%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET926^8 : 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 : n028.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 09:32:22 AM UTC 2026
% Result : Theorem 0.29s 1.38s
% Output : Refutation 0.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 12
% Syntax : Number of formulae : 92 ( 49 unt; 0 typ; 4 def)
% Number of atoms : 617 ( 128 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 974 ( 38 ~; 65 |; 0 &; 805 @)
% ( 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(f468,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f380,f387,f448,f454,f463]) ).
thf(f463,plain,
( ~ spl1_9
| ~ spl1_11 ),
inference(avatar_contradiction_clause,[status(thm)],[f462]) ).
thf(f462,plain,
( $false
| ~ spl1_9
| ~ spl1_11 ),
inference(trivial_inequality_removal,[status(thm)],[f456]) ).
thf(f456,plain,
( ( $true = $false )
| ~ spl1_9
| ~ spl1_11 ),
inference(superposition,[status(thm)],[f445,f374]) ).
thf(f374,plain,
( ( $false
= ( in @ sK2 @ sK3 @ mactual ) )
| ~ spl1_9 ),
inference(avatar_component_clause,[status(thm)],[f372]) ).
thf(f372,definition,
( spl1_9
<=> ( $false
= ( in @ sK2 @ sK3 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition]) ).
thf(f445,plain,
( ( $true
= ( in @ sK2 @ sK3 @ mactual ) )
| ~ spl1_11 ),
inference(avatar_component_clause,[status(thm)],[f443]) ).
thf(f443,definition,
( spl1_11
<=> ( $true
= ( in @ sK2 @ sK3 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition]) ).
thf(f454,plain,
~ spl1_10,
inference(avatar_contradiction_clause,[status(thm)],[f453]) ).
thf(f453,plain,
( $false
| ~ spl1_10 ),
inference(trivial_inequality_removal,[status(thm)],[f449]) ).
thf(f449,plain,
( ( $true = $false )
| ~ spl1_10 ),
inference(superposition,[status(thm)],[f378,f137]) ).
thf(f137,plain,
( $true
= ( eiw_di @ sK2 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f135,plain,
( ( ( eiw_di @ sK2 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ mactual ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,plain,
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual ) ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f133]) ).
thf(f133,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 )
| ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ 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 ) @ empty_set )
@ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f97,f107,f112,f112,f110]) ).
thf(f110,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f32]) ).
thf(f32,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
| ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f31]) ).
thf(f31,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X0 @ X2 ) ) )
= mor ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
| ( X1 @ X2 ) ) )
= mor ),
file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',mor_def) ).
thf(f112,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f48]) ).
thf(f48,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f47]) ).
thf(f47,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.5W2kHOLHbu/DTF2THF_14138.p',mforall_di_def) ).
thf(f107,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f63]) ).
thf(f63,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( mlocal
= ( ^ [X0: mworld > $o] : ( X0 @ mactual ) ) ),
file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',mlocal_def) ).
thf(f97,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.5W2kHOLHbu/DTF2THF_14138.p',t69_zfmisc_1) ).
thf(f378,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ~ spl1_10 ),
inference(avatar_component_clause,[status(thm)],[f376]) ).
thf(f376,definition,
( spl1_10
<=> ( ( eiw_di @ sK2 @ mactual )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition]) ).
thf(f448,plain,
( spl1_10
| spl1_11
| spl1_8 ),
inference(avatar_split_clause,[status(thm)],[f447,f368,f443,f376]) ).
thf(f368,definition,
( spl1_8
<=> ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f447,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( $true
= ( in @ sK2 @ sK3 @ mactual ) )
| spl1_8 ),
inference(subsumption_resolution,[status(thm)],[f431,f369]) ).
thf(f369,plain,
( ( $false
!= ( eiw_di @ sK3 @ mactual ) )
| spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f368]) ).
thf(f431,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( $true
= ( in @ sK2 @ sK3 @ mactual ) )
| ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f423]) ).
thf(f423,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( $true
= ( in @ sK2 @ sK3 @ mactual ) )
| ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f172,f142]) ).
thf(f142,plain,
( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ mactual )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
thf(f140,plain,
( ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ mactual ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f139,plain,
( ( ( eiw_di @ sK3 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ ( singleton @ sK2 ) @ mactual ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ mactual ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f136]) ).
thf(f136,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ empty_set @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ Y0 ) @ ( singleton @ sK2 ) @ mactual ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f135]) ).
thf(f172,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( in @ X1 @ X2 @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f169]) ).
thf(f169,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( ~ ( in @ X1 @ X2 @ mactual ) ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f168]) ).
thf(f168,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f167]) ).
thf(f167,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( ~ ( in @ X1 @ X2 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f166]) ).
thf(f166,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( ~ ( in @ X1 @ X2 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f165]) ).
thf(f165,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ~ ( in @ X1 @ Y0 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual ) ) )
@ X2 ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(pi_clausification,[status(thm)],[f164]) ).
thf(f164,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ~ ( in @ X1 @ Y0 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f163]) ).
thf(f163,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( ~ ( in @ X1 @ Y0 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ ( singleton @ X1 ) @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f162]) ).
thf(f162,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ~ ( in @ Y0 @ Y1 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f161]) ).
thf(f161,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( ~ ( in @ Y0 @ Y1 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) @ mactual ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f131]) ).
thf(f131,plain,
( ( ^ [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 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f115,f107,f112,f112,f93,f109]) ).
thf(f109,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f60]) ).
thf(f60,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f59]) ).
thf(f59,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.5W2kHOLHbu/DTF2THF_14138.p',mnot_def) ).
thf(f93,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f58]) ).
thf(f58,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f57]) ).
thf(f57,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) )
= mequiv ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
<=> ( X1 @ X2 ) ) )
= mequiv ),
file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',mequiv_def) ).
thf(f115,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f67]) ).
thf(f67,plain,
( ( mlocal
@ ( mforall_di
@ ^ [Y0: $i] :
( mforall_di
@ ^ [Y1: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ ( singleton @ Y0 ) ) @ ( mnot @ ( in @ Y0 @ Y1 ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f66]) ).
thf(f66,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.5W2kHOLHbu/DTF2THF_14138.p',l34_zfmisc_1) ).
thf(f387,plain,
~ spl1_8,
inference(avatar_contradiction_clause,[status(thm)],[f386]) ).
thf(f386,plain,
( $false
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f383]) ).
thf(f383,plain,
( ( $true = $false )
| ~ spl1_8 ),
inference(superposition,[status(thm)],[f141,f370]) ).
thf(f370,plain,
( ( $false
= ( eiw_di @ sK3 @ mactual ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f368]) ).
thf(f141,plain,
( $true
= ( eiw_di @ sK3 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f139]) ).
thf(f380,plain,
( spl1_10
| spl1_8
| spl1_9 ),
inference(avatar_split_clause,[status(thm)],[f356,f372,f368,f376]) ).
thf(f356,plain,
( ( $false
= ( in @ sK2 @ sK3 @ mactual ) )
| ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f350]) ).
thf(f350,plain,
( ( ( eiw_di @ sK2 @ mactual )
= $false )
| ( $true = $false )
| ( $false
= ( in @ sK2 @ sK3 @ mactual ) )
| ( $false
= ( eiw_di @ sK3 @ mactual ) ) ),
inference(superposition,[status(thm)],[f143,f181]) ).
thf(f181,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) )
| ( $false
= ( in @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,plain,
! [X2: $i,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f179]) ).
thf(f179,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( in @ X1 @ X2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f178]) ).
thf(f178,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( in @ X1 @ X2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f177]) ).
thf(f177,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( in @ X1 @ Y0 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual ) ) )
@ X2 ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(pi_clausification,[status(thm)],[f176]) ).
thf(f176,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( in @ X1 @ Y0 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f175]) ).
thf(f175,plain,
! [X1: $i] :
( $true
= ( ( eiw_di @ X1 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( in @ X1 @ Y0 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f174]) ).
thf(f174,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( in @ Y0 @ Y1 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f173]) ).
thf(f173,plain,
( ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ mactual )
=> ( ( in @ Y0 @ Y1 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ Y0 ) @ Y1 ) @ empty_set @ mactual ) ) ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f126]) ).
thf(f126,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 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f106,f107,f112,f112,f93]) ).
thf(f106,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)],[f52]) ).
thf(f52,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)],[f51]) ).
thf(f51,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.5W2kHOLHbu/DTF2THF_14138.p',l36_zfmisc_1) ).
thf(f143,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK2 ) @ sK3 ) @ empty_set @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET926^8 : 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 : n028.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 12:06:12 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
% 0.29/0.45 ---- Original DTF file ---
% 0.29/0.45 thf(spec,logic,$$dhol).
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 % File : SET926^8 : TPTP v9.2.1. Released v8.1.0.
% 0.29/0.45 % Domain : Set Theory
% 0.29/0.45 % Problem : TPTP problem SET926+1.p with axiomatized equality
% 0.29/0.45 % Version : [BP13] axioms.
% 0.29/0.45 % English :
% 0.29/0.45
% 0.29/0.45 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.29/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.29/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.29/0.45 % Source : [TPTP]
% 0.29/0.45 % Names : SET926+1 [QMLTP]
% 0.29/0.45
% 0.29/0.45 % Status : Theorem
% 0.29/0.45 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.29/0.45 % Syntax : Number of formulae : 48 ( 12 unt; 20 typ; 10 def)
% 0.29/0.45 % Number of atoms : 125 ( 10 equ; 0 cnn)
% 0.29/0.45 % Maximal formula atoms : 9 ( 4 avg)
% 0.29/0.45 % Number of connectives : 203 ( 1 ~; 1 |; 3 &; 194 @)
% 0.29/0.45 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.29/0.45 % Maximal formula depth : 14 ( 7 avg)
% 0.29/0.45 % Number of types : 3 ( 1 usr)
% 0.29/0.45 % Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% 0.29/0.45 % Number of symbols : 20 ( 19 usr; 2 con; 0-3 aty)
% 0.29/0.45 % Number of variables : 62 ( 55 ^; 4 !; 3 ?; 62 :)
% 0.29/0.45 % SPC : TH0_THM_EQU_NAR
% 0.29/0.45
% 0.29/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.29/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.29/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.29/0.45 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.29/0.45 % $modalities == $modal_system_T].
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 thf(mworld,type,
% 0.29/0.45 mworld: $tType ).
% 0.29/0.45
% 0.29/0.45 thf(mrel_type,type,
% 0.29/0.45 mrel: mworld > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mactual_type,type,
% 0.29/0.45 mactual: mworld ).
% 0.29/0.45
% 0.29/0.45 thf(mlocal_type,type,
% 0.29/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mlocal_def,definition,
% 0.29/0.45 ( mlocal
% 0.29/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mnot_type,type,
% 0.29/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mand_type,type,
% 0.29/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mor_type,type,
% 0.29/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mimplies_type,type,
% 0.29/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mequiv_type,type,
% 0.29/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mnot_def,definition,
% 0.29/0.45 ( mnot
% 0.29/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.29/0.45 ~ ( A @ W ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mand_def,definition,
% 0.29/0.45 ( mand
% 0.29/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.45 ( ( A @ W )
% 0.29/0.45 & ( B @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mor_def,definition,
% 0.29/0.45 ( mor
% 0.29/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.45 ( ( A @ W )
% 0.29/0.45 | ( B @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mimplies_def,definition,
% 0.29/0.45 ( mimplies
% 0.29/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.45 ( ( A @ W )
% 0.29/0.45 => ( B @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mequiv_def,definition,
% 0.29/0.45 ( mequiv
% 0.29/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.45 ( ( A @ W )
% 0.29/0.45 <=> ( B @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mbox_type,type,
% 0.29/0.45 mbox: ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mbox_def,definition,
% 0.29/0.45 ( mbox
% 0.29/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.45 ! [V: mworld] :
% 0.29/0.45 ( ( mrel @ W @ V )
% 0.29/0.45 => ( Phi @ V ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mdia_type,type,
% 0.29/0.45 mdia: ( mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mdia_def,definition,
% 0.29/0.45 ( mdia
% 0.29/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.45 ? [V: mworld] :
% 0.29/0.45 ( ( mrel @ W @ V )
% 0.29/0.45 & ( Phi @ V ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mrel_reflexive,axiom,
% 0.29/0.45 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.29/0.45
% 0.29/0.45 thf(eiw_di_type,type,
% 0.29/0.45 eiw_di: $i > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(eiw_di_nonempty,axiom,
% 0.29/0.45 ! [W: mworld] :
% 0.29/0.45 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.29/0.45
% 0.29/0.45 thf(mforall_di_type,type,
% 0.29/0.45 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mforall_di_def,definition,
% 0.29/0.45 ( mforall_di
% 0.29/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.29/0.45 ! [X: $i] :
% 0.29/0.45 ( ( eiw_di @ X @ W )
% 0.29/0.45 => ( A @ X @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(mexists_di_type,type,
% 0.29/0.45 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(mexists_di_def,definition,
% 0.29/0.45 ( mexists_di
% 0.29/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.29/0.45 ? [X: $i] :
% 0.29/0.45 ( ( eiw_di @ X @ W )
% 0.29/0.45 & ( A @ X @ W ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(empty_set_decl,type,
% 0.29/0.45 empty_set: $i ).
% 0.29/0.45
% 0.29/0.45 thf(qmltpeq_decl,type,
% 0.29/0.45 qmltpeq: $i > $i > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(in_decl,type,
% 0.29/0.45 in: $i > $i > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(empty_decl,type,
% 0.29/0.45 empty: $i > mworld > $o ).
% 0.29/0.45
% 0.29/0.45 thf(singleton_decl,type,
% 0.29/0.45 singleton: $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(set_difference_decl,type,
% 0.29/0.45 set_difference: $i > $i > $i ).
% 0.29/0.45
% 0.29/0.45 thf(reflexivity,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(symmetry,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [X: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(transitivity,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [X: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [Y: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(set_difference_substitution_1,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(set_difference_substitution_2,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(singleton_substitution_1,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(empty_substitution_1,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(in_substitution_1,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(in_substitution_2,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(antisymmetry_r2_hidden,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(fc1_xboole_0,axiom,
% 0.29/0.45 mlocal @ ( empty @ empty_set ) ).
% 0.29/0.45
% 0.29/0.45 thf(l34_zfmisc_1,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(l36_zfmisc_1,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(rc1_xboole_0,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mexists_di
% 0.29/0.45 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(rc2_xboole_0,axiom,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mexists_di
% 0.29/0.45 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 thf(t69_zfmisc_1,conjecture,
% 0.29/0.45 ( mlocal
% 0.29/0.45 @ ( mforall_di
% 0.29/0.45 @ ^ [A: $i] :
% 0.29/0.45 ( mforall_di
% 0.29/0.45 @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ).
% 0.29/0.45
% 0.29/0.45 %------------------------------------------------------------------------------
% 0.29/0.45 ------------------------
% 0.29/1.30 ---- Embedded in THF ---
% 0.29/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.29/1.30 %%% Generated on Tue Feb 24 12:06:12 EST 2026
% 0.29/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.29/1.30 %%% Logic specification used:
% 0.29/1.30 %%% thf(spec, logic, $$dhol).
% 0.29/1.30
% 0.29/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2DTF14138.p
% See solution above
% 0.29/1.30 ------------------------
% 0.29/1.32 ---- Cleaned THF ---
% 0.29/1.32 thf(mworld,type,
% 0.29/1.32 mworld: $tType ).
% 0.29/1.32
% 0.29/1.32 thf(mrel_type,type,
% 0.29/1.32 mrel: mworld > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mactual_type,type,
% 0.29/1.32 mactual: mworld ).
% 0.29/1.32
% 0.29/1.32 thf(mlocal_type,type,
% 0.29/1.32 mlocal: ( mworld > $o ) > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mlocal_def,definition,
% 0.29/1.32 ( mlocal
% 0.29/1.32 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mnot_type,type,
% 0.29/1.32 mnot: ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mand_type,type,
% 0.29/1.32 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mor_type,type,
% 0.29/1.32 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mimplies_type,type,
% 0.29/1.32 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mequiv_type,type,
% 0.29/1.32 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mnot_def,definition,
% 0.29/1.32 ( mnot
% 0.29/1.32 = ( ^ [A: mworld > $o,W: mworld] :
% 0.29/1.32 ~ ( A @ W ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mand_def,definition,
% 0.29/1.32 ( mand
% 0.29/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/1.32 ( ( A @ W )
% 0.29/1.32 & ( B @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mor_def,definition,
% 0.29/1.32 ( mor
% 0.29/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/1.32 ( ( A @ W )
% 0.29/1.32 | ( B @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mimplies_def,definition,
% 0.29/1.32 ( mimplies
% 0.29/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/1.32 ( ( A @ W )
% 0.29/1.32 => ( B @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mequiv_def,definition,
% 0.29/1.32 ( mequiv
% 0.29/1.32 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/1.32 ( ( A @ W )
% 0.29/1.32 <=> ( B @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mbox_type,type,
% 0.29/1.32 mbox: ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mbox_def,definition,
% 0.29/1.32 ( mbox
% 0.29/1.32 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/1.32 ! [V: mworld] :
% 0.29/1.32 ( ( mrel @ W @ V )
% 0.29/1.32 => ( Phi @ V ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mdia_type,type,
% 0.29/1.32 mdia: ( mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mdia_def,definition,
% 0.29/1.32 ( mdia
% 0.29/1.32 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/1.32 ? [V: mworld] :
% 0.29/1.32 ( ( mrel @ W @ V )
% 0.29/1.32 & ( Phi @ V ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mrel_reflexive,axiom,
% 0.29/1.32 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.29/1.32
% 0.29/1.32 thf(eiw_di_type,type,
% 0.29/1.32 eiw_di: $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(eiw_di_nonempty,axiom,
% 0.29/1.32 ! [W: mworld] :
% 0.29/1.32 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.29/1.32
% 0.29/1.32 thf(mforall_di_type,type,
% 0.29/1.32 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mforall_di_def,definition,
% 0.29/1.32 ( mforall_di
% 0.29/1.32 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.29/1.32 ! [X: $i] :
% 0.29/1.32 ( ( eiw_di @ X @ W )
% 0.29/1.32 => ( A @ X @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(mexists_di_type,type,
% 0.29/1.32 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(mexists_di_def,definition,
% 0.29/1.32 ( mexists_di
% 0.29/1.32 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.29/1.32 ? [X: $i] :
% 0.29/1.32 ( ( eiw_di @ X @ W )
% 0.29/1.32 & ( A @ X @ W ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(empty_set_decl,type,
% 0.29/1.32 empty_set: $i ).
% 0.29/1.32
% 0.29/1.32 thf(qmltpeq_decl,type,
% 0.29/1.32 qmltpeq: $i > $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(in_decl,type,
% 0.29/1.32 in: $i > $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(empty_decl,type,
% 0.29/1.32 empty: $i > mworld > $o ).
% 0.29/1.32
% 0.29/1.32 thf(singleton_decl,type,
% 0.29/1.32 singleton: $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(set_difference_decl,type,
% 0.29/1.32 set_difference: $i > $i > $i ).
% 0.29/1.32
% 0.29/1.32 thf(reflexivity,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(symmetry,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(transitivity,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [X: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [Y: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(set_difference_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(set_difference_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(singleton_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(empty_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(in_substitution_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(in_substitution_2,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(antisymmetry_r2_hidden,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(fc1_xboole_0,axiom,
% 0.29/1.32 mlocal @ ( empty @ empty_set ) ).
% 0.29/1.32
% 0.29/1.32 thf(l34_zfmisc_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(l36_zfmisc_1,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(rc1_xboole_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mexists_di
% 0.29/1.32 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(rc2_xboole_0,axiom,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mexists_di
% 0.29/1.32 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 0.29/1.32
% 0.29/1.32 thf(t69_zfmisc_1,conjecture,
% 0.29/1.32 ( mlocal
% 0.29/1.32 @ ( mforall_di
% 0.29/1.32 @ ^ [A: $i] :
% 0.29/1.32 ( mforall_di
% 0.29/1.32 @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ).
% 0.29/1.32 ------------------------
% 0.29/1.33 % (14249)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_14138 for (2999ds/27Mi)
% 0.29/1.33 % (14248)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_14138 for (2999ds/4Mi)
% 0.29/1.33 % (14248)Instruction limit reached!
% 0.29/1.33 % (14248)------------------------------
% 0.29/1.33 % (14248)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.33 % (14248)Termination reason: Unknown
% 0.29/1.33 % (14248)Termination phase: shuffling
% 0.29/1.33
% 0.29/1.33 % (14248)Memory used [KB]: 1023
% 0.29/1.33 % (14248)Time elapsed: 0.002 s
% 0.29/1.33 % (14248)Instructions burned: 4 (million)
% 0.29/1.33 % (14248)------------------------------
% 0.29/1.33 % (14248)------------------------------
% 0.29/1.34 % (14249)Instruction limit reached!
% 0.29/1.34 % (14249)------------------------------
% 0.29/1.34 % (14249)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (14249)Termination reason: Unknown
% 0.29/1.34 % (14249)Termination phase: Saturation
% 0.29/1.34
% 0.29/1.34 % (14249)Memory used [KB]: 5756
% 0.29/1.34 % (14249)Time elapsed: 0.009 s
% 0.29/1.34 % (14249)Instructions burned: 27 (million)
% 0.29/1.34 % (14249)------------------------------
% 0.29/1.34 % (14249)------------------------------
% 0.29/1.34 % (14247)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_14138 for (2999ds/183Mi)
% 0.29/1.34 % (14250)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_14138 for (2999ds/2Mi)
% 0.29/1.34 % (14251)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_14138 for (2999ds/2Mi)
% 0.29/1.34 % (14252)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_14138 for (2999ds/275Mi)
% 0.29/1.34 % (14253)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_14138 for (2999ds/18Mi)
% 0.29/1.34 % (14250)Instruction limit reached!
% 0.29/1.34 % (14250)------------------------------
% 0.29/1.34 % (14250)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (14250)Termination reason: Unknown
% 0.29/1.34 % (14250)Termination phase: shuffling
% 0.29/1.34
% 0.29/1.34 % (14250)Memory used [KB]: 1023
% 0.29/1.34 % (14250)Time elapsed: 0.003 s
% 0.29/1.34 % (14250)Instructions burned: 2 (million)
% 0.29/1.34 % (14250)------------------------------
% 0.29/1.34 % (14250)------------------------------
% 0.29/1.34 % (14251)Instruction limit reached!
% 0.29/1.34 % (14251)------------------------------
% 0.29/1.34 % (14251)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (14251)Termination reason: Unknown
% 0.29/1.34 % (14251)Termination phase: shuffling
% 0.29/1.34
% 0.29/1.34 % (14251)Memory used [KB]: 1023
% 0.29/1.34 % (14251)Time elapsed: 0.003 s
% 0.29/1.34 % (14251)Instructions burned: 2 (million)
% 0.29/1.34 % (14251)------------------------------
% 0.29/1.34 % (14251)------------------------------
% 0.29/1.34 % (14254)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_14138 for (2999ds/3Mi)
% 0.29/1.34 % (14252)Refutation not found, incomplete strategy
% 0.29/1.34 % (14252)------------------------------
% 0.29/1.34 % (14252)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (14252)Termination reason: Refutation not found, incomplete strategy
% 0.29/1.34
% 0.29/1.34
% 0.29/1.34 % (14252)Memory used [KB]: 5500
% 0.29/1.34 % (14252)Time elapsed: 0.006 s
% 0.29/1.34 % (14252)Instructions burned: 7 (million)
% 0.29/1.34 % (14252)------------------------------
% 0.29/1.34 % (14252)------------------------------
% 0.29/1.34 % (14254)Instruction limit reached!
% 0.29/1.34 % (14254)------------------------------
% 0.29/1.34 % (14254)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.34 % (14254)Termination reason: Unknown
% 0.29/1.34 % (14254)Termination phase: Property scanning
% 0.29/1.34
% 0.29/1.34 % (14254)Memory used [KB]: 1023
% 0.29/1.34 % (14254)Time elapsed: 0.003 s
% 0.29/1.34 % (14254)Instructions burned: 4 (million)
% 0.29/1.34 % (14254)------------------------------
% 0.29/1.34 % (14254)------------------------------
% 0.29/1.35 % (14255)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_14138 for (2999ds/37Mi)
% 0.29/1.35 % (14253)Instruction limit reached!
% 0.29/1.35 % (14253)------------------------------
% 0.29/1.35 % (14253)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.35 % (14253)Termination reason: Unknown
% 0.29/1.35 % (14253)Termination phase: Saturation
% 0.29/1.35
% 0.29/1.35 % (14253)Memory used [KB]: 5628
% 0.29/1.35 % (14253)Time elapsed: 0.012 s
% 0.29/1.35 % (14253)Instructions burned: 19 (million)
% 0.29/1.35 % (14253)------------------------------
% 0.29/1.35 % (14253)------------------------------
% 0.29/1.35 % (14258)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_14138 for (2999ds/1041Mi)
% 0.29/1.36 % (14256)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_14138 for (2999ds/15Mi)
% 0.29/1.36 % (14257)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_14138 for (2999ds/3Mi)
% 0.29/1.36 % (14255)Instruction limit reached!
% 0.29/1.36 % (14255)------------------------------
% 0.29/1.36 % (14255)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.36 % (14255)Termination reason: Unknown
% 0.29/1.36 % (14255)Termination phase: Saturation
% 0.29/1.36
% 0.29/1.36 % (14255)Memory used [KB]: 5884
% 0.29/1.36 % (14255)Time elapsed: 0.012 s
% 0.29/1.36 % (14255)Instructions burned: 39 (million)
% 0.29/1.36 % (14255)------------------------------
% 0.29/1.36 % (14255)------------------------------
% 0.29/1.36 % (14257)Instruction limit reached!
% 0.29/1.36 % (14257)------------------------------
% 0.29/1.36 % (14257)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.36 % (14257)Termination reason: Unknown
% 0.29/1.36 % (14257)Termination phase: shuffling
% 0.29/1.36
% 0.29/1.36 % (14257)Memory used [KB]: 1023
% 0.29/1.36 % (14257)Time elapsed: 0.004 s
% 0.29/1.36 % (14257)Instructions burned: 4 (million)
% 0.29/1.36 % (14257)------------------------------
% 0.29/1.36 % (14257)------------------------------
% 0.29/1.36 % (14259)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_14138 for (2999ds/7Mi)
% 0.29/1.37 % (14256)Instruction limit reached!
% 0.29/1.37 % (14256)------------------------------
% 0.29/1.37 % (14256)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.37 % (14256)Termination reason: Unknown
% 0.29/1.37 % (14256)Termination phase: Saturation
% 0.29/1.37
% 0.29/1.37 % (14256)Memory used [KB]: 1151
% 0.29/1.37 % (14256)Time elapsed: 0.010 s
% 0.29/1.37 % (14256)Instructions burned: 16 (million)
% 0.29/1.37 % (14256)------------------------------
% 0.29/1.37 % (14256)------------------------------
% 0.29/1.37 % (14259)Instruction limit reached!
% 0.29/1.37 % (14259)------------------------------
% 0.29/1.37 % (14259)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.37 % (14259)Termination reason: Unknown
% 0.29/1.37 % (14259)Termination phase: Function definition elimination
% 0.29/1.37
% 0.29/1.37 % (14259)Memory used [KB]: 1023
% 0.29/1.37 % (14259)Time elapsed: 0.006 s
% 0.29/1.37 % (14259)Instructions burned: 8 (million)
% 0.29/1.37 % (14259)------------------------------
% 0.29/1.37 % (14259)------------------------------
% 0.29/1.37 % (14260)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_14138 for (2999ds/16Mi)
% 0.29/1.38 % (14260)Instruction limit reached!
% 0.29/1.38 % (14260)------------------------------
% 0.29/1.38 % (14260)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.38 % (14260)Termination reason: Unknown
% 0.29/1.38 % (14260)Termination phase: Saturation
% 0.29/1.38
% 0.29/1.38 % (14260)Memory used [KB]: 5628
% 0.29/1.38 % (14260)Time elapsed: 0.010 s
% 0.29/1.38 % (14260)Instructions burned: 16 (million)
% 0.29/1.38 % (14260)------------------------------
% 0.29/1.38 % (14260)------------------------------
% 0.29/1.38 % (14247)First to succeed.
% 0.29/1.38 % (14261)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_14138 for (2999ds/3Mi)
% 0.29/1.38 % (14262)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_14138 for (2999ds/3Mi)
% 0.29/1.38 % (14261)Instruction limit reached!
% 0.29/1.38 % (14261)------------------------------
% 0.29/1.38 % (14261)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.38 % (14261)Termination reason: Unknown
% 0.29/1.38 % (14261)Termination phase: shuffling
% 0.29/1.38
% 0.29/1.38 % (14261)Memory used [KB]: 1023
% 0.29/1.38 % (14261)Time elapsed: 0.004 s
% 0.29/1.38 % (14261)Instructions burned: 4 (million)
% 0.29/1.38 % (14261)------------------------------
% 0.29/1.38 % (14261)------------------------------
% 0.29/1.38 % (14247)Refutation found. Thanks to Tanya!
% 0.29/1.38 % SZS status Theorem for DTF2THF_14138
% 0.29/1.38 % SZS output start Proof for DTF2THF_14138
% 0.29/1.38 thf(type_def_5, type, mworld: $tType).
% 0.29/1.38 thf(func_def_0, type, mworld: $tType).
% 0.29/1.38 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.29/1.38 thf(func_def_2, type, mactual: mworld).
% 0.29/1.38 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.29/1.38 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 0.29/1.38 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.29/1.38 thf(func_def_16, type, qmltpeq: $i > $i > mworld > $o).
% 0.29/1.38 thf(func_def_17, type, in: $i > $i > mworld > $o).
% 0.29/1.38 thf(func_def_18, type, empty: $i > mworld > $o).
% 0.29/1.38 thf(func_def_19, type, singleton: $i > $i).
% 0.29/1.38 thf(func_def_20, type, set_difference: $i > $i > $i).
% 0.29/1.38 thf(func_def_34, type, sK0: mworld > $i).
% 0.29/1.38 thf(f468,plain,(
% 0.29/1.38 $false),
% 0.29/1.38 inference(avatar_sat_refutation,[status(thm)],[f380,f387,f448,f454,f463])).
% 0.29/1.38 thf(f463,plain,(
% 0.29/1.38 ~spl1_9 | ~spl1_11),
% 0.29/1.38 inference(avatar_contradiction_clause,[status(thm)],[f462])).
% 0.29/1.38 thf(f462,plain,(
% 0.29/1.38 $false | (~spl1_9 | ~spl1_11)),
% 0.29/1.38 inference(trivial_inequality_removal,[status(thm)],[f456])).
% 0.29/1.38 thf(f456,plain,(
% 0.29/1.38 ($true = $false) | (~spl1_9 | ~spl1_11)),
% 0.29/1.38 inference(superposition,[status(thm)],[f445,f374])).
% 0.29/1.38 thf(f374,plain,(
% 0.29/1.38 ($false = (in @ sK2 @ sK3 @ mactual)) | ~spl1_9),
% 0.29/1.38 inference(avatar_component_clause,[status(thm)],[f372])).
% 0.29/1.38 thf(f372,definition,(
% 0.29/1.38 spl1_9 <=> ($false = (in @ sK2 @ sK3 @ mactual))),
% 0.29/1.38 introduced(definition,[new_symbols(naming,[spl1_9])],[avatar_definition])).
% 0.29/1.38 thf(f445,plain,(
% 0.29/1.38 ($true = (in @ sK2 @ sK3 @ mactual)) | ~spl1_11),
% 0.29/1.38 inference(avatar_component_clause,[status(thm)],[f443])).
% 0.29/1.38 thf(f443,definition,(
% 0.29/1.38 spl1_11 <=> ($true = (in @ sK2 @ sK3 @ mactual))),
% 0.29/1.38 introduced(definition,[new_symbols(naming,[spl1_11])],[avatar_definition])).
% 0.29/1.38 thf(f454,plain,(
% 0.29/1.38 ~spl1_10),
% 0.29/1.38 inference(avatar_contradiction_clause,[status(thm)],[f453])).
% 0.29/1.38 thf(f453,plain,(
% 0.29/1.38 $false | ~spl1_10),
% 0.29/1.38 inference(trivial_inequality_removal,[status(thm)],[f449])).
% 0.29/1.38 thf(f449,plain,(
% 0.29/1.38 ($true = $false) | ~spl1_10),
% 0.29/1.38 inference(superposition,[status(thm)],[f378,f137])).
% 0.29/1.38 thf(f137,plain,(
% 0.29/1.38 ($true = (eiw_di @ sK2 @ mactual))),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 0.29/1.38 thf(f135,plain,(
% 0.29/1.38 (((eiw_di @ sK2 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK2) @ Y0) @ empty_set @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK2) @ Y0) @ (singleton @ sK2) @ mactual)))))) = $false)),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f134])).
% 0.29/1.38 thf(f134,plain,(
% 0.29/1.38 ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual))))))) @ sK2))),
% 0.29/1.38 inference(sigma_clausification,[status(thm)],[f133])).
% 0.29/1.38 thf(f133,plain,(
% 0.29/1.38 ($true != (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual)))))))))),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f120])).
% 0.29/1.38 thf(f120,plain,(
% 0.29/1.38 ($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) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 0.29/1.38 inference(definition_unfolding,[status(thm)],[f97,f107,f112,f112,f110])).
% 0.29/1.38 thf(f110,plain,(
% 0.29/1.38 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.29/1.38 inference(cnf_transformation,[status(thm)],[f32])).
% 0.29/1.38 thf(f32,plain,(
% 0.29/1.38 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) | (Y1 @ Y2))))))))),
% 0.29/1.38 inference(fool_elimination,[status(thm)],[f31])).
% 0.29/1.38 thf(f31,plain,(
% 0.29/1.38 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X0 @ X2))) = mor)),
% 0.29/1.38 inference(rectify,[status(thm)],[f4])).
% 0.29/1.38 thf(f4,axiom,(
% 0.29/1.38 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) | (X1 @ X2))) = mor)),
% 0.29/1.38 file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',mor_def)).
% 0.29/1.38 thf(f112,plain,(
% 0.29/1.38 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.29/1.38 inference(cnf_transformation,[status(thm)],[f48])).
% 0.29/1.38 thf(f48,plain,(
% 0.29/1.38 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 0.29/1.38 inference(fool_elimination,[status(thm)],[f47])).
% 0.29/1.38 thf(f47,plain,(
% 0.29/1.38 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 0.29/1.38 inference(rectify,[status(thm)],[f11])).
% 0.29/1.38 thf(f11,axiom,(
% 0.29/1.38 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : ((eiw_di @ X5 @ X2) => (X1 @ X5 @ X2)))) = mforall_di)),
% 0.29/1.38 file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',mforall_di_def)).
% 0.29/1.38 thf(f107,plain,(
% 0.29/1.38 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.29/1.38 inference(cnf_transformation,[status(thm)],[f63])).
% 0.29/1.38 thf(f63,plain,(
% 0.29/1.38 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.29/1.38 inference(fool_elimination,[status(thm)],[f1])).
% 0.29/1.38 thf(f1,axiom,(
% 0.29/1.38 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 0.29/1.38 file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',mlocal_def)).
% 0.29/1.38 thf(f97,plain,(
% 0.29/1.38 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 0.29/1.38 inference(cnf_transformation,[status(thm)],[f86])).
% 0.29/1.38 thf(f86,plain,(
% 0.29/1.38 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 0.29/1.38 inference(flattening,[status(thm)],[f71])).
% 0.29/1.38 thf(f71,plain,(
% 0.29/1.38 ~($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)))))))))),
% 0.29/1.38 inference(fool_elimination,[status(thm)],[f70])).
% 0.29/1.38 thf(f70,plain,(
% 0.29/1.38 ~(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))))))))),
% 0.29/1.38 inference(rectify,[status(thm)],[f29])).
% 0.29/1.38 thf(f29,negated_conjecture,(
% 0.29/1.38 ~(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))))))))),
% 0.29/1.38 inference(negated_conjecture,[status(cth)],[f28])).
% 0.29/1.38 thf(f28,conjecture,(
% 0.29/1.38 (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))))))))),
% 0.29/1.38 file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',t69_zfmisc_1)).
% 0.29/1.38 thf(f378,plain,(
% 0.29/1.38 ((eiw_di @ sK2 @ mactual) = $false) | ~spl1_10),
% 0.29/1.38 inference(avatar_component_clause,[status(thm)],[f376])).
% 0.29/1.38 thf(f376,definition,(
% 0.29/1.38 spl1_10 <=> ((eiw_di @ sK2 @ mactual) = $false)),
% 0.29/1.38 introduced(definition,[new_symbols(naming,[spl1_10])],[avatar_definition])).
% 0.29/1.38 thf(f448,plain,(
% 0.29/1.38 spl1_10 | spl1_11 | spl1_8),
% 0.29/1.38 inference(avatar_split_clause,[status(thm)],[f447,f368,f443,f376])).
% 0.29/1.38 thf(f368,definition,(
% 0.29/1.38 spl1_8 <=> ($false = (eiw_di @ sK3 @ mactual))),
% 0.29/1.38 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 0.29/1.38 thf(f447,plain,(
% 0.29/1.38 ((eiw_di @ sK2 @ mactual) = $false) | ($true = (in @ sK2 @ sK3 @ mactual)) | spl1_8),
% 0.29/1.38 inference(subsumption_resolution,[status(thm)],[f431,f369])).
% 0.29/1.38 thf(f369,plain,(
% 0.29/1.38 ($false != (eiw_di @ sK3 @ mactual)) | spl1_8),
% 0.29/1.38 inference(avatar_component_clause,[status(thm)],[f368])).
% 0.29/1.38 thf(f431,plain,(
% 0.29/1.38 ((eiw_di @ sK2 @ mactual) = $false) | ($true = (in @ sK2 @ sK3 @ mactual)) | ($false = (eiw_di @ sK3 @ mactual))),
% 0.29/1.38 inference(trivial_inequality_removal,[status(thm)],[f423])).
% 0.29/1.38 thf(f423,plain,(
% 0.29/1.38 ((eiw_di @ sK2 @ mactual) = $false) | ($true = (in @ sK2 @ sK3 @ mactual)) | ($false = (eiw_di @ sK3 @ mactual)) | ($true = $false)),
% 0.29/1.38 inference(superposition,[status(thm)],[f172,f142])).
% 0.29/1.38 thf(f142,plain,(
% 0.29/1.38 ((qmltpeq @ (set_difference @ (singleton @ sK2) @ sK3) @ (singleton @ sK2) @ mactual) = $false)),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 0.29/1.38 thf(f140,plain,(
% 0.29/1.38 (((qmltpeq @ (set_difference @ (singleton @ sK2) @ sK3) @ empty_set @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK2) @ sK3) @ (singleton @ sK2) @ mactual)) = $false)),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 0.29/1.38 thf(f139,plain,(
% 0.29/1.38 (((eiw_di @ sK3 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK2) @ sK3) @ empty_set @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK2) @ sK3) @ (singleton @ sK2) @ mactual))) = $false)),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f138])).
% 0.29/1.38 thf(f138,plain,(
% 0.29/1.38 (((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK2) @ Y0) @ empty_set @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK2) @ Y0) @ (singleton @ sK2) @ mactual)))) @ sK3) = $false)),
% 0.29/1.38 inference(sigma_clausification,[status(thm)],[f136])).
% 0.29/1.38 thf(f136,plain,(
% 0.29/1.38 ($false = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK2) @ Y0) @ empty_set @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK2) @ Y0) @ (singleton @ sK2) @ mactual))))))),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f135])).
% 0.29/1.38 thf(f172,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)) | ((eiw_di @ X1 @ mactual) = $false) | ($false = (eiw_di @ X2 @ mactual)) | ($true = (in @ X1 @ X2 @ mactual))) )),
% 0.29/1.38 inference(not_proxy_clausification,[status(thm)],[f169])).
% 0.29/1.38 thf(f169,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($false = (~ (in @ X1 @ X2 @ mactual))) | ($false = (eiw_di @ X2 @ mactual)) | ($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f168])).
% 0.29/1.38 thf(f168,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ mactual)) | ((eiw_di @ X1 @ mactual) = $false) | ((qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual) = (~ (in @ X1 @ X2 @ mactual)))) )),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f167])).
% 0.29/1.38 thf(f167,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($true = ((~ (in @ X1 @ X2 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual))) | ((eiw_di @ X1 @ mactual) = $false) | ($false = (eiw_di @ X2 @ mactual))) )),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f166])).
% 0.29/1.38 thf(f166,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($true = ((eiw_di @ X2 @ mactual) => ((~ (in @ X1 @ X2 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)))) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f165])).
% 0.29/1.38 thf(f165,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((~ (in @ X1 @ Y0 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ (singleton @ X1) @ mactual)))) @ X2)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.29/1.38 inference(pi_clausification,[status(thm)],[f164])).
% 0.29/1.38 thf(f164,plain,(
% 0.29/1.38 ( ! [X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((~ (in @ X1 @ Y0 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ (singleton @ X1) @ mactual))))))) )),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f163])).
% 0.29/1.38 thf(f163,plain,(
% 0.29/1.38 ( ! [X1 : $i] : (($true = ((eiw_di @ X1 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((~ (in @ X1 @ Y0 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ (singleton @ X1) @ mactual)))))))) )),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f162])).
% 0.29/1.38 thf(f162,plain,(
% 0.29/1.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((~ (in @ Y0 @ Y1 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual))))))) @ X1))) )),
% 0.29/1.38 inference(pi_clausification,[status(thm)],[f161])).
% 0.29/1.38 thf(f161,plain,(
% 0.29/1.38 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((~ (in @ Y0 @ Y1 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual)))))))) = $true)),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f131])).
% 0.29/1.38 thf(f131,plain,(
% 0.29/1.38 (((^[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) @ (singleton @ Y0)) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (~ (Y2 @ Y3))))) @ (in @ Y0 @ Y1)))))))) = $true)),
% 0.29/1.38 inference(definition_unfolding,[status(thm)],[f115,f107,f112,f112,f93,f109])).
% 0.29/1.38 thf(f109,plain,(
% 0.29/1.38 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.29/1.38 inference(cnf_transformation,[status(thm)],[f60])).
% 0.29/1.38 thf(f60,plain,(
% 0.29/1.38 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 0.29/1.38 inference(fool_elimination,[status(thm)],[f59])).
% 0.29/1.38 thf(f59,plain,(
% 0.29/1.38 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 0.29/1.38 inference(rectify,[status(thm)],[f2])).
% 0.29/1.38 thf(f2,axiom,(
% 0.29/1.38 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 0.29/1.38 file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',mnot_def)).
% 0.29/1.38 thf(f93,plain,(
% 0.29/1.38 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 0.29/1.38 inference(cnf_transformation,[status(thm)],[f58])).
% 0.29/1.38 thf(f58,plain,(
% 0.29/1.38 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 0.29/1.38 inference(fool_elimination,[status(thm)],[f57])).
% 0.29/1.38 thf(f57,plain,(
% 0.29/1.38 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X0 @ X2))) = mequiv)),
% 0.29/1.38 inference(rectify,[status(thm)],[f6])).
% 0.29/1.38 thf(f6,axiom,(
% 0.29/1.38 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) <=> (X1 @ X2))) = mequiv)),
% 0.29/1.38 file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',mequiv_def)).
% 0.29/1.38 thf(f115,plain,(
% 0.29/1.38 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))) = $true)),
% 0.29/1.38 inference(cnf_transformation,[status(thm)],[f67])).
% 0.29/1.38 thf(f67,plain,(
% 0.29/1.38 ((mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))) = $true)),
% 0.29/1.38 inference(fool_elimination,[status(thm)],[f66])).
% 0.29/1.38 thf(f66,plain,(
% 0.29/1.38 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ (singleton @ X0)) @ (mnot @ (in @ X0 @ X1))))))))),
% 0.29/1.38 inference(rectify,[status(thm)],[f24])).
% 0.29/1.38 thf(f24,axiom,(
% 0.29/1.38 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ (singleton @ X1)) @ (mnot @ (in @ X1 @ X3))))))))),
% 0.29/1.38 file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',l34_zfmisc_1)).
% 0.29/1.38 thf(f387,plain,(
% 0.29/1.38 ~spl1_8),
% 0.29/1.38 inference(avatar_contradiction_clause,[status(thm)],[f386])).
% 0.29/1.38 thf(f386,plain,(
% 0.29/1.38 $false | ~spl1_8),
% 0.29/1.38 inference(trivial_inequality_removal,[status(thm)],[f383])).
% 0.29/1.38 thf(f383,plain,(
% 0.29/1.38 ($true = $false) | ~spl1_8),
% 0.29/1.38 inference(superposition,[status(thm)],[f141,f370])).
% 0.29/1.38 thf(f370,plain,(
% 0.29/1.38 ($false = (eiw_di @ sK3 @ mactual)) | ~spl1_8),
% 0.29/1.38 inference(avatar_component_clause,[status(thm)],[f368])).
% 0.29/1.38 thf(f141,plain,(
% 0.29/1.38 ($true = (eiw_di @ sK3 @ mactual))),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f139])).
% 0.29/1.38 thf(f380,plain,(
% 0.29/1.38 spl1_10 | spl1_8 | spl1_9),
% 0.29/1.38 inference(avatar_split_clause,[status(thm)],[f356,f372,f368,f376])).
% 0.29/1.38 thf(f356,plain,(
% 0.29/1.38 ($false = (in @ sK2 @ sK3 @ mactual)) | ((eiw_di @ sK2 @ mactual) = $false) | ($false = (eiw_di @ sK3 @ mactual))),
% 0.29/1.38 inference(trivial_inequality_removal,[status(thm)],[f350])).
% 0.29/1.38 thf(f350,plain,(
% 0.29/1.38 ((eiw_di @ sK2 @ mactual) = $false) | ($true = $false) | ($false = (in @ sK2 @ sK3 @ mactual)) | ($false = (eiw_di @ sK3 @ mactual))),
% 0.29/1.38 inference(superposition,[status(thm)],[f143,f181])).
% 0.29/1.38 thf(f181,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual)) | ($false = (in @ X1 @ X2 @ mactual)) | ($false = (eiw_di @ X2 @ mactual)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f180])).
% 0.29/1.38 thf(f180,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ((qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual) = (in @ X1 @ X2 @ mactual)) | ($false = (eiw_di @ X2 @ mactual))) )),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f179])).
% 0.29/1.38 thf(f179,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($true = ((in @ X1 @ X2 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual))) | ((eiw_di @ X1 @ mactual) = $false) | ($false = (eiw_di @ X2 @ mactual))) )),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f178])).
% 0.29/1.38 thf(f178,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($true = ((eiw_di @ X2 @ mactual) => ((in @ X1 @ X2 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual)))) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f177])).
% 0.29/1.38 thf(f177,plain,(
% 0.29/1.38 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((in @ X1 @ Y0 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ empty_set @ mactual)))) @ X2)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.29/1.38 inference(pi_clausification,[status(thm)],[f176])).
% 0.29/1.38 thf(f176,plain,(
% 0.29/1.38 ( ! [X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((in @ X1 @ Y0 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ empty_set @ mactual))))))) )),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f175])).
% 0.29/1.38 thf(f175,plain,(
% 0.29/1.38 ( ! [X1 : $i] : (($true = ((eiw_di @ X1 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((in @ X1 @ Y0 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ empty_set @ mactual)))))))) )),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f174])).
% 0.29/1.38 thf(f174,plain,(
% 0.29/1.38 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((in @ Y0 @ Y1 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual))))))) @ X1))) )),
% 0.29/1.38 inference(pi_clausification,[status(thm)],[f173])).
% 0.29/1.38 thf(f173,plain,(
% 0.29/1.38 ((!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((in @ Y0 @ Y1 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual)))))))) = $true)),
% 0.29/1.38 inference(beta_eta_normalization,[status(thm)],[f126])).
% 0.29/1.38 thf(f126,plain,(
% 0.29/1.38 ($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 > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 0.29/1.38 inference(definition_unfolding,[status(thm)],[f106,f107,f112,f112,f93])).
% 0.29/1.38 thf(f106,plain,(
% 0.29/1.38 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 0.29/1.38 inference(cnf_transformation,[status(thm)],[f52])).
% 0.29/1.38 thf(f52,plain,(
% 0.29/1.38 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 0.29/1.38 inference(fool_elimination,[status(thm)],[f51])).
% 0.29/1.38 thf(f51,plain,(
% 0.29/1.38 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ empty_set) @ (in @ X0 @ X1)))))))),
% 0.29/1.38 inference(rectify,[status(thm)],[f25])).
% 0.29/1.38 thf(f25,axiom,(
% 0.29/1.38 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ empty_set) @ (in @ X1 @ X3)))))))),
% 0.29/1.38 file('/export/starexec/sandbox/tmp/tmp.5W2kHOLHbu/DTF2THF_14138.p',l36_zfmisc_1)).
% 0.29/1.38 thf(f143,plain,(
% 0.29/1.38 ($false = (qmltpeq @ (set_difference @ (singleton @ sK2) @ sK3) @ empty_set @ mactual))),
% 0.29/1.38 inference(binary_proxy_clausification,[status(thm)],[f140])).
% 0.29/1.38 % SZS output end Proof for DTF2THF_14138
% 0.29/1.38 % (14247)------------------------------
% 0.29/1.38 % (14247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.29/1.38 % (14247)Termination reason: Refutation
% 0.29/1.38
% 0.29/1.38 % (14247)Memory used [KB]: 6012
% 0.29/1.38 % (14247)Time elapsed: 0.041 s
% 0.29/1.38 % (14247)Instructions burned: 65 (million)
% 0.29/1.38 % (14247)------------------------------
% 0.29/1.38 % (14247)------------------------------
% 0.29/1.38 % (14246)Success in time 0.05 s
%------------------------------------------------------------------------------