TPTP Problem File: LCL941^5.p
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%------------------------------------------------------------------------------
% File : LCL941^5 : TPTP v8.2.0. Released v8.1.0.
% Domain : Logic Calculi
% Problem : Goedel translation of ALG014+1 (from TPTP-v5.0.0)
% Version : [BP13] axioms.
% English :
% Refs : [RO12] Raths & Otten (2012), The QMLTP Problem Library for Fi
% : [BP13] Benzmueller & Paulson (2013), Quantified Multimodal Lo
% : [Ste22] Steen (2022), An Extensible Logic Embedding Tool for L
% Source : [TPTP]
% Names : GAL014+1 [QMLTP]
% Status : Theorem
% Rating : 0.90 v8.2.0, 0.85 v8.1.0
% Syntax : Number of formulae : 51 ( 11 unt; 21 typ; 10 def)
% Number of atoms : 1115 ( 10 equ; 0 cnn)
% Maximal formula atoms : 240 ( 37 avg)
% Number of connectives : 2735 ( 1 ~; 1 |; 3 &;2726 @)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 73 ( 13 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 63 ( 63 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 20 usr; 6 con; 0-3 aty)
% Number of variables : 45 ( 37 ^; 6 !; 2 ?; 45 :)
% SPC : TH0_THM_EQU_NAR
% Comments : This output was generated by embedproblem, version 1.7.1 (library
% version 1.3). Generated on Thu Apr 28 13:18:18 EDT 2022 using
% 'modal' embedding, version 1.5.2. Logic specification used:
% $modal == [$constants == $rigid,$quantification == $constant,
% $modalities == $modal_system_S5].
%------------------------------------------------------------------------------
thf(mworld,type,
mworld: $tType ).
thf(mrel_type,type,
mrel: mworld > mworld > $o ).
thf(mactual_type,type,
mactual: mworld ).
thf(mlocal_type,type,
mlocal: ( mworld > $o ) > $o ).
thf(mlocal_def,definition,
( mlocal
= ( ^ [Phi: mworld > $o] : ( Phi @ mactual ) ) ) ).
thf(mnot_type,type,
mnot: ( mworld > $o ) > mworld > $o ).
thf(mand_type,type,
mand: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mor_type,type,
mor: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mimplies_type,type,
mimplies: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mequiv_type,type,
mequiv: ( mworld > $o ) > ( mworld > $o ) > mworld > $o ).
thf(mnot_def,definition,
( mnot
= ( ^ [A: mworld > $o,W: mworld] :
~ ( A @ W ) ) ) ).
thf(mand_def,definition,
( mand
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
& ( B @ W ) ) ) ) ).
thf(mor_def,definition,
( mor
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
| ( B @ W ) ) ) ) ).
thf(mimplies_def,definition,
( mimplies
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
=> ( B @ W ) ) ) ) ).
thf(mequiv_def,definition,
( mequiv
= ( ^ [A: mworld > $o,B: mworld > $o,W: mworld] :
( ( A @ W )
<=> ( B @ W ) ) ) ) ).
thf(mbox_type,type,
mbox: ( mworld > $o ) > mworld > $o ).
thf(mbox_def,definition,
( mbox
= ( ^ [Phi: mworld > $o,W: mworld] :
! [V: mworld] :
( ( mrel @ W @ V )
=> ( Phi @ V ) ) ) ) ).
thf(mdia_type,type,
mdia: ( mworld > $o ) > mworld > $o ).
thf(mdia_def,definition,
( mdia
= ( ^ [Phi: mworld > $o,W: mworld] :
? [V: mworld] :
( ( mrel @ W @ V )
& ( Phi @ V ) ) ) ) ).
thf(mrel_reflexive,axiom,
! [W: mworld] : ( mrel @ W @ W ) ).
thf(mrel_euclidean,axiom,
! [W: mworld,V: mworld,U: mworld] :
( ( ( mrel @ W @ U )
& ( mrel @ W @ V ) )
=> ( mrel @ U @ V ) ) ).
thf(mforall_di_type,type,
mforall_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mforall_di_def,definition,
( mforall_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
! [X: $i] : ( A @ X @ W ) ) ) ).
thf(mexists_di_type,type,
mexists_di: ( $i > mworld > $o ) > mworld > $o ).
thf(mexists_di_def,definition,
( mexists_di
= ( ^ [A: $i > mworld > $o,W: mworld] :
? [X: $i] : ( A @ X @ W ) ) ) ).
thf(unit_decl,type,
unit: $i ).
thf(e0_decl,type,
e0: $i ).
thf(e1_decl,type,
e1: $i ).
thf(e2_decl,type,
e2: $i ).
thf(e3_decl,type,
e3: $i ).
thf(qmltpeq_decl,type,
qmltpeq: $i > $i > mworld > $o ).
thf(inv_decl,type,
inv: $i > $i ).
thf(op_decl,type,
op: $i > $i > $i ).
thf(reflexivity,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] : ( mbox @ ( qmltpeq @ X @ X ) ) ) ) ) ).
thf(symmetry,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] :
( mbox
@ ( mforall_di
@ ^ [Y: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
thf(transitivity,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [X: $i] :
( mbox
@ ( mforall_di
@ ^ [Y: $i] :
( mbox
@ ( mforall_di
@ ^ [Z: $i] : ( mbox @ ( mimplies @ ( mand @ ( mbox @ ( qmltpeq @ X @ Y ) ) @ ( mbox @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
thf(inv_substitution_1,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( inv @ A ) @ ( inv @ B ) ) ) ) ) ) ) ) ) ) ).
thf(op_substitution_1,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( op @ A @ C ) @ ( op @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(op_substitution_2,axiom,
( mlocal
@ ( mbox
@ ( mforall_di
@ ^ [A: $i] :
( mbox
@ ( mforall_di
@ ^ [B: $i] :
( mbox
@ ( mforall_di
@ ^ [C: $i] : ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ A @ B ) ) @ ( mbox @ ( qmltpeq @ ( op @ C @ A ) @ ( op @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax1,axiom,
mlocal @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ e3 ) ) ) ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax2,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e0 ) @ ( op @ e0 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e1 ) @ ( op @ e0 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e2 ) @ ( op @ e0 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e0 ) @ e3 ) @ ( op @ e0 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e0 ) @ ( op @ e0 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e1 ) @ ( op @ e0 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e2 ) @ ( op @ e0 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e1 ) @ e3 ) @ ( op @ e0 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e0 ) @ ( op @ e0 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e1 ) @ ( op @ e0 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e2 ) @ ( op @ e0 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e2 ) @ e3 ) @ ( op @ e0 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e0 ) @ ( op @ e0 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e1 ) @ ( op @ e0 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e2 ) @ ( op @ e0 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e0 @ e3 ) @ e3 ) @ ( op @ e0 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e0 ) @ ( op @ e1 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e1 ) @ ( op @ e1 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e2 ) @ ( op @ e1 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e0 ) @ e3 ) @ ( op @ e1 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e0 ) @ ( op @ e1 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e1 ) @ ( op @ e1 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e2 ) @ ( op @ e1 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e1 ) @ e3 ) @ ( op @ e1 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e0 ) @ ( op @ e1 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e1 ) @ ( op @ e1 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e2 ) @ ( op @ e1 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e2 ) @ e3 ) @ ( op @ e1 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e0 ) @ ( op @ e1 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e1 ) @ ( op @ e1 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e2 ) @ ( op @ e1 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e1 @ e3 ) @ e3 ) @ ( op @ e1 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e0 ) @ ( op @ e2 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e1 ) @ ( op @ e2 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e2 ) @ ( op @ e2 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e0 ) @ e3 ) @ ( op @ e2 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e0 ) @ ( op @ e2 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e1 ) @ ( op @ e2 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e2 ) @ ( op @ e2 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e1 ) @ e3 ) @ ( op @ e2 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e0 ) @ ( op @ e2 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e1 ) @ ( op @ e2 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e2 ) @ ( op @ e2 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e2 ) @ e3 ) @ ( op @ e2 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e0 ) @ ( op @ e2 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e1 ) @ ( op @ e2 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e2 ) @ ( op @ e2 @ ( op @ e3 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e2 @ e3 ) @ e3 ) @ ( op @ e2 @ ( op @ e3 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e0 ) @ ( op @ e3 @ ( op @ e0 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e1 ) @ ( op @ e3 @ ( op @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e2 ) @ ( op @ e3 @ ( op @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e0 ) @ e3 ) @ ( op @ e3 @ ( op @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e0 ) @ ( op @ e3 @ ( op @ e1 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e1 ) @ ( op @ e3 @ ( op @ e1 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e2 ) @ ( op @ e3 @ ( op @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e1 ) @ e3 ) @ ( op @ e3 @ ( op @ e1 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e0 ) @ ( op @ e3 @ ( op @ e2 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e1 ) @ ( op @ e3 @ ( op @ e2 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e2 ) @ ( op @ e3 @ ( op @ e2 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e2 ) @ e3 ) @ ( op @ e3 @ ( op @ e2 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e0 ) @ ( op @ e3 @ ( op @ e3 @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e1 ) @ ( op @ e3 @ ( op @ e3 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e2 ) @ ( op @ e3 @ ( op @ e3 @ e2 ) ) ) ) @ ( mbox @ ( qmltpeq @ ( op @ ( op @ e3 @ e3 ) @ e3 ) @ ( op @ e3 @ ( op @ e3 @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax3,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ unit ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ unit ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e2 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ unit ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ unit @ e3 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e3 @ unit ) @ e3 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ unit @ e2 ) ) @ ( mbox @ ( qmltpeq @ unit @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax4,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ ( inv @ e0 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e0 ) @ e0 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ ( inv @ e1 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e1 ) @ e1 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ ( inv @ e2 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e2 ) @ e2 ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e3 @ ( inv @ e3 ) ) @ unit ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ ( inv @ e3 ) @ e3 ) @ unit ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) ) ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) @ ( mor @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax5,axiom,
mlocal @ ( mbox @ ( qmltpeq @ unit @ e0 ) ) ).
thf(ax6,axiom,
mlocal @ ( mbox @ ( qmltpeq @ ( inv @ unit ) @ unit ) ) ).
thf(ax7,axiom,
mlocal @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e0 ) ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e1 ) ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e2 ) ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ ( inv @ e3 ) ) @ e3 ) ) ) ) ) ).
thf(ax8,axiom,
mlocal @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ e3 ) ) ) ) @ ( mbox @ ( mimplies @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( inv @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax9,axiom,
mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e0 ) @ ( inv @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e1 ) @ ( inv @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( inv @ e2 ) @ ( inv @ e3 ) ) ) ) ) ) ) ) ) ) ).
thf(ax10,axiom,
mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e1 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e2 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e2 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e3 @ e0 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e1 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e3 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e1 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e2 ) @ ( op @ e0 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e0 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e2 ) @ ( op @ e1 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e0 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e1 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ ( op @ e2 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e1 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e0 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e1 ) @ ( op @ e3 @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e2 ) @ ( op @ e3 @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax11,axiom,
mlocal @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e1 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e0 @ e3 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e1 @ e2 ) ) ) ) @ ( mand @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e1 @ e3 ) ) ) ) @ ( mbox @ ( mnot @ ( mbox @ ( qmltpeq @ e2 @ e3 ) ) ) ) ) ) ) ) ) ).
thf(co1,conjecture,
mlocal @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) @ ( mbox @ ( mnot @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e0 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e0 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e0 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e1 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e1 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e1 ) ) ) ) ) @ ( mor @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e2 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e2 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e2 ) ) ) ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e0 @ e0 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e1 @ e1 ) @ e3 ) ) @ ( mand @ ( mbox @ ( qmltpeq @ ( op @ e2 @ e2 ) @ e3 ) ) @ ( mbox @ ( qmltpeq @ ( op @ e3 @ e3 ) @ e3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------