%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SET926^20 : 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 : n015.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 1.94s 1.42s
% Output : Refutation 1.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 11
% Syntax : Number of formulae : 91 ( 49 unt; 0 typ; 3 def)
% Number of atoms : 617 ( 128 equ; 0 cnn)
% Maximal formula atoms : 7 ( 6 avg)
% Number of connectives : 972 ( 35 ~; 68 |; 0 &; 804 @)
% ( 5 <=>; 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 : 29 ( 25 usr; 10 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(f511,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f402,f424,f436,f508]) ).
thf(f508,plain,
( spl1_6
| spl1_7
| ~ spl1_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f507]) ).
thf(f507,plain,
( $false
| spl1_6
| spl1_7
| ~ spl1_8 ),
inference(trivial_inequality_removal,[status(thm)],[f501]) ).
thf(f501,plain,
( ( $true = $false )
| spl1_6
| spl1_7
| ~ spl1_8 ),
inference(superposition,[status(thm)],[f392,f498]) ).
thf(f498,plain,
( ( $true
= ( in @ sK4 @ sK5 @ mactual ) )
| spl1_6
| spl1_7 ),
inference(subsumption_resolution,[status(thm)],[f497,f387]) ).
thf(f387,plain,
( ( $false
!= ( eiw_di @ sK4 @ mactual ) )
| spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f386]) ).
thf(f386,definition,
( spl1_7
<=> ( $false
= ( eiw_di @ sK4 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f497,plain,
( ( $true
= ( in @ sK4 @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| spl1_6 ),
inference(subsumption_resolution,[status(thm)],[f490,f383]) ).
thf(f383,plain,
( ( $false
!= ( eiw_di @ sK5 @ mactual ) )
| spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f382]) ).
thf(f382,definition,
( spl1_6
<=> ( $false
= ( eiw_di @ sK5 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f490,plain,
( ( $false
= ( eiw_di @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $true
= ( in @ sK4 @ sK5 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f479]) ).
thf(f479,plain,
( ( $true
= ( in @ sK4 @ sK5 @ mactual ) )
| ( $true = $false )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $false
= ( eiw_di @ sK5 @ mactual ) ) ),
inference(superposition,[status(thm)],[f271,f221]) ).
thf(f221,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ sK5 ) @ ( singleton @ sK4 ) @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f218]) ).
thf(f218,plain,
( $false
= ( ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ sK5 ) @ ( singleton @ sK4 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ sK5 ) @ empty_set @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ( eiw_di @ sK5 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ sK5 ) @ ( singleton @ sK4 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ sK5 ) @ empty_set @ mactual ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f216]) ).
thf(f216,plain,
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ Y0 ) @ ( singleton @ sK4 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ Y0 ) @ empty_set @ mactual ) ) )
@ sK5 )
= $false ),
inference(sigma_clausification,[status(thm)],[f214]) ).
thf(f214,plain,
( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ Y0 ) @ ( singleton @ sK4 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f213]) ).
thf(f213,plain,
( ( ( eiw_di @ sK4 @ mactual )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ Y0 ) @ ( singleton @ sK4 ) @ mactual )
| ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f212]) ).
thf(f212,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 ) ) ) ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f211]) ).
thf(f211,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)],[f138]) ).
thf(f138,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)],[f118,f119,f115,f115,f102]) ).
thf(f102,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f86]) ).
thf(f86,plain,
( mor
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
| ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f85]) ).
thf(f85,plain,
( mor
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
| ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,axiom,
( mor
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
| ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',mor_def) ).
thf(f115,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f74]) ).
thf(f74,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f73]) ).
thf(f73,plain,
( mforall_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( mforall_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X5: $i] :
( ( eiw_di @ X5 @ X2 )
=> ( X1 @ X5 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',mforall_di_def) ).
thf(f119,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
thf(f36,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.e1jkKrXUvf/DTF2THF_4949.p',mlocal_def) ).
thf(f118,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)],[f89]) ).
thf(f89,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)],[f40]) ).
thf(f40,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)],[f39]) ).
thf(f39,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)],[f30]) ).
thf(f30,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)],[f29]) ).
thf(f29,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.e1jkKrXUvf/DTF2THF_4949.p',t69_zfmisc_1) ).
thf(f271,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( in @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(not_proxy_clausification,[status(thm)],[f268]) ).
thf(f268,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f267]) ).
thf(f267,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual )
= ( ~ ( in @ X1 @ X2 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f266]) ).
thf(f266,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $true
= ( ( ~ ( in @ X1 @ X2 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f265]) ).
thf(f265,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( ~ ( in @ X1 @ X2 @ mactual ) )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ ( singleton @ X1 ) @ mactual ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f264]) ).
thf(f264,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 ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f263]) ).
thf(f263,plain,
! [X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( $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)],[f262]) ).
thf(f262,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)],[f261]) ).
thf(f261,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)],[f260]) ).
thf(f260,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,
( $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 ) @ ( singleton @ Y0 ) )
@ ( ^ [Y2: mworld > $o,Y3: mworld] :
~ ( Y2 @ Y3 )
@ ( in @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f107,f119,f115,f115,f117,f95]) ).
thf(f95,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(cnf_transformation,[status(thm)],[f66]) ).
thf(f66,plain,
( mnot
= ( ^ [Y0: mworld > $o,Y1: mworld] :
~ ( Y0 @ Y1 ) ) ),
inference(fool_elimination,[status(thm)],[f65]) ).
thf(f65,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.e1jkKrXUvf/DTF2THF_4949.p',mnot_def) ).
thf(f117,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f52]) ).
thf(f52,plain,
( mequiv
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
= ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f51]) ).
thf(f51,plain,
( mequiv
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
<=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f6]) ).
thf(f6,axiom,
( mequiv
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
<=> ( X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',mequiv_def) ).
thf(f107,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)],[f46]) ).
thf(f46,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)],[f45]) ).
thf(f45,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)],[f25]) ).
thf(f25,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.e1jkKrXUvf/DTF2THF_4949.p',l34_zfmisc_1) ).
thf(f392,plain,
( ( $false
= ( in @ sK4 @ sK5 @ mactual ) )
| ~ spl1_8 ),
inference(avatar_component_clause,[status(thm)],[f390]) ).
thf(f390,definition,
( spl1_8
<=> ( $false
= ( in @ sK4 @ sK5 @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition]) ).
thf(f436,plain,
~ spl1_7,
inference(avatar_contradiction_clause,[status(thm)],[f435]) ).
thf(f435,plain,
( $false
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f428]) ).
thf(f428,plain,
( ( $true = $false )
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f388,f215]) ).
thf(f215,plain,
( $true
= ( eiw_di @ sK4 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f213]) ).
thf(f388,plain,
( ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f386]) ).
thf(f424,plain,
~ spl1_6,
inference(avatar_contradiction_clause,[status(thm)],[f423]) ).
thf(f423,plain,
( $false
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f416]) ).
thf(f416,plain,
( ( $true = $false )
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f384,f219]) ).
thf(f219,plain,
( $true
= ( eiw_di @ sK5 @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f217]) ).
thf(f384,plain,
( ( $false
= ( eiw_di @ sK5 @ mactual ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f382]) ).
thf(f402,plain,
( spl1_6
| spl1_8
| spl1_7 ),
inference(avatar_split_clause,[status(thm)],[f376,f386,f390,f382]) ).
thf(f376,plain,
( ( $false
= ( eiw_di @ sK5 @ mactual ) )
| ( $false
= ( in @ sK4 @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f369]) ).
thf(f369,plain,
( ( $false
= ( in @ sK4 @ sK5 @ mactual ) )
| ( $false
= ( eiw_di @ sK4 @ mactual ) )
| ( $true = $false )
| ( $false
= ( eiw_di @ sK5 @ mactual ) ) ),
inference(superposition,[status(thm)],[f186,f220]) ).
thf(f220,plain,
( $false
= ( qmltpeq @ ( set_difference @ ( singleton @ sK4 ) @ sK5 ) @ empty_set @ mactual ) ),
inference(binary_proxy_clausification,[status(thm)],[f218]) ).
thf(f186,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) )
| ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( $false
= ( in @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f185]) ).
thf(f185,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X2 @ mactual ) )
| ( ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual )
= ( in @ X1 @ X2 @ mactual ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f184]) ).
thf(f184,plain,
! [X2: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ mactual ) )
| ( ( ( in @ X1 @ X2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f183]) ).
thf(f183,plain,
! [X2: $i,X1: $i] :
( ( $true
= ( ( eiw_di @ X2 @ mactual )
=> ( ( in @ X1 @ X2 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ X2 ) @ empty_set @ mactual ) ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(beta_eta_normalization,[status(thm)],[f182]) ).
thf(f182,plain,
! [X2: $i,X1: $i] :
( ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( in @ X1 @ Y0 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual ) ) )
@ X2 )
= $true )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(pi_clausification,[status(thm)],[f181]) ).
thf(f181,plain,
! [X1: $i] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ mactual )
=> ( ( in @ X1 @ Y0 @ mactual )
= ( qmltpeq @ ( set_difference @ ( singleton @ X1 ) @ Y0 ) @ empty_set @ mactual ) ) ) ) )
| ( $false
= ( eiw_di @ X1 @ mactual ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f180]) ).
thf(f180,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)],[f179]) ).
thf(f179,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)],[f178]) ).
thf(f178,plain,
( $true
= ( !! @ $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 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f134]) ).
thf(f134,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)],[f110,f119,f115,f115,f117]) ).
thf(f110,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)],[f76]) ).
thf(f76,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)],[f75]) ).
thf(f75,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)],[f26]) ).
thf(f26,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.e1jkKrXUvf/DTF2THF_4949.p',l36_zfmisc_1) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET926^20 : TPTP v9.2.1. Released v8.1.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n015.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:06:16 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.31/0.46 ---- Original DTF file ---
% 0.31/0.46 thf(spec,logic,$$dhol).
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 % File : SET926^20 : TPTP v9.2.1. Released v8.1.0.
% 0.31/0.46 % Domain : Set Theory
% 0.31/0.46 % Problem : TPTP problem SET926+1.p with axiomatized equality
% 0.31/0.46 % Version : [BP13] axioms.
% 0.31/0.46 % English :
% 0.31/0.46
% 0.31/0.46 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.31/0.46 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.31/0.46 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.31/0.46 % Source : [TPTP]
% 0.31/0.46 % Names : SET926+1 [QMLTP]
% 0.31/0.46
% 0.31/0.46 % Status : Theorem
% 0.31/0.46 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.31/0.46 % Syntax : Number of formulae : 49 ( 12 unt; 20 typ; 10 def)
% 0.31/0.46 % Number of atoms : 128 ( 10 equ; 0 cnn)
% 0.31/0.46 % Maximal formula atoms : 9 ( 4 avg)
% 0.31/0.46 % Number of connectives : 211 ( 1 ~; 1 |; 4 &; 200 @)
% 0.31/0.46 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.31/0.46 % Maximal formula depth : 14 ( 7 avg)
% 0.31/0.46 % Number of types : 3 ( 1 usr)
% 0.31/0.46 % Number of type conns : 70 ( 70 >; 0 *; 0 +; 0 <<)
% 0.31/0.46 % Number of symbols : 20 ( 19 usr; 2 con; 0-3 aty)
% 0.31/0.46 % Number of variables : 65 ( 55 ^; 7 !; 3 ?; 65 :)
% 0.31/0.46 % SPC : TH0_THM_EQU_NAR
% 0.31/0.46
% 0.31/0.46 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.31/0.46 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.31/0.46 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.31/0.46 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.31/0.46 % $modalities == $modal_system_T].
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 thf(mworld,type,
% 0.31/0.46 mworld: $tType ).
% 0.31/0.46
% 0.31/0.46 thf(mrel_type,type,
% 0.31/0.46 mrel: mworld > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mactual_type,type,
% 0.31/0.46 mactual: mworld ).
% 0.31/0.46
% 0.31/0.46 thf(mlocal_type,type,
% 0.31/0.46 mlocal: ( mworld > $o ) > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mlocal_def,definition,
% 0.31/0.46 ( mlocal
% 0.31/0.46 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mnot_type,type,
% 0.31/0.46 mnot: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mand_type,type,
% 0.31/0.46 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mor_type,type,
% 0.31/0.46 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mimplies_type,type,
% 0.31/0.46 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mequiv_type,type,
% 0.31/0.46 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mnot_def,definition,
% 0.31/0.46 ( mnot
% 0.31/0.46 = ( ^ [A: mworld > $o,W: mworld] :
% 0.31/0.46 ~ ( A @ W ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mand_def,definition,
% 0.31/0.46 ( mand
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 & ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mor_def,definition,
% 0.31/0.46 ( mor
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 | ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mimplies_def,definition,
% 0.31/0.46 ( mimplies
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 => ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mequiv_def,definition,
% 0.31/0.46 ( mequiv
% 0.31/0.46 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/0.46 ( ( A @ W )
% 0.31/0.46 <=> ( B @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mbox_type,type,
% 0.31/0.46 mbox: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mbox_def,definition,
% 0.31/0.46 ( mbox
% 0.31/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/0.46 ! [V: mworld] :
% 0.31/0.46 ( ( mrel @ W @ V )
% 0.31/0.46 => ( Phi @ V ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mdia_type,type,
% 0.31/0.46 mdia: ( mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mdia_def,definition,
% 0.31/0.46 ( mdia
% 0.31/0.46 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/0.46 ? [V: mworld] :
% 0.31/0.46 ( ( mrel @ W @ V )
% 0.31/0.46 & ( Phi @ V ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mrel_reflexive,axiom,
% 0.31/0.46 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.31/0.46
% 0.31/0.46 thf(eiw_di_type,type,
% 0.31/0.46 eiw_di: $i > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(eiw_di_nonempty,axiom,
% 0.31/0.46 ! [W: mworld] :
% 0.31/0.46 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.31/0.46
% 0.31/0.46 thf(eiw_di_decr,axiom,
% 0.31/0.46 ! [W: mworld,V: mworld,X: $i] :
% 0.31/0.46 ( ( ( eiw_di @ X @ W )
% 0.31/0.46 & ( mrel @ V @ W ) )
% 0.31/0.46 => ( eiw_di @ X @ V ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mforall_di_type,type,
% 0.31/0.46 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mforall_di_def,definition,
% 0.31/0.46 ( mforall_di
% 0.31/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/0.46 ! [X: $i] :
% 0.31/0.46 ( ( eiw_di @ X @ W )
% 0.31/0.46 => ( A @ X @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(mexists_di_type,type,
% 0.31/0.46 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(mexists_di_def,definition,
% 0.31/0.46 ( mexists_di
% 0.31/0.46 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/0.46 ? [X: $i] :
% 0.31/0.46 ( ( eiw_di @ X @ W )
% 0.31/0.46 & ( A @ X @ W ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(empty_set_decl,type,
% 0.31/0.46 empty_set: $i ).
% 0.31/0.46
% 0.31/0.46 thf(qmltpeq_decl,type,
% 0.31/0.46 qmltpeq: $i > $i > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(in_decl,type,
% 0.31/0.46 in: $i > $i > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(empty_decl,type,
% 0.31/0.46 empty: $i > mworld > $o ).
% 0.31/0.46
% 0.31/0.46 thf(singleton_decl,type,
% 0.31/0.46 singleton: $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(set_difference_decl,type,
% 0.31/0.46 set_difference: $i > $i > $i ).
% 0.31/0.46
% 0.31/0.46 thf(reflexivity,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(symmetry,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(transitivity,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [X: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [Y: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(set_difference_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(set_difference_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(singleton_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(empty_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(in_substitution_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(in_substitution_2,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(antisymmetry_r2_hidden,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(fc1_xboole_0,axiom,
% 0.31/0.46 mlocal @ ( empty @ empty_set ) ).
% 0.31/0.46
% 0.31/0.46 thf(l34_zfmisc_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(l36_zfmisc_1,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(rc1_xboole_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mexists_di
% 0.31/0.46 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(rc2_xboole_0,axiom,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mexists_di
% 0.31/0.46 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 thf(t69_zfmisc_1,conjecture,
% 0.31/0.46 ( mlocal
% 0.31/0.46 @ ( mforall_di
% 0.31/0.46 @ ^ [A: $i] :
% 0.31/0.46 ( mforall_di
% 0.31/0.46 @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ).
% 0.31/0.46
% 0.31/0.46 %------------------------------------------------------------------------------
% 0.31/0.46 ------------------------
% 1.79/1.36 ---- Embedded in THF ---
% 1.79/1.36 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.79/1.36 %%% Generated on Tue Feb 24 12:06:17 EST 2026
% 1.79/1.36 %%% using '$$dhol' embedding, version 1.3.0.
% 1.79/1.36 %%% Logic specification used:
% 1.79/1.36 %%% thf(spec, logic, $$dhol).
% 1.79/1.36
% 1.79/1.36 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2DTF4949.p
% See solution above
% 1.79/1.36 ------------------------
% 1.79/1.38 ---- Cleaned THF ---
% 1.79/1.38 thf(mworld,type,
% 1.79/1.38 mworld: $tType ).
% 1.79/1.38
% 1.79/1.38 thf(mrel_type,type,
% 1.79/1.38 mrel: mworld > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mactual_type,type,
% 1.79/1.38 mactual: mworld ).
% 1.79/1.38
% 1.79/1.38 thf(mlocal_type,type,
% 1.79/1.38 mlocal: ( mworld > $o ) > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mlocal_def,definition,
% 1.79/1.38 ( mlocal
% 1.79/1.38 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mnot_type,type,
% 1.79/1.38 mnot: ( mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mand_type,type,
% 1.79/1.38 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mor_type,type,
% 1.79/1.38 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mimplies_type,type,
% 1.79/1.38 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mequiv_type,type,
% 1.79/1.38 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mnot_def,definition,
% 1.79/1.38 ( mnot
% 1.79/1.38 = ( ^ [A: mworld > $o,W: mworld] :
% 1.79/1.38 ~ ( A @ W ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mand_def,definition,
% 1.79/1.38 ( mand
% 1.79/1.38 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.79/1.38 ( ( A @ W )
% 1.79/1.38 & ( B @ W ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mor_def,definition,
% 1.79/1.38 ( mor
% 1.79/1.38 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.79/1.38 ( ( A @ W )
% 1.79/1.38 | ( B @ W ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mimplies_def,definition,
% 1.79/1.38 ( mimplies
% 1.79/1.38 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.79/1.38 ( ( A @ W )
% 1.79/1.38 => ( B @ W ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mequiv_def,definition,
% 1.79/1.38 ( mequiv
% 1.79/1.38 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.79/1.38 ( ( A @ W )
% 1.79/1.38 <=> ( B @ W ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mbox_type,type,
% 1.79/1.38 mbox: ( mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mbox_def,definition,
% 1.79/1.38 ( mbox
% 1.79/1.38 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.79/1.38 ! [V: mworld] :
% 1.79/1.38 ( ( mrel @ W @ V )
% 1.79/1.38 => ( Phi @ V ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mdia_type,type,
% 1.79/1.38 mdia: ( mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mdia_def,definition,
% 1.79/1.38 ( mdia
% 1.79/1.38 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.79/1.38 ? [V: mworld] :
% 1.79/1.38 ( ( mrel @ W @ V )
% 1.79/1.38 & ( Phi @ V ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mrel_reflexive,axiom,
% 1.79/1.38 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.79/1.38
% 1.79/1.38 thf(eiw_di_type,type,
% 1.79/1.38 eiw_di: $i > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(eiw_di_nonempty,axiom,
% 1.79/1.38 ! [W: mworld] :
% 1.79/1.38 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.79/1.38
% 1.79/1.38 thf(eiw_di_decr,axiom,
% 1.79/1.38 ! [W: mworld,V: mworld,X: $i] :
% 1.79/1.38 ( ( ( eiw_di @ X @ W )
% 1.79/1.38 & ( mrel @ V @ W ) )
% 1.79/1.38 => ( eiw_di @ X @ V ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mforall_di_type,type,
% 1.79/1.38 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mforall_di_def,definition,
% 1.79/1.38 ( mforall_di
% 1.79/1.38 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.79/1.38 ! [X: $i] :
% 1.79/1.38 ( ( eiw_di @ X @ W )
% 1.79/1.38 => ( A @ X @ W ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(mexists_di_type,type,
% 1.79/1.38 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(mexists_di_def,definition,
% 1.79/1.38 ( mexists_di
% 1.79/1.38 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.79/1.38 ? [X: $i] :
% 1.79/1.38 ( ( eiw_di @ X @ W )
% 1.79/1.38 & ( A @ X @ W ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(empty_set_decl,type,
% 1.79/1.38 empty_set: $i ).
% 1.79/1.38
% 1.79/1.38 thf(qmltpeq_decl,type,
% 1.79/1.38 qmltpeq: $i > $i > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(in_decl,type,
% 1.79/1.38 in: $i > $i > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(empty_decl,type,
% 1.79/1.38 empty: $i > mworld > $o ).
% 1.79/1.38
% 1.79/1.38 thf(singleton_decl,type,
% 1.79/1.38 singleton: $i > $i ).
% 1.79/1.38
% 1.79/1.38 thf(set_difference_decl,type,
% 1.79/1.38 set_difference: $i > $i > $i ).
% 1.79/1.38
% 1.79/1.38 thf(reflexivity,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [X: $i] : ( qmltpeq @ X @ X ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(symmetry,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [X: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [Y: $i] : ( mimplies @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ X ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(transitivity,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [X: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [Y: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [Z: $i] : ( mimplies @ ( mand @ ( qmltpeq @ X @ Y ) @ ( qmltpeq @ Y @ Z ) ) @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(set_difference_substitution_1,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ A @ C ) @ ( set_difference @ B @ C ) ) ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(set_difference_substitution_2,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [C: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( set_difference @ C @ A ) @ ( set_difference @ C @ B ) ) ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(singleton_substitution_1,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] : ( mimplies @ ( qmltpeq @ A @ B ) @ ( qmltpeq @ ( singleton @ A ) @ ( singleton @ B ) ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(empty_substitution_1,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( empty @ A ) ) @ ( empty @ B ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(in_substitution_1,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ A @ C ) ) @ ( in @ B @ C ) ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(in_substitution_2,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [C: $i] : ( mimplies @ ( mand @ ( qmltpeq @ A @ B ) @ ( in @ C @ A ) ) @ ( in @ C @ B ) ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(antisymmetry_r2_hidden,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] : ( mimplies @ ( in @ A @ B ) @ ( mnot @ ( in @ B @ A ) ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(fc1_xboole_0,axiom,
% 1.79/1.38 mlocal @ ( empty @ empty_set ) ).
% 1.79/1.38
% 1.79/1.38 thf(l34_zfmisc_1,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) @ ( mnot @ ( in @ A @ B ) ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(l36_zfmisc_1,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] : ( mequiv @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( in @ A @ B ) ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(rc1_xboole_0,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mexists_di
% 1.79/1.38 @ ^ [A: $i] : ( empty @ A ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(rc2_xboole_0,axiom,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mexists_di
% 1.79/1.38 @ ^ [A: $i] : ( mnot @ ( empty @ A ) ) ) ) ).
% 1.79/1.38
% 1.79/1.38 thf(t69_zfmisc_1,conjecture,
% 1.79/1.38 ( mlocal
% 1.79/1.38 @ ( mforall_di
% 1.79/1.38 @ ^ [A: $i] :
% 1.79/1.38 ( mforall_di
% 1.79/1.38 @ ^ [B: $i] : ( mor @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ empty_set ) @ ( qmltpeq @ ( set_difference @ ( singleton @ A ) @ B ) @ ( singleton @ A ) ) ) ) ) ) ).
% 1.79/1.38 ------------------------
% 1.79/1.40 % (5057)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4949 for (2999ds/183Mi)
% 1.94/1.40 % (5058)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_4949 for (2999ds/4Mi)
% 1.94/1.40 % (5060)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4949 for (2999ds/2Mi)
% 1.94/1.40 % (5061)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_4949 for (2999ds/2Mi)
% 1.94/1.40 % (5063)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4949 for (2999ds/18Mi)
% 1.94/1.40 % (5062)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_4949 for (2999ds/275Mi)
% 1.94/1.40 % (5060)Instruction limit reached!
% 1.94/1.40 % (5060)------------------------------
% 1.94/1.40 % (5060)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.40 % (5060)Termination reason: Unknown
% 1.94/1.40 % (5060)Termination phase: shuffling
% 1.94/1.40
% 1.94/1.40 % (5060)Memory used [KB]: 1023
% 1.94/1.40 % (5060)Time elapsed: 0.003 s
% 1.94/1.40 % (5060)Instructions burned: 2 (million)
% 1.94/1.40 % (5060)------------------------------
% 1.94/1.40 % (5060)------------------------------
% 1.94/1.40 % (5061)Instruction limit reached!
% 1.94/1.40 % (5061)------------------------------
% 1.94/1.40 % (5061)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.40 % (5061)Termination reason: Unknown
% 1.94/1.40 % (5061)Termination phase: shuffling
% 1.94/1.40
% 1.94/1.40 % (5061)Memory used [KB]: 1023
% 1.94/1.40 % (5061)Time elapsed: 0.003 s
% 1.94/1.40 % (5061)Instructions burned: 2 (million)
% 1.94/1.40 % (5061)------------------------------
% 1.94/1.40 % (5061)------------------------------
% 1.94/1.40 % (5059)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_4949 for (2999ds/27Mi)
% 1.94/1.41 % (5058)Instruction limit reached!
% 1.94/1.41 % (5058)------------------------------
% 1.94/1.41 % (5058)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.41 % (5058)Termination reason: Unknown
% 1.94/1.41 % (5058)Termination phase: Preprocessing 1
% 1.94/1.41
% 1.94/1.41 % (5058)Memory used [KB]: 1023
% 1.94/1.41 % (5058)Time elapsed: 0.005 s
% 1.94/1.41 % (5058)Instructions burned: 5 (million)
% 1.94/1.41 % (5058)------------------------------
% 1.94/1.41 % (5058)------------------------------
% 1.94/1.41 % (5062)Refutation not found, incomplete strategy
% 1.94/1.41 % (5062)------------------------------
% 1.94/1.41 % (5062)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.41 % (5062)Termination reason: Refutation not found, incomplete strategy
% 1.94/1.41
% 1.94/1.41
% 1.94/1.41 % (5062)Memory used [KB]: 5500
% 1.94/1.41 % (5062)Time elapsed: 0.007 s
% 1.94/1.41 % (5062)Instructions burned: 8 (million)
% 1.94/1.41 % (5062)------------------------------
% 1.94/1.41 % (5062)------------------------------
% 1.94/1.41 % (5063)Instruction limit reached!
% 1.94/1.41 % (5063)------------------------------
% 1.94/1.41 % (5063)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.41 % (5063)Termination reason: Unknown
% 1.94/1.41 % (5063)Termination phase: Saturation
% 1.94/1.41
% 1.94/1.41 % (5063)Memory used [KB]: 5628
% 1.94/1.41 % (5063)Time elapsed: 0.012 s
% 1.94/1.41 % (5063)Instructions burned: 19 (million)
% 1.94/1.41 % (5063)------------------------------
% 1.94/1.41 % (5063)------------------------------
% 1.94/1.42 % (5059)Instruction limit reached!
% 1.94/1.42 % (5059)------------------------------
% 1.94/1.42 % (5059)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.42 % (5059)Termination reason: Unknown
% 1.94/1.42 % (5059)Termination phase: Saturation
% 1.94/1.42
% 1.94/1.42 % (5059)Memory used [KB]: 5756
% 1.94/1.42 % (5059)Time elapsed: 0.016 s
% 1.94/1.42 % (5059)Instructions burned: 27 (million)
% 1.94/1.42 % (5059)------------------------------
% 1.94/1.42 % (5059)------------------------------
% 1.94/1.42 % (5067)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_4949 for (2999ds/3Mi)
% 1.94/1.42 % (5067)Instruction limit reached!
% 1.94/1.42 % (5067)------------------------------
% 1.94/1.42 % (5067)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.42 % (5067)Termination reason: Unknown
% 1.94/1.42 % (5067)Termination phase: shuffling
% 1.94/1.42
% 1.94/1.42 % (5067)Memory used [KB]: 1023
% 1.94/1.42 % (5067)Time elapsed: 0.003 s
% 1.94/1.42 % (5067)Instructions burned: 3 (million)
% 1.94/1.42 % (5067)------------------------------
% 1.94/1.42 % (5067)------------------------------
% 1.94/1.42 % (5057)First to succeed.
% 1.94/1.42 % (5068)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_4949 for (2999ds/37Mi)
% 1.94/1.42 % (5069)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_4949 for (2999ds/15Mi)
% 1.94/1.42 % (5057)Refutation found. Thanks to Tanya!
% 1.94/1.42 % SZS status Theorem for DTF2THF_4949
% 1.94/1.42 % SZS output start Proof for DTF2THF_4949
% 1.94/1.42 thf(type_def_5, type, mworld: $tType).
% 1.94/1.42 thf(func_def_0, type, mworld: $tType).
% 1.94/1.42 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.94/1.42 thf(func_def_2, type, mactual: mworld).
% 1.94/1.42 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.94/1.42 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.94/1.42 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.94/1.42 thf(func_def_16, type, qmltpeq: $i > $i > mworld > $o).
% 1.94/1.42 thf(func_def_17, type, in: $i > $i > mworld > $o).
% 1.94/1.42 thf(func_def_18, type, empty: $i > mworld > $o).
% 1.94/1.42 thf(func_def_19, type, singleton: $i > $i).
% 1.94/1.42 thf(func_def_20, type, set_difference: $i > $i > $i).
% 1.94/1.42 thf(func_def_34, type, sK0: mworld > $i).
% 1.94/1.42 thf(f511,plain,(
% 1.94/1.42 $false),
% 1.94/1.42 inference(avatar_sat_refutation,[status(thm)],[f402,f424,f436,f508])).
% 1.94/1.42 thf(f508,plain,(
% 1.94/1.42 spl1_6 | spl1_7 | ~spl1_8),
% 1.94/1.42 inference(avatar_contradiction_clause,[status(thm)],[f507])).
% 1.94/1.42 thf(f507,plain,(
% 1.94/1.42 $false | (spl1_6 | spl1_7 | ~spl1_8)),
% 1.94/1.42 inference(trivial_inequality_removal,[status(thm)],[f501])).
% 1.94/1.42 thf(f501,plain,(
% 1.94/1.42 ($true = $false) | (spl1_6 | spl1_7 | ~spl1_8)),
% 1.94/1.42 inference(superposition,[status(thm)],[f392,f498])).
% 1.94/1.42 thf(f498,plain,(
% 1.94/1.42 ($true = (in @ sK4 @ sK5 @ mactual)) | (spl1_6 | spl1_7)),
% 1.94/1.42 inference(subsumption_resolution,[status(thm)],[f497,f387])).
% 1.94/1.42 thf(f387,plain,(
% 1.94/1.42 ($false != (eiw_di @ sK4 @ mactual)) | spl1_7),
% 1.94/1.42 inference(avatar_component_clause,[status(thm)],[f386])).
% 1.94/1.42 thf(f386,definition,(
% 1.94/1.42 spl1_7 <=> ($false = (eiw_di @ sK4 @ mactual))),
% 1.94/1.42 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.94/1.42 thf(f497,plain,(
% 1.94/1.42 ($true = (in @ sK4 @ sK5 @ mactual)) | ($false = (eiw_di @ sK4 @ mactual)) | spl1_6),
% 1.94/1.42 inference(subsumption_resolution,[status(thm)],[f490,f383])).
% 1.94/1.42 thf(f383,plain,(
% 1.94/1.42 ($false != (eiw_di @ sK5 @ mactual)) | spl1_6),
% 1.94/1.42 inference(avatar_component_clause,[status(thm)],[f382])).
% 1.94/1.42 thf(f382,definition,(
% 1.94/1.42 spl1_6 <=> ($false = (eiw_di @ sK5 @ mactual))),
% 1.94/1.42 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.94/1.42 thf(f490,plain,(
% 1.94/1.42 ($false = (eiw_di @ sK5 @ mactual)) | ($false = (eiw_di @ sK4 @ mactual)) | ($true = (in @ sK4 @ sK5 @ mactual))),
% 1.94/1.42 inference(trivial_inequality_removal,[status(thm)],[f479])).
% 1.94/1.42 thf(f479,plain,(
% 1.94/1.42 ($true = (in @ sK4 @ sK5 @ mactual)) | ($true = $false) | ($false = (eiw_di @ sK4 @ mactual)) | ($false = (eiw_di @ sK5 @ mactual))),
% 1.94/1.42 inference(superposition,[status(thm)],[f271,f221])).
% 1.94/1.42 thf(f221,plain,(
% 1.94/1.42 ($false = (qmltpeq @ (set_difference @ (singleton @ sK4) @ sK5) @ (singleton @ sK4) @ mactual))),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f218])).
% 1.94/1.42 thf(f218,plain,(
% 1.94/1.42 ($false = ((qmltpeq @ (set_difference @ (singleton @ sK4) @ sK5) @ (singleton @ sK4) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK4) @ sK5) @ empty_set @ mactual)))),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f217])).
% 1.94/1.42 thf(f217,plain,(
% 1.94/1.42 (((eiw_di @ sK5 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK4) @ sK5) @ (singleton @ sK4) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK4) @ sK5) @ empty_set @ mactual))) = $false)),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f216])).
% 1.94/1.42 thf(f216,plain,(
% 1.94/1.42 (((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK4) @ Y0) @ (singleton @ sK4) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK4) @ Y0) @ empty_set @ mactual)))) @ sK5) = $false)),
% 1.94/1.42 inference(sigma_clausification,[status(thm)],[f214])).
% 1.94/1.42 thf(f214,plain,(
% 1.94/1.42 ($false = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK4) @ Y0) @ (singleton @ sK4) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK4) @ Y0) @ empty_set @ mactual))))))),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f213])).
% 1.94/1.42 thf(f213,plain,(
% 1.94/1.42 (((eiw_di @ sK4 @ mactual) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ sK4) @ Y0) @ (singleton @ sK4) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ sK4) @ Y0) @ empty_set @ mactual)))))) = $false)),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f212])).
% 1.94/1.42 thf(f212,plain,(
% 1.94/1.42 ($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual))))))) @ sK4))),
% 1.94/1.42 inference(sigma_clausification,[status(thm)],[f211])).
% 1.94/1.42 thf(f211,plain,(
% 1.94/1.42 ($true != (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0) @ mactual) | (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual)))))))))),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f138])).
% 1.94/1.42 thf(f138,plain,(
% 1.94/1.42 ($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)))))))))),
% 1.94/1.42 inference(definition_unfolding,[status(thm)],[f118,f119,f115,f115,f102])).
% 1.94/1.42 thf(f102,plain,(
% 1.94/1.42 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.94/1.42 inference(cnf_transformation,[status(thm)],[f86])).
% 1.94/1.42 thf(f86,plain,(
% 1.94/1.42 (mor = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) | (Y0 @ Y2))))))))),
% 1.94/1.42 inference(fool_elimination,[status(thm)],[f85])).
% 1.94/1.42 thf(f85,plain,(
% 1.94/1.42 (mor = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) | (X1 @ X2))))),
% 1.94/1.42 inference(rectify,[status(thm)],[f4])).
% 1.94/1.42 thf(f4,axiom,(
% 1.94/1.42 (mor = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) | (X3 @ X2))))),
% 1.94/1.42 file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',mor_def)).
% 1.94/1.42 thf(f115,plain,(
% 1.94/1.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.94/1.42 inference(cnf_transformation,[status(thm)],[f74])).
% 1.94/1.42 thf(f74,plain,(
% 1.94/1.42 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.94/1.42 inference(fool_elimination,[status(thm)],[f73])).
% 1.94/1.42 thf(f73,plain,(
% 1.94/1.42 (mforall_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))))),
% 1.94/1.42 inference(rectify,[status(thm)],[f12])).
% 1.94/1.42 thf(f12,axiom,(
% 1.94/1.42 (mforall_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (! [X5 : $i] : ((eiw_di @ X5 @ X2) => (X1 @ X5 @ X2)))))),
% 1.94/1.42 file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',mforall_di_def)).
% 1.94/1.42 thf(f119,plain,(
% 1.94/1.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.94/1.42 inference(cnf_transformation,[status(thm)],[f36])).
% 1.94/1.42 thf(f36,plain,(
% 1.94/1.42 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.94/1.42 inference(fool_elimination,[status(thm)],[f1])).
% 1.94/1.42 thf(f1,axiom,(
% 1.94/1.42 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.94/1.42 file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',mlocal_def)).
% 1.94/1.42 thf(f118,plain,(
% 1.94/1.42 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 1.94/1.42 inference(cnf_transformation,[status(thm)],[f89])).
% 1.94/1.42 thf(f89,plain,(
% 1.94/1.42 ($true != (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mor @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)))))))))),
% 1.94/1.42 inference(flattening,[status(thm)],[f40])).
% 1.94/1.42 thf(f40,plain,(
% 1.94/1.42 ~($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)))))))))),
% 1.94/1.42 inference(fool_elimination,[status(thm)],[f39])).
% 1.94/1.42 thf(f39,plain,(
% 1.94/1.42 ~(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))))))))),
% 1.94/1.42 inference(rectify,[status(thm)],[f30])).
% 1.94/1.42 thf(f30,negated_conjecture,(
% 1.94/1.42 ~(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))))))))),
% 1.94/1.42 inference(negated_conjecture,[status(cth)],[f29])).
% 1.94/1.42 thf(f29,conjecture,(
% 1.94/1.42 (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))))))))),
% 1.94/1.42 file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',t69_zfmisc_1)).
% 1.94/1.42 thf(f271,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)) | ($false = (eiw_di @ X2 @ mactual)) | ($true = (in @ X1 @ X2 @ mactual)) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.94/1.42 inference(not_proxy_clausification,[status(thm)],[f268])).
% 1.94/1.42 thf(f268,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)) | ($false = (eiw_di @ X2 @ mactual)) | ($false = (~ (in @ X1 @ X2 @ mactual)))) )),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f267])).
% 1.94/1.42 thf(f267,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ mactual)) | ($false = (eiw_di @ X1 @ mactual)) | ((qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual) = (~ (in @ X1 @ X2 @ mactual)))) )),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f266])).
% 1.94/1.42 thf(f266,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($false = (eiw_di @ X2 @ mactual)) | ($true = ((~ (in @ X1 @ X2 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual)))) )),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f265])).
% 1.94/1.42 thf(f265,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = ((eiw_di @ X2 @ mactual) => ((~ (in @ X1 @ X2 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ (singleton @ X1) @ mactual))))) )),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f264])).
% 1.94/1.42 thf(f264,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((~ (in @ X1 @ Y0 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ (singleton @ X1) @ mactual)))) @ X2)) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.94/1.42 inference(pi_clausification,[status(thm)],[f263])).
% 1.94/1.42 thf(f263,plain,(
% 1.94/1.42 ( ! [X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((~ (in @ X1 @ Y0 @ mactual)) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ (singleton @ X1) @ mactual))))))) )),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f262])).
% 1.94/1.42 thf(f262,plain,(
% 1.94/1.42 ( ! [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)))))))) )),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f261])).
% 1.94/1.42 thf(f261,plain,(
% 1.94/1.42 ( ! [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))) )),
% 1.94/1.42 inference(pi_clausification,[status(thm)],[f260])).
% 1.94/1.42 thf(f260,plain,(
% 1.94/1.42 ((!! @ $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)))))))) = $true)),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f131])).
% 1.94/1.42 thf(f131,plain,(
% 1.94/1.42 ($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) @ (singleton @ Y0)) @ ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: (~ (Y2 @ Y3))))) @ (in @ Y0 @ Y1)))))))))),
% 1.94/1.42 inference(definition_unfolding,[status(thm)],[f107,f119,f115,f115,f117,f95])).
% 1.94/1.42 thf(f95,plain,(
% 1.94/1.42 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.94/1.42 inference(cnf_transformation,[status(thm)],[f66])).
% 1.94/1.42 thf(f66,plain,(
% 1.94/1.42 (mnot = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (~ (Y0 @ Y1))))))),
% 1.94/1.42 inference(fool_elimination,[status(thm)],[f65])).
% 1.94/1.42 thf(f65,plain,(
% 1.94/1.42 (mnot = (^[X0 : mworld > $o, X1 : mworld] : (~(X0 @ X1))))),
% 1.94/1.42 inference(rectify,[status(thm)],[f2])).
% 1.94/1.42 thf(f2,axiom,(
% 1.94/1.42 (mnot = (^[X1 : mworld > $o, X2 : mworld] : (~(X1 @ X2))))),
% 1.94/1.42 file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',mnot_def)).
% 1.94/1.42 thf(f117,plain,(
% 1.94/1.42 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 1.94/1.42 inference(cnf_transformation,[status(thm)],[f52])).
% 1.94/1.42 thf(f52,plain,(
% 1.94/1.42 (mequiv = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) = (Y0 @ Y2))))))))),
% 1.94/1.42 inference(fool_elimination,[status(thm)],[f51])).
% 1.94/1.42 thf(f51,plain,(
% 1.94/1.42 (mequiv = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) <=> (X0 @ X2))))),
% 1.94/1.42 inference(rectify,[status(thm)],[f6])).
% 1.94/1.42 thf(f6,axiom,(
% 1.94/1.42 (mequiv = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) <=> (X1 @ X2))))),
% 1.94/1.42 file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',mequiv_def)).
% 1.94/1.42 thf(f107,plain,(
% 1.94/1.42 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.94/1.42 inference(cnf_transformation,[status(thm)],[f46])).
% 1.94/1.42 thf(f46,plain,(
% 1.94/1.42 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ (singleton @ Y0)) @ (mnot @ (in @ Y0 @ Y1)))))))))),
% 1.94/1.42 inference(fool_elimination,[status(thm)],[f45])).
% 1.94/1.42 thf(f45,plain,(
% 1.94/1.42 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ (singleton @ X0)) @ (mnot @ (in @ X0 @ X1))))))))),
% 1.94/1.42 inference(rectify,[status(thm)],[f25])).
% 1.94/1.42 thf(f25,axiom,(
% 1.94/1.42 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ (singleton @ X1)) @ (mnot @ (in @ X1 @ X3))))))))),
% 1.94/1.42 file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',l34_zfmisc_1)).
% 1.94/1.42 thf(f392,plain,(
% 1.94/1.42 ($false = (in @ sK4 @ sK5 @ mactual)) | ~spl1_8),
% 1.94/1.42 inference(avatar_component_clause,[status(thm)],[f390])).
% 1.94/1.42 thf(f390,definition,(
% 1.94/1.42 spl1_8 <=> ($false = (in @ sK4 @ sK5 @ mactual))),
% 1.94/1.42 introduced(definition,[new_symbols(naming,[spl1_8])],[avatar_definition])).
% 1.94/1.42 thf(f436,plain,(
% 1.94/1.42 ~spl1_7),
% 1.94/1.42 inference(avatar_contradiction_clause,[status(thm)],[f435])).
% 1.94/1.42 thf(f435,plain,(
% 1.94/1.42 $false | ~spl1_7),
% 1.94/1.42 inference(trivial_inequality_removal,[status(thm)],[f428])).
% 1.94/1.42 thf(f428,plain,(
% 1.94/1.42 ($true = $false) | ~spl1_7),
% 1.94/1.42 inference(superposition,[status(thm)],[f388,f215])).
% 1.94/1.42 thf(f215,plain,(
% 1.94/1.42 ($true = (eiw_di @ sK4 @ mactual))),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f213])).
% 1.94/1.42 thf(f388,plain,(
% 1.94/1.42 ($false = (eiw_di @ sK4 @ mactual)) | ~spl1_7),
% 1.94/1.42 inference(avatar_component_clause,[status(thm)],[f386])).
% 1.94/1.42 thf(f424,plain,(
% 1.94/1.42 ~spl1_6),
% 1.94/1.42 inference(avatar_contradiction_clause,[status(thm)],[f423])).
% 1.94/1.42 thf(f423,plain,(
% 1.94/1.42 $false | ~spl1_6),
% 1.94/1.42 inference(trivial_inequality_removal,[status(thm)],[f416])).
% 1.94/1.42 thf(f416,plain,(
% 1.94/1.42 ($true = $false) | ~spl1_6),
% 1.94/1.42 inference(superposition,[status(thm)],[f384,f219])).
% 1.94/1.42 thf(f219,plain,(
% 1.94/1.42 ($true = (eiw_di @ sK5 @ mactual))),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f217])).
% 1.94/1.42 thf(f384,plain,(
% 1.94/1.42 ($false = (eiw_di @ sK5 @ mactual)) | ~spl1_6),
% 1.94/1.42 inference(avatar_component_clause,[status(thm)],[f382])).
% 1.94/1.42 thf(f402,plain,(
% 1.94/1.42 spl1_6 | spl1_8 | spl1_7),
% 1.94/1.42 inference(avatar_split_clause,[status(thm)],[f376,f386,f390,f382])).
% 1.94/1.42 thf(f376,plain,(
% 1.94/1.42 ($false = (eiw_di @ sK5 @ mactual)) | ($false = (in @ sK4 @ sK5 @ mactual)) | ($false = (eiw_di @ sK4 @ mactual))),
% 1.94/1.42 inference(trivial_inequality_removal,[status(thm)],[f369])).
% 1.94/1.42 thf(f369,plain,(
% 1.94/1.42 ($false = (in @ sK4 @ sK5 @ mactual)) | ($false = (eiw_di @ sK4 @ mactual)) | ($true = $false) | ($false = (eiw_di @ sK5 @ mactual))),
% 1.94/1.42 inference(superposition,[status(thm)],[f186,f220])).
% 1.94/1.42 thf(f220,plain,(
% 1.94/1.42 ($false = (qmltpeq @ (set_difference @ (singleton @ sK4) @ sK5) @ empty_set @ mactual))),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f218])).
% 1.94/1.42 thf(f186,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($true = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual)) | ($false = (eiw_di @ X2 @ mactual)) | ($false = (in @ X1 @ X2 @ mactual)) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f185])).
% 1.94/1.42 thf(f185,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X2 @ mactual)) | ((qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual) = (in @ X1 @ X2 @ mactual)) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f184])).
% 1.94/1.42 thf(f184,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ mactual)) | (((in @ X1 @ X2 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual)) = $true) | ($false = (eiw_di @ X2 @ mactual))) )),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f183])).
% 1.94/1.42 thf(f183,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : (($true = ((eiw_di @ X2 @ mactual) => ((in @ X1 @ X2 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ X2) @ empty_set @ mactual)))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f182])).
% 1.94/1.42 thf(f182,plain,(
% 1.94/1.42 ( ! [X2 : $i,X1 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((in @ X1 @ Y0 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ empty_set @ mactual)))) @ X2) = $true) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.94/1.42 inference(pi_clausification,[status(thm)],[f181])).
% 1.94/1.42 thf(f181,plain,(
% 1.94/1.42 ( ! [X1 : $i] : (($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => ((in @ X1 @ Y0 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ X1) @ Y0) @ empty_set @ mactual)))))) | ($false = (eiw_di @ X1 @ mactual))) )),
% 1.94/1.42 inference(binary_proxy_clausification,[status(thm)],[f180])).
% 1.94/1.42 thf(f180,plain,(
% 1.94/1.42 ( ! [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)))))))) )),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f179])).
% 1.94/1.42 thf(f179,plain,(
% 1.94/1.42 ( ! [X1 : $i] : (($true = ((^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((in @ Y0 @ Y1 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual))))))) @ X1))) )),
% 1.94/1.42 inference(pi_clausification,[status(thm)],[f178])).
% 1.94/1.42 thf(f178,plain,(
% 1.94/1.42 ($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ mactual) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ mactual) => ((in @ Y0 @ Y1 @ mactual) = (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set @ mactual)))))))))),
% 1.94/1.42 inference(beta_eta_normalization,[status(thm)],[f134])).
% 1.94/1.42 thf(f134,plain,(
% 1.94/1.42 ($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 > $o]: ((^[Y4 : mworld]: ((Y3 @ Y4) = (Y2 @ Y4))))))) @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 1.94/1.42 inference(definition_unfolding,[status(thm)],[f110,f119,f115,f115,f117])).
% 1.94/1.42 thf(f110,plain,(
% 1.94/1.42 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 1.94/1.42 inference(cnf_transformation,[status(thm)],[f76])).
% 1.94/1.42 thf(f76,plain,(
% 1.94/1.42 ($true = (mlocal @ (mforall_di @ (^[Y0 : $i]: (mforall_di @ (^[Y1 : $i]: (mequiv @ (qmltpeq @ (set_difference @ (singleton @ Y0) @ Y1) @ empty_set) @ (in @ Y0 @ Y1))))))))),
% 1.94/1.42 inference(fool_elimination,[status(thm)],[f75])).
% 1.94/1.42 thf(f75,plain,(
% 1.94/1.42 (mlocal @ (mforall_di @ (^[X0 : $i] : (mforall_di @ (^[X1 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X0) @ X1) @ empty_set) @ (in @ X0 @ X1)))))))),
% 1.94/1.42 inference(rectify,[status(thm)],[f26])).
% 1.94/1.42 thf(f26,axiom,(
% 1.94/1.42 (mlocal @ (mforall_di @ (^[X1 : $i] : (mforall_di @ (^[X3 : $i] : (mequiv @ (qmltpeq @ (set_difference @ (singleton @ X1) @ X3) @ empty_set) @ (in @ X1 @ X3)))))))),
% 1.94/1.42 file('/export/starexec/sandbox/tmp/tmp.e1jkKrXUvf/DTF2THF_4949.p',l36_zfmisc_1)).
% 1.94/1.42 % SZS output end Proof for DTF2THF_4949
% 1.94/1.42 % (5057)------------------------------
% 1.94/1.42 % (5057)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.94/1.42 % (5057)Termination reason: Refutation
% 1.94/1.42
% 1.94/1.42 % (5057)Memory used [KB]: 6140
% 1.94/1.42 % (5057)Time elapsed: 0.028 s
% 1.94/1.42 % (5057)Instructions burned: 79 (million)
% 1.94/1.42 % (5057)------------------------------
% 1.94/1.42 % (5057)------------------------------
% 1.94/1.42 % (5056)Success in time 0.036 s
%------------------------------------------------------------------------------