%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO887^22 : TPTP v9.2.1. Released v8.1.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n028.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:55:06 AM UTC 2026
% Result : Theorem 0.31s 1.33s
% Output : Refutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 9
% Syntax : Number of formulae : 62 ( 36 unt; 0 typ; 2 def)
% Number of atoms : 314 ( 69 equ; 0 cnn)
% Maximal formula atoms : 8 ( 5 avg)
% Number of connectives : 436 ( 15 ~; 25 |; 29 &; 326 @)
% ( 2 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 36 ( 36 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 18 usr; 7 con; 0-3 aty)
% ( 5 !!; 19 ??; 0 @@+; 0 @@-)
% Number of variables : 121 ( 93 ^; 24 !; 4 ?; 121 :)
% 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,
f: $i > mworld > $o ).
thf(func_def_29,type,
sK0: mworld > $i ).
thf(func_def_31,type,
sK2: mworld > $i ).
thf(f136,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f115,f125,f135]) ).
thf(f135,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f134]) ).
thf(f134,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ( $true = $false )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f55,f109]) ).
thf(f109,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl1_1
<=> ( $false
= ( mrel @ mactual @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f55,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
! [X0: mworld] :
( $true
= ( mrel @ X0 @ X0 ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,plain,
! [X0: mworld] : ( mrel @ X0 @ X0 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld] : ( mrel @ X2 @ X2 ),
file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mrel_reflexive) ).
thf(f125,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f122,f111,f107]) ).
thf(f111,definition,
( spl1_2
<=> ( $false
= ( f @ ( sK2 @ mactual ) @ mactual ) ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f122,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f120]) ).
thf(f120,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ mactual ) )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f113,f79]) ).
thf(f79,plain,
! [X1: mworld] :
( ( $true
= ( f @ ( sK2 @ X1 ) @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
thf(f77,plain,
! [X1: mworld] :
( ( $true
= ( ( f @ ( sK2 @ X1 ) @ X1 )
& ( eiw_di @ ( sK2 @ X1 ) @ X1 ) ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(beta_eta_normalization,[status(thm)],[f76]) ).
thf(f76,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ^ [Y0: $i] :
( ( f @ Y0 @ X1 )
& ( eiw_di @ Y0 @ X1 ) )
@ ( sK2 @ X1 ) ) ) ),
inference(sigma_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: mworld] :
( ( $false
= ( mrel @ mactual @ X1 ) )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( f @ Y0 @ X1 )
& ( eiw_di @ Y0 @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( f @ Y0 @ X1 )
& ( eiw_di @ Y0 @ X1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( f @ Y1 @ Y0 )
& ( eiw_di @ Y1 @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f72]) ).
thf(f72,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( f @ Y1 @ Y0 )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
( $true
!= ( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( f @ Y1 @ Y0 )
& ( eiw_di @ Y1 @ Y0 ) ) ) ) )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( f @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) )
& ( eiw_di @ Y0 @ mactual ) ) ) ) ),
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] :
( !! @ 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] : ( f @ Y0 ) ) )
@ ( ^ [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] :
( ( Y1 @ Y3 )
& ( mrel @ Y2 @ Y3 ) ) )
@ ( f @ Y0 ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f61,f65,f58,f66,f60,f60,f59]) ).
thf(f59,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( mdia
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( ?? @ mworld
@ ^ [Y2: mworld] :
( ( Y0 @ Y2 )
& ( mrel @ Y1 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( mdia
= ( ^ [X0: mworld > $o,X1: mworld] :
? [X2: mworld] :
( ( mrel @ X1 @ X2 )
& ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f8]) ).
thf(f8,axiom,
( mdia
= ( ^ [X0: mworld > $o,X2: mworld] :
? [X4: mworld] :
( ( mrel @ X2 @ X4 )
& ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mdia_def) ).
thf(f60,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( Y0 @ Y2 @ Y1 )
& ( eiw_di @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,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/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mexists_di_def) ).
thf(f66,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f39]) ).
thf(f39,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/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mbox_def) ).
thf(f58,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( mimplies
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X0 @ X2 )
=> ( X1 @ X2 ) ) )
= mimplies ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
=> ( X3 @ X2 ) ) )
= mimplies ),
file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mimplies_def) ).
thf(f65,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
thf(f34,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.X9AaWoYnme/DTF2THF_4273.p',mlocal_def) ).
thf(f61,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( f @ Y0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f47]) ).
thf(f47,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( f @ Y0 ) ) ) ) ) ),
inference(flattening,[status(thm)],[f21]) ).
thf(f21,plain,
( $true
!= ( mlocal
@ ( mimplies
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( f @ Y0 ) ) )
@ ( mexists_di
@ ^ [Y0: $i] : ( mdia @ ( f @ Y0 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,plain,
~ ( mlocal
@ ( mimplies
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( f @ X0 ) ) )
@ ( mexists_di
@ ^ [X1: $i] : ( mdia @ ( f @ X1 ) ) ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,negated_conjecture,
~ ( mlocal
@ ( mimplies
@ ( mbox
@ ( mexists_di
@ ^ [X6: $i] : ( f @ X6 ) ) )
@ ( mexists_di
@ ^ [X6: $i] : ( mdia @ ( f @ X6 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f15]) ).
thf(f15,conjecture,
( mlocal
@ ( mimplies
@ ( mbox
@ ( mexists_di
@ ^ [X6: $i] : ( f @ X6 ) ) )
@ ( mexists_di
@ ^ [X6: $i] : ( mdia @ ( f @ X6 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',con) ).
thf(f113,plain,
( ( $false
= ( f @ ( sK2 @ mactual ) @ mactual ) )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f111]) ).
thf(f115,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f103,f111,f107]) ).
thf(f103,plain,
( ( $false
= ( f @ ( sK2 @ mactual ) @ mactual ) )
| ( $false
= ( mrel @ mactual @ mactual ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f98]) ).
thf(f98,plain,
( ( $false
= ( mrel @ mactual @ mactual ) )
| ( $true = $false )
| ( $false
= ( f @ ( sK2 @ mactual ) @ mactual ) ) ),
inference(superposition,[status(thm)],[f78,f92]) ).
thf(f92,plain,
! [X0: $i] :
( ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( ( f @ X0 @ mactual )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
! [X0: $i] :
( ( ( f @ X0 @ mactual )
= $false )
| ( $false
= ( eiw_di @ X0 @ mactual ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f85,f55]) ).
thf(f85,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( mrel @ mactual @ X2 ) )
| ( $false
= ( f @ X1 @ X2 ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f84]) ).
thf(f84,plain,
! [X2: mworld,X1: $i] :
( ( ( eiw_di @ X1 @ mactual )
= $false )
| ( $false
= ( ( f @ X1 @ X2 )
& ( mrel @ mactual @ X2 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f83]) ).
thf(f83,plain,
! [X2: mworld,X1: $i] :
( ( $false
= ( ^ [Y0: mworld] :
( ( f @ X1 @ Y0 )
& ( mrel @ mactual @ Y0 ) )
@ X2 ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(pi_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
! [X1: $i] :
( ( $false
= ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( f @ X1 @ Y0 )
& ( mrel @ mactual @ Y0 ) ) ) )
| ( ( eiw_di @ X1 @ mactual )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
! [X1: $i] :
( ( ( ?? @ mworld
@ ^ [Y0: mworld] :
( ( f @ X1 @ Y0 )
& ( mrel @ mactual @ Y0 ) ) )
& ( eiw_di @ X1 @ mactual ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( f @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) )
& ( eiw_di @ Y0 @ mactual ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( $false
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( ?? @ mworld
@ ^ [Y1: mworld] :
( ( f @ Y0 @ Y1 )
& ( mrel @ mactual @ Y1 ) ) )
& ( eiw_di @ Y0 @ mactual ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f78,plain,
! [X1: mworld] :
( ( ( eiw_di @ ( sK2 @ X1 ) @ X1 )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f77]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SYO887^22 : TPTP v9.2.1. Released v8.1.0.
% 0.12/0.14 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.15/0.35 % Computer : n028.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Tue Feb 24 14:53:12 EST 2026
% 0.15/0.35 % CPUTime :
% 0.15/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.47 ---- Original DTF file ---
% 0.30/0.47 thf(spec,logic,$$dhol).
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 % File : SYO887^22 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.47 % Domain : Syntactic
% 0.30/0.47 % Problem : Fitting and Mendelsohn problem
% 0.30/0.47 % Version : [BP13] axioms.
% 0.30/0.47 % English :
% 0.30/0.47
% 0.30/0.47 % Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.47 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.47 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.47 % Source : [TPTP]
% 0.30/0.47 % Names : SYM008+1 [QMLTP]
% 0.30/0.47
% 0.30/0.47 % Status : Theorem
% 0.30/0.47 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.30/0.47 % Syntax : Number of formulae : 30 ( 12 unt; 15 typ; 10 def)
% 0.30/0.47 % Number of atoms : 40 ( 10 equ; 0 cnn)
% 0.30/0.47 % Maximal formula atoms : 8 ( 2 avg)
% 0.30/0.47 % Number of connectives : 62 ( 1 ~; 1 |; 5 &; 49 @)
% 0.30/0.47 % ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% 0.30/0.47 % Maximal formula depth : 8 ( 3 avg)
% 0.30/0.47 % Number of types : 3 ( 1 usr)
% 0.30/0.47 % Number of type conns : 61 ( 61 >; 0 *; 0 +; 0 <<)
% 0.30/0.47 % Number of symbols : 15 ( 14 usr; 1 con; 0-3 aty)
% 0.30/0.47 % Number of variables : 38 ( 25 ^; 10 !; 3 ?; 38 :)
% 0.30/0.47 % SPC : TH0_THM_EQU_NAR
% 0.30/0.47
% 0.30/0.47 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.47 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.47 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.47 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.30/0.47 % $modalities == $modal_system_S4].
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 thf(mworld,type,
% 0.30/0.47 mworld: $tType ).
% 0.30/0.47
% 0.30/0.47 thf(mrel_type,type,
% 0.30/0.47 mrel: mworld > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mactual_type,type,
% 0.30/0.47 mactual: mworld ).
% 0.30/0.47
% 0.30/0.47 thf(mlocal_type,type,
% 0.30/0.47 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mlocal_def,definition,
% 0.30/0.47 ( mlocal
% 0.30/0.47 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mnot_type,type,
% 0.30/0.47 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mand_type,type,
% 0.30/0.47 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mor_type,type,
% 0.30/0.47 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mimplies_type,type,
% 0.30/0.47 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mequiv_type,type,
% 0.30/0.47 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mnot_def,definition,
% 0.30/0.47 ( mnot
% 0.30/0.47 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.47 ~ ( A @ W ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mand_def,definition,
% 0.30/0.47 ( mand
% 0.30/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.47 ( ( A @ W )
% 0.30/0.47 & ( B @ W ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mor_def,definition,
% 0.30/0.47 ( mor
% 0.30/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.47 ( ( A @ W )
% 0.30/0.47 | ( B @ W ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mimplies_def,definition,
% 0.30/0.47 ( mimplies
% 0.30/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.47 ( ( A @ W )
% 0.30/0.47 => ( B @ W ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mequiv_def,definition,
% 0.30/0.47 ( mequiv
% 0.30/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.47 ( ( A @ W )
% 0.30/0.47 <=> ( B @ W ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mbox_type,type,
% 0.30/0.47 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mbox_def,definition,
% 0.30/0.47 ( mbox
% 0.30/0.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.47 ! [V: mworld] :
% 0.30/0.47 ( ( mrel @ W @ V )
% 0.30/0.47 => ( Phi @ V ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mdia_type,type,
% 0.30/0.47 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mdia_def,definition,
% 0.30/0.47 ( mdia
% 0.30/0.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.47 ? [V: mworld] :
% 0.30/0.47 ( ( mrel @ W @ V )
% 0.30/0.47 & ( Phi @ V ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mrel_reflexive,axiom,
% 0.30/0.47 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.30/0.47
% 0.30/0.47 thf(mrel_transitive,axiom,
% 0.30/0.47 ! [W: mworld,V: mworld,U: mworld] :
% 0.30/0.47 ( ( ( mrel @ W @ V )
% 0.30/0.47 & ( mrel @ V @ U ) )
% 0.30/0.47 => ( mrel @ W @ U ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(eiw_di_type,type,
% 0.30/0.47 eiw_di: $i > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(eiw_di_nonempty,axiom,
% 0.30/0.47 ! [W: mworld] :
% 0.30/0.47 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.30/0.47
% 0.30/0.47 thf(eiw_di_decr,axiom,
% 0.30/0.47 ! [W: mworld,V: mworld,X: $i] :
% 0.30/0.47 ( ( ( eiw_di @ X @ W )
% 0.30/0.47 & ( mrel @ V @ W ) )
% 0.30/0.47 => ( eiw_di @ X @ V ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mforall_di_type,type,
% 0.30/0.47 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mforall_di_def,definition,
% 0.30/0.47 ( mforall_di
% 0.30/0.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.47 ! [X: $i] :
% 0.30/0.47 ( ( eiw_di @ X @ W )
% 0.30/0.47 => ( A @ X @ W ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(mexists_di_type,type,
% 0.30/0.47 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(mexists_di_def,definition,
% 0.30/0.47 ( mexists_di
% 0.30/0.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.47 ? [X: $i] :
% 0.30/0.47 ( ( eiw_di @ X @ W )
% 0.30/0.47 & ( A @ X @ W ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 thf(f_decl,type,
% 0.30/0.47 f: $i > mworld > $o ).
% 0.30/0.47
% 0.30/0.47 thf(con,conjecture,
% 0.30/0.47 ( mlocal
% 0.30/0.47 @ ( mimplies
% 0.30/0.47 @ ( mbox
% 0.30/0.47 @ ( mexists_di
% 0.30/0.47 @ ^ [X: $i] : ( f @ X ) ) )
% 0.30/0.47 @ ( mexists_di
% 0.30/0.47 @ ^ [X: $i] : ( mdia @ ( f @ X ) ) ) ) ) ).
% 0.30/0.47
% 0.30/0.47 %------------------------------------------------------------------------------
% 0.30/0.47 ------------------------
% 0.31/1.30 ---- Embedded in THF ---
% 0.31/1.30 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 0.31/1.30 %%% Generated on Tue Feb 24 14:53:12 EST 2026
% 0.31/1.30 %%% using '$$dhol' embedding, version 1.3.0.
% 0.31/1.30 %%% Logic specification used:
% 0.31/1.30 %%% thf(spec, logic, $$dhol).
% 0.31/1.30
% 0.31/1.30 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2DTF4273.p
% See solution above
% 0.31/1.30 ------------------------
% 0.31/1.31 ---- Cleaned THF ---
% 0.31/1.31 thf(mworld,type,
% 0.31/1.31 mworld: $tType ).
% 0.31/1.31
% 0.31/1.31 thf(mrel_type,type,
% 0.31/1.31 mrel: mworld > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mactual_type,type,
% 0.31/1.31 mactual: mworld ).
% 0.31/1.31
% 0.31/1.31 thf(mlocal_type,type,
% 0.31/1.31 mlocal: ( mworld > $o ) > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mlocal_def,definition,
% 0.31/1.31 ( mlocal
% 0.31/1.31 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mnot_type,type,
% 0.31/1.31 mnot: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mand_type,type,
% 0.31/1.31 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mor_type,type,
% 0.31/1.31 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mimplies_type,type,
% 0.31/1.31 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mequiv_type,type,
% 0.31/1.31 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mnot_def,definition,
% 0.31/1.31 ( mnot
% 0.31/1.31 = ( ^ [A: mworld > $o,W: mworld] :
% 0.31/1.31 ~ ( A @ W ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mand_def,definition,
% 0.31/1.31 ( mand
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 & ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mor_def,definition,
% 0.31/1.31 ( mor
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 | ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mimplies_def,definition,
% 0.31/1.31 ( mimplies
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 => ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mequiv_def,definition,
% 0.31/1.31 ( mequiv
% 0.31/1.31 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.31/1.31 ( ( A @ W )
% 0.31/1.31 <=> ( B @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mbox_type,type,
% 0.31/1.31 mbox: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mbox_def,definition,
% 0.31/1.31 ( mbox
% 0.31/1.31 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/1.31 ! [V: mworld] :
% 0.31/1.31 ( ( mrel @ W @ V )
% 0.31/1.31 => ( Phi @ V ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mdia_type,type,
% 0.31/1.31 mdia: ( mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mdia_def,definition,
% 0.31/1.31 ( mdia
% 0.31/1.31 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.31/1.31 ? [V: mworld] :
% 0.31/1.31 ( ( mrel @ W @ V )
% 0.31/1.31 & ( Phi @ V ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mrel_reflexive,axiom,
% 0.31/1.31 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.31/1.31
% 0.31/1.31 thf(mrel_transitive,axiom,
% 0.31/1.31 ! [W: mworld,V: mworld,U: mworld] :
% 0.31/1.31 ( ( ( mrel @ W @ V )
% 0.31/1.31 & ( mrel @ V @ U ) )
% 0.31/1.31 => ( mrel @ W @ U ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(eiw_di_type,type,
% 0.31/1.31 eiw_di: $i > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(eiw_di_nonempty,axiom,
% 0.31/1.31 ! [W: mworld] :
% 0.31/1.31 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.31/1.31
% 0.31/1.31 thf(eiw_di_decr,axiom,
% 0.31/1.31 ! [W: mworld,V: mworld,X: $i] :
% 0.31/1.31 ( ( ( eiw_di @ X @ W )
% 0.31/1.31 & ( mrel @ V @ W ) )
% 0.31/1.31 => ( eiw_di @ X @ V ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mforall_di_type,type,
% 0.31/1.31 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mforall_di_def,definition,
% 0.31/1.31 ( mforall_di
% 0.31/1.31 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/1.31 ! [X: $i] :
% 0.31/1.31 ( ( eiw_di @ X @ W )
% 0.31/1.31 => ( A @ X @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(mexists_di_type,type,
% 0.31/1.31 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(mexists_di_def,definition,
% 0.31/1.31 ( mexists_di
% 0.31/1.31 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.31/1.31 ? [X: $i] :
% 0.31/1.31 ( ( eiw_di @ X @ W )
% 0.31/1.31 & ( A @ X @ W ) ) ) ) ).
% 0.31/1.31
% 0.31/1.31 thf(f_decl,type,
% 0.31/1.31 f: $i > mworld > $o ).
% 0.31/1.31
% 0.31/1.31 thf(con,conjecture,
% 0.31/1.31 ( mlocal
% 0.31/1.31 @ ( mimplies
% 0.31/1.31 @ ( mbox
% 0.31/1.31 @ ( mexists_di
% 0.31/1.31 @ ^ [X: $i] : ( f @ X ) ) )
% 0.31/1.31 @ ( mexists_di
% 0.31/1.31 @ ^ [X: $i] : ( mdia @ ( f @ X ) ) ) ) ) ).
% 0.31/1.31 ------------------------
% 0.31/1.32 % (4463)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_4273 for (2999ds/183Mi)
% 0.31/1.32 % (4465)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_4273 for (2999ds/27Mi)
% 0.31/1.33 % (4469)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_4273 for (2999ds/18Mi)
% 0.31/1.33 % (4466)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_4273 for (2999ds/2Mi)
% 0.31/1.33 % (4464)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_4273 for (2999ds/4Mi)
% 0.31/1.33 % (4463)First to succeed.
% 0.31/1.33 % (4466)Instruction limit reached!
% 0.31/1.33 % (4466)------------------------------
% 0.31/1.33 % (4466)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (4466)Termination reason: Unknown
% 0.31/1.33 % (4466)Termination phase: Property scanning
% 0.31/1.33
% 0.31/1.33 % (4466)Memory used [KB]: 1023
% 0.31/1.33 % (4466)Time elapsed: 0.003 s
% 0.31/1.33 % (4466)Instructions burned: 3 (million)
% 0.31/1.33 % (4466)------------------------------
% 0.31/1.33 % (4466)------------------------------
% 0.31/1.33 % (4465)Also succeeded, but the first one will report.
% 0.31/1.33 % (4464)Instruction limit reached!
% 0.31/1.33 % (4464)------------------------------
% 0.31/1.33 % (4464)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (4464)Termination reason: Unknown
% 0.31/1.33 % (4464)Termination phase: Saturation
% 0.31/1.33
% 0.31/1.33 % (4464)Memory used [KB]: 5500
% 0.31/1.33 % (4464)Time elapsed: 0.003 s
% 0.31/1.33 % (4464)Instructions burned: 6 (million)
% 0.31/1.33 % (4464)------------------------------
% 0.31/1.33 % (4464)------------------------------
% 0.31/1.33 % (4463)Refutation found. Thanks to Tanya!
% 0.31/1.33 % SZS status Theorem for DTF2THF_4273
% 0.31/1.33 % SZS output start Proof for DTF2THF_4273
% 0.31/1.33 thf(type_def_5, type, mworld: $tType).
% 0.31/1.33 thf(func_def_0, type, mworld: $tType).
% 0.31/1.33 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 0.31/1.33 thf(func_def_2, type, mactual: mworld).
% 0.31/1.33 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 0.31/1.33 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 0.31/1.33 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 0.31/1.33 thf(func_def_15, type, f: $i > mworld > $o).
% 0.31/1.33 thf(func_def_29, type, sK0: mworld > $i).
% 0.31/1.33 thf(func_def_31, type, sK2: mworld > $i).
% 0.31/1.33 thf(f136,plain,(
% 0.31/1.33 $false),
% 0.31/1.33 inference(avatar_sat_refutation,[status(thm)],[f115,f125,f135])).
% 0.31/1.33 thf(f135,plain,(
% 0.31/1.33 ~spl1_1),
% 0.31/1.33 inference(avatar_contradiction_clause,[status(thm)],[f134])).
% 0.31/1.33 thf(f134,plain,(
% 0.31/1.33 $false | ~spl1_1),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 0.31/1.33 thf(f128,plain,(
% 0.31/1.33 ($true = $false) | ~spl1_1),
% 0.31/1.33 inference(superposition,[status(thm)],[f55,f109])).
% 0.31/1.33 thf(f109,plain,(
% 0.31/1.33 ($false = (mrel @ mactual @ mactual)) | ~spl1_1),
% 0.31/1.33 inference(avatar_component_clause,[status(thm)],[f107])).
% 0.31/1.33 thf(f107,definition,(
% 0.31/1.33 spl1_1 <=> ($false = (mrel @ mactual @ mactual))),
% 0.31/1.33 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 0.31/1.33 thf(f55,plain,(
% 0.31/1.33 ( ! [X0 : mworld] : (($true = (mrel @ X0 @ X0))) )),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f29])).
% 0.31/1.33 thf(f29,plain,(
% 0.31/1.33 ! [X0 : mworld] : ($true = (mrel @ X0 @ X0))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f28])).
% 0.31/1.33 thf(f28,plain,(
% 0.31/1.33 ! [X0 : mworld] : (mrel @ X0 @ X0)),
% 0.31/1.33 inference(rectify,[status(thm)],[f9])).
% 0.31/1.33 thf(f9,axiom,(
% 0.31/1.33 ! [X2 : mworld] : (mrel @ X2 @ X2)),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mrel_reflexive)).
% 0.31/1.33 thf(f125,plain,(
% 0.31/1.33 spl1_1 | ~spl1_2),
% 0.31/1.33 inference(avatar_split_clause,[status(thm)],[f122,f111,f107])).
% 0.31/1.33 thf(f111,definition,(
% 0.31/1.33 spl1_2 <=> ($false = (f @ (sK2 @ mactual) @ mactual))),
% 0.31/1.33 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 0.31/1.33 thf(f122,plain,(
% 0.31/1.33 ($false = (mrel @ mactual @ mactual)) | ~spl1_2),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f120])).
% 0.31/1.33 thf(f120,plain,(
% 0.31/1.33 ($true = $false) | ($false = (mrel @ mactual @ mactual)) | ~spl1_2),
% 0.31/1.33 inference(superposition,[status(thm)],[f113,f79])).
% 0.31/1.33 thf(f79,plain,(
% 0.31/1.33 ( ! [X1 : mworld] : (($true = (f @ (sK2 @ X1) @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 0.31/1.33 thf(f77,plain,(
% 0.31/1.33 ( ! [X1 : mworld] : (($true = ((f @ (sK2 @ X1) @ X1) & (eiw_di @ (sK2 @ X1) @ X1))) | ($false = (mrel @ mactual @ X1))) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f76])).
% 0.31/1.33 thf(f76,plain,(
% 0.31/1.33 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = ((^[Y0 : $i]: ((f @ Y0 @ X1) & (eiw_di @ Y0 @ X1))) @ (sK2 @ X1)))) )),
% 0.31/1.33 inference(sigma_clausification,[status(thm)],[f75])).
% 0.31/1.33 thf(f75,plain,(
% 0.31/1.33 ( ! [X1 : mworld] : (($false = (mrel @ mactual @ X1)) | ($true = (?? @ $i @ (^[Y0 : $i]: ((f @ Y0 @ X1) & (eiw_di @ Y0 @ X1)))))) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 0.31/1.33 thf(f74,plain,(
% 0.31/1.33 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => (?? @ $i @ (^[Y0 : $i]: ((f @ Y0 @ X1) & (eiw_di @ Y0 @ X1))))))) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f73])).
% 0.31/1.33 thf(f73,plain,(
% 0.31/1.33 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((f @ Y1 @ Y0) & (eiw_di @ Y1 @ Y0)))))) @ X1))) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f72])).
% 0.31/1.33 thf(f72,plain,(
% 0.31/1.33 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((f @ Y1 @ Y0) & (eiw_di @ Y1 @ Y0))))))))),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 0.31/1.33 thf(f70,plain,(
% 0.31/1.33 ($true != ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((f @ Y1 @ Y0) & (eiw_di @ Y1 @ Y0))))))) => (?? @ $i @ (^[Y0 : $i]: ((?? @ mworld @ (^[Y1 : mworld]: ((f @ Y0 @ Y1) & (mrel @ mactual @ Y1)))) & (eiw_di @ Y0 @ mactual))))))),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f69])).
% 0.31/1.33 thf(f69,plain,(
% 0.31/1.33 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ 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]: (f @ Y0)))) @ ((^[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]: ((Y1 @ Y3) & (mrel @ Y2 @ Y3))))))) @ (f @ Y0)))))))),
% 0.31/1.33 inference(definition_unfolding,[status(thm)],[f61,f65,f58,f66,f60,f60,f59])).
% 0.31/1.33 thf(f59,plain,(
% 0.31/1.33 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f23])).
% 0.31/1.33 thf(f23,plain,(
% 0.31/1.33 (mdia = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (?? @ mworld @ (^[Y2 : mworld]: ((Y0 @ Y2) & (mrel @ Y1 @ Y2))))))))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f22])).
% 0.31/1.33 thf(f22,plain,(
% 0.31/1.33 (mdia = (^[X0 : mworld > $o, X1 : mworld] : (? [X2 : mworld] : ((mrel @ X1 @ X2) & (X0 @ X2)))))),
% 0.31/1.33 inference(rectify,[status(thm)],[f8])).
% 0.31/1.33 thf(f8,axiom,(
% 0.31/1.33 (mdia = (^[X0 : mworld > $o, X2 : mworld] : (? [X4 : mworld] : ((mrel @ X2 @ X4) & (X0 @ X4)))))),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mdia_def)).
% 0.31/1.33 thf(f60,plain,(
% 0.31/1.33 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ Y2 @ Y1))))))))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f27])).
% 0.31/1.33 thf(f27,plain,(
% 0.31/1.33 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((Y0 @ Y2 @ Y1) & (eiw_di @ Y2 @ Y1))))))))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f26])).
% 0.31/1.33 thf(f26,plain,(
% 0.31/1.33 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((eiw_di @ X2 @ X1) & (X0 @ X2 @ X1)))))),
% 0.31/1.33 inference(rectify,[status(thm)],[f14])).
% 0.31/1.33 thf(f14,axiom,(
% 0.31/1.33 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X6 : $i] : ((eiw_di @ X6 @ X2) & (X1 @ X6 @ X2)))))),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mexists_di_def)).
% 0.31/1.33 thf(f66,plain,(
% 0.31/1.33 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f40])).
% 0.31/1.33 thf(f40,plain,(
% 0.31/1.33 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f39])).
% 0.31/1.33 thf(f39,plain,(
% 0.31/1.33 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 0.31/1.33 inference(rectify,[status(thm)],[f7])).
% 0.31/1.33 thf(f7,axiom,(
% 0.31/1.33 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mbox_def)).
% 0.31/1.33 thf(f58,plain,(
% 0.31/1.33 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f42])).
% 0.31/1.33 thf(f42,plain,(
% 0.31/1.33 (mimplies = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) => (Y1 @ Y2))))))))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f41])).
% 0.31/1.33 thf(f41,plain,(
% 0.31/1.33 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) => (X1 @ X2))) = mimplies)),
% 0.31/1.33 inference(rectify,[status(thm)],[f5])).
% 0.31/1.33 thf(f5,axiom,(
% 0.31/1.33 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) => (X3 @ X2))) = mimplies)),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mimplies_def)).
% 0.31/1.33 thf(f65,plain,(
% 0.31/1.33 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f34])).
% 0.31/1.33 thf(f34,plain,(
% 0.31/1.33 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f1])).
% 0.31/1.33 thf(f1,axiom,(
% 0.31/1.33 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',mlocal_def)).
% 0.31/1.33 thf(f61,plain,(
% 0.31/1.33 ($true != (mlocal @ (mimplies @ (mbox @ (mexists_di @ (^[Y0 : $i]: (f @ Y0)))) @ (mexists_di @ (^[Y0 : $i]: (mdia @ (f @ Y0)))))))),
% 0.31/1.33 inference(cnf_transformation,[status(thm)],[f47])).
% 0.31/1.33 thf(f47,plain,(
% 0.31/1.33 ($true != (mlocal @ (mimplies @ (mbox @ (mexists_di @ (^[Y0 : $i]: (f @ Y0)))) @ (mexists_di @ (^[Y0 : $i]: (mdia @ (f @ Y0)))))))),
% 0.31/1.33 inference(flattening,[status(thm)],[f21])).
% 0.31/1.33 thf(f21,plain,(
% 0.31/1.33 ~($true = (mlocal @ (mimplies @ (mbox @ (mexists_di @ (^[Y0 : $i]: (f @ Y0)))) @ (mexists_di @ (^[Y0 : $i]: (mdia @ (f @ Y0)))))))),
% 0.31/1.33 inference(fool_elimination,[status(thm)],[f20])).
% 0.31/1.33 thf(f20,plain,(
% 0.31/1.33 ~(mlocal @ (mimplies @ (mbox @ (mexists_di @ (^[X0 : $i] : (f @ X0)))) @ (mexists_di @ (^[X1 : $i] : (mdia @ (f @ X1))))))),
% 0.31/1.33 inference(rectify,[status(thm)],[f16])).
% 0.31/1.33 thf(f16,negated_conjecture,(
% 0.31/1.33 ~(mlocal @ (mimplies @ (mbox @ (mexists_di @ (^[X6 : $i] : (f @ X6)))) @ (mexists_di @ (^[X6 : $i] : (mdia @ (f @ X6))))))),
% 0.31/1.33 inference(negated_conjecture,[status(cth)],[f15])).
% 0.31/1.33 thf(f15,conjecture,(
% 0.31/1.33 (mlocal @ (mimplies @ (mbox @ (mexists_di @ (^[X6 : $i] : (f @ X6)))) @ (mexists_di @ (^[X6 : $i] : (mdia @ (f @ X6))))))),
% 0.31/1.33 file('/export/starexec/sandbox/tmp/tmp.X9AaWoYnme/DTF2THF_4273.p',con)).
% 0.31/1.33 thf(f113,plain,(
% 0.31/1.33 ($false = (f @ (sK2 @ mactual) @ mactual)) | ~spl1_2),
% 0.31/1.33 inference(avatar_component_clause,[status(thm)],[f111])).
% 0.31/1.33 thf(f115,plain,(
% 0.31/1.33 spl1_1 | spl1_2),
% 0.31/1.33 inference(avatar_split_clause,[status(thm)],[f103,f111,f107])).
% 0.31/1.33 thf(f103,plain,(
% 0.31/1.33 ($false = (f @ (sK2 @ mactual) @ mactual)) | ($false = (mrel @ mactual @ mactual))),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f98])).
% 0.31/1.33 thf(f98,plain,(
% 0.31/1.33 ($false = (mrel @ mactual @ mactual)) | ($true = $false) | ($false = (f @ (sK2 @ mactual) @ mactual))),
% 0.31/1.33 inference(superposition,[status(thm)],[f78,f92])).
% 0.31/1.33 thf(f92,plain,(
% 0.31/1.33 ( ! [X0 : $i] : (($false = (eiw_di @ X0 @ mactual)) | ((f @ X0 @ mactual) = $false)) )),
% 0.31/1.33 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 0.31/1.33 thf(f86,plain,(
% 0.31/1.33 ( ! [X0 : $i] : (((f @ X0 @ mactual) = $false) | ($false = (eiw_di @ X0 @ mactual)) | ($true = $false)) )),
% 0.31/1.33 inference(superposition,[status(thm)],[f85,f55])).
% 0.31/1.33 thf(f85,plain,(
% 0.31/1.33 ( ! [X2 : mworld,X1 : $i] : (($false = (mrel @ mactual @ X2)) | ($false = (f @ X1 @ X2)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f84])).
% 0.31/1.33 thf(f84,plain,(
% 0.31/1.33 ( ! [X2 : mworld,X1 : $i] : (((eiw_di @ X1 @ mactual) = $false) | ($false = ((f @ X1 @ X2) & (mrel @ mactual @ X2)))) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f83])).
% 0.31/1.33 thf(f83,plain,(
% 0.31/1.33 ( ! [X2 : mworld,X1 : $i] : (($false = ((^[Y0 : mworld]: ((f @ X1 @ Y0) & (mrel @ mactual @ Y0))) @ X2)) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f82])).
% 0.31/1.33 thf(f82,plain,(
% 0.31/1.33 ( ! [X1 : $i] : (($false = (?? @ mworld @ (^[Y0 : mworld]: ((f @ X1 @ Y0) & (mrel @ mactual @ Y0))))) | ((eiw_di @ X1 @ mactual) = $false)) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 0.31/1.33 thf(f81,plain,(
% 0.31/1.33 ( ! [X1 : $i] : ((((?? @ mworld @ (^[Y0 : mworld]: ((f @ X1 @ Y0) & (mrel @ mactual @ Y0)))) & (eiw_di @ X1 @ mactual)) = $false)) )),
% 0.31/1.33 inference(beta_eta_normalization,[status(thm)],[f80])).
% 0.31/1.33 thf(f80,plain,(
% 0.31/1.33 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((?? @ mworld @ (^[Y1 : mworld]: ((f @ Y0 @ Y1) & (mrel @ mactual @ Y1)))) & (eiw_di @ Y0 @ mactual))) @ X1))) )),
% 0.31/1.33 inference(pi_clausification,[status(thm)],[f71])).
% 0.31/1.33 thf(f71,plain,(
% 0.31/1.33 ($false = (?? @ $i @ (^[Y0 : $i]: ((?? @ mworld @ (^[Y1 : mworld]: ((f @ Y0 @ Y1) & (mrel @ mactual @ Y1)))) & (eiw_di @ Y0 @ mactual)))))),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 0.31/1.33 thf(f78,plain,(
% 0.31/1.33 ( ! [X1 : mworld] : (((eiw_di @ (sK2 @ X1) @ X1) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 0.31/1.33 inference(binary_proxy_clausification,[status(thm)],[f77])).
% 0.31/1.33 % SZS output end Proof for DTF2THF_4273
% 0.31/1.33 % (4463)------------------------------
% 0.31/1.33 % (4463)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 0.31/1.33 % (4463)Termination reason: Refutation
% 0.31/1.33
% 0.31/1.33 % (4463)Memory used [KB]: 5628
% 0.31/1.33 % (4463)Time elapsed: 0.006 s
% 0.31/1.33 % (4463)Instructions burned: 11 (million)
% 0.31/1.33 % (4463)------------------------------
% 0.31/1.33 % (4463)------------------------------
% 0.31/1.33 % (4462)Success in time 0.008 s
%------------------------------------------------------------------------------