%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO889^16 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n016.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 09:55:07 AM UTC 2026
% Result : Theorem 1.95s 1.54s
% Output : Refutation 1.95s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 12
% Syntax : Number of formulae : 104 ( 53 unt; 0 typ; 4 def)
% Number of atoms : 799 ( 161 equ; 0 cnn)
% Maximal formula atoms : 17 ( 7 avg)
% Number of connectives : 1172 ( 31 ~; 101 |; 78 &; 849 @)
% ( 4 <=>; 41 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 23 usr; 11 con; 0-3 aty)
% ( 25 !!; 43 ??; 0 @@+; 0 @@-)
% Number of variables : 250 ( 185 ^; 61 !; 4 ?; 250 :)
% 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_15,type,
a: $i > mworld > $o ).
thf(func_def_16,type,
b: $i > mworld > $o ).
thf(func_def_30,type,
sK0: mworld > $i ).
thf(func_def_33,type,
sK2: mworld > $i > mworld ).
thf(func_def_34,type,
sK3: mworld ).
thf(f368,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f234,f244,f335,f343,f367]) ).
thf(f367,plain,
( spl1_6
| spl1_13
| ~ spl1_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f366]) ).
thf(f366,plain,
( $false
| spl1_6
| spl1_13
| ~ spl1_14 ),
inference(subsumption_resolution,[status(thm)],[f365,f328]) ).
thf(f328,plain,
( ( $false
!= ( eiw_di @ sK4 @ sK3 ) )
| spl1_13 ),
inference(avatar_component_clause,[status(thm)],[f327]) ).
thf(f327,definition,
( spl1_13
<=> ( $false
= ( eiw_di @ sK4 @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_13])],[avatar_definition]) ).
thf(f365,plain,
( ( $false
= ( eiw_di @ sK4 @ sK3 ) )
| spl1_6
| ~ spl1_14 ),
inference(subsumption_resolution,[status(thm)],[f358,f228]) ).
thf(f228,plain,
( ( $false
!= ( mrel @ mactual @ sK3 ) )
| spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f227]) ).
thf(f227,definition,
( spl1_6
<=> ( $false
= ( mrel @ mactual @ sK3 ) ) ),
introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition]) ).
thf(f358,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( eiw_di @ sK4 @ sK3 ) )
| ~ spl1_14 ),
inference(trivial_inequality_removal,[status(thm)],[f354]) ).
thf(f354,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ sK4 @ sK3 ) )
| ~ spl1_14 ),
inference(superposition,[status(thm)],[f333,f84]) ).
thf(f84,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( mrel @ X1 @ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $true
= ( ( mrel @ X1 @ ( sK2 @ X1 @ X2 ) )
& ( b @ X2 @ ( sK2 @ X1 @ X2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f81]) ).
thf(f81,plain,
! [X2: $i,X1: mworld] :
( ( $true
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 ) )
@ ( sK2 @ X1 @ X2 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(sigma_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X2: $i,X1: mworld] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 ) ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f79]) ).
thf(f79,plain,
! [X2: $i,X1: mworld] :
( ( ( ( eiw_di @ X2 @ X1 )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 ) ) ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f78]) ).
thf(f78,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) )
@ X2 )
= $true ) ),
inference(pi_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X1: mworld] :
( ( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( !! @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
=> ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( $true
!= ( ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( !! @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
=> ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 ) ) ) ) ) ) )
& ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) )
=> ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 )
& ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f69]) ).
thf(f69,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( a @ Y0 ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ ( b @ Y0 ) ) ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( ?? @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
& ( Y1 @ Y3 ) ) )
@ ( ^ [Y1: mworld > $o,Y2: mworld > $o,Y3: mworld] :
( ( Y2 @ Y3 )
& ( Y1 @ Y3 ) )
@ ( a @ Y0 )
@ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f67,f55,f64,f60,f68,f66,f56,f56,f63,f68,f68,f66,f68,f60]) ).
thf(f63,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( mforall_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( !! @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
=> ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
! [X2: $i] :
( ( eiw_di @ X2 @ X1 )
=> ( X0 @ X2 @ X1 ) ) )
= mforall_di ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
! [X6: $i] :
( ( eiw_di @ X6 @ X2 )
=> ( X1 @ X6 @ X2 ) ) )
= mforall_di ),
file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mforall_di_def) ).
thf(f56,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mbox_def) ).
thf(f66,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f40]) ).
thf(f40,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( eiw_di @ X2 @ X1 )
& ( X0 @ X2 @ X1 ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,axiom,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X6: $i] :
( ( eiw_di @ X6 @ X2 )
& ( X1 @ X6 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mexists_di_def) ).
thf(f68,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f36]) ).
thf(f36,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( X0 @ X2 )
& ( mrel @ X1 @ X2 ) ) )
= mdia ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( X0 @ X4 )
& ( mrel @ X2 @ X4 ) ) )
= mdia ),
file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mdia_def) ).
thf(f60,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f46]) ).
thf(f46,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f45]) ).
thf(f45,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X3 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mand_def) ).
thf(f64,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
( mimplies
= ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( mimplies
= ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mimplies_def) ).
thf(f55,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mlocal_def) ).
thf(f67,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( a @ Y0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( b @ Y0 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( mand @ ( a @ Y0 ) @ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( a @ Y0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( b @ Y0 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( mand @ ( a @ Y0 ) @ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(flattening,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( a @ Y0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [Y0: $i] : ( mdia @ ( b @ Y0 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( mand @ ( a @ Y0 ) @ ( b @ Y0 ) ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
~ ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( a @ X0 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X1: $i] : ( mdia @ ( b @ X1 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X2: $i] : ( mdia @ ( mand @ ( a @ X2 ) @ ( b @ X2 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [X6: $i] : ( mbox @ ( a @ X6 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] : ( mdia @ ( b @ X6 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X6: $i] : ( mdia @ ( mand @ ( a @ X6 ) @ ( b @ X6 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f15,conjecture,
( mlocal
@ ( mimplies
@ ( mand
@ ( mdia
@ ( mexists_di
@ ^ [X6: $i] : ( mbox @ ( a @ X6 ) ) ) )
@ ( mbox
@ ( mforall_di
@ ^ [X6: $i] : ( mdia @ ( b @ X6 ) ) ) ) )
@ ( mdia
@ ( mexists_di
@ ^ [X6: $i] : ( mdia @ ( mand @ ( a @ X6 ) @ ( b @ X6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',con) ).
thf(f333,plain,
( ( $false
= ( mrel @ sK3 @ ( sK2 @ sK3 @ sK4 ) ) )
| ~ spl1_14 ),
inference(avatar_component_clause,[status(thm)],[f331]) ).
thf(f331,definition,
( spl1_14
<=> ( $false
= ( mrel @ sK3 @ ( sK2 @ sK3 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_14])],[avatar_definition]) ).
thf(f343,plain,
~ spl1_13,
inference(avatar_contradiction_clause,[status(thm)],[f342]) ).
thf(f342,plain,
( $false
| ~ spl1_13 ),
inference(trivial_inequality_removal,[status(thm)],[f336]) ).
thf(f336,plain,
( ( $false = $true )
| ~ spl1_13 ),
inference(superposition,[status(thm)],[f329,f91]) ).
thf(f91,plain,
( $true
= ( eiw_di @ sK4 @ sK3 ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f90,plain,
( $true
= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( a @ sK4 @ Y0 ) ) )
& ( eiw_di @ sK4 @ sK3 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f89]) ).
thf(f89,plain,
( $true
= ( ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK3 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ sK3 ) )
@ sK4 ) ),
inference(sigma_clausification,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK3 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ sK3 ) ) )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f86,plain,
( $true
= ( ( mrel @ mactual @ sK3 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ sK3 @ Y1 )
=> ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ sK3 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f85]) ).
thf(f85,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) )
@ sK3 )
= $true ),
inference(sigma_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
( $true
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
=> ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f72]) ).
thf(f329,plain,
( ( $false
= ( eiw_di @ sK4 @ sK3 ) )
| ~ spl1_13 ),
inference(avatar_component_clause,[status(thm)],[f327]) ).
thf(f335,plain,
( spl1_14
| spl1_13
| spl1_6
| ~ spl1_7 ),
inference(avatar_split_clause,[status(thm)],[f324,f231,f227,f327,f331]) ).
thf(f231,definition,
( spl1_7
<=> ! [X0: $i,X1: $i] :
( ( ( a @ X1 @ ( sK2 @ sK3 @ X0 ) )
= $false )
| ( $false
= ( b @ X1 @ ( sK2 @ sK3 @ X0 ) ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false
= ( eiw_di @ X1 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition]) ).
thf(f324,plain,
( ( $false
= ( mrel @ sK3 @ ( sK2 @ sK3 @ sK4 ) ) )
| ( $false
= ( eiw_di @ sK4 @ sK3 ) )
| spl1_6
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f323]) ).
thf(f323,plain,
( ( $false
= ( mrel @ sK3 @ ( sK2 @ sK3 @ sK4 ) ) )
| ( $false = $true )
| ( $false
= ( eiw_di @ sK4 @ sK3 ) )
| spl1_6
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f95,f321]) ).
thf(f321,plain,
( ! [X0: $i] :
( ( $false
= ( a @ X0 @ ( sK2 @ sK3 @ X0 ) ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) ) )
| spl1_6
| ~ spl1_7 ),
inference(subsumption_resolution,[status(thm)],[f320,f228]) ).
thf(f320,plain,
( ! [X0: $i] :
( ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false
= ( a @ X0 @ ( sK2 @ sK3 @ X0 ) ) )
| ( $false
= ( mrel @ mactual @ sK3 ) ) )
| ~ spl1_7 ),
inference(trivial_inequality_removal,[status(thm)],[f319]) ).
thf(f319,plain,
( ! [X0: $i] :
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( a @ X0 @ ( sK2 @ sK3 @ X0 ) ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false = $true ) )
| ~ spl1_7 ),
inference(duplicate_literal_removal,[status(thm)],[f316]) ).
thf(f316,plain,
( ! [X0: $i] :
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false
= ( a @ X0 @ ( sK2 @ sK3 @ X0 ) ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false = $true ) )
| ~ spl1_7 ),
inference(superposition,[status(thm)],[f83,f232]) ).
thf(f232,plain,
( ! [X0: $i,X1: $i] :
( ( $false
= ( b @ X1 @ ( sK2 @ sK3 @ X0 ) ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( ( a @ X1 @ ( sK2 @ sK3 @ X0 ) )
= $false )
| ( $false
= ( eiw_di @ X1 @ sK3 ) ) )
| ~ spl1_7 ),
inference(avatar_component_clause,[status(thm)],[f231]) ).
thf(f83,plain,
! [X2: $i,X1: mworld] :
( ( ( b @ X2 @ ( sK2 @ X1 @ X2 ) )
= $true )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f82]) ).
thf(f95,plain,
! [X1: mworld] :
( ( $true
= ( a @ sK4 @ X1 ) )
| ( $false
= ( mrel @ sK3 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f94]) ).
thf(f94,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ sK3 @ X1 )
=> ( a @ sK4 @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f93]) ).
thf(f93,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( a @ sK4 @ Y0 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f92]) ).
thf(f92,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ sK3 @ Y0 )
=> ( a @ sK4 @ Y0 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f90]) ).
thf(f244,plain,
~ spl1_6,
inference(avatar_contradiction_clause,[status(thm)],[f243]) ).
thf(f243,plain,
( $false
| ~ spl1_6 ),
inference(trivial_inequality_removal,[status(thm)],[f237]) ).
thf(f237,plain,
( ( $false = $true )
| ~ spl1_6 ),
inference(superposition,[status(thm)],[f88,f229]) ).
thf(f229,plain,
( ( $false
= ( mrel @ mactual @ sK3 ) )
| ~ spl1_6 ),
inference(avatar_component_clause,[status(thm)],[f227]) ).
thf(f88,plain,
( ( mrel @ mactual @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f86]) ).
thf(f234,plain,
( spl1_7
| spl1_6 ),
inference(avatar_split_clause,[status(thm)],[f221,f227,f231]) ).
thf(f221,plain,
! [X0: $i,X1: $i] :
( ( ( a @ X1 @ ( sK2 @ sK3 @ X0 ) )
= $false )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false
= ( b @ X1 @ ( sK2 @ sK3 @ X0 ) ) )
| ( $false
= ( eiw_di @ X1 @ sK3 ) )
| ( $false
= ( mrel @ mactual @ sK3 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f219]) ).
thf(f219,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( eiw_di @ X1 @ sK3 ) )
| ( $false
= ( b @ X1 @ ( sK2 @ sK3 @ X0 ) ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false
= ( mrel @ mactual @ sK3 ) )
| ( $false = $true )
| ( ( a @ X1 @ ( sK2 @ sK3 @ X0 ) )
= $false ) ),
inference(superposition,[status(thm)],[f84,f122]) ).
thf(f122,plain,
! [X0: $i,X1: mworld] :
( ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) )
| ( $false
= ( a @ X0 @ X1 ) )
| ( $false
= ( b @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
! [X0: $i,X1: mworld] :
( ( $false = $true )
| ( $false
= ( mrel @ sK3 @ X1 ) )
| ( $false
= ( b @ X0 @ X1 ) )
| ( $false
= ( a @ X0 @ X1 ) )
| ( $false
= ( eiw_di @ X0 @ sK3 ) ) ),
inference(superposition,[status(thm)],[f88,f105]) ).
thf(f105,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) )
| ( $false
= ( b @ X2 @ X3 ) )
| ( $false
= ( a @ X2 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f104]) ).
thf(f104,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ( b @ X2 @ X3 )
& ( a @ X2 @ X3 ) ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( mrel @ X1 @ X3 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f103]) ).
thf(f103,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) )
| ( $false
= ( ( mrel @ X1 @ X3 )
& ( b @ X2 @ X3 )
& ( a @ X2 @ X3 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f102]) ).
thf(f102,plain,
! [X2: $i,X3: mworld,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 )
& ( a @ X2 @ Y0 ) )
@ X3 ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f101]) ).
thf(f101,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 )
& ( a @ X2 @ Y0 ) ) ) )
| ( $false
= ( eiw_di @ X2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f100]) ).
thf(f100,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ X1 @ Y0 )
& ( b @ X2 @ Y0 )
& ( a @ X2 @ Y0 ) ) )
& ( eiw_di @ X2 @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f99]) ).
thf(f99,plain,
! [X2: $i,X1: mworld] :
( ( $false
= ( ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 )
& ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ X1 ) )
@ X2 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(pi_clausification,[status(thm)],[f98]) ).
thf(f98,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 )
& ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f97]) ).
thf(f97,plain,
! [X1: mworld] :
( $false
= ( ( mrel @ mactual @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ X1 @ Y1 )
& ( b @ Y0 @ Y1 )
& ( a @ Y0 @ Y1 ) ) )
& ( eiw_di @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f96]) ).
thf(f96,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 )
& ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( ?? @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y0 @ Y2 )
& ( b @ Y1 @ Y2 )
& ( a @ Y1 @ Y2 ) ) )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO889^16 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.20/0.37 % Computer : n016.cluster.edu
% 0.20/0.37 % Model : x86_64 x86_64
% 0.20/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.20/0.37 % Memory : 8042.1875MB
% 0.20/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.37 % CPULimit : 300
% 0.20/0.37 % WCLimit : 300
% 0.20/0.37 % DateTime : Tue Feb 24 14:53:36 EST 2026
% 0.20/0.37 % CPUTime :
% 0.20/0.37 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.29/0.47 ---- Original DTF file ---
% 0.29/0.47 thf(spec,logic,$$dhol).
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 % File : SYO889^16 : TPTP v9.2.1. Released v8.1.0.
% 0.29/0.47 % Domain : Syntactic
% 0.29/0.47 % Problem : Fitting and Mendelsohn problem
% 0.29/0.47 % Version : [BP13] axioms.
% 0.29/0.47 % English :
% 0.29/0.47
% 0.29/0.47 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.29/0.47 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.29/0.47 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.29/0.47 % Source : [TPTP]
% 0.29/0.47 % Names : SYM028+1 [QMLTP]
% 0.29/0.47
% 0.29/0.47 % Status : Theorem
% 0.29/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0
% 0.29/0.47 % Syntax : Number of formulae : 31 ( 12 unt; 16 typ; 10 def)
% 0.29/0.47 % Number of atoms : 49 ( 10 equ; 0 cnn)
% 0.29/0.47 % Maximal formula atoms : 17 ( 3 avg)
% 0.29/0.47 % Number of connectives : 73 ( 1 ~; 1 |; 5 &; 60 @)
% 0.29/0.47 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.29/0.47 % Maximal formula depth : 11 ( 3 avg)
% 0.29/0.47 % Number of types : 3 ( 1 usr)
% 0.29/0.47 % Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% 0.29/0.47 % Number of symbols : 16 ( 15 usr; 1 con; 0-3 aty)
% 0.29/0.47 % Number of variables : 39 ( 26 ^; 10 !; 3 ?; 39 :)
% 0.29/0.47 % SPC : TH0_THM_EQU_NAR
% 0.29/0.47
% 0.29/0.47 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.29/0.47 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.29/0.47 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.29/0.47 % $modal == [$constants == $rigid,$quantification == $cumulative,
% 0.29/0.47 % $modalities == $modal_system_S4].
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 thf(mworld,type,
% 0.29/0.47 mworld: $tType ).
% 0.29/0.47
% 0.29/0.47 thf(mrel_type,type,
% 0.29/0.47 mrel: mworld > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mactual_type,type,
% 0.29/0.47 mactual: mworld ).
% 0.29/0.47
% 0.29/0.47 thf(mlocal_type,type,
% 0.29/0.47 mlocal: ( mworld > $o ) > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mlocal_def,definition,
% 0.29/0.47 ( mlocal
% 0.29/0.47 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mnot_type,type,
% 0.29/0.47 mnot: ( mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mand_type,type,
% 0.29/0.47 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mor_type,type,
% 0.29/0.47 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mimplies_type,type,
% 0.29/0.47 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mequiv_type,type,
% 0.29/0.47 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mnot_def,definition,
% 0.29/0.47 ( mnot
% 0.29/0.47 = ( ^ [A: mworld > $o,W: mworld] :
% 0.29/0.47 ~ ( A @ W ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mand_def,definition,
% 0.29/0.47 ( mand
% 0.29/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.47 ( ( A @ W )
% 0.29/0.47 & ( B @ W ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mor_def,definition,
% 0.29/0.47 ( mor
% 0.29/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.47 ( ( A @ W )
% 0.29/0.47 | ( B @ W ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mimplies_def,definition,
% 0.29/0.47 ( mimplies
% 0.29/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.47 ( ( A @ W )
% 0.29/0.47 => ( B @ W ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mequiv_def,definition,
% 0.29/0.47 ( mequiv
% 0.29/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.29/0.47 ( ( A @ W )
% 0.29/0.47 <=> ( B @ W ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mbox_type,type,
% 0.29/0.47 mbox: ( mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mbox_def,definition,
% 0.29/0.47 ( mbox
% 0.29/0.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.47 ! [V: mworld] :
% 0.29/0.47 ( ( mrel @ W @ V )
% 0.29/0.47 => ( Phi @ V ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mdia_type,type,
% 0.29/0.47 mdia: ( mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mdia_def,definition,
% 0.29/0.47 ( mdia
% 0.29/0.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.29/0.47 ? [V: mworld] :
% 0.29/0.47 ( ( mrel @ W @ V )
% 0.29/0.47 & ( Phi @ V ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mrel_reflexive,axiom,
% 0.29/0.47 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.29/0.47
% 0.29/0.47 thf(mrel_transitive,axiom,
% 0.29/0.47 ! [W: mworld,V: mworld,U: mworld] :
% 0.29/0.47 ( ( ( mrel @ W @ V )
% 0.29/0.47 & ( mrel @ V @ U ) )
% 0.29/0.47 => ( mrel @ W @ U ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(eiw_di_type,type,
% 0.29/0.47 eiw_di: $i > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(eiw_di_nonempty,axiom,
% 0.29/0.47 ! [W: mworld] :
% 0.29/0.47 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.29/0.47
% 0.29/0.47 thf(eiw_di_cumul,axiom,
% 0.29/0.47 ! [W: mworld,V: mworld,X: $i] :
% 0.29/0.47 ( ( ( eiw_di @ X @ W )
% 0.29/0.47 & ( mrel @ W @ V ) )
% 0.29/0.47 => ( eiw_di @ X @ V ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mforall_di_type,type,
% 0.29/0.47 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mforall_di_def,definition,
% 0.29/0.47 ( mforall_di
% 0.29/0.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.29/0.47 ! [X: $i] :
% 0.29/0.47 ( ( eiw_di @ X @ W )
% 0.29/0.47 => ( A @ X @ W ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(mexists_di_type,type,
% 0.29/0.47 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(mexists_di_def,definition,
% 0.29/0.47 ( mexists_di
% 0.29/0.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.29/0.47 ? [X: $i] :
% 0.29/0.47 ( ( eiw_di @ X @ W )
% 0.29/0.47 & ( A @ X @ W ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 thf(a_decl,type,
% 0.29/0.47 a: $i > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(b_decl,type,
% 0.29/0.47 b: $i > mworld > $o ).
% 0.29/0.47
% 0.29/0.47 thf(con,conjecture,
% 0.29/0.47 ( mlocal
% 0.29/0.47 @ ( mimplies
% 0.29/0.47 @ ( mand
% 0.29/0.47 @ ( mdia
% 0.29/0.47 @ ( mexists_di
% 0.29/0.47 @ ^ [X: $i] : ( mbox @ ( a @ X ) ) ) )
% 0.29/0.47 @ ( mbox
% 0.29/0.47 @ ( mforall_di
% 0.29/0.47 @ ^ [X: $i] : ( mdia @ ( b @ X ) ) ) ) )
% 0.29/0.47 @ ( mdia
% 0.29/0.47 @ ( mexists_di
% 0.29/0.47 @ ^ [X: $i] : ( mdia @ ( mand @ ( a @ X ) @ ( b @ X ) ) ) ) ) ) ) ).
% 0.29/0.47
% 0.29/0.47 %------------------------------------------------------------------------------
% 0.29/0.47 ------------------------
% 1.79/1.47 ---- Embedded in THF ---
% 1.79/1.47 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.79/1.47 %%% Generated on Tue Feb 24 14:53:37 EST 2026
% 1.79/1.47 %%% using '$$dhol' embedding, version 1.3.0.
% 1.79/1.47 %%% Logic specification used:
% 1.79/1.47 %%% thf(spec, logic, $$dhol).
% 1.79/1.47
% 1.79/1.47 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2DTF29688.p
% See solution above
% 1.79/1.47 ------------------------
% 1.79/1.48 ---- Cleaned THF ---
% 1.79/1.49 thf(mworld,type,
% 1.79/1.49 mworld: $tType ).
% 1.79/1.49
% 1.79/1.49 thf(mrel_type,type,
% 1.79/1.49 mrel: mworld > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mactual_type,type,
% 1.79/1.49 mactual: mworld ).
% 1.79/1.49
% 1.79/1.49 thf(mlocal_type,type,
% 1.79/1.49 mlocal: ( mworld > $o ) > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mlocal_def,definition,
% 1.79/1.49 ( mlocal
% 1.79/1.49 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mnot_type,type,
% 1.79/1.49 mnot: ( mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mand_type,type,
% 1.79/1.49 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mor_type,type,
% 1.79/1.49 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mimplies_type,type,
% 1.79/1.49 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mequiv_type,type,
% 1.79/1.49 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mnot_def,definition,
% 1.79/1.49 ( mnot
% 1.79/1.49 = ( ^ [A: mworld > $o,W: mworld] :
% 1.79/1.49 ~ ( A @ W ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mand_def,definition,
% 1.79/1.49 ( mand
% 1.79/1.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.79/1.49 ( ( A @ W )
% 1.79/1.49 & ( B @ W ) ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mor_def,definition,
% 1.79/1.49 ( mor
% 1.79/1.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.79/1.49 ( ( A @ W )
% 1.79/1.49 | ( B @ W ) ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mimplies_def,definition,
% 1.79/1.49 ( mimplies
% 1.79/1.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.79/1.49 ( ( A @ W )
% 1.79/1.49 => ( B @ W ) ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mequiv_def,definition,
% 1.79/1.49 ( mequiv
% 1.79/1.49 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.79/1.49 ( ( A @ W )
% 1.79/1.49 <=> ( B @ W ) ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mbox_type,type,
% 1.79/1.49 mbox: ( mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mbox_def,definition,
% 1.79/1.49 ( mbox
% 1.79/1.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.79/1.49 ! [V: mworld] :
% 1.79/1.49 ( ( mrel @ W @ V )
% 1.79/1.49 => ( Phi @ V ) ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mdia_type,type,
% 1.79/1.49 mdia: ( mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mdia_def,definition,
% 1.79/1.49 ( mdia
% 1.79/1.49 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.79/1.49 ? [V: mworld] :
% 1.79/1.49 ( ( mrel @ W @ V )
% 1.79/1.49 & ( Phi @ V ) ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mrel_reflexive,axiom,
% 1.79/1.49 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.79/1.49
% 1.79/1.49 thf(mrel_transitive,axiom,
% 1.79/1.49 ! [W: mworld,V: mworld,U: mworld] :
% 1.79/1.49 ( ( ( mrel @ W @ V )
% 1.79/1.49 & ( mrel @ V @ U ) )
% 1.79/1.49 => ( mrel @ W @ U ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(eiw_di_type,type,
% 1.79/1.49 eiw_di: $i > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(eiw_di_nonempty,axiom,
% 1.79/1.49 ! [W: mworld] :
% 1.79/1.49 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.79/1.49
% 1.79/1.49 thf(eiw_di_cumul,axiom,
% 1.79/1.49 ! [W: mworld,V: mworld,X: $i] :
% 1.79/1.49 ( ( ( eiw_di @ X @ W )
% 1.79/1.49 & ( mrel @ W @ V ) )
% 1.79/1.49 => ( eiw_di @ X @ V ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mforall_di_type,type,
% 1.79/1.49 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mforall_di_def,definition,
% 1.79/1.49 ( mforall_di
% 1.79/1.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.79/1.49 ! [X: $i] :
% 1.79/1.49 ( ( eiw_di @ X @ W )
% 1.79/1.49 => ( A @ X @ W ) ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(mexists_di_type,type,
% 1.79/1.49 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(mexists_di_def,definition,
% 1.79/1.49 ( mexists_di
% 1.79/1.49 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.79/1.49 ? [X: $i] :
% 1.79/1.49 ( ( eiw_di @ X @ W )
% 1.79/1.49 & ( A @ X @ W ) ) ) ) ).
% 1.79/1.49
% 1.79/1.49 thf(a_decl,type,
% 1.79/1.49 a: $i > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(b_decl,type,
% 1.79/1.49 b: $i > mworld > $o ).
% 1.79/1.49
% 1.79/1.49 thf(con,conjecture,
% 1.79/1.49 ( mlocal
% 1.79/1.49 @ ( mimplies
% 1.79/1.49 @ ( mand
% 1.79/1.49 @ ( mdia
% 1.79/1.49 @ ( mexists_di
% 1.79/1.49 @ ^ [X: $i] : ( mbox @ ( a @ X ) ) ) )
% 1.79/1.49 @ ( mbox
% 1.79/1.49 @ ( mforall_di
% 1.79/1.49 @ ^ [X: $i] : ( mdia @ ( b @ X ) ) ) ) )
% 1.79/1.49 @ ( mdia
% 1.79/1.49 @ ( mexists_di
% 1.79/1.49 @ ^ [X: $i] : ( mdia @ ( mand @ ( a @ X ) @ ( b @ X ) ) ) ) ) ) ) ).
% 1.79/1.49 ------------------------
% 1.95/1.51 % (29790)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_29688 for (2999ds/27Mi)
% 1.95/1.51 % (29794)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_29688 for (2999ds/18Mi)
% 1.95/1.51 % (29788)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_29688 for (2999ds/183Mi)
% 1.95/1.51 % (29789)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_29688 for (2999ds/4Mi)
% 1.95/1.51 % (29793)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_29688 for (2999ds/275Mi)
% 1.95/1.51 % (29791)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_29688 for (2999ds/2Mi)
% 1.95/1.51 % (29792)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_29688 for (2999ds/2Mi)
% 1.95/1.51 % (29791)Instruction limit reached!
% 1.95/1.51 % (29791)------------------------------
% 1.95/1.51 % (29791)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.51 % (29791)Termination reason: Unknown
% 1.95/1.51 % (29791)Termination phase: Property scanning
% 1.95/1.51 % (29792)Instruction limit reached!
% 1.95/1.51 % (29792)------------------------------
% 1.95/1.51 % (29792)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.51
% 1.95/1.51 % (29791)Memory used [KB]: 1023
% 1.95/1.51 % (29791)Time elapsed: 0.003 s
% 1.95/1.51 % (29791)Instructions burned: 3 (million)
% 1.95/1.51 % (29791)------------------------------
% 1.95/1.51 % (29791)------------------------------
% 1.95/1.51 % (29792)Termination reason: Unknown
% 1.95/1.51 % (29792)Termination phase: Property scanning
% 1.95/1.51
% 1.95/1.51 % (29792)Memory used [KB]: 1023
% 1.95/1.51 % (29792)Time elapsed: 0.003 s
% 1.95/1.51 % (29792)Instructions burned: 2 (million)
% 1.95/1.51 % (29792)------------------------------
% 1.95/1.51 % (29792)------------------------------
% 1.95/1.51 % (29789)Instruction limit reached!
% 1.95/1.51 % (29789)------------------------------
% 1.95/1.51 % (29789)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.51 % (29789)Termination reason: Unknown
% 1.95/1.51 % (29789)Termination phase: Property scanning
% 1.95/1.51
% 1.95/1.51 % (29789)Memory used [KB]: 1023
% 1.95/1.51 % (29789)Time elapsed: 0.004 s
% 1.95/1.51 % (29789)Instructions burned: 5 (million)
% 1.95/1.51 % (29789)------------------------------
% 1.95/1.51 % (29789)------------------------------
% 1.95/1.51 % (29793)Refutation not found, incomplete strategy
% 1.95/1.51 % (29793)------------------------------
% 1.95/1.51 % (29793)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.51 % (29793)Termination reason: Refutation not found, incomplete strategy
% 1.95/1.51
% 1.95/1.51
% 1.95/1.51 % (29793)Memory used [KB]: 5500
% 1.95/1.51 % (29793)Time elapsed: 0.005 s
% 1.95/1.51 % (29793)Instructions burned: 6 (million)
% 1.95/1.51 % (29793)------------------------------
% 1.95/1.51 % (29793)------------------------------
% 1.95/1.52 % (29794)Instruction limit reached!
% 1.95/1.52 % (29794)------------------------------
% 1.95/1.52 % (29794)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.52 % (29794)Termination reason: Unknown
% 1.95/1.52 % (29794)Termination phase: Saturation
% 1.95/1.52
% 1.95/1.52 % (29794)Memory used [KB]: 5628
% 1.95/1.52 % (29794)Time elapsed: 0.011 s
% 1.95/1.52 % (29794)Instructions burned: 18 (million)
% 1.95/1.52 % (29794)------------------------------
% 1.95/1.52 % (29794)------------------------------
% 1.95/1.52 % (29790)Instruction limit reached!
% 1.95/1.52 % (29790)------------------------------
% 1.95/1.52 % (29790)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.52 % (29790)Termination reason: Unknown
% 1.95/1.52 % (29790)Termination phase: Saturation
% 1.95/1.52
% 1.95/1.52 % (29790)Memory used [KB]: 5628
% 1.95/1.52 % (29790)Time elapsed: 0.016 s
% 1.95/1.52 % (29790)Instructions burned: 27 (million)
% 1.95/1.52 % (29790)------------------------------
% 1.95/1.52 % (29790)------------------------------
% 1.95/1.52 % (29796)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_29688 for (2999ds/37Mi)
% 1.95/1.52 % (29795)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_29688 for (2999ds/3Mi)
% 1.95/1.52 % (29797)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_29688 for (2999ds/15Mi)
% 1.95/1.53 % (29795)Instruction limit reached!
% 1.95/1.53 % (29795)------------------------------
% 1.95/1.53 % (29795)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.53 % (29795)Termination reason: Unknown
% 1.95/1.53 % (29795)Termination phase: Property scanning
% 1.95/1.53
% 1.95/1.53 % (29795)Memory used [KB]: 1023
% 1.95/1.53 % (29795)Time elapsed: 0.003 s
% 1.95/1.53 % (29795)Instructions burned: 3 (million)
% 1.95/1.53 % (29795)------------------------------
% 1.95/1.53 % (29795)------------------------------
% 1.95/1.53 % (29798)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_29688 for (2999ds/3Mi)
% 1.95/1.53 % (29798)Instruction limit reached!
% 1.95/1.53 % (29798)------------------------------
% 1.95/1.53 % (29798)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.53 % (29798)Termination reason: Unknown
% 1.95/1.53 % (29798)Termination phase: Property scanning
% 1.95/1.53
% 1.95/1.53 % (29798)Memory used [KB]: 1023
% 1.95/1.53 % (29798)Time elapsed: 0.003 s
% 1.95/1.53 % (29798)Instructions burned: 3 (million)
% 1.95/1.53 % (29798)------------------------------
% 1.95/1.53 % (29798)------------------------------
% 1.95/1.53 % (29797)Instruction limit reached!
% 1.95/1.53 % (29797)------------------------------
% 1.95/1.53 % (29797)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.53 % (29799)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_29688 for (2999ds/1041Mi)
% 1.95/1.53 % (29797)Termination reason: Unknown
% 1.95/1.53 % (29797)Termination phase: Saturation
% 1.95/1.53
% 1.95/1.53 % (29797)Memory used [KB]: 5628
% 1.95/1.53 % (29797)Time elapsed: 0.009 s
% 1.95/1.53 % (29797)Instructions burned: 15 (million)
% 1.95/1.53 % (29797)------------------------------
% 1.95/1.53 % (29797)------------------------------
% 1.95/1.54 % (29800)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_29688 for (2999ds/7Mi)
% 1.95/1.54 % (29788)First to succeed.
% 1.95/1.54 % (29800)Instruction limit reached!
% 1.95/1.54 % (29800)------------------------------
% 1.95/1.54 % (29800)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.54 % (29800)Termination reason: Unknown
% 1.95/1.54 % (29800)Termination phase: Saturation
% 1.95/1.54
% 1.95/1.54 % (29800)Memory used [KB]: 1023
% 1.95/1.54 % (29800)Time elapsed: 0.005 s
% 1.95/1.54 % (29800)Instructions burned: 7 (million)
% 1.95/1.54 % (29800)------------------------------
% 1.95/1.54 % (29800)------------------------------
% 1.95/1.54 % (29788)Refutation found. Thanks to Tanya!
% 1.95/1.54 % SZS status Theorem for DTF2THF_29688
% 1.95/1.54 % SZS output start Proof for DTF2THF_29688
% 1.95/1.54 thf(type_def_5, type, mworld: $tType).
% 1.95/1.54 thf(func_def_0, type, mworld: $tType).
% 1.95/1.54 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.95/1.54 thf(func_def_2, type, mactual: mworld).
% 1.95/1.54 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.95/1.54 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.95/1.54 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.95/1.54 thf(func_def_15, type, a: $i > mworld > $o).
% 1.95/1.54 thf(func_def_16, type, b: $i > mworld > $o).
% 1.95/1.54 thf(func_def_30, type, sK0: mworld > $i).
% 1.95/1.54 thf(func_def_33, type, sK2: mworld > $i > mworld).
% 1.95/1.54 thf(func_def_34, type, sK3: mworld).
% 1.95/1.54 thf(f368,plain,(
% 1.95/1.54 $false),
% 1.95/1.54 inference(avatar_sat_refutation,[status(thm)],[f234,f244,f335,f343,f367])).
% 1.95/1.54 thf(f367,plain,(
% 1.95/1.54 spl1_6 | spl1_13 | ~spl1_14),
% 1.95/1.54 inference(avatar_contradiction_clause,[status(thm)],[f366])).
% 1.95/1.54 thf(f366,plain,(
% 1.95/1.54 $false | (spl1_6 | spl1_13 | ~spl1_14)),
% 1.95/1.54 inference(subsumption_resolution,[status(thm)],[f365,f328])).
% 1.95/1.54 thf(f328,plain,(
% 1.95/1.54 ($false != (eiw_di @ sK4 @ sK3)) | spl1_13),
% 1.95/1.54 inference(avatar_component_clause,[status(thm)],[f327])).
% 1.95/1.54 thf(f327,definition,(
% 1.95/1.54 spl1_13 <=> ($false = (eiw_di @ sK4 @ sK3))),
% 1.95/1.54 introduced(definition,[new_symbols(naming,[spl1_13])],[avatar_definition])).
% 1.95/1.54 thf(f365,plain,(
% 1.95/1.54 ($false = (eiw_di @ sK4 @ sK3)) | (spl1_6 | ~spl1_14)),
% 1.95/1.54 inference(subsumption_resolution,[status(thm)],[f358,f228])).
% 1.95/1.54 thf(f228,plain,(
% 1.95/1.54 ($false != (mrel @ mactual @ sK3)) | spl1_6),
% 1.95/1.54 inference(avatar_component_clause,[status(thm)],[f227])).
% 1.95/1.54 thf(f227,definition,(
% 1.95/1.54 spl1_6 <=> ($false = (mrel @ mactual @ sK3))),
% 1.95/1.54 introduced(definition,[new_symbols(naming,[spl1_6])],[avatar_definition])).
% 1.95/1.54 thf(f358,plain,(
% 1.95/1.54 ($false = (mrel @ mactual @ sK3)) | ($false = (eiw_di @ sK4 @ sK3)) | ~spl1_14),
% 1.95/1.54 inference(trivial_inequality_removal,[status(thm)],[f354])).
% 1.95/1.54 thf(f354,plain,(
% 1.95/1.54 ($false = (mrel @ mactual @ sK3)) | ($false = $true) | ($false = (eiw_di @ sK4 @ sK3)) | ~spl1_14),
% 1.95/1.54 inference(superposition,[status(thm)],[f333,f84])).
% 1.95/1.54 thf(f84,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (($true = (mrel @ X1 @ (sK2 @ X1 @ X2))) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.95/1.54 thf(f82,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($true = ((mrel @ X1 @ (sK2 @ X1 @ X2)) & (b @ X2 @ (sK2 @ X1 @ X2))))) )),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f81])).
% 1.95/1.54 thf(f81,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) & (b @ X2 @ Y0))) @ (sK2 @ X1 @ X2))) | ($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.95/1.54 inference(sigma_clausification,[status(thm)],[f80])).
% 1.95/1.54 thf(f80,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) & (b @ X2 @ Y0)))) = $true) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f79])).
% 1.95/1.54 thf(f79,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : ((((eiw_di @ X2 @ X1) => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) & (b @ X2 @ Y0))))) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f78])).
% 1.95/1.54 thf(f78,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) & (b @ Y0 @ Y1)))))) @ X2) = $true)) )),
% 1.95/1.54 inference(pi_clausification,[status(thm)],[f77])).
% 1.95/1.54 thf(f77,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : (($true = (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) & (b @ Y0 @ Y1)))))))) | ($false = (mrel @ mactual @ X1))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.95/1.54 thf(f76,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (!! @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) => (?? @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) & (b @ Y0 @ Y1)))))))))) )),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.95/1.54 thf(f75,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) & (b @ Y1 @ Y2))))))))) @ X1) = $true)) )),
% 1.95/1.54 inference(pi_clausification,[status(thm)],[f74])).
% 1.95/1.54 thf(f74,plain,(
% 1.95/1.54 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) & (b @ Y1 @ Y2)))))))))))),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.95/1.54 thf(f72,plain,(
% 1.95/1.54 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) & (b @ Y1 @ Y2)))))))))) & (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (a @ Y1 @ Y2)))) & (eiw_di @ Y1 @ Y0)))))))))),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.95/1.54 thf(f70,plain,(
% 1.95/1.54 ($true != (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (!! @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) => (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) & (b @ Y1 @ Y2)))))))))) & (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (a @ Y1 @ Y2)))) & (eiw_di @ Y1 @ Y0)))))))) => (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) & ((b @ Y1 @ Y2) & (a @ Y1 @ Y2))))) & (eiw_di @ Y1 @ Y0)))))))))),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f69])).
% 1.95/1.54 thf(f69,plain,(
% 1.95/1.54 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (a @ Y0))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) & (Y1 @ Y3))))))) @ (b @ Y0)))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ Y2 @ Y1))))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (?? @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) & (Y1 @ Y3))))))) @ ((^[Y1 : mworld > $o]: ((^[Y2 : mworld > $o]: ((^[Y3 : mworld]: ((Y2 @ Y3) & (Y1 @ Y3))))))) @ (a @ Y0) @ (b @ Y0)))))))))),
% 1.95/1.54 inference(definition_unfolding,[status(thm)],[f67,f55,f64,f60,f68,f66,f56,f56,f63,f68,f68,f66,f68,f60])).
% 1.95/1.54 thf(f63,plain,(
% 1.95/1.54 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.95/1.54 inference(cnf_transformation,[status(thm)],[f25])).
% 1.95/1.54 thf(f25,plain,(
% 1.95/1.54 (mforall_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (!! @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) => (Y0 @ Y2 @ Y1))))))))),
% 1.95/1.54 inference(fool_elimination,[status(thm)],[f24])).
% 1.95/1.54 thf(f24,plain,(
% 1.95/1.54 ((^[X0 : $i > mworld > $o, X1 : mworld] : (! [X2 : $i] : ((eiw_di @ X2 @ X1) => (X0 @ X2 @ X1)))) = mforall_di)),
% 1.95/1.54 inference(rectify,[status(thm)],[f13])).
% 1.95/1.54 thf(f13,axiom,(
% 1.95/1.54 ((^[X1 : $i > mworld > $o, X2 : mworld] : (! [X6 : $i] : ((eiw_di @ X6 @ X2) => (X1 @ X6 @ X2)))) = mforall_di)),
% 1.95/1.54 file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mforall_di_def)).
% 1.95/1.54 thf(f56,plain,(
% 1.95/1.54 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.95/1.54 inference(cnf_transformation,[status(thm)],[f23])).
% 1.95/1.54 thf(f23,plain,(
% 1.95/1.54 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.95/1.54 inference(fool_elimination,[status(thm)],[f22])).
% 1.95/1.54 thf(f22,plain,(
% 1.95/1.54 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.95/1.54 inference(rectify,[status(thm)],[f7])).
% 1.95/1.54 thf(f7,axiom,(
% 1.95/1.54 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.95/1.54 file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mbox_def)).
% 1.95/1.54 thf(f66,plain,(
% 1.95/1.54 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ Y2 @ Y1))))))))),
% 1.95/1.54 inference(cnf_transformation,[status(thm)],[f41])).
% 1.95/1.54 thf(f41,plain,(
% 1.95/1.54 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ Y2 @ Y1))))))))),
% 1.95/1.54 inference(fool_elimination,[status(thm)],[f40])).
% 1.95/1.54 thf(f40,plain,(
% 1.95/1.54 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((eiw_di @ X2 @ X1) & (X0 @ X2 @ X1)))))),
% 1.95/1.54 inference(rectify,[status(thm)],[f14])).
% 1.95/1.54 thf(f14,axiom,(
% 1.95/1.54 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : ((eiw_di @ X6 @ X2) & (X1 @ X6 @ X2)))))),
% 1.95/1.54 file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mexists_di_def)).
% 1.95/1.54 thf(f68,plain,(
% 1.95/1.54 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.95/1.54 inference(cnf_transformation,[status(thm)],[f37])).
% 1.95/1.54 thf(f37,plain,(
% 1.95/1.54 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.95/1.54 inference(fool_elimination,[status(thm)],[f36])).
% 1.95/1.54 thf(f36,plain,(
% 1.95/1.54 ((^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((X0 @ X2) & (mrel @ X1 @ X2)))) = mdia)),
% 1.95/1.54 inference(rectify,[status(thm)],[f8])).
% 1.95/1.54 thf(f8,axiom,(
% 1.95/1.54 ((^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((X0 @ X4) & (mrel @ X2 @ X4)))) = mdia)),
% 1.95/1.54 file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mdia_def)).
% 1.95/1.54 thf(f60,plain,(
% 1.95/1.54 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.95/1.54 inference(cnf_transformation,[status(thm)],[f46])).
% 1.95/1.54 thf(f46,plain,(
% 1.95/1.54 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.95/1.54 inference(fool_elimination,[status(thm)],[f45])).
% 1.95/1.54 thf(f45,plain,(
% 1.95/1.54 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 1.95/1.54 inference(rectify,[status(thm)],[f3])).
% 1.95/1.54 thf(f3,axiom,(
% 1.95/1.54 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 1.95/1.54 file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mand_def)).
% 1.95/1.54 thf(f64,plain,(
% 1.95/1.54 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.95/1.54 inference(cnf_transformation,[status(thm)],[f35])).
% 1.95/1.54 thf(f35,plain,(
% 1.95/1.54 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 1.95/1.54 inference(fool_elimination,[status(thm)],[f34])).
% 1.95/1.54 thf(f34,plain,(
% 1.95/1.54 (mimplies = (^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))))),
% 1.95/1.54 inference(rectify,[status(thm)],[f5])).
% 1.95/1.54 thf(f5,axiom,(
% 1.95/1.54 (mimplies = (^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))))),
% 1.95/1.54 file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mimplies_def)).
% 1.95/1.54 thf(f55,plain,(
% 1.95/1.54 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.95/1.54 inference(cnf_transformation,[status(thm)],[f44])).
% 1.95/1.54 thf(f44,plain,(
% 1.95/1.54 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.95/1.54 inference(fool_elimination,[status(thm)],[f1])).
% 1.95/1.54 thf(f1,axiom,(
% 1.95/1.54 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.95/1.54 file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',mlocal_def)).
% 1.95/1.54 thf(f67,plain,(
% 1.95/1.54 ($true != (mlocal @ (mimplies @ (mand @ (mdia @ (mexists_di @ (^[Y0 : $i]: (mbox @ (a @ Y0))))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mdia @ (b @ Y0)))))) @ (mdia @ (mexists_di @ (^[Y0 : $i]: (mdia @ (mand @ (a @ Y0) @ (b @ Y0)))))))))),
% 1.95/1.54 inference(cnf_transformation,[status(thm)],[f47])).
% 1.95/1.54 thf(f47,plain,(
% 1.95/1.54 ($true != (mlocal @ (mimplies @ (mand @ (mdia @ (mexists_di @ (^[Y0 : $i]: (mbox @ (a @ Y0))))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mdia @ (b @ Y0)))))) @ (mdia @ (mexists_di @ (^[Y0 : $i]: (mdia @ (mand @ (a @ Y0) @ (b @ Y0)))))))))),
% 1.95/1.54 inference(flattening,[status(thm)],[f33])).
% 1.95/1.54 thf(f33,plain,(
% 1.95/1.54 ~($true = (mlocal @ (mimplies @ (mand @ (mdia @ (mexists_di @ (^[Y0 : $i]: (mbox @ (a @ Y0))))) @ (mbox @ (mforall_di @ (^[Y0 : $i]: (mdia @ (b @ Y0)))))) @ (mdia @ (mexists_di @ (^[Y0 : $i]: (mdia @ (mand @ (a @ Y0) @ (b @ Y0)))))))))),
% 1.95/1.54 inference(fool_elimination,[status(thm)],[f32])).
% 1.95/1.54 thf(f32,plain,(
% 1.95/1.54 ~(mlocal @ (mimplies @ (mand @ (mdia @ (mexists_di @ (^[X0 : $i] : (mbox @ (a @ X0))))) @ (mbox @ (mforall_di @ (^[X1 : $i] : (mdia @ (b @ X1)))))) @ (mdia @ (mexists_di @ (^[X2 : $i] : (mdia @ (mand @ (a @ X2) @ (b @ X2))))))))),
% 1.95/1.54 inference(rectify,[status(thm)],[f16])).
% 1.95/1.54 thf(f16,negated_conjecture,(
% 1.95/1.54 ~(mlocal @ (mimplies @ (mand @ (mdia @ (mexists_di @ (^[X6 : $i] : (mbox @ (a @ X6))))) @ (mbox @ (mforall_di @ (^[X6 : $i] : (mdia @ (b @ X6)))))) @ (mdia @ (mexists_di @ (^[X6 : $i] : (mdia @ (mand @ (a @ X6) @ (b @ X6))))))))),
% 1.95/1.54 inference(negated_conjecture,[status(cth)],[f15])).
% 1.95/1.54 thf(f15,conjecture,(
% 1.95/1.54 (mlocal @ (mimplies @ (mand @ (mdia @ (mexists_di @ (^[X6 : $i] : (mbox @ (a @ X6))))) @ (mbox @ (mforall_di @ (^[X6 : $i] : (mdia @ (b @ X6)))))) @ (mdia @ (mexists_di @ (^[X6 : $i] : (mdia @ (mand @ (a @ X6) @ (b @ X6))))))))),
% 1.95/1.54 file('/export/starexec/sandbox2/tmp/tmp.nWcr6WWSlm/DTF2THF_29688.p',con)).
% 1.95/1.54 thf(f333,plain,(
% 1.95/1.54 ($false = (mrel @ sK3 @ (sK2 @ sK3 @ sK4))) | ~spl1_14),
% 1.95/1.54 inference(avatar_component_clause,[status(thm)],[f331])).
% 1.95/1.54 thf(f331,definition,(
% 1.95/1.54 spl1_14 <=> ($false = (mrel @ sK3 @ (sK2 @ sK3 @ sK4)))),
% 1.95/1.54 introduced(definition,[new_symbols(naming,[spl1_14])],[avatar_definition])).
% 1.95/1.54 thf(f343,plain,(
% 1.95/1.54 ~spl1_13),
% 1.95/1.54 inference(avatar_contradiction_clause,[status(thm)],[f342])).
% 1.95/1.54 thf(f342,plain,(
% 1.95/1.54 $false | ~spl1_13),
% 1.95/1.54 inference(trivial_inequality_removal,[status(thm)],[f336])).
% 1.95/1.54 thf(f336,plain,(
% 1.95/1.54 ($false = $true) | ~spl1_13),
% 1.95/1.54 inference(superposition,[status(thm)],[f329,f91])).
% 1.95/1.54 thf(f91,plain,(
% 1.95/1.54 ($true = (eiw_di @ sK4 @ sK3))),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.95/1.54 thf(f90,plain,(
% 1.95/1.54 ($true = ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (a @ sK4 @ Y0)))) & (eiw_di @ sK4 @ sK3)))),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f89])).
% 1.95/1.54 thf(f89,plain,(
% 1.95/1.54 ($true = ((^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (a @ Y0 @ Y1)))) & (eiw_di @ Y0 @ sK3))) @ sK4))),
% 1.95/1.54 inference(sigma_clausification,[status(thm)],[f87])).
% 1.95/1.54 thf(f87,plain,(
% 1.95/1.54 ((?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (a @ Y0 @ Y1)))) & (eiw_di @ Y0 @ sK3)))) = $true)),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.95/1.54 thf(f86,plain,(
% 1.95/1.54 ($true = ((mrel @ mactual @ sK3) & (?? @ $i @ (^[Y0 : $i]: ((!! @ mworld @ (^[Y1 : mworld]: ((mrel @ sK3 @ Y1) => (a @ Y0 @ Y1)))) & (eiw_di @ Y0 @ sK3))))))),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f85])).
% 1.95/1.54 thf(f85,plain,(
% 1.95/1.54 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (a @ Y1 @ Y2)))) & (eiw_di @ Y1 @ Y0)))))) @ sK3) = $true)),
% 1.95/1.54 inference(sigma_clausification,[status(thm)],[f73])).
% 1.95/1.54 thf(f73,plain,(
% 1.95/1.54 ($true = (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) => (a @ Y1 @ Y2)))) & (eiw_di @ Y1 @ Y0))))))))),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f72])).
% 1.95/1.54 thf(f329,plain,(
% 1.95/1.54 ($false = (eiw_di @ sK4 @ sK3)) | ~spl1_13),
% 1.95/1.54 inference(avatar_component_clause,[status(thm)],[f327])).
% 1.95/1.54 thf(f335,plain,(
% 1.95/1.54 spl1_14 | spl1_13 | spl1_6 | ~spl1_7),
% 1.95/1.54 inference(avatar_split_clause,[status(thm)],[f324,f231,f227,f327,f331])).
% 1.95/1.54 thf(f231,definition,(
% 1.95/1.54 spl1_7 <=> ! [X0 : $i,X1 : $i] : (((a @ X1 @ (sK2 @ sK3 @ X0)) = $false) | ($false = (b @ X1 @ (sK2 @ sK3 @ X0))) | ($false = (eiw_di @ X0 @ sK3)) | ($false = (eiw_di @ X1 @ sK3)))),
% 1.95/1.54 introduced(definition,[new_symbols(naming,[spl1_7])],[avatar_definition])).
% 1.95/1.54 thf(f324,plain,(
% 1.95/1.54 ($false = (mrel @ sK3 @ (sK2 @ sK3 @ sK4))) | ($false = (eiw_di @ sK4 @ sK3)) | (spl1_6 | ~spl1_7)),
% 1.95/1.54 inference(trivial_inequality_removal,[status(thm)],[f323])).
% 1.95/1.54 thf(f323,plain,(
% 1.95/1.54 ($false = (mrel @ sK3 @ (sK2 @ sK3 @ sK4))) | ($false = $true) | ($false = (eiw_di @ sK4 @ sK3)) | (spl1_6 | ~spl1_7)),
% 1.95/1.54 inference(superposition,[status(thm)],[f95,f321])).
% 1.95/1.54 thf(f321,plain,(
% 1.95/1.54 ( ! [X0 : $i] : (($false = (a @ X0 @ (sK2 @ sK3 @ X0))) | ($false = (eiw_di @ X0 @ sK3))) ) | (spl1_6 | ~spl1_7)),
% 1.95/1.54 inference(subsumption_resolution,[status(thm)],[f320,f228])).
% 1.95/1.54 thf(f320,plain,(
% 1.95/1.54 ( ! [X0 : $i] : (($false = (eiw_di @ X0 @ sK3)) | ($false = (a @ X0 @ (sK2 @ sK3 @ X0))) | ($false = (mrel @ mactual @ sK3))) ) | ~spl1_7),
% 1.95/1.54 inference(trivial_inequality_removal,[status(thm)],[f319])).
% 1.95/1.54 thf(f319,plain,(
% 1.95/1.54 ( ! [X0 : $i] : (($false = (mrel @ mactual @ sK3)) | ($false = (a @ X0 @ (sK2 @ sK3 @ X0))) | ($false = (eiw_di @ X0 @ sK3)) | ($false = $true)) ) | ~spl1_7),
% 1.95/1.54 inference(duplicate_literal_removal,[status(thm)],[f316])).
% 1.95/1.54 thf(f316,plain,(
% 1.95/1.54 ( ! [X0 : $i] : (($false = (mrel @ mactual @ sK3)) | ($false = (a @ X0 @ (sK2 @ sK3 @ X0))) | ($false = (eiw_di @ X0 @ sK3)) | ($false = (eiw_di @ X0 @ sK3)) | ($false = (eiw_di @ X0 @ sK3)) | ($false = $true)) ) | ~spl1_7),
% 1.95/1.54 inference(superposition,[status(thm)],[f83,f232])).
% 1.95/1.54 thf(f232,plain,(
% 1.95/1.54 ( ! [X0 : $i,X1 : $i] : (($false = (b @ X1 @ (sK2 @ sK3 @ X0))) | ($false = (eiw_di @ X0 @ sK3)) | ((a @ X1 @ (sK2 @ sK3 @ X0)) = $false) | ($false = (eiw_di @ X1 @ sK3))) ) | ~spl1_7),
% 1.95/1.54 inference(avatar_component_clause,[status(thm)],[f231])).
% 1.95/1.54 thf(f83,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (((b @ X2 @ (sK2 @ X1 @ X2)) = $true) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f82])).
% 1.95/1.54 thf(f95,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : (($true = (a @ sK4 @ X1)) | ($false = (mrel @ sK3 @ X1))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f94])).
% 1.95/1.54 thf(f94,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : (($true = ((mrel @ sK3 @ X1) => (a @ sK4 @ X1)))) )),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f93])).
% 1.95/1.54 thf(f93,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (a @ sK4 @ Y0))) @ X1))) )),
% 1.95/1.54 inference(pi_clausification,[status(thm)],[f92])).
% 1.95/1.54 thf(f92,plain,(
% 1.95/1.54 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ sK3 @ Y0) => (a @ sK4 @ Y0)))))),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f90])).
% 1.95/1.54 thf(f244,plain,(
% 1.95/1.54 ~spl1_6),
% 1.95/1.54 inference(avatar_contradiction_clause,[status(thm)],[f243])).
% 1.95/1.54 thf(f243,plain,(
% 1.95/1.54 $false | ~spl1_6),
% 1.95/1.54 inference(trivial_inequality_removal,[status(thm)],[f237])).
% 1.95/1.54 thf(f237,plain,(
% 1.95/1.54 ($false = $true) | ~spl1_6),
% 1.95/1.54 inference(superposition,[status(thm)],[f88,f229])).
% 1.95/1.54 thf(f229,plain,(
% 1.95/1.54 ($false = (mrel @ mactual @ sK3)) | ~spl1_6),
% 1.95/1.54 inference(avatar_component_clause,[status(thm)],[f227])).
% 1.95/1.54 thf(f88,plain,(
% 1.95/1.54 ((mrel @ mactual @ sK3) = $true)),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f86])).
% 1.95/1.54 thf(f234,plain,(
% 1.95/1.54 spl1_7 | spl1_6),
% 1.95/1.54 inference(avatar_split_clause,[status(thm)],[f221,f227,f231])).
% 1.95/1.54 thf(f221,plain,(
% 1.95/1.54 ( ! [X0 : $i,X1 : $i] : (((a @ X1 @ (sK2 @ sK3 @ X0)) = $false) | ($false = (eiw_di @ X0 @ sK3)) | ($false = (b @ X1 @ (sK2 @ sK3 @ X0))) | ($false = (eiw_di @ X1 @ sK3)) | ($false = (mrel @ mactual @ sK3))) )),
% 1.95/1.54 inference(trivial_inequality_removal,[status(thm)],[f219])).
% 1.95/1.54 thf(f219,plain,(
% 1.95/1.54 ( ! [X0 : $i,X1 : $i] : (($false = (eiw_di @ X1 @ sK3)) | ($false = (b @ X1 @ (sK2 @ sK3 @ X0))) | ($false = (eiw_di @ X0 @ sK3)) | ($false = (mrel @ mactual @ sK3)) | ($false = $true) | ((a @ X1 @ (sK2 @ sK3 @ X0)) = $false)) )),
% 1.95/1.54 inference(superposition,[status(thm)],[f84,f122])).
% 1.95/1.54 thf(f122,plain,(
% 1.95/1.54 ( ! [X0 : $i,X1 : mworld] : (($false = (mrel @ sK3 @ X1)) | ($false = (eiw_di @ X0 @ sK3)) | ($false = (a @ X0 @ X1)) | ($false = (b @ X0 @ X1))) )),
% 1.95/1.54 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.95/1.54 thf(f110,plain,(
% 1.95/1.54 ( ! [X0 : $i,X1 : mworld] : (($false = $true) | ($false = (mrel @ sK3 @ X1)) | ($false = (b @ X0 @ X1)) | ($false = (a @ X0 @ X1)) | ($false = (eiw_di @ X0 @ sK3))) )),
% 1.95/1.54 inference(superposition,[status(thm)],[f88,f105])).
% 1.95/1.54 thf(f105,plain,(
% 1.95/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ X1 @ X3)) | ($false = (b @ X2 @ X3)) | ($false = (a @ X2 @ X3))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f104])).
% 1.95/1.54 thf(f104,plain,(
% 1.95/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = ((b @ X2 @ X3) & (a @ X2 @ X3))) | ($false = (eiw_di @ X2 @ X1)) | ($false = (mrel @ X1 @ X3))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f103])).
% 1.95/1.54 thf(f103,plain,(
% 1.95/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (eiw_di @ X2 @ X1)) | ($false = ((mrel @ X1 @ X3) & ((b @ X2 @ X3) & (a @ X2 @ X3))))) )),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f102])).
% 1.95/1.54 thf(f102,plain,(
% 1.95/1.54 ( ! [X2 : $i,X3 : mworld,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = ((^[Y0 : mworld]: ((mrel @ X1 @ Y0) & ((b @ X2 @ Y0) & (a @ X2 @ Y0)))) @ X3)) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.95/1.54 inference(pi_clausification,[status(thm)],[f101])).
% 1.95/1.54 thf(f101,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) & ((b @ X2 @ Y0) & (a @ X2 @ Y0)))))) | ($false = (eiw_di @ X2 @ X1))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f100])).
% 1.95/1.54 thf(f100,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = ((?? @ mworld @ (^[Y0 : mworld]: ((mrel @ X1 @ Y0) & ((b @ X2 @ Y0) & (a @ X2 @ Y0))))) & (eiw_di @ X2 @ X1))) | ($false = (mrel @ mactual @ X1))) )),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f99])).
% 1.95/1.54 thf(f99,plain,(
% 1.95/1.54 ( ! [X2 : $i,X1 : mworld] : (($false = ((^[Y0 : $i]: ((?? @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) & ((b @ Y0 @ Y1) & (a @ Y0 @ Y1))))) & (eiw_di @ Y0 @ X1))) @ X2)) | ($false = (mrel @ mactual @ X1))) )),
% 1.95/1.54 inference(pi_clausification,[status(thm)],[f98])).
% 1.95/1.54 thf(f98,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($false = (?? @ $i @ (^[Y0 : $i]: ((?? @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) & ((b @ Y0 @ Y1) & (a @ Y0 @ Y1))))) & (eiw_di @ Y0 @ X1)))))) )),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f97])).
% 1.95/1.54 thf(f97,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : (($false = ((mrel @ mactual @ X1) & (?? @ $i @ (^[Y0 : $i]: ((?? @ mworld @ (^[Y1 : mworld]: ((mrel @ X1 @ Y1) & ((b @ Y0 @ Y1) & (a @ Y0 @ Y1))))) & (eiw_di @ Y0 @ X1))))))) )),
% 1.95/1.54 inference(beta_eta_normalization,[status(thm)],[f96])).
% 1.95/1.54 thf(f96,plain,(
% 1.95/1.54 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) & ((b @ Y1 @ Y2) & (a @ Y1 @ Y2))))) & (eiw_di @ Y1 @ Y0)))))) @ X1) = $false)) )),
% 1.95/1.54 inference(pi_clausification,[status(thm)],[f71])).
% 1.95/1.54 thf(f71,plain,(
% 1.95/1.54 ($false = (?? @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) & (?? @ $i @ (^[Y1 : $i]: ((?? @ mworld @ (^[Y2 : mworld]: ((mrel @ Y0 @ Y2) & ((b @ Y1 @ Y2) & (a @ Y1 @ Y2))))) & (eiw_di @ Y1 @ Y0))))))))),
% 1.95/1.54 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.95/1.54 % SZS output end Proof for DTF2THF_29688
% 1.95/1.54 % (29788)------------------------------
% 1.95/1.54 % (29788)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.95/1.54 % (29788)Termination reason: Refutation
% 1.95/1.54
% 1.95/1.54 % (29788)Memory used [KB]: 5884
% 1.95/1.54 % (29788)Time elapsed: 0.035 s
% 1.95/1.54 % (29788)Instructions burned: 57 (million)
% 1.95/1.54 % (29788)------------------------------
% 1.95/1.54 % (29788)------------------------------
% 1.95/1.54 % (29787)Success in time 0.045 s
%------------------------------------------------------------------------------