%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU817^2 : 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 : n012.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 09:37:28 AM UTC 2026
% Result : Theorem 1.64s 1.35s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 48 ( 23 unt; 0 typ; 0 def)
% Number of atoms : 473 ( 123 equ; 0 cnn)
% Maximal formula atoms : 8 ( 9 avg)
% Number of connectives : 434 ( 47 ~; 32 |; 42 &; 269 @)
% ( 3 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 19 ( 15 usr; 10 con; 0-2 aty)
% ( 6 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 95 ( 19 ^; 54 !; 22 ?; 95 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
in: $i > $i > $o ).
thf(func_def_2,type,
powerset: $i > $i ).
thf(func_def_3,type,
nonempty: $i > $o ).
thf(func_def_4,type,
subset: $i > $i > $o ).
thf(func_def_7,type,
transitiveset: $i > $o ).
thf(func_def_8,type,
stricttotalorderedByIn: $i > $o ).
thf(func_def_9,type,
wellorderedByIn: $i > $o ).
thf(func_def_10,type,
ordinal: $i > $o ).
thf(f71,plain,
$false,
inference(subsumption_resolution,[status(thm)],[f69,f37]) ).
thf(f37,plain,
( ( in @ sK2 @ sK1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( ( subsetE = $true )
& ( $true
= ( ordinal @ sK0 ) )
& ( ( in @ sK2 @ sK1 )
= $true )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK2 @ sK0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f28,f27]) ).
thf(f27,plain,
( ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X2 @ X0 ) ) ) )
=> ( ( $true
= ( ordinal @ sK0 ) )
& ? [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X1 @ sK0 ) )
& ( $true
!= ( in @ X2 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f28,plain,
( ? [X2: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X1 @ sK0 ) )
& ( $true
!= ( in @ X2 @ sK0 ) ) )
=> ( ( ( in @ sK2 @ sK1 )
= $true )
& ( $true
= ( in @ sK1 @ sK0 ) )
& ( ( in @ sK2 @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ( subsetE = $true )
& ? [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
& ? [X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X1 @ X0 ) )
& ( $true
!= ( in @ X2 @ X0 ) ) ) ) ),
inference(flattening,[status(thm)],[f23]) ).
thf(f23,plain,
( ? [X0: $i] :
( ? [X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
& ( ( in @ X2 @ X1 )
= $true )
& ( $true
= ( in @ X1 @ X0 ) ) )
& ( ( ordinal @ X0 )
= $true ) )
& ( subsetE = $true ) ),
inference(ennf_transformation,[status(thm)],[f16]) ).
thf(f16,plain,
~ ( ( subsetE = $true )
=> ! [X0: $i] :
( ( ( ordinal @ X0 )
= $true )
=> ! [X1: $i,X2: $i] :
( ( $true
= ( in @ X1 @ X0 ) )
=> ( ( ( in @ X2 @ X1 )
= $true )
=> ( $true
= ( in @ X2 @ X0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f15]) ).
thf(f15,plain,
~ ( subsetE
=> ! [X0: $i] :
( ( ordinal @ X0 )
=> ! [X1: $i,X2: $i] :
( ( in @ X1 @ X0 )
=> ( ( in @ X2 @ X1 )
=> ( in @ X2 @ X0 ) ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,negated_conjecture,
~ ( subsetE
=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
thf(f7,conjecture,
( subsetE
=> ! [X3: $i] :
( ( ordinal @ X3 )
=> ! [X1: $i,X0: $i] :
( ( in @ X1 @ X3 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2THF_24881.p',ordinalTransSet) ).
thf(f69,plain,
( ( in @ sK2 @ sK1 )
!= $true ),
inference(trivial_inequality_removal,[status(thm)],[f65]) ).
thf(f65,plain,
( ( $false = $true )
| ( ( in @ sK2 @ sK1 )
!= $true ) ),
inference(superposition,[status(thm)],[f36,f61]) ).
thf(f61,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
!= ( in @ sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f60]) ).
thf(f60,plain,
! [X0: $i] :
( ( $false
= ( in @ X0 @ sK0 ) )
| ( $true
!= ( in @ sK2 @ X0 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f59,f57]) ).
thf(f57,plain,
! [X1: $i] :
( ( $true
= ( subset @ X1 @ sK0 ) )
| ( $false
= ( in @ X1 @ sK0 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f56]) ).
thf(f56,plain,
! [X1: $i] :
( $true
= ( ( in @ X1 @ sK0 )
=> ( subset @ X1 @ sK0 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f53]) ).
thf(f53,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ( wellorderedByIn @ sK0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( in @ Y0 @ sK0 )
=> ( subset @ Y0 @ sK0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f46]) ).
thf(f46,plain,
( $true
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 ) )
@ sK0 ) ),
inference(definition_unfolding,[status(thm)],[f38,f45]) ).
thf(f45,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( in @ Y2 @ Y1 )
=> ( subset @ Y2 @ Y1 ) ) )
@ Y0 ) ) ) ),
inference(definition_unfolding,[status(thm)],[f34,f44]) ).
thf(f44,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
( transitiveset
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( in @ Y1 @ Y0 )
=> ( subset @ Y1 @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f19]) ).
thf(f19,plain,
( ( ^ [X0: $i] :
! [X1: $i] :
( ( in @ X1 @ X0 )
=> ( subset @ X1 @ X0 ) ) )
= transitiveset ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: $i] :
! [X3: $i] :
( ( in @ X3 @ X1 )
=> ( subset @ X3 @ X1 ) ) )
= transitiveset ),
file('/export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2THF_24881.p',transitiveset) ).
thf(f34,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ordinal
= ( ^ [Y0: $i] :
( ( wellorderedByIn @ Y0 )
& ( transitiveset @ Y0 ) ) ) ),
inference(fool_elimination,[status(thm)],[f13]) ).
thf(f13,plain,
( ordinal
= ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ordinal
= ( ^ [X0: $i] :
( ( transitiveset @ X0 )
& ( wellorderedByIn @ X0 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2THF_24881.p',ordinal) ).
thf(f38,plain,
( $true
= ( ordinal @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f59,plain,
! [X0: $i] :
( ( $true
!= ( subset @ X0 @ sK0 ) )
| ( $true
!= ( in @ sK2 @ X0 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f58]) ).
thf(f58,plain,
! [X0: $i] :
( ( $true
!= ( in @ sK2 @ X0 ) )
| ( $true != $true )
| ( $true
!= ( subset @ X0 @ sK0 ) ) ),
inference(superposition,[status(thm)],[f35,f51]) ).
thf(f51,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ X0 ) )
| ( $true
!= ( subset @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f47]) ).
thf(f47,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( $true != $true )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( subset @ X0 @ X1 ) ) ),
inference(definition_unfolding,[status(thm)],[f43,f39]) ).
thf(f39,plain,
subsetE = $true,
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f43,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( subset @ X0 @ X1 ) )
| ( subsetE != $true ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( subset @ X0 @ X1 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ( ( $true
= ( in @ sK5 @ sK3 ) )
& ( ( in @ sK5 @ sK4 )
!= $true )
& ( $true
= ( subset @ sK3 @ sK4 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f31,f32]) ).
thf(f32,plain,
( ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( $true
!= ( in @ X5 @ X4 ) )
& ( $true
= ( subset @ X3 @ X4 ) ) )
=> ( ( $true
= ( in @ sK5 @ sK3 ) )
& ( ( in @ sK5 @ sK4 )
!= $true )
& ( $true
= ( subset @ sK3 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f31,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( subset @ X0 @ X1 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X3: $i,X4: $i,X5: $i] :
( ( ( in @ X5 @ X3 )
= $true )
& ( $true
!= ( in @ X5 @ X4 ) )
& ( $true
= ( subset @ X3 @ X4 ) ) ) ) ),
inference(rectify,[status(thm)],[f30]) ).
thf(f30,plain,
( ( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( subset @ X0 @ X1 ) ) )
| ( subsetE != $true ) )
& ( ( subsetE = $true )
| ? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( in @ X2 @ X0 ) )
& ( ( in @ X2 @ X1 )
!= $true )
& ( $true
= ( subset @ X0 @ X1 ) ) ) ) ),
inference(nnf_transformation,[status(thm)],[f26]) ).
thf(f26,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( $true
!= ( in @ X2 @ X0 ) )
| ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( subset @ X0 @ X1 ) ) )
<=> ( subsetE = $true ) ),
inference(flattening,[status(thm)],[f25]) ).
thf(f25,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( ( in @ X2 @ X1 )
= $true )
| ( $true
!= ( in @ X2 @ X0 ) )
| ( $true
!= ( subset @ X0 @ X1 ) ) ) ),
inference(ennf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ( subsetE = $true )
<=> ! [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( subset @ X0 @ X1 ) )
=> ( ( $true
= ( in @ X2 @ X0 ) )
=> ( ( in @ X2 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( ( subset @ X0 @ X1 )
=> ( ( in @ X2 @ X0 )
=> ( in @ X2 @ X1 ) ) )
= subsetE ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X1: $i,X2: $i,X0: $i] :
( ( ( subset @ X1 @ X2 )
=> ( ( in @ X0 @ X1 )
=> ( in @ X0 @ X2 ) ) )
= subsetE ),
file('/export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2THF_24881.p',subsetE) ).
thf(f35,plain,
( ( in @ sK2 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f36,plain,
( $true
= ( in @ sK1 @ sK0 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU817^2 : TPTP v9.2.1. Released v3.7.0.
% 0.00/0.10 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.12/0.29 % Computer : n012.cluster.edu
% 0.12/0.29 % Model : x86_64 x86_64
% 0.12/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.29 % Memory : 8042.1875MB
% 0.12/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.29 % CPULimit : 300
% 0.12/0.29 % WCLimit : 300
% 0.12/0.29 % DateTime : Tue Feb 24 12:34:45 EST 2026
% 0.12/0.29 % CPUTime :
% 0.12/0.29 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.39 ---- Original DTF file ---
% 0.19/0.39 thf(spec,logic,$$dhol).
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 % File : SEU817^2 : TPTP v9.2.1. Released v3.7.0.
% 0.19/0.39 % Domain : Set Theory
% 0.19/0.39 % Problem : Ordinals
% 0.19/0.39 % Version : Especial > Reduced > Especial.
% 0.19/0.39 % English : (! X:i.ordinal X -> (! x:i.! A:i.in A X -> in x A -> in x X))
% 0.19/0.39
% 0.19/0.39 % Refs : [Bro08] Brown (2008), Email to G. Sutcliffe
% 0.19/0.39 % Source : [Bro08]
% 0.19/0.39 % Names : ZFC319l [Bro08]
% 0.19/0.39
% 0.19/0.39 % Status : Theorem
% 0.19/0.39 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.00 v7.1.0, 0.12 v7.0.0, 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
% 0.19/0.39 % Syntax : Number of formulae : 17 ( 6 unt; 10 typ; 6 def)
% 0.19/0.39 % Number of atoms : 45 ( 9 equ; 0 cnn)
% 0.19/0.39 % Maximal formula atoms : 5 ( 6 avg)
% 0.19/0.39 % Number of connectives : 82 ( 2 ~; 3 |; 6 &; 54 @)
% 0.19/0.39 % ( 0 <=>; 17 =>; 0 <=; 0 <~>)
% 0.19/0.39 % Maximal formula depth : 10 ( 2 avg)
% 0.19/0.39 % Number of types : 2 ( 0 usr)
% 0.19/0.39 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.19/0.39 % Number of symbols : 11 ( 10 usr; 2 con; 0-2 aty)
% 0.19/0.39 % Number of variables : 21 ( 5 ^; 15 !; 1 ?; 21 :)
% 0.19/0.39 % SPC : TH0_THM_EQU_NAR
% 0.19/0.39
% 0.19/0.39 % Comments : http://mathgate.info/detsetitem.php?id=513
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 thf(in_type,type,
% 0.19/0.39 in: $i > $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(emptyset_type,type,
% 0.19/0.39 emptyset: $i ).
% 0.19/0.39
% 0.19/0.39 thf(powerset_type,type,
% 0.19/0.39 powerset: $i > $i ).
% 0.19/0.39
% 0.19/0.39 thf(nonempty_type,type,
% 0.19/0.39 nonempty: $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(nonempty,definition,
% 0.19/0.39 ( nonempty
% 0.19/0.39 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(subset_type,type,
% 0.19/0.39 subset: $i > $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetE_type,type,
% 0.19/0.39 subsetE: $o ).
% 0.19/0.39
% 0.19/0.39 thf(subsetE,definition,
% 0.19/0.39 ( subsetE
% 0.19/0.39 = ( ! [A: $i,B: $i,Xx: $i] :
% 0.19/0.39 ( ( subset @ A @ B )
% 0.19/0.39 => ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xx @ B ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(transitiveset_type,type,
% 0.19/0.39 transitiveset: $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(transitiveset,definition,
% 0.19/0.39 ( transitiveset
% 0.19/0.39 = ( ^ [A: $i] :
% 0.19/0.39 ! [X: $i] :
% 0.19/0.39 ( ( in @ X @ A )
% 0.19/0.39 => ( subset @ X @ A ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(stricttotalorderedByIn_type,type,
% 0.19/0.39 stricttotalorderedByIn: $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(stricttotalorderedByIn,definition,
% 0.19/0.39 ( stricttotalorderedByIn
% 0.19/0.39 = ( ^ [A: $i] :
% 0.19/0.39 ( ! [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ A )
% 0.19/0.39 => ! [X: $i] :
% 0.19/0.39 ( ( in @ X @ A )
% 0.19/0.39 => ! [Y: $i] :
% 0.19/0.39 ( ( in @ Y @ A )
% 0.19/0.39 => ( ( ( in @ Xx @ X )
% 0.19/0.39 & ( in @ X @ Y ) )
% 0.19/0.39 => ( in @ Xx @ Y ) ) ) ) )
% 0.19/0.39 & ! [X: $i] :
% 0.19/0.39 ( ( in @ X @ A )
% 0.19/0.39 => ! [Y: $i] :
% 0.19/0.39 ( ( in @ Y @ A )
% 0.19/0.39 => ( ( X = Y )
% 0.19/0.39 | ( in @ X @ Y )
% 0.19/0.39 | ( in @ Y @ X ) ) ) )
% 0.19/0.39 & ! [X: $i] :
% 0.19/0.39 ( ( in @ X @ A )
% 0.19/0.39 => ~ ( in @ X @ X ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(wellorderedByIn_type,type,
% 0.19/0.39 wellorderedByIn: $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(wellorderedByIn,definition,
% 0.19/0.39 ( wellorderedByIn
% 0.19/0.39 = ( ^ [A: $i] :
% 0.19/0.39 ( ( stricttotalorderedByIn @ A )
% 0.19/0.39 & ! [X: $i] :
% 0.19/0.39 ( ( in @ X @ ( powerset @ A ) )
% 0.19/0.39 => ( ( nonempty @ X )
% 0.19/0.39 => ? [Xx: $i] :
% 0.19/0.39 ( ( in @ Xx @ X )
% 0.19/0.39 & ! [Y: $i] :
% 0.19/0.39 ( ( in @ Y @ X )
% 0.19/0.39 => ( ( Xx = Y )
% 0.19/0.39 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(ordinal_type,type,
% 0.19/0.39 ordinal: $i > $o ).
% 0.19/0.39
% 0.19/0.39 thf(ordinal,definition,
% 0.19/0.39 ( ordinal
% 0.19/0.39 = ( ^ [Xx: $i] :
% 0.19/0.39 ( ( transitiveset @ Xx )
% 0.19/0.39 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 thf(ordinalTransSet,conjecture,
% 0.19/0.39 ( subsetE
% 0.19/0.39 => ! [X: $i] :
% 0.19/0.39 ( ( ordinal @ X )
% 0.19/0.39 => ! [Xx: $i,A: $i] :
% 0.19/0.39 ( ( in @ A @ X )
% 0.19/0.39 => ( ( in @ Xx @ A )
% 0.19/0.39 => ( in @ Xx @ X ) ) ) ) ) ).
% 0.19/0.39
% 0.19/0.39 %------------------------------------------------------------------------------
% 0.19/0.39 ------------------------
% 1.64/1.31 ---- Embedded in THF ---
% 1.64/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.31 %%% Generated on Tue Feb 24 12:34:46 EST 2026
% 1.64/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.31 %%% Logic specification used:
% 1.64/1.31 %%% thf(spec, logic, $$dhol).
% 1.64/1.31
% 1.64/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2DTF24881.p
% See solution above
% 1.64/1.31 ------------------------
% 1.64/1.32 ---- Cleaned THF ---
% 1.64/1.32 thf(in_type,type,
% 1.64/1.32 in: $i > $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(emptyset_type,type,
% 1.64/1.32 emptyset: $i ).
% 1.64/1.32
% 1.64/1.32 thf(powerset_type,type,
% 1.64/1.32 powerset: $i > $i ).
% 1.64/1.32
% 1.64/1.32 thf(nonempty_type,type,
% 1.64/1.32 nonempty: $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(nonempty,definition,
% 1.64/1.32 ( nonempty
% 1.64/1.32 = ( ^ [Xx: $i] : ( Xx != emptyset ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(subset_type,type,
% 1.64/1.32 subset: $i > $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(subsetE_type,type,
% 1.64/1.32 subsetE: $o ).
% 1.64/1.32
% 1.64/1.32 thf(subsetE,definition,
% 1.64/1.32 ( subsetE
% 1.64/1.32 = ( ! [A: $i,B: $i,Xx: $i] :
% 1.64/1.32 ( ( subset @ A @ B )
% 1.64/1.32 => ( ( in @ Xx @ A )
% 1.64/1.32 => ( in @ Xx @ B ) ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(transitiveset_type,type,
% 1.64/1.32 transitiveset: $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(transitiveset,definition,
% 1.64/1.32 ( transitiveset
% 1.64/1.32 = ( ^ [A: $i] :
% 1.64/1.32 ! [X: $i] :
% 1.64/1.32 ( ( in @ X @ A )
% 1.64/1.32 => ( subset @ X @ A ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(stricttotalorderedByIn_type,type,
% 1.64/1.32 stricttotalorderedByIn: $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(stricttotalorderedByIn,definition,
% 1.64/1.32 ( stricttotalorderedByIn
% 1.64/1.32 = ( ^ [A: $i] :
% 1.64/1.32 ( ! [Xx: $i] :
% 1.64/1.32 ( ( in @ Xx @ A )
% 1.64/1.32 => ! [X: $i] :
% 1.64/1.32 ( ( in @ X @ A )
% 1.64/1.32 => ! [Y: $i] :
% 1.64/1.32 ( ( in @ Y @ A )
% 1.64/1.32 => ( ( ( in @ Xx @ X )
% 1.64/1.32 & ( in @ X @ Y ) )
% 1.64/1.32 => ( in @ Xx @ Y ) ) ) ) )
% 1.64/1.32 & ! [X: $i] :
% 1.64/1.32 ( ( in @ X @ A )
% 1.64/1.32 => ! [Y: $i] :
% 1.64/1.32 ( ( in @ Y @ A )
% 1.64/1.32 => ( ( X = Y )
% 1.64/1.32 | ( in @ X @ Y )
% 1.64/1.32 | ( in @ Y @ X ) ) ) )
% 1.64/1.32 & ! [X: $i] :
% 1.64/1.32 ( ( in @ X @ A )
% 1.64/1.32 => ~ ( in @ X @ X ) ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(wellorderedByIn_type,type,
% 1.64/1.32 wellorderedByIn: $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(wellorderedByIn,definition,
% 1.64/1.32 ( wellorderedByIn
% 1.64/1.32 = ( ^ [A: $i] :
% 1.64/1.32 ( ( stricttotalorderedByIn @ A )
% 1.64/1.32 & ! [X: $i] :
% 1.64/1.32 ( ( in @ X @ ( powerset @ A ) )
% 1.64/1.32 => ( ( nonempty @ X )
% 1.64/1.32 => ? [Xx: $i] :
% 1.64/1.32 ( ( in @ Xx @ X )
% 1.64/1.32 & ! [Y: $i] :
% 1.64/1.32 ( ( in @ Y @ X )
% 1.64/1.32 => ( ( Xx = Y )
% 1.64/1.32 | ( in @ Xx @ Y ) ) ) ) ) ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(ordinal_type,type,
% 1.64/1.32 ordinal: $i > $o ).
% 1.64/1.32
% 1.64/1.32 thf(ordinal,definition,
% 1.64/1.32 ( ordinal
% 1.64/1.32 = ( ^ [Xx: $i] :
% 1.64/1.32 ( ( transitiveset @ Xx )
% 1.64/1.32 & ( wellorderedByIn @ Xx ) ) ) ) ).
% 1.64/1.32
% 1.64/1.32 thf(ordinalTransSet,conjecture,
% 1.64/1.32 ( subsetE
% 1.64/1.32 => ! [X: $i] :
% 1.64/1.32 ( ( ordinal @ X )
% 1.64/1.32 => ! [Xx: $i,A: $i] :
% 1.64/1.32 ( ( in @ A @ X )
% 1.64/1.32 => ( ( in @ Xx @ A )
% 1.64/1.32 => ( in @ Xx @ X ) ) ) ) ) ).
% 1.64/1.32 ------------------------
% 1.64/1.34 % (24980)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_24881 for (2999ds/4Mi)
% 1.64/1.34 % (24984)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_24881 for (2999ds/275Mi)
% 1.64/1.34 % (24982)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24881 for (2999ds/2Mi)
% 1.64/1.34 % (24983)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_24881 for (2999ds/2Mi)
% 1.64/1.34 % (24981)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_24881 for (2999ds/27Mi)
% 1.64/1.34 % (24979)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24881 for (2999ds/183Mi)
% 1.64/1.34 % (24985)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24881 for (2999ds/18Mi)
% 1.64/1.34 % (24982)Instruction limit reached!
% 1.64/1.34 % (24982)------------------------------
% 1.64/1.34 % (24982)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (24982)Termination reason: Unknown
% 1.64/1.34 % (24983)Instruction limit reached!
% 1.64/1.34 % (24983)------------------------------
% 1.64/1.34 % (24983)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (24982)Termination phase: shuffling
% 1.64/1.34
% 1.64/1.34 % (24982)Memory used [KB]: 895
% 1.64/1.34 % (24982)Time elapsed: 0.002 s
% 1.64/1.34 % (24982)Instructions burned: 2 (million)
% 1.64/1.34 % (24982)------------------------------
% 1.64/1.34 % (24982)------------------------------
% 1.64/1.34 % (24983)Termination reason: Unknown
% 1.64/1.34 % (24983)Termination phase: shuffling
% 1.64/1.34
% 1.64/1.34 % (24983)Memory used [KB]: 895
% 1.64/1.34 % (24983)Time elapsed: 0.002 s
% 1.64/1.34 % (24983)Instructions burned: 2 (million)
% 1.64/1.34 % (24983)------------------------------
% 1.64/1.34 % (24983)------------------------------
% 1.64/1.34 % (24980)Instruction limit reached!
% 1.64/1.34 % (24980)------------------------------
% 1.64/1.34 % (24980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.34 % (24980)Termination reason: Unknown
% 1.64/1.34 % (24980)Termination phase: Property scanning
% 1.64/1.34
% 1.64/1.34 % (24980)Memory used [KB]: 1023
% 1.64/1.34 % (24980)Time elapsed: 0.003 s
% 1.64/1.34 % (24980)Instructions burned: 4 (million)
% 1.64/1.34 % (24980)------------------------------
% 1.64/1.34 % (24980)------------------------------
% 1.64/1.35 % (24984)First to succeed.
% 1.64/1.35 % (24984)Refutation found. Thanks to Tanya!
% 1.64/1.35 % SZS status Theorem for DTF2THF_24881
% 1.64/1.35 % SZS output start Proof for DTF2THF_24881
% 1.64/1.35 thf(func_def_0, type, in: $i > $i > $o).
% 1.64/1.35 thf(func_def_2, type, powerset: $i > $i).
% 1.64/1.35 thf(func_def_3, type, nonempty: $i > $o).
% 1.64/1.35 thf(func_def_4, type, subset: $i > $i > $o).
% 1.64/1.35 thf(func_def_7, type, transitiveset: $i > $o).
% 1.64/1.35 thf(func_def_8, type, stricttotalorderedByIn: $i > $o).
% 1.64/1.35 thf(func_def_9, type, wellorderedByIn: $i > $o).
% 1.64/1.35 thf(func_def_10, type, ordinal: $i > $o).
% 1.64/1.35 thf(f71,plain,(
% 1.64/1.35 $false),
% 1.64/1.35 inference(subsumption_resolution,[status(thm)],[f69,f37])).
% 1.64/1.35 thf(f37,plain,(
% 1.64/1.35 ((in @ sK2 @ sK1) = $true)),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.35 thf(f29,plain,(
% 1.64/1.35 (subsetE = $true) & (($true = (ordinal @ sK0)) & (((in @ sK2 @ sK1) = $true) & ($true = (in @ sK1 @ sK0)) & ((in @ sK2 @ sK0) != $true)))),
% 1.64/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2])],[f24,f28,f27])).
% 1.64/1.35 thf(f27,plain,(
% 1.64/1.35 ? [X0 : $i] : (((ordinal @ X0) = $true) & ? [X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X1 @ X0)) & ($true != (in @ X2 @ X0)))) => (($true = (ordinal @ sK0)) & ? [X2 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X1 @ sK0)) & ($true != (in @ X2 @ sK0))))),
% 1.64/1.35 introduced(definition,[],[choice_axiom])).
% 1.64/1.35 thf(f28,plain,(
% 1.64/1.35 ? [X2 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X1 @ sK0)) & ($true != (in @ X2 @ sK0))) => (((in @ sK2 @ sK1) = $true) & ($true = (in @ sK1 @ sK0)) & ((in @ sK2 @ sK0) != $true))),
% 1.64/1.35 introduced(definition,[],[choice_axiom])).
% 1.64/1.35 thf(f24,plain,(
% 1.64/1.35 (subsetE = $true) & ? [X0 : $i] : (((ordinal @ X0) = $true) & ? [X1 : $i,X2 : $i] : (((in @ X2 @ X1) = $true) & ($true = (in @ X1 @ X0)) & ($true != (in @ X2 @ X0))))),
% 1.64/1.35 inference(flattening,[status(thm)],[f23])).
% 1.64/1.35 thf(f23,plain,(
% 1.64/1.35 ? [X0 : $i] : (? [X1 : $i,X2 : $i] : ((($true != (in @ X2 @ X0)) & ((in @ X2 @ X1) = $true)) & ($true = (in @ X1 @ X0))) & ((ordinal @ X0) = $true)) & (subsetE = $true)),
% 1.64/1.35 inference(ennf_transformation,[status(thm)],[f16])).
% 1.64/1.35 thf(f16,plain,(
% 1.64/1.35 ~((subsetE = $true) => ! [X0 : $i] : (((ordinal @ X0) = $true) => ! [X1 : $i,X2 : $i] : (($true = (in @ X1 @ X0)) => (((in @ X2 @ X1) = $true) => ($true = (in @ X2 @ X0))))))),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f15])).
% 1.64/1.35 thf(f15,plain,(
% 1.64/1.35 ~(subsetE => ! [X0 : $i] : ((ordinal @ X0) => ! [X1 : $i,X2 : $i] : ((in @ X1 @ X0) => ((in @ X2 @ X1) => (in @ X2 @ X0)))))),
% 1.64/1.35 inference(rectify,[status(thm)],[f8])).
% 1.64/1.35 thf(f8,negated_conjecture,(
% 1.64/1.35 ~(subsetE => ! [X3 : $i] : ((ordinal @ X3) => ! [X1 : $i,X0 : $i] : ((in @ X1 @ X3) => ((in @ X0 @ X1) => (in @ X0 @ X3)))))),
% 1.64/1.35 inference(negated_conjecture,[status(cth)],[f7])).
% 1.64/1.35 thf(f7,conjecture,(
% 1.64/1.35 subsetE => ! [X3 : $i] : ((ordinal @ X3) => ! [X1 : $i,X0 : $i] : ((in @ X1 @ X3) => ((in @ X0 @ X1) => (in @ X0 @ X3))))),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2THF_24881.p',ordinalTransSet)).
% 1.64/1.35 thf(f69,plain,(
% 1.64/1.35 ((in @ sK2 @ sK1) != $true)),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f65])).
% 1.64/1.35 thf(f65,plain,(
% 1.64/1.35 ($false = $true) | ((in @ sK2 @ sK1) != $true)),
% 1.64/1.35 inference(superposition,[status(thm)],[f36,f61])).
% 1.64/1.35 thf(f61,plain,(
% 1.64/1.35 ( ! [X0 : $i] : (($false = (in @ X0 @ sK0)) | ($true != (in @ sK2 @ X0))) )),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f60])).
% 1.64/1.35 thf(f60,plain,(
% 1.64/1.35 ( ! [X0 : $i] : (($false = (in @ X0 @ sK0)) | ($true != (in @ sK2 @ X0)) | ($true != $true)) )),
% 1.64/1.35 inference(superposition,[status(thm)],[f59,f57])).
% 1.64/1.35 thf(f57,plain,(
% 1.64/1.35 ( ! [X1 : $i] : (($true = (subset @ X1 @ sK0)) | ($false = (in @ X1 @ sK0))) )),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f56])).
% 1.64/1.35 thf(f56,plain,(
% 1.64/1.35 ( ! [X1 : $i] : (($true = ((in @ X1 @ sK0) => (subset @ X1 @ sK0)))) )),
% 1.64/1.35 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.64/1.35 thf(f55,plain,(
% 1.64/1.35 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0))) @ X1))) )),
% 1.64/1.35 inference(pi_clausification,[status(thm)],[f53])).
% 1.64/1.35 thf(f53,plain,(
% 1.64/1.35 ($true = (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0)))))),
% 1.64/1.35 inference(binary_proxy_clausification,[status(thm)],[f52])).
% 1.64/1.35 thf(f52,plain,(
% 1.64/1.35 (((wellorderedByIn @ sK0) & (!! @ $i @ (^[Y0 : $i]: ((in @ Y0 @ sK0) => (subset @ Y0 @ sK0))))) = $true)),
% 1.64/1.35 inference(beta_eta_normalization,[status(thm)],[f46])).
% 1.64/1.35 thf(f46,plain,(
% 1.64/1.35 ($true = ((^[Y0 : $i]: ((wellorderedByIn @ Y0) & ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0))) @ sK0))),
% 1.64/1.35 inference(definition_unfolding,[status(thm)],[f38,f45])).
% 1.64/1.35 thf(f45,plain,(
% 1.64/1.35 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & ((^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((in @ Y2 @ Y1) => (subset @ Y2 @ Y1))))) @ Y0))))),
% 1.64/1.35 inference(definition_unfolding,[status(thm)],[f34,f44])).
% 1.64/1.35 thf(f44,plain,(
% 1.64/1.35 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f20])).
% 1.64/1.35 thf(f20,plain,(
% 1.64/1.35 (transitiveset = (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((in @ Y1 @ Y0) => (subset @ Y1 @ Y0))))))),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f19])).
% 1.64/1.35 thf(f19,plain,(
% 1.64/1.35 ((^[X0 : $i] : (! [X1 : $i] : ((in @ X1 @ X0) => (subset @ X1 @ X0)))) = transitiveset)),
% 1.64/1.35 inference(rectify,[status(thm)],[f3])).
% 1.64/1.35 thf(f3,axiom,(
% 1.64/1.35 ((^[X1 : $i] : (! [X3 : $i] : ((in @ X3 @ X1) => (subset @ X3 @ X1)))) = transitiveset)),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2THF_24881.p',transitiveset)).
% 1.64/1.35 thf(f34,plain,(
% 1.64/1.35 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))))),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.35 thf(f14,plain,(
% 1.64/1.35 (ordinal = (^[Y0 : $i]: ((wellorderedByIn @ Y0) & (transitiveset @ Y0))))),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f13])).
% 1.64/1.35 thf(f13,plain,(
% 1.64/1.35 (ordinal = (^[X0 : $i] : ((transitiveset @ X0) & (wellorderedByIn @ X0))))),
% 1.64/1.35 inference(rectify,[status(thm)],[f6])).
% 1.64/1.35 thf(f6,axiom,(
% 1.64/1.35 (ordinal = (^[X0 : $i] : ((transitiveset @ X0) & (wellorderedByIn @ X0))))),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2THF_24881.p',ordinal)).
% 1.64/1.35 thf(f38,plain,(
% 1.64/1.35 ($true = (ordinal @ sK0))),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.35 thf(f59,plain,(
% 1.64/1.35 ( ! [X0 : $i] : (($true != (subset @ X0 @ sK0)) | ($true != (in @ sK2 @ X0))) )),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f58])).
% 1.64/1.35 thf(f58,plain,(
% 1.64/1.35 ( ! [X0 : $i] : (($true != (in @ sK2 @ X0)) | ($true != $true) | ($true != (subset @ X0 @ sK0))) )),
% 1.64/1.35 inference(superposition,[status(thm)],[f35,f51])).
% 1.64/1.35 thf(f51,plain,(
% 1.64/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((in @ X2 @ X1) = $true) | ($true != (in @ X2 @ X0)) | ($true != (subset @ X0 @ X1))) )),
% 1.64/1.35 inference(trivial_inequality_removal,[status(thm)],[f47])).
% 1.64/1.35 thf(f47,plain,(
% 1.64/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ X0)) | ($true != $true) | ((in @ X2 @ X1) = $true) | ($true != (subset @ X0 @ X1))) )),
% 1.64/1.35 inference(definition_unfolding,[status(thm)],[f43,f39])).
% 1.64/1.35 thf(f39,plain,(
% 1.64/1.35 (subsetE = $true)),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.35 thf(f43,plain,(
% 1.64/1.35 ( ! [X2 : $i,X0 : $i,X1 : $i] : (($true != (in @ X2 @ X0)) | ((in @ X2 @ X1) = $true) | ($true != (subset @ X0 @ X1)) | (subsetE != $true)) )),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f33])).
% 1.64/1.35 thf(f33,plain,(
% 1.64/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X0)) | ((in @ X2 @ X1) = $true) | ($true != (subset @ X0 @ X1))) | (subsetE != $true)) & ((subsetE = $true) | (($true = (in @ sK5 @ sK3)) & ((in @ sK5 @ sK4) != $true) & ($true = (subset @ sK3 @ sK4))))),
% 1.64/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK3,sK4,sK5])],[f31,f32])).
% 1.64/1.35 thf(f32,plain,(
% 1.64/1.35 ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) & ($true != (in @ X5 @ X4)) & ($true = (subset @ X3 @ X4))) => (($true = (in @ sK5 @ sK3)) & ((in @ sK5 @ sK4) != $true) & ($true = (subset @ sK3 @ sK4)))),
% 1.64/1.35 introduced(definition,[],[choice_axiom])).
% 1.64/1.35 thf(f31,plain,(
% 1.64/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X0)) | ((in @ X2 @ X1) = $true) | ($true != (subset @ X0 @ X1))) | (subsetE != $true)) & ((subsetE = $true) | ? [X3 : $i,X4 : $i,X5 : $i] : (((in @ X5 @ X3) = $true) & ($true != (in @ X5 @ X4)) & ($true = (subset @ X3 @ X4))))),
% 1.64/1.35 inference(rectify,[status(thm)],[f30])).
% 1.64/1.35 thf(f30,plain,(
% 1.64/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X0)) | ((in @ X2 @ X1) = $true) | ($true != (subset @ X0 @ X1))) | (subsetE != $true)) & ((subsetE = $true) | ? [X0 : $i,X1 : $i,X2 : $i] : (($true = (in @ X2 @ X0)) & ((in @ X2 @ X1) != $true) & ($true = (subset @ X0 @ X1))))),
% 1.64/1.35 inference(nnf_transformation,[status(thm)],[f26])).
% 1.64/1.35 thf(f26,plain,(
% 1.64/1.35 ! [X0 : $i,X1 : $i,X2 : $i] : (($true != (in @ X2 @ X0)) | ((in @ X2 @ X1) = $true) | ($true != (subset @ X0 @ X1))) <=> (subsetE = $true)),
% 1.64/1.35 inference(flattening,[status(thm)],[f25])).
% 1.64/1.35 thf(f25,plain,(
% 1.64/1.35 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : ((((in @ X2 @ X1) = $true) | ($true != (in @ X2 @ X0))) | ($true != (subset @ X0 @ X1)))),
% 1.64/1.35 inference(ennf_transformation,[status(thm)],[f18])).
% 1.64/1.35 thf(f18,plain,(
% 1.64/1.35 (subsetE = $true) <=> ! [X0 : $i,X1 : $i,X2 : $i] : (($true = (subset @ X0 @ X1)) => (($true = (in @ X2 @ X0)) => ((in @ X2 @ X1) = $true)))),
% 1.64/1.35 inference(fool_elimination,[status(thm)],[f17])).
% 1.64/1.35 thf(f17,plain,(
% 1.64/1.35 (! [X0 : $i,X1 : $i,X2 : $i] : ((subset @ X0 @ X1) => ((in @ X2 @ X0) => (in @ X2 @ X1))) = subsetE)),
% 1.64/1.35 inference(rectify,[status(thm)],[f2])).
% 1.64/1.35 thf(f2,axiom,(
% 1.64/1.35 (! [X1 : $i,X2 : $i,X0 : $i] : ((subset @ X1 @ X2) => ((in @ X0 @ X1) => (in @ X0 @ X2))) = subsetE)),
% 1.64/1.35 file('/export/starexec/sandbox/tmp/tmp.t33Dem004z/DTF2THF_24881.p',subsetE)).
% 1.64/1.35 thf(f35,plain,(
% 1.64/1.35 ((in @ sK2 @ sK0) != $true)),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.35 thf(f36,plain,(
% 1.64/1.35 ($true = (in @ sK1 @ sK0))),
% 1.64/1.35 inference(cnf_transformation,[status(thm)],[f29])).
% 1.64/1.35 % SZS output end Proof for DTF2THF_24881
% 1.64/1.35 % (24984)------------------------------
% 1.64/1.35 % (24984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.35 % (24984)Termination reason: Refutation
% 1.64/1.35
% 1.64/1.35 % (24984)Memory used [KB]: 5500
% 1.64/1.35 % (24984)Time elapsed: 0.006 s
% 1.64/1.35 % (24984)Instructions burned: 7 (million)
% 1.64/1.35 % (24984)------------------------------
% 1.64/1.35 % (24984)------------------------------
% 1.64/1.35 % (24978)Success in time 0.021 s
%------------------------------------------------------------------------------