%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV459^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:41:17 AM UTC 2026
% Result : Theorem 1.65s 1.41s
% Output : Refutation 1.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 8 unt; 0 typ; 3 def)
% Number of atoms : 315 ( 76 equ; 0 cnn)
% Maximal formula atoms : 6 ( 7 avg)
% Number of connectives : 479 ( 45 ~; 36 |; 15 &; 372 @)
% ( 6 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 6 con; 0-4 aty)
% Number of variables : 82 ( 0 ^; 73 !; 9 ?; 82 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK1: $tType ).
thf(func_def_0,type,
'const/sets/SUBSET':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_2,type,
'const/sets/DELETE':
!>[X0: $tType] : ( ( X0 > $o ) > X0 > X0 > $o ) ).
thf(func_def_6,type,
sK0:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_7,type,
sK2: sK1 ).
thf(func_def_8,type,
sK3: sK1 > $o ).
thf(func_def_10,type,
ph5:
!>[X0: $tType] : X0 ).
thf(f104,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f36,f47,f52,f97]) ).
thf(f97,plain,
( ~ spl4_2
| spl4_3 ),
inference(avatar_contradiction_clause,[status(thm)],[f96]) ).
thf(f96,plain,
( $false
| ~ spl4_2
| spl4_3 ),
inference(subsumption_resolution,[status(thm)],[f93,f51]) ).
thf(f51,plain,
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ sK3 ) )
| spl4_3 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl4_3
<=> ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition]) ).
thf(f93,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ sK3 ) )
| ~ spl4_2 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $true
= ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ sK3 ) )
| ( $true != $true )
| ~ spl4_2 ),
inference(superposition,[status(thm)],[f29,f46]) ).
thf(f46,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) )
= $true )
| ~ spl4_2 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl4_2
<=> ( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition]) ).
thf(f29,plain,
! [X0: $tType,X2: X0,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X3 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
thf(f20,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
& ( X2 != X3 ) )
| ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X3 ) )
!= $true ) )
& ( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X3 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true )
| ( X2 = X3 ) ) ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
& ( X2 != X3 ) )
| ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X3 ) )
!= $true ) )
& ( ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X3 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
!= $true )
| ( X2 = X3 ) ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
& ( X2 != X3 ) )
<=> ( ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X3 ) )
= $true ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0,X3: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
& ( ( X2 != X3 )
= ( 'const/sets/IN' @ X0 @ X2 @ ( 'const/sets/DELETE' @ X0 @ X1 @ X3 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: X0 > $o,X3: X0,X4: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
& ( ( X3 != X4 )
= ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.msVNim2QwW/DTF2THF_24710.p','thm/sets/IN_DELETE_') ).
thf(f52,plain,
( ~ spl4_3
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f41,f33,f49]) ).
thf(f33,definition,
( spl4_1
<=> ( $true
= ( 'const/sets/SUBSET' @ sK1 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition]) ).
thf(f41,plain,
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ sK3 ) )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f39]) ).
thf(f39,plain,
( ( $true
!= ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ sK3 ) )
| ( $true != $true )
| spl4_1 ),
inference(superposition,[status(thm)],[f35,f24]) ).
thf(f24,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 )
!= $true )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
!= $true ) )
=> ( ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X2 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ? [X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X1 )
= $true )
& ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ! [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
| ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
!= $true ) )
& ( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ? [X3: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
& ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
!= $true ) ) ) ),
inference(nnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ! [X3: X0] :
( ( $true
!= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) )
<=> ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
<=> ! [X3: X0] :
( ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) )
=> ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
=> ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
= ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ X2 )
=> ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
= ( 'const/sets/SUBSET' @ X0 @ X2 @ X3 ) ),
file('/export/starexec/sandbox/tmp/tmp.msVNim2QwW/DTF2THF_24710.p','thm/sets/SUBSET_') ).
thf(f35,plain,
( ( $true
!= ( 'const/sets/SUBSET' @ sK1 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) @ sK3 ) )
| spl4_1 ),
inference(avatar_component_clause,[status(thm)],[f33]) ).
thf(f47,plain,
( spl4_2
| spl4_1 ),
inference(avatar_split_clause,[status(thm)],[f42,f33,f44]) ).
thf(f42,plain,
( ( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) )
= $true )
| spl4_1 ),
inference(trivial_inequality_removal,[status(thm)],[f38]) ).
thf(f38,plain,
( ( $true != $true )
| ( ( 'const/sets/IN' @ sK1 @ ( sK0 @ sK1 @ sK3 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) ) @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) )
= $true )
| spl4_1 ),
inference(superposition,[status(thm)],[f35,f25]) ).
thf(f25,plain,
! [X0: $tType,X2: X0 > $o,X1: X0 > $o] :
( ( ( 'const/sets/SUBSET' @ X0 @ X1 @ X2 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ ( sK0 @ X0 @ X2 @ X1 ) @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f36,plain,
~ spl4_1,
inference(avatar_split_clause,[status(thm)],[f30,f33]) ).
thf(f30,plain,
( $true
!= ( 'const/sets/SUBSET' @ sK1 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) @ sK3 ) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
thf(f22,plain,
( $true
!= ( 'const/sets/SUBSET' @ sK1 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) @ sK3 ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f13,f21]) ).
thf(f21,plain,
( ? [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X1 ) @ X2 )
!= $true )
=> ( $true
!= ( 'const/sets/SUBSET' @ sK1 @ ( 'const/sets/DELETE' @ sK1 @ sK3 @ sK2 ) @ sK3 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
? [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X1 ) @ X2 )
!= $true ),
inference(ennf_transformation,[status(thm)],[f12]) ).
thf(f12,plain,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] :
( ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X1 ) @ X2 )
= $true ),
inference(fool_elimination,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0,X2: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X2 @ X1 ) @ X2 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X2: X0,X3: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X3 @ X2 ) @ X3 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X2: X0,X3: X0 > $o] : ( 'const/sets/SUBSET' @ X0 @ ( 'const/sets/DELETE' @ X0 @ X3 @ X2 ) @ X3 ),
file('/export/starexec/sandbox/tmp/tmp.msVNim2QwW/DTF2THF_24710.p','thm/sets/DELETE_SUBSET_') ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV459^1 : TPTP v9.2.1. Released v7.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.25 % Computer : n024.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Tue Feb 24 07:47:10 EST 2026
% 0.06/0.25 % CPUTime :
% 0.06/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.06/0.35 ---- Original DTF file ---
% 0.06/0.35 thf(spec,logic,$$dhol).
% 0.06/0.35 %------------------------------------------------------------------------------
% 0.06/0.35 % File : SEV459^1 : TPTP v9.2.1. Released v7.0.0.
% 0.06/0.35 % Domain : Analysis
% 0.06/0.35 % Problem : DELETE_SUBSET
% 0.06/0.35 % Version : Especial.
% 0.06/0.35 % English :
% 0.06/0.35
% 0.06/0.35 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.06/0.35 % Source : [Kal16]
% 0.06/0.35 % Names : DELETE_SUBSET_.p [Kal16]
% 0.06/0.35
% 0.06/0.35 % Status : Theorem
% 0.06/0.35 % Rating : 0.00 v7.1.0
% 0.06/0.35 % Syntax : Number of formulae : 7 ( 3 unt; 3 typ; 0 def)
% 0.06/0.35 % Number of atoms : 13 ( 4 equ; 0 cnn)
% 0.06/0.35 % Maximal formula atoms : 2 ( 3 avg)
% 0.06/0.35 % Number of connectives : 31 ( 1 ~; 0 |; 1 &; 28 @)
% 0.06/0.35 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.06/0.35 % Maximal formula depth : 9 ( 6 avg)
% 0.06/0.35 % Number of types : 1 ( 0 usr)
% 0.06/0.35 % Number of type conns : 16 ( 16 >; 0 *; 0 +; 0 <<)
% 0.06/0.35 % Number of symbols : 4 ( 3 usr; 0 con; 2-4 aty)
% 0.06/0.35 % Number of variables : 17 ( 0 ^; 14 !; 0 ?; 17 :)
% 0.06/0.35 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.06/0.35 % SPC : TH1_THM_EQU_NAR
% 0.06/0.35
% 0.06/0.35 % Comments : Exported from core HOL Light.
% 0.06/0.35 %------------------------------------------------------------------------------
% 0.06/0.35 thf('thf_const_const/sets/SUBSET',type,
% 0.06/0.35 'const/sets/SUBSET':
% 0.06/0.35 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 0.06/0.35
% 0.06/0.35 thf('thf_const_const/sets/IN',type,
% 0.06/0.35 'const/sets/IN':
% 0.06/0.35 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.06/0.35
% 0.06/0.35 thf('thf_const_const/sets/DELETE',type,
% 0.06/0.35 'const/sets/DELETE':
% 0.06/0.35 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 0.06/0.35
% 0.06/0.35 thf('thm/sets/IN_',axiom,
% 0.06/0.35 ! [A: $tType,P: A > $o,A0: A] :
% 0.06/0.35 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.06/0.35 = ( P @ A0 ) ) ).
% 0.06/0.35
% 0.06/0.35 thf('thm/sets/IN_DELETE_',axiom,
% 0.06/0.35 ! [A: $tType,A0: A > $o,A1: A,A2: A] :
% 0.06/0.35 ( ( 'const/sets/IN' @ A @ A1 @ ( 'const/sets/DELETE' @ A @ A0 @ A2 ) )
% 0.06/0.35 = ( ( 'const/sets/IN' @ A @ A1 @ A0 )
% 0.06/0.35 & ( A1 != A2 ) ) ) ).
% 0.06/0.35
% 0.06/0.35 thf('thm/sets/SUBSET_',axiom,
% 0.06/0.35 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.06/0.35 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 0.06/0.35 = ( ! [A2: A] :
% 0.06/0.35 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.06/0.35 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.06/0.35
% 0.06/0.35 thf('thm/sets/DELETE_SUBSET_',conjecture,
% 0.06/0.35 ! [A: $tType,A0: A,A1: A > $o] : ( 'const/sets/SUBSET' @ A @ ( 'const/sets/DELETE' @ A @ A1 @ A0 ) @ A1 ) ).
% 0.06/0.35
% 0.06/0.35 %------------------------------------------------------------------------------
% 0.06/0.35 ------------------------
% 1.54/1.35 ---- Embedded in THF ---
% 1.54/1.35 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.54/1.35 %%% Generated on Tue Feb 24 07:47:11 EST 2026
% 1.54/1.35 %%% using '$$dhol' embedding, version 1.3.0.
% 1.54/1.35 %%% Logic specification used:
% 1.54/1.35 %%% thf(spec, logic, $$dhol).
% 1.54/1.35
% 1.54/1.35 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.msVNim2QwW/DTF2DTF24710.p
% See solution above
% 1.54/1.35 ------------------------
% 1.54/1.36 ---- Cleaned THF ---
% 1.54/1.36 thf('thf_const_const/sets/SUBSET',type,
% 1.54/1.36 'const/sets/SUBSET':
% 1.54/1.36 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > $o ) ).
% 1.54/1.36
% 1.54/1.36 thf('thf_const_const/sets/IN',type,
% 1.54/1.36 'const/sets/IN':
% 1.54/1.36 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.54/1.36
% 1.54/1.36 thf('thf_const_const/sets/DELETE',type,
% 1.54/1.36 'const/sets/DELETE':
% 1.54/1.36 !>[A: $tType] : ( ( A > $o ) > A > A > $o ) ).
% 1.54/1.36
% 1.54/1.36 thf('thm/sets/IN_',axiom,
% 1.54/1.36 ! [A: $tType,P: A > $o,A0: A] :
% 1.54/1.36 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 1.54/1.36 = ( P @ A0 ) ) ).
% 1.54/1.36
% 1.54/1.36 thf('thm/sets/IN_DELETE_',axiom,
% 1.54/1.36 ! [A: $tType,A0: A > $o,A1: A,A2: A] :
% 1.54/1.36 ( ( 'const/sets/IN' @ A @ A1 @ ( 'const/sets/DELETE' @ A @ A0 @ A2 ) )
% 1.54/1.36 = ( ( 'const/sets/IN' @ A @ A1 @ A0 )
% 1.54/1.36 & ( A1 != A2 ) ) ) ).
% 1.54/1.36
% 1.54/1.36 thf('thm/sets/SUBSET_',axiom,
% 1.54/1.36 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.54/1.36 ( ( 'const/sets/SUBSET' @ A @ A0 @ A1 )
% 1.54/1.36 = ( ! [A2: A] :
% 1.54/1.36 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.54/1.36 => ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.54/1.36
% 1.54/1.36 thf('thm/sets/DELETE_SUBSET_',conjecture,
% 1.54/1.36 ! [A: $tType,A0: A,A1: A > $o] : ( 'const/sets/SUBSET' @ A @ ( 'const/sets/DELETE' @ A @ A1 @ A0 ) @ A1 ) ).
% 1.54/1.36 ------------------------
% 1.54/1.38 % (24810)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_24710 for (2999ds/2Mi)
% 1.54/1.38 % (24807)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_24710 for (2999ds/183Mi)
% 1.54/1.38 % (24813)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_24710 for (2999ds/18Mi)
% 1.54/1.38 % (24808)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_24710 for (2999ds/4Mi)
% 1.54/1.38 % (24809)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_24710 for (2999ds/27Mi)
% 1.54/1.38 % (24811)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_24710 for (2999ds/2Mi)
% 1.54/1.38 % (24812)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_24710 for (2999ds/275Mi)
% 1.54/1.38 % Exception at run slice level
% 1.54/1.38 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.54/1.38 % (24810)Instruction limit reached!
% 1.54/1.38 % (24810)------------------------------
% 1.54/1.38 % (24810)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.38 % (24810)Termination reason: Unknown
% 1.54/1.38 % (24810)Termination phase: Saturation
% 1.54/1.38
% 1.54/1.38 % (24810)Memory used [KB]: 5500
% 1.54/1.38 % (24810)Time elapsed: 0.003 s
% 1.54/1.38 % (24810)Instructions burned: 2 (million)
% 1.54/1.38 % (24810)------------------------------
% 1.54/1.38 % (24810)------------------------------
% 1.54/1.39 % (24808)Instruction limit reached!
% 1.54/1.39 % (24808)------------------------------
% 1.54/1.39 % (24808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.39 % (24808)Termination reason: Unknown
% 1.54/1.39 % (24808)Termination phase: Saturation
% 1.54/1.39
% 1.54/1.39 % (24808)Memory used [KB]: 5500
% 1.54/1.39 % (24808)Time elapsed: 0.004 s
% 1.54/1.39 % (24808)Instructions burned: 4 (million)
% 1.54/1.39 % (24808)------------------------------
% 1.54/1.39 % (24808)------------------------------
% 1.54/1.39 % (24812)Refutation not found, incomplete strategy
% 1.54/1.39 % (24812)------------------------------
% 1.54/1.39 % (24812)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.39 % (24812)Termination reason: Refutation not found, incomplete strategy
% 1.54/1.39
% 1.54/1.39
% 1.54/1.39 % (24812)Memory used [KB]: 5500
% 1.54/1.39 % (24812)Time elapsed: 0.004 s
% 1.54/1.39 % (24812)Instructions burned: 2 (million)
% 1.54/1.39 % (24812)------------------------------
% 1.54/1.39 % (24812)------------------------------
% 1.54/1.39 % (24813)Instruction limit reached!
% 1.54/1.39 % (24813)------------------------------
% 1.54/1.39 % (24813)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.54/1.39 % (24813)Termination reason: Unknown
% 1.54/1.39 % (24813)Termination phase: Saturation
% 1.54/1.39
% 1.54/1.39 % (24813)Memory used [KB]: 5628
% 1.54/1.39 % (24813)Time elapsed: 0.012 s
% 1.54/1.39 % (24813)Instructions burned: 19 (million)
% 1.54/1.39 % (24813)------------------------------
% 1.54/1.39 % (24813)------------------------------
% 1.65/1.40 % (24809)Instruction limit reached!
% 1.65/1.40 % (24809)------------------------------
% 1.65/1.40 % (24809)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (24809)Termination reason: Unknown
% 1.65/1.40 % (24809)Termination phase: Saturation
% 1.65/1.40
% 1.65/1.40 % (24809)Memory used [KB]: 5628
% 1.65/1.40 % (24809)Time elapsed: 0.016 s
% 1.65/1.40 % (24809)Instructions burned: 27 (million)
% 1.65/1.40 % (24809)------------------------------
% 1.65/1.40 % (24809)------------------------------
% 1.65/1.40 % (24814)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_24710 for (2999ds/3Mi)
% 1.65/1.40 % (24815)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_24710 for (2999ds/37Mi)
% 1.65/1.40 % (24816)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_24710 for (2999ds/15Mi)
% 1.65/1.40 % Exception at run slice level
% 1.65/1.40 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.65/1.40 % (24814)Instruction limit reached!
% 1.65/1.40 % (24814)------------------------------
% 1.65/1.40 % (24814)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.40 % (24814)Termination reason: Unknown
% 1.65/1.40 % (24814)Termination phase: Saturation
% 1.65/1.40
% 1.65/1.40 % (24814)Memory used [KB]: 5500
% 1.65/1.40 % (24814)Time elapsed: 0.004 s
% 1.65/1.40 % (24814)Instructions burned: 3 (million)
% 1.65/1.40 % (24814)------------------------------
% 1.65/1.40 % (24814)------------------------------
% 1.65/1.40 % (24817)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_24710 for (2999ds/3Mi)
% 1.65/1.40 % (24817)Instruction limit reached!
% 1.65/1.40 % (24817)------------------------------
% 1.65/1.40 % (24817)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (24817)Termination reason: Unknown
% 1.65/1.41 % (24817)Termination phase: Saturation
% 1.65/1.41
% 1.65/1.41 % (24817)Memory used [KB]: 5500
% 1.65/1.41 % (24817)Time elapsed: 0.003 s
% 1.65/1.41 % (24817)Instructions burned: 3 (million)
% 1.65/1.41 % (24817)------------------------------
% 1.65/1.41 % (24817)------------------------------
% 1.65/1.41 % (24816)First to succeed.
% 1.65/1.41 % (24816)Refutation found. Thanks to Tanya!
% 1.65/1.41 % SZS status Theorem for DTF2THF_24710
% 1.65/1.41 % SZS output start Proof for DTF2THF_24710
% 1.65/1.41 thf(type_def_6, type, sK1: $tType).
% 1.65/1.41 thf(func_def_0, type, 'const/sets/SUBSET': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > $o)).
% 1.65/1.41 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.65/1.41 thf(func_def_2, type, 'const/sets/DELETE': !>[X0: $tType]:((X0 > $o) > X0 > X0 > $o)).
% 1.65/1.41 thf(func_def_6, type, sK0: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.65/1.41 thf(func_def_7, type, sK2: sK1).
% 1.65/1.41 thf(func_def_8, type, sK3: sK1 > $o).
% 1.65/1.41 thf(func_def_10, type, ph5: !>[X0: $tType]:(X0)).
% 1.65/1.41 thf(f104,plain,(
% 1.65/1.41 $false),
% 1.65/1.41 inference(avatar_sat_refutation,[status(thm)],[f36,f47,f52,f97])).
% 1.65/1.41 thf(f97,plain,(
% 1.65/1.41 ~spl4_2 | spl4_3),
% 1.65/1.41 inference(avatar_contradiction_clause,[status(thm)],[f96])).
% 1.65/1.41 thf(f96,plain,(
% 1.65/1.41 $false | (~spl4_2 | spl4_3)),
% 1.65/1.41 inference(subsumption_resolution,[status(thm)],[f93,f51])).
% 1.65/1.41 thf(f51,plain,(
% 1.65/1.41 ($true != ('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ sK3)) | spl4_3),
% 1.65/1.41 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.65/1.41 thf(f49,definition,(
% 1.65/1.41 spl4_3 <=> ($true = ('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ sK3))),
% 1.65/1.41 introduced(definition,[new_symbols(naming,[spl4_3])],[avatar_definition])).
% 1.65/1.41 thf(f93,plain,(
% 1.65/1.41 ($true = ('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ sK3)) | ~spl4_2),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.65/1.41 thf(f92,plain,(
% 1.65/1.41 ($true = ('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ sK3)) | ($true != $true) | ~spl4_2),
% 1.65/1.41 inference(superposition,[status(thm)],[f29,f46])).
% 1.65/1.41 thf(f46,plain,(
% 1.65/1.41 (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) = $true) | ~spl4_2),
% 1.65/1.41 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.65/1.41 thf(f44,definition,(
% 1.65/1.41 spl4_2 <=> (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) = $true)),
% 1.65/1.41 introduced(definition,[new_symbols(naming,[spl4_2])],[avatar_definition])).
% 1.65/1.41 thf(f29,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X2 : X0,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = $true) | (('const/sets/IN' @ X0 @ X2 @ ('const/sets/DELETE' @ X0 @ X1 @ X3)) != $true)) )),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f20])).
% 1.65/1.41 thf(f20,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((((('const/sets/IN' @ X0 @ X2 @ X1) = $true) & (X2 != X3)) | (('const/sets/IN' @ X0 @ X2 @ ('const/sets/DELETE' @ X0 @ X1 @ X3)) != $true)) & ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/DELETE' @ X0 @ X1 @ X3)) = $true) | (('const/sets/IN' @ X0 @ X2 @ X1) != $true) | (X2 = X3)))),
% 1.65/1.41 inference(flattening,[status(thm)],[f19])).
% 1.65/1.41 thf(f19,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : ((((('const/sets/IN' @ X0 @ X2 @ X1) = $true) & (X2 != X3)) | (('const/sets/IN' @ X0 @ X2 @ ('const/sets/DELETE' @ X0 @ X1 @ X3)) != $true)) & ((('const/sets/IN' @ X0 @ X2 @ ('const/sets/DELETE' @ X0 @ X1 @ X3)) = $true) | ((('const/sets/IN' @ X0 @ X2 @ X1) != $true) | (X2 = X3))))),
% 1.65/1.41 inference(nnf_transformation,[status(thm)],[f10])).
% 1.65/1.41 thf(f10,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : (((('const/sets/IN' @ X0 @ X2 @ X1) = $true) & (X2 != X3)) <=> (('const/sets/IN' @ X0 @ X2 @ ('const/sets/DELETE' @ X0 @ X1 @ X3)) = $true))),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f9])).
% 1.65/1.41 thf(f9,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0,X3 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) & (X2 != X3) = ('const/sets/IN' @ X0 @ X2 @ ('const/sets/DELETE' @ X0 @ X1 @ X3)))),
% 1.65/1.41 inference(rectify,[status(thm)],[f2])).
% 1.65/1.41 thf(f2,axiom,(
% 1.65/1.41 ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X4 : X0] : (('const/sets/IN' @ X0 @ X3 @ X2) & (X3 != X4) = ('const/sets/IN' @ X0 @ X3 @ ('const/sets/DELETE' @ X0 @ X2 @ X4)))),
% 1.65/1.41 file('/export/starexec/sandbox/tmp/tmp.msVNim2QwW/DTF2THF_24710.p','thm/sets/IN_DELETE_')).
% 1.65/1.41 thf(f52,plain,(
% 1.65/1.41 ~spl4_3 | spl4_1),
% 1.65/1.41 inference(avatar_split_clause,[status(thm)],[f41,f33,f49])).
% 1.65/1.41 thf(f33,definition,(
% 1.65/1.41 spl4_1 <=> ($true = ('const/sets/SUBSET' @ sK1 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2) @ sK3))),
% 1.65/1.41 introduced(definition,[new_symbols(naming,[spl4_1])],[avatar_definition])).
% 1.65/1.41 thf(f41,plain,(
% 1.65/1.41 ($true != ('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ sK3)) | spl4_1),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f39])).
% 1.65/1.41 thf(f39,plain,(
% 1.65/1.41 ($true != ('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ sK3)) | ($true != $true) | spl4_1),
% 1.65/1.41 inference(superposition,[status(thm)],[f35,f24])).
% 1.65/1.41 thf(f24,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2) != $true) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true)) )),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.41 thf(f18,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | (($true = ('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1)) & (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2) != $true))))),
% 1.65/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0])],[f16,f17])).
% 1.65/1.41 thf(f17,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) = $true) & (('const/sets/IN' @ X0 @ X4 @ X2) != $true)) => (($true = ('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1)) & (('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X2) != $true)))),
% 1.65/1.41 introduced(definition,[],[choice_axiom])).
% 1.65/1.41 thf(f16,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ? [X4 : X0] : ((('const/sets/IN' @ X0 @ X4 @ X1) = $true) & (('const/sets/IN' @ X0 @ X4 @ X2) != $true))))),
% 1.65/1.41 inference(rectify,[status(thm)],[f15])).
% 1.65/1.41 thf(f15,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((! [X3 : X0] : (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) | (('const/sets/SUBSET' @ X0 @ X1 @ X2) != $true)) & ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ? [X3 : X0] : (($true = ('const/sets/IN' @ X0 @ X3 @ X1)) & (('const/sets/IN' @ X0 @ X3 @ X2) != $true))))),
% 1.65/1.41 inference(nnf_transformation,[status(thm)],[f14])).
% 1.65/1.41 thf(f14,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (($true != ('const/sets/IN' @ X0 @ X3 @ X1)) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true)) <=> (('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true))),
% 1.65/1.41 inference(ennf_transformation,[status(thm)],[f8])).
% 1.65/1.41 thf(f8,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) <=> ! [X3 : X0] : (($true = ('const/sets/IN' @ X0 @ X3 @ X1)) => (('const/sets/IN' @ X0 @ X3 @ X2) = $true)))),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f7])).
% 1.65/1.41 thf(f7,plain,(
% 1.65/1.41 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o] : (! [X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ X1) => ('const/sets/IN' @ X0 @ X3 @ X2)) = ('const/sets/SUBSET' @ X0 @ X1 @ X2))),
% 1.65/1.41 inference(rectify,[status(thm)],[f3])).
% 1.65/1.41 thf(f3,axiom,(
% 1.65/1.41 ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o] : (! [X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ X2) => ('const/sets/IN' @ X0 @ X4 @ X3)) = ('const/sets/SUBSET' @ X0 @ X2 @ X3))),
% 1.65/1.41 file('/export/starexec/sandbox/tmp/tmp.msVNim2QwW/DTF2THF_24710.p','thm/sets/SUBSET_')).
% 1.65/1.41 thf(f35,plain,(
% 1.65/1.41 ($true != ('const/sets/SUBSET' @ sK1 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2) @ sK3)) | spl4_1),
% 1.65/1.41 inference(avatar_component_clause,[status(thm)],[f33])).
% 1.65/1.41 thf(f47,plain,(
% 1.65/1.41 spl4_2 | spl4_1),
% 1.65/1.41 inference(avatar_split_clause,[status(thm)],[f42,f33,f44])).
% 1.65/1.41 thf(f42,plain,(
% 1.65/1.41 (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) = $true) | spl4_1),
% 1.65/1.41 inference(trivial_inequality_removal,[status(thm)],[f38])).
% 1.65/1.41 thf(f38,plain,(
% 1.65/1.41 ($true != $true) | (('const/sets/IN' @ sK1 @ (sK0 @ sK1 @ sK3 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2)) = $true) | spl4_1),
% 1.65/1.41 inference(superposition,[status(thm)],[f35,f25])).
% 1.65/1.41 thf(f25,plain,(
% 1.65/1.41 ( ! [X0 : $tType,X2 : X0 > $o,X1 : X0 > $o] : ((('const/sets/SUBSET' @ X0 @ X1 @ X2) = $true) | ($true = ('const/sets/IN' @ X0 @ (sK0 @ X0 @ X2 @ X1) @ X1))) )),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f18])).
% 1.65/1.41 thf(f36,plain,(
% 1.65/1.41 ~spl4_1),
% 1.65/1.41 inference(avatar_split_clause,[status(thm)],[f30,f33])).
% 1.65/1.41 thf(f30,plain,(
% 1.65/1.41 ($true != ('const/sets/SUBSET' @ sK1 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2) @ sK3))),
% 1.65/1.41 inference(cnf_transformation,[status(thm)],[f22])).
% 1.65/1.41 thf(f22,plain,(
% 1.65/1.41 ($true != ('const/sets/SUBSET' @ sK1 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2) @ sK3))),
% 1.65/1.41 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1,sK2,sK3])],[f13,f21])).
% 1.65/1.41 thf(f21,plain,(
% 1.65/1.41 ? [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ ('const/sets/DELETE' @ X0 @ X2 @ X1) @ X2) != $true) => ($true != ('const/sets/SUBSET' @ sK1 @ ('const/sets/DELETE' @ sK1 @ sK3 @ sK2) @ sK3))),
% 1.65/1.41 introduced(definition,[],[choice_axiom])).
% 1.65/1.41 thf(f13,plain,(
% 1.65/1.41 ? [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ ('const/sets/DELETE' @ X0 @ X2 @ X1) @ X2) != $true)),
% 1.65/1.41 inference(ennf_transformation,[status(thm)],[f12])).
% 1.65/1.41 thf(f12,plain,(
% 1.65/1.41 ~! [X0 : $tType,X1 : X0,X2 : X0 > $o] : (('const/sets/SUBSET' @ X0 @ ('const/sets/DELETE' @ X0 @ X2 @ X1) @ X2) = $true)),
% 1.65/1.41 inference(fool_elimination,[status(thm)],[f11])).
% 1.65/1.41 thf(f11,plain,(
% 1.65/1.41 ~! [X0 : $tType,X1 : X0,X2 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ ('const/sets/DELETE' @ X0 @ X2 @ X1) @ X2)),
% 1.65/1.41 inference(rectify,[status(thm)],[f5])).
% 1.65/1.41 thf(f5,negated_conjecture,(
% 1.65/1.41 ~! [X0 : $tType,X2 : X0,X3 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ ('const/sets/DELETE' @ X0 @ X3 @ X2) @ X3)),
% 1.65/1.41 inference(negated_conjecture,[status(cth)],[f4])).
% 1.65/1.41 thf(f4,conjecture,(
% 1.65/1.41 ! [X0 : $tType,X2 : X0,X3 : X0 > $o] : ('const/sets/SUBSET' @ X0 @ ('const/sets/DELETE' @ X0 @ X3 @ X2) @ X3)),
% 1.65/1.41 file('/export/starexec/sandbox/tmp/tmp.msVNim2QwW/DTF2THF_24710.p','thm/sets/DELETE_SUBSET_')).
% 1.65/1.41 % SZS output end Proof for DTF2THF_24710
% 1.65/1.41 % (24816)------------------------------
% 1.65/1.41 % (24816)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.65/1.41 % (24816)Termination reason: Refutation
% 1.65/1.41
% 1.65/1.41 % (24816)Memory used [KB]: 5628
% 1.65/1.41 % (24816)Time elapsed: 0.009 s
% 1.65/1.41 % (24816)Instructions burned: 10 (million)
% 1.65/1.41 % (24816)------------------------------
% 1.65/1.41 % (24816)------------------------------
% 1.65/1.41 % (24806)Success in time 0.037 s
%------------------------------------------------------------------------------