%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET926^12 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n027.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:32:21 AM UTC 2026
% Result : Theorem 1.81s 1.34s
% Output : Refutation 1.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 12
% Syntax : Number of formulae : 90 ( 49 unt; 0 typ; 4 def)
% Number of atoms : 602 ( 125 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 963 ( 37 ~; 62 |; 0 &; 798 @)
% ( 6 <=>; 37 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 53 ( 53 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 26 usr; 11 con; 0-3 aty)
% ( 23 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 162 ( 132 ^; 30 !; 0 ?; 162 :)
% 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,
eiw_di: $i > mworld > $o ).
thf(func_def_13,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_14,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_16,type,
qmltpeq: $i > $i > mworld > $o ).
thf(func_def_17,type,
in: $i > $i > mworld > $o ).
thf(func_def_18,type,
empty: $i > mworld > $o ).
thf(func_def_19,type,
singleton: $i > $i ).
thf(func_def_20,type,
set_difference: $i > $i > $i ).
thf(func_def_34,type,
sK0: mworld > $i ).
thf(f461,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f395,f426,f432,f447,f457]) ).
thf(f457,plain,
( ~ spl1_9
| ~ spl1_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f456]) ).
thf(f456,plain,
( $false
| ~ spl1_9
| ~ spl1_12 ),
inference(trivial_inequality_removal,[status(thm)],[f451]) ).
thf(f451,plain,
( ( $true = $false )
| ~ spl1_9
| ~ spl1_12 ),
inference(superposition,[status(thm)],[f385,f424]) ).
thf(f424,plain,
( ( $true
= ( in @ sK3 @ sK4 @ mactual ) )
| ~ spl1_12 ),
inference(avatar_component_clause,[status(thm)],[f422]) ).
thf(f422,definition,
( spl1_12
<=> ( $true
= ( in @ sK3 @ sK4 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_12])],[avatar_definition]) ).
thf(f385,plain,
( ( ( in @ sK3 @ sK4 @ mactual )
= $false )
| ~ spl1_9 ),
inference(avatar_component_clause,[status(thm)],[f383]) ).
thf(f383,definition,
( spl1_9
<=> ( ( in @ sK3 @ sK4 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition]) ).
thf(f447,plain,
~ spl1_11,
inference(avatar_contradiction_clause,[status(thm)],[f446]) ).
thf(f446,plain,
( $false
| ~ spl1_11 ),
inference(trivial_inequality_removal,[status(thm)],[f443]) ).
thf(f443,plain,
( ( $true = $false )
| ~ spl1_11 ),
inference(superposition,[status(thm)],[f198,f393]) ).
thf(f393,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f391]) ).
thf(f391,definition,
( spl1_11
<=> ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition]) ).
thf(f198,plain,
( $true
= ( eiw_di @ sK3 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f196]) ).
thf(f196,plain,
( $false
= ( ( eiw_di @ sK3 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f195]) ).
thf(f195,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) )
@ sK3 ) ),
inference(sigma_clausification,[status(thm)],[f194]) ).
thf(f194,plain,
( $true
!= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f132]) ).
thf(f132,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y3 @ Y4 )
| ( Y2 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f115,f100,f106,f106,f99]) ).
thf(f99,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f61]) ).
thf(f61,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f60]) ).
thf(f60,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X3 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mor_def) ).
thf(f106,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f35]) ).
thf(f35,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] :
( ( eiw_di @ X5 @ X2 )
=> ( X1 @ X5 @ X2 ) ) )
= mforall_di ),
file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mforall_di_def) ).
thf(f100,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f45]) ).
thf(f45,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/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mlocal_def) ).
thf(f115,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
thf(f86,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f71]) ).
thf(f71,plain,
( $true
!= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f70]) ).
thf(f70,plain,
~ ( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f29]) ).
thf(f29,negated_conjecture,
~ ( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ ( singleton @ X1 ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
thf(f28,conjecture,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ ( singleton @ X1 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',t69_zfmisc_1) ).
thf(f432,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[status(thm)],[f431]) ).
thf(f431,plain,
( $false
| ~ spl1_10 ),
inference(trivial_inequality_removal,[status(thm)],[f427]) ).
thf(f427,plain,
( ( $true = $false )
| ~ spl1_10 ),
inference(superposition,[status(thm)],[f389,f202]) ).
thf(f202,plain,
( $true
= ( eiw_di @ sK4 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f200]) ).
thf(f200,plain,
( ( ( eiw_di @ sK4 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ mactual ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f199]) ).
thf(f199,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ mactual ) ) )
@ sK4 )
= $false ),
inference(sigma_clausification,[status(thm)],[f197]) ).
thf(f197,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ ( singleton @ sK3 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ Y0 ) @ empty_set @ mactual ) ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f196]) ).
thf(f389,plain,
( ( ( eiw_di @ sK4 @ mactual )
= $false )
| ~ spl1_10 ),
inference(avatar_component_clause,[status(thm)],[f387]) ).
thf(f387,definition,
( spl1_10
<=> ( ( eiw_di @ sK4 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition]) ).
thf(f426,plain,
( spl1_12
| spl1_10
| spl1_11 ),
inference(avatar_split_clause,[status(thm)],[f415,f391,f387,f422]) ).
thf(f415,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( ( eiw_di @ sK4 @ mactual )
= $false )
| ( $true
= ( in @ sK3 @ sK4 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f409]) ).
thf(f409,plain,
( ( $true
= ( in @ sK3 @ sK4 @ mactual ) )
| ( $true = $false )
| ( ( eiw_di @ sK4 @ mactual )
= $false )
| ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
inference(superposition,[status(thm)],[f260,f204]) ).
thf(f204,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ mactual )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f201]) ).
thf(f201,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ ( singleton @ sK3 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ mactual ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f200]) ).
thf(f260,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $true
= ( in @ X1 @ X2 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f259]) ).
thf(f259,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( ( ~ ( in @ X1 @ X2 @ mactual ) )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f257]) ).
thf(f257,plain,
! [X2: $i,X1: $i] :
( ( ( ~ ( in @ X1 @ X2 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f256]) ).
thf(f256,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f255]) ).
thf(f255,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f254]) ).
thf(f254,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) )
@ X2 ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f253]) ).
thf(f253,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f252]) ).
thf(f252,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ Y0 @ mactual ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f251]) ).
thf(f251,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
= ( ~ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f250]) ).
thf(f250,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual )
= ( ~ ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f120]) ).
thf(f120,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f94,f100,f106,f106,f112,f92]) ).
thf(f92,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f53]) ).
thf(f53,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f52]) ).
thf(f52,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/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mnot_def) ).
thf(f112,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f75]) ).
thf(f75,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
= ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f74]) ).
thf(f74,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/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mequiv_def) ).
thf(f94,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f39]) ).
thf(f39,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ ( singleton @ X0 ) ) @ ( mnot @ ( in @ X0 @ X1 ) ) ) ) ) ),
inference(rectify,[status(thm)],[f24]) ).
thf(f24,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ ( singleton @ X1 ) ) @ ( mnot @ ( in @ X1 @ X3 ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',l34_zfmisc_1) ).
thf(f395,plain,
( spl1_11
| spl1_10
| spl1_9 ),
inference(avatar_split_clause,[status(thm)],[f367,f383,f387,f391]) ).
thf(f367,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( ( eiw_di @ sK4 @ mactual )
= $false )
| ( ( in @ sK3 @ sK4 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f360]) ).
thf(f360,plain,
( ( ( in @ sK3 @ sK4 @ mactual )
= $false )
| ( ( eiw_di @ sK4 @ mactual )
= $false )
| ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f203,f193]) ).
thf(f193,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) )
| ( ( eiw_di @ X2 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( in @ X1 @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f191]) ).
thf(f191,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X2 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( in @ X1 @ X2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f190]) ).
thf(f190,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) ) )
| ( ( eiw_di @ X2 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f189]) ).
thf(f189,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f188]) ).
thf(f188,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) )
@ X2 ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f187]) ).
thf(f187,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f186]) ).
thf(f186,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual )
= ( in @ X1 @ Y0 @ mactual ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f185]) ).
thf(f185,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual )
= ( in @ Y0 @ Y1 @ mactual ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual )
= ( in @ Y0 @ Y1 @ mactual ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f124]) ).
thf(f124,plain,
( $true
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: $i > mworld > $o,Y2: mworld] :
( !! @ $i
@ ^ [Y3: $i] :
( ( eiw_di @ Y3 @ Y2 )
=> ( Y1 @ Y3 @ Y2 ) ) )
@ ^ [Y1: $i] :
( ^ [Y2: mworld > $o,Y3: mworld > $o,Y4: mworld] :
( ( Y2 @ Y4 )
= ( Y3 @ Y4 ) )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f101,f100,f106,f106,f112]) ).
thf(f101,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f65]) ).
thf(f65,plain,
( $true
= ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set ) @ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f64]) ).
thf(f64,plain,
( mlocal
@ ( mforall_di
@ ^ [X0: $i] :
( mforall_di
@ ^ [X1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X0 ) @ X1 ) @ empty_set ) @ ( in @ X0 @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f25]) ).
thf(f25,axiom,
( mlocal
@ ( mforall_di
@ ^ [X1: $i] :
( mforall_di
@ ^ [X3: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X3 ) @ empty_set ) @ ( in @ X1 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',l36_zfmisc_1) ).
thf(f203,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK3 ) @ sK4 ) @ empty_set @ mactual )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f201]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET926^12 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.33 % Computer : n027.cluster.edu
% 0.15/0.33 % Model : x86_64 x86_64
% 0.15/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.33 % Memory : 8042.1875MB
% 0.15/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.33 % CPULimit : 300
% 0.15/0.33 % WCLimit : 300
% 0.15/0.33 % DateTime : Tue Feb 24 12:06:22 EST 2026
% 0.15/0.33 % CPUTime :
% 0.15/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.45 ---- Original DTF file ---
% 0.19/0.45 thf(spec,logic,$$dhol).
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 % File : SET926^12 : TPTP v9.2.1. Released v8.1.0.
% 0.19/0.45 % Domain : Set Theory
% 0.19/0.45 % Problem : TPTP problem SET926+1.p with axiomatized equality
% 0.19/0.45 % Version : [BP13] axioms.
% 0.19/0.45 % English :
% 0.19/0.45
% 0.19/0.45 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.19/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.19/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.19/0.45 % Source : [TPTP]
% 0.19/0.45 % Names : SET926+1 [QMLTP]
% 0.19/0.45
% 0.19/0.45 % Status : Theorem
% 0.19/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.19/0.45 % Syntax : Number of formulae : 48 ( 12 unt; 20 typ; 10 def)
% 0.19/0.45 % Number of atoms : 125 ( 10 equ; 0 cnn)
% 0.19/0.45 % Maximal formula atoms : 9 ( 4 avg)
% 0.19/0.45 % Number of connectives : 203 ( 1 ~; 1 |; 3 &; 194 @)
% 0.19/0.45 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.19/0.45 % Maximal formula depth : 14 ( 7 avg)
% 0.19/0.45 % Number of types : 3 ( 1 usr)
% 0.19/0.45 % Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% 0.19/0.45 % Number of symbols : 20 ( 19 usr; 2 con; 0-3 aty)
% 0.19/0.45 % Number of variables : 63 ( 55 ^; 5 !; 3 ?; 63 :)
% 0.19/0.45 % SPC : TH0_THM_EQU_NAR
% 0.19/0.45
% 0.19/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.19/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.19/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.19/0.45 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.19/0.45 % $modalities == $modal_system_S5U].
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 thf(mworld,type,
% 0.19/0.45 mworld: $tType ).
% 0.19/0.45
% 0.19/0.45 thf(mrel_type,type,
% 0.19/0.45 mrel: mworld > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mactual_type,type,
% 0.19/0.45 mactual: mworld ).
% 0.19/0.45
% 0.19/0.45 thf(mlocal_type,type,
% 0.19/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mlocal_def,definition,
% 0.19/0.45 ( mlocal
% 0.19/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mnot_type,type,
% 0.19/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mand_type,type,
% 0.19/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mor_type,type,
% 0.19/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mimplies_type,type,
% 0.19/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mequiv_type,type,
% 0.19/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mnot_def,definition,
% 0.19/0.45 ( mnot
% 0.19/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.19/0.45 ~ ( A @ W ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mand_def,definition,
% 0.19/0.45 ( mand
% 0.19/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.45 ( ( A @ W )
% 0.19/0.45 & ( B @ W ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mor_def,definition,
% 0.19/0.45 ( mor
% 0.19/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.45 ( ( A @ W )
% 0.19/0.45 | ( B @ W ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mimplies_def,definition,
% 0.19/0.45 ( mimplies
% 0.19/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.45 ( ( A @ W )
% 0.19/0.45 => ( B @ W ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mequiv_def,definition,
% 0.19/0.45 ( mequiv
% 0.19/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.19/0.45 ( ( A @ W )
% 0.19/0.45 <=> ( B @ W ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mbox_type,type,
% 0.19/0.45 mbox: ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mbox_def,definition,
% 0.19/0.45 ( mbox
% 0.19/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.19/0.45 ! [V: mworld] :
% 0.19/0.45 ( ( mrel @ W @ V )
% 0.19/0.45 => ( Phi @ V ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mdia_type,type,
% 0.19/0.45 mdia: ( mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mdia_def,definition,
% 0.19/0.45 ( mdia
% 0.19/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.19/0.45 ? [V: mworld] :
% 0.19/0.45 ( ( mrel @ W @ V )
% 0.19/0.45 & ( Phi @ V ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mrel_universal,axiom,
% 0.19/0.45 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 0.19/0.45
% 0.19/0.45 thf(eiw_di_type,type,
% 0.19/0.45 eiw_di: $i > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(eiw_di_nonempty,axiom,
% 0.19/0.45 ! [W: mworld] :
% 0.19/0.45 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.19/0.45
% 0.19/0.45 thf(mforall_di_type,type,
% 0.19/0.45 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mforall_di_def,definition,
% 0.19/0.45 ( mforall_di
% 0.19/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.19/0.45 ! [X: $i] :
% 0.19/0.45 ( ( eiw_di @ X @ W )
% 0.19/0.45 => ( A @ X @ W ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(mexists_di_type,type,
% 0.19/0.45 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(mexists_di_def,definition,
% 0.19/0.45 ( mexists_di
% 0.19/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.19/0.45 ? [X: $i] :
% 0.19/0.45 ( ( eiw_di @ X @ W )
% 0.19/0.45 & ( A @ X @ W ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %%% This output was generated by tptputils, version 1.2.
% 0.19/0.45 %%% Generated on Wed Apr 27 15:38:22 CEST 2022 using command 'downgrade(tff)'.
% 0.19/0.45 thf(empty_set_decl,type,
% 0.19/0.45 empty_set: $i ).
% 0.19/0.45
% 0.19/0.45 thf(qmltpeq_decl,type,
% 0.19/0.45 qmltpeq: $i > $i > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(in_decl,type,
% 0.19/0.45 in: $i > $i > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(empty_decl,type,
% 0.19/0.45 empty: $i > mworld > $o ).
% 0.19/0.45
% 0.19/0.45 thf(singleton_decl,type,
% 0.19/0.45 singleton: $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(set_difference_decl,type,
% 0.19/0.45 set_difference: $i > $i > $i ).
% 0.19/0.45
% 0.19/0.45 thf(reflexivity,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(symmetry,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [X: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(transitivity,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [X: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [Y: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(set_difference_substitution_1,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(set_difference_substitution_2,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(singleton_substitution_1,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(empty_substitution_1,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(in_substitution_1,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(in_substitution_2,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(antisymmetry_r2_hidden,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(fc1_xboole_0,axiom,
% 0.19/0.45 mlocal @ ( empty @ empty_set ) ).
% 0.19/0.45
% 0.19/0.45 thf(l34_zfmisc_1,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(l36_zfmisc_1,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(rc1_xboole_0,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mexists_di
% 0.19/0.45 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(rc2_xboole_0,axiom,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mexists_di
% 0.19/0.45 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 thf(t69_zfmisc_1,conjecture,
% 0.19/0.45 ( mlocal
% 0.19/0.45 @ ( mforall_di
% 0.19/0.45 @ ^ [A: $i] :
% 0.19/0.45 ( mforall_di
% 0.19/0.45 @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ).
% 0.19/0.45
% 0.19/0.45 %------------------------------------------------------------------------------
% 0.19/0.45 ------------------------
% 1.58/1.29 ---- Embedded in THF ---
% 1.58/1.29 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.58/1.29 %%% Generated on Tue Feb 24 12:06:23 EST 2026
% 1.58/1.29 %%% using '$$dhol' embedding, version 1.3.0.
% 1.58/1.29 %%% Logic specification used:
% 1.58/1.29 %%% thf(spec, logic, $$dhol).
% 1.58/1.29
% 1.58/1.29 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2DTF1625.p
% See solution above
% 1.58/1.29 ------------------------
% 1.81/1.30 ---- Cleaned THF ---
% 1.81/1.30 thf(mworld,type,
% 1.81/1.30 mworld: $tType ).
% 1.81/1.30
% 1.81/1.30 thf(mrel_type,type,
% 1.81/1.30 mrel: mworld > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mactual_type,type,
% 1.81/1.30 mactual: mworld ).
% 1.81/1.30
% 1.81/1.30 thf(mlocal_type,type,
% 1.81/1.30 mlocal: ( mworld > $o ) > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mlocal_def,definition,
% 1.81/1.30 ( mlocal
% 1.81/1.30 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mnot_type,type,
% 1.81/1.30 mnot: ( mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mand_type,type,
% 1.81/1.30 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mor_type,type,
% 1.81/1.30 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mimplies_type,type,
% 1.81/1.30 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mequiv_type,type,
% 1.81/1.30 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mnot_def,definition,
% 1.81/1.30 ( mnot
% 1.81/1.30 = ( ^ [A: mworld > $o,W: mworld] :
% 1.81/1.30 ~ ( A @ W ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mand_def,definition,
% 1.81/1.30 ( mand
% 1.81/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.81/1.30 ( ( A @ W )
% 1.81/1.30 & ( B @ W ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mor_def,definition,
% 1.81/1.30 ( mor
% 1.81/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.81/1.30 ( ( A @ W )
% 1.81/1.30 | ( B @ W ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mimplies_def,definition,
% 1.81/1.30 ( mimplies
% 1.81/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.81/1.30 ( ( A @ W )
% 1.81/1.30 => ( B @ W ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mequiv_def,definition,
% 1.81/1.30 ( mequiv
% 1.81/1.30 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.81/1.30 ( ( A @ W )
% 1.81/1.30 <=> ( B @ W ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mbox_type,type,
% 1.81/1.30 mbox: ( mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mbox_def,definition,
% 1.81/1.30 ( mbox
% 1.81/1.30 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.81/1.30 ! [V: mworld] :
% 1.81/1.30 ( ( mrel @ W @ V )
% 1.81/1.30 => ( Phi @ V ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mdia_type,type,
% 1.81/1.30 mdia: ( mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mdia_def,definition,
% 1.81/1.30 ( mdia
% 1.81/1.30 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.81/1.30 ? [V: mworld] :
% 1.81/1.30 ( ( mrel @ W @ V )
% 1.81/1.30 & ( Phi @ V ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mrel_universal,axiom,
% 1.81/1.30 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 1.81/1.30
% 1.81/1.30 thf(eiw_di_type,type,
% 1.81/1.30 eiw_di: $i > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(eiw_di_nonempty,axiom,
% 1.81/1.30 ! [W: mworld] :
% 1.81/1.30 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.81/1.30
% 1.81/1.30 thf(mforall_di_type,type,
% 1.81/1.30 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mforall_di_def,definition,
% 1.81/1.30 ( mforall_di
% 1.81/1.30 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.81/1.30 ! [X: $i] :
% 1.81/1.30 ( ( eiw_di @ X @ W )
% 1.81/1.30 => ( A @ X @ W ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(mexists_di_type,type,
% 1.81/1.30 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(mexists_di_def,definition,
% 1.81/1.30 ( mexists_di
% 1.81/1.30 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.81/1.30 ? [X: $i] :
% 1.81/1.30 ( ( eiw_di @ X @ W )
% 1.81/1.30 & ( A @ X @ W ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(empty_set_decl,type,
% 1.81/1.30 empty_set: $i ).
% 1.81/1.30
% 1.81/1.30 thf(qmltpeq_decl,type,
% 1.81/1.30 qmltpeq: $i > $i > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(in_decl,type,
% 1.81/1.30 in: $i > $i > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(empty_decl,type,
% 1.81/1.30 empty: $i > mworld > $o ).
% 1.81/1.30
% 1.81/1.30 thf(singleton_decl,type,
% 1.81/1.30 singleton: $i > $i ).
% 1.81/1.30
% 1.81/1.30 thf(set_difference_decl,type,
% 1.81/1.30 set_difference: $i > $i > $i ).
% 1.81/1.30
% 1.81/1.30 thf(reflexivity,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(symmetry,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [X: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(transitivity,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [X: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [Y: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(set_difference_substitution_1,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(set_difference_substitution_2,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(singleton_substitution_1,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(empty_substitution_1,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(in_substitution_1,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(in_substitution_2,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(antisymmetry_r2_hidden,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(fc1_xboole_0,axiom,
% 1.81/1.30 mlocal @ ( empty @ empty_set ) ).
% 1.81/1.30
% 1.81/1.30 thf(l34_zfmisc_1,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(l36_zfmisc_1,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(rc1_xboole_0,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mexists_di
% 1.81/1.30 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(rc2_xboole_0,axiom,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mexists_di
% 1.81/1.30 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 1.81/1.30
% 1.81/1.30 thf(t69_zfmisc_1,conjecture,
% 1.81/1.30 ( mlocal
% 1.81/1.30 @ ( mforall_di
% 1.81/1.30 @ ^ [A: $i] :
% 1.81/1.30 ( mforall_di
% 1.81/1.30 @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ).
% 1.81/1.30 ------------------------
% 1.81/1.31 % (1974)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_1625 for (2999ds/4Mi)
% 1.81/1.31 % (1973)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1625 for (2999ds/183Mi)
% 1.81/1.32 % (1974)Instruction limit reached!
% 1.81/1.32 % (1974)------------------------------
% 1.81/1.32 % (1974)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.32 % (1974)Termination reason: Unknown
% 1.81/1.32 % (1974)Termination phase: Clausification
% 1.81/1.32
% 1.81/1.32 % (1974)Memory used [KB]: 1023
% 1.81/1.32 % (1974)Time elapsed: 0.003 s
% 1.81/1.32 % (1974)Instructions burned: 5 (million)
% 1.81/1.32 % (1974)------------------------------
% 1.81/1.32 % (1974)------------------------------
% 1.81/1.32 % (1975)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_1625 for (2999ds/27Mi)
% 1.81/1.32 % (1976)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1625 for (2999ds/2Mi)
% 1.81/1.32 % (1977)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_1625 for (2999ds/2Mi)
% 1.81/1.32 % (1978)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_1625 for (2999ds/275Mi)
% 1.81/1.32 % (1979)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1625 for (2999ds/18Mi)
% 1.81/1.32 % (1976)Instruction limit reached!
% 1.81/1.32 % (1976)------------------------------
% 1.81/1.32 % (1976)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.32 % (1976)Termination reason: Unknown
% 1.81/1.32 % (1976)Termination phase: shuffling
% 1.81/1.32
% 1.81/1.32 % (1976)Memory used [KB]: 1023
% 1.81/1.32 % (1976)Time elapsed: 0.003 s
% 1.81/1.32 % (1976)Instructions burned: 2 (million)
% 1.81/1.32 % (1976)------------------------------
% 1.81/1.32 % (1976)------------------------------
% 1.81/1.32 % (1977)Instruction limit reached!
% 1.81/1.32 % (1977)------------------------------
% 1.81/1.32 % (1977)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.32 % (1977)Termination reason: Unknown
% 1.81/1.32 % (1977)Termination phase: shuffling
% 1.81/1.32
% 1.81/1.32 % (1977)Memory used [KB]: 1023
% 1.81/1.32 % (1977)Time elapsed: 0.003 s
% 1.81/1.32 % (1977)Instructions burned: 2 (million)
% 1.81/1.32 % (1977)------------------------------
% 1.81/1.32 % (1977)------------------------------
% 1.81/1.33 % (1980)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1625 for (2999ds/3Mi)
% 1.81/1.33 % (1980)Instruction limit reached!
% 1.81/1.33 % (1980)------------------------------
% 1.81/1.33 % (1980)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.33 % (1980)Termination reason: Unknown
% 1.81/1.33 % (1980)Termination phase: shuffling
% 1.81/1.33
% 1.81/1.33 % (1980)Memory used [KB]: 1023
% 1.81/1.33 % (1980)Time elapsed: 0.002 s
% 1.81/1.33 % (1980)Instructions burned: 4 (million)
% 1.81/1.33 % (1980)------------------------------
% 1.81/1.33 % (1980)------------------------------
% 1.81/1.33 % (1978)Refutation not found, incomplete strategy
% 1.81/1.33 % (1978)------------------------------
% 1.81/1.33 % (1978)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.33 % (1978)Termination reason: Refutation not found, incomplete strategy
% 1.81/1.33
% 1.81/1.33
% 1.81/1.33 % (1978)Memory used [KB]: 5500
% 1.81/1.33 % (1978)Time elapsed: 0.007 s
% 1.81/1.33 % (1978)Instructions burned: 7 (million)
% 1.81/1.33 % (1978)------------------------------
% 1.81/1.33 % (1978)------------------------------
% 1.81/1.33 % (1979)Instruction limit reached!
% 1.81/1.33 % (1979)------------------------------
% 1.81/1.33 % (1979)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.33 % (1979)Termination reason: Unknown
% 1.81/1.33 % (1979)Termination phase: Saturation
% 1.81/1.33
% 1.81/1.33 % (1979)Memory used [KB]: 5628
% 1.81/1.33 % (1979)Time elapsed: 0.012 s
% 1.81/1.33 % (1979)Instructions burned: 19 (million)
% 1.81/1.33 % (1979)------------------------------
% 1.81/1.33 % (1979)------------------------------
% 1.81/1.33 % (1975)Instruction limit reached!
% 1.81/1.33 % (1975)------------------------------
% 1.81/1.33 % (1975)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.33 % (1975)Termination reason: Unknown
% 1.81/1.33 % (1975)Termination phase: Saturation
% 1.81/1.33
% 1.81/1.33 % (1975)Memory used [KB]: 5756
% 1.81/1.33 % (1975)Time elapsed: 0.015 s
% 1.81/1.33 % (1975)Instructions burned: 27 (million)
% 1.81/1.33 % (1975)------------------------------
% 1.81/1.33 % (1975)------------------------------
% 1.81/1.33 % (1973)First to succeed.
% 1.81/1.34 % (1984)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_1625 for (2999ds/3Mi)
% 1.81/1.34 % (1984)Instruction limit reached!
% 1.81/1.34 % (1984)------------------------------
% 1.81/1.34 % (1984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.34 % (1984)Termination reason: Unknown
% 1.81/1.34 % (1984)Termination phase: shuffling
% 1.81/1.34
% 1.81/1.34 % (1984)Memory used [KB]: 1023
% 1.81/1.34 % (1984)Time elapsed: 0.002 s
% 1.81/1.34 % (1984)Instructions burned: 4 (million)
% 1.81/1.34 % (1984)------------------------------
% 1.81/1.34 % (1984)------------------------------
% 1.81/1.34 % (1973)Refutation found. Thanks to Tanya!
% 1.81/1.34 % SZS status Theorem for DTF2THF_1625
% 1.81/1.34 % SZS output start Proof for DTF2THF_1625
% 1.81/1.34 thf(type_def_5, type, mworld: $tType).
% 1.81/1.34 thf(func_def_0, type, mworld: $tType).
% 1.81/1.34 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.81/1.34 thf(func_def_2, type, mactual: mworld).
% 1.81/1.34 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.81/1.34 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.81/1.34 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.81/1.34 thf(func_def_16, type, qmltpeq: $i > $i > mworld > $o).
% 1.81/1.34 thf(func_def_17, type, in: $i > $i > mworld > $o).
% 1.81/1.34 thf(func_def_18, type, empty: $i > mworld > $o).
% 1.81/1.34 thf(func_def_19, type, singleton: $i > $i).
% 1.81/1.34 thf(func_def_20, type, set_difference: $i > $i > $i).
% 1.81/1.34 thf(func_def_34, type, sK0: mworld > $i).
% 1.81/1.34 thf(f461,plain,(
% 1.81/1.34 $false),
% 1.81/1.34 inference(avatar_sat_refutation,[status(thm)],[f395,f426,f432,f447,f457])).
% 1.81/1.34 thf(f457,plain,(
% 1.81/1.34 ~spl1_9 | ~spl1_12),
% 1.81/1.34 inference(avatar_contradiction_clause,[status(thm)],[f456])).
% 1.81/1.34 thf(f456,plain,(
% 1.81/1.34 $false | (~spl1_9 | ~spl1_12)),
% 1.81/1.34 inference(trivial_inequality_removal,[status(thm)],[f451])).
% 1.81/1.34 thf(f451,plain,(
% 1.81/1.34 ($true = $false) | (~spl1_9 | ~spl1_12)),
% 1.81/1.34 inference(superposition,[status(thm)],[f385,f424])).
% 1.81/1.34 thf(f424,plain,(
% 1.81/1.34 ($true = (in @ sK3 @ sK4 @ mactual)) | ~spl1_12),
% 1.81/1.34 inference(avatar_component_clause,[status(thm)],[f422])).
% 1.81/1.34 thf(f422,definition,(
% 1.81/1.34 spl1_12 <=> ($true = (in @ sK3 @ sK4 @ mactual))),
% 1.81/1.34 introduced(definition,[new_symbols(naming,[spl1_12])],[avatar_definition])).
% 1.81/1.34 thf(f385,plain,(
% 1.81/1.34 ((in @ sK3 @ sK4 @ mactual) = $false) | ~spl1_9),
% 1.81/1.34 inference(avatar_component_clause,[status(thm)],[f383])).
% 1.81/1.34 thf(f383,definition,(
% 1.81/1.34 spl1_9 <=> ((in @ sK3 @ sK4 @ mactual) = $false)),
% 1.81/1.34 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 1.81/1.34 thf(f447,plain,(
% 1.81/1.34 ~spl1_11),
% 1.81/1.34 inference(avatar_contradiction_clause,[status(thm)],[f446])).
% 1.81/1.34 thf(f446,plain,(
% 1.81/1.34 $false | ~spl1_11),
% 1.81/1.34 inference(trivial_inequality_removal,[status(thm)],[f443])).
% 1.81/1.34 thf(f443,plain,(
% 1.81/1.34 ($true = $false) | ~spl1_11),
% 1.81/1.34 inference(superposition,[status(thm)],[f198,f393])).
% 1.81/1.34 thf(f393,plain,(
% 1.81/1.34 ($false = (eiw_di @ sK3 @ mactual)) | ~spl1_11),
% 1.81/1.34 inference(avatar_component_clause,[status(thm)],[f391])).
% 1.81/1.34 thf(f391,definition,(
% 1.81/1.34 spl1_11 <=> ($false = (eiw_di @ sK3 @ mactual))),
% 1.81/1.34 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 1.81/1.34 thf(f198,plain,(
% 1.81/1.34 ($true = (eiw_di @ sK3 @ mactual))),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f196])).
% 1.81/1.34 thf(f196,plain,(
% 1.81/1.34 ($false = ((eiw_di @ sK3 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK3) @ Y0) @ (singleton @ sK3) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK3) @ Y0) @ empty_set @ mactual)))))))),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f195])).
% 1.81/1.34 thf(f195,plain,(
% 1.81/1.34 ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual))))))) @ sK3))),
% 1.81/1.34 inference(sigma_clausification,[status(thm)],[f194])).
% 1.81/1.34 thf(f194,plain,(
% 1.81/1.34 ($true != (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual)))))))))),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f132])).
% 1.81/1.34 thf(f132,plain,(
% 1.81/1.34 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) | (Y2 @ Y4))))))) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 1.81/1.34 inference(definition_unfolding,[status(thm)],[f115,f100,f106,f106,f99])).
% 1.81/1.34 thf(f99,plain,(
% 1.81/1.34 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.81/1.34 inference(cnf_transformation,[status(thm)],[f61])).
% 1.81/1.34 thf(f61,plain,(
% 1.81/1.34 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.81/1.34 inference(fool_elimination,[status(thm)],[f60])).
% 1.81/1.34 thf(f60,plain,(
% 1.81/1.34 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) | (X1 @ X2))) = mor)),
% 1.81/1.34 inference(rectify,[status(thm)],[f4])).
% 1.81/1.34 thf(f4,axiom,(
% 1.81/1.34 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X3 @ X2))) = mor)),
% 1.81/1.34 file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mor_def)).
% 1.81/1.34 thf(f106,plain,(
% 1.81/1.34 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.81/1.34 inference(cnf_transformation,[status(thm)],[f36])).
% 1.81/1.34 thf(f36,plain,(
% 1.81/1.34 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.81/1.34 inference(fool_elimination,[status(thm)],[f35])).
% 1.81/1.34 thf(f35,plain,(
% 1.81/1.34 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 1.81/1.34 inference(rectify,[status(thm)],[f11])).
% 1.81/1.34 thf(f11,axiom,(
% 1.81/1.34 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : ((eiw_di @ X5 @ X2) => (X1 @ X5 @ X2)))) = mforall_di)),
% 1.81/1.34 file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mforall_di_def)).
% 1.81/1.34 thf(f100,plain,(
% 1.81/1.34 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.81/1.34 inference(cnf_transformation,[status(thm)],[f45])).
% 1.81/1.34 thf(f45,plain,(
% 1.81/1.34 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.81/1.34 inference(fool_elimination,[status(thm)],[f1])).
% 1.81/1.34 thf(f1,axiom,(
% 1.81/1.34 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.81/1.34 file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mlocal_def)).
% 1.81/1.34 thf(f115,plain,(
% 1.81/1.34 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 1.81/1.34 inference(cnf_transformation,[status(thm)],[f86])).
% 1.81/1.34 thf(f86,plain,(
% 1.81/1.34 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 1.81/1.34 inference(flattening,[status(thm)],[f71])).
% 1.81/1.34 thf(f71,plain,(
% 1.81/1.34 ~($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 1.81/1.34 inference(fool_elimination,[status(thm)],[f70])).
% 1.81/1.34 thf(f70,plain,(
% 1.81/1.34 ~(mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mor @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ (singleton @ X0))))))))),
% 1.81/1.34 inference(rectify,[status(thm)],[f29])).
% 1.81/1.34 thf(f29,negated_conjecture,(
% 1.81/1.34 ~(mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mor @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ (singleton @ X1))))))))),
% 1.81/1.34 inference(negated_conjecture,[status(cth)],[f28])).
% 1.81/1.34 thf(f28,conjecture,(
% 1.81/1.34 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mor @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ (singleton @ X1))))))))),
% 1.81/1.34 file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',t69_zfmisc_1)).
% 1.81/1.34 thf(f432,plain,(
% 1.81/1.34 ~spl1_10),
% 1.81/1.34 inference(avatar_contradiction_clause,[status(thm)],[f431])).
% 1.81/1.34 thf(f431,plain,(
% 1.81/1.34 $false | ~spl1_10),
% 1.81/1.34 inference(trivial_inequality_removal,[status(thm)],[f427])).
% 1.81/1.34 thf(f427,plain,(
% 1.81/1.34 ($true = $false) | ~spl1_10),
% 1.81/1.34 inference(superposition,[status(thm)],[f389,f202])).
% 1.81/1.34 thf(f202,plain,(
% 1.81/1.34 ($true = (eiw_di @ sK4 @ mactual))),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f200])).
% 1.81/1.34 thf(f200,plain,(
% 1.81/1.34 (((eiw_di @ sK4 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK3) @ sK4) @ (singleton @ sK3) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK3) @ sK4) @ empty_set @ mactual))) = $false)),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f199])).
% 1.81/1.34 thf(f199,plain,(
% 1.81/1.34 (((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK3) @ Y0) @ (singleton @ sK3) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK3) @ Y0) @ empty_set @ mactual)))) @ sK4) = $false)),
% 1.81/1.34 inference(sigma_clausification,[status(thm)],[f197])).
% 1.81/1.34 thf(f197,plain,(
% 1.81/1.34 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK3) @ Y0) @ (singleton @ sK3) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK3) @ Y0) @ empty_set @ mactual))))) = $false)),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f196])).
% 1.81/1.34 thf(f389,plain,(
% 1.81/1.34 ((eiw_di @ sK4 @ mactual) = $false) | ~spl1_10),
% 1.81/1.34 inference(avatar_component_clause,[status(thm)],[f387])).
% 1.81/1.34 thf(f387,definition,(
% 1.81/1.34 spl1_10 <=> ((eiw_di @ sK4 @ mactual) = $false)),
% 1.81/1.34 introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition])).
% 1.81/1.34 thf(f426,plain,(
% 1.81/1.34 spl1_12 | spl1_10 | spl1_11),
% 1.81/1.34 inference(avatar_split_clause,[status(thm)],[f415,f391,f387,f422])).
% 1.81/1.34 thf(f415,plain,(
% 1.81/1.34 ($false = (eiw_di @ sK3 @ mactual)) | ((eiw_di @ sK4 @ mactual) = $false) | ($true = (in @ sK3 @ sK4 @ mactual))),
% 1.81/1.34 inference(trivial_inequality_removal,[status(thm)],[f409])).
% 1.81/1.34 thf(f409,plain,(
% 1.81/1.34 ($true = (in @ sK3 @ sK4 @ mactual)) | ($true = $false) | ((eiw_di @ sK4 @ mactual) = $false) | ($false = (eiw_di @ sK3 @ mactual))),
% 1.81/1.34 inference(superposition,[status(thm)],[f260,f204])).
% 1.81/1.34 thf(f204,plain,(
% 1.81/1.34 ((qmltpeq @ (set_difference @ (singleton @ sK3) @ sK4) @ (singleton @ sK3) @ mactual) = $false)),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f201])).
% 1.81/1.34 thf(f201,plain,(
% 1.81/1.34 (((qmltpeq @ (set_difference @ (singleton @ sK3) @ sK4) @ (singleton @ sK3) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK3) @ sK4) @ empty_set @ mactual)) = $false)),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f200])).
% 1.81/1.34 thf(f260,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)) | ($true = (in @ X1 @ X2 @ mactual)) | ((eiw_di @ X2 @ mactual) = $false) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.81/1.34 inference(not_proxy_clausification,[status(thm)],[f259])).
% 1.81/1.34 thf(f259,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ((eiw_di @ X2 @ mactual) = $false) | ($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)) | ((~ (in @ X1 @ X2 @ mactual)) = $false)) )),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f257])).
% 1.81/1.34 thf(f257,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (((~ (in @ X1 @ X2 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)) | ((eiw_di @ X2 @ mactual) = $false) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f256])).
% 1.81/1.34 thf(f256,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = ((qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual) = (~ (in @ X1 @ X2 @ mactual)))) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f255])).
% 1.81/1.34 thf(f255,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((eiw_di @ X2 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual) = (~ (in @ X1 @ X2 @ mactual))))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f254])).
% 1.81/1.34 thf(f254,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ (singleton @ X1) @ mactual) = (~ (in @ X1 @ Y0 @ mactual))))) @ X2)) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.81/1.34 inference(pi_clausification,[status(thm)],[f253])).
% 1.81/1.34 thf(f253,plain,(
% 1.81/1.34 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ (singleton @ X1) @ mactual) = (~ (in @ X1 @ Y0 @ mactual))))))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f252])).
% 1.81/1.34 thf(f252,plain,(
% 1.81/1.34 ( ! [X1 : $i] : (($true = ((eiw_di @ X1 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ (singleton @ X1) @ mactual) = (~ (in @ X1 @ Y0 @ mactual))))))))) )),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f251])).
% 1.81/1.34 thf(f251,plain,(
% 1.81/1.34 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual) = (~ (in @ Y0 @ Y1 @ mactual)))))))) @ X1))) )),
% 1.81/1.34 inference(pi_clausification,[status(thm)],[f250])).
% 1.81/1.34 thf(f250,plain,(
% 1.81/1.34 ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual) = (~ (in @ Y0 @ Y1 @ mactual))))))))))),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f120])).
% 1.81/1.34 thf(f120,plain,(
% 1.81/1.34 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (~ (Y2 @ Y3))))) @ (in @ Y0 @ Y1)))))))))),
% 1.81/1.34 inference(definition_unfolding,[status(thm)],[f94,f100,f106,f106,f112,f92])).
% 1.81/1.34 thf(f92,plain,(
% 1.81/1.34 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.81/1.34 inference(cnf_transformation,[status(thm)],[f53])).
% 1.81/1.34 thf(f53,plain,(
% 1.81/1.34 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.81/1.34 inference(fool_elimination,[status(thm)],[f52])).
% 1.81/1.34 thf(f52,plain,(
% 1.81/1.34 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 1.81/1.34 inference(rectify,[status(thm)],[f2])).
% 1.81/1.34 thf(f2,axiom,(
% 1.81/1.34 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 1.81/1.34 file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mnot_def)).
% 1.81/1.34 thf(f112,plain,(
% 1.81/1.34 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.81/1.34 inference(cnf_transformation,[status(thm)],[f75])).
% 1.81/1.34 thf(f75,plain,(
% 1.81/1.34 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) = (Y1 @ Y2))))))))),
% 1.81/1.34 inference(fool_elimination,[status(thm)],[f74])).
% 1.81/1.34 thf(f74,plain,(
% 1.81/1.34 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) <=> (X1 @ X2))))),
% 1.81/1.34 inference(rectify,[status(thm)],[f6])).
% 1.81/1.34 thf(f6,axiom,(
% 1.81/1.34 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X3 @ X2))))),
% 1.81/1.34 file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',mequiv_def)).
% 1.81/1.34 thf(f94,plain,(
% 1.81/1.34 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.81/1.34 inference(cnf_transformation,[status(thm)],[f40])).
% 1.81/1.34 thf(f40,plain,(
% 1.81/1.34 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.81/1.34 inference(fool_elimination,[status(thm)],[f39])).
% 1.81/1.34 thf(f39,plain,(
% 1.81/1.34 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ (singleton @ X0)) @ (mnot @ (in @ X0 @ X1))))))))),
% 1.81/1.34 inference(rectify,[status(thm)],[f24])).
% 1.81/1.34 thf(f24,axiom,(
% 1.81/1.34 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ (singleton @ X1)) @ (mnot @ (in @ X1 @ X3))))))))),
% 1.81/1.34 file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',l34_zfmisc_1)).
% 1.81/1.34 thf(f395,plain,(
% 1.81/1.34 spl1_11 | spl1_10 | spl1_9),
% 1.81/1.34 inference(avatar_split_clause,[status(thm)],[f367,f383,f387,f391])).
% 1.81/1.34 thf(f367,plain,(
% 1.81/1.34 ($false = (eiw_di @ sK3 @ mactual)) | ((eiw_di @ sK4 @ mactual) = $false) | ((in @ sK3 @ sK4 @ mactual) = $false)),
% 1.81/1.34 inference(trivial_inequality_removal,[status(thm)],[f360])).
% 1.81/1.34 thf(f360,plain,(
% 1.81/1.34 ((in @ sK3 @ sK4 @ mactual) = $false) | ((eiw_di @ sK4 @ mactual) = $false) | ($false = (eiw_di @ sK3 @ mactual)) | ($true = $false)),
% 1.81/1.34 inference(superposition,[status(thm)],[f203,f193])).
% 1.81/1.34 thf(f193,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual)) | ((eiw_di @ X2 @ mactual) = $false) | ($false = (eiw_di @ X1 @ mactual)) | ((in @ X1 @ X2 @ mactual) = $false)) )),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f191])).
% 1.81/1.34 thf(f191,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (((eiw_di @ X2 @ mactual) = $false) | ($false = (eiw_di @ X1 @ mactual)) | ((in @ X1 @ X2 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual))) )),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f190])).
% 1.81/1.34 thf(f190,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = ((qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual) = (in @ X1 @ X2 @ mactual))) | ((eiw_di @ X2 @ mactual) = $false)) )),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f189])).
% 1.81/1.34 thf(f189,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((eiw_di @ X2 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual) = (in @ X1 @ X2 @ mactual)))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f188])).
% 1.81/1.34 thf(f188,plain,(
% 1.81/1.34 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ empty_set @ mactual) = (in @ X1 @ Y0 @ mactual)))) @ X2)) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.81/1.34 inference(pi_clausification,[status(thm)],[f187])).
% 1.81/1.34 thf(f187,plain,(
% 1.81/1.34 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ empty_set @ mactual) = (in @ X1 @ Y0 @ mactual))))))) )),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f186])).
% 1.81/1.34 thf(f186,plain,(
% 1.81/1.34 ( ! [X1 : $i] : ((((eiw_di @ X1 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ empty_set @ mactual) = (in @ X1 @ Y0 @ mactual)))))) = $true)) )),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f185])).
% 1.81/1.34 thf(f185,plain,(
% 1.81/1.34 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual) = (in @ Y0 @ Y1 @ mactual))))))) @ X1) = $true)) )),
% 1.81/1.34 inference(pi_clausification,[status(thm)],[f184])).
% 1.81/1.34 thf(f184,plain,(
% 1.81/1.34 ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual) = (in @ Y0 @ Y1 @ mactual)))))))))),
% 1.81/1.34 inference(beta_eta_normalization,[status(thm)],[f124])).
% 1.81/1.34 thf(f124,plain,(
% 1.81/1.34 ($true = ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : $i > mworld > $o]: ((^[Y2 : mworld]: (!! @ $i @ (^[Y3 : $i]: ((eiw_di @ Y3 @ Y2) => (Y1 @ Y3 @ Y2))))))) @ (^[Y1 : $i]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld > $o]: ((^[Y4 : mworld]: ((Y2 @ Y4) = (Y3 @ Y4))))))) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 1.81/1.34 inference(definition_unfolding,[status(thm)],[f101,f100,f106,f106,f112])).
% 1.81/1.34 thf(f101,plain,(
% 1.81/1.34 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 1.81/1.34 inference(cnf_transformation,[status(thm)],[f65])).
% 1.81/1.34 thf(f65,plain,(
% 1.81/1.34 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 1.81/1.34 inference(fool_elimination,[status(thm)],[f64])).
% 1.81/1.34 thf(f64,plain,(
% 1.81/1.34 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ empty_set) @ (in @ X0 @ X1)))))))),
% 1.81/1.34 inference(rectify,[status(thm)],[f25])).
% 1.81/1.34 thf(f25,axiom,(
% 1.81/1.34 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ empty_set) @ (in @ X1 @ X3)))))))),
% 1.81/1.34 file('/export/starexec/sandbox/tmp/tmp.MFPRp1wHGh/DTF2THF_1625.p',l36_zfmisc_1)).
% 1.81/1.34 thf(f203,plain,(
% 1.81/1.34 ((qmltpeq @ (set_difference @ (singleton @ sK3) @ sK4) @ empty_set @ mactual) = $false)),
% 1.81/1.34 inference(binary_proxy_clausification,[status(thm)],[f201])).
% 1.81/1.34 % SZS output end Proof for DTF2THF_1625
% 1.81/1.34 % (1973)------------------------------
% 1.81/1.34 % (1973)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.81/1.34 % (1973)Termination reason: Refutation
% 1.81/1.34
% 1.81/1.34 % (1973)Memory used [KB]: 6012
% 1.81/1.34 % (1973)Time elapsed: 0.023 s
% 1.81/1.34 % (1973)Instructions burned: 61 (million)
% 1.81/1.34 % (1973)------------------------------
% 1.81/1.34 % (1973)------------------------------
% 1.81/1.34 % (1972)Success in time 0.029 s
%------------------------------------------------------------------------------