SET007 Axioms: SET007+234.ax
%------------------------------------------------------------------------------
% File : SET007+234 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Lattice of Real Numbers. The Lattice of Real Functions
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : real_lat [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 68 ( 23 unt; 0 def)
% Number of atoms : 253 ( 70 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 219 ( 34 ~; 0 |; 75 &)
% ( 4 <=>; 106 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 21 ( 19 usr; 1 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 4 con; 0-6 aty)
% Number of variables : 107 ( 107 !; 0 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_real_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_real_lat))
=> v1_xreal_0(A) ) ).
fof(fc1_real_lat,axiom,
( ~ v3_struct_0(k3_real_lat)
& v3_lattices(k3_real_lat) ) ).
fof(fc2_real_lat,axiom,
( ~ v3_struct_0(k3_real_lat)
& v3_lattices(k3_real_lat)
& v4_lattices(k3_real_lat)
& v5_lattices(k3_real_lat)
& v6_lattices(k3_real_lat)
& v7_lattices(k3_real_lat)
& v8_lattices(k3_real_lat)
& v9_lattices(k3_real_lat)
& v10_lattices(k3_real_lat) ) ).
fof(fc3_real_lat,axiom,
( ~ v3_struct_0(k3_real_lat)
& v3_lattices(k3_real_lat)
& v4_lattices(k3_real_lat)
& v5_lattices(k3_real_lat)
& v6_lattices(k3_real_lat)
& v7_lattices(k3_real_lat)
& v8_lattices(k3_real_lat)
& v9_lattices(k3_real_lat)
& v10_lattices(k3_real_lat)
& v11_lattices(k3_real_lat)
& v12_lattices(k3_real_lat) ) ).
fof(d1_real_lat,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
=> ( A = k1_real_lat
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k3_square_1(B,C) ) ) ) ) ).
fof(d2_real_lat,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(A,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) )
=> ( A = k2_real_lat
<=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> k2_binop_1(k1_numbers,k1_numbers,k1_numbers,A,B,C) = k4_square_1(B,C) ) ) ) ) ).
fof(d3_real_lat,axiom,
$true ).
fof(d4_real_lat,axiom,
k3_real_lat = g3_lattices(k1_numbers,k2_real_lat,k1_real_lat) ).
fof(t1_real_lat,axiom,
$true ).
fof(t2_real_lat,axiom,
$true ).
fof(t3_real_lat,axiom,
$true ).
fof(t4_real_lat,axiom,
$true ).
fof(t5_real_lat,axiom,
$true ).
fof(t6_real_lat,axiom,
$true ).
fof(t7_real_lat,axiom,
$true ).
fof(t8_real_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_real_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_real_lat))
=> k1_binop_1(k2_real_lat,A,B) = k1_binop_1(k2_real_lat,B,A) ) ) ).
fof(t9_real_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_real_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_real_lat))
=> k1_binop_1(k1_real_lat,A,B) = k1_binop_1(k1_real_lat,B,A) ) ) ).
fof(t10_real_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_real_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_real_lat))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_real_lat))
=> ( k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,B,C),A)
& k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,A,B),C)
& k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,B,A),C)
& k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,C,A),B)
& k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,C,B),A)
& k1_binop_1(k2_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k2_real_lat,A,C),B) ) ) ) ) ).
fof(t11_real_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_real_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_real_lat))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_real_lat))
=> ( k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,B,C),A)
& k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,A,B),C)
& k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,B,A),C)
& k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,C,A),B)
& k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,C,B),A)
& k1_binop_1(k1_real_lat,A,k1_binop_1(k1_real_lat,B,C)) = k1_binop_1(k1_real_lat,k1_binop_1(k1_real_lat,A,C),B) ) ) ) ) ).
fof(t12_real_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_real_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_real_lat))
=> ( k1_binop_1(k2_real_lat,k1_binop_1(k1_real_lat,A,B),B) = B
& k1_binop_1(k2_real_lat,B,k1_binop_1(k1_real_lat,A,B)) = B
& k1_binop_1(k2_real_lat,B,k1_binop_1(k1_real_lat,B,A)) = B
& k1_binop_1(k2_real_lat,k1_binop_1(k1_real_lat,B,A),B) = B ) ) ) ).
fof(t13_real_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_real_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_real_lat))
=> ( k1_binop_1(k1_real_lat,A,k1_binop_1(k2_real_lat,A,B)) = A
& k1_binop_1(k1_real_lat,k1_binop_1(k2_real_lat,B,A),A) = A
& k1_binop_1(k1_real_lat,A,k1_binop_1(k2_real_lat,B,A)) = A
& k1_binop_1(k1_real_lat,k1_binop_1(k2_real_lat,A,B),A) = A ) ) ) ).
fof(t14_real_lat,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k3_real_lat))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_real_lat))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_real_lat))
=> k1_binop_1(k1_real_lat,A,k1_binop_1(k2_real_lat,B,C)) = k1_binop_1(k2_real_lat,k1_binop_1(k1_real_lat,A,B),k1_binop_1(k1_real_lat,A,C)) ) ) ) ).
fof(d5_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
& m2_relset_1(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) )
=> ( B = k4_real_lat(A)
<=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,B,C,D) = k4_funcsdom(k1_numbers,A,k2_real_lat,C,D) ) ) ) ) ) ).
fof(d6_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
& m2_relset_1(B,k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) )
=> ( B = k5_real_lat(A)
<=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,B,C,D) = k4_funcsdom(k1_numbers,A,k1_real_lat,C,D) ) ) ) ) ) ).
fof(t15_real_lat,axiom,
$true ).
fof(t16_real_lat,axiom,
$true ).
fof(t17_real_lat,axiom,
$true ).
fof(t18_real_lat,axiom,
$true ).
fof(t19_real_lat,axiom,
$true ).
fof(t20_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C) = k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,B) ) ) ) ).
fof(t21_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C) = k1_funcsdom(A,k1_numbers,k5_real_lat(A),C,B) ) ) ) ).
fof(t22_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k4_real_lat(A),k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C),D) = k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,D)) ) ) ) ) ).
fof(t23_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k5_real_lat(A),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C),D) = k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,k1_funcsdom(A,k1_numbers,k5_real_lat(A),C,D)) ) ) ) ) ).
fof(t24_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C)) = B ) ) ) ).
fof(t25_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k4_real_lat(A),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C),B) = B ) ) ) ).
fof(t26_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k4_real_lat(A),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C),C) = C ) ) ) ).
fof(t27_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,k1_funcsdom(A,k1_numbers,k5_real_lat(A),C,B)) = B ) ) ) ).
fof(t28_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C)) = B ) ) ) ).
fof(t29_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,B)) = B ) ) ) ).
fof(t30_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k5_real_lat(A),k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C),C) = C ) ) ) ).
fof(t31_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k5_real_lat(A),k1_funcsdom(A,k1_numbers,k4_real_lat(A),B,C),B) = B ) ) ) ).
fof(t32_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_fraenkel(B,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [C] :
( m2_fraenkel(C,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> ! [D] :
( m2_fraenkel(D,A,k1_numbers,k1_fraenkel(A,k1_numbers))
=> k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,k1_funcsdom(A,k1_numbers,k4_real_lat(A),C,D)) = k1_funcsdom(A,k1_numbers,k4_real_lat(A),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,C),k1_funcsdom(A,k1_numbers,k5_real_lat(A),B,D)) ) ) ) ) ).
fof(d7_real_lat,axiom,
$true ).
fof(d8_real_lat,axiom,
$true ).
fof(d9_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(g3_lattices(k1_fraenkel(A,k1_numbers),k4_real_lat(A),k5_real_lat(A))))
=> k6_real_lat(A,B) = B ) ) ).
fof(d10_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> k7_real_lat(A) = g3_lattices(k1_fraenkel(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)) ) ).
fof(t33_real_lat,axiom,
$true ).
fof(t34_real_lat,axiom,
$true ).
fof(t35_real_lat,axiom,
$true ).
fof(t36_real_lat,axiom,
$true ).
fof(t37_real_lat,axiom,
$true ).
fof(t38_real_lat,axiom,
$true ).
fof(t39_real_lat,axiom,
$true ).
fof(t40_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
=> k1_binop_1(k4_real_lat(A),B,C) = k1_binop_1(k4_real_lat(A),C,B) ) ) ) ).
fof(t41_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
=> k1_binop_1(k5_real_lat(A),B,C) = k1_binop_1(k5_real_lat(A),C,B) ) ) ) ).
fof(t42_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k7_real_lat(A)))
=> ( k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),C,D),B)
& k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),B,C),D)
& k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),C,B),D)
& k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),D,B),C)
& k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),D,C),B)
& k1_binop_1(k4_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k4_real_lat(A),B,D),C) ) ) ) ) ) ).
fof(t43_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k7_real_lat(A)))
=> ( k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),C,D),B)
& k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),B,C),D)
& k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),C,B),D)
& k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),D,B),C)
& k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),D,C),B)
& k1_binop_1(k5_real_lat(A),B,k1_binop_1(k5_real_lat(A),C,D)) = k1_binop_1(k5_real_lat(A),k1_binop_1(k5_real_lat(A),B,D),C) ) ) ) ) ) ).
fof(t44_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
=> ( k1_binop_1(k4_real_lat(A),k1_binop_1(k5_real_lat(A),B,C),C) = C
& k1_binop_1(k4_real_lat(A),C,k1_binop_1(k5_real_lat(A),B,C)) = C
& k1_binop_1(k4_real_lat(A),C,k1_binop_1(k5_real_lat(A),C,B)) = C
& k1_binop_1(k4_real_lat(A),k1_binop_1(k5_real_lat(A),C,B),C) = C ) ) ) ) ).
fof(t45_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
=> ( k1_binop_1(k5_real_lat(A),B,k1_binop_1(k4_real_lat(A),B,C)) = B
& k1_binop_1(k5_real_lat(A),k1_binop_1(k4_real_lat(A),C,B),B) = B
& k1_binop_1(k5_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,B)) = B
& k1_binop_1(k5_real_lat(A),k1_binop_1(k4_real_lat(A),B,C),B) = B ) ) ) ) ).
fof(t46_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k7_real_lat(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_real_lat(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k7_real_lat(A)))
=> k1_binop_1(k5_real_lat(A),B,k1_binop_1(k4_real_lat(A),C,D)) = k1_binop_1(k4_real_lat(A),k1_binop_1(k5_real_lat(A),B,C),k1_binop_1(k5_real_lat(A),B,D)) ) ) ) ) ).
fof(t47_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k7_real_lat(A))
& v10_lattices(k7_real_lat(A))
& v11_lattices(k7_real_lat(A))
& l3_lattices(k7_real_lat(A)) ) ) ).
fof(dt_k1_real_lat,axiom,
( v1_funct_1(k1_real_lat)
& v1_funct_2(k1_real_lat,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(k1_real_lat,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ) ).
fof(dt_k2_real_lat,axiom,
( v1_funct_1(k2_real_lat)
& v1_funct_2(k2_real_lat,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers)
& m2_relset_1(k2_real_lat,k2_zfmisc_1(k1_numbers,k1_numbers),k1_numbers) ) ).
fof(dt_k3_real_lat,axiom,
( v3_lattices(k3_real_lat)
& l3_lattices(k3_real_lat) ) ).
fof(dt_k4_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v1_funct_1(k4_real_lat(A))
& v1_funct_2(k4_real_lat(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
& m2_relset_1(k4_real_lat(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) ) ) ).
fof(dt_k5_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( v1_funct_1(k5_real_lat(A))
& v1_funct_2(k5_real_lat(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers))
& m2_relset_1(k5_real_lat(A),k2_zfmisc_1(k1_fraenkel(A,k1_numbers),k1_fraenkel(A,k1_numbers)),k1_fraenkel(A,k1_numbers)) ) ) ).
fof(dt_k6_real_lat,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(B,u1_struct_0(g3_lattices(k1_fraenkel(A,k1_numbers),k4_real_lat(A),k5_real_lat(A)))) )
=> m2_fraenkel(k6_real_lat(A,B),A,k1_numbers,k1_fraenkel(A,k1_numbers)) ) ).
fof(dt_k7_real_lat,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k7_real_lat(A))
& v3_lattices(k7_real_lat(A))
& v10_lattices(k7_real_lat(A))
& l3_lattices(k7_real_lat(A)) ) ) ).
%------------------------------------------------------------------------------