%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT334^19 : 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 : n001.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 08:45:29 AM UTC 2026
% Result : Theorem 1.51s 1.23s
% Output : Refutation 1.51s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 59 ( 34 unt; 0 typ; 2 def)
% Number of atoms : 397 ( 61 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 514 ( 15 ~; 20 |; 41 &; 404 @)
% ( 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 > $i ).
thf(func_def_38,type,
sK3: mworld ).
thf(f117,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f100,f106,f116]) ).
thf(f116,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[status(thm)],[f115]) ).
thf(f115,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
( ( $true = $false )
| ~ spl1_1 ),
inference(superposition,[status(thm)],[f94,f83]) ).
thf(f83,plain,
( ( mrel @ mactual @ sK3 )
= $true ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f81,plain,
( ( ( mrel @ mactual @ sK3 )
=> ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( teach @ Y0 @ cs @ sK3 ) ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) ) )
@ sK3 )
= $false ),
inference(sigma_clausification,[status(thm)],[f79]) ).
thf(f79,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)],[f63]) ).
thf(f63,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)],[f49,f51,f52,f54]) ).
thf(f54,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] :
( ( eiw_di @ Y2 @ Y1 )
& ( Y0 @ Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f39]) ).
thf(f39,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.gGgTA5ccPl/DTF2THF_28856.p',mexists_di_def) ).
thf(f52,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
thf(f42,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f41]) ).
thf(f41,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.gGgTA5ccPl/DTF2THF_28856.p',mbox_def) ).
thf(f51,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f43]) ).
thf(f43,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.gGgTA5ccPl/DTF2THF_28856.p',mlocal_def) ).
thf(f49,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)],[f38]) ).
thf(f38,plain,
( ( mlocal
@ ( mbox
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f37]) ).
thf(f37,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.gGgTA5ccPl/DTF2THF_28856.p',query) ).
thf(f94,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f92,definition,
( spl1_1
<=> ( ( mrel @ mactual @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition]) ).
thf(f106,plain,
( spl1_1
| ~ spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f103,f96,f92]) ).
thf(f96,definition,
( spl1_2
<=> ( ( eiw_di @ ( sK2 @ sK3 ) @ sK3 )
= $false ) ),
introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition]) ).
thf(f103,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ~ spl1_2 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ( $true = $false )
| ~ spl1_2 ),
inference(superposition,[status(thm)],[f98,f78]) ).
thf(f78,plain,
! [X1: mworld] :
( ( ( eiw_di @ ( sK2 @ X1 ) @ X1 )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
thf(f76,plain,
! [X1: mworld] :
( ( $true
= ( ( eiw_di @ ( sK2 @ X1 ) @ X1 )
& ( teach @ ( sK2 @ X1 ) @ cs @ X1 ) ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f75]) ).
thf(f75,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) )
@ ( sK2 @ X1 ) )
= $true ) ),
inference(sigma_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: mworld] :
( ( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: mworld] :
( ( ( ( teach @ sue @ psych @ X1 )
& ( teach @ mary @ psych @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: mworld] :
( ( ( ( teach @ sue @ psych @ X1 )
& ( teach @ mary @ psych @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ john @ math @ X1 ) )
= $true )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( teach @ sue @ psych @ X1 )
& ( teach @ mary @ psych @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ X1 )
& ( teach @ Y0 @ cs @ X1 ) ) )
& ( teach @ john @ math @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f66]) ).
thf(f66,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ sue @ psych @ Y0 )
& ( teach @ mary @ psych @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) )
& ( teach @ john @ math @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f65]) ).
thf(f65,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ sue @ psych @ Y0 )
& ( teach @ mary @ psych @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] :
( ( eiw_di @ Y1 @ Y0 )
& ( teach @ Y1 @ cs @ Y0 ) ) )
& ( teach @ john @ math @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f64]) ).
thf(f64,plain,
( $true
= ( ^ [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] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( teach @ john @ math )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( 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 ) )
@ ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) )
@ ( teach @ mary @ psych )
@ ( teach @ sue @ psych ) ) ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f55,f51,f52,f50,f50,f54,f50]) ).
thf(f50,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
thf(f30,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f29]) ).
thf(f29,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.gGgTA5ccPl/DTF2THF_28856.p',mand_def) ).
thf(f55,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)],[f24]) ).
thf(f24,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)],[f23]) ).
thf(f23,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.gGgTA5ccPl/DTF2THF_28856.p',db) ).
thf(f98,plain,
( ( ( eiw_di @ ( sK2 @ sK3 ) @ sK3 )
= $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f100,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[status(thm)],[f89,f96,f92]) ).
thf(f89,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ( ( eiw_di @ ( sK2 @ sK3 ) @ sK3 )
= $false ) ),
inference(trivial_inequality_removal,[status(thm)],[f87]) ).
thf(f87,plain,
( ( ( mrel @ mactual @ sK3 )
= $false )
| ( $true = $false )
| ( ( eiw_di @ ( sK2 @ sK3 ) @ sK3 )
= $false ) ),
inference(superposition,[status(thm)],[f77,f86]) ).
thf(f86,plain,
! [X1: $i] :
( ( ( teach @ X1 @ cs @ sK3 )
= $false )
| ( ( eiw_di @ X1 @ sK3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f85]) ).
thf(f85,plain,
! [X1: $i] :
( ( ( eiw_di @ X1 @ sK3 )
& ( teach @ X1 @ cs @ sK3 ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f84]) ).
thf(f84,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( teach @ Y0 @ cs @ sK3 ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f82]) ).
thf(f82,plain,
( ( ?? @ $i
@ ^ [Y0: $i] :
( ( eiw_di @ Y0 @ sK3 )
& ( teach @ Y0 @ cs @ sK3 ) ) )
= $false ),
inference(binary_proxy_clausification,[status(thm)],[f81]) ).
thf(f77,plain,
! [X1: mworld] :
( ( $true
= ( teach @ ( sK2 @ X1 ) @ cs @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f76]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : DAT334^19 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.11 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.12/0.31 % Computer : n001.cluster.edu
% 0.12/0.31 % Model : x86_64 x86_64
% 0.12/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.31 % Memory : 8042.1875MB
% 0.12/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.31 % CPULimit : 300
% 0.12/0.31 % WCLimit : 300
% 0.12/0.31 % DateTime : Tue Feb 24 06:15:50 EST 2026
% 0.12/0.31 % CPUTime :
% 0.12/0.31 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.15/0.42 ---- Original DTF file ---
% 0.15/0.42 thf(spec,logic,$$dhol).
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 % File : DAT334^19 : TPTP v9.2.1. Released v8.1.0.
% 0.15/0.42 % Domain : Data Structures
% 0.15/0.42 % Problem : Database querying
% 0.15/0.42 % Version : [BP13] axioms.
% 0.15/0.42 % English :
% 0.15/0.42
% 0.15/0.42 % Refs : [Rei92] Reiter (1992), What Should a Database Know?
% 0.15/0.42 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.15/0.42 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.15/0.42 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.15/0.42 % Source : [TPTP]
% 0.15/0.42 % Names : APM009+1 [QMLTP]
% 0.15/0.42
% 0.15/0.42 % Status : Theorem
% 0.15/0.42 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.20 v8.2.0, 0.31 v8.1.0
% 0.15/0.42 % Syntax : Number of formulae : 35 ( 11 unt; 21 typ; 10 def)
% 0.15/0.42 % Number of atoms : 42 ( 10 equ; 0 cnn)
% 0.15/0.42 % Maximal formula atoms : 10 ( 3 avg)
% 0.15/0.42 % Number of connectives : 65 ( 1 ~; 1 |; 4 &; 54 @)
% 0.15/0.42 % ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% 0.15/0.42 % Maximal formula depth : 10 ( 3 avg)
% 0.15/0.42 % Number of types : 3 ( 1 usr)
% 0.15/0.42 % Number of type conns : 62 ( 62 >; 0 *; 0 +; 0 <<)
% 0.15/0.42 % Number of symbols : 21 ( 20 usr; 7 con; 0-3 aty)
% 0.15/0.42 % Number of variables : 34 ( 25 ^; 6 !; 3 ?; 34 :)
% 0.15/0.42 % SPC : TH0_THM_EQU_NAR
% 0.15/0.42
% 0.15/0.42 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.15/0.42 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.15/0.42 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.15/0.42 % $modal == [$constants == $rigid,$quantification == $decreasing,
% 0.15/0.42 % $modalities == $modal_system_K].
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 thf(mworld,type,
% 0.15/0.42 mworld: $tType ).
% 0.15/0.42
% 0.15/0.42 thf(mrel_type,type,
% 0.15/0.42 mrel: mworld > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mactual_type,type,
% 0.15/0.42 mactual: mworld ).
% 0.15/0.42
% 0.15/0.42 thf(mlocal_type,type,
% 0.15/0.42 mlocal: ( mworld > $o ) > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mlocal_def,definition,
% 0.15/0.42 ( mlocal
% 0.15/0.42 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mnot_type,type,
% 0.15/0.42 mnot: ( mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mand_type,type,
% 0.15/0.42 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mor_type,type,
% 0.15/0.42 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mimplies_type,type,
% 0.15/0.42 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mequiv_type,type,
% 0.15/0.42 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mnot_def,definition,
% 0.15/0.42 ( mnot
% 0.15/0.42 = ( ^ [A: mworld > $o,W: mworld] :
% 0.15/0.42 ~ ( A @ W ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mand_def,definition,
% 0.15/0.42 ( mand
% 0.15/0.42 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.15/0.42 ( ( A @ W )
% 0.15/0.42 & ( B @ W ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mor_def,definition,
% 0.15/0.42 ( mor
% 0.15/0.42 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.15/0.42 ( ( A @ W )
% 0.15/0.42 | ( B @ W ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mimplies_def,definition,
% 0.15/0.42 ( mimplies
% 0.15/0.42 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.15/0.42 ( ( A @ W )
% 0.15/0.42 => ( B @ W ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mequiv_def,definition,
% 0.15/0.42 ( mequiv
% 0.15/0.42 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.15/0.42 ( ( A @ W )
% 0.15/0.42 <=> ( B @ W ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mbox_type,type,
% 0.15/0.42 mbox: ( mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mbox_def,definition,
% 0.15/0.42 ( mbox
% 0.15/0.42 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.15/0.42 ! [V: mworld] :
% 0.15/0.42 ( ( mrel @ W @ V )
% 0.15/0.42 => ( Phi @ V ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mdia_type,type,
% 0.15/0.42 mdia: ( mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mdia_def,definition,
% 0.15/0.42 ( mdia
% 0.15/0.42 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.15/0.42 ? [V: mworld] :
% 0.15/0.42 ( ( mrel @ W @ V )
% 0.15/0.42 & ( Phi @ V ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(eiw_di_type,type,
% 0.15/0.42 eiw_di: $i > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(eiw_di_nonempty,axiom,
% 0.15/0.42 ! [W: mworld] :
% 0.15/0.42 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 0.15/0.42
% 0.15/0.42 thf(eiw_di_decr,axiom,
% 0.15/0.42 ! [W: mworld,V: mworld,X: $i] :
% 0.15/0.42 ( ( ( eiw_di @ X @ W )
% 0.15/0.42 & ( mrel @ V @ W ) )
% 0.15/0.42 => ( eiw_di @ X @ V ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mforall_di_type,type,
% 0.15/0.42 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mforall_di_def,definition,
% 0.15/0.42 ( mforall_di
% 0.15/0.42 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.15/0.42 ! [X: $i] :
% 0.15/0.42 ( ( eiw_di @ X @ W )
% 0.15/0.42 => ( A @ X @ W ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(mexists_di_type,type,
% 0.15/0.42 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(mexists_di_def,definition,
% 0.15/0.42 ( mexists_di
% 0.15/0.42 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.15/0.42 ? [X: $i] :
% 0.15/0.42 ( ( eiw_di @ X @ W )
% 0.15/0.42 & ( A @ X @ W ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(cs_decl,type,
% 0.15/0.42 cs: $i ).
% 0.15/0.42
% 0.15/0.42 thf(sue_decl,type,
% 0.15/0.42 sue: $i ).
% 0.15/0.42
% 0.15/0.42 thf(mary_decl,type,
% 0.15/0.42 mary: $i ).
% 0.15/0.42
% 0.15/0.42 thf(john_decl,type,
% 0.15/0.42 john: $i ).
% 0.15/0.42
% 0.15/0.42 thf(math_decl,type,
% 0.15/0.42 math: $i ).
% 0.15/0.42
% 0.15/0.42 thf(psych_decl,type,
% 0.15/0.42 psych: $i ).
% 0.15/0.42
% 0.15/0.42 thf(teach_decl,type,
% 0.15/0.42 teach: $i > $i > mworld > $o ).
% 0.15/0.42
% 0.15/0.42 thf(db,axiom,
% 0.15/0.42 ( mlocal
% 0.15/0.42 @ ( mbox
% 0.15/0.42 @ ( mand @ ( teach @ john @ math )
% 0.15/0.42 @ ( mand
% 0.15/0.42 @ ( mexists_di
% 0.15/0.42 @ ^ [X: $i] : ( teach @ X @ cs ) )
% 0.15/0.42 @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 thf(query,conjecture,
% 0.15/0.42 ( mlocal
% 0.15/0.42 @ ( mbox
% 0.15/0.42 @ ( mexists_di
% 0.15/0.42 @ ^ [X: $i] : ( teach @ X @ cs ) ) ) ) ).
% 0.15/0.42
% 0.15/0.42 %------------------------------------------------------------------------------
% 0.15/0.42 ------------------------
% 1.51/1.21 ---- Embedded in THF ---
% 1.51/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.21 %%% Generated on Tue Feb 24 06:15:51 EST 2026
% 1.51/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.21 %%% Logic specification used:
% 1.51/1.21 %%% thf(spec, logic, $$dhol).
% 1.51/1.21
% 1.51/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.gGgTA5ccPl/DTF2DTF28856.p
% See solution above
% 1.51/1.21 ------------------------
% 1.51/1.21 ---- Cleaned THF ---
% 1.51/1.21 thf(mworld,type,
% 1.51/1.21 mworld: $tType ).
% 1.51/1.21
% 1.51/1.21 thf(mrel_type,type,
% 1.51/1.21 mrel: mworld > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mactual_type,type,
% 1.51/1.21 mactual: mworld ).
% 1.51/1.21
% 1.51/1.21 thf(mlocal_type,type,
% 1.51/1.21 mlocal: ( mworld > $o ) > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mlocal_def,definition,
% 1.51/1.21 ( mlocal
% 1.51/1.21 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mnot_type,type,
% 1.51/1.21 mnot: ( mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mand_type,type,
% 1.51/1.21 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mor_type,type,
% 1.51/1.21 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mimplies_type,type,
% 1.51/1.21 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mequiv_type,type,
% 1.51/1.21 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mnot_def,definition,
% 1.51/1.21 ( mnot
% 1.51/1.21 = ( ^ [A: mworld > $o,W: mworld] :
% 1.51/1.21 ~ ( A @ W ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mand_def,definition,
% 1.51/1.21 ( mand
% 1.51/1.21 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.51/1.21 ( ( A @ W )
% 1.51/1.21 & ( B @ W ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mor_def,definition,
% 1.51/1.21 ( mor
% 1.51/1.21 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.51/1.21 ( ( A @ W )
% 1.51/1.21 | ( B @ W ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mimplies_def,definition,
% 1.51/1.21 ( mimplies
% 1.51/1.21 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.51/1.21 ( ( A @ W )
% 1.51/1.21 => ( B @ W ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mequiv_def,definition,
% 1.51/1.21 ( mequiv
% 1.51/1.21 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.51/1.21 ( ( A @ W )
% 1.51/1.21 <=> ( B @ W ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mbox_type,type,
% 1.51/1.21 mbox: ( mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mbox_def,definition,
% 1.51/1.21 ( mbox
% 1.51/1.21 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.51/1.21 ! [V: mworld] :
% 1.51/1.21 ( ( mrel @ W @ V )
% 1.51/1.21 => ( Phi @ V ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mdia_type,type,
% 1.51/1.21 mdia: ( mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mdia_def,definition,
% 1.51/1.21 ( mdia
% 1.51/1.21 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.51/1.21 ? [V: mworld] :
% 1.51/1.21 ( ( mrel @ W @ V )
% 1.51/1.21 & ( Phi @ V ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(eiw_di_type,type,
% 1.51/1.21 eiw_di: $i > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(eiw_di_nonempty,axiom,
% 1.51/1.21 ! [W: mworld] :
% 1.51/1.21 ? [X: $i] : ( eiw_di @ X @ W ) ).
% 1.51/1.21
% 1.51/1.21 thf(eiw_di_decr,axiom,
% 1.51/1.21 ! [W: mworld,V: mworld,X: $i] :
% 1.51/1.21 ( ( ( eiw_di @ X @ W )
% 1.51/1.21 & ( mrel @ V @ W ) )
% 1.51/1.21 => ( eiw_di @ X @ V ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mforall_di_type,type,
% 1.51/1.21 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mforall_di_def,definition,
% 1.51/1.21 ( mforall_di
% 1.51/1.21 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.51/1.21 ! [X: $i] :
% 1.51/1.21 ( ( eiw_di @ X @ W )
% 1.51/1.21 => ( A @ X @ W ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(mexists_di_type,type,
% 1.51/1.21 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(mexists_di_def,definition,
% 1.51/1.21 ( mexists_di
% 1.51/1.21 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.51/1.21 ? [X: $i] :
% 1.51/1.21 ( ( eiw_di @ X @ W )
% 1.51/1.21 & ( A @ X @ W ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(cs_decl,type,
% 1.51/1.21 cs: $i ).
% 1.51/1.21
% 1.51/1.21 thf(sue_decl,type,
% 1.51/1.21 sue: $i ).
% 1.51/1.21
% 1.51/1.21 thf(mary_decl,type,
% 1.51/1.21 mary: $i ).
% 1.51/1.21
% 1.51/1.21 thf(john_decl,type,
% 1.51/1.21 john: $i ).
% 1.51/1.21
% 1.51/1.21 thf(math_decl,type,
% 1.51/1.21 math: $i ).
% 1.51/1.21
% 1.51/1.21 thf(psych_decl,type,
% 1.51/1.21 psych: $i ).
% 1.51/1.21
% 1.51/1.21 thf(teach_decl,type,
% 1.51/1.21 teach: $i > $i > mworld > $o ).
% 1.51/1.21
% 1.51/1.21 thf(db,axiom,
% 1.51/1.21 ( mlocal
% 1.51/1.21 @ ( mbox
% 1.51/1.21 @ ( mand @ ( teach @ john @ math )
% 1.51/1.21 @ ( mand
% 1.51/1.21 @ ( mexists_di
% 1.51/1.21 @ ^ [X: $i] : ( teach @ X @ cs ) )
% 1.51/1.21 @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 1.51/1.21
% 1.51/1.21 thf(query,conjecture,
% 1.51/1.21 ( mlocal
% 1.51/1.21 @ ( mbox
% 1.51/1.21 @ ( mexists_di
% 1.51/1.21 @ ^ [X: $i] : ( teach @ X @ cs ) ) ) ) ).
% 1.51/1.21 ------------------------
% 1.51/1.23 % (28963)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_28856 for (2999ds/183Mi)
% 1.51/1.23 % (28963)First to succeed.
% 1.51/1.23 % (28963)Refutation found. Thanks to Tanya!
% 1.51/1.23 % SZS status Theorem for DTF2THF_28856
% 1.51/1.23 % SZS output start Proof for DTF2THF_28856
% 1.51/1.23 thf(type_def_5, type, mworld: $tType).
% 1.51/1.23 thf(func_def_0, type, mworld: $tType).
% 1.51/1.23 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.51/1.23 thf(func_def_2, type, mactual: mworld).
% 1.51/1.23 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.51/1.23 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_12, type, eiw_di: $i > mworld > $o).
% 1.51/1.23 thf(func_def_13, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_14, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.51/1.23 thf(func_def_21, type, teach: $i > $i > mworld > $o).
% 1.51/1.23 thf(func_def_35, type, sK0: mworld > $i).
% 1.51/1.23 thf(func_def_37, type, sK2: mworld > $i).
% 1.51/1.23 thf(func_def_38, type, sK3: mworld).
% 1.51/1.23 thf(f117,plain,(
% 1.51/1.23 $false),
% 1.51/1.23 inference(avatar_sat_refutation,[status(thm)],[f100,f106,f116])).
% 1.51/1.23 thf(f116,plain,(
% 1.51/1.23 ~spl1_1),
% 1.51/1.23 inference(avatar_contradiction_clause,[status(thm)],[f115])).
% 1.51/1.23 thf(f115,plain,(
% 1.51/1.23 $false | ~spl1_1),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.51/1.23 thf(f111,plain,(
% 1.51/1.23 ($true = $false) | ~spl1_1),
% 1.51/1.23 inference(superposition,[status(thm)],[f94,f83])).
% 1.51/1.23 thf(f83,plain,(
% 1.51/1.23 ((mrel @ mactual @ sK3) = $true)),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.51/1.23 thf(f81,plain,(
% 1.51/1.23 (((mrel @ mactual @ sK3) => (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (teach @ Y0 @ cs @ sK3))))) = $false)),
% 1.51/1.23 inference(beta_eta_normalization,[status(thm)],[f80])).
% 1.51/1.23 thf(f80,plain,(
% 1.51/1.23 (((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (teach @ Y1 @ cs @ Y0)))))) @ sK3) = $false)),
% 1.51/1.23 inference(sigma_clausification,[status(thm)],[f79])).
% 1.51/1.23 thf(f79,plain,(
% 1.51/1.23 ($true != (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (teach @ Y1 @ cs @ Y0))))))))),
% 1.51/1.23 inference(beta_eta_normalization,[status(thm)],[f63])).
% 1.51/1.23 thf(f63,plain,(
% 1.51/1.23 ($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))))))),
% 1.51/1.23 inference(definition_unfolding,[status(thm)],[f49,f51,f52,f54])).
% 1.51/1.23 thf(f54,plain,(
% 1.51/1.23 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.51/1.23 inference(cnf_transformation,[status(thm)],[f40])).
% 1.51/1.23 thf(f40,plain,(
% 1.51/1.23 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: ((eiw_di @ Y2 @ Y1) & (Y0 @ Y2 @ Y1))))))))),
% 1.51/1.23 inference(fool_elimination,[status(thm)],[f39])).
% 1.51/1.23 thf(f39,plain,(
% 1.51/1.23 ((^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : ((X0 @ X2 @ X1) & (eiw_di @ X2 @ X1)))) = mexists_di)),
% 1.51/1.23 inference(rectify,[status(thm)],[f12])).
% 1.51/1.23 thf(f12,axiom,(
% 1.51/1.23 ((^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5 : $i] : ((X1 @ X5 @ X2) & (eiw_di @ X5 @ X2)))) = mexists_di)),
% 1.51/1.23 file('/export/starexec/sandbox2/tmp/tmp.gGgTA5ccPl/DTF2THF_28856.p',mexists_di_def)).
% 1.51/1.23 thf(f52,plain,(
% 1.51/1.23 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.51/1.23 inference(cnf_transformation,[status(thm)],[f42])).
% 1.51/1.23 thf(f42,plain,(
% 1.51/1.23 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.51/1.23 inference(fool_elimination,[status(thm)],[f41])).
% 1.51/1.23 thf(f41,plain,(
% 1.51/1.23 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.51/1.23 inference(rectify,[status(thm)],[f7])).
% 1.51/1.23 thf(f7,axiom,(
% 1.51/1.23 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.51/1.23 file('/export/starexec/sandbox2/tmp/tmp.gGgTA5ccPl/DTF2THF_28856.p',mbox_def)).
% 1.51/1.23 thf(f51,plain,(
% 1.51/1.23 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.51/1.23 inference(cnf_transformation,[status(thm)],[f43])).
% 1.51/1.23 thf(f43,plain,(
% 1.51/1.23 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.51/1.23 inference(fool_elimination,[status(thm)],[f1])).
% 1.51/1.23 thf(f1,axiom,(
% 1.51/1.23 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.51/1.23 file('/export/starexec/sandbox2/tmp/tmp.gGgTA5ccPl/DTF2THF_28856.p',mlocal_def)).
% 1.51/1.23 thf(f49,plain,(
% 1.51/1.23 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))))) != $true)),
% 1.51/1.23 inference(cnf_transformation,[status(thm)],[f44])).
% 1.51/1.23 thf(f44,plain,(
% 1.51/1.23 ((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))))) != $true)),
% 1.51/1.23 inference(flattening,[status(thm)],[f38])).
% 1.51/1.23 thf(f38,plain,(
% 1.51/1.23 ~((mlocal @ (mbox @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))))) = $true)),
% 1.51/1.23 inference(fool_elimination,[status(thm)],[f37])).
% 1.51/1.23 thf(f37,plain,(
% 1.51/1.23 ~(mlocal @ (mbox @ (mexists_di @ (^[X0 : $i] : (teach @ X0 @ cs)))))),
% 1.51/1.23 inference(rectify,[status(thm)],[f15])).
% 1.51/1.23 thf(f15,negated_conjecture,(
% 1.51/1.23 ~(mlocal @ (mbox @ (mexists_di @ (^[X5 : $i] : (teach @ X5 @ cs)))))),
% 1.51/1.23 inference(negated_conjecture,[status(cth)],[f14])).
% 1.51/1.23 thf(f14,conjecture,(
% 1.51/1.23 (mlocal @ (mbox @ (mexists_di @ (^[X5 : $i] : (teach @ X5 @ cs)))))),
% 1.51/1.23 file('/export/starexec/sandbox2/tmp/tmp.gGgTA5ccPl/DTF2THF_28856.p',query)).
% 1.51/1.23 thf(f94,plain,(
% 1.51/1.23 ((mrel @ mactual @ sK3) = $false) | ~spl1_1),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.51/1.23 thf(f92,definition,(
% 1.51/1.23 spl1_1 <=> ((mrel @ mactual @ sK3) = $false)),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl1_1])],[avatar_definition])).
% 1.51/1.23 thf(f106,plain,(
% 1.51/1.23 spl1_1 | ~spl1_2),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f103,f96,f92])).
% 1.51/1.23 thf(f96,definition,(
% 1.51/1.23 spl1_2 <=> ((eiw_di @ (sK2 @ sK3) @ sK3) = $false)),
% 1.51/1.23 introduced(definition,[new_symbols(naming,[spl1_2])],[avatar_definition])).
% 1.51/1.23 thf(f103,plain,(
% 1.51/1.23 ((mrel @ mactual @ sK3) = $false) | ~spl1_2),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.51/1.23 thf(f101,plain,(
% 1.51/1.23 ((mrel @ mactual @ sK3) = $false) | ($true = $false) | ~spl1_2),
% 1.51/1.23 inference(superposition,[status(thm)],[f98,f78])).
% 1.51/1.23 thf(f78,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : (((eiw_di @ (sK2 @ X1) @ X1) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.51/1.23 thf(f76,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : (($true = ((eiw_di @ (sK2 @ X1) @ X1) & (teach @ (sK2 @ X1) @ cs @ X1))) | ((mrel @ mactual @ X1) = $false)) )),
% 1.51/1.23 inference(beta_eta_normalization,[status(thm)],[f75])).
% 1.51/1.23 thf(f75,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | (((^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1))) @ (sK2 @ X1)) = $true)) )),
% 1.51/1.23 inference(sigma_clausification,[status(thm)],[f71])).
% 1.51/1.23 thf(f71,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : (((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1)))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f70])).
% 1.51/1.23 thf(f70,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : (((((teach @ sue @ psych @ X1) & (teach @ mary @ psych @ X1)) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1))))) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.51/1.23 thf(f68,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : ((((((teach @ sue @ psych @ X1) & (teach @ mary @ psych @ X1)) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1))))) & (teach @ john @ math @ X1)) = $true) | ((mrel @ mactual @ X1) = $false)) )),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f67])).
% 1.51/1.23 thf(f67,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => ((((teach @ sue @ psych @ X1) & (teach @ mary @ psych @ X1)) & (?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ X1) & (teach @ Y0 @ cs @ X1))))) & (teach @ john @ math @ X1))) = $true)) )),
% 1.51/1.23 inference(beta_eta_normalization,[status(thm)],[f66])).
% 1.51/1.23 thf(f66,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((((teach @ sue @ psych @ Y0) & (teach @ mary @ psych @ Y0)) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (teach @ Y1 @ cs @ Y0))))) & (teach @ john @ math @ Y0)))) @ X1))) )),
% 1.51/1.23 inference(pi_clausification,[status(thm)],[f65])).
% 1.51/1.23 thf(f65,plain,(
% 1.51/1.23 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((((teach @ sue @ psych @ Y0) & (teach @ mary @ psych @ Y0)) & (?? @ $i @ (^[Y1 : $i]: ((eiw_di @ Y1 @ Y0) & (teach @ Y1 @ cs @ Y0))))) & (teach @ john @ math @ Y0))))) = $true)),
% 1.51/1.23 inference(beta_eta_normalization,[status(thm)],[f64])).
% 1.51/1.23 thf(f64,plain,(
% 1.51/1.23 ($true = ((^[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]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ (teach @ john @ math) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((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))) @ ((^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))) @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))))),
% 1.51/1.23 inference(definition_unfolding,[status(thm)],[f55,f51,f52,f50,f50,f54,f50])).
% 1.51/1.23 thf(f50,plain,(
% 1.51/1.23 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.51/1.23 inference(cnf_transformation,[status(thm)],[f30])).
% 1.51/1.23 thf(f30,plain,(
% 1.51/1.23 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.51/1.23 inference(fool_elimination,[status(thm)],[f29])).
% 1.51/1.23 thf(f29,plain,(
% 1.51/1.23 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 1.51/1.23 inference(rectify,[status(thm)],[f3])).
% 1.51/1.23 thf(f3,axiom,(
% 1.51/1.23 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 1.51/1.23 file('/export/starexec/sandbox2/tmp/tmp.gGgTA5ccPl/DTF2THF_28856.p',mand_def)).
% 1.51/1.23 thf(f55,plain,(
% 1.51/1.23 ($true = (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))))),
% 1.51/1.23 inference(cnf_transformation,[status(thm)],[f24])).
% 1.51/1.23 thf(f24,plain,(
% 1.51/1.23 ($true = (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))))),
% 1.51/1.23 inference(fool_elimination,[status(thm)],[f23])).
% 1.51/1.23 thf(f23,plain,(
% 1.51/1.23 (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[X0 : $i] : (teach @ X0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),
% 1.51/1.23 inference(rectify,[status(thm)],[f13])).
% 1.51/1.23 thf(f13,axiom,(
% 1.51/1.23 (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[X5 : $i] : (teach @ X5 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),
% 1.51/1.23 file('/export/starexec/sandbox2/tmp/tmp.gGgTA5ccPl/DTF2THF_28856.p',db)).
% 1.51/1.23 thf(f98,plain,(
% 1.51/1.23 ((eiw_di @ (sK2 @ sK3) @ sK3) = $false) | ~spl1_2),
% 1.51/1.23 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.51/1.23 thf(f100,plain,(
% 1.51/1.23 spl1_1 | spl1_2),
% 1.51/1.23 inference(avatar_split_clause,[status(thm)],[f89,f96,f92])).
% 1.51/1.23 thf(f89,plain,(
% 1.51/1.23 ((mrel @ mactual @ sK3) = $false) | ((eiw_di @ (sK2 @ sK3) @ sK3) = $false)),
% 1.51/1.23 inference(trivial_inequality_removal,[status(thm)],[f87])).
% 1.51/1.23 thf(f87,plain,(
% 1.51/1.23 ((mrel @ mactual @ sK3) = $false) | ($true = $false) | ((eiw_di @ (sK2 @ sK3) @ sK3) = $false)),
% 1.51/1.23 inference(superposition,[status(thm)],[f77,f86])).
% 1.51/1.23 thf(f86,plain,(
% 1.51/1.23 ( ! [X1 : $i] : (((teach @ X1 @ cs @ sK3) = $false) | ((eiw_di @ X1 @ sK3) = $false)) )),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f85])).
% 1.51/1.23 thf(f85,plain,(
% 1.51/1.23 ( ! [X1 : $i] : ((((eiw_di @ X1 @ sK3) & (teach @ X1 @ cs @ sK3)) = $false)) )),
% 1.51/1.23 inference(beta_eta_normalization,[status(thm)],[f84])).
% 1.51/1.23 thf(f84,plain,(
% 1.51/1.23 ( ! [X1 : $i] : ((((^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (teach @ Y0 @ cs @ sK3))) @ X1) = $false)) )),
% 1.51/1.23 inference(pi_clausification,[status(thm)],[f82])).
% 1.51/1.23 thf(f82,plain,(
% 1.51/1.23 ((?? @ $i @ (^[Y0 : $i]: ((eiw_di @ Y0 @ sK3) & (teach @ Y0 @ cs @ sK3)))) = $false)),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f81])).
% 1.51/1.23 thf(f77,plain,(
% 1.51/1.23 ( ! [X1 : mworld] : (($true = (teach @ (sK2 @ X1) @ cs @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.51/1.23 inference(binary_proxy_clausification,[status(thm)],[f76])).
% 1.51/1.23 % SZS output end Proof for DTF2THF_28856
% 1.51/1.23 % (28963)------------------------------
% 1.51/1.23 % (28963)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.51/1.23 % (28963)Termination reason: Refutation
% 1.51/1.23
% 1.51/1.23 % (28963)Memory used [KB]: 5628
% 1.51/1.23 % (28963)Time elapsed: 0.006 s
% 1.51/1.23 % (28963)Instructions burned: 9 (million)
% 1.51/1.23 % (28963)------------------------------
% 1.51/1.23 % (28963)------------------------------
% 1.51/1.23 % (28962)Success in time 0.016 s
%------------------------------------------------------------------------------