%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET002^3 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.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 09:30:53 AM UTC 2026
% Result : Theorem 0.31s 1.34s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 44 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 177 ( 38 equ; 0 cnn)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 286 ( 7 ~; 2 |; 0 &; 255 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 20 usr; 5 con; 0-3 aty)
% ( 12 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 87 ( 75 ^; 12 !; 0 ?; 87 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
mworld: $tType ).
thf(func_def_0,type,
mworld: $tType ).
thf(func_def_1,type,
mrel: mworld > mworld > $o ).
thf(func_def_2,type,
mactual: mworld ).
thf(func_def_3,type,
mlocal: ( mworld > $o ) > $o ).
thf(func_def_5,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(func_def_6,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_7,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_8,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_9,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(func_def_10,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(func_def_11,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(func_def_12,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_15,type,
member: $i > $i > mworld > $o ).
thf(func_def_16,type,
subset: $i > $i > mworld > $o ).
thf(func_def_17,type,
union: $i > $i > $i ).
thf(func_def_31,type,
sK0: mworld > mworld ).
thf(func_def_35,type,
sK2: $i > $i > $i ).
thf(func_def_36,type,
sK3: $i > $i > $i ).
thf(f320,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f318]) ).
thf(f318,plain,
$false = $true,
inference(superposition,[status(thm)],[f313,f141]) ).
thf(f141,plain,
! [X1: $i] :
( ( subset @ X1 @ X1 @ mactual )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f140]) ).
thf(f140,plain,
! [X1: $i] :
( ( ^ [Y0: $i] : ( subset @ Y0 @ Y0 @ mactual )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f93,f95,f102]) ).
thf(f102,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
thf(f75,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) )
= mforall_di ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] : ( X1 @ X5 @ X2 ) )
= mforall_di ),
file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',mforall_di_def) ).
thf(f95,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',mlocal_def) ).
thf(f93,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f69]) ).
thf(f69,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( subset @ Y0 @ Y0 ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f68]) ).
thf(f68,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( subset @ X0 @ X0 ) ) ),
inference(rectify,[status(thm)],[f26]) ).
thf(f26,axiom,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] : ( subset @ X3 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',reflexivity_of_subset) ).
thf(f313,plain,
( $false
= ( subset @ sK4 @ sK4 @ mactual ) ),
inference(trivial_inequality_removal,[status(thm)],[f309]) ).
thf(f309,plain,
( ( $false
= ( subset @ sK4 @ sK4 @ mactual ) )
| ( $false = $true ) ),
inference(superposition,[status(thm)],[f230,f214]) ).
thf(f214,plain,
! [X2: $i,X1: $i] :
( ( ( qmltpeq @ ( union @ X1 @ X2 ) @ X2 @ mactual )
= $true )
| ( $false
= ( subset @ X1 @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f213]) ).
thf(f213,plain,
! [X2: $i,X1: $i] :
( ( ( subset @ X1 @ X2 @ mactual )
=> ( qmltpeq @ ( union @ X1 @ X2 ) @ X2 @ mactual ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f212]) ).
thf(f212,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
=> ( qmltpeq @ ( union @ X1 @ Y0 ) @ Y0 @ mactual ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f211]) ).
thf(f211,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
=> ( qmltpeq @ ( union @ X1 @ Y0 ) @ Y0 @ mactual ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f210]) ).
thf(f210,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
=> ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 @ mactual ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f209]) ).
thf(f209,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
=> ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] : ( Y1 @ Y3 @ Y2 ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
=> ( Y3 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f106,f95,f102,f102,f105]) ).
thf(f105,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f77]) ).
thf(f77,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f76]) ).
thf(f76,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',mimplies_def) ).
thf(f106,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f55]) ).
thf(f55,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mimplies @ ( subset @ Y0 @ Y1 ) @ ( qmltpeq @ ( union @ Y0 @ Y1 ) @ Y1 ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f54]) ).
thf(f54,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mimplies @ ( subset @ X0 @ X1 ) @ ( qmltpeq @ ( union @ X0 @ X1 ) @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f21]) ).
thf(f21,axiom,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] :
( mforall_di
@ ^ [X8: $i] : ( mimplies @ ( subset @ X3 @ X8 ) @ ( qmltpeq @ ( union @ X3 @ X8 ) @ X8 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',subset_union) ).
thf(f230,plain,
( $false
= ( qmltpeq @ ( union @ sK4 @ sK4 ) @ sK4 @ mactual ) ),
inference(beta_eta_normalization,[status(thm)],[f229]) ).
thf(f229,plain,
( $false
= ( ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 @ mactual )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f228]) ).
thf(f228,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 @ mactual ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f121]) ).
thf(f121,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f97,f95,f102]) ).
thf(f97,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f86]) ).
thf(f86,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(flattening,[status(thm)],[f47]) ).
thf(f47,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( qmltpeq @ ( union @ Y0 @ Y0 ) @ Y0 ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f46]) ).
thf(f46,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( qmltpeq @ ( union @ X0 @ X0 ) @ X0 ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X3: $i] : ( qmltpeq @ ( union @ X3 @ X3 ) @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f28,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X3: $i] : ( qmltpeq @ ( union @ X3 @ X3 ) @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',prove_idempotency_of_union) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET002^3 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 11:48:24 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.28/0.46 ---- Original DTF file ---
% 0.28/0.46 thf(spec,logic,$$dhol).
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 % File : SET002^3 : TPTP v9.2.1. Released v8.1.0.
% 0.28/0.46 % Domain : Set Theory
% 0.28/0.46 % Problem : TPTP problem SET002+3.p with axiomatized equality
% 0.28/0.46 % Version : [BP13] axioms.
% 0.28/0.46 % English :
% 0.28/0.46
% 0.28/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.28/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.28/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.28/0.46 % Source : [TPTP]
% 0.28/0.46 % Names : SET002+1 [QMLTP]
% 0.28/0.46
% 0.28/0.46 % Status : Theorem
% 0.28/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.28/0.46 % Syntax : Number of formulae : 45 ( 11 unt; 17 typ; 10 def)
% 0.28/0.46 % Number of atoms : 142 ( 10 equ; 0 cnn)
% 0.28/0.46 % Maximal formula atoms : 9 ( 5 avg)
% 0.28/0.46 % Number of connectives : 227 ( 1 ~; 1 |; 2 &; 220 @)
% 0.28/0.46 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.28/0.46 % Maximal formula depth : 14 ( 8 avg)
% 0.28/0.46 % Number of types : 3 ( 1 usr)
% 0.28/0.46 % Number of type conns : 68 ( 68 >; 0 *; 0 +; 0 <<)
% 0.28/0.46 % Number of symbols : 17 ( 16 usr; 1 con; 0-3 aty)
% 0.28/0.46 % Number of variables : 70 ( 64 ^; 3 !; 3 ?; 70 :)
% 0.28/0.46 % SPC : TH0_THM_EQU_NAR
% 0.28/0.46
% 0.28/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.28/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.28/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.28/0.46 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.28/0.46 % $modalities == $modal_system_D].
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 thf(mworld,type,
% 0.28/0.46 mworld: $tType ).
% 0.28/0.46
% 0.28/0.46 thf(mrel_type,type,
% 0.28/0.46 mrel: mworld > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mactual_type,type,
% 0.28/0.46 mactual: mworld ).
% 0.28/0.46
% 0.28/0.46 thf(mlocal_type,type,
% 0.28/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mlocal_def,definition,
% 0.28/0.46 ( mlocal
% 0.28/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mnot_type,type,
% 0.28/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mand_type,type,
% 0.28/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mor_type,type,
% 0.28/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mimplies_type,type,
% 0.28/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mequiv_type,type,
% 0.28/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mnot_def,definition,
% 0.28/0.46 ( mnot
% 0.28/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.28/0.46 ~ ( A @ W ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mand_def,definition,
% 0.28/0.46 ( mand
% 0.28/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.46 ( ( A @ W )
% 0.28/0.46 & ( B @ W ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mor_def,definition,
% 0.28/0.46 ( mor
% 0.28/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.46 ( ( A @ W )
% 0.28/0.46 | ( B @ W ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mimplies_def,definition,
% 0.28/0.46 ( mimplies
% 0.28/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.46 ( ( A @ W )
% 0.28/0.46 => ( B @ W ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mequiv_def,definition,
% 0.28/0.46 ( mequiv
% 0.28/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.46 ( ( A @ W )
% 0.28/0.46 <=> ( B @ W ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mbox_type,type,
% 0.28/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mbox_def,definition,
% 0.28/0.46 ( mbox
% 0.28/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.28/0.46 ! [V: mworld] :
% 0.28/0.46 ( ( mrel @ W @ V )
% 0.28/0.46 => ( Phi @ V ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mdia_type,type,
% 0.28/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mdia_def,definition,
% 0.28/0.46 ( mdia
% 0.28/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.28/0.46 ? [V: mworld] :
% 0.28/0.46 ( ( mrel @ W @ V )
% 0.28/0.46 & ( Phi @ V ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mrel_serial,axiom,
% 0.28/0.46 ! [W: mworld] :
% 0.28/0.46 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.28/0.46
% 0.28/0.46 thf(mforall_di_type,type,
% 0.28/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mforall_di_def,definition,
% 0.28/0.46 ( mforall_di
% 0.28/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.28/0.46 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(mexists_di_type,type,
% 0.28/0.46 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(mexists_di_def,definition,
% 0.28/0.46 ( mexists_di
% 0.28/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.28/0.46 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(qmltpeq_decl,type,
% 0.28/0.46 qmltpeq: $i > $i > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(member_decl,type,
% 0.28/0.46 member: $i > $i > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(subset_decl,type,
% 0.28/0.46 subset: $i > $i > mworld > $o ).
% 0.28/0.46
% 0.28/0.46 thf(union_decl,type,
% 0.28/0.46 union: $i > $i > $i ).
% 0.28/0.46
% 0.28/0.46 thf(reflexivity,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(symmetry,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [X: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(transitivity,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [X: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [Y: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(union_substitution_1,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [A: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(union_substitution_2,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [A: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(member_substitution_1,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [A: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(member_substitution_2,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [A: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subset_substitution_1,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [A: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subset_substitution_2,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [A: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subset_union,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( mimplies @ ( subset @ B @ C ) @ ( qmltpeq @ ( union @ B @ C ) @ C ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(union_defn,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [D: $i] : ( mequiv @ ( member @ D @ ( union @ B @ C ) ) @ ( mor @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(equal_defn,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(commutativity_of_union,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] : ( qmltpeq @ ( union @ B @ C ) @ ( union @ C @ B ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(subset_defn,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] :
% 0.28/0.46 ( mequiv @ ( subset @ B @ C )
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(reflexivity_of_subset,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [B: $i] : ( subset @ B @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(equal_member_defn,axiom,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [B: $i] :
% 0.28/0.46 ( mforall_di
% 0.28/0.46 @ ^ [C: $i] :
% 0.28/0.46 ( mequiv @ ( qmltpeq @ B @ C )
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [D: $i] : ( mequiv @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.28/0.46
% 0.28/0.46 thf(prove_idempotency_of_union,conjecture,
% 0.28/0.46 ( mlocal
% 0.28/0.46 @ ( mforall_di
% 0.28/0.46 @ ^ [B: $i] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) ) ).
% 0.28/0.46
% 0.28/0.46 %------------------------------------------------------------------------------
% 0.28/0.46 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 11:48:25 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2DTF7983.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(mworld,type,
% 0.31/1.31 mworld: $tType ).
% 0.31/1.31
% 0.31/1.31 thf(mrel_type,type,
% 0.31/1.31 mrel: mworld > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mactual_type,type,
% 0.31/1.31 mactual: mworld ).
% 0.31/1.31
% 0.31/1.31 thf(mlocal_type,type,
% 0.31/1.31 mlocal: ( mworld > $o ) > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mlocal_def,definition,
% 0.31/1.31 ( mlocal
% 0.31/1.31 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mnot_type,type,
% 0.31/1.31 mnot: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mand_type,type,
% 0.31/1.31 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mor_type,type,
% 0.31/1.31 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mimplies_type,type,
% 0.31/1.31 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mequiv_type,type,
% 0.31/1.31 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mnot_def,definition,
% 0.31/1.31 ( mnot
% 0.31/1.31 = ( ^ [A: mworld > $o,W: mworld] :
% 0.31/1.31 ~ ( A @ W ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mand_def,definition,
% 0.31/1.31 ( mand
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 & ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mor_def,definition,
% 0.31/1.31 ( mor
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 | ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mimplies_def,definition,
% 0.31/1.31 ( mimplies
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 => ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mequiv_def,definition,
% 0.31/1.31 ( mequiv
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 <=> ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mbox_type,type,
% 0.31/1.31 mbox: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mbox_def,definition,
% 0.31/1.31 ( mbox
% 0.31/1.31 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/1.31 ! [V: mworld] :
% 0.31/1.31 ( ( mrel @ W @ V )
% 0.31/1.31 => ( Phi @ V ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mdia_type,type,
% 0.31/1.31 mdia: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mdia_def,definition,
% 0.31/1.31 ( mdia
% 0.31/1.31 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/1.31 ? [V: mworld] :
% 0.31/1.31 ( ( mrel @ W @ V )
% 0.31/1.31 & ( Phi @ V ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mrel_serial,axiom,
% 0.31/1.31 ! [W: mworld] :
% 0.31/1.31 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.31/1.31
% 0.31/1.31 thf(mforall_di_type,type,
% 0.31/1.31 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mforall_di_def,definition,
% 0.31/1.31 ( mforall_di
% 0.31/1.31 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/1.31 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mexists_di_type,type,
% 0.31/1.31 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mexists_di_def,definition,
% 0.31/1.31 ( mexists_di
% 0.31/1.31 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/1.31 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(qmltpeq_decl,type,
% 0.31/1.31 qmltpeq: $i > $i > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(member_decl,type,
% 0.31/1.31 member: $i > $i > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(subset_decl,type,
% 0.31/1.31 subset: $i > $i > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(union_decl,type,
% 0.31/1.31 union: $i > $i > $i ).
% 0.31/1.31
% 0.31/1.31 thf(reflexivity,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(symmetry,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [X: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(transitivity,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [X: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [Y: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(union_substitution_1,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [A: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(union_substitution_2,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [A: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(member_substitution_1,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [A: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(member_substitution_2,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [A: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(subset_substitution_1,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [A: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(subset_substitution_2,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [A: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(subset_union,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mimplies @ ( subset @ B @ C ) @ ( qmltpeq @ ( union @ B @ C ) @ C ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(union_defn,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [D: $i] : ( mequiv @ ( member @ D @ ( union @ B @ C ) ) @ ( mor @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(equal_defn,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( mequiv @ ( qmltpeq @ B @ C ) @ ( mand @ ( subset @ B @ C ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(commutativity_of_union,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] : ( qmltpeq @ ( union @ B @ C ) @ ( union @ C @ B ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(subset_defn,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] :
% 0.31/1.31 ( mequiv @ ( subset @ B @ C )
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [D: $i] : ( mimplies @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(reflexivity_of_subset,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] : ( subset @ B @ B ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(equal_member_defn,axiom,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] :
% 0.31/1.31 ( mforall_di
% 0.31/1.31 @ ^ [C: $i] :
% 0.31/1.31 ( mequiv @ ( qmltpeq @ B @ C )
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [D: $i] : ( mequiv @ ( member @ D @ B ) @ ( member @ D @ C ) ) ) ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(prove_idempotency_of_union,conjecture,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mforall_di
% 0.31/1.31 @ ^ [B: $i] : ( qmltpeq @ ( union @ B @ B ) @ B ) ) ) ).
% 0.31/1.31 ------------------------
% 0.31/1.33 % (8287)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7983 for (2999ds/183Mi)
% 0.31/1.33 % (8288)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_7983 for (2999ds/4Mi)
% 0.31/1.33 % (8289)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_7983 for (2999ds/27Mi)
% 0.31/1.33 % (8288)Instruction limit reached!
% 0.31/1.33 % (8288)------------------------------
% 0.31/1.33 % (8288)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (8288)Termination reason: Unknown
% 0.31/1.33 % (8288)Termination phase: shuffling
% 0.31/1.33
% 0.31/1.33 % (8288)Memory used [KB]: 1023
% 0.31/1.33 % (8288)Time elapsed: 0.002 s
% 0.31/1.33 % (8288)Instructions burned: 4 (million)
% 0.31/1.33 % (8288)------------------------------
% 0.31/1.33 % (8288)------------------------------
% 0.31/1.34 % (8290)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7983 for (2999ds/2Mi)
% 0.31/1.34 % (8291)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_7983 for (2999ds/2Mi)
% 0.31/1.34 % (8292)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_7983 for (2999ds/275Mi)
% 0.31/1.34 % (8293)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7983 for (2999ds/18Mi)
% 0.31/1.34 % (8289)Instruction limit reached!
% 0.31/1.34 % (8289)------------------------------
% 0.31/1.34 % (8289)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (8289)Termination reason: Unknown
% 0.31/1.34 % (8289)Termination phase: Saturation
% 0.31/1.34
% 0.31/1.34 % (8289)Memory used [KB]: 5756
% 0.31/1.34 % (8289)Time elapsed: 0.009 s
% 0.31/1.34 % (8289)Instructions burned: 27 (million)
% 0.31/1.34 % (8289)------------------------------
% 0.31/1.34 % (8289)------------------------------
% 0.31/1.34 % (8290)Instruction limit reached!
% 0.31/1.34 % (8290)------------------------------
% 0.31/1.34 % (8290)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (8290)Termination reason: Unknown
% 0.31/1.34 % (8290)Termination phase: shuffling
% 0.31/1.34
% 0.31/1.34 % (8290)Memory used [KB]: 1023
% 0.31/1.34 % (8290)Time elapsed: 0.003 s
% 0.31/1.34 % (8290)Instructions burned: 2 (million)
% 0.31/1.34 % (8290)------------------------------
% 0.31/1.34 % (8290)------------------------------
% 0.31/1.34 % (8291)Instruction limit reached!
% 0.31/1.34 % (8291)------------------------------
% 0.31/1.34 % (8291)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (8291)Termination reason: Unknown
% 0.31/1.34 % (8291)Termination phase: shuffling
% 0.31/1.34
% 0.31/1.34 % (8291)Memory used [KB]: 1023
% 0.31/1.34 % (8291)Time elapsed: 0.003 s
% 0.31/1.34 % (8291)Instructions burned: 2 (million)
% 0.31/1.34 % (8291)------------------------------
% 0.31/1.34 % (8291)------------------------------
% 0.31/1.34 % (8287)First to succeed.
% 0.31/1.34 % (8294)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7983 for (2999ds/3Mi)
% 0.31/1.34 % (8287)Refutation found. Thanks to Tanya!
% 0.31/1.34 % SZS status Theorem for DTF2THF_7983
% 0.31/1.34 % SZS output start Proof for DTF2THF_7983
% 0.31/1.34 thf(type_def_5, type, mworld: $tType).
% 0.31/1.34 thf(func_def_0, type, mworld: $tType).
% 0.31/1.34 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.31/1.34 thf(func_def_2, type, mactual: mworld).
% 0.31/1.34 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.31/1.34 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.31/1.34 thf(func_def_14, type, qmltpeq: $i > $i > mworld > $o).
% 0.31/1.34 thf(func_def_15, type, member: $i > $i > mworld > $o).
% 0.31/1.34 thf(func_def_16, type, subset: $i > $i > mworld > $o).
% 0.31/1.34 thf(func_def_17, type, union: $i > $i > $i).
% 0.31/1.34 thf(func_def_31, type, sK0: mworld > mworld).
% 0.31/1.34 thf(func_def_35, type, sK2: $i > $i > $i).
% 0.31/1.34 thf(func_def_36, type, sK3: $i > $i > $i).
% 0.31/1.34 thf(f320,plain,(
% 0.31/1.34 $false),
% 0.31/1.34 inference(trivial_inequality_removal,[status(thm)],[f318])).
% 0.31/1.34 thf(f318,plain,(
% 0.31/1.34 ($false = $true)),
% 0.31/1.34 inference(superposition,[status(thm)],[f313,f141])).
% 0.31/1.34 thf(f141,plain,(
% 0.31/1.34 ( ! [X1 : $i] : (((subset @ X1 @ X1 @ mactual) = $true)) )),
% 0.31/1.34 inference(beta_eta_normalization,[status(thm)],[f140])).
% 0.31/1.34 thf(f140,plain,(
% 0.31/1.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: (subset @ Y0 @ Y0 @ mactual)) @ X1) = $true)) )),
% 0.31/1.34 inference(pi_clausification,[status(thm)],[f139])).
% 0.31/1.34 thf(f139,plain,(
% 0.31/1.34 ((!! @ $i @ (^[Y0 : $i]: (subset @ Y0 @ Y0 @ mactual))) = $true)),
% 0.31/1.34 inference(beta_eta_normalization,[status(thm)],[f120])).
% 0.31/1.34 thf(f120,plain,(
% 0.31/1.34 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))) = $true)),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f93,f95,f102])).
% 0.31/1.34 thf(f102,plain,(
% 0.31/1.34 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f75])).
% 0.31/1.34 thf(f75,plain,(
% 0.31/1.34 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 0.31/1.34 inference(fool_elimination,[status(thm)],[f74])).
% 0.31/1.34 thf(f74,plain,(
% 0.31/1.34 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))) = mforall_di)),
% 0.31/1.34 inference(rectify,[status(thm)],[f10])).
% 0.31/1.34 thf(f10,axiom,(
% 0.31/1.34 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : (X1 @ X5 @ X2))) = mforall_di)),
% 0.31/1.34 file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',mforall_di_def)).
% 0.31/1.34 thf(f95,plain,(
% 0.31/1.34 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f33])).
% 0.31/1.34 thf(f33,plain,(
% 0.31/1.34 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.31/1.34 inference(fool_elimination,[status(thm)],[f1])).
% 0.31/1.34 thf(f1,axiom,(
% 0.31/1.34 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 0.31/1.34 file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',mlocal_def)).
% 0.31/1.34 thf(f93,plain,(
% 0.31/1.34 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))) = $true)),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f69])).
% 0.31/1.34 thf(f69,plain,(
% 0.31/1.34 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (subset @ Y0 @ Y0)))) = $true)),
% 0.31/1.34 inference(fool_elimination,[status(thm)],[f68])).
% 0.31/1.34 thf(f68,plain,(
% 0.31/1.34 (mlocal @ (mforall_di @ (^[X0 : $i] : (subset @ X0 @ X0))))),
% 0.31/1.34 inference(rectify,[status(thm)],[f26])).
% 0.31/1.34 thf(f26,axiom,(
% 0.31/1.34 (mlocal @ (mforall_di @ (^[X3 : $i] : (subset @ X3 @ X3))))),
% 0.31/1.34 file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',reflexivity_of_subset)).
% 0.31/1.34 thf(f313,plain,(
% 0.31/1.34 ($false = (subset @ sK4 @ sK4 @ mactual))),
% 0.31/1.34 inference(trivial_inequality_removal,[status(thm)],[f309])).
% 0.31/1.34 thf(f309,plain,(
% 0.31/1.34 ($false = (subset @ sK4 @ sK4 @ mactual)) | ($false = $true)),
% 0.31/1.34 inference(superposition,[status(thm)],[f230,f214])).
% 0.31/1.34 thf(f214,plain,(
% 0.31/1.34 ( ! [X2 : $i,X1 : $i] : (((qmltpeq @ (union @ X1 @ X2) @ X2 @ mactual) = $true) | ($false = (subset @ X1 @ X2 @ mactual))) )),
% 0.31/1.34 inference(binary_proxy_clausification,[status(thm)],[f213])).
% 0.31/1.34 thf(f213,plain,(
% 0.31/1.34 ( ! [X2 : $i,X1 : $i] : ((((subset @ X1 @ X2 @ mactual) => (qmltpeq @ (union @ X1 @ X2) @ X2 @ mactual)) = $true)) )),
% 0.31/1.34 inference(beta_eta_normalization,[status(thm)],[f212])).
% 0.31/1.34 thf(f212,plain,(
% 0.31/1.34 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((subset @ X1 @ Y0 @ mactual) => (qmltpeq @ (union @ X1 @ Y0) @ Y0 @ mactual))) @ X2) = $true)) )),
% 0.31/1.34 inference(pi_clausification,[status(thm)],[f211])).
% 0.31/1.34 thf(f211,plain,(
% 0.31/1.34 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0 @ mactual) => (qmltpeq @ (union @ X1 @ Y0) @ Y0 @ mactual)))) = $true)) )),
% 0.31/1.34 inference(beta_eta_normalization,[status(thm)],[f210])).
% 0.31/1.34 thf(f210,plain,(
% 0.31/1.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1 @ mactual) => (qmltpeq @ (union @ Y0 @ Y1) @ Y1 @ mactual))))) @ X1) = $true)) )),
% 0.31/1.34 inference(pi_clausification,[status(thm)],[f209])).
% 0.31/1.34 thf(f209,plain,(
% 0.31/1.34 ((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1 @ mactual) => (qmltpeq @ (union @ Y0 @ Y1) @ Y1 @ mactual)))))) = $true)),
% 0.31/1.34 inference(beta_eta_normalization,[status(thm)],[f126])).
% 0.31/1.34 thf(f126,plain,(
% 0.31/1.34 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: (Y1 @ Y3 @ Y2)))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) => (Y3 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (qmltpeq @ (union @ Y0 @ Y1) @ Y1))))))) = $true)),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f106,f95,f102,f102,f105])).
% 0.31/1.34 thf(f105,plain,(
% 0.31/1.34 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f77])).
% 0.31/1.34 thf(f77,plain,(
% 0.31/1.34 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.31/1.34 inference(fool_elimination,[status(thm)],[f76])).
% 0.31/1.34 thf(f76,plain,(
% 0.31/1.34 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 0.31/1.34 inference(rectify,[status(thm)],[f5])).
% 0.31/1.34 thf(f5,axiom,(
% 0.31/1.34 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 0.31/1.34 file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',mimplies_def)).
% 0.31/1.34 thf(f106,plain,(
% 0.31/1.34 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (subset @ Y0 @ Y1) @ (qmltpeq @ (union @ Y0 @ Y1) @ Y1))))))) = $true)),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f55])).
% 0.31/1.34 thf(f55,plain,(
% 0.31/1.34 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mimplies @ (subset @ Y0 @ Y1) @ (qmltpeq @ (union @ Y0 @ Y1) @ Y1))))))) = $true)),
% 0.31/1.34 inference(fool_elimination,[status(thm)],[f54])).
% 0.31/1.34 thf(f54,plain,(
% 0.31/1.34 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mimplies @ (subset @ X0 @ X1) @ (qmltpeq @ (union @ X0 @ X1) @ X1)))))))),
% 0.31/1.34 inference(rectify,[status(thm)],[f21])).
% 0.31/1.34 thf(f21,axiom,(
% 0.31/1.34 (mlocal @ (mforall_di @ (^[X3 : $i] : (mforall_di @ (^[X8 : $i] : (mimplies @ (subset @ X3 @ X8) @ (qmltpeq @ (union @ X3 @ X8) @ X8)))))))),
% 0.31/1.34 file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',subset_union)).
% 0.31/1.34 thf(f230,plain,(
% 0.31/1.34 ($false = (qmltpeq @ (union @ sK4 @ sK4) @ sK4 @ mactual))),
% 0.31/1.34 inference(beta_eta_normalization,[status(thm)],[f229])).
% 0.31/1.34 thf(f229,plain,(
% 0.31/1.34 ($false = ((^[Y0 : $i]: (qmltpeq @ (union @ Y0 @ Y0) @ Y0 @ mactual)) @ sK4))),
% 0.31/1.34 inference(sigma_clausification,[status(thm)],[f228])).
% 0.31/1.34 thf(f228,plain,(
% 0.31/1.34 ((!! @ $i @ (^[Y0 : $i]: (qmltpeq @ (union @ Y0 @ Y0) @ Y0 @ mactual))) != $true)),
% 0.31/1.34 inference(beta_eta_normalization,[status(thm)],[f121])).
% 0.31/1.34 thf(f121,plain,(
% 0.31/1.34 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: (qmltpeq @ (union @ Y0 @ Y0) @ Y0)))) != $true)),
% 0.31/1.34 inference(definition_unfolding,[status(thm)],[f97,f95,f102])).
% 0.31/1.34 thf(f97,plain,(
% 0.31/1.34 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (qmltpeq @ (union @ Y0 @ Y0) @ Y0)))) != $true)),
% 0.31/1.34 inference(cnf_transformation,[status(thm)],[f86])).
% 0.31/1.34 thf(f86,plain,(
% 0.31/1.34 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (qmltpeq @ (union @ Y0 @ Y0) @ Y0)))) != $true)),
% 0.31/1.34 inference(flattening,[status(thm)],[f47])).
% 0.31/1.34 thf(f47,plain,(
% 0.31/1.34 ~((mlocal @ (mforall_di @ (^[Y0 : $i]: (qmltpeq @ (union @ Y0 @ Y0) @ Y0)))) = $true)),
% 0.31/1.34 inference(fool_elimination,[status(thm)],[f46])).
% 0.31/1.34 thf(f46,plain,(
% 0.31/1.34 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (qmltpeq @ (union @ X0 @ X0) @ X0))))),
% 0.31/1.34 inference(rectify,[status(thm)],[f29])).
% 0.31/1.34 thf(f29,negated_conjecture,(
% 0.31/1.34 ~(mlocal @ (mforall_di @ (^[X3 : $i] : (qmltpeq @ (union @ X3 @ X3) @ X3))))),
% 0.31/1.34 inference(negated_conjecture,[status(cth)],[f28])).
% 0.31/1.34 thf(f28,conjecture,(
% 0.31/1.34 (mlocal @ (mforall_di @ (^[X3 : $i] : (qmltpeq @ (union @ X3 @ X3) @ X3))))),
% 0.31/1.34 file('/export/starexec/sandbox/tmp/tmp.nQ1Vdxo9m6/DTF2THF_7983.p',prove_idempotency_of_union)).
% 0.31/1.34 % SZS output end Proof for DTF2THF_7983
% 0.31/1.34 % (8287)------------------------------
% 0.31/1.34 % (8287)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.34 % (8287)Termination reason: Refutation
% 0.31/1.34
% 0.31/1.34 % (8287)Memory used [KB]: 5884
% 0.31/1.34 % (8287)Time elapsed: 0.013 s
% 0.31/1.34 % (8287)Instructions burned: 36 (million)
% 0.31/1.34 % (8287)------------------------------
% 0.31/1.34 % (8287)------------------------------
% 0.31/1.34 % (8286)Success in time 0.022 s
%------------------------------------------------------------------------------