%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU819^2 : TPTP v9.2.1. Released v3.7.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n020.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 09:37:29 AM UTC 2026
% Result : Theorem 1.70s 1.34s
% Output : Refutation 1.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 38 ( 11 unt; 0 typ; 0 def)
% Number of atoms : 346 ( 101 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 308 ( 46 ~; 37 |; 26 &; 176 @)
% ( 2 <=>; 21 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 5 con; 0-2 aty)
% Number of variables : 52 ( 5 ^; 38 !; 9 ?; 52 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
setunion: $i > $i ).
thf(func_def_4,type,
nonempty: $i > $o ).
thf(func_def_5,type,
subset: $i > $i > $o ).
thf(func_def_6,type,
transitiveset: $i > $o ).
thf(func_def_9,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_10,type,
wellorderedByIn: $i > $o ).
thf(func_def_11,type,
ordinal: $i > $o ).
thf(func_def_27,type,
sK1: $i > $i ).
thf(f58,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f57,f51]) ).
thf(f51,plain,
( ( transitiveset @ ( sK1 @ sK0 ) )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f50]) ).
thf(f50,plain,
( ( ( transitiveset @ ( sK1 @ sK0 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f34,f45]) ).
thf(f45,plain,
! [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
= $true )
| ( ( transitiveset @ ( sK1 @ X0 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X0: $i] :
( ( ( transitiveset @ ( sK1 @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f38,f33]) ).
thf(f33,plain,
setunionTransitive = $true,
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( ( ordinal @ X1 )
= $true ) )
& ( ( transitiveset @ ( setunion @ sK0 ) )
!= $true )
& ( setunionTransitive = $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f25]) ).
thf(f25,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( ordinal @ X1 )
= $true ) )
& ( ( transitiveset @ ( setunion @ X0 ) )
!= $true ) )
=> ( ! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( ( ordinal @ X1 )
= $true ) )
& ( ( transitiveset @ ( setunion @ sK0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( ( ordinal @ X1 )
= $true ) )
& ( ( transitiveset @ ( setunion @ X0 ) )
!= $true ) )
& ( setunionTransitive = $true ) ),
inference(ennf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( ( setunionTransitive = $true )
=> ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( ( ordinal @ X1 )
= $true ) )
=> ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f14]) ).
thf(f14,plain,
~ ( setunionTransitive
=> ! [X0: $i] :
( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( ordinal @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( setunionTransitive
=> ! [X2: $i] :
( ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ( ordinal @ X0 ) )
=> ( transitiveset @ ( setunion @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( setunionTransitive
=> ! [X2: $i] :
( ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ( ordinal @ X0 ) )
=> ( transitiveset @ ( setunion @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.PPk0UYlczK/DTF2THF_20768.p',setunionOrdinalLem1) ).
thf(f38,plain,
! [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
= $true )
| ( ( transitiveset @ ( sK1 @ X0 ) )
!= $true )
| ( setunionTransitive != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ! [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
= $true )
| ( ( ( in @ ( sK1 @ X0 ) @ X0 )
= $true )
& ( ( transitiveset @ ( sK1 @ X0 ) )
!= $true ) ) )
| ( setunionTransitive != $true ) )
& ( ( setunionTransitive = $true )
| ( ( ( transitiveset @ ( setunion @ sK2 ) )
!= $true )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK2 ) )
| ( $true
= ( transitiveset @ X3 ) ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f28,f30,f29]) ).
thf(f29,plain,
! [X0: $i] :
( ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( transitiveset @ X1 ) ) )
=> ( ( ( in @ ( sK1 @ X0 ) @ X0 )
= $true )
& ( ( transitiveset @ ( sK1 @ X0 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f30,plain,
( ? [X2: $i] :
( ( ( transitiveset @ ( setunion @ X2 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( transitiveset @ X3 ) ) ) )
=> ( ( ( transitiveset @ ( setunion @ sK2 ) )
!= $true )
& ! [X3: $i] :
( ( $true
!= ( in @ X3 @ sK2 ) )
| ( $true
= ( transitiveset @ X3 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ( ! [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
= $true )
| ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( transitiveset @ X1 ) ) ) )
| ( setunionTransitive != $true ) )
& ( ( setunionTransitive = $true )
| ? [X2: $i] :
( ( ( transitiveset @ ( setunion @ X2 ) )
!= $true )
& ! [X3: $i] :
( ( ( in @ X3 @ X2 )
!= $true )
| ( $true
= ( transitiveset @ X3 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f27]) ).
thf(f27,plain,
( ( ! [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
= $true )
| ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( transitiveset @ X1 ) ) ) )
| ( setunionTransitive != $true ) )
& ( ( setunionTransitive = $true )
| ? [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
!= $true )
& ! [X1: $i] :
( ( ( in @ X1 @ X0 )
!= $true )
| ( $true
= ( transitiveset @ X1 ) ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
= $true )
| ? [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
& ( $true
!= ( transitiveset @ X1 ) ) ) )
<=> ( setunionTransitive = $true ) ),
inference(ennf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( ! [X0: $i] :
( ! [X1: $i] :
( ( ( in @ X1 @ X0 )
= $true )
=> ( $true
= ( transitiveset @ X1 ) ) )
=> ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) )
<=> ( setunionTransitive = $true ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $i] :
( ( ! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( transitiveset @ X1 ) )
=> ( transitiveset @ ( setunion @ X0 ) ) )
= setunionTransitive ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X2: $i] :
( ( ! [X0: $i] :
( ( in @ X0 @ X2 )
=> ( transitiveset @ X0 ) )
=> ( transitiveset @ ( setunion @ X2 ) ) )
= setunionTransitive ),
file('/export/starexec/sandbox2/tmp/tmp.PPk0UYlczK/DTF2THF_20768.p',setunionTransitive) ).
thf(f34,plain,
( ( transitiveset @ ( setunion @ sK0 ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f26]) ).
thf(f57,plain,
( ( transitiveset @ ( sK1 @ sK0 ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f56,f34]) ).
thf(f56,plain,
( ( ( transitiveset @ ( setunion @ sK0 ) )
= $true )
| ( ( transitiveset @ ( sK1 @ sK0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f55]) ).
thf(f55,plain,
( ( ( transitiveset @ ( setunion @ sK0 ) )
= $true )
| ( ( transitiveset @ ( sK1 @ sK0 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f49,f46]) ).
thf(f46,plain,
! [X0: $i] :
( ( ( in @ ( sK1 @ X0 ) @ X0 )
= $true )
| ( ( transitiveset @ ( setunion @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X0: $i] :
( ( ( in @ ( sK1 @ X0 ) @ X0 )
= $true )
| ( ( transitiveset @ ( setunion @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(definition_unfolding,[status(thm)],[f39,f33]) ).
thf(f39,plain,
! [X0: $i] :
( ( ( transitiveset @ ( setunion @ X0 ) )
= $true )
| ( ( in @ ( sK1 @ X0 ) @ X0 )
= $true )
| ( setunionTransitive != $true ) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
thf(f49,plain,
! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( $true
= ( transitiveset @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f47]) ).
thf(f47,plain,
! [X1: $i] :
( ( $true
= ( ( transitiveset @ X1 )
& ( wellorderedByIn @ X1 ) ) )
| ( $true
!= ( in @ X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f40]) ).
thf(f40,plain,
! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) )
@ X1 )
= $true ) ),
inference(definition_unfolding,[status(thm)],[f35,f32]) ).
thf(f32,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( transitiveset @ Y0 )
& ( wellorderedByIn @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f21]) ).
thf(f21,plain,
( ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) )
= ordinal ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X0: $i] :
( ( wellorderedByIn @ X0 )
& ( transitiveset @ X0 ) ) )
= ordinal ),
file('/export/starexec/sandbox2/tmp/tmp.PPk0UYlczK/DTF2THF_20768.p',ordinal) ).
thf(f35,plain,
! [X1: $i] :
( ( $true
!= ( in @ X1 @ sK0 ) )
| ( ( ordinal @ X1 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : SEU819^2 : TPTP v9.2.1. Released v3.7.0.
% 0.10/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.35 % Computer : n020.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Tue Feb 24 12:35:12 EST 2026
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.48 ---- Original DTF file ---
% 0.26/0.48 thf(spec,logic,$$dhol).
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 % File : SEU819^2 : TPTP v9.2.1. Released v3.7.0.
% 0.26/0.48 % Domain : Set Theory
% 0.26/0.48 % Problem : Ordinals
% 0.26/0.48 % Version : Especial > Reduced > Especial.
% 0.26/0.48 % English : (! X:i.(! x:i.in x X -> ordinal x) -> transitiveset (setunion X))
% 0.26/0.48
% 0.26/0.48 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.26/0.48 % Source : [Bro08]
% 0.26/0.48 % Names : ZFC321l [Bro08]
% 0.26/0.48
% 0.26/0.48 % Status : Theorem
% 0.26/0.48 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.0.0, 0.14 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 v4.0.0, 0.00 v3.7.0
% 0.26/0.48 % Syntax : Number of formulae : 18 ( 6 unt; 11 typ; 6 def)
% 0.26/0.48 % Number of atoms : 44 ( 9 equ; 0 cnn)
% 0.26/0.48 % Maximal formula atoms : 4 ( 6 avg)
% 0.26/0.48 % Number of connectives : 78 ( 2 ~; 3 |; 6 &; 51 @)
% 0.26/0.48 % ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% 0.26/0.48 % Maximal formula depth : 8 ( 2 avg)
% 0.26/0.48 % Number of types : 2 ( 0 usr)
% 0.26/0.48 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.26/0.48 % Number of symbols : 12 ( 11 usr; 2 con; 0-2 aty)
% 0.26/0.48 % Number of variables : 19 ( 5 ^; 13 !; 1 ?; 19 :)
% 0.26/0.48 % SPC : TH0_THM_EQU_NAR
% 0.26/0.48
% 0.26/0.48 % Comments : http://mathgate.info/detsetitem.php?id=515
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 thf(in_type,type,
% 0.26/0.48 in: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(emptyset_type,type,
% 0.26/0.48 emptyset: $i ).
% 0.26/0.48
% 0.26/0.48 thf(powerset_type,type,
% 0.26/0.48 powerset: $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(setunion_type,type,
% 0.26/0.48 setunion: $i > $i ).
% 0.26/0.48
% 0.26/0.48 thf(nonempty_type,type,
% 0.26/0.48 nonempty: $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(nonempty,definition,
% 0.26/0.48 ( nonempty
% 0.26/0.48 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(subset_type,type,
% 0.26/0.48 subset: $i > $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(transitiveset_type,type,
% 0.26/0.48 transitiveset: $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(transitiveset,definition,
% 0.26/0.48 ( transitiveset
% 0.26/0.48 = ( ^ [A: $i] :
% 0.26/0.48 ! [X: $i] :
% 0.26/0.48 ( ( in @ X @ A )
% 0.26/0.48 => ( subset @ X @ A ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(setunionTransitive_type,type,
% 0.26/0.48 setunionTransitive: $o ).
% 0.26/0.48
% 0.26/0.48 thf(setunionTransitive,definition,
% 0.26/0.48 ( setunionTransitive
% 0.26/0.48 = ( ! [X: $i] :
% 0.26/0.48 ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ X )
% 0.26/0.48 => ( transitiveset @ Xx ) )
% 0.26/0.48 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(stricttotalorderedByIn_type,type,
% 0.26/0.48 stricttotalorderedByIn: $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(stricttotalorderedByIn,definition,
% 0.26/0.48 ( stricttotalorderedByIn
% 0.26/0.48 = ( ^ [A: $i] :
% 0.26/0.48 ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ A )
% 0.26/0.48 => ! [X: $i] :
% 0.26/0.48 ( ( in @ X @ A )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ A )
% 0.26/0.48 => ( ( ( in @ Xx @ X )
% 0.26/0.48 & ( in @ X @ Y ) )
% 0.26/0.48 => ( in @ Xx @ Y ) ) ) ) )
% 0.26/0.48 & ! [X: $i] :
% 0.26/0.48 ( ( in @ X @ A )
% 0.26/0.48 => ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ A )
% 0.26/0.48 => ( ( X = Y )
% 0.26/0.48 | ( in @ X @ Y )
% 0.26/0.48 | ( in @ Y @ X ) ) ) )
% 0.26/0.48 & ! [X: $i] :
% 0.26/0.48 ( ( in @ X @ A )
% 0.26/0.48 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(wellorderedByIn_type,type,
% 0.26/0.48 wellorderedByIn: $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(wellorderedByIn,definition,
% 0.26/0.48 ( wellorderedByIn
% 0.26/0.48 = ( ^ [A: $i] :
% 0.26/0.48 ( ( stricttotalorderedByIn @ A )
% 0.26/0.48 & ! [X: $i] :
% 0.26/0.48 ( ( in @ X @ ( powerset @ A ) )
% 0.26/0.48 => ( ( nonempty @ X )
% 0.26/0.48 => ? [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ X )
% 0.26/0.48 & ! [Y: $i] :
% 0.26/0.48 ( ( in @ Y @ X )
% 0.26/0.48 => ( ( Xx = Y )
% 0.26/0.48 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(ordinal_type,type,
% 0.26/0.48 ordinal: $i > $o ).
% 0.26/0.48
% 0.26/0.48 thf(ordinal,definition,
% 0.26/0.48 ( ordinal
% 0.26/0.48 = ( ^ [Xx: $i] :
% 0.26/0.48 ( ( transitiveset @ Xx )
% 0.26/0.48 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 thf(setunionOrdinalLem1,conjecture,
% 0.26/0.48 ( setunionTransitive
% 0.26/0.48 => ! [X: $i] :
% 0.26/0.48 ( ! [Xx: $i] :
% 0.26/0.48 ( ( in @ Xx @ X )
% 0.26/0.48 => ( ordinal @ Xx ) )
% 0.26/0.48 => ( transitiveset @ ( setunion @ X ) ) ) ) ).
% 0.26/0.48
% 0.26/0.48 %------------------------------------------------------------------------------
% 0.26/0.48 ------------------------
% 1.47/1.29 ---- Embedded in THF ---
% 1.47/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.47/1.29 %%% Generated on Tue Feb 24 12:35:13 EST 2026
% 1.47/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.47/1.29 %%% Logic specification used:
% 1.47/1.29 %%% thf(spec, logic, $$dhol).
% 1.47/1.29
% 1.47/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.PPk0UYlczK/DTF2DTF20768.p
% See solution above
% 1.47/1.29 ------------------------
% 1.70/1.31 ---- Cleaned THF ---
% 1.70/1.31 thf(in_type,type,
% 1.70/1.31 in: $i > $i > $o ).
% 1.70/1.31
% 1.70/1.31 thf(emptyset_type,type,
% 1.70/1.31 emptyset: $i ).
% 1.70/1.31
% 1.70/1.31 thf(powerset_type,type,
% 1.70/1.31 powerset: $i > $i ).
% 1.70/1.31
% 1.70/1.31 thf(setunion_type,type,
% 1.70/1.31 setunion: $i > $i ).
% 1.70/1.31
% 1.70/1.31 thf(nonempty_type,type,
% 1.70/1.31 nonempty: $i > $o ).
% 1.70/1.31
% 1.70/1.31 thf(nonempty,definition,
% 1.70/1.31 ( nonempty
% 1.70/1.31 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.70/1.31
% 1.70/1.31 thf(subset_type,type,
% 1.70/1.31 subset: $i > $i > $o ).
% 1.70/1.31
% 1.70/1.31 thf(transitiveset_type,type,
% 1.70/1.31 transitiveset: $i > $o ).
% 1.70/1.31
% 1.70/1.31 thf(transitiveset,definition,
% 1.70/1.31 ( transitiveset
% 1.70/1.31 = ( ^ [A: $i] :
% 1.70/1.31 ! [X: $i] :
% 1.70/1.31 ( ( in @ X @ A )
% 1.70/1.31 => ( subset @ X @ A ) ) ) ) ).
% 1.70/1.31
% 1.70/1.31 thf(setunionTransitive_type,type,
% 1.70/1.31 setunionTransitive: $o ).
% 1.70/1.31
% 1.70/1.31 thf(setunionTransitive,definition,
% 1.70/1.31 ( setunionTransitive
% 1.70/1.31 = ( ! [X: $i] :
% 1.70/1.31 ( ! [Xx: $i] :
% 1.70/1.31 ( ( in @ Xx @ X )
% 1.70/1.31 => ( transitiveset @ Xx ) )
% 1.70/1.31 => ( transitiveset @ ( setunion @ X ) ) ) ) ) ).
% 1.70/1.31
% 1.70/1.31 thf(stricttotalorderedByIn_type,type,
% 1.70/1.31 stricttotalorderedByIn: $i > $o ).
% 1.70/1.31
% 1.70/1.31 thf(stricttotalorderedByIn,definition,
% 1.70/1.31 ( stricttotalorderedByIn
% 1.70/1.31 = ( ^ [A: $i] :
% 1.70/1.31 ( ! [Xx: $i] :
% 1.70/1.31 ( ( in @ Xx @ A )
% 1.70/1.31 => ! [X: $i] :
% 1.70/1.31 ( ( in @ X @ A )
% 1.70/1.31 => ! [Y: $i] :
% 1.70/1.31 ( ( in @ Y @ A )
% 1.70/1.31 => ( ( ( in @ Xx @ X )
% 1.70/1.31 & ( in @ X @ Y ) )
% 1.70/1.31 => ( in @ Xx @ Y ) ) ) ) )
% 1.70/1.31 & ! [X: $i] :
% 1.70/1.31 ( ( in @ X @ A )
% 1.70/1.31 => ! [Y: $i] :
% 1.70/1.31 ( ( in @ Y @ A )
% 1.70/1.31 => ( ( X = Y )
% 1.70/1.31 | ( in @ X @ Y )
% 1.70/1.31 | ( in @ Y @ X ) ) ) )
% 1.70/1.31 & ! [X: $i] :
% 1.70/1.31 ( ( in @ X @ A )
% 1.70/1.31 => ~ ( in @ X @ X ) ) ) ) ) ).
% 1.70/1.31
% 1.70/1.31 thf(wellorderedByIn_type,type,
% 1.70/1.31 wellorderedByIn: $i > $o ).
% 1.70/1.31
% 1.70/1.31 thf(wellorderedByIn,definition,
% 1.70/1.31 ( wellorderedByIn
% 1.70/1.31 = ( ^ [A: $i] :
% 1.70/1.31 ( ( stricttotalorderedByIn @ A )
% 1.70/1.31 & ! [X: $i] :
% 1.70/1.31 ( ( in @ X @ ( powerset @ A ) )
% 1.70/1.31 => ( ( nonempty @ X )
% 1.70/1.31 => ? [Xx: $i] :
% 1.70/1.31 ( ( in @ Xx @ X )
% 1.70/1.31 & ! [Y: $i] :
% 1.70/1.31 ( ( in @ Y @ X )
% 1.70/1.31 => ( ( Xx = Y )
% 1.70/1.31 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 1.70/1.31
% 1.70/1.31 thf(ordinal_type,type,
% 1.70/1.31 ordinal: $i > $o ).
% 1.70/1.31
% 1.70/1.31 thf(ordinal,definition,
% 1.70/1.31 ( ordinal
% 1.70/1.31 = ( ^ [Xx: $i] :
% 1.70/1.31 ( ( transitiveset @ Xx )
% 1.70/1.31 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 1.70/1.31
% 1.70/1.31 thf(setunionOrdinalLem1,conjecture,
% 1.70/1.31 ( setunionTransitive
% 1.70/1.31 => ! [X: $i] :
% 1.70/1.31 ( ! [Xx: $i] :
% 1.70/1.31 ( ( in @ Xx @ X )
% 1.70/1.31 => ( ordinal @ Xx ) )
% 1.70/1.31 => ( transitiveset @ ( setunion @ X ) ) ) ) ).
% 1.70/1.31 ------------------------
% 1.70/1.32 % (20919)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_20768 for (3000ds/18Mi)
% 1.70/1.33 % (20914)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_20768 for (3000ds/4Mi)
% 1.70/1.33 % (20919)Instruction limit reached!
% 1.70/1.33 % (20919)------------------------------
% 1.70/1.33 % (20919)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (20919)Termination reason: Unknown
% 1.70/1.33 % (20919)Termination phase: Saturation
% 1.70/1.33
% 1.70/1.33 % (20919)Memory used [KB]: 5628
% 1.70/1.33 % (20919)Time elapsed: 0.008 s
% 1.70/1.33 % (20919)Instructions burned: 19 (million)
% 1.70/1.33 % (20919)------------------------------
% 1.70/1.33 % (20919)------------------------------
% 1.70/1.33 % (20914)Instruction limit reached!
% 1.70/1.33 % (20914)------------------------------
% 1.70/1.33 % (20914)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (20914)Termination reason: Unknown
% 1.70/1.33 % (20914)Termination phase: Function definition elimination
% 1.70/1.33 % (20915)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_20768 for (3000ds/27Mi)
% 1.70/1.33
% 1.70/1.33 % (20914)Memory used [KB]: 1023
% 1.70/1.33 % (20914)Time elapsed: 0.004 s
% 1.70/1.33 % (20914)Instructions burned: 4 (million)
% 1.70/1.33 % (20914)------------------------------
% 1.70/1.33 % (20914)------------------------------
% 1.70/1.33 % (20917)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_20768 for (3000ds/2Mi)
% 1.70/1.33 % (20917)Instruction limit reached!
% 1.70/1.33 % (20917)------------------------------
% 1.70/1.33 % (20917)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.33 % (20917)Termination reason: Unknown
% 1.70/1.33 % (20917)Termination phase: Property scanning
% 1.70/1.33
% 1.70/1.33 % (20917)Memory used [KB]: 1023
% 1.70/1.33 % (20917)Time elapsed: 0.003 s
% 1.70/1.33 % (20917)Instructions burned: 3 (million)
% 1.70/1.33 % (20917)------------------------------
% 1.70/1.33 % (20917)------------------------------
% 1.70/1.33 % (20913)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_20768 for (3000ds/183Mi)
% 1.70/1.33 % (20918)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_20768 for (3000ds/275Mi)
% 1.70/1.34 % (20916)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_20768 for (3000ds/2Mi)
% 1.70/1.34 % (20916)Instruction limit reached!
% 1.70/1.34 % (20916)------------------------------
% 1.70/1.34 % (20916)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (20916)Termination reason: Unknown
% 1.70/1.34 % (20916)Termination phase: shuffling
% 1.70/1.34
% 1.70/1.34 % (20916)Memory used [KB]: 1023
% 1.70/1.34 % (20916)Time elapsed: 0.003 s
% 1.70/1.34 % (20916)Instructions burned: 2 (million)
% 1.70/1.34 % (20916)------------------------------
% 1.70/1.34 % (20916)------------------------------
% 1.70/1.34 % (20918)First to succeed.
% 1.70/1.34 % (20915)Also succeeded, but the first one will report.
% 1.70/1.34 % (20918)Refutation found. Thanks to Tanya!
% 1.70/1.34 % SZS status Theorem for DTF2THF_20768
% 1.70/1.34 % SZS output start Proof for DTF2THF_20768
% 1.70/1.34 thf(func_def_0, type, in: $i > $i > $o).
% 1.70/1.34 thf(func_def_2, type, powerset: $i > $i).
% 1.70/1.34 thf(func_def_3, type, setunion: $i > $i).
% 1.70/1.34 thf(func_def_4, type, nonempty: $i > $o).
% 1.70/1.34 thf(func_def_5, type, subset: $i > $i > $o).
% 1.70/1.34 thf(func_def_6, type, transitiveset: $i > $o).
% 1.70/1.34 thf(func_def_9, type, stricttotalorderedByIn: $i > $o).
% 1.70/1.34 thf(func_def_10, type, wellorderedByIn: $i > $o).
% 1.70/1.34 thf(func_def_11, type, ordinal: $i > $o).
% 1.70/1.34 thf(func_def_27, type, sK1: $i > $i).
% 1.70/1.34 thf(f58,plain,(
% 1.70/1.34 $false),
% 1.70/1.34 inference(subsumption_resolution,[status(thm)],[f57,f51])).
% 1.70/1.34 thf(f51,plain,(
% 1.70/1.34 ((transitiveset @ (sK1 @ sK0)) != $true)),
% 1.70/1.34 inference(trivial_inequality_removal,[status(thm)],[f50])).
% 1.70/1.34 thf(f50,plain,(
% 1.70/1.34 ((transitiveset @ (sK1 @ sK0)) != $true) | ($true != $true)),
% 1.70/1.34 inference(superposition,[status(thm)],[f34,f45])).
% 1.70/1.34 thf(f45,plain,(
% 1.70/1.34 ( ! [X0 : $i] : (((transitiveset @ (setunion @ X0)) = $true) | ((transitiveset @ (sK1 @ X0)) != $true)) )),
% 1.70/1.34 inference(trivial_inequality_removal,[status(thm)],[f42])).
% 1.70/1.34 thf(f42,plain,(
% 1.70/1.34 ( ! [X0 : $i] : (((transitiveset @ (sK1 @ X0)) != $true) | ($true != $true) | ((transitiveset @ (setunion @ X0)) = $true)) )),
% 1.70/1.34 inference(definition_unfolding,[status(thm)],[f38,f33])).
% 1.70/1.34 thf(f33,plain,(
% 1.70/1.34 (setunionTransitive = $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f26])).
% 1.70/1.34 thf(f26,plain,(
% 1.70/1.34 (! [X1 : $i] : (($true != (in @ X1 @ sK0)) | ((ordinal @ X1) = $true)) & ((transitiveset @ (setunion @ sK0)) != $true)) & (setunionTransitive = $true)),
% 1.70/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f24,f25])).
% 1.70/1.34 thf(f25,plain,(
% 1.70/1.34 ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0) != $true) | ((ordinal @ X1) = $true)) & ((transitiveset @ (setunion @ X0)) != $true)) => (! [X1 : $i] : (($true != (in @ X1 @ sK0)) | ((ordinal @ X1) = $true)) & ((transitiveset @ (setunion @ sK0)) != $true))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f24,plain,(
% 1.70/1.34 ? [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0) != $true) | ((ordinal @ X1) = $true)) & ((transitiveset @ (setunion @ X0)) != $true)) & (setunionTransitive = $true)),
% 1.70/1.34 inference(ennf_transformation,[status(thm)],[f15])).
% 1.70/1.34 thf(f15,plain,(
% 1.70/1.34 ~((setunionTransitive = $true) => ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0) = $true) => ((ordinal @ X1) = $true)) => ((transitiveset @ (setunion @ X0)) = $true)))),
% 1.70/1.34 inference(fool_elimination,[status(thm)],[f14])).
% 1.70/1.34 thf(f14,plain,(
% 1.70/1.34 ~(setunionTransitive => ! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (ordinal @ X1)) => (transitiveset @ (setunion @ X0))))),
% 1.70/1.34 inference(rectify,[status(thm)],[f8])).
% 1.70/1.34 thf(f8,negated_conjecture,(
% 1.70/1.34 ~(setunionTransitive => ! [X2 : $i] : (! [X0 : $i] : ((in @ X0 @ X2) => (ordinal @ X0)) => (transitiveset @ (setunion @ X2))))),
% 1.70/1.34 inference(negated_conjecture,[status(cth)],[f7])).
% 1.70/1.34 thf(f7,conjecture,(
% 1.70/1.34 setunionTransitive => ! [X2 : $i] : (! [X0 : $i] : ((in @ X0 @ X2) => (ordinal @ X0)) => (transitiveset @ (setunion @ X2)))),
% 1.70/1.34 file('/export/starexec/sandbox2/tmp/tmp.PPk0UYlczK/DTF2THF_20768.p',setunionOrdinalLem1)).
% 1.70/1.34 thf(f38,plain,(
% 1.70/1.34 ( ! [X0 : $i] : (((transitiveset @ (setunion @ X0)) = $true) | ((transitiveset @ (sK1 @ X0)) != $true) | (setunionTransitive != $true)) )),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f31])).
% 1.70/1.34 thf(f31,plain,(
% 1.70/1.34 (! [X0 : $i] : (((transitiveset @ (setunion @ X0)) = $true) | (((in @ (sK1 @ X0) @ X0) = $true) & ((transitiveset @ (sK1 @ X0)) != $true))) | (setunionTransitive != $true)) & ((setunionTransitive = $true) | (((transitiveset @ (setunion @ sK2)) != $true) & ! [X3 : $i] : (($true != (in @ X3 @ sK2)) | ($true = (transitiveset @ X3)))))),
% 1.70/1.34 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2])],[f28,f30,f29])).
% 1.70/1.34 thf(f29,plain,(
% 1.70/1.34 ! [X0 : $i] : (? [X1 : $i] : (((in @ X1 @ X0) = $true) & ($true != (transitiveset @ X1))) => (((in @ (sK1 @ X0) @ X0) = $true) & ((transitiveset @ (sK1 @ X0)) != $true)))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f30,plain,(
% 1.70/1.34 ? [X2 : $i] : (((transitiveset @ (setunion @ X2)) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) != $true) | ($true = (transitiveset @ X3)))) => (((transitiveset @ (setunion @ sK2)) != $true) & ! [X3 : $i] : (($true != (in @ X3 @ sK2)) | ($true = (transitiveset @ X3))))),
% 1.70/1.34 introduced(definition,[],[choice_axiom])).
% 1.70/1.34 thf(f28,plain,(
% 1.70/1.34 (! [X0 : $i] : (((transitiveset @ (setunion @ X0)) = $true) | ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ($true != (transitiveset @ X1)))) | (setunionTransitive != $true)) & ((setunionTransitive = $true) | ? [X2 : $i] : (((transitiveset @ (setunion @ X2)) != $true) & ! [X3 : $i] : (((in @ X3 @ X2) != $true) | ($true = (transitiveset @ X3)))))),
% 1.70/1.34 inference(rectify,[status(thm)],[f27])).
% 1.70/1.34 thf(f27,plain,(
% 1.70/1.34 (! [X0 : $i] : (((transitiveset @ (setunion @ X0)) = $true) | ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ($true != (transitiveset @ X1)))) | (setunionTransitive != $true)) & ((setunionTransitive = $true) | ? [X0 : $i] : (((transitiveset @ (setunion @ X0)) != $true) & ! [X1 : $i] : (((in @ X1 @ X0) != $true) | ($true = (transitiveset @ X1)))))),
% 1.70/1.34 inference(nnf_transformation,[status(thm)],[f23])).
% 1.70/1.34 thf(f23,plain,(
% 1.70/1.34 ! [X0 : $i] : (((transitiveset @ (setunion @ X0)) = $true) | ? [X1 : $i] : (((in @ X1 @ X0) = $true) & ($true != (transitiveset @ X1)))) <=> (setunionTransitive = $true)),
% 1.70/1.34 inference(ennf_transformation,[status(thm)],[f20])).
% 1.70/1.34 thf(f20,plain,(
% 1.70/1.34 ! [X0 : $i] : (! [X1 : $i] : (((in @ X1 @ X0) = $true) => ($true = (transitiveset @ X1))) => ((transitiveset @ (setunion @ X0)) = $true)) <=> (setunionTransitive = $true)),
% 1.70/1.34 inference(fool_elimination,[status(thm)],[f19])).
% 1.70/1.34 thf(f19,plain,(
% 1.70/1.34 (! [X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (transitiveset @ X1)) => (transitiveset @ (setunion @ X0))) = setunionTransitive)),
% 1.70/1.34 inference(rectify,[status(thm)],[f3])).
% 1.70/1.34 thf(f3,axiom,(
% 1.70/1.34 (! [X2 : $i] : (! [X0 : $i] : ((in @ X0 @ X2) => (transitiveset @ X0)) => (transitiveset @ (setunion @ X2))) = setunionTransitive)),
% 1.70/1.34 file('/export/starexec/sandbox2/tmp/tmp.PPk0UYlczK/DTF2THF_20768.p',setunionTransitive)).
% 1.70/1.34 thf(f34,plain,(
% 1.70/1.34 ((transitiveset @ (setunion @ sK0)) != $true)),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f26])).
% 1.70/1.34 thf(f57,plain,(
% 1.70/1.34 ((transitiveset @ (sK1 @ sK0)) = $true)),
% 1.70/1.34 inference(subsumption_resolution,[status(thm)],[f56,f34])).
% 1.70/1.34 thf(f56,plain,(
% 1.70/1.34 ((transitiveset @ (setunion @ sK0)) = $true) | ((transitiveset @ (sK1 @ sK0)) = $true)),
% 1.70/1.34 inference(trivial_inequality_removal,[status(thm)],[f55])).
% 1.70/1.34 thf(f55,plain,(
% 1.70/1.34 ((transitiveset @ (setunion @ sK0)) = $true) | ((transitiveset @ (sK1 @ sK0)) = $true) | ($true != $true)),
% 1.70/1.34 inference(superposition,[status(thm)],[f49,f46])).
% 1.70/1.34 thf(f46,plain,(
% 1.70/1.34 ( ! [X0 : $i] : (((in @ (sK1 @ X0) @ X0) = $true) | ((transitiveset @ (setunion @ X0)) = $true)) )),
% 1.70/1.34 inference(trivial_inequality_removal,[status(thm)],[f41])).
% 1.70/1.34 thf(f41,plain,(
% 1.70/1.34 ( ! [X0 : $i] : (((in @ (sK1 @ X0) @ X0) = $true) | ((transitiveset @ (setunion @ X0)) = $true) | ($true != $true)) )),
% 1.70/1.34 inference(definition_unfolding,[status(thm)],[f39,f33])).
% 1.70/1.34 thf(f39,plain,(
% 1.70/1.34 ( ! [X0 : $i] : (((transitiveset @ (setunion @ X0)) = $true) | ((in @ (sK1 @ X0) @ X0) = $true) | (setunionTransitive != $true)) )),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f31])).
% 1.70/1.34 thf(f49,plain,(
% 1.70/1.34 ( ! [X1 : $i] : (($true != (in @ X1 @ sK0)) | ($true = (transitiveset @ X1))) )),
% 1.70/1.34 inference(binary_proxy_clausification,[status(thm)],[f47])).
% 1.70/1.34 thf(f47,plain,(
% 1.70/1.34 ( ! [X1 : $i] : (($true = ((transitiveset @ X1) & (wellorderedByIn @ X1))) | ($true != (in @ X1 @ sK0))) )),
% 1.70/1.34 inference(beta_eta_normalization,[status(thm)],[f40])).
% 1.70/1.34 thf(f40,plain,(
% 1.70/1.34 ( ! [X1 : $i] : (($true != (in @ X1 @ sK0)) | (((^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))) @ X1) = $true)) )),
% 1.70/1.34 inference(definition_unfolding,[status(thm)],[f35,f32])).
% 1.70/1.34 thf(f32,plain,(
% 1.70/1.34 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))))),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f22])).
% 1.70/1.34 thf(f22,plain,(
% 1.70/1.34 (ordinal = (^[Y0 : $i]: ((transitiveset @ Y0) & (wellorderedByIn @ Y0))))),
% 1.70/1.34 inference(fool_elimination,[status(thm)],[f21])).
% 1.70/1.34 thf(f21,plain,(
% 1.70/1.34 ((^[X0 : $i] : ((wellorderedByIn @ X0) & (transitiveset @ X0))) = ordinal)),
% 1.70/1.34 inference(rectify,[status(thm)],[f6])).
% 1.70/1.34 thf(f6,axiom,(
% 1.70/1.34 ((^[X0 : $i] : ((wellorderedByIn @ X0) & (transitiveset @ X0))) = ordinal)),
% 1.70/1.34 file('/export/starexec/sandbox2/tmp/tmp.PPk0UYlczK/DTF2THF_20768.p',ordinal)).
% 1.70/1.34 thf(f35,plain,(
% 1.70/1.34 ( ! [X1 : $i] : (($true != (in @ X1 @ sK0)) | ((ordinal @ X1) = $true)) )),
% 1.70/1.34 inference(cnf_transformation,[status(thm)],[f26])).
% 1.70/1.34 % SZS output end Proof for DTF2THF_20768
% 1.70/1.34 % (20918)------------------------------
% 1.70/1.34 % (20918)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.70/1.34 % (20918)Termination reason: Refutation
% 1.70/1.34
% 1.70/1.34 % (20918)Memory used [KB]: 5500
% 1.70/1.34 % (20918)Time elapsed: 0.006 s
% 1.70/1.34 % (20918)Instructions burned: 5 (million)
% 1.70/1.34 % (20918)------------------------------
% 1.70/1.34 % (20918)------------------------------
% 1.70/1.34 % (20912)Success in time 0.026 s
%------------------------------------------------------------------------------