%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET063^4 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n009.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 09:31:07 AM UTC 2026
% Result : Theorem 2.04s 1.54s
% Output : Refutation 2.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 13
% Syntax : Number of formulae : 106 ( 73 unt; 0 typ; 2 def)
% Number of atoms : 641 ( 117 equ; 0 cnn)
% Maximal formula atoms : 9 ( 6 avg)
% Number of connectives : 966 ( 39 ~; 20 |; 22 &; 819 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 77 ( 77 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 31 usr; 10 con; 0-3 aty)
% ( 42 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 242 ( 205 ^; 37 !; 0 ?; 242 :)
% 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_15,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_16,type,
equal_set: $i > $i > mworld > $o ).
thf(func_def_17,type,
member: $i > $i > mworld > $o ).
thf(func_def_18,type,
subset: $i > $i > mworld > $o ).
thf(func_def_19,type,
singleton: $i > $i ).
thf(func_def_20,type,
product: $i > $i ).
thf(func_def_21,type,
unordered_pair: $i > $i > $i ).
thf(func_def_22,type,
intersection: $i > $i > $i ).
thf(func_def_23,type,
difference: $i > $i > $i ).
thf(func_def_24,type,
sum: $i > $i ).
thf(func_def_25,type,
union: $i > $i > $i ).
thf(func_def_26,type,
power_set: $i > $i ).
thf(func_def_44,type,
ph2:
!>[X0: $tType] : X0 ).
thf(f537,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f464,f518,f536]) ).
thf(f536,plain,
~ spl0_1,
inference(avatar_contradiction_clause,[status(thm)],[f535]) ).
thf(f535,plain,
( $false
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f534]) ).
thf(f534,plain,
( ( $true = $false )
| ~ spl0_1 ),
inference(forward_demodulation,[status(thm)],[f527,f361]) ).
thf(f361,plain,
! [X1: $i] :
( ( member @ X1 @ empty_set @ mactual )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f360]) ).
thf(f360,plain,
! [X1: $i] :
( $true
= ( ~ ( member @ X1 @ empty_set @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f359]) ).
thf(f359,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
~ ( member @ Y0 @ empty_set @ mactual )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f358]) ).
thf(f358,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
~ ( member @ Y0 @ empty_set @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f185]) ).
thf(f185,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
~ ( Y1 @ Y2 )
@ ( member @ Y0 @ empty_set ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f142,f159,f143,f150]) ).
thf(f150,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f126]) ).
thf(f126,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f125]) ).
thf(f125,plain,
( mnot
= ( ^ [X0: mworld > $o,X1: mworld] :
~ ( X0 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
( mnot
= ( ^ [X1: mworld > $o,X2: mworld] :
~ ( X1 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mnot_def) ).
thf(f143,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f110]) ).
thf(f110,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f109]) ).
thf(f109,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X6: $i] : ( X1 @ X6 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mforall_di_def) ).
thf(f159,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f72]) ).
thf(f72,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mlocal_def) ).
thf(f142,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( mnot @ ( member @ Y0 @ empty_set ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f94]) ).
thf(f94,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( mnot @ ( member @ Y0 @ empty_set ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f93]) ).
thf(f93,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( mnot @ ( member @ X0 @ empty_set ) ) ) ),
inference(rectify,[status(thm)],[f39]) ).
thf(f39,axiom,
( mlocal
@ ( mforall_di
@ ^ [X6: $i] : ( mnot @ ( member @ X6 @ empty_set ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',empty_set_0) ).
thf(f527,plain,
( ( $true
= ( member @ sK4 @ empty_set @ mactual ) )
| ~ spl0_1 ),
inference(binary_proxy_clausification,[status(thm)],[f525]) ).
thf(f525,plain,
( ( ( ( member @ sK4 @ empty_set @ mactual )
=> ( member @ sK4 @ ( intersection @ sK1 @ empty_set ) @ mactual ) )
= $false )
| ~ spl0_1 ),
inference(beta_eta_normalization,[status(thm)],[f524]) ).
thf(f524,plain,
( ( ( ^ [Y0: $i] :
( ( member @ Y0 @ empty_set @ mactual )
=> ( member @ Y0 @ ( intersection @ sK1 @ empty_set ) @ mactual ) )
@ sK4 )
= $false )
| ~ spl0_1 ),
inference(sigma_clausification,[status(thm)],[f523]) ).
thf(f523,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ empty_set @ mactual )
=> ( member @ Y0 @ ( intersection @ sK1 @ empty_set ) @ mactual ) ) )
= $false )
| ~ spl0_1 ),
inference(not_proxy_clausification,[status(thm)],[f522]) ).
thf(f522,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ empty_set @ mactual )
=> ( member @ Y0 @ ( intersection @ sK1 @ empty_set ) @ mactual ) ) ) ) )
| ~ spl0_1 ),
inference(boolean_simplification,[status(thm)],[f519]) ).
thf(f519,plain,
( ( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ empty_set @ mactual )
=> ( member @ Y0 @ ( intersection @ sK1 @ empty_set ) @ mactual ) ) ) )
= $true )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f343,f459]) ).
thf(f459,plain,
( ( ( subset @ empty_set @ ( intersection @ sK1 @ empty_set ) @ mactual )
= $false )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f457]) ).
thf(f457,definition,
( spl0_1
<=> ( ( subset @ empty_set @ ( intersection @ sK1 @ empty_set ) @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f343,plain,
! [X2: $i,X1: $i] :
( $true
= ( ( subset @ X1 @ X2 @ mactual )
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ X1 @ mactual )
=> ( member @ Y0 @ X2 @ mactual ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f342]) ).
thf(f342,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f341]) ).
thf(f341,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( subset @ X1 @ Y0 @ mactual )
= ( !! @ $i
@ ^ [Y1: $i] :
( ( member @ Y1 @ X1 @ mactual )
=> ( member @ Y1 @ Y0 @ mactual ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f340]) ).
thf(f340,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f339]) ).
thf(f339,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( subset @ Y0 @ Y1 @ mactual )
= ( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y2 @ Y0 @ mactual )
=> ( member @ Y2 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f186]) ).
thf(f186,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 )
@ ( ^ [Y2: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
=> ( Y4 @ Y5 ) )
@ ( member @ Y2 @ Y0 )
@ ( member @ Y2 @ Y1 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f144,f159,f143,f143,f141,f143,f161]) ).
thf(f161,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f52]) ).
thf(f52,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mimplies_def) ).
thf(f141,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f76]) ).
thf(f76,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f75]) ).
thf(f75,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( mequiv
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mequiv_def) ).
thf(f144,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f132]) ).
thf(f132,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mequiv @ ( subset @ Y0 @ Y1 )
@ ( mforall_di
@ ^ [Y2: $i] : ( mimplies @ ( member @ Y2 @ Y0 ) @ ( member @ Y2 @ Y1 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f131]) ).
thf(f131,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mequiv @ ( subset @ X0 @ X1 )
@ ( mforall_di
@ ^ [X2: $i] : ( mimplies @ ( member @ X2 @ X0 ) @ ( member @ X2 @ X1 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f34]) ).
thf(f34,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] :
( mequiv @ ( subset @ X1 @ X3 )
@ ( mforall_di
@ ^ [X6: $i] : ( mimplies @ ( member @ X6 @ X1 ) @ ( member @ X6 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',subset_0) ).
thf(f518,plain,
~ spl0_2,
inference(avatar_contradiction_clause,[status(thm)],[f517]) ).
thf(f517,plain,
( $false
| ~ spl0_2 ),
inference(trivial_inequality_removal,[status(thm)],[f516]) ).
thf(f516,plain,
( ( $true = $false )
| ~ spl0_2 ),
inference(forward_demodulation,[status(thm)],[f515,f477]) ).
thf(f477,plain,
! [X0: $i,X1: $i] :
( ( member @ X0 @ ( intersection @ X1 @ empty_set ) @ mactual )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f476]) ).
thf(f476,plain,
! [X0: $i,X1: $i] :
( ( ~ ( member @ X0 @ ( intersection @ X1 @ empty_set ) @ mactual ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f475]) ).
thf(f475,plain,
! [X0: $i,X1: $i] :
( $true
= ( ( member @ X0 @ ( intersection @ X1 @ empty_set ) @ mactual )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f474]) ).
thf(f474,plain,
! [X0: $i,X1: $i] :
( $true
= ( ( member @ X0 @ ( intersection @ X1 @ empty_set ) @ mactual )
= ( $false
& ( member @ X0 @ X1 @ mactual ) ) ) ),
inference(superposition,[status(thm)],[f314,f361]) ).
thf(f314,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ( member @ X1 @ ( intersection @ X2 @ X3 ) @ mactual )
= ( ( member @ X1 @ X3 @ mactual )
& ( member @ X1 @ X2 @ mactual ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f313]) ).
thf(f313,plain,
! [X2: $i,X3: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( member @ X1 @ ( intersection @ X2 @ Y0 ) @ mactual )
= ( ( member @ X1 @ Y0 @ mactual )
& ( member @ X1 @ X2 @ mactual ) ) )
@ X3 ) ),
inference(pi_clausification,[status(thm)],[f312]) ).
thf(f312,plain,
! [X2: $i,X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ X1 @ ( intersection @ X2 @ Y0 ) @ mactual )
= ( ( member @ X1 @ Y0 @ mactual )
& ( member @ X1 @ X2 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f311]) ).
thf(f311,plain,
! [X2: $i,X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( member @ X1 @ ( intersection @ Y0 @ Y1 ) @ mactual )
= ( ( member @ X1 @ Y1 @ mactual )
& ( member @ X1 @ Y0 @ mactual ) ) ) )
@ X2 )
= $true ),
inference(pi_clausification,[status(thm)],[f310]) ).
thf(f310,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( member @ X1 @ ( intersection @ Y0 @ Y1 ) @ mactual )
= ( ( member @ X1 @ Y1 @ mactual )
& ( member @ X1 @ Y0 @ mactual ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f309]) ).
thf(f309,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) @ mactual )
= ( ( member @ Y0 @ Y2 @ mactual )
& ( member @ Y0 @ Y1 @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f308]) ).
thf(f308,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( !! @ $i
@ ^ [Y2: $i] :
( ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) @ mactual )
= ( ( member @ Y0 @ Y2 @ mactual )
& ( member @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f194]) ).
thf(f194,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: $i > mworld > $o,Y3: mworld] :
( !! @ $i
@ ^ [Y4: $i] : ( Y2 @ Y4 @ Y3 ) )
@ ^ [Y2: $i] :
( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y3 @ Y5 )
= ( Y4 @ Y5 ) )
@ ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) )
@ ( ^ [Y3: mworld > $o,Y4: mworld > $o,Y5: mworld] :
( ( Y4 @ Y5 )
& ( Y3 @ Y5 ) )
@ ( member @ Y0 @ Y1 )
@ ( member @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f153,f159,f143,f143,f143,f141,f172]) ).
thf(f172,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
thf(f128,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f127]) ).
thf(f127,plain,
( mand
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( mand
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mand_def) ).
thf(f153,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) ) @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f63]) ).
thf(f63,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] :
( mforall_di
@ ^ [Y2: $i] : ( mequiv @ ( member @ Y0 @ ( intersection @ Y1 @ Y2 ) ) @ ( mand @ ( member @ Y0 @ Y1 ) @ ( member @ Y0 @ Y2 ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f62]) ).
thf(f62,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X2: $i] : ( mequiv @ ( member @ X0 @ ( intersection @ X1 @ X2 ) ) @ ( mand @ ( member @ X0 @ X1 ) @ ( member @ X0 @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f37]) ).
thf(f37,axiom,
( mlocal
@ ( mforall_di
@ ^ [X6: $i] :
( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( member @ X6 @ ( intersection @ X1 @ X3 ) ) @ ( mand @ ( member @ X6 @ X1 ) @ ( member @ X6 @ X3 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',intersection_0) ).
thf(f515,plain,
( ( $true
= ( member @ sK3 @ ( intersection @ sK1 @ empty_set ) @ mactual ) )
| ~ spl0_2 ),
inference(binary_proxy_clausification,[status(thm)],[f513]) ).
thf(f513,plain,
( ( $false
= ( ( member @ sK3 @ ( intersection @ sK1 @ empty_set ) @ mactual )
=> ( member @ sK3 @ empty_set @ mactual ) ) )
| ~ spl0_2 ),
inference(beta_eta_normalization,[status(thm)],[f512]) ).
thf(f512,plain,
( ( $false
= ( ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK1 @ empty_set ) @ mactual )
=> ( member @ Y0 @ empty_set @ mactual ) )
@ sK3 ) )
| ~ spl0_2 ),
inference(sigma_clausification,[status(thm)],[f511]) ).
thf(f511,plain,
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK1 @ empty_set ) @ mactual )
=> ( member @ Y0 @ empty_set @ mactual ) ) )
= $false )
| ~ spl0_2 ),
inference(not_proxy_clausification,[status(thm)],[f510]) ).
thf(f510,plain,
( ( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK1 @ empty_set ) @ mactual )
=> ( member @ Y0 @ empty_set @ mactual ) ) ) ) )
| ~ spl0_2 ),
inference(boolean_simplification,[status(thm)],[f509]) ).
thf(f509,plain,
( ( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( member @ Y0 @ ( intersection @ sK1 @ empty_set ) @ mactual )
=> ( member @ Y0 @ empty_set @ mactual ) ) ) )
= $true )
| ~ spl0_2 ),
inference(superposition,[status(thm)],[f343,f463]) ).
thf(f463,plain,
( ( $false
= ( subset @ ( intersection @ sK1 @ empty_set ) @ empty_set @ mactual ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f461]) ).
thf(f461,definition,
( spl0_2
<=> ( $false
= ( subset @ ( intersection @ sK1 @ empty_set ) @ empty_set @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f464,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f455,f461,f457]) ).
thf(f455,plain,
( ( $false
= ( subset @ ( intersection @ sK1 @ empty_set ) @ empty_set @ mactual ) )
| ( ( subset @ empty_set @ ( intersection @ sK1 @ empty_set ) @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f454]) ).
thf(f454,plain,
( ( ( subset @ empty_set @ ( intersection @ sK1 @ empty_set ) @ mactual )
& ( subset @ ( intersection @ sK1 @ empty_set ) @ empty_set @ mactual ) )
= $false ),
inference(not_proxy_clausification,[status(thm)],[f453]) ).
thf(f453,plain,
( ( ~ ( ( subset @ empty_set @ ( intersection @ sK1 @ empty_set ) @ mactual )
& ( subset @ ( intersection @ sK1 @ empty_set ) @ empty_set @ mactual ) ) )
= $true ),
inference(boolean_simplification,[status(thm)],[f452]) ).
thf(f452,plain,
( ( $false
= ( ( subset @ empty_set @ ( intersection @ sK1 @ empty_set ) @ mactual )
& ( subset @ ( intersection @ sK1 @ empty_set ) @ empty_set @ mactual ) ) )
= $true ),
inference(superposition,[status(thm)],[f285,f428]) ).
thf(f428,plain,
( ( equal_set @ ( intersection @ sK1 @ empty_set ) @ empty_set @ mactual )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f427]) ).
thf(f427,plain,
( ( ^ [Y0: $i] : ( equal_set @ ( intersection @ Y0 @ empty_set ) @ empty_set @ mactual )
@ sK1 )
= $false ),
inference(sigma_clausification,[status(thm)],[f426]) ).
thf(f426,plain,
( ( !! @ $i
@ ^ [Y0: $i] : ( equal_set @ ( intersection @ Y0 @ empty_set ) @ empty_set @ mactual ) )
!= $true ),
inference(beta_eta_normalization,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] : ( equal_set @ ( intersection @ Y0 @ empty_set ) @ empty_set ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f158,f159,f143]) ).
thf(f158,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( equal_set @ ( intersection @ Y0 @ empty_set ) @ empty_set ) ) ) ),
inference(cnf_transformation,[status(thm)],[f137]) ).
thf(f137,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( equal_set @ ( intersection @ Y0 @ empty_set ) @ empty_set ) ) ) ),
inference(flattening,[status(thm)],[f116]) ).
thf(f116,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] : ( equal_set @ ( intersection @ Y0 @ empty_set ) @ empty_set ) ) ) ),
inference(fool_elimination,[status(thm)],[f115]) ).
thf(f115,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] : ( equal_set @ ( intersection @ X0 @ empty_set ) @ empty_set ) ) ),
inference(rectify,[status(thm)],[f46]) ).
thf(f46,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X1: $i] : ( equal_set @ ( intersection @ X1 @ empty_set ) @ empty_set ) ) ),
inference(negated_conjecture,[status(cth)],[f45]) ).
thf(f45,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] : ( equal_set @ ( intersection @ X1 @ empty_set ) @ empty_set ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',thI17) ).
thf(f285,plain,
! [X2: $i,X1: $i] :
( ( ( equal_set @ X1 @ X2 @ mactual )
= ( ( subset @ X2 @ X1 @ mactual )
& ( subset @ X1 @ X2 @ mactual ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f284]) ).
thf(f284,plain,
! [X2: $i,X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( equal_set @ X1 @ Y0 @ mactual )
= ( ( subset @ Y0 @ X1 @ mactual )
& ( subset @ X1 @ Y0 @ mactual ) ) )
@ X2 ) ),
inference(pi_clausification,[status(thm)],[f283]) ).
thf(f283,plain,
! [X1: $i] :
( ( !! @ $i
@ ^ [Y0: $i] :
( ( equal_set @ X1 @ Y0 @ mactual )
= ( ( subset @ Y0 @ X1 @ mactual )
& ( subset @ X1 @ Y0 @ mactual ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f282]) ).
thf(f282,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( equal_set @ Y0 @ Y1 @ mactual )
= ( ( subset @ Y1 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f281]) ).
thf(f281,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( equal_set @ Y0 @ Y1 @ mactual )
= ( ( subset @ Y1 @ Y0 @ mactual )
& ( subset @ Y0 @ Y1 @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f200]) ).
thf(f200,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 ) )
@ ( equal_set @ Y0 @ Y1 )
@ ( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
& ( Y2 @ Y4 ) )
@ ( subset @ Y0 @ Y1 )
@ ( subset @ Y1 @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f160,f159,f143,f143,f141,f172]) ).
thf(f160,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f88]) ).
thf(f88,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( equal_set @ Y0 @ Y1 ) @ ( mand @ ( subset @ Y0 @ Y1 ) @ ( subset @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f87]) ).
thf(f87,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( equal_set @ X0 @ X1 ) @ ( mand @ ( subset @ X0 @ X1 ) @ ( subset @ X1 @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f35]) ).
thf(f35,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( equal_set @ X1 @ X3 ) @ ( mand @ ( subset @ X1 @ X3 ) @ ( subset @ X3 @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',equal_set_0) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET063^4 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.18/0.34 % Computer : n009.cluster.edu
% 0.18/0.34 % Model : x86_64 x86_64
% 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.34 % Memory : 8042.1875MB
% 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.34 % CPULimit : 300
% 0.18/0.34 % WCLimit : 300
% 0.18/0.34 % DateTime : Tue Feb 24 11:50:55 EST 2026
% 0.18/0.34 % CPUTime :
% 0.18/0.35 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.28/0.48 ---- Original DTF file ---
% 0.28/0.48 thf(spec,logic,$$dhol).
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 % File : SET063^4 : TPTP v9.2.1. Released v8.1.0.
% 0.28/0.48 % Domain : Set Theory
% 0.28/0.48 % Problem : TPTP problem SET063+1.p with axiomatized equality
% 0.28/0.48 % Version : [BP13] axioms.
% 0.28/0.48 % English :
% 0.28/0.48
% 0.28/0.48 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.28/0.48 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.28/0.48 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.28/0.48 % Source : [TPTP]
% 0.28/0.48 % Names : SET063+1 [QMLTP]
% 0.28/0.48
% 0.28/0.48 % Status : Theorem
% 0.28/0.48 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.20 v8.2.0, 0.23 v8.1.0
% 0.28/0.48 % Syntax : Number of formulae : 71 ( 11 unt; 26 typ; 10 def)
% 0.28/0.48 % Number of atoms : 269 ( 10 equ; 0 cnn)
% 0.28/0.48 % Maximal formula atoms : 10 ( 5 avg)
% 0.28/0.48 % Number of connectives : 457 ( 1 ~; 1 |; 3 &; 448 @)
% 0.28/0.48 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.28/0.48 % Maximal formula depth : 14 ( 9 avg)
% 0.28/0.48 % Number of types : 3 ( 1 usr)
% 0.28/0.48 % Number of type conns : 81 ( 81 >; 0 *; 0 +; 0 <<)
% 0.28/0.48 % Number of symbols : 26 ( 25 usr; 2 con; 0-3 aty)
% 0.28/0.48 % Number of variables : 116 ( 108 ^; 6 !; 2 ?; 116 :)
% 0.28/0.48 % SPC : TH0_THM_EQU_NAR
% 0.28/0.48
% 0.28/0.48 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.28/0.48 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.28/0.48 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.28/0.48 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.28/0.48 % $modalities == $modal_system_S4].
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 thf(mworld,type,
% 0.28/0.48 mworld: $tType ).
% 0.28/0.48
% 0.28/0.48 thf(mrel_type,type,
% 0.28/0.48 mrel: mworld > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mactual_type,type,
% 0.28/0.48 mactual: mworld ).
% 0.28/0.48
% 0.28/0.48 thf(mlocal_type,type,
% 0.28/0.48 mlocal: ( mworld > $o ) > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mlocal_def,definition,
% 0.28/0.48 ( mlocal
% 0.28/0.48 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mnot_type,type,
% 0.28/0.48 mnot: ( mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mand_type,type,
% 0.28/0.48 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mor_type,type,
% 0.28/0.48 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mimplies_type,type,
% 0.28/0.48 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mequiv_type,type,
% 0.28/0.48 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mnot_def,definition,
% 0.28/0.48 ( mnot
% 0.28/0.48 = ( ^ [A: mworld > $o,W: mworld] :
% 0.28/0.48 ~ ( A @ W ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mand_def,definition,
% 0.28/0.48 ( mand
% 0.28/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.48 ( ( A @ W )
% 0.28/0.48 & ( B @ W ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mor_def,definition,
% 0.28/0.48 ( mor
% 0.28/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.48 ( ( A @ W )
% 0.28/0.48 | ( B @ W ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mimplies_def,definition,
% 0.28/0.48 ( mimplies
% 0.28/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.48 ( ( A @ W )
% 0.28/0.48 => ( B @ W ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mequiv_def,definition,
% 0.28/0.48 ( mequiv
% 0.28/0.48 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.28/0.48 ( ( A @ W )
% 0.28/0.48 <=> ( B @ W ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mbox_type,type,
% 0.28/0.48 mbox: ( mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mbox_def,definition,
% 0.28/0.48 ( mbox
% 0.28/0.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.28/0.48 ! [V: mworld] :
% 0.28/0.48 ( ( mrel @ W @ V )
% 0.28/0.48 => ( Phi @ V ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mdia_type,type,
% 0.28/0.48 mdia: ( mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mdia_def,definition,
% 0.28/0.48 ( mdia
% 0.28/0.48 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.28/0.48 ? [V: mworld] :
% 0.28/0.48 ( ( mrel @ W @ V )
% 0.28/0.48 & ( Phi @ V ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mrel_reflexive,axiom,
% 0.28/0.48 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.28/0.48
% 0.28/0.48 thf(mrel_transitive,axiom,
% 0.28/0.48 ! [W: mworld,V: mworld,U: mworld] :
% 0.28/0.48 ( ( ( mrel @ W @ V )
% 0.28/0.48 & ( mrel @ V @ U ) )
% 0.28/0.48 => ( mrel @ W @ U ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mforall_di_type,type,
% 0.28/0.48 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mforall_di_def,definition,
% 0.28/0.48 ( mforall_di
% 0.28/0.48 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.28/0.48 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(mexists_di_type,type,
% 0.28/0.48 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(mexists_di_def,definition,
% 0.28/0.48 ( mexists_di
% 0.28/0.48 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.28/0.48 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(empty_set_decl,type,
% 0.28/0.48 empty_set: $i ).
% 0.28/0.48
% 0.28/0.48 thf(qmltpeq_decl,type,
% 0.28/0.48 qmltpeq: $i > $i > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(equal_set_decl,type,
% 0.28/0.48 equal_set: $i > $i > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(member_decl,type,
% 0.28/0.48 member: $i > $i > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(subset_decl,type,
% 0.28/0.48 subset: $i > $i > mworld > $o ).
% 0.28/0.48
% 0.28/0.48 thf(singleton_decl,type,
% 0.28/0.48 singleton: $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(product_decl,type,
% 0.28/0.48 product: $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(unordered_pair_decl,type,
% 0.28/0.48 unordered_pair: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(intersection_decl,type,
% 0.28/0.48 intersection: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(difference_decl,type,
% 0.28/0.48 difference: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(sum_decl,type,
% 0.28/0.48 sum: $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(union_decl,type,
% 0.28/0.48 union: $i > $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(power_set_decl,type,
% 0.28/0.48 power_set: $i > $i ).
% 0.28/0.48
% 0.28/0.48 thf(reflexivity,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(symmetry,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(transitivity,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [Y: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(difference_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(difference_substitution_2,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(intersection_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(intersection_substitution_2,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(power_set_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(product_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(singleton_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(sum_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(union_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(union_substitution_2,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(unordered_pair_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(unordered_pair_substitution_2,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(equal_set_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(equal_set_substitution_2,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(member_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(member_substitution_2,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subset_substitution_1,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subset_substitution_2,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(subset_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mequiv @ ( subset @ A @ B )
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(equal_set_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(power_set_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(intersection_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(union_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(empty_set_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(difference_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [B: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(singleton_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(unordered_pair_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(sum_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 0.28/0.48 @ ( mexists_di
% 0.28/0.48 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(product_0,axiom,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [X: $i] :
% 0.28/0.48 ( mforall_di
% 0.28/0.48 @ ^ [A: $i] :
% 0.28/0.48 ( mequiv @ ( member @ X @ ( product @ A ) )
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 0.28/0.48
% 0.28/0.48 thf(thI17,conjecture,
% 0.28/0.48 ( mlocal
% 0.28/0.48 @ ( mforall_di
% 0.28/0.48 @ ^ [A: $i] : ( equal_set @ ( intersection @ A @ empty_set ) @ empty_set ) ) ) ).
% 0.28/0.48
% 0.28/0.48 %------------------------------------------------------------------------------
% 0.28/0.48 ------------------------
% 1.84/1.37 ---- Embedded in THF ---
% 1.84/1.37 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.84/1.37 %%% Generated on Tue Feb 24 11:50:56 EST 2026
% 1.84/1.37 %%% using '$$dhol' embedding, version 1.3.0.
% 1.84/1.37 %%% Logic specification used:
% 1.84/1.37 %%% thf(spec, logic, $$dhol).
% 1.84/1.37
% 1.84/1.37 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2DTF13268.p
% See solution above
% 1.84/1.37 ------------------------
% 1.84/1.39 ---- Cleaned THF ---
% 1.84/1.39 thf(mworld,type,
% 1.84/1.39 mworld: $tType ).
% 1.84/1.39
% 1.84/1.39 thf(mrel_type,type,
% 1.84/1.39 mrel: mworld > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mactual_type,type,
% 1.84/1.39 mactual: mworld ).
% 1.84/1.39
% 1.84/1.39 thf(mlocal_type,type,
% 1.84/1.39 mlocal: ( mworld > $o ) > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mlocal_def,definition,
% 1.84/1.39 ( mlocal
% 1.84/1.39 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mnot_type,type,
% 1.84/1.39 mnot: ( mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mand_type,type,
% 1.84/1.39 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mor_type,type,
% 1.84/1.39 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mimplies_type,type,
% 1.84/1.39 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mequiv_type,type,
% 1.84/1.39 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mnot_def,definition,
% 1.84/1.39 ( mnot
% 1.84/1.39 = ( ^ [A: mworld > $o,W: mworld] :
% 1.84/1.39 ~ ( A @ W ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mand_def,definition,
% 1.84/1.39 ( mand
% 1.84/1.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.84/1.39 ( ( A @ W )
% 1.84/1.39 & ( B @ W ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mor_def,definition,
% 1.84/1.39 ( mor
% 1.84/1.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.84/1.39 ( ( A @ W )
% 1.84/1.39 | ( B @ W ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mimplies_def,definition,
% 1.84/1.39 ( mimplies
% 1.84/1.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.84/1.39 ( ( A @ W )
% 1.84/1.39 => ( B @ W ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mequiv_def,definition,
% 1.84/1.39 ( mequiv
% 1.84/1.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.84/1.39 ( ( A @ W )
% 1.84/1.39 <=> ( B @ W ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mbox_type,type,
% 1.84/1.39 mbox: ( mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mbox_def,definition,
% 1.84/1.39 ( mbox
% 1.84/1.39 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.84/1.39 ! [V: mworld] :
% 1.84/1.39 ( ( mrel @ W @ V )
% 1.84/1.39 => ( Phi @ V ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mdia_type,type,
% 1.84/1.39 mdia: ( mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mdia_def,definition,
% 1.84/1.39 ( mdia
% 1.84/1.39 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.84/1.39 ? [V: mworld] :
% 1.84/1.39 ( ( mrel @ W @ V )
% 1.84/1.39 & ( Phi @ V ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mrel_reflexive,axiom,
% 1.84/1.39 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.84/1.39
% 1.84/1.39 thf(mrel_transitive,axiom,
% 1.84/1.39 ! [W: mworld,V: mworld,U: mworld] :
% 1.84/1.39 ( ( ( mrel @ W @ V )
% 1.84/1.39 & ( mrel @ V @ U ) )
% 1.84/1.39 => ( mrel @ W @ U ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mforall_di_type,type,
% 1.84/1.39 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mforall_di_def,definition,
% 1.84/1.39 ( mforall_di
% 1.84/1.39 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.84/1.39 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(mexists_di_type,type,
% 1.84/1.39 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(mexists_di_def,definition,
% 1.84/1.39 ( mexists_di
% 1.84/1.39 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.84/1.39 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(empty_set_decl,type,
% 1.84/1.39 empty_set: $i ).
% 1.84/1.39
% 1.84/1.39 thf(qmltpeq_decl,type,
% 1.84/1.39 qmltpeq: $i > $i > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(equal_set_decl,type,
% 1.84/1.39 equal_set: $i > $i > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(member_decl,type,
% 1.84/1.39 member: $i > $i > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(subset_decl,type,
% 1.84/1.39 subset: $i > $i > mworld > $o ).
% 1.84/1.39
% 1.84/1.39 thf(singleton_decl,type,
% 1.84/1.39 singleton: $i > $i ).
% 1.84/1.39
% 1.84/1.39 thf(product_decl,type,
% 1.84/1.39 product: $i > $i ).
% 1.84/1.39
% 1.84/1.39 thf(unordered_pair_decl,type,
% 1.84/1.39 unordered_pair: $i > $i > $i ).
% 1.84/1.39
% 1.84/1.39 thf(intersection_decl,type,
% 1.84/1.39 intersection: $i > $i > $i ).
% 1.84/1.39
% 1.84/1.39 thf(difference_decl,type,
% 1.84/1.39 difference: $i > $i > $i ).
% 1.84/1.39
% 1.84/1.39 thf(sum_decl,type,
% 1.84/1.39 sum: $i > $i ).
% 1.84/1.39
% 1.84/1.39 thf(union_decl,type,
% 1.84/1.39 union: $i > $i > $i ).
% 1.84/1.39
% 1.84/1.39 thf(power_set_decl,type,
% 1.84/1.39 power_set: $i > $i ).
% 1.84/1.39
% 1.84/1.39 thf(reflexivity,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(symmetry,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(transitivity,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [Y: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(difference_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ A @ C ) @ ( difference @ B @ C ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(difference_substitution_2,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( difference @ C @ A ) @ ( difference @ C @ B ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(intersection_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ A @ C ) @ ( intersection @ B @ C ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(intersection_substitution_2,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( intersection @ C @ A ) @ ( intersection @ C @ B ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(power_set_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( power_set @ A ) @ ( power_set @ B ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(product_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( product @ A ) @ ( product @ B ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(singleton_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(sum_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( sum @ A ) @ ( sum @ B ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(union_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ A @ C ) @ ( union @ B @ C ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(union_substitution_2,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( union @ C @ A ) @ ( union @ C @ B ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(unordered_pair_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ A @ C ) @ ( unordered_pair @ B @ C ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(unordered_pair_substitution_2,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( unordered_pair @ C @ A ) @ ( unordered_pair @ C @ B ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(equal_set_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ A @ C ) ) @ ( equal_set @ B @ C ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(equal_set_substitution_2,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( equal_set @ C @ A ) ) @ ( equal_set @ C @ B ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(member_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ A @ C ) ) @ ( member @ B @ C ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(member_substitution_2,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( member @ C @ A ) ) @ ( member @ C @ B ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(subset_substitution_1,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ A @ C ) ) @ ( subset @ B @ C ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(subset_substitution_2,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( subset @ C @ A ) ) @ ( subset @ C @ B ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(subset_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mequiv @ ( subset @ A @ B )
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] : ( mimplies @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(equal_set_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] : ( mequiv @ ( equal_set @ A @ B ) @ ( mand @ ( subset @ A @ B ) @ ( subset @ B @ A ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(power_set_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( power_set @ A ) ) @ ( subset @ X @ A ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(intersection_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( intersection @ A @ B ) ) @ ( mand @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(union_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( union @ A @ B ) ) @ ( mor @ ( member @ X @ A ) @ ( member @ X @ B ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(empty_set_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] : ( mnot @ ( member @ X @ empty_set ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(difference_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [B: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [E: $i] : ( mequiv @ ( member @ B @ ( difference @ E @ A ) ) @ ( mand @ ( member @ B @ E ) @ ( mnot @ ( member @ B @ A ) ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(singleton_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [A: $i] : ( mequiv @ ( member @ X @ ( singleton @ A ) ) @ ( qmltpeq @ X @ A ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(unordered_pair_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [B: $i] : ( mequiv @ ( member @ X @ ( unordered_pair @ A @ B ) ) @ ( mor @ ( qmltpeq @ X @ A ) @ ( qmltpeq @ X @ B ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(sum_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mequiv @ ( member @ X @ ( sum @ A ) )
% 1.84/1.39 @ ( mexists_di
% 1.84/1.39 @ ^ [Y: $i] : ( mand @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(product_0,axiom,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [X: $i] :
% 1.84/1.39 ( mforall_di
% 1.84/1.39 @ ^ [A: $i] :
% 1.84/1.39 ( mequiv @ ( member @ X @ ( product @ A ) )
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [Y: $i] : ( mimplies @ ( member @ Y @ A ) @ ( member @ X @ Y ) ) ) ) ) ) ) ).
% 1.84/1.39
% 1.84/1.39 thf(thI17,conjecture,
% 1.84/1.39 ( mlocal
% 1.84/1.39 @ ( mforall_di
% 1.84/1.39 @ ^ [A: $i] : ( equal_set @ ( intersection @ A @ empty_set ) @ empty_set ) ) ) ).
% 1.84/1.39 ------------------------
% 2.04/1.41 % (13549)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_13268 for (2999ds/2Mi)
% 2.04/1.41 % (13549)Instruction limit reached!
% 2.04/1.41 % (13549)------------------------------
% 2.04/1.41 % (13549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.41 % (13549)Termination reason: Unknown
% 2.04/1.41 % (13549)Termination phase: shuffling
% 2.04/1.41
% 2.04/1.41 % (13549)Memory used [KB]: 1023
% 2.04/1.41 % (13549)Time elapsed: 0.002 s
% 2.04/1.41 % (13549)Instructions burned: 3 (million)
% 2.04/1.41 % (13549)------------------------------
% 2.04/1.41 % (13549)------------------------------
% 2.04/1.41 % (13546)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_13268 for (2999ds/4Mi)
% 2.04/1.41 % (13546)Instruction limit reached!
% 2.04/1.41 % (13546)------------------------------
% 2.04/1.41 % (13546)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.41 % (13546)Termination reason: Unknown
% 2.04/1.41 % (13546)Termination phase: shuffling
% 2.04/1.41
% 2.04/1.41 % (13546)Memory used [KB]: 1151
% 2.04/1.41 % (13546)Time elapsed: 0.003 s
% 2.04/1.41 % (13546)Instructions burned: 6 (million)
% 2.04/1.41 % (13546)------------------------------
% 2.04/1.41 % (13546)------------------------------
% 2.04/1.41 % (13545)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/183Mi)
% 2.04/1.41 % (13547)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_13268 for (2999ds/27Mi)
% 2.04/1.41 % (13550)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_13268 for (2999ds/275Mi)
% 2.04/1.41 % (13551)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/18Mi)
% 2.04/1.41 % (13548)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/2Mi)
% 2.04/1.41 % (13548)Instruction limit reached!
% 2.04/1.41 % (13548)------------------------------
% 2.04/1.41 % (13548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.41 % (13548)Termination reason: Unknown
% 2.04/1.41 % (13548)Termination phase: shuffling
% 2.04/1.41
% 2.04/1.41 % (13548)Memory used [KB]: 1023
% 2.04/1.41 % (13548)Time elapsed: 0.003 s
% 2.04/1.41 % (13548)Instructions burned: 3 (million)
% 2.04/1.41 % (13548)------------------------------
% 2.04/1.41 % (13548)------------------------------
% 2.04/1.42 % (13552)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/3Mi)
% 2.04/1.42 % (13552)Instruction limit reached!
% 2.04/1.42 % (13552)------------------------------
% 2.04/1.42 % (13552)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.42 % (13552)Termination reason: Unknown
% 2.04/1.42 % (13552)Termination phase: shuffling
% 2.04/1.42
% 2.04/1.42 % (13552)Memory used [KB]: 1023
% 2.04/1.42 % (13552)Time elapsed: 0.003 s
% 2.04/1.42 % (13552)Instructions burned: 5 (million)
% 2.04/1.42 % (13552)------------------------------
% 2.04/1.42 % (13552)------------------------------
% 2.04/1.42 % (13550)Refutation not found, incomplete strategy
% 2.04/1.42 % (13550)------------------------------
% 2.04/1.42 % (13550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.42 % (13550)Termination reason: Refutation not found, incomplete strategy
% 2.04/1.42
% 2.04/1.42
% 2.04/1.42 % (13550)Memory used [KB]: 5628
% 2.04/1.42 % (13550)Time elapsed: 0.010 s
% 2.04/1.42 % (13550)Instructions burned: 15 (million)
% 2.04/1.42 % (13550)------------------------------
% 2.04/1.42 % (13550)------------------------------
% 2.04/1.42 % (13551)Instruction limit reached!
% 2.04/1.42 % (13551)------------------------------
% 2.04/1.42 % (13551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.42 % (13551)Termination reason: Unknown
% 2.04/1.42 % (13551)Termination phase: Property scanning
% 2.04/1.42
% 2.04/1.42 % (13551)Memory used [KB]: 1151
% 2.04/1.42 % (13551)Time elapsed: 0.011 s
% 2.04/1.42 % (13551)Instructions burned: 19 (million)
% 2.04/1.42 % (13551)------------------------------
% 2.04/1.42 % (13551)------------------------------
% 2.04/1.42 % (13553)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_13268 for (2999ds/37Mi)
% 2.04/1.43 % (13547)Instruction limit reached!
% 2.04/1.43 % (13547)------------------------------
% 2.04/1.43 % (13547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.43 % (13547)Termination reason: Unknown
% 2.04/1.43 % (13547)Termination phase: Saturation
% 2.04/1.43
% 2.04/1.43 % (13547)Memory used [KB]: 5756
% 2.04/1.43 % (13547)Time elapsed: 0.016 s
% 2.04/1.43 % (13547)Instructions burned: 28 (million)
% 2.04/1.43 % (13547)------------------------------
% 2.04/1.43 % (13547)------------------------------
% 2.04/1.43 % (13555)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_13268 for (2999ds/3Mi)
% 2.04/1.43 % (13555)Instruction limit reached!
% 2.04/1.43 % (13555)------------------------------
% 2.04/1.43 % (13555)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.43 % (13555)Termination reason: Unknown
% 2.04/1.43 % (13555)Termination phase: shuffling
% 2.04/1.43
% 2.04/1.43 % (13555)Memory used [KB]: 1023
% 2.04/1.43 % (13555)Time elapsed: 0.003 s
% 2.04/1.43 % (13555)Instructions burned: 5 (million)
% 2.04/1.43 % (13555)------------------------------
% 2.04/1.43 % (13555)------------------------------
% 2.04/1.43 % (13554)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_13268 for (2999ds/15Mi)
% 2.04/1.43 % (13556)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_13268 for (2999ds/1041Mi)
% 2.04/1.43 % (13553)Instruction limit reached!
% 2.04/1.43 % (13553)------------------------------
% 2.04/1.43 % (13553)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.43 % (13553)Termination reason: Unknown
% 2.04/1.43 % (13553)Termination phase: Saturation
% 2.04/1.43
% 2.04/1.43 % (13553)Memory used [KB]: 6012
% 2.04/1.43 % (13553)Time elapsed: 0.012 s
% 2.04/1.43 % (13553)Instructions burned: 39 (million)
% 2.04/1.43 % (13553)------------------------------
% 2.04/1.43 % (13553)------------------------------
% 2.04/1.44 % (13554)Instruction limit reached!
% 2.04/1.44 % (13554)------------------------------
% 2.04/1.44 % (13554)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.44 % (13554)Termination reason: Unknown
% 2.04/1.44 % (13554)Termination phase: Function definition elimination
% 2.04/1.44
% 2.04/1.44 % (13554)Memory used [KB]: 1151
% 2.04/1.44 % (13554)Time elapsed: 0.009 s
% 2.04/1.44 % (13554)Instructions burned: 15 (million)
% 2.04/1.44 % (13554)------------------------------
% 2.04/1.44 % (13554)------------------------------
% 2.04/1.44 % (13557)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/7Mi)
% 2.04/1.44 % (13559)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/3Mi)
% 2.04/1.44 % (13559)Instruction limit reached!
% 2.04/1.44 % (13559)------------------------------
% 2.04/1.44 % (13559)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.44 % (13559)Termination reason: Unknown
% 2.04/1.44 % (13559)Termination phase: shuffling
% 2.04/1.44
% 2.04/1.44 % (13559)Memory used [KB]: 1023
% 2.04/1.44 % (13559)Time elapsed: 0.003 s
% 2.04/1.44 % (13559)Instructions burned: 5 (million)
% 2.04/1.44 % (13559)------------------------------
% 2.04/1.44 % (13559)------------------------------
% 2.04/1.44 % (13557)Instruction limit reached!
% 2.04/1.44 % (13557)------------------------------
% 2.04/1.44 % (13557)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.44 % (13557)Termination reason: Unknown
% 2.04/1.44 % (13557)Termination phase: shuffling
% 2.04/1.44
% 2.04/1.44 % (13557)Memory used [KB]: 1151
% 2.04/1.44 % (13557)Time elapsed: 0.005 s
% 2.04/1.44 % (13557)Instructions burned: 8 (million)
% 2.04/1.44 % (13557)------------------------------
% 2.04/1.44 % (13557)------------------------------
% 2.04/1.44 % (13560)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/3Mi)
% 2.04/1.44 % (13558)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/16Mi)
% 2.04/1.44 % (13560)Instruction limit reached!
% 2.04/1.44 % (13560)------------------------------
% 2.04/1.44 % (13560)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.44 % (13560)Termination reason: Unknown
% 2.04/1.44 % (13560)Termination phase: shuffling
% 2.04/1.44
% 2.04/1.44 % (13560)Memory used [KB]: 1151
% 2.04/1.44 % (13560)Time elapsed: 0.003 s
% 2.04/1.44 % (13560)Instructions burned: 5 (million)
% 2.04/1.44 % (13560)------------------------------
% 2.04/1.44 % (13560)------------------------------
% 2.04/1.45 % (13562)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/3Mi)
% 2.04/1.45 % (13562)Instruction limit reached!
% 2.04/1.45 % (13562)------------------------------
% 2.04/1.45 % (13562)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.45 % (13562)Termination reason: Unknown
% 2.04/1.45 % (13562)Termination phase: shuffling
% 2.04/1.45
% 2.04/1.45 % (13562)Memory used [KB]: 1151
% 2.04/1.45 % (13562)Time elapsed: 0.003 s
% 2.04/1.45 % (13562)Instructions burned: 5 (million)
% 2.04/1.45 % (13562)------------------------------
% 2.04/1.45 % (13562)------------------------------
% 2.04/1.45 % (13558)Instruction limit reached!
% 2.04/1.45 % (13558)------------------------------
% 2.04/1.45 % (13558)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.45 % (13558)Termination reason: Unknown
% 2.04/1.45 % (13558)Termination phase: Property scanning
% 2.04/1.45
% 2.04/1.45 % (13558)Memory used [KB]: 1151
% 2.04/1.45 % (13558)Time elapsed: 0.010 s
% 2.04/1.45 % (13558)Instructions burned: 17 (million)
% 2.04/1.45 % (13558)------------------------------
% 2.04/1.45 % (13558)------------------------------
% 2.04/1.45 % (13564)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/18Mi)
% 2.04/1.45 % (13563)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/4Mi)
% 2.04/1.46 % (13563)Instruction limit reached!
% 2.04/1.46 % (13563)------------------------------
% 2.04/1.46 % (13563)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.46 % (13563)Termination reason: Unknown
% 2.04/1.46 % (13563)Termination phase: shuffling
% 2.04/1.46
% 2.04/1.46 % (13563)Memory used [KB]: 1023
% 2.04/1.46 % (13563)Time elapsed: 0.003 s
% 2.04/1.46 % (13563)Instructions burned: 5 (million)
% 2.04/1.46 % (13563)------------------------------
% 2.04/1.46 % (13563)------------------------------
% 2.04/1.46 % (13561)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/7Mi)
% 2.04/1.46 % (13561)Instruction limit reached!
% 2.04/1.46 % (13561)------------------------------
% 2.04/1.46 % (13561)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.46 % (13561)Termination reason: Unknown
% 2.04/1.46 % (13561)Termination phase: shuffling
% 2.04/1.46
% 2.04/1.46 % (13561)Memory used [KB]: 1151
% 2.04/1.46 % (13561)Time elapsed: 0.005 s
% 2.04/1.46 % (13561)Instructions burned: 7 (million)
% 2.04/1.46 % (13561)------------------------------
% 2.04/1.46 % (13561)------------------------------
% 2.04/1.46 % (13564)Instruction limit reached!
% 2.04/1.46 % (13564)------------------------------
% 2.04/1.46 % (13564)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.46 % (13564)Termination reason: Unknown
% 2.04/1.46 % (13564)Termination phase: Saturation
% 2.04/1.46
% 2.04/1.46 % (13564)Memory used [KB]: 5628
% 2.04/1.46 % (13564)Time elapsed: 0.007 s
% 2.04/1.46 % (13564)Instructions burned: 19 (million)
% 2.04/1.46 % (13564)------------------------------
% 2.04/1.46 % (13564)------------------------------
% 2.04/1.47 % (13567)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/902Mi)
% 2.04/1.47 % (13565)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/710Mi)
% 2.04/1.47 % (13566)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/6Mi)
% 2.04/1.47 % (13568)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/21Mi)
% 2.04/1.47 % (13567)Refutation not found, incomplete strategy
% 2.04/1.47 % (13567)------------------------------
% 2.04/1.47 % (13567)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.47 % (13567)Termination reason: Refutation not found, incomplete strategy
% 2.04/1.47
% 2.04/1.47
% 2.04/1.47 % (13567)Memory used [KB]: 5628
% 2.04/1.47 % (13567)Time elapsed: 0.006 s
% 2.04/1.47 % (13567)Instructions burned: 15 (million)
% 2.04/1.47 % (13567)------------------------------
% 2.04/1.47 % (13567)------------------------------
% 2.04/1.47 % (13566)Instruction limit reached!
% 2.04/1.47 % (13566)------------------------------
% 2.04/1.47 % (13566)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.47 % (13566)Termination reason: Unknown
% 2.04/1.47 % (13566)Termination phase: shuffling
% 2.04/1.47
% 2.04/1.47 % (13566)Memory used [KB]: 1151
% 2.04/1.47 % (13566)Time elapsed: 0.005 s
% 2.04/1.47 % (13566)Instructions burned: 6 (million)
% 2.04/1.47 % (13566)------------------------------
% 2.04/1.47 % (13566)------------------------------
% 2.04/1.48 % (13568)Instruction limit reached!
% 2.04/1.48 % (13568)------------------------------
% 2.04/1.48 % (13568)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.48 % (13568)Termination reason: Unknown
% 2.04/1.48 % (13568)Termination phase: Property scanning
% 2.04/1.48
% 2.04/1.48 % (13568)Memory used [KB]: 1151
% 2.04/1.48 % (13568)Time elapsed: 0.008 s
% 2.04/1.48 % (13568)Instructions burned: 23 (million)
% 2.04/1.48 % (13568)------------------------------
% 2.04/1.48 % (13568)------------------------------
% 2.04/1.48 % (13569)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/5Mi)
% 2.04/1.48 % (13569)Instruction limit reached!
% 2.04/1.48 % (13569)------------------------------
% 2.04/1.48 % (13569)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.48 % (13569)Termination reason: Unknown
% 2.04/1.48 % (13569)Termination phase: shuffling
% 2.04/1.48
% 2.04/1.48 % (13569)Memory used [KB]: 1151
% 2.04/1.48 % (13569)Time elapsed: 0.004 s
% 2.04/1.48 % (13569)Instructions burned: 5 (million)
% 2.04/1.48 % (13569)------------------------------
% 2.04/1.48 % (13569)------------------------------
% 2.04/1.48 % (13570)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/6Mi)
% 2.04/1.48 % (13570)Instruction limit reached!
% 2.04/1.48 % (13570)------------------------------
% 2.04/1.48 % (13570)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.48 % (13570)Termination reason: Unknown
% 2.04/1.48 % (13570)Termination phase: Property scanning
% 2.04/1.48
% 2.04/1.48 % (13570)Memory used [KB]: 1151
% 2.04/1.48 % (13570)Time elapsed: 0.004 s
% 2.04/1.48 % (13570)Instructions burned: 9 (million)
% 2.04/1.48 % (13570)------------------------------
% 2.04/1.48 % (13570)------------------------------
% 2.04/1.49 % (13572)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/779Mi)
% 2.04/1.49 % (13571)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/377Mi)
% 2.04/1.49 % (13545)Instruction limit reached!
% 2.04/1.49 % (13545)------------------------------
% 2.04/1.49 % (13545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.49 % (13545)Termination reason: Unknown
% 2.04/1.49 % (13545)Termination phase: Saturation
% 2.04/1.49
% 2.04/1.49 % (13545)Memory used [KB]: 6908
% 2.04/1.49 % (13545)Time elapsed: 0.081 s
% 2.04/1.49 % (13545)Instructions burned: 186 (million)
% 2.04/1.49 % (13545)------------------------------
% 2.04/1.49 % (13545)------------------------------
% 2.04/1.49 % (13574)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/879Mi)
% 2.04/1.50 % (13573)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/19Mi)
% 2.04/1.50 % (13575)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/17Mi)
% 2.04/1.50 % (13572)Refutation not found, incomplete strategy
% 2.04/1.50 % (13572)------------------------------
% 2.04/1.50 % (13572)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.50 % (13572)Termination reason: Refutation not found, incomplete strategy
% 2.04/1.50
% 2.04/1.50
% 2.04/1.50 % (13572)Memory used [KB]: 5756
% 2.04/1.50 % (13572)Time elapsed: 0.017 s
% 2.04/1.50 % (13572)Instructions burned: 51 (million)
% 2.04/1.50 % (13572)------------------------------
% 2.04/1.50 % (13572)------------------------------
% 2.04/1.50 % (13565)Refutation not found, incomplete strategy
% 2.04/1.50 % (13565)------------------------------
% 2.04/1.50 % (13565)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.50 % (13565)Termination reason: Refutation not found, incomplete strategy
% 2.04/1.50
% 2.04/1.50
% 2.04/1.50 % (13565)Memory used [KB]: 6012
% 2.04/1.50 % (13565)Time elapsed: 0.037 s
% 2.04/1.50 % (13565)Instructions burned: 59 (million)
% 2.04/1.50 % (13565)------------------------------
% 2.04/1.50 % (13565)------------------------------
% 2.04/1.50 % (13573)Refutation not found, incomplete strategy
% 2.04/1.50 % (13573)------------------------------
% 2.04/1.50 % (13573)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.50 % (13573)Termination reason: Refutation not found, incomplete strategy
% 2.04/1.50
% 2.04/1.50
% 2.04/1.50 % (13573)Memory used [KB]: 5756
% 2.04/1.50 % (13573)Time elapsed: 0.011 s
% 2.04/1.50 % (13573)Instructions burned: 17 (million)
% 2.04/1.50 % (13573)------------------------------
% 2.04/1.50 % (13573)------------------------------
% 2.04/1.51 % (13575)Instruction limit reached!
% 2.04/1.51 % (13575)------------------------------
% 2.04/1.51 % (13575)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.51 % (13575)Termination reason: Unknown
% 2.04/1.51 % (13575)Termination phase: Property scanning
% 2.04/1.51
% 2.04/1.51 % (13575)Memory used [KB]: 1151
% 2.04/1.51 % (13575)Time elapsed: 0.007 s
% 2.04/1.51 % (13575)Instructions burned: 19 (million)
% 2.04/1.51 % (13575)------------------------------
% 2.04/1.51 % (13575)------------------------------
% 2.04/1.51 % (13576)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/3Mi)
% 2.04/1.51 % (13576)Instruction limit reached!
% 2.04/1.51 % (13576)------------------------------
% 2.04/1.51 % (13576)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.51 % (13576)Termination reason: Unknown
% 2.04/1.51 % (13576)Termination phase: shuffling
% 2.04/1.51
% 2.04/1.51 % (13576)Memory used [KB]: 1023
% 2.04/1.51 % (13576)Time elapsed: 0.003 s
% 2.04/1.51 % (13576)Instructions burned: 5 (million)
% 2.04/1.51 % (13576)------------------------------
% 2.04/1.51 % (13576)------------------------------
% 2.04/1.51 % (13577)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/30Mi)
% 2.04/1.52 % (13579)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/100Mi)
% 2.04/1.52 % (13578)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_13268 for (2999ds/127Mi)
% 2.04/1.52 % (13577)Instruction limit reached!
% 2.04/1.52 % (13577)------------------------------
% 2.04/1.52 % (13577)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.52 % (13577)Termination reason: Unknown
% 2.04/1.52 % (13577)Termination phase: Saturation
% 2.04/1.52
% 2.04/1.52 % (13577)Memory used [KB]: 5756
% 2.04/1.52 % (13577)Time elapsed: 0.010 s
% 2.04/1.52 % (13577)Instructions burned: 30 (million)
% 2.04/1.52 % (13577)------------------------------
% 2.04/1.52 % (13577)------------------------------
% 2.04/1.52 % (13580)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_13268 for (2998ds/3Mi)
% 2.04/1.52 % (13580)Instruction limit reached!
% 2.04/1.52 % (13580)------------------------------
% 2.04/1.52 % (13580)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.52 % (13580)Termination reason: Unknown
% 2.04/1.52 % (13580)Termination phase: shuffling
% 2.04/1.52
% 2.04/1.52 % (13580)Memory used [KB]: 1151
% 2.04/1.52 % (13580)Time elapsed: 0.003 s
% 2.04/1.52 % (13580)Instructions burned: 5 (million)
% 2.04/1.52 % (13580)------------------------------
% 2.04/1.52 % (13580)------------------------------
% 2.04/1.53 % (13581)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_13268 for (2998ds/20Mi)
% 2.04/1.53 % (13582)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_13268 for (2998ds/86Mi)
% 2.04/1.54 % (13578)First to succeed.
% 2.04/1.54 % (13581)Instruction limit reached!
% 2.04/1.54 % (13581)------------------------------
% 2.04/1.54 % (13581)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.54 % (13581)Termination reason: Unknown
% 2.04/1.54 % (13581)Termination phase: Saturation
% 2.04/1.54
% 2.04/1.54 % (13581)Memory used [KB]: 5628
% 2.04/1.54 % (13581)Time elapsed: 0.007 s
% 2.04/1.54 % (13581)Instructions burned: 20 (million)
% 2.04/1.54 % (13581)------------------------------
% 2.04/1.54 % (13581)------------------------------
% 2.04/1.54 % (13578)Refutation found. Thanks to Tanya!
% 2.04/1.54 % SZS status Theorem for DTF2THF_13268
% 2.04/1.54 % SZS output start Proof for DTF2THF_13268
% 2.04/1.54 thf(type_def_5, type, mworld: $tType).
% 2.04/1.54 thf(func_def_0, type, mworld: $tType).
% 2.04/1.54 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 2.04/1.54 thf(func_def_2, type, mactual: mworld).
% 2.04/1.54 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 2.04/1.54 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 2.04/1.54 thf(func_def_15, type, qmltpeq: $i > $i > mworld > $o).
% 2.04/1.54 thf(func_def_16, type, equal_set: $i > $i > mworld > $o).
% 2.04/1.54 thf(func_def_17, type, member: $i > $i > mworld > $o).
% 2.04/1.54 thf(func_def_18, type, subset: $i > $i > mworld > $o).
% 2.04/1.54 thf(func_def_19, type, singleton: $i > $i).
% 2.04/1.54 thf(func_def_20, type, product: $i > $i).
% 2.04/1.54 thf(func_def_21, type, unordered_pair: $i > $i > $i).
% 2.04/1.54 thf(func_def_22, type, intersection: $i > $i > $i).
% 2.04/1.54 thf(func_def_23, type, difference: $i > $i > $i).
% 2.04/1.54 thf(func_def_24, type, sum: $i > $i).
% 2.04/1.54 thf(func_def_25, type, union: $i > $i > $i).
% 2.04/1.54 thf(func_def_26, type, power_set: $i > $i).
% 2.04/1.54 thf(func_def_44, type, ph2: !>[X0: $tType]:(X0)).
% 2.04/1.54 thf(f537,plain,(
% 2.04/1.54 $false),
% 2.04/1.54 inference(avatar_sat_refutation,[status(thm)],[f464,f518,f536])).
% 2.04/1.54 thf(f536,plain,(
% 2.04/1.54 ~spl0_1),
% 2.04/1.54 inference(avatar_contradiction_clause,[status(thm)],[f535])).
% 2.04/1.54 thf(f535,plain,(
% 2.04/1.54 $false | ~spl0_1),
% 2.04/1.54 inference(trivial_inequality_removal,[status(thm)],[f534])).
% 2.04/1.54 thf(f534,plain,(
% 2.04/1.54 ($true = $false) | ~spl0_1),
% 2.04/1.54 inference(forward_demodulation,[status(thm)],[f527,f361])).
% 2.04/1.54 thf(f361,plain,(
% 2.04/1.54 ( ! [X1 : $i] : (((member @ X1 @ empty_set @ mactual) = $false)) )),
% 2.04/1.54 inference(not_proxy_clausification,[status(thm)],[f360])).
% 2.04/1.54 thf(f360,plain,(
% 2.04/1.54 ( ! [X1 : $i] : (($true = (~ (member @ X1 @ empty_set @ mactual)))) )),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f359])).
% 2.04/1.54 thf(f359,plain,(
% 2.04/1.54 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (~ (member @ Y0 @ empty_set @ mactual))) @ X1))) )),
% 2.04/1.54 inference(pi_clausification,[status(thm)],[f358])).
% 2.04/1.54 thf(f358,plain,(
% 2.04/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: (~ (member @ Y0 @ empty_set @ mactual)))))),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f185])).
% 2.04/1.54 thf(f185,plain,(
% 2.04/1.54 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (~ (Y1 @ Y2))))) @ (member @ Y0 @ empty_set))))) = $true)),
% 2.04/1.54 inference(definition_unfolding,[status(thm)],[f142,f159,f143,f150])).
% 2.04/1.54 thf(f150,plain,(
% 2.04/1.54 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f126])).
% 2.04/1.54 thf(f126,plain,(
% 2.04/1.54 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f125])).
% 2.04/1.54 thf(f125,plain,(
% 2.04/1.54 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f2])).
% 2.04/1.54 thf(f2,axiom,(
% 2.04/1.54 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mnot_def)).
% 2.04/1.54 thf(f143,plain,(
% 2.04/1.54 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f110])).
% 2.04/1.54 thf(f110,plain,(
% 2.04/1.54 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f109])).
% 2.04/1.54 thf(f109,plain,(
% 2.04/1.54 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : (X0 @ X2 @ X1))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f11])).
% 2.04/1.54 thf(f11,axiom,(
% 2.04/1.54 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : (X1 @ X6 @ X2))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mforall_di_def)).
% 2.04/1.54 thf(f159,plain,(
% 2.04/1.54 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f72])).
% 2.04/1.54 thf(f72,plain,(
% 2.04/1.54 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f1])).
% 2.04/1.54 thf(f1,axiom,(
% 2.04/1.54 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mlocal_def)).
% 2.04/1.54 thf(f142,plain,(
% 2.04/1.54 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mnot @ (member @ Y0 @ empty_set))))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f94])).
% 2.04/1.54 thf(f94,plain,(
% 2.04/1.54 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mnot @ (member @ Y0 @ empty_set))))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f93])).
% 2.04/1.54 thf(f93,plain,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X0 : $i] : (mnot @ (member @ X0 @ empty_set)))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f39])).
% 2.04/1.54 thf(f39,axiom,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X6 : $i] : (mnot @ (member @ X6 @ empty_set)))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',empty_set_0)).
% 2.04/1.54 thf(f527,plain,(
% 2.04/1.54 ($true = (member @ sK4 @ empty_set @ mactual)) | ~spl0_1),
% 2.04/1.54 inference(binary_proxy_clausification,[status(thm)],[f525])).
% 2.04/1.54 thf(f525,plain,(
% 2.04/1.54 (((member @ sK4 @ empty_set @ mactual) => (member @ sK4 @ (intersection @ sK1 @ empty_set) @ mactual)) = $false) | ~spl0_1),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f524])).
% 2.04/1.54 thf(f524,plain,(
% 2.04/1.54 (((^[Y0 : $i]: ((member @ Y0 @ empty_set @ mactual) => (member @ Y0 @ (intersection @ sK1 @ empty_set) @ mactual))) @ sK4) = $false) | ~spl0_1),
% 2.04/1.54 inference(sigma_clausification,[status(thm)],[f523])).
% 2.04/1.54 thf(f523,plain,(
% 2.04/1.54 ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ empty_set @ mactual) => (member @ Y0 @ (intersection @ sK1 @ empty_set) @ mactual)))) = $false) | ~spl0_1),
% 2.04/1.54 inference(not_proxy_clausification,[status(thm)],[f522])).
% 2.04/1.54 thf(f522,plain,(
% 2.04/1.54 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ empty_set @ mactual) => (member @ Y0 @ (intersection @ sK1 @ empty_set) @ mactual)))))) | ~spl0_1),
% 2.04/1.54 inference(boolean_simplification,[status(thm)],[f519])).
% 2.04/1.54 thf(f519,plain,(
% 2.04/1.54 (($false = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ empty_set @ mactual) => (member @ Y0 @ (intersection @ sK1 @ empty_set) @ mactual))))) = $true) | ~spl0_1),
% 2.04/1.54 inference(superposition,[status(thm)],[f343,f459])).
% 2.04/1.54 thf(f459,plain,(
% 2.04/1.54 ((subset @ empty_set @ (intersection @ sK1 @ empty_set) @ mactual) = $false) | ~spl0_1),
% 2.04/1.54 inference(avatar_component_clause,[status(thm)],[f457])).
% 2.04/1.54 thf(f457,definition,(
% 2.04/1.54 spl0_1 <=> ((subset @ empty_set @ (intersection @ sK1 @ empty_set) @ mactual) = $false)),
% 2.04/1.54 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 2.04/1.54 thf(f343,plain,(
% 2.04/1.54 ( ! [X2 : $i,X1 : $i] : (($true = ((subset @ X1 @ X2 @ mactual) = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ X1 @ mactual) => (member @ Y0 @ X2 @ mactual))))))) )),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f342])).
% 2.04/1.54 thf(f342,plain,(
% 2.04/1.54 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((subset @ X1 @ Y0 @ mactual) = (!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual)))))) @ X2))) )),
% 2.04/1.54 inference(pi_clausification,[status(thm)],[f341])).
% 2.04/1.54 thf(f341,plain,(
% 2.04/1.54 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((subset @ X1 @ Y0 @ mactual) = (!! @ $i @ (^[Y1 : $i]: ((member @ Y1 @ X1 @ mactual) => (member @ Y1 @ Y0 @ mactual))))))) = $true)) )),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f340])).
% 2.04/1.54 thf(f340,plain,(
% 2.04/1.54 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1 @ mactual) = (!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual)))))))) @ X1))) )),
% 2.04/1.54 inference(pi_clausification,[status(thm)],[f339])).
% 2.04/1.54 thf(f339,plain,(
% 2.04/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((subset @ Y0 @ Y1 @ mactual) = (!! @ $i @ (^[Y2 : $i]: ((member @ Y2 @ Y0 @ mactual) => (member @ Y2 @ Y1 @ mactual))))))))))),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f186])).
% 2.04/1.54 thf(f186,plain,(
% 2.04/1.54 (((^[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) @ ((^[Y2 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) => (Y4 @ Y5))))))) @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))) = $true)),
% 2.04/1.54 inference(definition_unfolding,[status(thm)],[f144,f159,f143,f143,f141,f143,f161])).
% 2.04/1.54 thf(f161,plain,(
% 2.04/1.54 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f53])).
% 2.04/1.54 thf(f53,plain,(
% 2.04/1.54 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f52])).
% 2.04/1.54 thf(f52,plain,(
% 2.04/1.54 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 2.04/1.54 inference(rectify,[status(thm)],[f5])).
% 2.04/1.54 thf(f5,axiom,(
% 2.04/1.54 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mimplies_def)).
% 2.04/1.54 thf(f141,plain,(
% 2.04/1.54 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f76])).
% 2.04/1.54 thf(f76,plain,(
% 2.04/1.54 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f75])).
% 2.04/1.54 thf(f75,plain,(
% 2.04/1.54 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f6])).
% 2.04/1.54 thf(f6,axiom,(
% 2.04/1.54 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mequiv_def)).
% 2.04/1.54 thf(f144,plain,(
% 2.04/1.54 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f132])).
% 2.04/1.54 thf(f132,plain,(
% 2.04/1.54 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (subset @ Y0 @ Y1) @ (mforall_di @ (^[Y2 : $i]: (mimplies @ (member @ Y2 @ Y0) @ (member @ Y2 @ Y1)))))))))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f131])).
% 2.04/1.54 thf(f131,plain,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (subset @ X0 @ X1) @ (mforall_di @ (^[X2 : $i] : (mimplies @ (member @ X2 @ X0) @ (member @ X2 @ X1))))))))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f34])).
% 2.04/1.54 thf(f34,axiom,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (subset @ X1 @ X3) @ (mforall_di @ (^[X6 : $i] : (mimplies @ (member @ X6 @ X1) @ (member @ X6 @ X3))))))))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',subset_0)).
% 2.04/1.54 thf(f518,plain,(
% 2.04/1.54 ~spl0_2),
% 2.04/1.54 inference(avatar_contradiction_clause,[status(thm)],[f517])).
% 2.04/1.54 thf(f517,plain,(
% 2.04/1.54 $false | ~spl0_2),
% 2.04/1.54 inference(trivial_inequality_removal,[status(thm)],[f516])).
% 2.04/1.54 thf(f516,plain,(
% 2.04/1.54 ($true = $false) | ~spl0_2),
% 2.04/1.54 inference(forward_demodulation,[status(thm)],[f515,f477])).
% 2.04/1.54 thf(f477,plain,(
% 2.04/1.54 ( ! [X0 : $i,X1 : $i] : (((member @ X0 @ (intersection @ X1 @ empty_set) @ mactual) = $false)) )),
% 2.04/1.54 inference(not_proxy_clausification,[status(thm)],[f476])).
% 2.04/1.54 thf(f476,plain,(
% 2.04/1.54 ( ! [X0 : $i,X1 : $i] : (((~ (member @ X0 @ (intersection @ X1 @ empty_set) @ mactual)) = $true)) )),
% 2.04/1.54 inference(boolean_simplification,[status(thm)],[f475])).
% 2.04/1.54 thf(f475,plain,(
% 2.04/1.54 ( ! [X0 : $i,X1 : $i] : (($true = ((member @ X0 @ (intersection @ X1 @ empty_set) @ mactual) = $false))) )),
% 2.04/1.54 inference(boolean_simplification,[status(thm)],[f474])).
% 2.04/1.54 thf(f474,plain,(
% 2.04/1.54 ( ! [X0 : $i,X1 : $i] : (($true = ((member @ X0 @ (intersection @ X1 @ empty_set) @ mactual) = ($false & (member @ X0 @ X1 @ mactual))))) )),
% 2.04/1.54 inference(superposition,[status(thm)],[f314,f361])).
% 2.04/1.54 thf(f314,plain,(
% 2.04/1.54 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((member @ X1 @ (intersection @ X2 @ X3) @ mactual) = ((member @ X1 @ X3 @ mactual) & (member @ X1 @ X2 @ mactual))))) )),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f313])).
% 2.04/1.54 thf(f313,plain,(
% 2.04/1.54 ( ! [X2 : $i,X3 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((member @ X1 @ (intersection @ X2 @ Y0) @ mactual) = ((member @ X1 @ Y0 @ mactual) & (member @ X1 @ X2 @ mactual)))) @ X3))) )),
% 2.04/1.54 inference(pi_clausification,[status(thm)],[f312])).
% 2.04/1.54 thf(f312,plain,(
% 2.04/1.54 ( ! [X2 : $i,X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((member @ X1 @ (intersection @ X2 @ Y0) @ mactual) = ((member @ X1 @ Y0 @ mactual) & (member @ X1 @ X2 @ mactual))))) = $true)) )),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f311])).
% 2.04/1.54 thf(f311,plain,(
% 2.04/1.54 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((member @ X1 @ (intersection @ Y0 @ Y1) @ mactual) = ((member @ X1 @ Y1 @ mactual) & (member @ X1 @ Y0 @ mactual)))))) @ X2) = $true)) )),
% 2.04/1.54 inference(pi_clausification,[status(thm)],[f310])).
% 2.04/1.54 thf(f310,plain,(
% 2.04/1.54 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((member @ X1 @ (intersection @ Y0 @ Y1) @ mactual) = ((member @ X1 @ Y1 @ mactual) & (member @ X1 @ Y0 @ mactual))))))) = $true)) )),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f309])).
% 2.04/1.54 thf(f309,plain,(
% 2.04/1.54 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((member @ Y0 @ (intersection @ Y1 @ Y2) @ mactual) = ((member @ Y0 @ Y2 @ mactual) & (member @ Y0 @ Y1 @ mactual)))))))) @ X1))) )),
% 2.04/1.54 inference(pi_clausification,[status(thm)],[f308])).
% 2.04/1.54 thf(f308,plain,(
% 2.04/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: (!! @ $i @ (^[Y2 : $i]: ((member @ Y0 @ (intersection @ Y1 @ Y2) @ mactual) = ((member @ Y0 @ Y2 @ mactual) & (member @ Y0 @ Y1 @ mactual))))))))))),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f194])).
% 2.04/1.54 thf(f194,plain,(
% 2.04/1.54 (((^[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 : $i > mworld > $o]: ((^[Y3 : mworld]: (!! @ $i @ (^[Y4 : $i]: (Y2 @ Y4 @ Y3)))))) @ (^[Y2 : $i]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y3 @ Y5) = (Y4 @ Y5))))))) @ (member @ Y0 @ (intersection @ Y1 @ Y2)) @ ((^[Y3 : mworld > $o]: ((^[Y4 : mworld > $o]: ((^[Y5 : mworld]: ((Y4 @ Y5) & (Y3 @ Y5))))))) @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))) = $true)),
% 2.04/1.54 inference(definition_unfolding,[status(thm)],[f153,f159,f143,f143,f143,f141,f172])).
% 2.04/1.54 thf(f172,plain,(
% 2.04/1.54 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f128])).
% 2.04/1.54 thf(f128,plain,(
% 2.04/1.54 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f127])).
% 2.04/1.54 thf(f127,plain,(
% 2.04/1.54 (mand = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f3])).
% 2.04/1.54 thf(f3,axiom,(
% 2.04/1.54 (mand = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',mand_def)).
% 2.04/1.54 thf(f153,plain,(
% 2.04/1.54 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (member @ Y0 @ (intersection @ Y1 @ Y2)) @ (mand @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))) = $true)),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f63])).
% 2.04/1.54 thf(f63,plain,(
% 2.04/1.54 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mforall_di @ (^[Y2 : $i]: (mequiv @ (member @ Y0 @ (intersection @ Y1 @ Y2)) @ (mand @ (member @ Y0 @ Y1) @ (member @ Y0 @ Y2)))))))))) = $true)),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f62])).
% 2.04/1.54 thf(f62,plain,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X2 : $i] : (mequiv @ (member @ X0 @ (intersection @ X1 @ X2)) @ (mand @ (member @ X0 @ X1) @ (member @ X0 @ X2))))))))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f37])).
% 2.04/1.54 thf(f37,axiom,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X6 : $i] : (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (member @ X6 @ (intersection @ X1 @ X3)) @ (mand @ (member @ X6 @ X1) @ (member @ X6 @ X3))))))))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',intersection_0)).
% 2.04/1.54 thf(f515,plain,(
% 2.04/1.54 ($true = (member @ sK3 @ (intersection @ sK1 @ empty_set) @ mactual)) | ~spl0_2),
% 2.04/1.54 inference(binary_proxy_clausification,[status(thm)],[f513])).
% 2.04/1.54 thf(f513,plain,(
% 2.04/1.54 ($false = ((member @ sK3 @ (intersection @ sK1 @ empty_set) @ mactual) => (member @ sK3 @ empty_set @ mactual))) | ~spl0_2),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f512])).
% 2.04/1.54 thf(f512,plain,(
% 2.04/1.54 ($false = ((^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK1 @ empty_set) @ mactual) => (member @ Y0 @ empty_set @ mactual))) @ sK3)) | ~spl0_2),
% 2.04/1.54 inference(sigma_clausification,[status(thm)],[f511])).
% 2.04/1.54 thf(f511,plain,(
% 2.04/1.54 ((!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK1 @ empty_set) @ mactual) => (member @ Y0 @ empty_set @ mactual)))) = $false) | ~spl0_2),
% 2.04/1.54 inference(not_proxy_clausification,[status(thm)],[f510])).
% 2.04/1.54 thf(f510,plain,(
% 2.04/1.54 ($true = (~ (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK1 @ empty_set) @ mactual) => (member @ Y0 @ empty_set @ mactual)))))) | ~spl0_2),
% 2.04/1.54 inference(boolean_simplification,[status(thm)],[f509])).
% 2.04/1.54 thf(f509,plain,(
% 2.04/1.54 (($false = (!! @ $i @ (^[Y0 : $i]: ((member @ Y0 @ (intersection @ sK1 @ empty_set) @ mactual) => (member @ Y0 @ empty_set @ mactual))))) = $true) | ~spl0_2),
% 2.04/1.54 inference(superposition,[status(thm)],[f343,f463])).
% 2.04/1.54 thf(f463,plain,(
% 2.04/1.54 ($false = (subset @ (intersection @ sK1 @ empty_set) @ empty_set @ mactual)) | ~spl0_2),
% 2.04/1.54 inference(avatar_component_clause,[status(thm)],[f461])).
% 2.04/1.54 thf(f461,definition,(
% 2.04/1.54 spl0_2 <=> ($false = (subset @ (intersection @ sK1 @ empty_set) @ empty_set @ mactual))),
% 2.04/1.54 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 2.04/1.54 thf(f464,plain,(
% 2.04/1.54 spl0_1 | spl0_2),
% 2.04/1.54 inference(avatar_split_clause,[status(thm)],[f455,f461,f457])).
% 2.04/1.54 thf(f455,plain,(
% 2.04/1.54 ($false = (subset @ (intersection @ sK1 @ empty_set) @ empty_set @ mactual)) | ((subset @ empty_set @ (intersection @ sK1 @ empty_set) @ mactual) = $false)),
% 2.04/1.54 inference(binary_proxy_clausification,[status(thm)],[f454])).
% 2.04/1.54 thf(f454,plain,(
% 2.04/1.54 (((subset @ empty_set @ (intersection @ sK1 @ empty_set) @ mactual) & (subset @ (intersection @ sK1 @ empty_set) @ empty_set @ mactual)) = $false)),
% 2.04/1.54 inference(not_proxy_clausification,[status(thm)],[f453])).
% 2.04/1.54 thf(f453,plain,(
% 2.04/1.54 ((~ ((subset @ empty_set @ (intersection @ sK1 @ empty_set) @ mactual) & (subset @ (intersection @ sK1 @ empty_set) @ empty_set @ mactual))) = $true)),
% 2.04/1.54 inference(boolean_simplification,[status(thm)],[f452])).
% 2.04/1.54 thf(f452,plain,(
% 2.04/1.54 (($false = ((subset @ empty_set @ (intersection @ sK1 @ empty_set) @ mactual) & (subset @ (intersection @ sK1 @ empty_set) @ empty_set @ mactual))) = $true)),
% 2.04/1.54 inference(superposition,[status(thm)],[f285,f428])).
% 2.04/1.54 thf(f428,plain,(
% 2.04/1.54 ((equal_set @ (intersection @ sK1 @ empty_set) @ empty_set @ mactual) = $false)),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f427])).
% 2.04/1.54 thf(f427,plain,(
% 2.04/1.54 (((^[Y0 : $i]: (equal_set @ (intersection @ Y0 @ empty_set) @ empty_set @ mactual)) @ sK1) = $false)),
% 2.04/1.54 inference(sigma_clausification,[status(thm)],[f426])).
% 2.04/1.54 thf(f426,plain,(
% 2.04/1.54 ((!! @ $i @ (^[Y0 : $i]: (equal_set @ (intersection @ Y0 @ empty_set) @ empty_set @ mactual))) != $true)),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f199])).
% 2.04/1.54 thf(f199,plain,(
% 2.04/1.54 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: (equal_set @ (intersection @ Y0 @ empty_set) @ empty_set)))) != $true)),
% 2.04/1.54 inference(definition_unfolding,[status(thm)],[f158,f159,f143])).
% 2.04/1.54 thf(f158,plain,(
% 2.04/1.54 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (equal_set @ (intersection @ Y0 @ empty_set) @ empty_set)))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f137])).
% 2.04/1.54 thf(f137,plain,(
% 2.04/1.54 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (equal_set @ (intersection @ Y0 @ empty_set) @ empty_set)))))),
% 2.04/1.54 inference(flattening,[status(thm)],[f116])).
% 2.04/1.54 thf(f116,plain,(
% 2.04/1.54 ~($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (equal_set @ (intersection @ Y0 @ empty_set) @ empty_set)))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f115])).
% 2.04/1.54 thf(f115,plain,(
% 2.04/1.54 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (equal_set @ (intersection @ X0 @ empty_set) @ empty_set))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f46])).
% 2.04/1.54 thf(f46,negated_conjecture,(
% 2.04/1.54 ~(mlocal @ (mforall_di @ (^[X1 : $i] : (equal_set @ (intersection @ X1 @ empty_set) @ empty_set))))),
% 2.04/1.54 inference(negated_conjecture,[status(cth)],[f45])).
% 2.04/1.54 thf(f45,conjecture,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X1 : $i] : (equal_set @ (intersection @ X1 @ empty_set) @ empty_set))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',thI17)).
% 2.04/1.54 thf(f285,plain,(
% 2.04/1.54 ( ! [X2 : $i,X1 : $i] : ((((equal_set @ X1 @ X2 @ mactual) = ((subset @ X2 @ X1 @ mactual) & (subset @ X1 @ X2 @ mactual))) = $true)) )),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f284])).
% 2.04/1.54 thf(f284,plain,(
% 2.04/1.54 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((equal_set @ X1 @ Y0 @ mactual) = ((subset @ Y0 @ X1 @ mactual) & (subset @ X1 @ Y0 @ mactual)))) @ X2))) )),
% 2.04/1.54 inference(pi_clausification,[status(thm)],[f283])).
% 2.04/1.54 thf(f283,plain,(
% 2.04/1.54 ( ! [X1 : $i] : (((!! @ $i @ (^[Y0 : $i]: ((equal_set @ X1 @ Y0 @ mactual) = ((subset @ Y0 @ X1 @ mactual) & (subset @ X1 @ Y0 @ mactual))))) = $true)) )),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f282])).
% 2.04/1.54 thf(f282,plain,(
% 2.04/1.54 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((equal_set @ Y0 @ Y1 @ mactual) = ((subset @ Y1 @ Y0 @ mactual) & (subset @ Y0 @ Y1 @ mactual)))))) @ X1) = $true)) )),
% 2.04/1.54 inference(pi_clausification,[status(thm)],[f281])).
% 2.04/1.54 thf(f281,plain,(
% 2.04/1.54 ($true = (!! @ $i @ (^[Y0 : $i]: (!! @ $i @ (^[Y1 : $i]: ((equal_set @ Y0 @ Y1 @ mactual) = ((subset @ Y1 @ Y0 @ mactual) & (subset @ Y0 @ Y1 @ mactual))))))))),
% 2.04/1.54 inference(beta_eta_normalization,[status(thm)],[f200])).
% 2.04/1.54 thf(f200,plain,(
% 2.04/1.54 (((^[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))))))) @ (equal_set @ Y0 @ Y1) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) & (Y2 @ Y4))))))) @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))) = $true)),
% 2.04/1.54 inference(definition_unfolding,[status(thm)],[f160,f159,f143,f143,f141,f172])).
% 2.04/1.54 thf(f160,plain,(
% 2.04/1.54 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 2.04/1.54 inference(cnf_transformation,[status(thm)],[f88])).
% 2.04/1.54 thf(f88,plain,(
% 2.04/1.54 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (equal_set @ Y0 @ Y1) @ (mand @ (subset @ Y0 @ Y1) @ (subset @ Y1 @ Y0)))))))))),
% 2.04/1.54 inference(fool_elimination,[status(thm)],[f87])).
% 2.04/1.54 thf(f87,plain,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (equal_set @ X0 @ X1) @ (mand @ (subset @ X0 @ X1) @ (subset @ X1 @ X0))))))))),
% 2.04/1.54 inference(rectify,[status(thm)],[f35])).
% 2.04/1.54 thf(f35,axiom,(
% 2.04/1.54 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (equal_set @ X1 @ X3) @ (mand @ (subset @ X1 @ X3) @ (subset @ X3 @ X1))))))))),
% 2.04/1.54 file('/export/starexec/sandbox2/tmp/tmp.nt3FSsSJVh/DTF2THF_13268.p',equal_set_0)).
% 2.04/1.54 % SZS output end Proof for DTF2THF_13268
% 2.04/1.54 % (13578)------------------------------
% 2.04/1.54 % (13578)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 2.04/1.54 % (13578)Termination reason: Refutation
% 2.04/1.54
% 2.04/1.54 % (13578)Memory used [KB]: 6268
% 2.04/1.54 % (13578)Time elapsed: 0.024 s
% 2.04/1.54 % (13578)Instructions burned: 66 (million)
% 2.04/1.54 % (13578)------------------------------
% 2.04/1.54 % (13578)------------------------------
% 2.04/1.54 % (13544)Success in time 0.132 s
%------------------------------------------------------------------------------