%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV450^1 : 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 : n027.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 09:41:16 AM UTC 2026
% Result : Theorem 1.61s 1.30s
% Output : Refutation 1.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 53 ( 12 unt; 0 typ; 4 def)
% Number of atoms : 276 ( 69 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 318 ( 34 ~; 55 |; 0 &; 224 @)
% ( 4 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 7 con; 0-4 aty)
% Number of variables : 70 ( 0 ^; 66 !; 4 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK0: $tType ).
thf(func_def_0,type,
'const/sets/UNION':
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 > $o ) ).
thf(func_def_1,type,
'const/sets/IN':
!>[X0: $tType] : ( X0 > ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_11,type,
sK1: sK0 > $o ).
thf(func_def_13,type,
sK3:
!>[X0: $tType] : ( ( X0 > $o ) > ( X0 > $o ) > X0 ) ).
thf(func_def_14,type,
ph4:
!>[X0: $tType] : X0 ).
thf(func_def_15,type,
sK5: sK0 ).
thf(f181,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f52,f61,f125,f131,f180]) ).
thf(f180,plain,
( ~ spl2_1
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f179]) ).
thf(f179,plain,
( $false
| ~ spl2_1
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f178]) ).
thf(f178,plain,
( ( $false = $true )
| ~ spl2_1
| ~ spl2_4 ),
inference(forward_demodulation,[status(thm)],[f171,f60]) ).
thf(f60,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl2_4 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl2_4
<=> ( $false
= ( sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition]) ).
thf(f171,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f170]) ).
thf(f170,plain,
( ( $false = $true )
| ( ( sK1 @ sK5 )
= $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f20,f159]) ).
thf(f159,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 )
= $true )
| ~ spl2_1 ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 )
= $true )
| ( $false = $true )
| ~ spl2_1 ),
inference(duplicate_literal_removal,[status(thm)],[f155]) ).
thf(f155,plain,
( ( ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 )
= $true )
| ( $false = $true )
| ( ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 )
= $true )
| ~ spl2_1 ),
inference(superposition,[status(thm)],[f47,f64]) ).
thf(f64,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $false )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f63]) ).
thf(f63,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ X1 @ X2 ) )
| ( $false = $true )
| ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $false ) ),
inference(superposition,[status(thm)],[f23,f19]) ).
thf(f19,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $true )
| ( ( X1 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
inference(cnf_transformation,[status(thm)],[f1]) ).
thf(f1,axiom,
! [X0: $tType,X1: X0 > $o,X2: X0] :
( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= ( X1 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.dVMtFoK4la/DTF2THF_8521.p','thm/sets/IN_') ).
thf(f23,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $false )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $true )
| ( $true
= ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f22]) ).
thf(f22,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $false )
| ( $true
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f16,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ),
inference(fool_elimination,[status(thm)],[f9]) ).
thf(f9,plain,
! [X0: $tType,X1: X0 > $o,X2: X0 > $o,X3: X0] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= ( 'const/sets/IN' @ X0 @ X3 @ X2 ) )
| ( 'const/sets/IN' @ X0 @ X3 @ X1 ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X4: X0] :
( ( ( 'const/sets/IN' @ X0 @ X4 @ ( 'const/sets/UNION' @ X0 @ X2 @ X3 ) )
= ( 'const/sets/IN' @ X0 @ X4 @ X3 ) )
| ( 'const/sets/IN' @ X0 @ X4 @ X2 ) ),
file('/export/starexec/sandbox/tmp/tmp.dVMtFoK4la/DTF2THF_8521.p','thm/sets/IN_UNION_') ).
thf(f47,plain,
( ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $true )
| ~ spl2_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl2_1
<=> ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition]) ).
thf(f20,plain,
! [X0: $tType,X2: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X2 @ X1 )
= $false )
| ( ( X1 @ X2 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f17]) ).
thf(f131,plain,
( ~ spl2_2
| ~ spl2_4 ),
inference(avatar_contradiction_clause,[status(thm)],[f130]) ).
thf(f130,plain,
( $false
| ~ spl2_2
| ~ spl2_4 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( $false = $true )
| ~ spl2_2
| ~ spl2_4 ),
inference(backward_demodulation,[status(thm)],[f51,f60]) ).
thf(f51,plain,
( ( ( sK1 @ sK5 )
= $true )
| ~ spl2_2 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl2_2
<=> ( ( sK1 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition]) ).
thf(f125,plain,
( spl2_4
| ~ spl2_3 ),
inference(avatar_split_clause,[status(thm)],[f121,f54,f58]) ).
thf(f54,definition,
( spl2_3
<=> ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 ) ) ),
introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition]) ).
thf(f121,plain,
( ( $false
= ( sK1 @ sK5 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f119]) ).
thf(f119,plain,
( ( $false = $true )
| ( $false
= ( sK1 @ sK5 ) )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f19,f115]) ).
thf(f115,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ~ spl2_3 ),
inference(trivial_inequality_removal,[status(thm)],[f113]) ).
thf(f113,plain,
( ( $false
= ( 'const/sets/IN' @ sK0 @ sK5 @ sK1 ) )
| ( $false = $true )
| ~ spl2_3 ),
inference(superposition,[status(thm)],[f98,f56]) ).
thf(f56,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 ) )
| ~ spl2_3 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f98,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f91]) ).
thf(f91,plain,
! [X0: $tType,X2: X0 > $o,X3: X0 > $o,X1: X0] :
( ( ( 'const/sets/IN' @ X0 @ X1 @ X3 )
= $false )
| ( ( 'const/sets/UNION' @ X0 @ X2 @ X3 @ X1 )
= $true )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f24,f20]) ).
thf(f24,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( ( 'const/sets/IN' @ X0 @ X3 @ X2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f21]) ).
thf(f21,plain,
! [X0: $tType,X2: X0 > $o,X3: X0,X1: X0 > $o] :
( ( ( 'const/sets/IN' @ X0 @ X3 @ ( 'const/sets/UNION' @ X0 @ X1 @ X2 ) )
= $true )
| ( $false
= ( ( 'const/sets/IN' @ X0 @ X3 @ X1 )
| ( 'const/sets/IN' @ X0 @ X3 @ X2 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f16]) ).
thf(f61,plain,
( spl2_3
| spl2_4 ),
inference(avatar_split_clause,[status(thm)],[f43,f58,f54]) ).
thf(f43,plain,
( ( $false
= ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 ) )
| ( $false
= ( sK1 @ sK5 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
!= ( sK1 @ sK5 ) ),
inference(negative_extensionality,[status(thm)],[f15]) ).
thf(f15,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
!= sK1 ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
!= sK1 ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13]) ).
thf(f13,plain,
( ? [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
!= X1 )
=> ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 )
!= sK1 ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
? [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
!= X1 ),
inference(ennf_transformation,[status(thm)],[f11]) ).
thf(f11,plain,
~ ! [X0: $tType,X1: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X1 @ X1 )
= X1 ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,negated_conjecture,
~ ! [X0: $tType,X2: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ X2 )
= X2 ),
inference(negated_conjecture,[status(cth)],[f4]) ).
thf(f4,conjecture,
! [X0: $tType,X2: X0 > $o] :
( ( 'const/sets/UNION' @ X0 @ X2 @ X2 )
= X2 ),
file('/export/starexec/sandbox/tmp/tmp.dVMtFoK4la/DTF2THF_8521.p','thm/sets/UNION_IDEMPOT_') ).
thf(f52,plain,
( spl2_1
| spl2_2 ),
inference(avatar_split_clause,[status(thm)],[f42,f49,f45]) ).
thf(f42,plain,
( ( ( 'const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5 )
= $true )
| ( ( sK1 @ sK5 )
= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV450^1 : TPTP v9.2.1. Released v7.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:47:22 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.45 ---- Original DTF file ---
% 0.31/0.45 thf(spec,logic,$$dhol).
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 % File : SEV450^1 : TPTP v9.2.1. Released v7.0.0.
% 0.31/0.45 % Domain : Analysis
% 0.31/0.45 % Problem : UNION_IDEMPOT
% 0.31/0.45 % Version : Especial.
% 0.31/0.45 % English :
% 0.31/0.45
% 0.31/0.45 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.31/0.45 % Source : [Kal16]
% 0.31/0.45 % Names : UNION_IDEMPOT_.p [Kal16]
% 0.31/0.45
% 0.31/0.45 % Status : Theorem
% 0.31/0.45 % Rating : 0.33 v8.1.0, 0.25 v7.5.0, 0.00 v7.1.0
% 0.31/0.45 % Syntax : Number of formulae : 6 ( 4 unt; 2 typ; 0 def)
% 0.31/0.45 % Number of atoms : 14 ( 6 equ; 0 cnn)
% 0.31/0.45 % Maximal formula atoms : 1 ( 3 avg)
% 0.31/0.45 % Number of connectives : 26 ( 0 ~; 1 |; 0 &; 25 @)
% 0.31/0.45 % ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% 0.31/0.45 % Maximal formula depth : 5 ( 4 avg)
% 0.31/0.45 % Number of types : 1 ( 0 usr)
% 0.31/0.45 % Number of type conns : 14 ( 14 >; 0 *; 0 +; 0 <<)
% 0.31/0.45 % Number of symbols : 3 ( 2 usr; 0 con; 2-4 aty)
% 0.31/0.45 % Number of variables : 15 ( 0 ^; 13 !; 0 ?; 15 :)
% 0.31/0.45 % ( 2 !>; 0 ?*; 0 @-; 0 @+)
% 0.31/0.45 % SPC : TH1_THM_EQU_NAR
% 0.31/0.45
% 0.31/0.45 % Comments : Exported from core HOL Light.
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 thf('thf_const_const/sets/UNION',type,
% 0.31/0.45 'const/sets/UNION':
% 0.31/0.45 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf('thf_const_const/sets/IN',type,
% 0.31/0.45 'const/sets/IN':
% 0.31/0.45 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 0.31/0.45
% 0.31/0.45 thf('thm/sets/IN_',axiom,
% 0.31/0.45 ! [A: $tType,P: A > $o,A0: A] :
% 0.31/0.45 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 0.31/0.45 = ( P @ A0 ) ) ).
% 0.31/0.45
% 0.31/0.45 thf('thm/sets/IN_UNION_',axiom,
% 0.31/0.45 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A] :
% 0.31/0.45 ( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) )
% 0.31/0.45 = ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.31/0.45 | ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf('thm/sets/EXTENSION_',axiom,
% 0.31/0.45 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 0.31/0.45 ( ( A0 = A1 )
% 0.31/0.45 = ( ! [A2: A] :
% 0.31/0.45 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 0.31/0.45 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 0.31/0.45
% 0.31/0.45 thf('thm/sets/UNION_IDEMPOT_',conjecture,
% 0.31/0.45 ! [A: $tType,A0: A > $o] :
% 0.31/0.45 ( ( 'const/sets/UNION' @ A @ A0 @ A0 )
% 0.31/0.45 = A0 ) ).
% 0.31/0.45
% 0.31/0.45 %------------------------------------------------------------------------------
% 0.31/0.45 ------------------------
% 1.48/1.25 ---- Embedded in THF ---
% 1.48/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.48/1.25 %%% Generated on Tue Feb 24 12:47:23 EST 2026
% 1.48/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.48/1.25 %%% Logic specification used:
% 1.48/1.25 %%% thf(spec, logic, $$dhol).
% 1.48/1.25
% 1.48/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dVMtFoK4la/DTF2DTF8521.p
% See solution above
% 1.48/1.25 ------------------------
% 1.48/1.26 ---- Cleaned THF ---
% 1.48/1.26 thf('thf_const_const/sets/UNION',type,
% 1.48/1.26 'const/sets/UNION':
% 1.48/1.26 !>[A: $tType] : ( ( A > $o ) > ( A > $o ) > A > $o ) ).
% 1.48/1.26
% 1.48/1.26 thf('thf_const_const/sets/IN',type,
% 1.48/1.26 'const/sets/IN':
% 1.48/1.26 !>[A: $tType] : ( A > ( A > $o ) > $o ) ).
% 1.48/1.26
% 1.48/1.26 thf('thm/sets/IN_',axiom,
% 1.48/1.26 ! [A: $tType,P: A > $o,A0: A] :
% 1.48/1.26 ( ( 'const/sets/IN' @ A @ A0 @ P )
% 1.48/1.26 = ( P @ A0 ) ) ).
% 1.48/1.26
% 1.48/1.26 thf('thm/sets/IN_UNION_',axiom,
% 1.48/1.26 ! [A: $tType,A0: A > $o,A1: A > $o,A2: A] :
% 1.48/1.26 ( ( 'const/sets/IN' @ A @ A2 @ ( 'const/sets/UNION' @ A @ A0 @ A1 ) )
% 1.48/1.26 = ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.48/1.26 | ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ).
% 1.48/1.26
% 1.48/1.26 thf('thm/sets/EXTENSION_',axiom,
% 1.48/1.26 ! [A: $tType,A0: A > $o,A1: A > $o] :
% 1.48/1.26 ( ( A0 = A1 )
% 1.48/1.26 = ( ! [A2: A] :
% 1.48/1.26 ( ( 'const/sets/IN' @ A @ A2 @ A0 )
% 1.48/1.26 = ( 'const/sets/IN' @ A @ A2 @ A1 ) ) ) ) ).
% 1.48/1.26
% 1.48/1.26 thf('thm/sets/UNION_IDEMPOT_',conjecture,
% 1.48/1.26 ! [A: $tType,A0: A > $o] :
% 1.48/1.26 ( ( 'const/sets/UNION' @ A @ A0 @ A0 )
% 1.48/1.26 = A0 ) ).
% 1.48/1.26 ------------------------
% 1.48/1.27 % (8801)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_8521 for (2999ds/183Mi)
% 1.48/1.27 % (8802)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_8521 for (2999ds/4Mi)
% 1.48/1.27 % (8802)Instruction limit reached!
% 1.48/1.27 % (8802)------------------------------
% 1.48/1.27 % (8802)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.27 % (8802)Termination reason: Unknown
% 1.48/1.27 % (8802)Termination phase: Saturation
% 1.48/1.27
% 1.48/1.27 % (8802)Memory used [KB]: 5500
% 1.48/1.27 % (8802)Time elapsed: 0.003 s
% 1.48/1.27 % (8802)Instructions burned: 6 (million)
% 1.48/1.27 % (8802)------------------------------
% 1.48/1.27 % (8802)------------------------------
% 1.48/1.28 % (8803)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_8521 for (2999ds/27Mi)
% 1.48/1.28 % (8804)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_8521 for (2999ds/2Mi)
% 1.48/1.28 % (8805)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_8521 for (2999ds/2Mi)
% 1.48/1.28 % (8806)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_8521 for (2999ds/275Mi)
% 1.48/1.28 % (8807)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_8521 for (2999ds/18Mi)
% 1.48/1.28 % (8804)Instruction limit reached!
% 1.48/1.28 % (8804)------------------------------
% 1.48/1.28 % (8804)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (8804)Termination reason: Unknown
% 1.48/1.28 % (8804)Termination phase: Saturation
% 1.48/1.28
% 1.48/1.28 % (8804)Memory used [KB]: 895
% 1.48/1.28 % (8804)Time elapsed: 0.003 s
% 1.48/1.28 % (8804)Instructions burned: 2 (million)
% 1.48/1.28 % (8804)------------------------------
% 1.48/1.28 % (8804)------------------------------
% 1.48/1.28 % (8805)Instruction limit reached!
% 1.48/1.28 % (8805)------------------------------
% 1.48/1.28 % (8805)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (8805)Termination reason: Unknown
% 1.48/1.28 % (8805)Termination phase: shuffling
% 1.48/1.28
% 1.48/1.28 % (8805)Memory used [KB]: 895
% 1.48/1.28 % (8805)Time elapsed: 0.003 s
% 1.48/1.28 % (8805)Instructions burned: 2 (million)
% 1.48/1.28 % (8805)------------------------------
% 1.48/1.28 % (8805)------------------------------
% 1.48/1.28 % (8806)Refutation not found, incomplete strategy
% 1.48/1.28 % (8806)------------------------------
% 1.48/1.28 % (8806)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.28 % (8806)Termination reason: Refutation not found, incomplete strategy
% 1.48/1.28
% 1.48/1.28
% 1.48/1.28 % (8806)Memory used [KB]: 5500
% 1.48/1.28 % (8806)Time elapsed: 0.004 s
% 1.48/1.28 % (8806)Instructions burned: 3 (million)
% 1.48/1.28 % (8806)------------------------------
% 1.48/1.28 % (8806)------------------------------
% 1.48/1.28 % (8808)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_8521 for (2999ds/3Mi)
% 1.48/1.29 % (8808)Instruction limit reached!
% 1.48/1.29 % (8808)------------------------------
% 1.48/1.29 % (8808)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (8808)Termination reason: Unknown
% 1.48/1.29 % (8808)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (8808)Memory used [KB]: 5500
% 1.48/1.29 % (8808)Time elapsed: 0.003 s
% 1.48/1.29 % (8808)Instructions burned: 3 (million)
% 1.48/1.29 % (8808)------------------------------
% 1.48/1.29 % (8808)------------------------------
% 1.48/1.29 % (8807)Instruction limit reached!
% 1.48/1.29 % (8807)------------------------------
% 1.48/1.29 % (8807)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.48/1.29 % (8807)Termination reason: Unknown
% 1.48/1.29 % (8807)Termination phase: Saturation
% 1.48/1.29
% 1.48/1.29 % (8807)Memory used [KB]: 5628
% 1.48/1.29 % (8807)Time elapsed: 0.014 s
% 1.48/1.29 % (8807)Instructions burned: 18 (million)
% 1.48/1.29 % (8807)------------------------------
% 1.48/1.29 % (8807)------------------------------
% 1.48/1.29 % (8803)First to succeed.
% 1.48/1.30 % (8812)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_8521 for (2999ds/1041Mi)
% 1.48/1.30 % Exception at run slice level
% 1.48/1.30 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
% 1.61/1.30 % (8803)Refutation found. Thanks to Tanya!
% 1.61/1.30 % SZS status Theorem for DTF2THF_8521
% 1.61/1.30 % SZS output start Proof for DTF2THF_8521
% 1.61/1.30 thf(type_def_6, type, sK0: $tType).
% 1.61/1.30 thf(func_def_0, type, 'const/sets/UNION': !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0 > $o)).
% 1.61/1.30 thf(func_def_1, type, 'const/sets/IN': !>[X0: $tType]:(X0 > (X0 > $o) > $o)).
% 1.61/1.30 thf(func_def_3, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.61/1.30 thf(func_def_11, type, sK1: sK0 > $o).
% 1.61/1.30 thf(func_def_13, type, sK3: !>[X0: $tType]:((X0 > $o) > (X0 > $o) > X0)).
% 1.61/1.30 thf(func_def_14, type, ph4: !>[X0: $tType]:(X0)).
% 1.61/1.30 thf(func_def_15, type, sK5: sK0).
% 1.61/1.30 thf(f181,plain,(
% 1.61/1.30 $false),
% 1.61/1.30 inference(avatar_sat_refutation,[status(thm)],[f52,f61,f125,f131,f180])).
% 1.61/1.30 thf(f180,plain,(
% 1.61/1.30 ~spl2_1 | ~spl2_4),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f179])).
% 1.61/1.30 thf(f179,plain,(
% 1.61/1.30 $false | (~spl2_1 | ~spl2_4)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f178])).
% 1.61/1.30 thf(f178,plain,(
% 1.61/1.30 ($false = $true) | (~spl2_1 | ~spl2_4)),
% 1.61/1.30 inference(forward_demodulation,[status(thm)],[f171,f60])).
% 1.61/1.30 thf(f60,plain,(
% 1.61/1.30 ($false = (sK1 @ sK5)) | ~spl2_4),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.61/1.30 thf(f58,definition,(
% 1.61/1.30 spl2_4 <=> ($false = (sK1 @ sK5))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl2_4])],[avatar_definition])).
% 1.61/1.30 thf(f171,plain,(
% 1.61/1.30 ((sK1 @ sK5) = $true) | ~spl2_1),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f170])).
% 1.61/1.30 thf(f170,plain,(
% 1.61/1.30 ($false = $true) | ((sK1 @ sK5) = $true) | ~spl2_1),
% 1.61/1.30 inference(superposition,[status(thm)],[f20,f159])).
% 1.61/1.30 thf(f159,plain,(
% 1.61/1.30 (('const/sets/IN' @ sK0 @ sK5 @ sK1) = $true) | ~spl2_1),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.61/1.30 thf(f158,plain,(
% 1.61/1.30 (('const/sets/IN' @ sK0 @ sK5 @ sK1) = $true) | ($false = $true) | ~spl2_1),
% 1.61/1.30 inference(duplicate_literal_removal,[status(thm)],[f155])).
% 1.61/1.30 thf(f155,plain,(
% 1.61/1.30 (('const/sets/IN' @ sK0 @ sK5 @ sK1) = $true) | ($false = $true) | (('const/sets/IN' @ sK0 @ sK5 @ sK1) = $true) | ~spl2_1),
% 1.61/1.30 inference(superposition,[status(thm)],[f47,f64])).
% 1.61/1.30 thf(f64,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0] : ((('const/sets/UNION' @ X0 @ X2 @ X3 @ X1) = $false) | ($true = ('const/sets/IN' @ X0 @ X1 @ X2)) | (('const/sets/IN' @ X0 @ X1 @ X3) = $true)) )),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f63])).
% 1.61/1.30 thf(f63,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ X3) = $true) | ($true = ('const/sets/IN' @ X0 @ X1 @ X2)) | ($false = $true) | (('const/sets/UNION' @ X0 @ X2 @ X3 @ X1) = $false)) )),
% 1.61/1.30 inference(superposition,[status(thm)],[f23,f19])).
% 1.61/1.30 thf(f19,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = $true) | ((X1 @ X2) = $false)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.61/1.30 thf(f17,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f1])).
% 1.61/1.30 thf(f1,axiom,(
% 1.61/1.30 ! [X0 : $tType,X1 : X0 > $o,X2 : X0] : (('const/sets/IN' @ X0 @ X2 @ X1) = (X1 @ X2))),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.dVMtFoK4la/DTF2THF_8521.p','thm/sets/IN_')).
% 1.61/1.30 thf(f23,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = $false) | (('const/sets/IN' @ X0 @ X3 @ X2) = $true) | ($true = ('const/sets/IN' @ X0 @ X3 @ X1))) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f22])).
% 1.61/1.30 thf(f22,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = $false) | ($true = (('const/sets/IN' @ X0 @ X3 @ X1) | ('const/sets/IN' @ X0 @ X3 @ X2)))) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.61/1.30 thf(f16,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = (('const/sets/IN' @ X0 @ X3 @ X1) | ('const/sets/IN' @ X0 @ X3 @ X2)))) )),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f10])).
% 1.61/1.30 thf(f10,plain,(
% 1.61/1.30 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = (('const/sets/IN' @ X0 @ X3 @ X1) | ('const/sets/IN' @ X0 @ X3 @ X2)))),
% 1.61/1.30 inference(fool_elimination,[status(thm)],[f9])).
% 1.61/1.30 thf(f9,plain,(
% 1.61/1.30 ! [X0 : $tType,X1 : X0 > $o,X2 : X0 > $o,X3 : X0] : (('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = ('const/sets/IN' @ X0 @ X3 @ X2) | ('const/sets/IN' @ X0 @ X3 @ X1))),
% 1.61/1.30 inference(rectify,[status(thm)],[f2])).
% 1.61/1.30 thf(f2,axiom,(
% 1.61/1.30 ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X4 : X0] : (('const/sets/IN' @ X0 @ X4 @ ('const/sets/UNION' @ X0 @ X2 @ X3)) = ('const/sets/IN' @ X0 @ X4 @ X3) | ('const/sets/IN' @ X0 @ X4 @ X2))),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.dVMtFoK4la/DTF2THF_8521.p','thm/sets/IN_UNION_')).
% 1.61/1.30 thf(f47,plain,(
% 1.61/1.30 (('const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5) = $true) | ~spl2_1),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.61/1.30 thf(f45,definition,(
% 1.61/1.30 spl2_1 <=> (('const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5) = $true)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl2_1])],[avatar_definition])).
% 1.61/1.30 thf(f20,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X2 @ X1) = $false) | ((X1 @ X2) = $true)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f17])).
% 1.61/1.30 thf(f131,plain,(
% 1.61/1.30 ~spl2_2 | ~spl2_4),
% 1.61/1.30 inference(avatar_contradiction_clause,[status(thm)],[f130])).
% 1.61/1.30 thf(f130,plain,(
% 1.61/1.30 $false | (~spl2_2 | ~spl2_4)),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.61/1.30 thf(f126,plain,(
% 1.61/1.30 ($false = $true) | (~spl2_2 | ~spl2_4)),
% 1.61/1.30 inference(backward_demodulation,[status(thm)],[f51,f60])).
% 1.61/1.30 thf(f51,plain,(
% 1.61/1.30 ((sK1 @ sK5) = $true) | ~spl2_2),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.61/1.30 thf(f49,definition,(
% 1.61/1.30 spl2_2 <=> ((sK1 @ sK5) = $true)),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl2_2])],[avatar_definition])).
% 1.61/1.30 thf(f125,plain,(
% 1.61/1.30 spl2_4 | ~spl2_3),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f121,f54,f58])).
% 1.61/1.30 thf(f54,definition,(
% 1.61/1.30 spl2_3 <=> ($false = ('const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5))),
% 1.61/1.30 introduced(definition,[new_symbols(naming,[spl2_3])],[avatar_definition])).
% 1.61/1.30 thf(f121,plain,(
% 1.61/1.30 ($false = (sK1 @ sK5)) | ~spl2_3),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f119])).
% 1.61/1.30 thf(f119,plain,(
% 1.61/1.30 ($false = $true) | ($false = (sK1 @ sK5)) | ~spl2_3),
% 1.61/1.30 inference(superposition,[status(thm)],[f19,f115])).
% 1.61/1.30 thf(f115,plain,(
% 1.61/1.30 ($false = ('const/sets/IN' @ sK0 @ sK5 @ sK1)) | ~spl2_3),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f113])).
% 1.61/1.30 thf(f113,plain,(
% 1.61/1.30 ($false = ('const/sets/IN' @ sK0 @ sK5 @ sK1)) | ($false = $true) | ~spl2_3),
% 1.61/1.30 inference(superposition,[status(thm)],[f98,f56])).
% 1.61/1.30 thf(f56,plain,(
% 1.61/1.30 ($false = ('const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5)) | ~spl2_3),
% 1.61/1.30 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.61/1.30 thf(f98,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0] : ((('const/sets/UNION' @ X0 @ X2 @ X3 @ X1) = $true) | (('const/sets/IN' @ X0 @ X1 @ X3) = $false)) )),
% 1.61/1.30 inference(trivial_inequality_removal,[status(thm)],[f91])).
% 1.61/1.30 thf(f91,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0 > $o,X1 : X0] : ((('const/sets/IN' @ X0 @ X1 @ X3) = $false) | (('const/sets/UNION' @ X0 @ X2 @ X3 @ X1) = $true) | ($false = $true)) )),
% 1.61/1.30 inference(superposition,[status(thm)],[f24,f20])).
% 1.61/1.30 thf(f24,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = $true) | (('const/sets/IN' @ X0 @ X3 @ X2) = $false)) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f21])).
% 1.61/1.30 thf(f21,plain,(
% 1.61/1.30 ( ! [X0 : $tType,X2 : X0 > $o,X3 : X0,X1 : X0 > $o] : ((('const/sets/IN' @ X0 @ X3 @ ('const/sets/UNION' @ X0 @ X1 @ X2)) = $true) | ($false = (('const/sets/IN' @ X0 @ X3 @ X1) | ('const/sets/IN' @ X0 @ X3 @ X2)))) )),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f16])).
% 1.61/1.30 thf(f61,plain,(
% 1.61/1.30 spl2_3 | spl2_4),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f43,f58,f54])).
% 1.61/1.30 thf(f43,plain,(
% 1.61/1.30 ($false = ('const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5)) | ($false = (sK1 @ sK5))),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.61/1.30 thf(f41,plain,(
% 1.61/1.30 (('const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5) != (sK1 @ sK5))),
% 1.61/1.30 inference(negative_extensionality,[status(thm)],[f15])).
% 1.61/1.30 thf(f15,plain,(
% 1.61/1.30 (('const/sets/UNION' @ sK0 @ sK1 @ sK1) != sK1)),
% 1.61/1.30 inference(cnf_transformation,[status(thm)],[f14])).
% 1.61/1.30 thf(f14,plain,(
% 1.61/1.30 (('const/sets/UNION' @ sK0 @ sK1 @ sK1) != sK1)),
% 1.61/1.30 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1])],[f12,f13])).
% 1.61/1.30 thf(f13,plain,(
% 1.61/1.30 ? [X0 : $tType,X1 : X0 > $o] : (('const/sets/UNION' @ X0 @ X1 @ X1) != X1) => (('const/sets/UNION' @ sK0 @ sK1 @ sK1) != sK1)),
% 1.61/1.30 introduced(definition,[],[choice_axiom])).
% 1.61/1.30 thf(f12,plain,(
% 1.61/1.30 ? [X0 : $tType,X1 : X0 > $o] : (('const/sets/UNION' @ X0 @ X1 @ X1) != X1)),
% 1.61/1.30 inference(ennf_transformation,[status(thm)],[f11])).
% 1.61/1.30 thf(f11,plain,(
% 1.61/1.30 ~! [X0 : $tType,X1 : X0 > $o] : (('const/sets/UNION' @ X0 @ X1 @ X1) = X1)),
% 1.61/1.30 inference(rectify,[status(thm)],[f5])).
% 1.61/1.30 thf(f5,negated_conjecture,(
% 1.61/1.30 ~! [X0 : $tType,X2 : X0 > $o] : (('const/sets/UNION' @ X0 @ X2 @ X2) = X2)),
% 1.61/1.30 inference(negated_conjecture,[status(cth)],[f4])).
% 1.61/1.30 thf(f4,conjecture,(
% 1.61/1.30 ! [X0 : $tType,X2 : X0 > $o] : (('const/sets/UNION' @ X0 @ X2 @ X2) = X2)),
% 1.61/1.30 file('/export/starexec/sandbox/tmp/tmp.dVMtFoK4la/DTF2THF_8521.p','thm/sets/UNION_IDEMPOT_')).
% 1.61/1.30 thf(f52,plain,(
% 1.61/1.30 spl2_1 | spl2_2),
% 1.61/1.30 inference(avatar_split_clause,[status(thm)],[f42,f49,f45])).
% 1.61/1.30 thf(f42,plain,(
% 1.61/1.30 (('const/sets/UNION' @ sK0 @ sK1 @ sK1 @ sK5) = $true) | ((sK1 @ sK5) = $true)),
% 1.61/1.30 inference(binary_proxy_clausification,[status(thm)],[f41])).
% 1.61/1.30 % SZS output end Proof for DTF2THF_8521
% 1.61/1.30 % (8803)------------------------------
% 1.61/1.30 % (8803)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.61/1.30 % (8803)Termination reason: Refutation
% 1.61/1.30
% 1.61/1.30 % (8803)Memory used [KB]: 5628
% 1.61/1.30 % (8803)Time elapsed: 0.018 s
% 1.61/1.30 % (8803)Instructions burned: 23 (million)
% 1.61/1.30 % (8803)------------------------------
% 1.61/1.30 % (8803)------------------------------
% 1.61/1.30 % (8800)Success in time 0.032 s
%------------------------------------------------------------------------------