95/1.51 inference(flattening,[status(thm)],[f36])).
% 1.95/1.51 thf(f36,plain,(
% 1.95/1.51 (emptysetAx = $true) <=> ! [X0 : $i] : ~($true = (in @ X0 @ emptyset))),
% 1.95/1.51 inference(fool_elimination,[status(thm)],[f35])).
% 1.95/1.51 thf(f35,plain,(
% 1.95/1.51 (emptysetAx = ! [X0 : $i] : ~(in @ X0 @ emptyset))),
% 1.95/1.51 inference(rectify,[status(thm)],[f3])).
% 1.95/1.51 thf(f3,axiom,(
% 1.95/1.51 (emptysetAx = ! [X1 : $i] : ~(in @ X1 @ emptyset))),
% 1.95/1.51 file('/export/starexec/sandbox/tmp/tmp.U6moXOrfhg/DTF2THF_19517.p',emptysetAx)).
% 1.95/1.51 thf(f300,plain,(
% 1.95/1.51 ($true = (in @ sK57 @ emptyset))),
% 1.95/1.51 inference(cnf_transformation,[status(thm)],[f183])).
% 1.95/1.51 % SZS output end Proof for DTF2THF_19517
% 1.95/1.51 % (19620)------------------------------
% 1.95/1.51 % (19620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.51 % (19620)Termination reason: Refutation
% 1.95/1.51
% 1.95/1.51 % (19620)Memory used [KB]: 5884
% 1.95/1.51 % (19620)Time elapsed: 0.015 s
% 1.95/1.51 % (19620)Instructions burned: 26 (million)
% 1.95/1.51 % (19620)------------------------------
% 1.95/1.51 % (19620)------------------------------
% 1.95/1.51 % (19614)Success in time 0.03 s
%------------------------------------------------------------------------------