%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU500^1 : 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 : n022.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 09:34:56 AM UTC 2026
% Result : Theorem 0.31s 1.35s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 32 ( 13 unt; 0 typ; 0 def)
% Number of atoms : 439 ( 128 equ; 0 cnn)
% Maximal formula atoms : 18 ( 13 avg)
% Number of connectives : 328 ( 28 ~; 17 |; 61 &; 147 @)
% ( 2 <=>; 73 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% Number of symbols : 72 ( 69 usr; 23 con; 0-3 aty)
% Number of variables : 82 ( 26 ^; 41 !; 15 ?; 82 :)
% 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_39,type,
sP1: $i > $i > $o ).
thf(func_def_40,type,
sP2: $i > $o ).
thf(func_def_41,type,
sP3: $i > $i > $o ).
thf(func_def_42,type,
sP4: $i > $i > $o ).
thf(func_def_44,type,
sK6: $i > $i > $o ).
thf(func_def_45,type,
sK7: $i > $i ).
thf(func_def_46,type,
sK8: $i > $i ).
thf(func_def_47,type,
sK9: ( $i > $i > $o ) > $i > $i ).
thf(func_def_48,type,
sK10: ( $i > $i > $o ) > $i > $i ).
thf(func_def_49,type,
sK11: $i > ( $i > $i > $o ) > $i > $i ).
thf(func_def_52,type,
sK14: $i > $i > $i ).
thf(func_def_59,type,
sK21: ( $i > $o ) > $i ).
thf(func_def_60,type,
sK22: $i > $o ).
thf(func_def_61,type,
sK23: $i > $i ).
thf(func_def_62,type,
sK24: $i > $i ).
thf(func_def_65,type,
sK27: $i > $i ).
thf(func_def_68,type,
sK30: $i > $o ).
thf(func_def_70,type,
sK32: $i > $i > $i ).
thf(func_def_71,type,
sK33: $i > $i > $i ).
thf(func_def_72,type,
sK34: $i > $i > $i ).
thf(func_def_73,type,
sK35: $i > $i > $i ).
thf(func_def_74,type,
sK36: $i > $i > $i ).
thf(func_def_75,type,
sK37: $i > $i > $i > $i ).
thf(func_def_76,type,
sK38: $i > $i ).
thf(func_def_77,type,
sK39: $i > $i ).
thf(func_def_78,type,
sK40: $i > $i ).
thf(func_def_79,type,
sK41: $i > $i ).
thf(func_def_80,type,
sK42: $i > $i > $i ).
thf(func_def_81,type,
sK43: $i > $i > $i > $i ).
thf(func_def_82,type,
sK44: $i > $i > $i > $i ).
thf(func_def_83,type,
sK45: $i > $i > $i ).
thf(func_def_84,type,
sK46: $i > $i > $i ).
thf(func_def_86,type,
sK48: $i > $i ).
thf(func_def_87,type,
sK49: $i > $i ).
thf(func_def_88,type,
sK50: $i > $i ).
thf(func_def_89,type,
sK51: $i > $i > $i ).
thf(func_def_94,type,
sK56: $i > $i ).
thf(func_def_96,type,
sK58: $i > $o ).
thf(func_def_100,type,
sK62: $i > $o ).
thf(func_def_103,type,
ph65:
!>[X0: $tType] : X0 ).
thf(f506,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f494,f204]) ).
thf(f204,plain,
sK12 != $true,
inference(cnf_transformation,[status(thm)],[f94]) ).
thf(f94,plain,
( ( wellorderingAx = $true )
& ( setextAx = $true )
& ( foundationAx = $true )
& ( descrp = $true )
& ( emptysetAx = $true )
& ( $true
= ( in @ sK13 @ ( prop2set @ sK12 ) ) )
& ( sK12 != $true )
& ( setunionAx = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( omegaIndAx = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( dsetconstrEL = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f73,f93]) ).
thf(f93,plain,
( ? [X0: $o,X1: $i] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
= $true )
& ( $true != X0 ) )
=> ( ( $true
= ( in @ sK13 @ ( prop2set @ sK12 ) ) )
& ( sK12 != $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f73,plain,
( ( wellorderingAx = $true )
& ( setextAx = $true )
& ( foundationAx = $true )
& ( descrp = $true )
& ( emptysetAx = $true )
& ? [X0: $o,X1: $i] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
= $true )
& ( $true != X0 ) )
& ( setunionAx = $true )
& ( dsetconstrER = $true )
& ( exuE1 = $true )
& ( omega0Ax = $true )
& ( setadjoinAx = $true )
& ( powersetAx = $true )
& ( omegaIndAx = $true )
& ( replAx = $true )
& ( omegaSAx = $true )
& ( dsetconstrI = $true )
& ( dsetconstrEL = $true ) ),
inference(flattening,[status(thm)],[f72]) ).
thf(f72,plain,
( ? [X0: $o,X1: $i] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
= $true )
& ( $true != X0 ) )
& ( 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)],[f32]) ).
thf(f32,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 )
=> ! [X0: $o,X1: $i] :
( ( ( in @ X1 @ ( prop2set @ X0 ) )
= $true )
=> ( $true = X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f31]) ).
thf(f31,plain,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f20]) ).
thf(f20,negated_conjecture,
~ ( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
thf(f19,conjecture,
( setextAx
=> ( emptysetAx
=> ( setadjoinAx
=> ( powersetAx
=> ( setunionAx
=> ( omega0Ax
=> ( omegaSAx
=> ( omegaIndAx
=> ( replAx
=> ( foundationAx
=> ( wellorderingAx
=> ( descrp
=> ( dsetconstrI
=> ( dsetconstrEL
=> ( dsetconstrER
=> ( exuE1
=> ! [X0: $o,X1: $i] :
( ( in @ X1 @ ( prop2set @ X0 ) )
=> X0 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.o0rrXd4Krc/DTF2THF_26735.p',prop2setE) ).
thf(f494,plain,
sK12 = $true,
inference(beta_eta_normalization,[status(thm)],[f493]) ).
thf(f493,plain,
( $true
= ( ^ [Y0: $i] : sK12
@ sK13 ) ),
inference(trivial_inequality_removal,[status(thm)],[f480]) ).
thf(f480,plain,
( ( $true != $true )
| ( $true
= ( ^ [Y0: $i] : sK12
@ sK13 ) ) ),
inference(superposition,[status(thm)],[f388,f376]) ).
thf(f376,plain,
( $true
= ( in @ sK13
@ ( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y0: $i] : sK12 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f299]) ).
thf(f299,plain,
( $true
= ( in @ sK13
@ ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 )
@ sK12 ) ) ),
inference(definition_unfolding,[status(thm)],[f205,f228]) ).
thf(f228,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( prop2set
= ( ^ [Y0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [Y1: $i] : Y0 ) ) ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,axiom,
( ( ^ [X0: $o] :
( dsetconstr @ ( powerset @ emptyset )
@ ^ [X1: $i] : X0 ) )
= prop2set ),
file('/export/starexec/sandbox/tmp/tmp.o0rrXd4Krc/DTF2THF_26735.p',prop2set) ).
thf(f205,plain,
( $true
= ( in @ sK13 @ ( prop2set @ sK12 ) ) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
thf(f388,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( in @ X2 @ ( dsetconstr @ X0 @ X1 ) ) )
| ( $true
= ( X1 @ X2 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f387]) ).
thf(f387,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( $true
= ( X1 @ X2 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f324]) ).
thf(f324,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true != $true )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( $true
= ( X1 @ X2 ) ) ),
inference(definition_unfolding,[status(thm)],[f238,f202]) ).
thf(f202,plain,
dsetconstrER = $true,
inference(cnf_transformation,[status(thm)],[f94]) ).
thf(f238,plain,
! [X2: $i,X0: $i,X1: $i > $o] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
| ( dsetconstrER != $true ) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ( ( $true
!= ( sK30 @ sK31 ) )
& ( $true
= ( in @ sK31
@ ( dsetconstr @ sK29
@ ^ [Y0: $i] : ( sK30 @ Y0 ) ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f124,f125]) ).
thf(f125,plain,
( ? [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
!= ( X4 @ X5 ) )
& ( $true
= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) ) )
=> ( ( $true
!= ( sK30 @ sK31 ) )
& ( $true
= ( in @ sK31
@ ( dsetconstr @ sK29
@ ^ [Y0: $i] : ( sK30 @ Y0 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f124,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X3: $i,X4: $i > $o,X5: $i] :
( ( $true
!= ( X4 @ X5 ) )
& ( $true
= ( in @ X5
@ ( dsetconstr @ X3
@ ^ [Y0: $i] : ( X4 @ Y0 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f123]) ).
thf(f123,plain,
( ( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
| ( dsetconstrER != $true ) )
& ( ( dsetconstrER = $true )
| ? [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
!= ( X1 @ X2 ) )
& ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
( ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
= ( X1 @ X2 ) )
| ( $true
!= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) ) )
<=> ( dsetconstrER = $true ) ),
inference(ennf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ( dsetconstrER = $true )
<=> ! [X0: $i,X1: $i > $o,X2: $i] :
( ( $true
= ( in @ X2
@ ( dsetconstr @ X0
@ ^ [Y0: $i] : ( X1 @ Y0 ) ) ) )
=> ( $true
= ( X1 @ X2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f25]) ).
thf(f25,plain,
! [X0: $i,X1: $i > $o,X2: $i] :
( ( ( in @ X2
@ ( dsetconstr @ X0
@ ^ [X3: $i] : ( X1 @ X3 ) ) )
=> ( X1 @ X2 ) )
= dsetconstrER ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,axiom,
! [X3: $i,X0: $i > $o,X1: $i] :
( ( ( in @ X1
@ ( dsetconstr @ X3
@ ^ [X2: $i] : ( X0 @ X2 ) ) )
=> ( X0 @ X1 ) )
= dsetconstrER ),
file('/export/starexec/sandbox/tmp/tmp.o0rrXd4Krc/DTF2THF_26735.p',dsetconstrER) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU500^1 : 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
% 0.17/0.34 % Computer : n022.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:24:21 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SEU500^1 : TPTP v9.2.1. Released v3.7.0.
% 0.29/0.47 % Domain : Set Theory
% 0.29/0.47 % Problem : Preliminary Notions - Propositions as Sets
% 0.29/0.47 % Version : Especial.
% 0.29/0.47 % English : (! phi:o.! x:i.in x (prop2set phi) -> phi)
% 0.29/0.47
% 0.29/0.47 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.29/0.47 % Source : [Bro08]
% 0.29/0.47 % Names : ZFC002g [Bro08]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.38 v8.1.0, 0.36 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.12 v7.1.0, 0.25 v7.0.0, 0.00 v6.2.0, 0.43 v6.1.0, 0.29 v5.5.0, 0.50 v5.4.0, 0.60 v5.2.0, 0.40 v5.1.0, 0.20 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v3.7.0
% 0.29/0.47 % Syntax : Number of formulae : 45 ( 18 unt; 26 typ; 18 def)
% 0.29/0.47 % Number of atoms : 117 ( 23 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 17 ( 6 avg)
% 0.29/0.47 % Number of connectives : 231 ( 3 ~; 3 |; 18 &; 155 @)
% 0.29/0.47 % ( 6 <=>; 46 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 22 ( 2 avg)
% 0.29/0.47 % Number of types : 2 ( 0 usr)
% 0.29/0.47 % Number of type conns : 22 ( 22 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 27 ( 26 usr; 18 con; 0-2 aty)
% 0.29/0.47 % Number of variables : 73 ( 10 ^; 50 !; 13 ?; 73 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : http://mathgate.info/detsetitem.php?id=53
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(in_type,type,
% 0.29/0.47 in: $i > $i > $o ).
% 0.29/0.47
% 0.29/0.47 thf(exu_type,type,
% 0.29/0.47 exu: ( $i > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(exu,definition,
% 0.29/0.47 ( exu
% 0.29/0.47 = ( ^ [Xphi: $i > $o] :
% 0.29/0.47 ? [Xx: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setextAx_type,type,
% 0.29/0.47 setextAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setextAx,definition,
% 0.29/0.47 ( setextAx
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 <=> ( in @ Xx @ B ) )
% 0.29/0.47 => ( A = B ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(emptyset_type,type,
% 0.29/0.47 emptyset: $i ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetAx_type,type,
% 0.29/0.47 emptysetAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(emptysetAx,definition,
% 0.29/0.47 ( emptysetAx
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoin_type,type,
% 0.29/0.47 setadjoin: $i > $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinAx_type,type,
% 0.29/0.47 setadjoinAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setadjoinAx,definition,
% 0.29/0.47 ( setadjoinAx
% 0.29/0.47 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.29/0.47 <=> ( ( Xy = Xx )
% 0.29/0.47 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(powerset_type,type,
% 0.29/0.47 powerset: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(powersetAx_type,type,
% 0.29/0.47 powersetAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(powersetAx,definition,
% 0.29/0.47 ( powersetAx
% 0.29/0.47 = ( ! [A: $i,B: $i] :
% 0.29/0.47 ( ( in @ B @ ( powerset @ A ) )
% 0.29/0.47 <=> ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(setunion_type,type,
% 0.29/0.47 setunion: $i > $i ).
% 0.29/0.47
% 0.29/0.47 thf(setunionAx_type,type,
% 0.29/0.47 setunionAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(setunionAx,definition,
% 0.29/0.47 ( setunionAx
% 0.29/0.47 = ( ! [A: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( setunion @ A ) )
% 0.29/0.47 <=> ? [B: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 & ( in @ B @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omega_type,type,
% 0.29/0.47 omega: $i ).
% 0.29/0.47
% 0.29/0.47 thf(omega0Ax_type,type,
% 0.29/0.47 omega0Ax: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omega0Ax,definition,
% 0.29/0.47 ( omega0Ax
% 0.29/0.47 = ( in @ emptyset @ omega ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omegaSAx_type,type,
% 0.29/0.47 omegaSAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omegaSAx,definition,
% 0.29/0.47 ( omegaSAx
% 0.29/0.47 = ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ omega )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(omegaIndAx_type,type,
% 0.29/0.47 omegaIndAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(omegaIndAx,definition,
% 0.29/0.47 ( omegaIndAx
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ( ( in @ emptyset @ A )
% 0.29/0.47 & ! [Xx: $i] :
% 0.29/0.47 ( ( ( in @ Xx @ omega )
% 0.29/0.47 & ( in @ Xx @ A ) )
% 0.29/0.47 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ omega )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(replAx_type,type,
% 0.29/0.47 replAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(replAx,definition,
% 0.29/0.47 ( replAx
% 0.29/0.47 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.29/0.47 ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( exu
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.29/0.47 => ? [B: $i] :
% 0.29/0.47 ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 <=> ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ A )
% 0.29/0.47 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(foundationAx_type,type,
% 0.29/0.47 foundationAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(foundationAx,definition,
% 0.29/0.47 ( foundationAx
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.29/0.47 => ? [B: $i] :
% 0.29/0.47 ( ( in @ B @ A )
% 0.29/0.47 & ~ ? [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ B )
% 0.29/0.47 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(wellorderingAx_type,type,
% 0.29/0.47 wellorderingAx: $o ).
% 0.29/0.47
% 0.29/0.47 thf(wellorderingAx,definition,
% 0.29/0.47 ( wellorderingAx
% 0.29/0.47 = ( ! [A: $i] :
% 0.29/0.47 ? [B: $i] :
% 0.29/0.47 ( ! [C: $i] :
% 0.29/0.47 ( ( in @ C @ B )
% 0.29/0.47 => ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ C )
% 0.29/0.47 => ( in @ Xx @ A ) ) )
% 0.29/0.47 & ! [Xx: $i,Xy: $i] :
% 0.29/0.47 ( ( ( in @ Xx @ A )
% 0.29/0.47 & ( in @ Xy @ A ) )
% 0.29/0.47 => ( ! [C: $i] :
% 0.29/0.47 ( ( in @ C @ B )
% 0.29/0.47 => ( ( in @ Xx @ C )
% 0.29/0.47 <=> ( in @ Xy @ C ) ) )
% 0.29/0.47 => ( Xx = Xy ) ) )
% 0.29/0.47 & ! [C: $i,D: $i] :
% 0.29/0.47 ( ( ( in @ C @ B )
% 0.29/0.47 & ( in @ D @ B ) )
% 0.29/0.47 => ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ C )
% 0.29/0.47 => ( in @ Xx @ D ) )
% 0.29/0.47 | ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ D )
% 0.29/0.47 => ( in @ Xx @ C ) ) ) )
% 0.29/0.47 & ! [C: $i] :
% 0.29/0.47 ( ( ! [Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ C )
% 0.29/0.47 => ( in @ Xx @ A ) )
% 0.29/0.47 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.29/0.47 => ? [D: $i,Xx: $i] :
% 0.29/0.47 ( ( in @ D @ B )
% 0.29/0.47 & ( in @ Xx @ C )
% 0.29/0.47 & ~ ? [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ D )
% 0.29/0.47 & ( in @ Xy @ C ) )
% 0.29/0.47 & ! [E: $i] :
% 0.29/0.47 ( ( in @ E @ B )
% 0.29/0.47 => ( ! [Xy: $i] :
% 0.29/0.47 ( ( in @ Xy @ E )
% 0.29/0.47 => ( in @ Xy @ D ) )
% 0.29/0.47 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(descr_type,type,
% 0.29/0.47 descr: ( $i > $o ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(descrp_type,type,
% 0.29/0.47 descrp: $o ).
% 0.29/0.47
% 0.29/0.47 thf(descrp,definition,
% 0.29/0.47 ( descrp
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ( Xphi
% 0.29/0.47 @ ( descr
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstr_type,type,
% 0.29/0.47 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrI_type,type,
% 0.29/0.47 dsetconstrI: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrI,definition,
% 0.29/0.47 ( dsetconstrI
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ A )
% 0.29/0.47 => ( ( Xphi @ Xx )
% 0.29/0.47 => ( in @ Xx
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrEL_type,type,
% 0.29/0.47 dsetconstrEL: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrEL,definition,
% 0.29/0.47 ( dsetconstrEL
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.47 => ( in @ Xx @ A ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrER_type,type,
% 0.29/0.47 dsetconstrER: $o ).
% 0.29/0.47
% 0.29/0.47 thf(dsetconstrER,definition,
% 0.29/0.47 ( dsetconstrER
% 0.29/0.47 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx
% 0.29/0.47 @ ( dsetconstr @ A
% 0.29/0.47 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.29/0.47 => ( Xphi @ Xx ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(exuE1_type,type,
% 0.29/0.47 exuE1: $o ).
% 0.29/0.47
% 0.29/0.47 thf(exuE1,definition,
% 0.29/0.47 ( exuE1
% 0.29/0.47 = ( ! [Xphi: $i > $o] :
% 0.29/0.47 ( ( exu
% 0.29/0.47 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.29/0.47 => ? [Xx: $i] :
% 0.29/0.47 ( ( Xphi @ Xx )
% 0.29/0.47 & ! [Xy: $i] :
% 0.29/0.47 ( ( Xphi @ Xy )
% 0.29/0.47 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set_type,type,
% 0.29/0.47 prop2set: $o > $i ).
% 0.29/0.47
% 0.29/0.47 thf(prop2set,definition,
% 0.29/0.47 ( prop2set
% 0.29/0.47 = ( ^ [Xphi: $o] :
% 0.29/0.47 ( dsetconstr @ ( powerset @ emptyset )
% 0.29/0.47 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(prop2setE,conjecture,
% 0.29/0.47 ( setextAx
% 0.29/0.47 => ( emptysetAx
% 0.29/0.47 => ( setadjoinAx
% 0.29/0.47 => ( powersetAx
% 0.29/0.47 => ( setunionAx
% 0.29/0.47 => ( omega0Ax
% 0.29/0.47 => ( omegaSAx
% 0.29/0.47 => ( omegaIndAx
% 0.29/0.47 => ( replAx
% 0.29/0.47 => ( foundationAx
% 0.29/0.47 => ( wellorderingAx
% 0.29/0.47 => ( descrp
% 0.29/0.47 => ( dsetconstrI
% 0.29/0.47 => ( dsetconstrEL
% 0.29/0.47 => ( dsetconstrER
% 0.29/0.47 => ( exuE1
% 0.29/0.47 => ! [Xphi: $o,Xx: $i] :
% 0.29/0.47 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.29/0.47 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 12:24:22 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.o0rrXd4Krc/DTF2DTF26735.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.32 ---- Cleaned THF ---
% 0.31/1.32 thf(in_type,type,
% 0.31/1.32 in: $i > $i > $o ).
% 0.31/1.32
% 0.31/1.32 thf(exu_type,type,
% 0.31/1.32 exu: ( $i > $o ) > $o ).
% 0.31/1.32
% 0.31/1.32 thf(exu,definition,
% 0.31/1.32 ( exu
% 0.31/1.32 = ( ^ [Xphi: $i > $o] :
% 0.31/1.32 ? [Xx: $i] :
% 0.31/1.32 ( ( Xphi @ Xx )
% 0.31/1.32 & ! [Xy: $i] :
% 0.31/1.32 ( ( Xphi @ Xy )
% 0.31/1.32 => ( Xx = Xy ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(setextAx_type,type,
% 0.31/1.32 setextAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(setextAx,definition,
% 0.31/1.32 ( setextAx
% 0.31/1.32 = ( ! [A: $i,B: $i] :
% 0.31/1.32 ( ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ A )
% 0.31/1.32 <=> ( in @ Xx @ B ) )
% 0.31/1.32 => ( A = B ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(emptyset_type,type,
% 0.31/1.32 emptyset: $i ).
% 0.31/1.32
% 0.31/1.32 thf(emptysetAx_type,type,
% 0.31/1.32 emptysetAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(emptysetAx,definition,
% 0.31/1.32 ( emptysetAx
% 0.31/1.32 = ( ! [Xx: $i] :
% 0.31/1.32 ~ ( in @ Xx @ emptyset ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(setadjoin_type,type,
% 0.31/1.32 setadjoin: $i > $i > $i ).
% 0.31/1.32
% 0.31/1.32 thf(setadjoinAx_type,type,
% 0.31/1.32 setadjoinAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(setadjoinAx,definition,
% 0.31/1.32 ( setadjoinAx
% 0.31/1.32 = ( ! [Xx: $i,A: $i,Xy: $i] :
% 0.31/1.32 ( ( in @ Xy @ ( setadjoin @ Xx @ A ) )
% 0.31/1.32 <=> ( ( Xy = Xx )
% 0.31/1.32 | ( in @ Xy @ A ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(powerset_type,type,
% 0.31/1.32 powerset: $i > $i ).
% 0.31/1.32
% 0.31/1.32 thf(powersetAx_type,type,
% 0.31/1.32 powersetAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(powersetAx,definition,
% 0.31/1.32 ( powersetAx
% 0.31/1.32 = ( ! [A: $i,B: $i] :
% 0.31/1.32 ( ( in @ B @ ( powerset @ A ) )
% 0.31/1.32 <=> ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ B )
% 0.31/1.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(setunion_type,type,
% 0.31/1.32 setunion: $i > $i ).
% 0.31/1.32
% 0.31/1.32 thf(setunionAx_type,type,
% 0.31/1.32 setunionAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(setunionAx,definition,
% 0.31/1.32 ( setunionAx
% 0.31/1.32 = ( ! [A: $i,Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ ( setunion @ A ) )
% 0.31/1.32 <=> ? [B: $i] :
% 0.31/1.32 ( ( in @ Xx @ B )
% 0.31/1.32 & ( in @ B @ A ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(omega_type,type,
% 0.31/1.32 omega: $i ).
% 0.31/1.32
% 0.31/1.32 thf(omega0Ax_type,type,
% 0.31/1.32 omega0Ax: $o ).
% 0.31/1.32
% 0.31/1.32 thf(omega0Ax,definition,
% 0.31/1.32 ( omega0Ax
% 0.31/1.32 = ( in @ emptyset @ omega ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(omegaSAx_type,type,
% 0.31/1.32 omegaSAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(omegaSAx,definition,
% 0.31/1.32 ( omegaSAx
% 0.31/1.32 = ( ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ omega )
% 0.31/1.32 => ( in @ ( setadjoin @ Xx @ Xx ) @ omega ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(omegaIndAx_type,type,
% 0.31/1.32 omegaIndAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(omegaIndAx,definition,
% 0.31/1.32 ( omegaIndAx
% 0.31/1.32 = ( ! [A: $i] :
% 0.31/1.32 ( ( ( in @ emptyset @ A )
% 0.31/1.32 & ! [Xx: $i] :
% 0.31/1.32 ( ( ( in @ Xx @ omega )
% 0.31/1.32 & ( in @ Xx @ A ) )
% 0.31/1.32 => ( in @ ( setadjoin @ Xx @ Xx ) @ A ) ) )
% 0.31/1.32 => ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ omega )
% 0.31/1.32 => ( in @ Xx @ A ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(replAx_type,type,
% 0.31/1.32 replAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(replAx,definition,
% 0.31/1.32 ( replAx
% 0.31/1.32 = ( ! [Xphi: $i > $i > $o,A: $i] :
% 0.31/1.32 ( ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ A )
% 0.31/1.32 => ( exu
% 0.31/1.32 @ ^ [Xy: $i] : ( Xphi @ Xx @ Xy ) ) )
% 0.31/1.32 => ? [B: $i] :
% 0.31/1.32 ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ B )
% 0.31/1.32 <=> ? [Xy: $i] :
% 0.31/1.32 ( ( in @ Xy @ A )
% 0.31/1.32 & ( Xphi @ Xy @ Xx ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(foundationAx_type,type,
% 0.31/1.32 foundationAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(foundationAx,definition,
% 0.31/1.32 ( foundationAx
% 0.31/1.32 = ( ! [A: $i] :
% 0.31/1.32 ( ? [Xx: $i] : ( in @ Xx @ A )
% 0.31/1.32 => ? [B: $i] :
% 0.31/1.32 ( ( in @ B @ A )
% 0.31/1.32 & ~ ? [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ B )
% 0.31/1.32 & ( in @ Xx @ A ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(wellorderingAx_type,type,
% 0.31/1.32 wellorderingAx: $o ).
% 0.31/1.32
% 0.31/1.32 thf(wellorderingAx,definition,
% 0.31/1.32 ( wellorderingAx
% 0.31/1.32 = ( ! [A: $i] :
% 0.31/1.32 ? [B: $i] :
% 0.31/1.32 ( ! [C: $i] :
% 0.31/1.32 ( ( in @ C @ B )
% 0.31/1.32 => ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ C )
% 0.31/1.32 => ( in @ Xx @ A ) ) )
% 0.31/1.32 & ! [Xx: $i,Xy: $i] :
% 0.31/1.32 ( ( ( in @ Xx @ A )
% 0.31/1.32 & ( in @ Xy @ A ) )
% 0.31/1.32 => ( ! [C: $i] :
% 0.31/1.32 ( ( in @ C @ B )
% 0.31/1.32 => ( ( in @ Xx @ C )
% 0.31/1.32 <=> ( in @ Xy @ C ) ) )
% 0.31/1.32 => ( Xx = Xy ) ) )
% 0.31/1.32 & ! [C: $i,D: $i] :
% 0.31/1.32 ( ( ( in @ C @ B )
% 0.31/1.32 & ( in @ D @ B ) )
% 0.31/1.32 => ( ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ C )
% 0.31/1.32 => ( in @ Xx @ D ) )
% 0.31/1.32 | ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ D )
% 0.31/1.32 => ( in @ Xx @ C ) ) ) )
% 0.31/1.32 & ! [C: $i] :
% 0.31/1.32 ( ( ! [Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ C )
% 0.31/1.32 => ( in @ Xx @ A ) )
% 0.31/1.32 & ? [Xx: $i] : ( in @ Xx @ C ) )
% 0.31/1.32 => ? [D: $i,Xx: $i] :
% 0.31/1.32 ( ( in @ D @ B )
% 0.31/1.32 & ( in @ Xx @ C )
% 0.31/1.32 & ~ ? [Xy: $i] :
% 0.31/1.32 ( ( in @ Xy @ D )
% 0.31/1.32 & ( in @ Xy @ C ) )
% 0.31/1.32 & ! [E: $i] :
% 0.31/1.32 ( ( in @ E @ B )
% 0.31/1.32 => ( ! [Xy: $i] :
% 0.31/1.32 ( ( in @ Xy @ E )
% 0.31/1.32 => ( in @ Xy @ D ) )
% 0.31/1.32 | ( in @ Xx @ E ) ) ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(descr_type,type,
% 0.31/1.32 descr: ( $i > $o ) > $i ).
% 0.31/1.32
% 0.31/1.32 thf(descrp_type,type,
% 0.31/1.32 descrp: $o ).
% 0.31/1.32
% 0.31/1.32 thf(descrp,definition,
% 0.31/1.32 ( descrp
% 0.31/1.32 = ( ! [Xphi: $i > $o] :
% 0.31/1.32 ( ( exu
% 0.31/1.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.32 => ( Xphi
% 0.31/1.32 @ ( descr
% 0.31/1.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(dsetconstr_type,type,
% 0.31/1.32 dsetconstr: $i > ( $i > $o ) > $i ).
% 0.31/1.32
% 0.31/1.32 thf(dsetconstrI_type,type,
% 0.31/1.32 dsetconstrI: $o ).
% 0.31/1.32
% 0.31/1.32 thf(dsetconstrI,definition,
% 0.31/1.32 ( dsetconstrI
% 0.31/1.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ A )
% 0.31/1.32 => ( ( Xphi @ Xx )
% 0.31/1.32 => ( in @ Xx
% 0.31/1.32 @ ( dsetconstr @ A
% 0.31/1.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(dsetconstrEL_type,type,
% 0.31/1.32 dsetconstrEL: $o ).
% 0.31/1.32
% 0.31/1.32 thf(dsetconstrEL,definition,
% 0.31/1.32 ( dsetconstrEL
% 0.31/1.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.32 ( ( in @ Xx
% 0.31/1.32 @ ( dsetconstr @ A
% 0.31/1.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/1.32 => ( in @ Xx @ A ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(dsetconstrER_type,type,
% 0.31/1.32 dsetconstrER: $o ).
% 0.31/1.32
% 0.31/1.32 thf(dsetconstrER,definition,
% 0.31/1.32 ( dsetconstrER
% 0.31/1.32 = ( ! [A: $i,Xphi: $i > $o,Xx: $i] :
% 0.31/1.32 ( ( in @ Xx
% 0.31/1.32 @ ( dsetconstr @ A
% 0.31/1.32 @ ^ [Xy: $i] : ( Xphi @ Xy ) ) )
% 0.31/1.32 => ( Xphi @ Xx ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(exuE1_type,type,
% 0.31/1.32 exuE1: $o ).
% 0.31/1.32
% 0.31/1.32 thf(exuE1,definition,
% 0.31/1.32 ( exuE1
% 0.31/1.32 = ( ! [Xphi: $i > $o] :
% 0.31/1.32 ( ( exu
% 0.31/1.32 @ ^ [Xx: $i] : ( Xphi @ Xx ) )
% 0.31/1.32 => ? [Xx: $i] :
% 0.31/1.32 ( ( Xphi @ Xx )
% 0.31/1.32 & ! [Xy: $i] :
% 0.31/1.32 ( ( Xphi @ Xy )
% 0.31/1.32 => ( Xx = Xy ) ) ) ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(prop2set_type,type,
% 0.31/1.32 prop2set: $o > $i ).
% 0.31/1.32
% 0.31/1.32 thf(prop2set,definition,
% 0.31/1.32 ( prop2set
% 0.31/1.32 = ( ^ [Xphi: $o] :
% 0.31/1.32 ( dsetconstr @ ( powerset @ emptyset )
% 0.31/1.32 @ ^ [Xx: $i] : Xphi ) ) ) ).
% 0.31/1.32
% 0.31/1.32 thf(prop2setE,conjecture,
% 0.31/1.32 ( setextAx
% 0.31/1.32 => ( emptysetAx
% 0.31/1.32 => ( setadjoinAx
% 0.31/1.32 => ( powersetAx
% 0.31/1.32 => ( setunionAx
% 0.31/1.32 => ( omega0Ax
% 0.31/1.32 => ( omegaSAx
% 0.31/1.32 => ( omegaIndAx
% 0.31/1.32 => ( replAx
% 0.31/1.32 => ( foundationAx
% 0.31/1.32 => ( wellorderingAx
% 0.31/1.32 => ( descrp
% 0.31/1.32 => ( dsetconstrI
% 0.31/1.32 => ( dsetconstrEL
% 0.31/1.32 => ( dsetconstrER
% 0.31/1.32 => ( exuE1
% 0.31/1.32 => ! [Xphi: $o,Xx: $i] :
% 0.31/1.32 ( ( in @ Xx @ ( prop2set @ Xphi ) )
% 0.31/1.32 => Xphi ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 0.31/1.32 ------------------------
% 0.31/1.33 % (26856)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_26735 for (2999ds/275Mi)
% 0.31/1.33 % (26853)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_26735 for (2999ds/27Mi)
% 0.31/1.33 % (26857)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26735 for (2999ds/18Mi)
% 0.31/1.34 % (26851)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26735 for (2999ds/183Mi)
% 0.31/1.34 % (26852)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_26735 for (2999ds/4Mi)
% 0.31/1.34 % (26854)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26735 for (2999ds/2Mi)
% 0.31/1.34 % (26855)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_26735 for (2999ds/2Mi)
% 0.31/1.34 % (26857)Instruction limit reached!
% 0.31/1.34 % (26857)------------------------------
% 0.31/1.34 % (26857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (26857)Termination reason: Unknown
% 0.31/1.34 % (26857)Termination phase: Property scanning
% 0.31/1.34
% 0.31/1.34 % (26857)Memory used [KB]: 1279
% 0.31/1.34 % (26857)Time elapsed: 0.007 s
% 0.31/1.34 % (26857)Instructions burned: 20 (million)
% 0.31/1.34 % (26857)------------------------------
% 0.31/1.34 % (26857)------------------------------
% 0.31/1.34 % (26854)Instruction limit reached!
% 0.31/1.34 % (26854)------------------------------
% 0.31/1.34 % (26854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (26854)Termination reason: Unknown
% 0.31/1.34 % (26855)Instruction limit reached!
% 0.31/1.34 % (26855)------------------------------
% 0.31/1.34 % (26855)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (26854)Termination phase: shuffling
% 0.31/1.34
% 0.31/1.34 % (26855)Termination reason: Unknown
% 0.31/1.34 % (26854)Memory used [KB]: 1023
% 0.31/1.34 % (26854)Time elapsed: 0.003 s
% 0.31/1.34 % (26855)Termination phase: shuffling
% 0.31/1.34 % (26854)Instructions burned: 2 (million)
% 0.31/1.34
% 0.31/1.34 % (26854)------------------------------
% 0.31/1.34 % (26854)------------------------------
% 0.31/1.34 % (26855)Memory used [KB]: 1023
% 0.31/1.34 % (26855)Time elapsed: 0.003 s
% 0.31/1.34 % (26855)Instructions burned: 2 (million)
% 0.31/1.34 % (26855)------------------------------
% 0.31/1.34 % (26855)------------------------------
% 0.31/1.34 % (26853)Instruction limit reached!
% 0.31/1.34 % (26853)------------------------------
% 0.31/1.34 % (26853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (26853)Termination reason: Unknown
% 0.31/1.34 % (26853)Termination phase: Saturation
% 0.31/1.34
% 0.31/1.34 % (26853)Memory used [KB]: 5756
% 0.31/1.34 % (26853)Time elapsed: 0.010 s
% 0.31/1.34 % (26853)Instructions burned: 29 (million)
% 0.31/1.34 % (26853)------------------------------
% 0.31/1.34 % (26853)------------------------------
% 0.31/1.34 % (26852)Instruction limit reached!
% 0.31/1.34 % (26852)------------------------------
% 0.31/1.34 % (26852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (26852)Termination reason: Unknown
% 0.31/1.34 % (26852)Termination phase: Property scanning
% 0.31/1.34
% 0.31/1.34 % (26852)Memory used [KB]: 1023
% 0.31/1.34 % (26852)Time elapsed: 0.005 s
% 0.31/1.34 % (26852)Instructions burned: 5 (million)
% 0.31/1.34 % (26852)------------------------------
% 0.31/1.34 % (26852)------------------------------
% 0.31/1.35 % (26858)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26735 for (2999ds/3Mi)
% 0.31/1.35 % (26856)First to succeed.
% 0.31/1.35 % (26858)Instruction limit reached!
% 0.31/1.35 % (26858)------------------------------
% 0.31/1.35 % (26858)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (26858)Termination reason: Unknown
% 0.31/1.35 % (26858)Termination phase: shuffling
% 0.31/1.35
% 0.31/1.35 % (26858)Memory used [KB]: 1023
% 0.31/1.35 % (26858)Time elapsed: 0.002 s
% 0.31/1.35 % (26858)Instructions burned: 3 (million)
% 0.31/1.35 % (26858)------------------------------
% 0.31/1.35 % (26858)------------------------------
% 0.31/1.35 % (26861)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26735 for (2999ds/3Mi)
% 0.31/1.35 % (26856)Refutation found. Thanks to Tanya!
% 0.31/1.35 % SZS status Theorem for DTF2THF_26735
% 0.31/1.35 % SZS output start Proof for DTF2THF_26735
% 0.31/1.35 thf(func_def_0, type, in: $i > $i > $o).
% 0.31/1.35 thf(func_def_1, type, exu: ($i > $o) > $o).
% 0.31/1.35 thf(func_def_6, type, setadjoin: $i > $i > $i).
% 0.31/1.35 thf(func_def_8, type, powerset: $i > $i).
% 0.31/1.35 thf(func_def_10, type, setunion: $i > $i).
% 0.31/1.35 thf(func_def_19, type, descr: ($i > $o) > $i).
% 0.31/1.35 thf(func_def_21, type, dsetconstr: $i > ($i > $o) > $i).
% 0.31/1.35 thf(func_def_26, type, prop2set: $o > $i).
% 0.31/1.35 thf(func_def_39, type, sP1: $i > $i > $o).
% 0.31/1.35 thf(func_def_40, type, sP2: $i > $o).
% 0.31/1.35 thf(func_def_41, type, sP3: $i > $i > $o).
% 0.31/1.35 thf(func_def_42, type, sP4: $i > $i > $o).
% 0.31/1.35 thf(func_def_44, type, sK6: $i > $i > $o).
% 0.31/1.35 thf(func_def_45, type, sK7: $i > $i).
% 0.31/1.35 thf(func_def_46, type, sK8: $i > $i).
% 0.31/1.35 thf(func_def_47, type, sK9: ($i > $i > $o) > $i > $i).
% 0.31/1.35 thf(func_def_48, type, sK10: ($i > $i > $o) > $i > $i).
% 0.31/1.35 thf(func_def_49, type, sK11: $i > ($i > $i > $o) > $i > $i).
% 0.31/1.35 thf(func_def_52, type, sK14: $i > $i > $i).
% 0.31/1.35 thf(func_def_59, type, sK21: ($i > $o) > $i).
% 0.31/1.35 thf(func_def_60, type, sK22: $i > $o).
% 0.31/1.35 thf(func_def_61, type, sK23: $i > $i).
% 0.31/1.35 thf(func_def_62, type, sK24: $i > $i).
% 0.31/1.35 thf(func_def_65, type, sK27: $i > $i).
% 0.31/1.35 thf(func_def_68, type, sK30: $i > $o).
% 0.31/1.35 thf(func_def_70, type, sK32: $i > $i > $i).
% 0.31/1.35 thf(func_def_71, type, sK33: $i > $i > $i).
% 0.31/1.35 thf(func_def_72, type, sK34: $i > $i > $i).
% 0.31/1.35 thf(func_def_73, type, sK35: $i > $i > $i).
% 0.31/1.35 thf(func_def_74, type, sK36: $i > $i > $i).
% 0.31/1.35 thf(func_def_75, type, sK37: $i > $i > $i > $i).
% 0.31/1.35 thf(func_def_76, type, sK38: $i > $i).
% 0.31/1.35 thf(func_def_77, type, sK39: $i > $i).
% 0.31/1.35 thf(func_def_78, type, sK40: $i > $i).
% 0.31/1.35 thf(func_def_79, type, sK41: $i > $i).
% 0.31/1.35 thf(func_def_80, type, sK42: $i > $i > $i).
% 0.31/1.35 thf(func_def_81, type, sK43: $i > $i > $i > $i).
% 0.31/1.35 thf(func_def_82, type, sK44: $i > $i > $i > $i).
% 0.31/1.35 thf(func_def_83, type, sK45: $i > $i > $i).
% 0.31/1.35 thf(func_def_84, type, sK46: $i > $i > $i).
% 0.31/1.35 thf(func_def_86, type, sK48: $i > $i).
% 0.31/1.35 thf(func_def_87, type, sK49: $i > $i).
% 0.31/1.35 thf(func_def_88, type, sK50: $i > $i).
% 0.31/1.35 thf(func_def_89, type, sK51: $i > $i > $i).
% 0.31/1.35 thf(func_def_94, type, sK56: $i > $i).
% 0.31/1.35 thf(func_def_96, type, sK58: $i > $o).
% 0.31/1.35 thf(func_def_100, type, sK62: $i > $o).
% 0.31/1.35 thf(func_def_103, type, ph65: !>[X0: $tType]:(X0)).
% 0.31/1.35 thf(f506,plain,(
% 0.31/1.35 $false),
% 0.31/1.35 inference(subsumption_resolution,[status(thm)],[f494,f204])).
% 0.31/1.35 thf(f204,plain,(
% 0.31/1.35 (sK12 != $true)),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f94])).
% 0.31/1.35 thf(f94,plain,(
% 0.31/1.35 (wellorderingAx = $true) & (setextAx = $true) & (foundationAx = $true) & (descrp = $true) & (emptysetAx = $true) & (($true = (in @ sK13 @ (prop2set @ sK12))) & (sK12 != $true)) & (setunionAx = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (omega0Ax = $true) & (setadjoinAx = $true) & (powersetAx = $true) & (omegaIndAx = $true) & (replAx = $true) & (omegaSAx = $true) & (dsetconstrI = $true) & (dsetconstrEL = $true)),
% 0.31/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK12,sK13])],[f73,f93])).
% 0.31/1.35 thf(f93,plain,(
% 0.31/1.35 ? [X0 : $o,X1 : $i] : (((in @ X1 @ (prop2set @ X0)) = $true) & ($true != X0)) => (($true = (in @ sK13 @ (prop2set @ sK12))) & (sK12 != $true))),
% 0.31/1.35 introduced(definition,[],[choice_axiom])).
% 0.31/1.35 thf(f73,plain,(
% 0.31/1.35 (wellorderingAx = $true) & (setextAx = $true) & (foundationAx = $true) & (descrp = $true) & (emptysetAx = $true) & ? [X0 : $o,X1 : $i] : (((in @ X1 @ (prop2set @ X0)) = $true) & ($true != X0)) & (setunionAx = $true) & (dsetconstrER = $true) & (exuE1 = $true) & (omega0Ax = $true) & (setadjoinAx = $true) & (powersetAx = $true) & (omegaIndAx = $true) & (replAx = $true) & (omegaSAx = $true) & (dsetconstrI = $true) & (dsetconstrEL = $true)),
% 0.31/1.35 inference(flattening,[status(thm)],[f72])).
% 0.31/1.35 thf(f72,plain,(
% 0.31/1.35 (((((((((((((((? [X0 : $o,X1 : $i] : (((in @ X1 @ (prop2set @ X0)) = $true) & ($true != X0)) & (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)),
% 0.31/1.35 inference(ennf_transformation,[status(thm)],[f32])).
% 0.31/1.35 thf(f32,plain,(
% 0.31/1.35 ~((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) => ! [X0 : $o,X1 : $i] : (((in @ X1 @ (prop2set @ X0)) = $true) => ($true = X0))))))))))))))))))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f31])).
% 0.31/1.35 thf(f31,plain,(
% 0.31/1.35 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0)))))))))))))))))),
% 0.31/1.35 inference(rectify,[status(thm)],[f20])).
% 0.31/1.35 thf(f20,negated_conjecture,(
% 0.31/1.35 ~(setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0)))))))))))))))))),
% 0.31/1.35 inference(negated_conjecture,[status(cth)],[f19])).
% 0.31/1.35 thf(f19,conjecture,(
% 0.31/1.35 setextAx => (emptysetAx => (setadjoinAx => (powersetAx => (setunionAx => (omega0Ax => (omegaSAx => (omegaIndAx => (replAx => (foundationAx => (wellorderingAx => (descrp => (dsetconstrI => (dsetconstrEL => (dsetconstrER => (exuE1 => ! [X0 : $o,X1 : $i] : ((in @ X1 @ (prop2set @ X0)) => X0))))))))))))))))),
% 0.31/1.35 file('/export/starexec/sandbox/tmp/tmp.o0rrXd4Krc/DTF2THF_26735.p',prop2setE)).
% 0.31/1.35 thf(f494,plain,(
% 0.31/1.35 (sK12 = $true)),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f493])).
% 0.31/1.35 thf(f493,plain,(
% 0.31/1.35 ($true = ((^[Y0 : $i]: (sK12)) @ sK13))),
% 0.31/1.35 inference(trivial_inequality_removal,[status(thm)],[f480])).
% 0.31/1.35 thf(f480,plain,(
% 0.31/1.35 ($true != $true) | ($true = ((^[Y0 : $i]: (sK12)) @ sK13))),
% 0.31/1.35 inference(superposition,[status(thm)],[f388,f376])).
% 0.31/1.35 thf(f376,plain,(
% 0.31/1.35 ($true = (in @ sK13 @ (dsetconstr @ (powerset @ emptyset) @ (^[Y0 : $i]: (sK12)))))),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f299])).
% 0.31/1.35 thf(f299,plain,(
% 0.31/1.35 ($true = (in @ sK13 @ ((^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))) @ sK12)))),
% 0.31/1.35 inference(definition_unfolding,[status(thm)],[f205,f228])).
% 0.31/1.35 thf(f228,plain,(
% 0.31/1.35 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f22])).
% 0.31/1.35 thf(f22,plain,(
% 0.31/1.35 (prop2set = (^[Y0 : $o]: (dsetconstr @ (powerset @ emptyset) @ (^[Y1 : $i]: (Y0)))))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f18])).
% 0.31/1.35 thf(f18,axiom,(
% 0.31/1.35 ((^[X0 : $o] : (dsetconstr @ (powerset @ emptyset) @ (^[X1 : $i] : (X0)))) = prop2set)),
% 0.31/1.35 file('/export/starexec/sandbox/tmp/tmp.o0rrXd4Krc/DTF2THF_26735.p',prop2set)).
% 0.31/1.35 thf(f205,plain,(
% 0.31/1.35 ($true = (in @ sK13 @ (prop2set @ sK12)))),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f94])).
% 0.31/1.35 thf(f388,plain,(
% 0.31/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ X2 @ (dsetconstr @ X0 @ X1))) | ($true = (X1 @ X2))) )),
% 0.31/1.35 inference(beta_eta_normalization,[status(thm)],[f387])).
% 0.31/1.35 thf(f387,plain,(
% 0.31/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) | ($true = (X1 @ X2))) )),
% 0.31/1.35 inference(trivial_inequality_removal,[status(thm)],[f324])).
% 0.31/1.35 thf(f324,plain,(
% 0.31/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true != $true) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) | ($true = (X1 @ X2))) )),
% 0.31/1.35 inference(definition_unfolding,[status(thm)],[f238,f202])).
% 0.31/1.35 thf(f202,plain,(
% 0.31/1.35 (dsetconstrER = $true)),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f94])).
% 0.31/1.35 thf(f238,plain,(
% 0.31/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i > $o] : (($true = (X1 @ X2)) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) | (dsetconstrER != $true)) )),
% 0.31/1.35 inference(cnf_transformation,[status(thm)],[f126])).
% 0.31/1.35 thf(f126,plain,(
% 0.31/1.35 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true = (X1 @ X2)) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | (($true != (sK30 @ sK31)) & ($true = (in @ sK31 @ (dsetconstr @ sK29 @ (^[Y0 : $i]: (sK30 @ Y0)))))))),
% 0.31/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK29,sK30,sK31])],[f124,f125])).
% 0.31/1.35 thf(f125,plain,(
% 0.31/1.35 ? [X3 : $i,X4 : $i > $o,X5 : $i] : (($true != (X4 @ X5)) & ($true = (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))) => (($true != (sK30 @ sK31)) & ($true = (in @ sK31 @ (dsetconstr @ sK29 @ (^[Y0 : $i]: (sK30 @ Y0))))))),
% 0.31/1.35 introduced(definition,[],[choice_axiom])).
% 0.31/1.35 thf(f124,plain,(
% 0.31/1.35 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true = (X1 @ X2)) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X3 : $i,X4 : $i > $o,X5 : $i] : (($true != (X4 @ X5)) & ($true = (in @ X5 @ (dsetconstr @ X3 @ (^[Y0 : $i]: (X4 @ Y0)))))))),
% 0.31/1.35 inference(rectify,[status(thm)],[f123])).
% 0.31/1.35 thf(f123,plain,(
% 0.31/1.35 (! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true = (X1 @ X2)) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) | (dsetconstrER != $true)) & ((dsetconstrER = $true) | ? [X0 : $i,X1 : $i > $o,X2 : $i] : (($true != (X1 @ X2)) & ($true = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))))),
% 0.31/1.35 inference(nnf_transformation,[status(thm)],[f60])).
% 0.31/1.35 thf(f60,plain,(
% 0.31/1.35 ! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true = (X1 @ X2)) | ($true != (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0)))))) <=> (dsetconstrER = $true)),
% 0.31/1.35 inference(ennf_transformation,[status(thm)],[f26])).
% 0.31/1.35 thf(f26,plain,(
% 0.31/1.35 (dsetconstrER = $true) <=> ! [X0 : $i,X1 : $i > $o,X2 : $i] : (($true = (in @ X2 @ (dsetconstr @ X0 @ (^[Y0 : $i]: (X1 @ Y0))))) => ($true = (X1 @ X2)))),
% 0.31/1.35 inference(fool_elimination,[status(thm)],[f25])).
% 0.31/1.35 thf(f25,plain,(
% 0.31/1.35 (! [X0 : $i,X1 : $i > $o,X2 : $i] : ((in @ X2 @ (dsetconstr @ X0 @ (^[X3 : $i] : (X1 @ X3)))) => (X1 @ X2)) = dsetconstrER)),
% 0.31/1.35 inference(rectify,[status(thm)],[f16])).
% 0.31/1.35 thf(f16,axiom,(
% 0.31/1.35 (! [X3 : $i,X0 : $i > $o,X1 : $i] : ((in @ X1 @ (dsetconstr @ X3 @ (^[X2 : $i] : (X0 @ X2)))) => (X0 @ X1)) = dsetconstrER)),
% 0.31/1.35 file('/export/starexec/sandbox/tmp/tmp.o0rrXd4Krc/DTF2THF_26735.p',dsetconstrER)).
% 0.31/1.35 % SZS output end Proof for DTF2THF_26735
% 0.31/1.35 % (26856)------------------------------
% 0.31/1.35 % (26856)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.35 % (26856)Termination reason: Refutation
% 0.31/1.35
% 0.31/1.35 % (26856)Memory used [KB]: 6012
% 0.31/1.35 % (26856)Time elapsed: 0.021 s
% 0.31/1.35 % (26856)Instructions burned: 59 (million)
% 0.31/1.35 % (26856)------------------------------
% 0.31/1.35 % (26856)------------------------------
% 0.31/1.35 % (26850)Success in time 0.015 s
%------------------------------------------------------------------------------