SET007 Axioms: SET007+736.ax
%------------------------------------------------------------------------------
% File : SET007+736 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Subalgebras of an Order Sorted Algebra. Lattice of Subalgebras
% 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 : osalg_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 115 ( 11 unt; 0 def)
% Number of atoms : 1125 ( 45 equ)
% Maximal formula atoms : 23 ( 9 avg)
% Number of connectives : 1215 ( 205 ~; 0 |; 713 &)
% ( 23 <=>; 274 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 9 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 55 ( 53 usr; 1 prp; 0-3 aty)
% Number of functors : 59 ( 59 usr; 0 con; 1-6 aty)
% Number of variables : 335 ( 320 !; 15 ?)
% 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(rc1_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& v2_relat_1(B)
& v11_osalg_1(B,A)
& m1_pboole(B,u1_struct_0(A)) )
=> ? [C] :
( m1_osalg_2(C,A,B)
& v1_relat_1(C)
& v2_relat_1(C)
& v1_funct_1(C) ) ) ).
fof(rc2_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ? [B] :
( l3_msualg_1(B,A)
& v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& v13_osalg_1(B,A) ) ) ).
fof(rc3_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m2_osalg_2(C,A,B)
& v1_relat_1(C)
& v2_relat_1(C)
& v1_funct_1(C) ) ) ).
fof(rc4_osalg_2,axiom,
? [A] :
( l3_osalg_1(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& ~ v2_msualg_1(A)
& v3_osalg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_msualg_2(A) ) ).
fof(rc5_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m1_msualg_2(C,A,B)
& v12_osalg_1(C,A) ) ) ).
fof(rc6_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m1_msualg_2(C,A,B)
& v4_msualg_1(C,A)
& v12_osalg_1(C,A) ) ) ).
fof(rc7_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m1_msualg_2(C,A,B)
& v4_msualg_1(C,A)
& v5_msualg_1(C,A)
& v12_osalg_1(C,A) ) ) ).
fof(fc1_osalg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& m2_osalg_2(C,A,B) )
=> ~ v1_xboole_0(k5_osalg_2(A,B,C)) ) ).
fof(fc2_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ~ v1_xboole_0(k6_osalg_2(A,B)) ) ).
fof(fc3_osalg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& m2_osalg_2(C,A,B)
& m1_subset_1(D,u1_struct_0(A)) )
=> ~ v1_xboole_0(k8_osalg_2(A,B,C,D)) ) ).
fof(rc8_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] :
( m2_osalg_2(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v3_msualg_2(C,A,B) ) ) ).
fof(fc4_osalg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& m2_osalg_2(C,A,B) )
=> ( v1_relat_1(k9_osalg_2(A,B,C))
& v1_funct_1(k9_osalg_2(A,B,C))
& v3_msualg_2(k9_osalg_2(A,B,C),A,B) ) ) ).
fof(fc5_osalg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v3_msualg_2(C,A,B)
& m2_osalg_2(C,A,B) )
=> ( v4_msualg_1(k10_msualg_2(A,B,C),A)
& v12_osalg_1(k10_msualg_2(A,B,C),A) ) ) ).
fof(fc6_osalg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v12_osalg_1(C,A)
& m1_msualg_2(C,A,B)
& v12_osalg_1(D,A)
& m1_msualg_2(D,A,B) )
=> ( v4_msualg_1(k11_msualg_2(A,B,C,D),A)
& v12_osalg_1(k11_msualg_2(A,B,C,D),A) ) ) ).
fof(fc7_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ~ v1_xboole_0(k12_osalg_2(A,B)) ) ).
fof(fc8_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( ~ v3_struct_0(k16_osalg_2(A,B))
& v3_lattices(k16_osalg_2(A,B))
& v4_lattices(k16_osalg_2(A,B))
& v5_lattices(k16_osalg_2(A,B))
& v6_lattices(k16_osalg_2(A,B))
& v7_lattices(k16_osalg_2(A,B))
& v8_lattices(k16_osalg_2(A,B))
& v9_lattices(k16_osalg_2(A,B))
& v10_lattices(k16_osalg_2(A,B))
& v13_lattices(k16_osalg_2(A,B))
& v14_lattices(k16_osalg_2(A,B))
& v15_lattices(k16_osalg_2(A,B)) ) ) ).
fof(t1_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v11_osalg_1(B,A)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v11_osalg_1(C,A)
& m1_pboole(C,u1_struct_0(A)) )
=> ( v11_osalg_1(k3_pboole(u1_struct_0(A),B,C),A)
& m1_pboole(k3_pboole(u1_struct_0(A),B,C),u1_struct_0(A)) ) ) ) ) ).
fof(t2_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v11_osalg_1(B,A)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( ( v11_osalg_1(C,A)
& m1_pboole(C,u1_struct_0(A)) )
=> ( v11_osalg_1(k2_pboole(u1_struct_0(A),B,C),A)
& m1_pboole(k2_pboole(u1_struct_0(A),B,C),u1_struct_0(A)) ) ) ) ) ).
fof(d1_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v11_osalg_1(B,A)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),B)
=> ( m1_osalg_2(C,A,B)
<=> ( v11_osalg_1(C,A)
& m1_pboole(C,u1_struct_0(A)) ) ) ) ) ) ).
fof(d2_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( m2_osalg_2(C,A,B)
<=> ( v11_osalg_1(C,A)
& m1_pboole(C,u1_struct_0(A)) ) ) ) ) ) ).
fof(t3_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_msualg_1(A)
& ~ v2_msualg_1(A)
& v2_msualg_2(A)
& l1_msualg_1(A) )
=> v2_msualg_2(k2_osalg_1(A)) ) ).
fof(t4_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> v12_osalg_1(g3_msualg_1(A,u4_msualg_1(A,B),u5_msualg_1(A,B)),A) ) ) ).
fof(t5_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( l3_msualg_1(C,A)
=> ( ( v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
<=> ( m2_osalg_2(u4_msualg_1(A,C),A,B)
& ! [D] :
( m2_osalg_2(D,A,B)
=> ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
=> ( v3_msualg_2(D,A,B)
& r6_pboole(u1_msualg_1(A),u5_msualg_1(A,C),k4_msualg_2(A,B,D)) ) ) ) ) ) ) ) ) ).
fof(t6_osalg_2,axiom,
$true ).
fof(t7_osalg_2,axiom,
$true ).
fof(t8_osalg_2,axiom,
$true ).
fof(t9_osalg_2,axiom,
$true ).
fof(t10_osalg_2,axiom,
$true ).
fof(t11_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_tarski(k1_msualg_2(A,B,C),k1_osalg_2(A,B,C)) ) ) ) ).
fof(t12_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> r2_pboole(u1_struct_0(A),B,k2_osalg_2(A,B)) ) ) ).
fof(t13_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( ( v11_osalg_1(C,A)
& m1_pboole(C,u1_struct_0(A)) )
=> ( r2_pboole(u1_struct_0(A),B,C)
=> r2_pboole(u1_struct_0(A),k2_osalg_2(A,B),C) ) ) ) ) ).
fof(t14_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v11_osalg_1(B,A)
& m1_pboole(B,u1_struct_0(A)) )
=> r6_pboole(u1_struct_0(A),k2_osalg_2(A,B),B) ) ) ).
fof(d5_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ( C = k3_osalg_2(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k1_osalg_2(A,B,D) ) ) ) ) ) ).
fof(t15_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),k3_osalg_2(A,B)) ) ) ).
fof(t16_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ( r2_pboole(u1_struct_0(A),k2_msualg_2(A,B),C)
=> r2_pboole(u1_struct_0(A),k3_osalg_2(A,B),C) ) ) ) ) ).
fof(t17_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> r6_pboole(u1_struct_0(A),k3_osalg_2(A,B),k2_osalg_2(A,k2_msualg_2(A,B))) ) ) ) ).
fof(t18_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> m2_osalg_2(k3_osalg_2(A,B),A,C) ) ) ) ).
fof(t19_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& v2_msualg_2(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v5_msualg_1(C,A)
& v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ( v2_relat_1(k3_osalg_2(A,B))
& m2_osalg_2(k3_osalg_2(A,B),A,C) ) ) ) ) ).
fof(t20_osalg_2,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ! [C] :
( m4_pboole(C,A,B)
<=> r2_hidden(C,k4_card_3(k1_mboolean(A,B))) ) ) ).
fof(d6_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v11_osalg_1(B,A)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( C = k4_osalg_2(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> m1_osalg_2(D,A,B) ) ) ) ) ).
fof(t21_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> r1_tarski(k5_osalg_2(A,B,C),k5_msualg_2(A,B,C)) ) ) ) ).
fof(t22_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> r2_hidden(u4_msualg_1(A,B),k5_osalg_2(A,B,C)) ) ) ) ).
fof(t23_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> r1_tarski(k5_osalg_2(A,B,C),k6_osalg_2(A,B)) ) ) ) ).
fof(d9_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,k6_osalg_2(A,B))
=> k7_osalg_2(A,B,C) = C ) ) ) ).
fof(t24_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ! [D] :
( m2_osalg_2(D,A,B)
=> ( r2_hidden(D,k5_osalg_2(A,B,C))
<=> ( v3_msualg_2(D,A,B)
& r2_pboole(u1_struct_0(A),k3_osalg_2(A,B),D)
& r2_pboole(u1_struct_0(A),C,D) ) ) ) ) ) ) ).
fof(t25_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ( r2_hidden(C,k6_osalg_2(A,B))
<=> v3_msualg_2(C,A,B) ) ) ) ) ).
fof(d10_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( E = k8_osalg_2(A,B,C,D)
<=> ! [F] :
( r2_hidden(F,E)
<=> ? [G] :
( m2_osalg_2(G,A,B)
& r2_hidden(G,k5_osalg_2(A,B,C))
& F = k1_funct_1(G,D) ) ) ) ) ) ) ) ).
fof(t26_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r3_orders_2(A,D,E)
=> r2_setfam_1(k8_osalg_2(A,B,C,D),k8_osalg_2(A,B,C,E)) ) ) ) ) ) ) ).
fof(t27_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r1_tarski(k8_osalg_2(A,B,C,D),k8_msualg_2(A,B,C,D)) ) ) ) ) ).
fof(t28_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> r2_hidden(k1_funct_1(u4_msualg_1(A,B),D),k8_osalg_2(A,B,C,D)) ) ) ) ) ).
fof(d11_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ! [D] :
( m2_osalg_2(D,A,B)
=> ( D = k9_osalg_2(A,B,C)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_funct_1(D,E) = k1_setfam_1(k8_osalg_2(A,B,C,E)) ) ) ) ) ) ) ).
fof(t29_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> r2_pboole(u1_struct_0(A),k2_pboole(u1_struct_0(A),k3_osalg_2(A,B),C),k9_osalg_2(A,B,C)) ) ) ) ).
fof(t30_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ( v2_relat_1(k2_pboole(u1_struct_0(A),k3_osalg_2(A,B),C))
=> v2_relat_1(k9_osalg_2(A,B,C)) ) ) ) ) ).
fof(t31_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m2_osalg_2(D,A,B)
=> ! [E] :
( m2_osalg_2(E,A,B)
=> ( r2_hidden(E,k5_osalg_2(A,B,D))
=> r1_tarski(k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_osalg_2(A,B,D))),C),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),E)),C)) ) ) ) ) ) ) ).
fof(t32_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m2_osalg_2(D,A,B)
=> ! [E] :
( m2_osalg_2(E,A,B)
=> ( r2_hidden(E,k5_osalg_2(A,B,D))
=> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_osalg_2(A,B,D))),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),E),C)) ) ) ) ) ) ) ).
fof(t33_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_msualg_1(A))
=> ! [D] :
( m2_osalg_2(D,A,B)
=> r1_tarski(k2_relat_1(k7_relat_1(k5_msualg_1(A,C,B),k1_funct_1(k7_pboole(u1_msualg_1(A),k3_finseq_2(u1_struct_0(A)),u2_msualg_1(A),k6_pboole(u1_struct_0(A),k9_osalg_2(A,B,D))),C))),k1_funct_1(k7_pboole(u1_msualg_1(A),u1_struct_0(A),u3_msualg_1(A),k9_osalg_2(A,B,D)),C)) ) ) ) ) ).
fof(t34_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ( v3_msualg_2(k9_osalg_2(A,B,C),A,B)
& r2_pboole(u1_struct_0(A),C,k9_osalg_2(A,B,C)) ) ) ) ) ).
fof(d12_osalg_2,axiom,
$true ).
fof(d13_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ! [D] :
( ( v4_msualg_1(D,A)
& v12_osalg_1(D,A)
& m1_msualg_2(D,A,B) )
=> ( D = k10_osalg_2(A,B,C)
<=> ( m2_osalg_2(C,A,D)
& ! [E] :
( ( v12_osalg_1(E,A)
& m1_msualg_2(E,A,B) )
=> ( m2_osalg_2(C,A,E)
=> ( v12_osalg_1(D,A)
& m1_msualg_2(D,A,E) ) ) ) ) ) ) ) ) ) ).
fof(t35_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ( k10_osalg_2(A,B,C) = k10_msualg_2(A,B,k9_osalg_2(A,B,C))
& r6_pboole(u1_struct_0(A),u4_msualg_1(A,k10_osalg_2(A,B,C)),k9_osalg_2(A,B,C)) ) ) ) ) ).
fof(t36_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& l1_msualg_1(A) )
=> ! [B] :
( l3_msualg_1(B,A)
=> ! [C] :
( m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B))
=> ( k12_msualg_2(A,B,C) = k10_msualg_2(A,B,k9_msualg_2(A,B,C))
& r6_pboole(u1_struct_0(A),u4_msualg_1(A,k12_msualg_2(A,B,C)),k9_msualg_2(A,B,C)) ) ) ) ) ).
fof(t37_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> r2_pboole(u1_struct_0(A),u4_msualg_1(A,k12_msualg_2(A,B,C)),u4_msualg_1(A,k10_osalg_2(A,B,C))) ) ) ) ).
fof(t38_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> m1_msualg_2(k12_msualg_2(A,B,C),A,k10_osalg_2(A,B,C)) ) ) ) ).
fof(t39_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v4_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
=> k10_osalg_2(A,B,C) = B ) ) ) ) ).
fof(t40_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v4_msualg_1(C,A)
& v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( m2_osalg_2(D,A,B)
=> ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,C))
=> k10_osalg_2(A,B,D) = C ) ) ) ) ) ).
fof(t41_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> k11_msualg_2(A,B,k10_osalg_2(A,B,k3_osalg_2(A,B)),C) = k10_osalg_2(A,B,k3_osalg_2(A,B)) ) ) ) ).
fof(d14_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( v12_osalg_1(D,A)
& m1_msualg_2(D,A,B) )
=> ! [E] :
( ( v4_msualg_1(E,A)
& v12_osalg_1(E,A)
& m1_msualg_2(E,A,B) )
=> ( E = k11_osalg_2(A,B,C,D)
<=> ! [F] :
( m2_osalg_2(F,A,B)
=> ( r6_pboole(u1_struct_0(A),F,k2_pboole(u1_struct_0(A),u4_msualg_1(A,C),u4_msualg_1(A,D)))
=> E = k10_osalg_2(A,B,F) ) ) ) ) ) ) ) ) ).
fof(t42_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( m2_osalg_2(D,A,B)
=> ! [E] :
( m2_osalg_2(E,A,B)
=> ( r6_pboole(u1_struct_0(A),E,k2_pboole(u1_struct_0(A),D,u4_msualg_1(A,C)))
=> k11_osalg_2(A,B,k10_osalg_2(A,B,D),C) = k10_osalg_2(A,B,E) ) ) ) ) ) ) ).
fof(t43_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( m2_osalg_2(D,A,B)
=> ( r6_pboole(u1_struct_0(A),D,u4_msualg_1(A,B))
=> k11_osalg_2(A,B,k10_osalg_2(A,B,D),C) = k10_osalg_2(A,B,D) ) ) ) ) ) ).
fof(t44_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( v12_osalg_1(D,A)
& m1_msualg_2(D,A,B) )
=> k11_osalg_2(A,B,C,D) = k11_osalg_2(A,B,D,C) ) ) ) ) ).
fof(t45_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v4_msualg_1(C,A)
& v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( v4_msualg_1(D,A)
& v12_osalg_1(D,A)
& m1_msualg_2(D,A,B) )
=> k11_msualg_2(A,B,C,k11_osalg_2(A,B,C,D)) = C ) ) ) ) ).
fof(t46_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v4_msualg_1(C,A)
& v12_osalg_1(C,A)
& m1_msualg_2(C,A,B) )
=> ! [D] :
( ( v4_msualg_1(D,A)
& v12_osalg_1(D,A)
& m1_msualg_2(D,A,B) )
=> k11_osalg_2(A,B,k11_msualg_2(A,B,C,D),D) = D ) ) ) ) ).
fof(d15_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( C = k12_osalg_2(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( v4_msualg_1(D,A)
& v12_osalg_1(D,A)
& m1_msualg_2(D,A,B) ) ) ) ) ) ).
fof(t47_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> r1_tarski(k12_osalg_2(A,B),k14_msualg_2(A,B)) ) ) ).
fof(d16_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B))
& m2_relset_1(C,k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B)) )
=> ( C = k14_osalg_2(A,B)
<=> ! [D] :
( m2_subset_1(D,k14_msualg_2(A,B),k13_osalg_2(A,B))
=> ! [E] :
( m2_subset_1(E,k14_msualg_2(A,B),k13_osalg_2(A,B))
=> ! [F] :
( ( v4_msualg_1(F,A)
& v12_osalg_1(F,A)
& m1_msualg_2(F,A,B) )
=> ! [G] :
( ( v4_msualg_1(G,A)
& v12_osalg_1(G,A)
& m1_msualg_2(G,A,B) )
=> ( ( D = F
& E = G )
=> k2_binop_1(k13_osalg_2(A,B),k13_osalg_2(A,B),k13_osalg_2(A,B),C,D,E) = k11_osalg_2(A,B,F,G) ) ) ) ) ) ) ) ) ) ).
fof(d17_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B))
& m2_relset_1(C,k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B)) )
=> ( C = k15_osalg_2(A,B)
<=> ! [D] :
( m2_subset_1(D,k14_msualg_2(A,B),k13_osalg_2(A,B))
=> ! [E] :
( m2_subset_1(E,k14_msualg_2(A,B),k13_osalg_2(A,B))
=> ! [F] :
( ( v4_msualg_1(F,A)
& v12_osalg_1(F,A)
& m1_msualg_2(F,A,B) )
=> ! [G] :
( ( v4_msualg_1(G,A)
& v12_osalg_1(G,A)
& m1_msualg_2(G,A,B) )
=> ( ( D = F
& E = G )
=> k2_binop_1(k13_osalg_2(A,B),k13_osalg_2(A,B),k13_osalg_2(A,B),C,D,E) = k11_msualg_2(A,B,F,G) ) ) ) ) ) ) ) ) ) ).
fof(t48_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_subset_1(C,k14_msualg_2(A,B),k13_osalg_2(A,B))
=> ! [D] :
( m2_subset_1(D,k14_msualg_2(A,B),k13_osalg_2(A,B))
=> k2_binop_1(k13_osalg_2(A,B),k13_osalg_2(A,B),k13_osalg_2(A,B),k15_osalg_2(A,B),C,D) = k2_binop_1(k14_msualg_2(A,B),k14_msualg_2(A,B),k14_msualg_2(A,B),k16_msualg_2(A,B),C,D) ) ) ) ) ).
fof(t49_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> v1_binop_1(k14_osalg_2(A,B),k13_osalg_2(A,B)) ) ) ).
fof(t50_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> v2_binop_1(k14_osalg_2(A,B),k13_osalg_2(A,B)) ) ) ).
fof(t51_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> v1_binop_1(k15_osalg_2(A,B),k13_osalg_2(A,B)) ) ) ).
fof(t52_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> v2_binop_1(k15_osalg_2(A,B),k13_osalg_2(A,B)) ) ) ).
fof(d18_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> k16_osalg_2(A,B) = g3_lattices(k13_osalg_2(A,B),k14_osalg_2(A,B),k15_osalg_2(A,B)) ) ) ).
fof(t53_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> v15_lattices(k16_osalg_2(A,B)) ) ) ).
fof(t54_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> k5_lattices(k16_osalg_2(A,B)) = k10_osalg_2(A,B,k3_osalg_2(A,B)) ) ) ).
fof(t55_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> ( r6_pboole(u1_struct_0(A),C,u4_msualg_1(A,B))
=> k6_lattices(k16_osalg_2(A,B)) = k10_osalg_2(A,B,C) ) ) ) ) ).
fof(t56_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v4_msualg_1(B,A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> k6_lattices(k16_osalg_2(A,B)) = B ) ) ).
fof(dt_m1_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& v11_osalg_1(B,A)
& m1_pboole(B,u1_struct_0(A)) )
=> ! [C] :
( m1_osalg_2(C,A,B)
=> m4_pboole(C,u1_struct_0(A),B) ) ) ).
fof(existence_m1_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& v11_osalg_1(B,A)
& m1_pboole(B,u1_struct_0(A)) )
=> ? [C] : m1_osalg_2(C,A,B) ) ).
fof(dt_m2_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> m4_pboole(C,u1_struct_0(A),u4_msualg_1(A,B)) ) ) ).
fof(existence_m2_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ? [C] : m2_osalg_2(C,A,B) ) ).
fof(dt_k1_osalg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k1_osalg_2(A,B,C),k1_zfmisc_1(k1_funct_1(u4_msualg_1(A,B),C))) ) ).
fof(dt_k2_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& m1_pboole(B,u1_struct_0(A)) )
=> ( v11_osalg_1(k2_osalg_2(A,B),A)
& m1_pboole(k2_osalg_2(A,B),u1_struct_0(A)) ) ) ).
fof(dt_k3_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> m2_osalg_2(k3_osalg_2(A,B),A,B) ) ).
fof(dt_k4_osalg_2,axiom,
$true ).
fof(dt_k5_osalg_2,axiom,
$true ).
fof(dt_k6_osalg_2,axiom,
$true ).
fof(dt_k7_osalg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& m1_subset_1(C,k6_osalg_2(A,B)) )
=> m2_osalg_2(k7_osalg_2(A,B,C),A,B) ) ).
fof(dt_k8_osalg_2,axiom,
$true ).
fof(dt_k9_osalg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& m2_osalg_2(C,A,B) )
=> m2_osalg_2(k9_osalg_2(A,B,C),A,B) ) ).
fof(dt_k10_osalg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& m2_osalg_2(C,A,B) )
=> ( v4_msualg_1(k10_osalg_2(A,B,C),A)
& v12_osalg_1(k10_osalg_2(A,B,C),A)
& m1_msualg_2(k10_osalg_2(A,B,C),A,B) ) ) ).
fof(dt_k11_osalg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A)
& v12_osalg_1(C,A)
& m1_msualg_2(C,A,B)
& v12_osalg_1(D,A)
& m1_msualg_2(D,A,B) )
=> ( v4_msualg_1(k11_osalg_2(A,B,C,D),A)
& v12_osalg_1(k11_osalg_2(A,B,C,D),A)
& m1_msualg_2(k11_osalg_2(A,B,C,D),A,B) ) ) ).
fof(dt_k12_osalg_2,axiom,
$true ).
fof(dt_k13_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> m1_subset_1(k13_osalg_2(A,B),k1_zfmisc_1(k14_msualg_2(A,B))) ) ).
fof(redefinition_k13_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> k13_osalg_2(A,B) = k12_osalg_2(A,B) ) ).
fof(dt_k14_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v1_funct_1(k14_osalg_2(A,B))
& v1_funct_2(k14_osalg_2(A,B),k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B))
& m2_relset_1(k14_osalg_2(A,B),k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B)) ) ) ).
fof(dt_k15_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( v1_funct_1(k15_osalg_2(A,B))
& v1_funct_2(k15_osalg_2(A,B),k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B))
& m2_relset_1(k15_osalg_2(A,B),k2_zfmisc_1(k13_osalg_2(A,B),k13_osalg_2(A,B)),k13_osalg_2(A,B)) ) ) ).
fof(dt_k16_osalg_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A)
& v5_msualg_1(B,A)
& v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ( ~ v3_struct_0(k16_osalg_2(A,B))
& v3_lattices(k16_osalg_2(A,B))
& v10_lattices(k16_osalg_2(A,B))
& l3_lattices(k16_osalg_2(A,B)) ) ) ).
fof(d3_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_osalg_2(A,B,C) = k3_tarski(a_3_0_osalg_2(A,B,C)) ) ) ) ).
fof(d4_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( m1_pboole(B,u1_struct_0(A))
=> ! [C] :
( ( v11_osalg_1(C,A)
& m1_pboole(C,u1_struct_0(A)) )
=> ( C = k2_osalg_2(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(C,D) = k3_tarski(a_3_1_osalg_2(A,B,D)) ) ) ) ) ) ).
fof(d7_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> ! [C] :
( m2_osalg_2(C,A,B)
=> k5_osalg_2(A,B,C) = a_3_2_osalg_2(A,B,C) ) ) ) ).
fof(d8_osalg_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v2_msualg_1(A)
& v4_osalg_1(A)
& v5_osalg_1(A)
& l3_osalg_1(A) )
=> ! [B] :
( ( v12_osalg_1(B,A)
& l3_msualg_1(B,A) )
=> k6_osalg_2(A,B) = a_2_0_osalg_2(A,B) ) ) ).
fof(fraenkel_a_3_0_osalg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& l3_osalg_1(B)
& v12_osalg_1(C,B)
& l3_msualg_1(C,B)
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_0_osalg_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k1_msualg_2(B,C,E)
& r3_orders_2(B,E,D) ) ) ) ).
fof(fraenkel_a_3_1_osalg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& l3_osalg_1(B)
& m1_pboole(C,u1_struct_0(B))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_1_osalg_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k1_funct_1(C,E)
& r3_orders_2(B,E,D) ) ) ) ).
fof(fraenkel_a_3_2_osalg_2,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& l3_osalg_1(B)
& v12_osalg_1(C,B)
& l3_msualg_1(C,B)
& m2_osalg_2(D,B,C) )
=> ( r2_hidden(A,a_3_2_osalg_2(B,C,D))
<=> ? [E] :
( m1_subset_1(E,k5_msualg_2(B,C,D))
& A = E
& v11_osalg_1(E,B)
& m1_pboole(E,u1_struct_0(B)) ) ) ) ).
fof(fraenkel_a_2_0_osalg_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& ~ v2_msualg_1(B)
& v4_osalg_1(B)
& v5_osalg_1(B)
& l3_osalg_1(B)
& v12_osalg_1(C,B)
& l3_msualg_1(C,B) )
=> ( r2_hidden(A,a_2_0_osalg_2(B,C))
<=> ? [D] :
( m1_subset_1(D,k6_msualg_2(B,C))
& A = D
& v11_osalg_1(D,B)
& m1_pboole(D,u1_struct_0(B)) ) ) ) ).
%------------------------------------------------------------------------------