%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT333^6 : 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 : n013.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 1.80s 1.31s
% Output : Refutation 1.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 296 ( 41 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 373 ( 7 ~; 3 |; 19 &; 313 @)
% ( 0 <=>; 14 =>; 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 : 26 ( 21 usr; 11 con; 0-3 aty)
% ( 8 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 103 ( 82 ^; 19 !; 2 ?; 103 :)
% 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,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_13,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(func_def_20,type,
teach: $i > $i > mworld > $o ).
thf(func_def_35,type,
sK1: mworld > $i ).
thf(func_def_36,type,
sK2: $i > mworld ).
thf(f82,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
$true = $false,
inference(superposition,[status(thm)],[f79,f50]) ).
thf(f50,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(cnf_transformation,[status(thm)],[f38]) ).
thf(f38,plain,
! [X0: mworld,X1: mworld] :
( ( mrel @ X0 @ X1 )
= $true ),
inference(fool_elimination,[status(thm)],[f37]) ).
thf(f37,plain,
! [X0: mworld,X1: mworld] : ( mrel @ X0 @ X1 ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,axiom,
! [X2: mworld,X4: mworld] : ( mrel @ X2 @ X4 ),
file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mrel_universal) ).
thf(f79,plain,
( ( mrel @ mactual @ ( sK2 @ math ) )
= $false ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( $true = $false )
| ( ( mrel @ mactual @ ( sK2 @ math ) )
= $false ) ),
inference(superposition,[status(thm)],[f74,f62]) ).
thf(f62,plain,
! [X1: mworld] :
( ( $true
= ( teach @ john @ math @ X1 ) )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: mworld] :
( ( ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] : ( teach @ Y0 @ cs @ X1 ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) )
= $true )
| ( $false
= ( mrel @ mactual @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
=> ( ( teach @ john @ math @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] : ( teach @ Y0 @ cs @ X1 ) )
& ( teach @ mary @ psych @ X1 )
& ( teach @ sue @ psych @ X1 ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( teach @ Y1 @ cs @ Y0 ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f57]) ).
thf(f57,plain,
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ john @ math @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( teach @ Y1 @ cs @ Y0 ) )
& ( teach @ mary @ psych @ Y0 )
& ( teach @ sue @ psych @ Y0 ) ) ) )
= $true ),
inference(beta_eta_normalization,[status(thm)],[f55]) ).
thf(f55,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] : ( 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)],[f51,f44,f53,f45,f45,f47,f45]) ).
thf(f47,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f39]) ).
thf(f39,plain,
( mexists_di
= ( ^ [X0: $i > mworld > $o,X1: mworld] :
? [X2: $i] : ( X0 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,axiom,
( mexists_di
= ( ^ [X1: $i > mworld > $o,X2: mworld] :
? [X5: $i] : ( X1 @ X5 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mexists_di_def) ).
thf(f45,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
thf(f29,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y0 @ Y2 )
& ( Y1 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,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/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mand_def) ).
thf(f53,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f22]) ).
thf(f22,plain,
( ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) )
= mbox ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) )
= mbox ),
file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mbox_def) ).
thf(f44,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.9WSfrPu12H/DTF2THF_30579.p',mlocal_def) ).
thf(f51,plain,
( ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( mlocal
@ ( mbox
@ ( mand @ ( teach @ john @ math )
@ ( mand
@ ( mexists_di
@ ^ [Y0: $i] : ( teach @ Y0 @ cs ) )
@ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) )
= $true ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,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)],[f12]) ).
thf(f12,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/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',db) ).
thf(f74,plain,
! [X1: $i] :
( $false
= ( teach @ john @ X1 @ ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f73]) ).
thf(f73,plain,
! [X1: $i] :
( ( ( mrel @ mactual @ ( sK2 @ X1 ) )
=> ( teach @ john @ X1 @ ( sK2 @ X1 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f72]) ).
thf(f72,plain,
! [X1: $i] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( teach @ john @ X1 @ Y0 ) )
@ ( sK2 @ X1 ) )
= $false ),
inference(sigma_clausification,[status(thm)],[f71]) ).
thf(f71,plain,
! [X1: $i] :
( ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( teach @ john @ X1 @ Y0 ) ) )
= $false ),
inference(beta_eta_normalization,[status(thm)],[f70]) ).
thf(f70,plain,
! [X1: $i] :
( $false
= ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( teach @ john @ Y0 @ Y1 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( teach @ john @ Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f56]) ).
thf(f56,plain,
( ( ^ [Y0: mworld > $o] : ( Y0 @ mactual )
@ ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) )
@ ^ [Y0: $i] :
( ^ [Y1: mworld > $o,Y2: mworld] :
( !! @ mworld
@ ^ [Y3: mworld] :
( ( mrel @ Y2 @ Y3 )
=> ( Y1 @ Y3 ) ) )
@ ( teach @ john @ Y0 ) ) ) )
!= $true ),
inference(definition_unfolding,[status(thm)],[f54,f44,f47,f53]) ).
thf(f54,plain,
( ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) )
!= $true ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) )
!= $true ),
inference(flattening,[status(thm)],[f19]) ).
thf(f19,plain,
( ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) )
!= $true ),
inference(fool_elimination,[status(thm)],[f18]) ).
thf(f18,plain,
~ ( mlocal
@ ( mexists_di
@ ^ [X0: $i] : ( mbox @ ( teach @ john @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f14]) ).
thf(f14,negated_conjecture,
~ ( mlocal
@ ( mexists_di
@ ^ [X5: $i] : ( mbox @ ( teach @ john @ X5 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
thf(f13,conjecture,
( mlocal
@ ( mexists_di
@ ^ [X5: $i] : ( mbox @ ( teach @ john @ X5 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',query) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : DAT333^6 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n013.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 06:14:53 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : DAT333^6 : TPTP v9.2.1. Released v8.1.0.
% 0.30/0.45 % Domain : Data Structures
% 0.30/0.45 % Problem : Database querying
% 0.30/0.45 % Version : [BP13] axioms.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Rei92] Reiter (1992), What Should a Database Know?
% 0.30/0.45 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.30/0.45 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.30/0.45 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.30/0.45 % Source : [TPTP]
% 0.30/0.45 % Names : APM008+1 [QMLTP]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.00 v8.2.0, 0.15 v8.1.0
% 0.30/0.45 % Syntax : Number of formulae : 33 ( 11 unt; 20 typ; 10 def)
% 0.30/0.45 % Number of atoms : 37 ( 10 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 10 ( 2 avg)
% 0.30/0.45 % Number of connectives : 51 ( 1 ~; 1 |; 2 &; 44 @)
% 0.30/0.45 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 10 ( 2 avg)
% 0.30/0.45 % Number of types : 3 ( 1 usr)
% 0.30/0.45 % Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 20 ( 19 usr; 7 con; 0-3 aty)
% 0.30/0.45 % Number of variables : 31 ( 25 ^; 4 !; 2 ?; 31 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.30/0.45 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.30/0.45 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.30/0.45 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.30/0.45 % $modalities == $modal_system_S5U].
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(mworld,type,
% 0.30/0.45 mworld: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(mrel_type,type,
% 0.30/0.45 mrel: mworld > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mactual_type,type,
% 0.30/0.45 mactual: mworld ).
% 0.30/0.45
% 0.30/0.45 thf(mlocal_type,type,
% 0.30/0.45 mlocal: ( mworld > $o ) > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mlocal_def,definition,
% 0.30/0.45 ( mlocal
% 0.30/0.45 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mnot_type,type,
% 0.30/0.45 mnot: ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mand_type,type,
% 0.30/0.45 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mor_type,type,
% 0.30/0.45 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mimplies_type,type,
% 0.30/0.45 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mequiv_type,type,
% 0.30/0.45 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mnot_def,definition,
% 0.30/0.45 ( mnot
% 0.30/0.45 = ( ^ [A: mworld > $o,W: mworld] :
% 0.30/0.45 ~ ( A @ W ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mand_def,definition,
% 0.30/0.45 ( mand
% 0.30/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.45 ( ( A @ W )
% 0.30/0.45 & ( B @ W ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mor_def,definition,
% 0.30/0.45 ( mor
% 0.30/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.45 ( ( A @ W )
% 0.30/0.45 | ( B @ W ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mimplies_def,definition,
% 0.30/0.45 ( mimplies
% 0.30/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.45 ( ( A @ W )
% 0.30/0.45 => ( B @ W ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mequiv_def,definition,
% 0.30/0.45 ( mequiv
% 0.30/0.45 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.30/0.45 ( ( A @ W )
% 0.30/0.45 <=> ( B @ W ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mbox_type,type,
% 0.30/0.45 mbox: ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mbox_def,definition,
% 0.30/0.45 ( mbox
% 0.30/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.45 ! [V: mworld] :
% 0.30/0.45 ( ( mrel @ W @ V )
% 0.30/0.45 => ( Phi @ V ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mdia_type,type,
% 0.30/0.45 mdia: ( mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mdia_def,definition,
% 0.30/0.45 ( mdia
% 0.30/0.45 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.30/0.45 ? [V: mworld] :
% 0.30/0.45 ( ( mrel @ W @ V )
% 0.30/0.45 & ( Phi @ V ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mrel_universal,axiom,
% 0.30/0.45 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 0.30/0.45
% 0.30/0.45 thf(mforall_di_type,type,
% 0.30/0.45 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mforall_di_def,definition,
% 0.30/0.45 ( mforall_di
% 0.30/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.45 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(mexists_di_type,type,
% 0.30/0.45 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(mexists_di_def,definition,
% 0.30/0.45 ( mexists_di
% 0.30/0.45 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.30/0.45 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %%% This output was generated by tptputils, version 1.2.
% 0.30/0.45 %%% Generated on Wed Apr 27 15:22:09 CEST 2022 using command 'downgrade(tff)'.
% 0.30/0.45 thf(cs_decl,type,
% 0.30/0.45 cs: $i ).
% 0.30/0.45
% 0.30/0.45 thf(sue_decl,type,
% 0.30/0.45 sue: $i ).
% 0.30/0.45
% 0.30/0.45 thf(mary_decl,type,
% 0.30/0.45 mary: $i ).
% 0.30/0.45
% 0.30/0.45 thf(john_decl,type,
% 0.30/0.45 john: $i ).
% 0.30/0.45
% 0.30/0.45 thf(math_decl,type,
% 0.30/0.45 math: $i ).
% 0.30/0.45
% 0.30/0.45 thf(psych_decl,type,
% 0.30/0.45 psych: $i ).
% 0.30/0.45
% 0.30/0.45 thf(teach_decl,type,
% 0.30/0.45 teach: $i > $i > mworld > $o ).
% 0.30/0.45
% 0.30/0.45 thf(db,axiom,
% 0.30/0.45 ( mlocal
% 0.30/0.45 @ ( mbox
% 0.30/0.45 @ ( mand @ ( teach @ john @ math )
% 0.30/0.45 @ ( mand
% 0.30/0.45 @ ( mexists_di
% 0.30/0.45 @ ^ [X: $i] : ( teach @ X @ cs ) )
% 0.30/0.45 @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 thf(query,conjecture,
% 0.30/0.45 ( mlocal
% 0.30/0.45 @ ( mexists_di
% 0.30/0.45 @ ^ [X: $i] : ( mbox @ ( teach @ john @ X ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.60/1.28 ---- Embedded in THF ---
% 1.60/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.60/1.28 %%% Generated on Tue Feb 24 06:14:54 EST 2026
% 1.60/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.60/1.28 %%% Logic specification used:
% 1.60/1.28 %%% thf(spec, logic, $$dhol).
% 1.60/1.28
% 1.60/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2DTF30579.p
% See solution above
% 1.60/1.28 ------------------------
% 1.60/1.29 ---- Cleaned THF ---
% 1.60/1.29 thf(mworld,type,
% 1.60/1.29 mworld: $tType ).
% 1.60/1.29
% 1.60/1.29 thf(mrel_type,type,
% 1.60/1.29 mrel: mworld > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mactual_type,type,
% 1.60/1.29 mactual: mworld ).
% 1.60/1.29
% 1.60/1.29 thf(mlocal_type,type,
% 1.60/1.29 mlocal: ( mworld > $o ) > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mlocal_def,definition,
% 1.60/1.29 ( mlocal
% 1.60/1.29 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mnot_type,type,
% 1.60/1.29 mnot: ( mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mand_type,type,
% 1.60/1.29 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mor_type,type,
% 1.60/1.29 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mimplies_type,type,
% 1.60/1.29 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mequiv_type,type,
% 1.60/1.29 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mnot_def,definition,
% 1.60/1.29 ( mnot
% 1.60/1.29 = ( ^ [A: mworld > $o,W: mworld] :
% 1.60/1.29 ~ ( A @ W ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mand_def,definition,
% 1.60/1.29 ( mand
% 1.60/1.29 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.60/1.29 ( ( A @ W )
% 1.60/1.29 & ( B @ W ) ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mor_def,definition,
% 1.60/1.29 ( mor
% 1.60/1.29 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.60/1.29 ( ( A @ W )
% 1.60/1.29 | ( B @ W ) ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mimplies_def,definition,
% 1.60/1.29 ( mimplies
% 1.60/1.29 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.60/1.29 ( ( A @ W )
% 1.60/1.29 => ( B @ W ) ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mequiv_def,definition,
% 1.60/1.29 ( mequiv
% 1.60/1.29 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.60/1.29 ( ( A @ W )
% 1.60/1.29 <=> ( B @ W ) ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mbox_type,type,
% 1.60/1.29 mbox: ( mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mbox_def,definition,
% 1.60/1.29 ( mbox
% 1.60/1.29 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.60/1.29 ! [V: mworld] :
% 1.60/1.29 ( ( mrel @ W @ V )
% 1.60/1.29 => ( Phi @ V ) ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mdia_type,type,
% 1.60/1.29 mdia: ( mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mdia_def,definition,
% 1.60/1.29 ( mdia
% 1.60/1.29 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.60/1.29 ? [V: mworld] :
% 1.60/1.29 ( ( mrel @ W @ V )
% 1.60/1.29 & ( Phi @ V ) ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mrel_universal,axiom,
% 1.60/1.29 ! [W: mworld,V: mworld] : ( mrel @ W @ V ) ).
% 1.60/1.29
% 1.60/1.29 thf(mforall_di_type,type,
% 1.60/1.29 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mforall_di_def,definition,
% 1.60/1.29 ( mforall_di
% 1.60/1.29 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.60/1.29 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(mexists_di_type,type,
% 1.60/1.29 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(mexists_di_def,definition,
% 1.60/1.29 ( mexists_di
% 1.60/1.29 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.60/1.29 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(cs_decl,type,
% 1.60/1.29 cs: $i ).
% 1.60/1.29
% 1.60/1.29 thf(sue_decl,type,
% 1.60/1.29 sue: $i ).
% 1.60/1.29
% 1.60/1.29 thf(mary_decl,type,
% 1.60/1.29 mary: $i ).
% 1.60/1.29
% 1.60/1.29 thf(john_decl,type,
% 1.60/1.29 john: $i ).
% 1.60/1.29
% 1.60/1.29 thf(math_decl,type,
% 1.60/1.29 math: $i ).
% 1.60/1.29
% 1.60/1.29 thf(psych_decl,type,
% 1.60/1.29 psych: $i ).
% 1.60/1.29
% 1.60/1.29 thf(teach_decl,type,
% 1.60/1.29 teach: $i > $i > mworld > $o ).
% 1.60/1.29
% 1.60/1.29 thf(db,axiom,
% 1.60/1.29 ( mlocal
% 1.60/1.29 @ ( mbox
% 1.60/1.29 @ ( mand @ ( teach @ john @ math )
% 1.60/1.29 @ ( mand
% 1.60/1.29 @ ( mexists_di
% 1.60/1.29 @ ^ [X: $i] : ( teach @ X @ cs ) )
% 1.60/1.29 @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 1.60/1.29
% 1.60/1.29 thf(query,conjecture,
% 1.60/1.29 ( mlocal
% 1.60/1.29 @ ( mexists_di
% 1.60/1.29 @ ^ [X: $i] : ( mbox @ ( teach @ john @ X ) ) ) ) ).
% 1.60/1.29 ------------------------
% 1.80/1.31 % (30768)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_30579 for (2999ds/183Mi)
% 1.80/1.31 % (30772)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_30579 for (2999ds/2Mi)
% 1.80/1.31 % (30771)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_30579 for (2999ds/2Mi)
% 1.80/1.31 % (30772)Instruction limit reached!
% 1.80/1.31 % (30772)------------------------------
% 1.80/1.31 % (30772)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.31 % (30772)Termination reason: Unknown
% 1.80/1.31 % (30772)Termination phase: Property scanning
% 1.80/1.31
% 1.80/1.31 % (30772)Memory used [KB]: 1023
% 1.80/1.31 % (30772)Time elapsed: 0.002 s
% 1.80/1.31 % (30772)Instructions burned: 3 (million)
% 1.80/1.31 % (30772)------------------------------
% 1.80/1.31 % (30772)------------------------------
% 1.80/1.31 % (30771)Instruction limit reached!
% 1.80/1.31 % (30771)------------------------------
% 1.80/1.31 % (30771)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.31 % (30771)Termination reason: Unknown
% 1.80/1.31 % (30771)Termination phase: Saturation
% 1.80/1.31
% 1.80/1.31 % (30771)Memory used [KB]: 1023
% 1.80/1.31 % (30771)Time elapsed: 0.002 s
% 1.80/1.31 % (30771)Instructions burned: 4 (million)
% 1.80/1.31 % (30771)------------------------------
% 1.80/1.31 % (30771)------------------------------
% 1.80/1.31 % (30768)First to succeed.
% 1.80/1.31 % (30768)Refutation found. Thanks to Tanya!
% 1.80/1.31 % SZS status Theorem for DTF2THF_30579
% 1.80/1.31 % SZS output start Proof for DTF2THF_30579
% 1.80/1.31 thf(type_def_5, type, mworld: $tType).
% 1.80/1.31 thf(func_def_0, type, mworld: $tType).
% 1.80/1.31 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.80/1.31 thf(func_def_2, type, mactual: mworld).
% 1.80/1.31 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.80/1.31 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.80/1.31 thf(func_def_20, type, teach: $i > $i > mworld > $o).
% 1.80/1.31 thf(func_def_35, type, sK1: mworld > $i).
% 1.80/1.31 thf(func_def_36, type, sK2: $i > mworld).
% 1.80/1.31 thf(f82,plain,(
% 1.80/1.31 $false),
% 1.80/1.31 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.80/1.31 thf(f80,plain,(
% 1.80/1.31 ($true = $false)),
% 1.80/1.31 inference(superposition,[status(thm)],[f79,f50])).
% 1.80/1.31 thf(f50,plain,(
% 1.80/1.31 ( ! [X0 : mworld,X1 : mworld] : (((mrel @ X0 @ X1) = $true)) )),
% 1.80/1.31 inference(cnf_transformation,[status(thm)],[f38])).
% 1.80/1.31 thf(f38,plain,(
% 1.80/1.31 ! [X0 : mworld,X1 : mworld] : ((mrel @ X0 @ X1) = $true)),
% 1.80/1.31 inference(fool_elimination,[status(thm)],[f37])).
% 1.80/1.31 thf(f37,plain,(
% 1.80/1.31 ! [X0 : mworld,X1 : mworld] : (mrel @ X0 @ X1)),
% 1.80/1.31 inference(rectify,[status(thm)],[f9])).
% 1.80/1.31 thf(f9,axiom,(
% 1.80/1.31 ! [X2 : mworld,X4 : mworld] : (mrel @ X2 @ X4)),
% 1.80/1.31 file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mrel_universal)).
% 1.80/1.31 thf(f79,plain,(
% 1.80/1.31 ((mrel @ mactual @ (sK2 @ math)) = $false)),
% 1.80/1.31 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.80/1.31 thf(f77,plain,(
% 1.80/1.31 ($true = $false) | ((mrel @ mactual @ (sK2 @ math)) = $false)),
% 1.80/1.31 inference(superposition,[status(thm)],[f74,f62])).
% 1.80/1.31 thf(f62,plain,(
% 1.80/1.31 ( ! [X1 : mworld] : (($true = (teach @ john @ math @ X1)) | ($false = (mrel @ mactual @ X1))) )),
% 1.80/1.31 inference(binary_proxy_clausification,[status(thm)],[f60])).
% 1.80/1.31 thf(f60,plain,(
% 1.80/1.31 ( ! [X1 : mworld] : ((((teach @ john @ math @ X1) & ((?? @ $i @ (^[Y0 : $i]: (teach @ Y0 @ cs @ X1))) & ((teach @ mary @ psych @ X1) & (teach @ sue @ psych @ X1)))) = $true) | ($false = (mrel @ mactual @ X1))) )),
% 1.80/1.31 inference(binary_proxy_clausification,[status(thm)],[f59])).
% 1.80/1.31 thf(f59,plain,(
% 1.80/1.31 ( ! [X1 : mworld] : ((((mrel @ mactual @ X1) => ((teach @ john @ math @ X1) & ((?? @ $i @ (^[Y0 : $i]: (teach @ Y0 @ cs @ X1))) & ((teach @ mary @ psych @ X1) & (teach @ sue @ psych @ X1))))) = $true)) )),
% 1.80/1.31 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.80/1.31 thf(f58,plain,(
% 1.80/1.31 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((teach @ john @ math @ Y0) & ((?? @ $i @ (^[Y1 : $i]: (teach @ Y1 @ cs @ Y0))) & ((teach @ mary @ psych @ Y0) & (teach @ sue @ psych @ Y0)))))) @ X1))) )),
% 1.80/1.31 inference(pi_clausification,[status(thm)],[f57])).
% 1.80/1.31 thf(f57,plain,(
% 1.80/1.31 ((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((teach @ john @ math @ Y0) & ((?? @ $i @ (^[Y1 : $i]: (teach @ Y1 @ cs @ Y0))) & ((teach @ mary @ psych @ Y0) & (teach @ sue @ psych @ Y0))))))) = $true)),
% 1.80/1.31 inference(beta_eta_normalization,[status(thm)],[f55])).
% 1.80/1.31 thf(f55,plain,(
% 1.80/1.31 (((^[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]: (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)),
% 1.80/1.31 inference(definition_unfolding,[status(thm)],[f51,f44,f53,f45,f45,f47,f45])).
% 1.80/1.31 thf(f47,plain,(
% 1.80/1.31 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.80/1.31 inference(cnf_transformation,[status(thm)],[f40])).
% 1.80/1.31 thf(f40,plain,(
% 1.80/1.31 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.80/1.31 inference(fool_elimination,[status(thm)],[f39])).
% 1.80/1.31 thf(f39,plain,(
% 1.80/1.31 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.80/1.31 inference(rectify,[status(thm)],[f11])).
% 1.80/1.31 thf(f11,axiom,(
% 1.80/1.31 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5 : $i] : (X1 @ X5 @ X2))))),
% 1.80/1.31 file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mexists_di_def)).
% 1.80/1.31 thf(f45,plain,(
% 1.80/1.31 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.80/1.31 inference(cnf_transformation,[status(thm)],[f29])).
% 1.80/1.31 thf(f29,plain,(
% 1.80/1.31 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y0 @ Y2) & (Y1 @ Y2))))))))),
% 1.80/1.31 inference(fool_elimination,[status(thm)],[f28])).
% 1.80/1.31 thf(f28,plain,(
% 1.80/1.31 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X0 @ X2))) = mand)),
% 1.80/1.31 inference(rectify,[status(thm)],[f3])).
% 1.80/1.31 thf(f3,axiom,(
% 1.80/1.31 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X3 @ X2) & (X1 @ X2))) = mand)),
% 1.80/1.31 file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mand_def)).
% 1.80/1.31 thf(f53,plain,(
% 1.80/1.31 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.80/1.31 inference(cnf_transformation,[status(thm)],[f23])).
% 1.80/1.31 thf(f23,plain,(
% 1.80/1.31 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.80/1.31 inference(fool_elimination,[status(thm)],[f22])).
% 1.80/1.31 thf(f22,plain,(
% 1.80/1.31 ((^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))) = mbox)),
% 1.80/1.31 inference(rectify,[status(thm)],[f7])).
% 1.80/1.31 thf(f7,axiom,(
% 1.80/1.31 ((^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))) = mbox)),
% 1.80/1.31 file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mbox_def)).
% 1.80/1.31 thf(f44,plain,(
% 1.80/1.31 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.80/1.31 inference(cnf_transformation,[status(thm)],[f34])).
% 1.80/1.31 thf(f34,plain,(
% 1.80/1.31 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.80/1.31 inference(fool_elimination,[status(thm)],[f1])).
% 1.80/1.31 thf(f1,axiom,(
% 1.80/1.31 (mlocal = (^[X0 : mworld > $o] : (X0 @ mactual)))),
% 1.80/1.31 file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',mlocal_def)).
% 1.80/1.31 thf(f51,plain,(
% 1.80/1.31 ((mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))) = $true)),
% 1.80/1.31 inference(cnf_transformation,[status(thm)],[f25])).
% 1.80/1.31 thf(f25,plain,(
% 1.80/1.31 ((mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))) = $true)),
% 1.80/1.31 inference(fool_elimination,[status(thm)],[f24])).
% 1.80/1.31 thf(f24,plain,(
% 1.80/1.31 (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[X0 : $i] : (teach @ X0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),
% 1.80/1.31 inference(rectify,[status(thm)],[f12])).
% 1.80/1.31 thf(f12,axiom,(
% 1.80/1.31 (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[X5 : $i] : (teach @ X5 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),
% 1.80/1.31 file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',db)).
% 1.80/1.31 thf(f74,plain,(
% 1.80/1.31 ( ! [X1 : $i] : (($false = (teach @ john @ X1 @ (sK2 @ X1)))) )),
% 1.80/1.31 inference(binary_proxy_clausification,[status(thm)],[f73])).
% 1.80/1.31 thf(f73,plain,(
% 1.80/1.31 ( ! [X1 : $i] : ((((mrel @ mactual @ (sK2 @ X1)) => (teach @ john @ X1 @ (sK2 @ X1))) = $false)) )),
% 1.80/1.31 inference(beta_eta_normalization,[status(thm)],[f72])).
% 1.80/1.31 thf(f72,plain,(
% 1.80/1.31 ( ! [X1 : $i] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (teach @ john @ X1 @ Y0))) @ (sK2 @ X1)) = $false)) )),
% 1.80/1.31 inference(sigma_clausification,[status(thm)],[f71])).
% 1.80/1.31 thf(f71,plain,(
% 1.80/1.31 ( ! [X1 : $i] : (((!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (teach @ john @ X1 @ Y0)))) = $false)) )),
% 1.80/1.31 inference(beta_eta_normalization,[status(thm)],[f70])).
% 1.80/1.31 thf(f70,plain,(
% 1.80/1.31 ( ! [X1 : $i] : (($false = ((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (teach @ john @ Y0 @ Y1))))) @ X1))) )),
% 1.80/1.31 inference(pi_clausification,[status(thm)],[f69])).
% 1.80/1.31 thf(f69,plain,(
% 1.80/1.31 ($true != (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (teach @ john @ Y0 @ Y1)))))))),
% 1.80/1.31 inference(beta_eta_normalization,[status(thm)],[f56])).
% 1.80/1.31 thf(f56,plain,(
% 1.80/1.31 (((^[Y0 : mworld > $o]: (Y0 @ mactual)) @ ((^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))) @ (^[Y0 : $i]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: (!! @ mworld @ (^[Y3 : mworld]: ((mrel @ Y2 @ Y3) => (Y1 @ Y3))))))) @ (teach @ john @ Y0))))) != $true)),
% 1.80/1.31 inference(definition_unfolding,[status(thm)],[f54,f44,f47,f53])).
% 1.80/1.31 thf(f54,plain,(
% 1.80/1.31 ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (teach @ john @ Y0))))) != $true)),
% 1.80/1.31 inference(cnf_transformation,[status(thm)],[f41])).
% 1.80/1.31 thf(f41,plain,(
% 1.80/1.31 ((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (teach @ john @ Y0))))) != $true)),
% 1.80/1.31 inference(flattening,[status(thm)],[f19])).
% 1.80/1.31 thf(f19,plain,(
% 1.80/1.31 ~((mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (teach @ john @ Y0))))) = $true)),
% 1.80/1.31 inference(fool_elimination,[status(thm)],[f18])).
% 1.80/1.31 thf(f18,plain,(
% 1.80/1.31 ~(mlocal @ (mexists_di @ (^[X0 : $i] : (mbox @ (teach @ john @ X0)))))),
% 1.80/1.31 inference(rectify,[status(thm)],[f14])).
% 1.80/1.31 thf(f14,negated_conjecture,(
% 1.80/1.31 ~(mlocal @ (mexists_di @ (^[X5 : $i] : (mbox @ (teach @ john @ X5)))))),
% 1.80/1.31 inference(negated_conjecture,[status(cth)],[f13])).
% 1.80/1.31 thf(f13,conjecture,(
% 1.80/1.31 (mlocal @ (mexists_di @ (^[X5 : $i] : (mbox @ (teach @ john @ X5)))))),
% 1.80/1.31 file('/export/starexec/sandbox/tmp/tmp.9WSfrPu12H/DTF2THF_30579.p',query)).
% 1.80/1.31 % SZS output end Proof for DTF2THF_30579
% 1.80/1.31 % (30768)------------------------------
% 1.80/1.31 % (30768)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.80/1.31 % (30768)Termination reason: Refutation
% 1.80/1.31
% 1.80/1.31 % (30768)Memory used [KB]: 5628
% 1.80/1.31 % (30768)Time elapsed: 0.004 s
% 1.80/1.31 % (30768)Instructions burned: 5 (million)
% 1.80/1.31 % (30768)------------------------------
% 1.80/1.31 % (30768)------------------------------
% 1.80/1.31 % (30767)Success in time 0.003 s
%------------------------------------------------------------------------------