TPTP Problem File: ALG020^7.p
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%------------------------------------------------------------------------------
% File : ALG020^7 : TPTP v8.2.0. Released v5.5.0.
% Domain : General Algebra
% Problem : Groups 4: REPRESENTATIVES-PAIRWISE-NOT-ISO-PROBLEM-1
% Version : [Ben12] axioms.
% English :
% Refs : [Goe69] Goedel (1969), An Interpretation of the Intuitionistic
% : [CM+04] Colton et al. (2004), Automatic Generation of Classifi
% : [Ben12] Benzmueller (2012), Email to Geoff Sutcliffe
% Source : [Ben12]
% Names : s4-cumul-GAL020+1 [Ben12]
% Status : Theorem
% Rating : 1.00 v5.5.0
% Syntax : Number of formulae : 111 ( 45 unt; 48 typ; 32 def)
% Number of atoms : 679 ( 36 equ; 0 cnn)
% Maximal formula atoms : 219 ( 10 avg)
% Number of connectives : 1378 ( 5 ~; 5 |; 9 &;1349 @)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 51 ( 6 avg)
% Number of types : 3 ( 1 usr)
% Number of type conns : 186 ( 186 >; 0 *; 0 +; 0 <<)
% Number of symbols : 58 ( 56 usr; 18 con; 0-3 aty)
% Number of variables : 130 ( 71 ^; 52 !; 7 ?; 130 :)
% SPC : TH0_THM_EQU_NAR
% Comments : Goedel translation of ALG020+1
%------------------------------------------------------------------------------
%----Include axioms for Modal logic S4 under cumulative domains
include('Axioms/LCL015^0.ax').
include('Axioms/LCL013^5.ax').
include('Axioms/LCL015^1.ax').
%------------------------------------------------------------------------------
thf(op2_type,type,
op2: mu > mu > mu ).
thf(existence_of_op2_ax,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( op2 @ V2 @ V1 ) @ V ) ).
thf(op1_type,type,
op1: mu > mu > mu ).
thf(existence_of_op1_ax,axiom,
! [V: $i,V2: mu,V1: mu] : ( exists_in_world @ ( op1 @ V2 @ V1 ) @ V ) ).
thf(j_type,type,
j: mu > mu ).
thf(existence_of_j_ax,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( j @ V1 ) @ V ) ).
thf(e13_type,type,
e13: mu ).
thf(existence_of_e13_ax,axiom,
! [V: $i] : ( exists_in_world @ e13 @ V ) ).
thf(e12_type,type,
e12: mu ).
thf(existence_of_e12_ax,axiom,
! [V: $i] : ( exists_in_world @ e12 @ V ) ).
thf(e11_type,type,
e11: mu ).
thf(existence_of_e11_ax,axiom,
! [V: $i] : ( exists_in_world @ e11 @ V ) ).
thf(e23_type,type,
e23: mu ).
thf(existence_of_e23_ax,axiom,
! [V: $i] : ( exists_in_world @ e23 @ V ) ).
thf(e22_type,type,
e22: mu ).
thf(existence_of_e22_ax,axiom,
! [V: $i] : ( exists_in_world @ e22 @ V ) ).
thf(e21_type,type,
e21: mu ).
thf(existence_of_e21_ax,axiom,
! [V: $i] : ( exists_in_world @ e21 @ V ) ).
thf(e20_type,type,
e20: mu ).
thf(existence_of_e20_ax,axiom,
! [V: $i] : ( exists_in_world @ e20 @ V ) ).
thf(e10_type,type,
e10: mu ).
thf(existence_of_e10_ax,axiom,
! [V: $i] : ( exists_in_world @ e10 @ V ) ).
thf(h_type,type,
h: mu > mu ).
thf(existence_of_h_ax,axiom,
! [V: $i,V1: mu] : ( exists_in_world @ ( h @ V1 ) @ V ) ).
thf(reflexivity,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] : ( mbox_s4 @ ( qmltpeq @ X @ X ) ) ) ) ) ).
thf(symmetry,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ X ) ) ) ) ) ) ) ) ) ).
thf(transitivity,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [X: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Y: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [Z: mu] : ( mbox_s4 @ ( mimplies @ ( mand @ ( mbox_s4 @ ( qmltpeq @ X @ Y ) ) @ ( mbox_s4 @ ( qmltpeq @ Y @ Z ) ) ) @ ( mbox_s4 @ ( qmltpeq @ X @ Z ) ) ) ) ) ) ) ) ) ) ) ).
thf(h_substitution_1,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( h @ A ) @ ( h @ B ) ) ) ) ) ) ) ) ) ) ).
thf(j_substitution_1,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( j @ A ) @ ( j @ B ) ) ) ) ) ) ) ) ) ) ).
thf(op1_substitution_1,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ A @ C ) @ ( op1 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(op1_substitution_2,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ C @ A ) @ ( op1 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(op2_substitution_1,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ A @ C ) @ ( op2 @ B @ C ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(op2_substitution_2,axiom,
( mvalid
@ ( mbox_s4
@ ( mforall_ind
@ ^ [A: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [B: mu] :
( mbox_s4
@ ( mforall_ind
@ ^ [C: mu] : ( mbox_s4 @ ( mimplies @ ( mbox_s4 @ ( qmltpeq @ A @ B ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ C @ A ) @ ( op2 @ C @ B ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax1,axiom,
mvalid @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e10 @ e11 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e10 @ e12 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e10 @ e13 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e11 @ e12 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e11 @ e13 ) ) ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e12 @ e13 ) ) ) ) ) ) ) ) ) ).
thf(ax2,axiom,
mvalid @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e20 @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e20 @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e20 @ e23 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e21 @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e21 @ e23 ) ) ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e22 @ e23 ) ) ) ) ) ) ) ) ) ).
thf(ax3,axiom,
mvalid @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e10 @ e20 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e10 @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e10 @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e10 @ e23 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e11 @ e20 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e11 @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e11 @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e11 @ e23 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e12 @ e20 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e12 @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e12 @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e12 @ e23 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e13 @ e20 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e13 @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e13 @ e22 ) ) ) ) @ ( mbox_s4 @ ( mnot @ ( mbox_s4 @ ( qmltpeq @ e13 @ e23 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax4,axiom,
mvalid @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e10 @ e10 ) @ e10 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e10 @ e11 ) @ e11 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e10 @ e12 ) @ e12 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e10 @ e13 ) @ e13 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e11 @ e10 ) @ e11 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e11 @ e11 ) @ e10 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e11 @ e12 ) @ e13 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e11 @ e13 ) @ e12 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e12 @ e10 ) @ e12 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e12 @ e11 ) @ e13 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e12 @ e12 ) @ e10 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e12 @ e13 ) @ e11 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e13 @ e10 ) @ e13 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e13 @ e11 ) @ e12 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e13 @ e12 ) @ e11 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op1 @ e13 @ e13 ) @ e10 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(ax5,axiom,
mvalid @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e20 @ e20 ) @ e20 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e20 @ e21 ) @ e21 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e20 @ e22 ) @ e22 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e20 @ e23 ) @ e23 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e21 @ e20 ) @ e21 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e21 @ e21 ) @ e23 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e21 @ e22 ) @ e20 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e21 @ e23 ) @ e22 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e22 @ e20 ) @ e22 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e22 @ e21 ) @ e20 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e22 @ e22 ) @ e23 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e22 @ e23 ) @ e21 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e23 @ e20 ) @ e23 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e23 @ e21 ) @ e22 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e23 @ e22 ) @ e21 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( op2 @ e23 @ e23 ) @ e20 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
thf(co1,conjecture,
mvalid @ ( mbox_s4 @ ( mimplies @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e10 ) @ e20 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e10 ) @ e21 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e10 ) @ e22 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( h @ e10 ) @ e23 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e11 ) @ e20 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e11 ) @ e21 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e11 ) @ e22 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( h @ e11 ) @ e23 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e12 ) @ e20 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e12 ) @ e21 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e12 ) @ e22 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( h @ e12 ) @ e23 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e13 ) @ e20 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e13 ) @ e21 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( h @ e13 ) @ e22 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( h @ e13 ) @ e23 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e20 ) @ e10 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e20 ) @ e11 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e20 ) @ e12 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( j @ e20 ) @ e13 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e21 ) @ e10 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e21 ) @ e11 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e21 ) @ e12 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( j @ e21 ) @ e13 ) ) ) ) ) @ ( mand @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e22 ) @ e10 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e22 ) @ e11 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e22 ) @ e12 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( j @ e22 ) @ e13 ) ) ) ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e23 ) @ e10 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e23 ) @ e11 ) ) @ ( mor @ ( mbox_s4 @ ( qmltpeq @ ( j @ e23 ) @ e12 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( j @ e23 ) @ e13 ) ) ) ) ) ) ) ) ) ) ) ) @ ( mbox_s4 @ ( mnot @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e10 @ e10 ) ) @ ( op2 @ ( h @ e10 ) @ ( h @ e10 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e10 @ e11 ) ) @ ( op2 @ ( h @ e10 ) @ ( h @ e11 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e10 @ e12 ) ) @ ( op2 @ ( h @ e10 ) @ ( h @ e12 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e10 @ e13 ) ) @ ( op2 @ ( h @ e10 ) @ ( h @ e13 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e11 @ e10 ) ) @ ( op2 @ ( h @ e11 ) @ ( h @ e10 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e11 @ e11 ) ) @ ( op2 @ ( h @ e11 ) @ ( h @ e11 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e11 @ e12 ) ) @ ( op2 @ ( h @ e11 ) @ ( h @ e12 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e11 @ e13 ) ) @ ( op2 @ ( h @ e11 ) @ ( h @ e13 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e12 @ e10 ) ) @ ( op2 @ ( h @ e12 ) @ ( h @ e10 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e12 @ e11 ) ) @ ( op2 @ ( h @ e12 ) @ ( h @ e11 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e12 @ e12 ) ) @ ( op2 @ ( h @ e12 ) @ ( h @ e12 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e12 @ e13 ) ) @ ( op2 @ ( h @ e12 ) @ ( h @ e13 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e13 @ e10 ) ) @ ( op2 @ ( h @ e13 ) @ ( h @ e10 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e13 @ e11 ) ) @ ( op2 @ ( h @ e13 ) @ ( h @ e11 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e13 @ e12 ) ) @ ( op2 @ ( h @ e13 ) @ ( h @ e12 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( op1 @ e13 @ e13 ) ) @ ( op2 @ ( h @ e13 ) @ ( h @ e13 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e20 @ e20 ) ) @ ( op1 @ ( j @ e20 ) @ ( j @ e20 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e20 @ e21 ) ) @ ( op1 @ ( j @ e20 ) @ ( j @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e20 @ e22 ) ) @ ( op1 @ ( j @ e20 ) @ ( j @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e20 @ e23 ) ) @ ( op1 @ ( j @ e20 ) @ ( j @ e23 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e21 @ e20 ) ) @ ( op1 @ ( j @ e21 ) @ ( j @ e20 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e21 @ e21 ) ) @ ( op1 @ ( j @ e21 ) @ ( j @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e21 @ e22 ) ) @ ( op1 @ ( j @ e21 ) @ ( j @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e21 @ e23 ) ) @ ( op1 @ ( j @ e21 ) @ ( j @ e23 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e22 @ e20 ) ) @ ( op1 @ ( j @ e22 ) @ ( j @ e20 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e22 @ e21 ) ) @ ( op1 @ ( j @ e22 ) @ ( j @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e22 @ e22 ) ) @ ( op1 @ ( j @ e22 ) @ ( j @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e22 @ e23 ) ) @ ( op1 @ ( j @ e22 ) @ ( j @ e23 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e23 @ e20 ) ) @ ( op1 @ ( j @ e23 ) @ ( j @ e20 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e23 @ e21 ) ) @ ( op1 @ ( j @ e23 ) @ ( j @ e21 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e23 @ e22 ) ) @ ( op1 @ ( j @ e23 ) @ ( j @ e22 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( op2 @ e23 @ e23 ) ) @ ( op1 @ ( j @ e23 ) @ ( j @ e23 ) ) ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( j @ e20 ) ) @ e20 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( j @ e21 ) ) @ e21 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( j @ e22 ) ) @ e22 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( h @ ( j @ e23 ) ) @ e23 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( h @ e10 ) ) @ e10 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( h @ e11 ) ) @ e11 ) ) @ ( mand @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( h @ e12 ) ) @ e12 ) ) @ ( mbox_s4 @ ( qmltpeq @ ( j @ ( h @ e13 ) ) @ e13 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
%------------------------------------------------------------------------------