%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : DAT333^3 : 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 : n017.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 08:45:28 AM UTC 2026
% Result : Theorem 1.73s 1.37s
% Output : Refutation 1.73s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 43 ( 35 unt; 0 typ; 0 def)
% Number of atoms : 291 ( 40 equ; 0 cnn)
% Maximal formula atoms : 17 ( 6 avg)
% Number of connectives : 368 ( 7 ~; 3 |; 19 &; 308 @)
% ( 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 : 27 ( 22 usr; 11 con; 0-3 aty)
% ( 8 !!; 9 ??; 0 @@+; 0 @@-)
% Number of variables : 96 ( 82 ^; 12 !; 2 ?; 96 :)
% 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_34,type,
sK0: mworld > mworld ).
thf(func_def_36,type,
sK2: $i > mworld ).
thf(func_def_37,type,
sK3: mworld > $i ).
thf(f84,plain,
$false,
inference(trivial_inequality_removal,[status(thm)],[f82]) ).
thf(f82,plain,
$true = $false,
inference(superposition,[status(thm)],[f81,f65]) ).
thf(f65,plain,
! [X1: $i] :
( $true
= ( mrel @ mactual @ ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
thf(f63,plain,
! [X1: $i] :
( $false
= ( ( mrel @ mactual @ ( sK2 @ X1 ) )
=> ( teach @ john @ X1 @ ( sK2 @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f62]) ).
thf(f62,plain,
! [X1: $i] :
( ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( teach @ john @ X1 @ Y0 ) )
@ ( sK2 @ X1 ) )
= $false ),
inference(sigma_clausification,[status(thm)],[f61]) ).
thf(f61,plain,
! [X1: $i] :
( $false
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( teach @ john @ X1 @ Y0 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f60]) ).
thf(f60,plain,
! [X1: $i] :
( ( ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( teach @ john @ Y0 @ Y1 ) ) )
@ X1 )
= $false ),
inference(pi_clausification,[status(thm)],[f59]) ).
thf(f59,plain,
( $true
!= ( ?? @ $i
@ ^ [Y0: $i] :
( !! @ mworld
@ ^ [Y1: mworld] :
( ( mrel @ mactual @ Y1 )
=> ( teach @ john @ Y0 @ Y1 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f57]) ).
thf(f57,plain,
( $true
!= ( ^ [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 ) ) ) ) ),
inference(definition_unfolding,[status(thm)],[f50,f44,f52,f51]) ).
thf(f51,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
thf(f35,plain,
( mbox
= ( ^ [Y0: mworld > $o,Y1: mworld] :
( !! @ mworld
@ ^ [Y2: mworld] :
( ( mrel @ Y1 @ Y2 )
=> ( Y0 @ Y2 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f34]) ).
thf(f34,plain,
( mbox
= ( ^ [X0: mworld > $o,X1: mworld] :
! [X2: mworld] :
( ( mrel @ X1 @ X2 )
=> ( X0 @ X2 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,axiom,
( mbox
= ( ^ [X0: mworld > $o,X2: mworld] :
! [X4: mworld] :
( ( mrel @ X2 @ X4 )
=> ( X0 @ X4 ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',mbox_def) ).
thf(f52,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f21]) ).
thf(f21,plain,
( mexists_di
= ( ^ [Y0: $i > mworld > $o,Y1: mworld] :
( ?? @ $i
@ ^ [Y2: $i] : ( Y0 @ Y2 @ Y1 ) ) ) ),
inference(fool_elimination,[status(thm)],[f20]) ).
thf(f20,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/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',mexists_di_def) ).
thf(f44,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
thf(f40,plain,
( mlocal
= ( ^ [Y0: mworld > $o] : ( Y0 @ mactual ) ) ),
inference(fool_elimination,[status(thm)],[f1]) ).
thf(f1,axiom,
( ( ^ [X0: mworld > $o] : ( X0 @ mactual ) )
= mlocal ),
file('/export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',mlocal_def) ).
thf(f50,plain,
( $true
!= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f41]) ).
thf(f41,plain,
( $true
!= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) ) ),
inference(flattening,[status(thm)],[f29]) ).
thf(f29,plain,
( $true
!= ( mlocal
@ ( mexists_di
@ ^ [Y0: $i] : ( mbox @ ( teach @ john @ Y0 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f28]) ).
thf(f28,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/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',query) ).
thf(f81,plain,
( $false
= ( mrel @ mactual @ ( sK2 @ math ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f79]) ).
thf(f79,plain,
( ( $true = $false )
| ( $false
= ( mrel @ mactual @ ( sK2 @ math ) ) ) ),
inference(superposition,[status(thm)],[f64,f70]) ).
thf(f70,plain,
! [X1: mworld] :
( ( $true
= ( teach @ john @ math @ X1 ) )
| ( ( mrel @ mactual @ X1 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f69]) ).
thf(f69,plain,
! [X1: mworld] :
( ( ( mrel @ mactual @ X1 )
= $false )
| ( $true
= ( ( teach @ sue @ psych @ X1 )
& ( teach @ mary @ psych @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] : ( teach @ Y0 @ cs @ X1 ) )
& ( teach @ john @ math @ X1 ) ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f68]) ).
thf(f68,plain,
! [X1: mworld] :
( $true
= ( ( mrel @ mactual @ X1 )
=> ( ( teach @ sue @ psych @ X1 )
& ( teach @ mary @ psych @ X1 )
& ( ?? @ $i
@ ^ [Y0: $i] : ( teach @ Y0 @ cs @ X1 ) )
& ( teach @ john @ math @ X1 ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f67]) ).
thf(f67,plain,
! [X1: mworld] :
( $true
= ( ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ sue @ psych @ Y0 )
& ( teach @ mary @ psych @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( teach @ Y1 @ cs @ Y0 ) )
& ( teach @ john @ math @ Y0 ) ) )
@ X1 ) ),
inference(pi_clausification,[status(thm)],[f66]) ).
thf(f66,plain,
( $true
= ( !! @ mworld
@ ^ [Y0: mworld] :
( ( mrel @ mactual @ Y0 )
=> ( ( teach @ sue @ psych @ Y0 )
& ( teach @ mary @ psych @ Y0 )
& ( ?? @ $i
@ ^ [Y1: $i] : ( teach @ Y1 @ cs @ Y0 ) )
& ( teach @ john @ math @ Y0 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f58]) ).
thf(f58,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] : ( 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)],[f54,f44,f51,f45,f45,f52,f45]) ).
thf(f45,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( mand
= ( ^ [Y0: mworld > $o,Y1: mworld > $o,Y2: mworld] :
( ( Y1 @ Y2 )
& ( Y0 @ Y2 ) ) ) ),
inference(fool_elimination,[status(thm)],[f24]) ).
thf(f24,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.CxRV48i255/DTF2THF_11135.p',mand_def) ).
thf(f54,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)],[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/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',db) ).
thf(f64,plain,
! [X1: $i] :
( $false
= ( teach @ john @ X1 @ ( sK2 @ X1 ) ) ),
inference(binary_proxy_clausification,[status(thm)],[f63]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : DAT333^3 : TPTP v9.2.1. Released v8.1.0.
% 0.00/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.34 % Computer : n017.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 06:13:26 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : DAT333^3 : TPTP v9.2.1. Released v8.1.0.
% 0.27/0.47 % Domain : Data Structures
% 0.27/0.47 % Problem : Database querying
% 0.27/0.47 % Version : [BP13] axioms.
% 0.27/0.47 % English :
% 0.27/0.47
% 0.27/0.47 % Refs : [Rei92] Reiter (1992), What Should a Database Know?
% 0.27/0.47 % : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% 0.27/0.47 % : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% 0.27/0.47 % : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% 0.27/0.47 % Source : [TPTP]
% 0.27/0.47 % Names : APM008+1 [QMLTP]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.11 v9.1.0, 0.12 v9.0.0, 0.10 v8.2.0, 0.23 v8.1.0
% 0.27/0.47 % Syntax : Number of formulae : 33 ( 11 unt; 20 typ; 10 def)
% 0.27/0.47 % Number of atoms : 37 ( 10 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 10 ( 2 avg)
% 0.27/0.47 % Number of connectives : 51 ( 1 ~; 1 |; 2 &; 44 @)
% 0.27/0.47 % ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 10 ( 2 avg)
% 0.27/0.47 % Number of types : 3 ( 1 usr)
% 0.27/0.47 % Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 20 ( 19 usr; 7 con; 0-3 aty)
% 0.27/0.47 % Number of variables : 31 ( 25 ^; 3 !; 3 ?; 31 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This output was generated by embedproblem, version 1.7.1 (library
% 0.27/0.47 % version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 0.27/0.47 % 'modal' embedding, version 1.5.2. Logic specification used:
% 0.27/0.47 % $modal == [$constants == $rigid,$quantification == $constant,
% 0.27/0.47 % $modalities == $modal_system_D].
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(mworld,type,
% 0.27/0.47 mworld: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(mrel_type,type,
% 0.27/0.47 mrel: mworld > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mactual_type,type,
% 0.27/0.47 mactual: mworld ).
% 0.27/0.47
% 0.27/0.47 thf(mlocal_type,type,
% 0.27/0.47 mlocal: ( mworld > $o ) > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mlocal_def,definition,
% 0.27/0.47 ( mlocal
% 0.27/0.47 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mnot_type,type,
% 0.27/0.47 mnot: ( mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mand_type,type,
% 0.27/0.47 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mor_type,type,
% 0.27/0.47 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mimplies_type,type,
% 0.27/0.47 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mequiv_type,type,
% 0.27/0.47 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mnot_def,definition,
% 0.27/0.47 ( mnot
% 0.27/0.47 = ( ^ [A: mworld > $o,W: mworld] :
% 0.27/0.47 ~ ( A @ W ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mand_def,definition,
% 0.27/0.47 ( mand
% 0.27/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.47 ( ( A @ W )
% 0.27/0.47 & ( B @ W ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mor_def,definition,
% 0.27/0.47 ( mor
% 0.27/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.47 ( ( A @ W )
% 0.27/0.47 | ( B @ W ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mimplies_def,definition,
% 0.27/0.47 ( mimplies
% 0.27/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.47 ( ( A @ W )
% 0.27/0.47 => ( B @ W ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mequiv_def,definition,
% 0.27/0.47 ( mequiv
% 0.27/0.47 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 0.27/0.47 ( ( A @ W )
% 0.27/0.47 <=> ( B @ W ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mbox_type,type,
% 0.27/0.47 mbox: ( mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mbox_def,definition,
% 0.27/0.47 ( mbox
% 0.27/0.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.27/0.47 ! [V: mworld] :
% 0.27/0.47 ( ( mrel @ W @ V )
% 0.27/0.47 => ( Phi @ V ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mdia_type,type,
% 0.27/0.47 mdia: ( mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mdia_def,definition,
% 0.27/0.47 ( mdia
% 0.27/0.47 = ( ^ [Phi: mworld > $o,W: mworld] :
% 0.27/0.47 ? [V: mworld] :
% 0.27/0.47 ( ( mrel @ W @ V )
% 0.27/0.47 & ( Phi @ V ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mrel_serial,axiom,
% 0.27/0.47 ! [W: mworld] :
% 0.27/0.47 ? [V: mworld] : ( mrel @ W @ V ) ).
% 0.27/0.47
% 0.27/0.47 thf(mforall_di_type,type,
% 0.27/0.47 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mforall_di_def,definition,
% 0.27/0.47 ( mforall_di
% 0.27/0.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.27/0.47 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(mexists_di_type,type,
% 0.27/0.47 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(mexists_di_def,definition,
% 0.27/0.47 ( mexists_di
% 0.27/0.47 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 0.27/0.47 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(cs_decl,type,
% 0.27/0.47 cs: $i ).
% 0.27/0.47
% 0.27/0.47 thf(sue_decl,type,
% 0.27/0.47 sue: $i ).
% 0.27/0.47
% 0.27/0.47 thf(mary_decl,type,
% 0.27/0.47 mary: $i ).
% 0.27/0.47
% 0.27/0.47 thf(john_decl,type,
% 0.27/0.47 john: $i ).
% 0.27/0.47
% 0.27/0.47 thf(math_decl,type,
% 0.27/0.47 math: $i ).
% 0.27/0.47
% 0.27/0.47 thf(psych_decl,type,
% 0.27/0.47 psych: $i ).
% 0.27/0.47
% 0.27/0.47 thf(teach_decl,type,
% 0.27/0.47 teach: $i > $i > mworld > $o ).
% 0.27/0.47
% 0.27/0.47 thf(db,axiom,
% 0.27/0.47 ( mlocal
% 0.27/0.47 @ ( mbox
% 0.27/0.47 @ ( mand @ ( teach @ john @ math )
% 0.27/0.47 @ ( mand
% 0.27/0.47 @ ( mexists_di
% 0.27/0.47 @ ^ [X: $i] : ( teach @ X @ cs ) )
% 0.27/0.47 @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 thf(query,conjecture,
% 0.27/0.47 ( mlocal
% 0.27/0.47 @ ( mexists_di
% 0.27/0.47 @ ^ [X: $i] : ( mbox @ ( teach @ john @ X ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.73/1.32 ---- Embedded in THF ---
% 1.73/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.73/1.33 %%% Generated on Tue Feb 24 06:13:27 EST 2026
% 1.73/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.73/1.33 %%% Logic specification used:
% 1.73/1.33 %%% thf(spec, logic, $$dhol).
% 1.73/1.33
% 1.73/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2DTF11135.p
% See solution above
% 1.73/1.33 ------------------------
% 1.73/1.34 ---- Cleaned THF ---
% 1.73/1.34 thf(mworld,type,
% 1.73/1.34 mworld: $tType ).
% 1.73/1.34
% 1.73/1.34 thf(mrel_type,type,
% 1.73/1.34 mrel: mworld > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mactual_type,type,
% 1.73/1.34 mactual: mworld ).
% 1.73/1.34
% 1.73/1.34 thf(mlocal_type,type,
% 1.73/1.34 mlocal: ( mworld > $o ) > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mlocal_def,definition,
% 1.73/1.34 ( mlocal
% 1.73/1.34 = ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mnot_type,type,
% 1.73/1.34 mnot: ( mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mand_type,type,
% 1.73/1.34 mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mor_type,type,
% 1.73/1.34 mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mimplies_type,type,
% 1.73/1.34 mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mequiv_type,type,
% 1.73/1.34 mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mnot_def,definition,
% 1.73/1.34 ( mnot
% 1.73/1.34 = ( ^ [A: mworld > $o,W: mworld] :
% 1.73/1.34 ~ ( A @ W ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mand_def,definition,
% 1.73/1.34 ( mand
% 1.73/1.34 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.73/1.34 ( ( A @ W )
% 1.73/1.34 & ( B @ W ) ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mor_def,definition,
% 1.73/1.34 ( mor
% 1.73/1.34 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.73/1.34 ( ( A @ W )
% 1.73/1.34 | ( B @ W ) ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mimplies_def,definition,
% 1.73/1.34 ( mimplies
% 1.73/1.34 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.73/1.34 ( ( A @ W )
% 1.73/1.34 => ( B @ W ) ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mequiv_def,definition,
% 1.73/1.34 ( mequiv
% 1.73/1.34 = ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
% 1.73/1.34 ( ( A @ W )
% 1.73/1.34 <=> ( B @ W ) ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mbox_type,type,
% 1.73/1.34 mbox: ( mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mbox_def,definition,
% 1.73/1.34 ( mbox
% 1.73/1.34 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.73/1.34 ! [V: mworld] :
% 1.73/1.34 ( ( mrel @ W @ V )
% 1.73/1.34 => ( Phi @ V ) ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mdia_type,type,
% 1.73/1.34 mdia: ( mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mdia_def,definition,
% 1.73/1.34 ( mdia
% 1.73/1.34 = ( ^ [Phi: mworld > $o,W: mworld] :
% 1.73/1.34 ? [V: mworld] :
% 1.73/1.34 ( ( mrel @ W @ V )
% 1.73/1.34 & ( Phi @ V ) ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mrel_serial,axiom,
% 1.73/1.34 ! [W: mworld] :
% 1.73/1.34 ? [V: mworld] : ( mrel @ W @ V ) ).
% 1.73/1.34
% 1.73/1.34 thf(mforall_di_type,type,
% 1.73/1.34 mforall_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mforall_di_def,definition,
% 1.73/1.34 ( mforall_di
% 1.73/1.34 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.73/1.34 ! [X: $i] : ( A @ X @ W ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(mexists_di_type,type,
% 1.73/1.34 mexists_di: ( $i > mworld > $o ) > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(mexists_di_def,definition,
% 1.73/1.34 ( mexists_di
% 1.73/1.34 = ( ^ [A: $i > mworld > $o,W: mworld] :
% 1.73/1.34 ? [X: $i] : ( A @ X @ W ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(cs_decl,type,
% 1.73/1.34 cs: $i ).
% 1.73/1.34
% 1.73/1.34 thf(sue_decl,type,
% 1.73/1.34 sue: $i ).
% 1.73/1.34
% 1.73/1.34 thf(mary_decl,type,
% 1.73/1.34 mary: $i ).
% 1.73/1.34
% 1.73/1.34 thf(john_decl,type,
% 1.73/1.34 john: $i ).
% 1.73/1.34
% 1.73/1.34 thf(math_decl,type,
% 1.73/1.34 math: $i ).
% 1.73/1.34
% 1.73/1.34 thf(psych_decl,type,
% 1.73/1.34 psych: $i ).
% 1.73/1.34
% 1.73/1.34 thf(teach_decl,type,
% 1.73/1.34 teach: $i > $i > mworld > $o ).
% 1.73/1.34
% 1.73/1.34 thf(db,axiom,
% 1.73/1.34 ( mlocal
% 1.73/1.34 @ ( mbox
% 1.73/1.34 @ ( mand @ ( teach @ john @ math )
% 1.73/1.34 @ ( mand
% 1.73/1.34 @ ( mexists_di
% 1.73/1.34 @ ^ [X: $i] : ( teach @ X @ cs ) )
% 1.73/1.34 @ ( mand @ ( teach @ mary @ psych ) @ ( teach @ sue @ psych ) ) ) ) ) ) ).
% 1.73/1.34
% 1.73/1.34 thf(query,conjecture,
% 1.73/1.34 ( mlocal
% 1.73/1.34 @ ( mexists_di
% 1.73/1.34 @ ^ [X: $i] : ( mbox @ ( teach @ john @ X ) ) ) ) ).
% 1.73/1.34 ------------------------
% 1.73/1.35 % (11411)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_11135 for (2999ds/275Mi)
% 1.73/1.35 % (11410)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_11135 for (2999ds/2Mi)
% 1.73/1.36 % (11411)Refutation not found, incomplete strategy
% 1.73/1.36 % (11411)------------------------------
% 1.73/1.36 % (11411)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.36 % (11411)Termination reason: Refutation not found, incomplete strategy
% 1.73/1.36
% 1.73/1.36
% 1.73/1.36 % (11411)Memory used [KB]: 5500
% 1.73/1.36 % (11411)Time elapsed: 0.002 s
% 1.73/1.36 % (11411)Instructions burned: 2 (million)
% 1.73/1.36 % (11411)------------------------------
% 1.73/1.36 % (11411)------------------------------
% 1.73/1.36 % (11410)Instruction limit reached!
% 1.73/1.36 % (11410)------------------------------
% 1.73/1.36 % (11410)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.36 % (11410)Termination reason: Unknown
% 1.73/1.36 % (11410)Termination phase: Property scanning
% 1.73/1.36
% 1.73/1.36 % (11410)Memory used [KB]: 1023
% 1.73/1.36 % (11410)Time elapsed: 0.002 s
% 1.73/1.36 % (11410)Instructions burned: 3 (million)
% 1.73/1.36 % (11410)------------------------------
% 1.73/1.36 % (11410)------------------------------
% 1.73/1.36 % (11406)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_11135 for (2999ds/183Mi)
% 1.73/1.36 % (11407)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_11135 for (2999ds/4Mi)
% 1.73/1.36 % (11408)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_11135 for (2999ds/27Mi)
% 1.73/1.36 % (11409)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_11135 for (2999ds/2Mi)
% 1.73/1.36 % (11412)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_11135 for (2999ds/18Mi)
% 1.73/1.36 % (11407)Instruction limit reached!
% 1.73/1.36 % (11407)------------------------------
% 1.73/1.36 % (11407)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.36 % (11407)Termination reason: Unknown
% 1.73/1.36 % (11407)Termination phase: Saturation
% 1.73/1.36
% 1.73/1.36 % (11407)Memory used [KB]: 1023
% 1.73/1.36 % (11407)Time elapsed: 0.004 s
% 1.73/1.36 % (11407)Instructions burned: 4 (million)
% 1.73/1.36 % (11407)------------------------------
% 1.73/1.36 % (11407)------------------------------
% 1.73/1.36 % (11409)Instruction limit reached!
% 1.73/1.36 % (11409)------------------------------
% 1.73/1.36 % (11409)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.36 % (11409)Termination reason: Unknown
% 1.73/1.36 % (11409)Termination phase: Property scanning
% 1.73/1.36
% 1.73/1.36 % (11409)Memory used [KB]: 1023
% 1.73/1.36 % (11409)Time elapsed: 0.004 s
% 1.73/1.36 % (11409)Instructions burned: 3 (million)
% 1.73/1.36 % (11409)------------------------------
% 1.73/1.36 % (11409)------------------------------
% 1.73/1.37 % (11414)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_11135 for (2999ds/37Mi)
% 1.73/1.37 % (11413)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_11135 for (2999ds/3Mi)
% 1.73/1.37 % (11406)First to succeed.
% 1.73/1.37 % (11413)Instruction limit reached!
% 1.73/1.37 % (11413)------------------------------
% 1.73/1.37 % (11413)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.37 % (11413)Termination reason: Unknown
% 1.73/1.37 % (11413)Termination phase: Saturation
% 1.73/1.37
% 1.73/1.37 % (11413)Memory used [KB]: 1023
% 1.73/1.37 % (11413)Time elapsed: 0.003 s
% 1.73/1.37 % (11413)Instructions burned: 4 (million)
% 1.73/1.37 % (11413)------------------------------
% 1.73/1.37 % (11413)------------------------------
% 1.73/1.37 % (11412)Also succeeded, but the first one will report.
% 1.73/1.37 % (11406)Refutation found. Thanks to Tanya!
% 1.73/1.37 % SZS status Theorem for DTF2THF_11135
% 1.73/1.37 % SZS output start Proof for DTF2THF_11135
% 1.73/1.37 thf(type_def_5, type, mworld: $tType).
% 1.73/1.37 thf(func_def_0, type, mworld: $tType).
% 1.73/1.37 thf(func_def_1, type, mrel: mworld > mworld > $o).
% 1.73/1.37 thf(func_def_2, type, mactual: mworld).
% 1.73/1.37 thf(func_def_3, type, mlocal: (mworld > $o) > $o).
% 1.73/1.37 thf(func_def_5, type, mnot: (mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_6, type, mand: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_7, type, mor: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_8, type, mimplies: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_9, type, mequiv: (mworld > $o) > (mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_10, type, mbox: (mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_11, type, mdia: (mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_12, type, mforall_di: ($i > mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_13, type, mexists_di: ($i > mworld > $o) > mworld > $o).
% 1.73/1.37 thf(func_def_20, type, teach: $i > $i > mworld > $o).
% 1.73/1.37 thf(func_def_34, type, sK0: mworld > mworld).
% 1.73/1.37 thf(func_def_36, type, sK2: $i > mworld).
% 1.73/1.37 thf(func_def_37, type, sK3: mworld > $i).
% 1.73/1.37 thf(f84,plain,(
% 1.73/1.37 $false),
% 1.73/1.37 inference(trivial_inequality_removal,[status(thm)],[f82])).
% 1.73/1.37 thf(f82,plain,(
% 1.73/1.37 ($true = $false)),
% 1.73/1.37 inference(superposition,[status(thm)],[f81,f65])).
% 1.73/1.37 thf(f65,plain,(
% 1.73/1.37 ( ! [X1 : $i] : (($true = (mrel @ mactual @ (sK2 @ X1)))) )),
% 1.73/1.37 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.73/1.37 thf(f63,plain,(
% 1.73/1.37 ( ! [X1 : $i] : (($false = ((mrel @ mactual @ (sK2 @ X1)) => (teach @ john @ X1 @ (sK2 @ X1))))) )),
% 1.73/1.37 inference(beta_eta_normalization,[status(thm)],[f62])).
% 1.73/1.37 thf(f62,plain,(
% 1.73/1.37 ( ! [X1 : $i] : ((((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (teach @ john @ X1 @ Y0))) @ (sK2 @ X1)) = $false)) )),
% 1.73/1.37 inference(sigma_clausification,[status(thm)],[f61])).
% 1.73/1.37 thf(f61,plain,(
% 1.73/1.37 ( ! [X1 : $i] : (($false = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => (teach @ john @ X1 @ Y0)))))) )),
% 1.73/1.37 inference(beta_eta_normalization,[status(thm)],[f60])).
% 1.73/1.37 thf(f60,plain,(
% 1.73/1.37 ( ! [X1 : $i] : ((((^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (teach @ john @ Y0 @ Y1))))) @ X1) = $false)) )),
% 1.73/1.37 inference(pi_clausification,[status(thm)],[f59])).
% 1.73/1.37 thf(f59,plain,(
% 1.73/1.37 ($true != (?? @ $i @ (^[Y0 : $i]: (!! @ mworld @ (^[Y1 : mworld]: ((mrel @ mactual @ Y1) => (teach @ john @ Y0 @ Y1)))))))),
% 1.73/1.37 inference(beta_eta_normalization,[status(thm)],[f57])).
% 1.73/1.37 thf(f57,plain,(
% 1.73/1.37 ($true != ((^[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))))))),
% 1.73/1.37 inference(definition_unfolding,[status(thm)],[f50,f44,f52,f51])).
% 1.73/1.37 thf(f51,plain,(
% 1.73/1.37 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.73/1.37 inference(cnf_transformation,[status(thm)],[f35])).
% 1.73/1.37 thf(f35,plain,(
% 1.73/1.37 (mbox = (^[Y0 : mworld > $o]: ((^[Y1 : mworld]: (!! @ mworld @ (^[Y2 : mworld]: ((mrel @ Y1 @ Y2) => (Y0 @ Y2))))))))),
% 1.73/1.37 inference(fool_elimination,[status(thm)],[f34])).
% 1.73/1.37 thf(f34,plain,(
% 1.73/1.37 (mbox = (^[X0 : mworld > $o, X1 : mworld] : (! [X2 : mworld] : ((mrel @ X1 @ X2) => (X0 @ X2)))))),
% 1.73/1.37 inference(rectify,[status(thm)],[f7])).
% 1.73/1.37 thf(f7,axiom,(
% 1.73/1.37 (mbox = (^[X0 : mworld > $o, X2 : mworld] : (! [X4 : mworld] : ((mrel @ X2 @ X4) => (X0 @ X4)))))),
% 1.73/1.37 file('/export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',mbox_def)).
% 1.73/1.37 thf(f52,plain,(
% 1.73/1.37 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.73/1.37 inference(cnf_transformation,[status(thm)],[f21])).
% 1.73/1.37 thf(f21,plain,(
% 1.73/1.37 (mexists_di = (^[Y0 : $i > mworld > $o]: ((^[Y1 : mworld]: (?? @ $i @ (^[Y2 : $i]: (Y0 @ Y2 @ Y1)))))))),
% 1.73/1.37 inference(fool_elimination,[status(thm)],[f20])).
% 1.73/1.37 thf(f20,plain,(
% 1.73/1.37 (mexists_di = (^[X0 : $i > mworld > $o, X1 : mworld] : (? [X2 : $i] : (X0 @ X2 @ X1))))),
% 1.73/1.37 inference(rectify,[status(thm)],[f11])).
% 1.73/1.37 thf(f11,axiom,(
% 1.73/1.37 (mexists_di = (^[X1 : $i > mworld > $o, X2 : mworld] : (? [X5 : $i] : (X1 @ X5 @ X2))))),
% 1.73/1.37 file('/export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',mexists_di_def)).
% 1.73/1.37 thf(f44,plain,(
% 1.73/1.37 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.73/1.37 inference(cnf_transformation,[status(thm)],[f40])).
% 1.73/1.37 thf(f40,plain,(
% 1.73/1.37 (mlocal = (^[Y0 : mworld > $o]: (Y0 @ mactual)))),
% 1.73/1.37 inference(fool_elimination,[status(thm)],[f1])).
% 1.73/1.37 thf(f1,axiom,(
% 1.73/1.37 ((^[X0 : mworld > $o] : (X0 @ mactual)) = mlocal)),
% 1.73/1.37 file('/export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',mlocal_def)).
% 1.73/1.37 thf(f50,plain,(
% 1.73/1.37 ($true != (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (teach @ john @ Y0))))))),
% 1.73/1.37 inference(cnf_transformation,[status(thm)],[f41])).
% 1.73/1.37 thf(f41,plain,(
% 1.73/1.37 ($true != (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (teach @ john @ Y0))))))),
% 1.73/1.37 inference(flattening,[status(thm)],[f29])).
% 1.73/1.37 thf(f29,plain,(
% 1.73/1.37 ~($true = (mlocal @ (mexists_di @ (^[Y0 : $i]: (mbox @ (teach @ john @ Y0))))))),
% 1.73/1.37 inference(fool_elimination,[status(thm)],[f28])).
% 1.73/1.37 thf(f28,plain,(
% 1.73/1.37 ~(mlocal @ (mexists_di @ (^[X0 : $i] : (mbox @ (teach @ john @ X0)))))),
% 1.73/1.37 inference(rectify,[status(thm)],[f14])).
% 1.73/1.37 thf(f14,negated_conjecture,(
% 1.73/1.37 ~(mlocal @ (mexists_di @ (^[X5 : $i] : (mbox @ (teach @ john @ X5)))))),
% 1.73/1.37 inference(negated_conjecture,[status(cth)],[f13])).
% 1.73/1.37 thf(f13,conjecture,(
% 1.73/1.37 (mlocal @ (mexists_di @ (^[X5 : $i] : (mbox @ (teach @ john @ X5)))))),
% 1.73/1.37 file('/export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',query)).
% 1.73/1.37 thf(f81,plain,(
% 1.73/1.37 ($false = (mrel @ mactual @ (sK2 @ math)))),
% 1.73/1.37 inference(trivial_inequality_removal,[status(thm)],[f79])).
% 1.73/1.37 thf(f79,plain,(
% 1.73/1.37 ($true = $false) | ($false = (mrel @ mactual @ (sK2 @ math)))),
% 1.73/1.37 inference(superposition,[status(thm)],[f64,f70])).
% 1.73/1.37 thf(f70,plain,(
% 1.73/1.37 ( ! [X1 : mworld] : (($true = (teach @ john @ math @ X1)) | ((mrel @ mactual @ X1) = $false)) )),
% 1.73/1.37 inference(binary_proxy_clausification,[status(thm)],[f69])).
% 1.73/1.37 thf(f69,plain,(
% 1.73/1.37 ( ! [X1 : mworld] : (((mrel @ mactual @ X1) = $false) | ($true = ((((teach @ sue @ psych @ X1) & (teach @ mary @ psych @ X1)) & (?? @ $i @ (^[Y0 : $i]: (teach @ Y0 @ cs @ X1)))) & (teach @ john @ math @ X1)))) )),
% 1.73/1.37 inference(binary_proxy_clausification,[status(thm)],[f68])).
% 1.73/1.37 thf(f68,plain,(
% 1.73/1.37 ( ! [X1 : mworld] : (($true = ((mrel @ mactual @ X1) => ((((teach @ sue @ psych @ X1) & (teach @ mary @ psych @ X1)) & (?? @ $i @ (^[Y0 : $i]: (teach @ Y0 @ cs @ X1)))) & (teach @ john @ math @ X1))))) )),
% 1.73/1.37 inference(beta_eta_normalization,[status(thm)],[f67])).
% 1.73/1.37 thf(f67,plain,(
% 1.73/1.37 ( ! [X1 : mworld] : (($true = ((^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((((teach @ sue @ psych @ Y0) & (teach @ mary @ psych @ Y0)) & (?? @ $i @ (^[Y1 : $i]: (teach @ Y1 @ cs @ Y0)))) & (teach @ john @ math @ Y0)))) @ X1))) )),
% 1.73/1.37 inference(pi_clausification,[status(thm)],[f66])).
% 1.73/1.37 thf(f66,plain,(
% 1.73/1.37 ($true = (!! @ mworld @ (^[Y0 : mworld]: ((mrel @ mactual @ Y0) => ((((teach @ sue @ psych @ Y0) & (teach @ mary @ psych @ Y0)) & (?? @ $i @ (^[Y1 : $i]: (teach @ Y1 @ cs @ Y0)))) & (teach @ john @ math @ Y0))))))),
% 1.73/1.37 inference(beta_eta_normalization,[status(thm)],[f58])).
% 1.73/1.37 thf(f58,plain,(
% 1.73/1.37 ($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]: (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)))))))),
% 1.73/1.37 inference(definition_unfolding,[status(thm)],[f54,f44,f51,f45,f45,f52,f45])).
% 1.73/1.37 thf(f45,plain,(
% 1.73/1.37 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.73/1.37 inference(cnf_transformation,[status(thm)],[f25])).
% 1.73/1.37 thf(f25,plain,(
% 1.73/1.37 (mand = (^[Y0 : mworld > $o]: ((^[Y1 : mworld > $o]: ((^[Y2 : mworld]: ((Y1 @ Y2) & (Y0 @ Y2))))))))),
% 1.73/1.37 inference(fool_elimination,[status(thm)],[f24])).
% 1.73/1.37 thf(f24,plain,(
% 1.73/1.37 ((^[X0 : mworld > $o, X1 : mworld > $o, X2 : mworld] : ((X0 @ X2) & (X1 @ X2))) = mand)),
% 1.73/1.37 inference(rectify,[status(thm)],[f3])).
% 1.73/1.37 thf(f3,axiom,(
% 1.73/1.37 ((^[X1 : mworld > $o, X3 : mworld > $o, X2 : mworld] : ((X1 @ X2) & (X3 @ X2))) = mand)),
% 1.73/1.37 file('/export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',mand_def)).
% 1.73/1.37 thf(f54,plain,(
% 1.73/1.37 ($true = (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))))),
% 1.73/1.37 inference(cnf_transformation,[status(thm)],[f33])).
% 1.73/1.37 thf(f33,plain,(
% 1.73/1.37 ($true = (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[Y0 : $i]: (teach @ Y0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych)))))))),
% 1.73/1.37 inference(fool_elimination,[status(thm)],[f32])).
% 1.73/1.37 thf(f32,plain,(
% 1.73/1.37 (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[X0 : $i] : (teach @ X0 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),
% 1.73/1.37 inference(rectify,[status(thm)],[f12])).
% 1.73/1.37 thf(f12,axiom,(
% 1.73/1.37 (mlocal @ (mbox @ (mand @ (teach @ john @ math) @ (mand @ (mexists_di @ (^[X5 : $i] : (teach @ X5 @ cs))) @ (mand @ (teach @ mary @ psych) @ (teach @ sue @ psych))))))),
% 1.73/1.37 file('/export/starexec/sandbox2/tmp/tmp.CxRV48i255/DTF2THF_11135.p',db)).
% 1.73/1.37 thf(f64,plain,(
% 1.73/1.37 ( ! [X1 : $i] : (($false = (teach @ john @ X1 @ (sK2 @ X1)))) )),
% 1.73/1.37 inference(binary_proxy_clausification,[status(thm)],[f63])).
% 1.73/1.37 % SZS output end Proof for DTF2THF_11135
% 1.73/1.37 % (11406)------------------------------
% 1.73/1.37 % (11406)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.73/1.37 % (11406)Termination reason: Refutation
% 1.73/1.37
% 1.73/1.37 % (11406)Memory used [KB]: 5628
% 1.73/1.37 % (11406)Time elapsed: 0.008 s
% 1.73/1.37 % (11406)Instructions burned: 6 (million)
% 1.73/1.37 % (11406)------------------------------
% 1.73/1.37 % (11406)------------------------------
% 1.73/1.37 % (11405)Success in time 0.023 s
%------------------------------------------------------------------------------