%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT334^8 : 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 : n005.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 08:45:30 AM UTC 2026
% Result : Theorem 1.40s 1.17s
% Output : Refutation 1.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 61 ( 34 unt; 0 typ; 2 def)
% Number of atoms : 404 ( 62 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 521 ( 17 ~; 23 |; 41 &; 406 @)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 2 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 25 usr; 14 con; 0-3 aty)
% ( 6 !!; 14 ??; 0 @@+; 0 @@-)
% Number of variables : 102 ( 86 ^; 14 !; 2 ?; 102 :)
% 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_21,type,
teach: $i > $i > mworld > $o ).
thf(func_def_35,type,
sK0: mworld > $i ).
thf(func_def_37,type,
sK2: mworld ).
thf(func_def_38,type,
sK3: mworld > $i ).
thf(f114,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f98,f104,f113]) ).
thf(f113,plain,
( ~ spl1_1
| spl1_2 ),
inference(avatar_contradiction_clause,[status(thm)],[f112]) ).
thf(f112,plain,
( $false
| ~ spl1_1
| spl1_2 ),
inference(subsumption_resolution,[status(thm)],[f108,f95]) ).
thf(f95,plain,
( ( ( mrel @ mactual @ sK2 )
!= $false )
| spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f94,definition,
( spl1_2
<=> ( ( mrel @ mactual @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f108,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true = $false )
| ( ( mrel @ mactual @ sK2 )
= $false )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f92,f82]) ).
thf(f82,plain,
! [X1: mworld] :
( ( ( eiw_di @ ( sK3 @ X1 ) @ X1 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f80,plain,
! [X1: mworld] :
( ( $true
= ( ( eiw_di @ ( sK3 @ X1 ) @ X1 )
& ( teach @ ( sK3 @ X1 ) @ cs @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f79]) ).
thf(f79,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) )
@ ( sK3 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f78]) ).
thf(f78,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: mworld] :
( ( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f74]) ).
thf(f74,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: mworld] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) )
@ X1 )
= $true ),
inference(pi_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( teach @ john @ math )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) )
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) )
@ ( teach @ mary @ psych )
@ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[status(thm)],[f60,f58,f59,f53,f53,f50,f53]) ).
thf(f50,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] :
( ( X0 @ X2 @ X1 )
& ( eiw_di @ X2 @ X1 ) ) )
= mexists_di ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,axiom,
( ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X5: $i] :
( ( X1 @ X5 @ X2 )
& ( eiw_di @ X5 @ X2 ) ) )
= mexists_di ),
file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',mexists_di_def) ).
thf(f53,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f27]) ).
thf(f27,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f26]) ).
thf(f26,plain,
( ( ^ [X0: mworld > $o,X1: mworld > $o,X2: mworld] :
( ( X1 @ X2 )
& ( X0 @ X2 ) ) )
= mand ),
inference(rectify,[status(thm)],[f3]) ).
thf(f3,axiom,
( ( ^ [X1: mworld > $o,X3: mworld > $o,X2: mworld] :
( ( X3 @ X2 )
& ( X1 @ X2 ) ) )
= mand ),
file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',mand_def) ).
thf(f59,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f37]) ).
thf(f37,plain,
( mbox
= ( ^ [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] :
( ( 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.eBvCh088eU/DTF2THF_7148.p',mbox_def) ).
thf(f58,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,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/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',mlocal_def) ).
thf(f60,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
thf(f33,plain,
( $true
= ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f32]) ).
thf(f32,plain,
( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
inference(rectify,[status(thm)],[f13]) ).
thf(f13,axiom,
( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [X5: $i] : ( teach @ X5 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',db) ).
thf(f92,plain,
( ( ( eiw_di @ ( sK3 @ sK2 ) @ sK2 )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl1_1
<=> ( ( eiw_di @ ( sK3 @ sK2 ) @ sK2 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f104,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[status(thm)],[f103]) ).
thf(f103,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f100]) ).
thf(f100,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f67,f96]) ).
thf(f96,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f67,plain,
( $true
= ( mrel @ mactual @ sK2 ) ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( $false
= ( ( mrel @ mactual @ sK2 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( teach @ Y0 @ cs @ sK2 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
( $false
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) ) )
@ sK2 ) ),
inference(sigma_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
( $true
!= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f61]) ).
thf(f61,plain,
( $true
!= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [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] : ( teach @ Y0 @ cs ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f55,f58,f59,f50]) ).
thf(f55,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f44]) ).
thf(f44,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f39]) ).
thf(f39,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f38]) ).
thf(f38,plain,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X0: $i] : ( teach @ X0 @ cs ) ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,negated_conjecture,
~ ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X5: $i] : ( teach @ X5 @ cs ) ) ) ),
inference(negated_conjecture,[status(cth)],[f14]) ).
thf(f14,conjecture,
( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [X5: $i] : ( teach @ X5 @ cs ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',query) ).
thf(f98,plain,
( spl1_2
| spl1_1 ),
inference(avatar_split_clause,[status(thm)],[f87,f90,f94]) ).
thf(f87,plain,
( ( ( mrel @ mactual @ sK2 )
= $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ sK2 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f86]) ).
thf(f86,plain,
( ( $true = $false )
| ( ( eiw_di @ ( sK3 @ sK2 ) @ sK2 )
= $false )
| ( ( mrel @ mactual @ sK2 )
= $false ) ),
inference(superposition,[status(thm)],[f70,f81]) ).
thf(f81,plain,
! [X1: mworld] :
( ( $true
= ( teach @ ( sK3 @ X1 ) @ cs @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f80]) ).
thf(f70,plain,
! [X1: $i] :
( ( ( teach @ X1 @ cs @ sK2 )
= $false )
| ( ( eiw_di @ X1 @ sK2 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ sK2 )
& ( teach @ X1 @ cs @ sK2 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( teach @ Y0 @ cs @ sK2 ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK2 )
& ( teach @ Y0 @ cs @ sK2 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : DAT334^8 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n005.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 06:15:59 EST 2026
% 0.11/0.30 % CPUTime :
% 0.11/0.30 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : DAT334^8 : TPTP v9.2.1. Released v8.1.0.
% 0.16/0.39 % Domain : Data Structures
% 0.16/0.39 % Problem : Database querying
% 0.16/0.39 % Version : [BP13] axioms.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Rei92] Reiter (1992), What Should a Database Know?
% 0.16/0.39 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.16/0.39 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.16/0.39 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.16/0.39 % Source : [TPTP]
% 0.16/0.39 % Names : APM009+1 [QMLTP]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.16/0.39 % Syntax : Number of formulae : 35 ( 12 unt; 21 typ; 10 def)
% 0.16/0.39 % Number of atoms : 40 ( 10 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 10 ( 2 avg)
% 0.16/0.39 % Number of connectives : 59 ( 1 ~; 1 |; 3 &; 50 @)
% 0.16/0.39 % ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 10 ( 3 avg)
% 0.16/0.39 % Number of types : 3 ( 1 usr)
% 0.16/0.39 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 21 ( 20 usr; 7 con; 0-3 aty)
% 0.16/0.39 % Number of variables : 32 ( 25 ^; 4 !; 3 ?; 32 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.16/0.39 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.16/0.39 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.16/0.39 % $modal == [$constants == $rigid,$quantification == $varying,
% 0.16/0.39 % $modalities == $modal_system_T].
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(mworld,type,
% 0.16/0.39 mworld: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(mrel_type,type,
% 0.16/0.39 mrel: mworld > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mactual_type,type,
% 0.16/0.39 mactual: mworld ).
% 0.16/0.39
% 0.16/0.39 thf(mlocal_type,type,
% 0.16/0.39 mlocal: ( mworld > $o ) > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mlocal_def,definition,
% 0.16/0.39 ( mlocal
% 0.16/0.39 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mnot_type,type,
% 0.16/0.39 mnot: ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mand_type,type,
% 0.16/0.39 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mor_type,type,
% 0.16/0.39 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mimplies_type,type,
% 0.16/0.39 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mequiv_type,type,
% 0.16/0.39 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mnot_def,definition,
% 0.16/0.39 ( mnot
% 0.16/0.39 = ( ^ [A: mworld > $o,W: mworld] :
% 0.16/0.39 ~ ( A @ W ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mand_def,definition,
% 0.16/0.39 ( mand
% 0.16/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.39 ( ( A @ W )
% 0.16/0.39 & ( B @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mor_def,definition,
% 0.16/0.39 ( mor
% 0.16/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.39 ( ( A @ W )
% 0.16/0.39 | ( B @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mimplies_def,definition,
% 0.16/0.39 ( mimplies
% 0.16/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.39 ( ( A @ W )
% 0.16/0.39 => ( B @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mequiv_def,definition,
% 0.16/0.39 ( mequiv
% 0.16/0.39 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.16/0.39 ( ( A @ W )
% 0.16/0.39 <=> ( B @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mbox_type,type,
% 0.16/0.39 mbox: ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mbox_def,definition,
% 0.16/0.39 ( mbox
% 0.16/0.39 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.16/0.39 ! [V: mworld] :
% 0.16/0.39 ( ( mrel @ W @ V )
% 0.16/0.39 => ( Phi @ V ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mdia_type,type,
% 0.16/0.39 mdia: ( mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mdia_def,definition,
% 0.16/0.39 ( mdia
% 0.16/0.39 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.16/0.39 ? [V: mworld] :
% 0.16/0.39 ( ( mrel @ W @ V )
% 0.16/0.39 & ( Phi @ V ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mrel_reflexive,axiom,
% 0.16/0.39 ! [W: mworld] : ( mrel @ W @ W ) ).
% 0.16/0.39
% 0.16/0.39 thf(eiw_di_type,type,
% 0.16/0.39 eiw_di: $i > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(eiw_di_nonempty,axiom,
% 0.16/0.39 ! [W: mworld] :
% 0.16/0.39 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.16/0.39
% 0.16/0.39 thf(mforall_di_type,type,
% 0.16/0.39 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mforall_di_def,definition,
% 0.16/0.39 ( mforall_di
% 0.16/0.39 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.16/0.39 ! [X: $i] :
% 0.16/0.39 ( ( eiw_di @ X @ W )
% 0.16/0.39 => ( A @ X @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(mexists_di_type,type,
% 0.16/0.39 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(mexists_di_def,definition,
% 0.16/0.39 ( mexists_di
% 0.16/0.39 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.16/0.39 ? [X: $i] :
% 0.16/0.39 ( ( eiw_di @ X @ W )
% 0.16/0.39 & ( A @ X @ W ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(cs_decl,type,
% 0.16/0.39 cs: $i ).
% 0.16/0.39
% 0.16/0.39 thf(sue_decl,type,
% 0.16/0.39 sue: $i ).
% 0.16/0.39
% 0.16/0.39 thf(mary_decl,type,
% 0.16/0.39 mary: $i ).
% 0.16/0.39
% 0.16/0.39 thf(john_decl,type,
% 0.16/0.39 john: $i ).
% 0.16/0.39
% 0.16/0.39 thf(math_decl,type,
% 0.16/0.39 math: $i ).
% 0.16/0.39
% 0.16/0.39 thf(psych_decl,type,
% 0.16/0.39 psych: $i ).
% 0.16/0.39
% 0.16/0.39 thf(teach_decl,type,
% 0.16/0.39 teach: $i > $i > mworld > $o ).
% 0.16/0.39
% 0.16/0.39 thf(db,axiom,
% 0.16/0.39 ( mlocal
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mand @ ( teach @ john @ math )
% 0.16/0.39 @ ( mand
% 0.16/0.39 @ ( mexists_di
% 0.16/0.39 @ ^ [X: $i] : ( teach @ X @ cs ) )
% 0.16/0.39 @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 thf(query,conjecture,
% 0.16/0.39 ( mlocal
% 0.16/0.39 @ ( mbox
% 0.16/0.39 @ ( mexists_di
% 0.16/0.39 @ ^ [X: $i] : ( teach @ X @ cs ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.40/1.14 ---- Embedded in THF ---
% 1.40/1.14 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.40/1.14 %%% Generated on Tue Feb 24 06:16:00 EST 2026
% 1.40/1.14 %%% using '$$dhol' embedding, version 1.3.0.
% 1.40/1.14 %%% Logic specification used:
% 1.40/1.14 %%% thf(spec, logic, $$dhol).
% 1.40/1.14
% 1.40/1.14 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2DTF7148.p
% See solution above
% 1.40/1.14 ------------------------
% 1.40/1.15 ---- Cleaned THF ---
% 1.40/1.15 thf(mworld,type,
% 1.40/1.15 mworld: $tType ).
% 1.40/1.15
% 1.40/1.15 thf(mrel_type,type,
% 1.40/1.15 mrel: mworld > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mactual_type,type,
% 1.40/1.15 mactual: mworld ).
% 1.40/1.15
% 1.40/1.15 thf(mlocal_type,type,
% 1.40/1.15 mlocal: ( mworld > $o ) > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mlocal_def,definition,
% 1.40/1.15 ( mlocal
% 1.40/1.15 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mnot_type,type,
% 1.40/1.15 mnot: ( mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mand_type,type,
% 1.40/1.15 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mor_type,type,
% 1.40/1.15 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mimplies_type,type,
% 1.40/1.15 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mequiv_type,type,
% 1.40/1.15 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mnot_def,definition,
% 1.40/1.15 ( mnot
% 1.40/1.15 = ( ^ [A: mworld > $o,W: mworld] :
% 1.40/1.15 ~ ( A @ W ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mand_def,definition,
% 1.40/1.15 ( mand
% 1.40/1.15 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.40/1.15 ( ( A @ W )
% 1.40/1.15 & ( B @ W ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mor_def,definition,
% 1.40/1.15 ( mor
% 1.40/1.15 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.40/1.15 ( ( A @ W )
% 1.40/1.15 | ( B @ W ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mimplies_def,definition,
% 1.40/1.15 ( mimplies
% 1.40/1.15 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.40/1.15 ( ( A @ W )
% 1.40/1.15 => ( B @ W ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mequiv_def,definition,
% 1.40/1.15 ( mequiv
% 1.40/1.15 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.40/1.15 ( ( A @ W )
% 1.40/1.15 <=> ( B @ W ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mbox_type,type,
% 1.40/1.15 mbox: ( mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mbox_def,definition,
% 1.40/1.15 ( mbox
% 1.40/1.15 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.40/1.15 ! [V: mworld] :
% 1.40/1.15 ( ( mrel @ W @ V )
% 1.40/1.15 => ( Phi @ V ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mdia_type,type,
% 1.40/1.15 mdia: ( mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mdia_def,definition,
% 1.40/1.15 ( mdia
% 1.40/1.15 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.40/1.15 ? [V: mworld] :
% 1.40/1.15 ( ( mrel @ W @ V )
% 1.40/1.15 & ( Phi @ V ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mrel_reflexive,axiom,
% 1.40/1.15 ! [W: mworld] : ( mrel @ W @ W ) ).
% 1.40/1.15
% 1.40/1.15 thf(eiw_di_type,type,
% 1.40/1.15 eiw_di: $i > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(eiw_di_nonempty,axiom,
% 1.40/1.15 ! [W: mworld] :
% 1.40/1.15 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.40/1.15
% 1.40/1.15 thf(mforall_di_type,type,
% 1.40/1.15 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mforall_di_def,definition,
% 1.40/1.15 ( mforall_di
% 1.40/1.15 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.40/1.15 ! [X: $i] :
% 1.40/1.15 ( ( eiw_di @ X @ W )
% 1.40/1.15 => ( A @ X @ W ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(mexists_di_type,type,
% 1.40/1.15 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(mexists_di_def,definition,
% 1.40/1.15 ( mexists_di
% 1.40/1.15 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.40/1.15 ? [X: $i] :
% 1.40/1.15 ( ( eiw_di @ X @ W )
% 1.40/1.15 & ( A @ X @ W ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(cs_decl,type,
% 1.40/1.15 cs: $i ).
% 1.40/1.15
% 1.40/1.15 thf(sue_decl,type,
% 1.40/1.15 sue: $i ).
% 1.40/1.15
% 1.40/1.15 thf(mary_decl,type,
% 1.40/1.15 mary: $i ).
% 1.40/1.15
% 1.40/1.15 thf(john_decl,type,
% 1.40/1.15 john: $i ).
% 1.40/1.15
% 1.40/1.15 thf(math_decl,type,
% 1.40/1.15 math: $i ).
% 1.40/1.15
% 1.40/1.15 thf(psych_decl,type,
% 1.40/1.15 psych: $i ).
% 1.40/1.15
% 1.40/1.15 thf(teach_decl,type,
% 1.40/1.15 teach: $i > $i > mworld > $o ).
% 1.40/1.15
% 1.40/1.15 thf(db,axiom,
% 1.40/1.15 ( mlocal
% 1.40/1.15 @ ( mbox
% 1.40/1.15 @ ( mand @ ( teach @ john @ math )
% 1.40/1.15 @ ( mand
% 1.40/1.15 @ ( mexists_di
% 1.40/1.15 @ ^ [X: $i] : ( teach @ X @ cs ) )
% 1.40/1.15 @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 1.40/1.15
% 1.40/1.15 thf(query,conjecture,
% 1.40/1.15 ( mlocal
% 1.40/1.15 @ ( mbox
% 1.40/1.15 @ ( mexists_di
% 1.40/1.15 @ ^ [X: $i] : ( teach @ X @ cs ) ) ) ) ).
% 1.40/1.15 ------------------------
% 1.40/1.16 % (7247)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7148 for (2999ds/183Mi)
% 1.40/1.17 % (7247)First to succeed.
% 1.40/1.17 % (7247)Refutation found. Thanks to Tanya!
% 1.40/1.17 % SZS status Theorem for DTF2THF_7148
% 1.40/1.17 % SZS output start Proof for DTF2THF_7148
% 1.40/1.17 thf(type_def_5, type, mworld: $tType).
% 1.40/1.17 thf(func_def_0, type, mworld: $tType).
% 1.40/1.17 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.40/1.17 thf(func_def_2, type, mactual: mworld).
% 1.40/1.17 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.40/1.17 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.40/1.17 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.40/1.17 thf(func_def_21, type, teach: $i > $i > mworld > $o).
% 1.40/1.17 thf(func_def_35, type, sK0: mworld > $i).
% 1.40/1.17 thf(func_def_37, type, sK2: mworld).
% 1.40/1.17 thf(func_def_38, type, sK3: mworld > $i).
% 1.40/1.17 thf(f114,plain,(
% 1.40/1.17 $false),
% 1.40/1.17 inference(avatar_sat_refutation,[status(thm)],[f98,f104,f113])).
% 1.40/1.17 thf(f113,plain,(
% 1.40/1.17 ~spl1_1 | spl1_2),
% 1.40/1.17 inference(avatar_contradiction_clause,[status(thm)],[f112])).
% 1.40/1.17 thf(f112,plain,(
% 1.40/1.17 $false | (~spl1_1 | spl1_2)),
% 1.40/1.17 inference(subsumption_resolution,[status(thm)],[f108,f95])).
% 1.40/1.17 thf(f95,plain,(
% 1.40/1.17 ((mrel @ mactual @ sK2) != $false) | spl1_2),
% 1.40/1.17 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.40/1.17 thf(f94,definition,(
% 1.40/1.17 spl1_2 <=> ((mrel @ mactual @ sK2) = $false)),
% 1.40/1.17 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.40/1.17 thf(f108,plain,(
% 1.40/1.17 ((mrel @ mactual @ sK2) = $false) | ~spl1_1),
% 1.40/1.17 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.40/1.17 thf(f106,plain,(
% 1.40/1.17 ($true = $false) | ((mrel @ mactual @ sK2) = $false) | ~spl1_1),
% 1.40/1.17 inference(superposition,[status(thm)],[f92,f82])).
% 1.40/1.17 thf(f82,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : (((eiw_di @ (sK3 @ X1) @ X1) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.40/1.17 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.40/1.17 thf(f80,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : (($true = ((eiw_di @ (sK3 @ X1) @ X1) & (teach @ (sK3 @ X1) @ cs @ X1))) | ((mrel @ mactual @ X1) = $false)) )),
% 1.40/1.17 inference(beta_eta_normalization,[status(thm)],[f79])).
% 1.40/1.17 thf(f79,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1))) @ (sK3 @ X1)) = $true)) )),
% 1.40/1.17 inference(sigma_clausification,[status(thm)],[f78])).
% 1.40/1.17 thf(f78,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1)))))) )),
% 1.40/1.17 inference(binary_proxy_clausification,[status(thm)],[f75])).
% 1.40/1.17 thf(f75,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : ((((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1)))) & ((teach @ mary @ psych @ X1) & (teach @ sue @ psych @ X1))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.40/1.17 inference(binary_proxy_clausification,[status(thm)],[f74])).
% 1.40/1.17 thf(f74,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((teach @ john @ math @ X1) & ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1)))) & ((teach @ mary @ psych @ X1) & (teach @ sue @ psych @ X1)))))) )),
% 1.40/1.17 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.40/1.17 thf(f73,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => ((teach @ john @ math @ X1) & ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1)))) & ((teach @ mary @ psych @ X1) & (teach @ sue @ psych @ X1))))))) )),
% 1.40/1.17 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.40/1.17 thf(f72,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((teach @ john @ math @ Y0) & ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (teach @ Y1 @ cs @ Y0)))) & ((teach @ mary @ psych @ Y0) & (teach @ sue @ psych @ Y0)))))) @ X1) = $true)) )),
% 1.40/1.17 inference(pi_clausification,[status(thm)],[f71])).
% 1.40/1.17 thf(f71,plain,(
% 1.40/1.17 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((teach @ john @ math @ Y0) & ((?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (teach @ Y1 @ cs @ Y0)))) & ((teach @ mary @ psych @ Y0) & (teach @ sue @ psych @ Y0))))))) = $true)),
% 1.40/1.17 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.40/1.17 thf(f62,plain,(
% 1.40/1.17 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ (teach @ john @ math) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))) @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))) @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))) = $true)),
% 1.40/1.17 inference(definition_unfolding,[status(thm)],[f60,f58,f59,f53,f53,f50,f53])).
% 1.40/1.17 thf(f50,plain,(
% 1.40/1.17 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.40/1.17 inference(cnf_transformation,[status(thm)],[f23])).
% 1.40/1.17 thf(f23,plain,(
% 1.40/1.17 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.40/1.17 inference(fool_elimination,[status(thm)],[f22])).
% 1.40/1.17 thf(f22,plain,(
% 1.40/1.17 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))) = mexists_di)),
% 1.40/1.17 inference(rectify,[status(thm)],[f12])).
% 1.40/1.17 thf(f12,axiom,(
% 1.40/1.17 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5 : $i] : ((X1 @ X5 @ X2) & (eiw_di @ X5 @ X2)))) = mexists_di)),
% 1.40/1.17 file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',mexists_di_def)).
% 1.40/1.17 thf(f53,plain,(
% 1.40/1.17 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.40/1.17 inference(cnf_transformation,[status(thm)],[f27])).
% 1.40/1.17 thf(f27,plain,(
% 1.40/1.17 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.40/1.17 inference(fool_elimination,[status(thm)],[f26])).
% 1.40/1.17 thf(f26,plain,(
% 1.40/1.17 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 1.40/1.17 inference(rectify,[status(thm)],[f3])).
% 1.40/1.17 thf(f3,axiom,(
% 1.40/1.17 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 1.40/1.17 file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',mand_def)).
% 1.40/1.17 thf(f59,plain,(
% 1.40/1.17 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.40/1.17 inference(cnf_transformation,[status(thm)],[f37])).
% 1.40/1.17 thf(f37,plain,(
% 1.40/1.17 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.40/1.17 inference(fool_elimination,[status(thm)],[f36])).
% 1.40/1.17 thf(f36,plain,(
% 1.40/1.17 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.40/1.17 inference(rectify,[status(thm)],[f7])).
% 1.40/1.17 thf(f7,axiom,(
% 1.40/1.17 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.40/1.17 file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',mbox_def)).
% 1.40/1.17 thf(f58,plain,(
% 1.40/1.17 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.40/1.17 inference(cnf_transformation,[status(thm)],[f17])).
% 1.40/1.17 thf(f17,plain,(
% 1.40/1.17 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.40/1.17 inference(fool_elimination,[status(thm)],[f1])).
% 1.40/1.17 thf(f1,axiom,(
% 1.40/1.17 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.40/1.17 file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',mlocal_def)).
% 1.40/1.17 thf(f60,plain,(
% 1.40/1.17 ($true = (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))))),
% 1.40/1.17 inference(cnf_transformation,[status(thm)],[f33])).
% 1.40/1.17 thf(f33,plain,(
% 1.40/1.17 ($true = (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))))),
% 1.40/1.17 inference(fool_elimination,[status(thm)],[f32])).
% 1.40/1.17 thf(f32,plain,(
% 1.40/1.17 (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[X0 : $i] : (teach @ X0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),
% 1.40/1.17 inference(rectify,[status(thm)],[f13])).
% 1.40/1.17 thf(f13,axiom,(
% 1.40/1.17 (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[X5 : $i] : (teach @ X5 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),
% 1.40/1.17 file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',db)).
% 1.40/1.17 thf(f92,plain,(
% 1.40/1.17 ((eiw_di @ (sK3 @ sK2) @ sK2) = $false) | ~spl1_1),
% 1.40/1.17 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.40/1.17 thf(f90,definition,(
% 1.40/1.17 spl1_1 <=> ((eiw_di @ (sK3 @ sK2) @ sK2) = $false)),
% 1.40/1.17 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.40/1.17 thf(f104,plain,(
% 1.40/1.17 ~spl1_2),
% 1.40/1.17 inference(avatar_contradiction_clause,[status(thm)],[f103])).
% 1.40/1.17 thf(f103,plain,(
% 1.40/1.17 $false | ~spl1_2),
% 1.40/1.17 inference(trivial_inequality_removal,[status(thm)],[f100])).
% 1.40/1.17 thf(f100,plain,(
% 1.40/1.17 ($true = $false) | ~spl1_2),
% 1.40/1.17 inference(superposition,[status(thm)],[f67,f96])).
% 1.40/1.17 thf(f96,plain,(
% 1.40/1.17 ((mrel @ mactual @ sK2) = $false) | ~spl1_2),
% 1.40/1.17 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.40/1.17 thf(f67,plain,(
% 1.40/1.17 ($true = (mrel @ mactual @ sK2))),
% 1.40/1.17 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.40/1.17 thf(f65,plain,(
% 1.40/1.17 ($false = ((mrel @ mactual @ sK2) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (teach @ Y0 @ cs @ sK2))))))),
% 1.40/1.17 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.40/1.17 thf(f64,plain,(
% 1.40/1.17 ($false = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (teach @ Y1 @ cs @ Y0)))))) @ sK2))),
% 1.40/1.17 inference(sigma_clausification,[status(thm)],[f63])).
% 1.40/1.17 thf(f63,plain,(
% 1.40/1.17 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (teach @ Y1 @ cs @ Y0))))))))),
% 1.40/1.17 inference(beta_eta_normalization,[status(thm)],[f61])).
% 1.40/1.17 thf(f61,plain,(
% 1.40/1.17 ($true != ((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[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]: (teach @ Y0 @ cs))))))),
% 1.40/1.17 inference(definition_unfolding,[status(thm)],[f55,f58,f59,f50])).
% 1.40/1.17 thf(f55,plain,(
% 1.40/1.17 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))))) != $true)),
% 1.40/1.17 inference(cnf_transformation,[status(thm)],[f44])).
% 1.40/1.17 thf(f44,plain,(
% 1.40/1.17 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))))) != $true)),
% 1.40/1.17 inference(flattening,[status(thm)],[f39])).
% 1.40/1.17 thf(f39,plain,(
% 1.40/1.17 ~((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))))) = $true)),
% 1.40/1.17 inference(fool_elimination,[status(thm)],[f38])).
% 1.40/1.17 thf(f38,plain,(
% 1.40/1.17 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : (teach @ X0 @ cs)))))),
% 1.40/1.17 inference(rectify,[status(thm)],[f15])).
% 1.40/1.17 thf(f15,negated_conjecture,(
% 1.40/1.17 ~(mlocal @ (mbox @ (mexists_di @ (^[X5 : $i] : (teach @ X5 @ cs)))))),
% 1.40/1.17 inference(negated_conjecture,[status(cth)],[f14])).
% 1.40/1.17 thf(f14,conjecture,(
% 1.40/1.17 (mlocal @ (mbox @ (mexists_di @ (^[X5 : $i] : (teach @ X5 @ cs)))))),
% 1.40/1.17 file('/export/starexec/sandbox2/tmp/tmp.eBvCh088eU/DTF2THF_7148.p',query)).
% 1.40/1.17 thf(f98,plain,(
% 1.40/1.17 spl1_2 | spl1_1),
% 1.40/1.17 inference(avatar_split_clause,[status(thm)],[f87,f90,f94])).
% 1.40/1.17 thf(f87,plain,(
% 1.40/1.17 ((mrel @ mactual @ sK2) = $false) | ((eiw_di @ (sK3 @ sK2) @ sK2) = $false)),
% 1.40/1.17 inference(trivial_inequality_removal,[status(thm)],[f86])).
% 1.40/1.17 thf(f86,plain,(
% 1.40/1.17 ($true = $false) | ((eiw_di @ (sK3 @ sK2) @ sK2) = $false) | ((mrel @ mactual @ sK2) = $false)),
% 1.40/1.17 inference(superposition,[status(thm)],[f70,f81])).
% 1.40/1.17 thf(f81,plain,(
% 1.40/1.17 ( ! [X1 : mworld] : (($true = (teach @ (sK3 @ X1) @ cs @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.40/1.17 inference(binary_proxy_clausification,[status(thm)],[f80])).
% 1.40/1.17 thf(f70,plain,(
% 1.40/1.17 ( ! [X1 : $i] : (((teach @ X1 @ cs @ sK2) = $false) | ((eiw_di @ X1 @ sK2) = $false)) )),
% 1.40/1.17 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.40/1.17 thf(f69,plain,(
% 1.40/1.17 ( ! [X1 : $i] : ((((eiw_di @ X1 @ sK2) & (teach @ X1 @ cs @ sK2)) = $false)) )),
% 1.40/1.17 inference(beta_eta_normalization,[status(thm)],[f68])).
% 1.40/1.17 thf(f68,plain,(
% 1.40/1.17 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (teach @ Y0 @ cs @ sK2))) @ X1))) )),
% 1.40/1.17 inference(pi_clausification,[status(thm)],[f66])).
% 1.40/1.17 thf(f66,plain,(
% 1.40/1.17 ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK2) & (teach @ Y0 @ cs @ sK2)))) = $false)),
% 1.40/1.17 inference(binary_proxy_clausification,[status(thm)],[f65])).
% 1.40/1.17 % SZS output end Proof for DTF2THF_7148
% 1.40/1.17 % (7247)------------------------------
% 1.40/1.17 % (7247)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.40/1.17 % (7247)Termination reason: Refutation
% 1.40/1.17
% 1.40/1.17 % (7247)Memory used [KB]: 5628
% 1.40/1.17 % (7247)Time elapsed: 0.006 s
% 1.40/1.17 % (7247)Instructions burned: 7 (million)
% 1.40/1.17 % (7247)------------------------------
% 1.40/1.17 % (7247)------------------------------
% 1.40/1.17 % (7246)Success in time 0.015 s
%------------------------------------------------------------------------------