SET007 Axioms: SET007+784.ax
%------------------------------------------------------------------------------
% File : SET007+784 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On Semilattice Structure of Mizar Types
% 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 : abcmiz_0 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 172 ( 6 unt; 0 def)
% Number of atoms : 1558 ( 116 equ)
% Maximal formula atoms : 27 ( 9 avg)
% Number of connectives : 1568 ( 182 ~; 1 |; 863 &)
% ( 35 <=>; 487 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 76 ( 74 usr; 1 prp; 0-3 aty)
% Number of functors : 60 ( 60 usr; 6 con; 0-6 aty)
% Number of variables : 491 ( 467 !; 24 ?)
% 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_abcmiz_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_realset2(A)
& v2_orders_2(A) )
=> ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc2_abcmiz_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v1_abcmiz_0(A) ) ) ) ).
fof(cc3_abcmiz_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_abcmiz_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A)
& v1_abcmiz_0(A) ) ) ) ).
fof(cc4_abcmiz_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A)
& v1_abcmiz_0(A)
& v2_abcmiz_0(A) ) ) ) ).
fof(rc1_abcmiz_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_abcmiz_0(A)
& v2_abcmiz_0(A) ) ).
fof(fc1_abcmiz_0,axiom,
! [A] :
( ( v1_abcmiz_0(A)
& l1_orders_2(A) )
=> ( v1_relat_1(u1_orders_2(A))
& v1_rewrite1(u1_orders_2(A)) ) ) ).
fof(rc2_abcmiz_0,axiom,
? [A] :
( l1_abcmiz_0(A)
& v3_abcmiz_0(A) ) ).
fof(rc3_abcmiz_0,axiom,
? [A] :
( l1_abcmiz_0(A)
& v3_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v5_abcmiz_0(A)
& v6_abcmiz_0(A) ) ).
fof(fc2_abcmiz_0,axiom,
! [A] :
( ( ~ v4_abcmiz_0(A)
& l1_abcmiz_0(A) )
=> ~ v1_xboole_0(u1_abcmiz_0(A)) ) ).
fof(rc4_abcmiz_0,axiom,
? [A] :
( l2_abcmiz_0(A)
& v7_abcmiz_0(A) ) ).
fof(fc3_abcmiz_0,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& m1_relset_1(C,A,A)
& v1_funct_1(D)
& v1_funct_2(D,B,B)
& m1_relset_1(D,B,B)
& v1_funct_1(E)
& v1_funct_2(E,A,k5_finsub_1(B))
& m1_relset_1(E,A,k5_finsub_1(B)) )
=> ( ~ v3_struct_0(g2_abcmiz_0(A,B,C,D,E))
& v7_abcmiz_0(g2_abcmiz_0(A,B,C,D,E)) ) ) ).
fof(fc4_abcmiz_0,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(B)
& m1_relset_1(C,A,A)
& v1_funct_1(D)
& v1_funct_2(D,B,B)
& m1_relset_1(D,B,B)
& v1_funct_1(E)
& v1_funct_2(E,A,k5_finsub_1(B))
& m1_relset_1(E,A,k5_finsub_1(B)) )
=> ( ~ v4_abcmiz_0(g2_abcmiz_0(A,B,C,D,E))
& v7_abcmiz_0(g2_abcmiz_0(A,B,C,D,E)) ) ) ).
fof(rc5_abcmiz_0,axiom,
? [A] :
( l2_abcmiz_0(A)
& ~ v3_struct_0(A)
& v3_realset2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_abcmiz_0(A)
& v2_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v5_abcmiz_0(A)
& v6_abcmiz_0(A)
& v7_abcmiz_0(A) ) ).
fof(rc6_abcmiz_0,axiom,
? [A] :
( l2_abcmiz_0(A)
& ~ v3_struct_0(A)
& v3_realset2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_abcmiz_0(A)
& v2_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v5_abcmiz_0(A)
& v6_abcmiz_0(A)
& v7_abcmiz_0(A)
& v8_abcmiz_0(A)
& v9_abcmiz_0(A)
& v10_abcmiz_0(A) ) ).
fof(fc5_abcmiz_0,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A)
& m1_subset_1(B,u1_abcmiz_0(A)) )
=> ( v1_waybel_0(k3_abcmiz_0(A,B),A)
& v12_waybel_0(k3_abcmiz_0(A,B),A) ) ) ).
fof(fc6_abcmiz_0,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A)
& m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A))) )
=> ( v1_waybel_0(k4_abcmiz_0(A,B),A)
& v12_waybel_0(k4_abcmiz_0(A,B),A) ) ) ).
fof(fc7_abcmiz_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_finseq_1(C,u1_abcmiz_0(A)) )
=> ( ~ v1_xboole_0(k7_abcmiz_0(A,B,C))
& v1_relat_1(k7_abcmiz_0(A,B,C))
& v1_funct_1(k7_abcmiz_0(A,B,C))
& v1_finset_1(k7_abcmiz_0(A,B,C))
& v1_finseq_1(k7_abcmiz_0(A,B,C)) ) ) ).
fof(rc7_abcmiz_0,axiom,
? [A] :
( l3_abcmiz_0(A)
& v11_abcmiz_0(A) ) ).
fof(rc8_abcmiz_0,axiom,
? [A] :
( l3_abcmiz_0(A)
& ~ v3_struct_0(A)
& v3_realset2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_abcmiz_0(A)
& v2_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v11_abcmiz_0(A) ) ).
fof(rc9_abcmiz_0,axiom,
? [A] :
( l3_abcmiz_0(A)
& ~ v3_struct_0(A)
& v3_realset2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_abcmiz_0(A)
& v2_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v5_abcmiz_0(A)
& v6_abcmiz_0(A)
& v8_abcmiz_0(A)
& v9_abcmiz_0(A)
& v10_abcmiz_0(A)
& v11_abcmiz_0(A)
& v12_abcmiz_0(A)
& v13_abcmiz_0(A)
& v14_abcmiz_0(A) ) ).
fof(d1_abcmiz_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_abcmiz_0(A)
<=> v1_rewrite1(u1_orders_2(A)) ) ) ).
fof(d2_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v1_abcmiz_0(A)
<=> ! [B] :
( ( ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& r2_hidden(C,B)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ~ ( r2_hidden(D,B)
& r2_orders_2(A,C,D) ) ) ) ) ) ) ).
fof(d3_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v2_abcmiz_0(A)
<=> ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A)
& v1_abcmiz_0(A) ) ) ) ).
fof(t1_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r1_yellow_0(A,B)
& r2_hidden(k1_yellow_0(A,B),B) ) ) ) ).
fof(d4_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ( v4_abcmiz_0(A)
<=> v1_xboole_0(u1_abcmiz_0(A)) ) ) ).
fof(t2_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ! [B] :
( l1_abcmiz_0(B)
=> ( ( u1_abcmiz_0(A) = u1_abcmiz_0(B)
& v4_abcmiz_0(A) )
=> v4_abcmiz_0(B) ) ) ) ).
fof(d5_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> k1_abcmiz_0(A,B) = k1_funct_1(u2_abcmiz_0(A),B) ) ) ).
fof(t3_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ! [B] :
( l1_abcmiz_0(B)
=> ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m1_subset_1(D,u1_abcmiz_0(B))
=> ( C = D
=> k1_abcmiz_0(A,C) = k1_abcmiz_0(B,D) ) ) ) ) ) ) ).
fof(d6_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ( v5_abcmiz_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> k1_abcmiz_0(A,k1_abcmiz_0(A,B)) = B ) ) ) ).
fof(d7_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ( v6_abcmiz_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> k1_abcmiz_0(A,B) != B ) ) ) ).
fof(t4_abcmiz_0,axiom,
! [A,B] :
( A != B
=> ! [C] :
( l1_abcmiz_0(C)
=> ( ( u1_abcmiz_0(C) = k2_tarski(A,B)
& k1_funct_1(u2_abcmiz_0(C),A) = B
& k1_funct_1(u2_abcmiz_0(C),B) = A )
=> ( ~ v4_abcmiz_0(C)
& v5_abcmiz_0(C)
& v6_abcmiz_0(C) ) ) ) ) ).
fof(t5_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ! [B] :
( l1_abcmiz_0(B)
=> ( ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
& v5_abcmiz_0(A) )
=> v5_abcmiz_0(B) ) ) ) ).
fof(t6_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ! [B] :
( l1_abcmiz_0(B)
=> ( ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
& v6_abcmiz_0(A) )
=> v6_abcmiz_0(B) ) ) ) ).
fof(d8_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_abcmiz_0(A,B) = k1_funct_1(u3_abcmiz_0(A),B) ) ) ).
fof(t7_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( l2_abcmiz_0(B)
=> ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> k2_abcmiz_0(A,C) = k2_abcmiz_0(B,D) ) ) ) ) ) ) ).
fof(d9_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ( v8_abcmiz_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ~ ( r2_hidden(C,k2_abcmiz_0(A,B))
& r2_hidden(k1_abcmiz_0(A,C),k2_abcmiz_0(A,B)) ) ) ) ) ) ).
fof(t8_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( l2_abcmiz_0(B)
=> ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
& v8_abcmiz_0(A) )
=> v8_abcmiz_0(B) ) ) ) ).
fof(d10_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_abcmiz_0(A) )
=> ( v9_abcmiz_0(A)
<=> ( v1_funct_1(u3_abcmiz_0(A))
& v1_funct_2(u3_abcmiz_0(A),u1_struct_0(A),u1_struct_0(k7_lattice3(k3_yellow_1(u1_abcmiz_0(A)))))
& v20_waybel_0(u3_abcmiz_0(A),A,k7_lattice3(k3_yellow_1(u1_abcmiz_0(A))))
& m2_relset_1(u3_abcmiz_0(A),u1_struct_0(A),u1_struct_0(k7_lattice3(k3_yellow_1(u1_abcmiz_0(A))))) ) ) ) ).
fof(t9_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_abcmiz_0(B) )
=> ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
& v9_abcmiz_0(A) )
=> v9_abcmiz_0(B) ) ) ) ).
fof(d11_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l2_abcmiz_0(A) )
=> ( v9_abcmiz_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_abcmiz_0(A,k13_lattice3(A,B,C)) = k3_finsub_1(k1_zfmisc_1(u1_abcmiz_0(A)),k2_abcmiz_0(A,B),k2_abcmiz_0(A,C)) ) ) ) ) ).
fof(t10_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l2_abcmiz_0(A) )
=> ( v9_abcmiz_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> r1_tarski(k2_abcmiz_0(A,C),k2_abcmiz_0(A,B)) ) ) ) ) ) ).
fof(d12_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = k3_abcmiz_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(A))
& D = E
& r2_hidden(B,k2_abcmiz_0(A,E)) ) ) ) ) ) ) ).
fof(d13_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ( C = k4_abcmiz_0(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,C)
<=> ! [E] :
( m1_subset_1(E,u1_abcmiz_0(A))
=> ( r2_hidden(E,B)
=> r2_hidden(D,k3_abcmiz_0(A,E)) ) ) ) ) ) ) ) ) ).
fof(t11_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( l2_abcmiz_0(B)
=> ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m1_subset_1(D,u1_abcmiz_0(B))
=> ( C = D
=> k3_abcmiz_0(A,C) = k3_abcmiz_0(B,D) ) ) ) ) ) ) ).
fof(t13_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r2_hidden(C,k2_abcmiz_0(A,B))
<=> r2_hidden(B,k3_abcmiz_0(A,C)) ) ) ) ) ).
fof(t14_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( r1_tarski(C,k2_abcmiz_0(A,B))
<=> r2_hidden(B,k4_abcmiz_0(A,C)) ) ) ) ) ).
fof(t16_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_abcmiz_0(A) )
=> k4_abcmiz_0(A,k1_subset_1(u1_abcmiz_0(A))) = u1_struct_0(A) ) ).
fof(d14_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ( v10_abcmiz_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> ~ v1_xboole_0(k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B)))) ) ) ) ).
fof(t17_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( l2_abcmiz_0(B)
=> ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
& v10_abcmiz_0(A) )
=> v10_abcmiz_0(B) ) ) ) ).
fof(t18_abcmiz_0,axiom,
! [A] :
( ( v8_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> r1_xboole_0(k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B))) ) ) ).
fof(d15_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r1_abcmiz_0(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r2_hidden(D,k3_abcmiz_0(A,C))
& r1_orders_2(A,D,B) ) ) ) ) ) ).
fof(d16_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( r2_abcmiz_0(A,B,C)
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(A))
& r1_tarski(C,k2_abcmiz_0(A,D))
& r1_orders_2(A,D,B) ) ) ) ) ) ).
fof(t19_abcmiz_0,axiom,
$true ).
fof(t20_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_abcmiz_0(A,C,B)
=> ( ~ v1_xboole_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)))
& v1_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
& v12_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
& m1_subset_1(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(d17_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> k5_abcmiz_0(A,B,C) = k1_yellow_0(A,k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,C),k6_waybel_0(A,B))) ) ) ) ).
fof(t21_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r1_abcmiz_0(A,B,C)
=> r3_orders_2(A,k5_abcmiz_0(A,B,C),B) ) ) ) ) ).
fof(t22_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r1_abcmiz_0(A,B,C)
=> r2_hidden(C,k2_abcmiz_0(A,k5_abcmiz_0(A,B,C))) ) ) ) ) ).
fof(t23_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r1_abcmiz_0(A,B,C)
=> r2_hidden(k5_abcmiz_0(A,B,C),k3_abcmiz_0(A,C)) ) ) ) ) ).
fof(t24_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r3_orders_2(A,D,B)
& r2_hidden(C,k2_abcmiz_0(A,D)) )
=> ( r1_abcmiz_0(A,B,C)
& r3_orders_2(A,D,k5_abcmiz_0(A,B,C)) ) ) ) ) ) ) ).
fof(t25_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r2_hidden(C,k2_abcmiz_0(A,B))
=> ( r1_abcmiz_0(A,B,C)
& k5_abcmiz_0(A,B,C) = B ) ) ) ) ) ).
fof(t26_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m1_subset_1(D,u1_abcmiz_0(A))
=> ( ( r1_abcmiz_0(A,B,C)
& r1_abcmiz_0(A,k5_abcmiz_0(A,B,C),D) )
=> ( r1_abcmiz_0(A,B,D)
& r1_abcmiz_0(A,k5_abcmiz_0(A,B,D),C)
& k5_abcmiz_0(A,k5_abcmiz_0(A,B,D),C) = k5_abcmiz_0(A,k5_abcmiz_0(A,B,C),D) ) ) ) ) ) ) ).
fof(t27_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r2_abcmiz_0(A,C,B)
=> ( ~ v1_xboole_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)))
& v1_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
& v12_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
& m1_subset_1(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ).
fof(d18_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> k6_abcmiz_0(A,B,C) = k1_yellow_0(A,k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,C),k6_waybel_0(A,B))) ) ) ) ).
fof(t28_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_abcmiz_0(A,B,k1_subset_1(u1_abcmiz_0(A))) = B ) ) ).
fof(d19_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_struct_0(A))
=> ( D = k7_abcmiz_0(A,B,C)
<=> ( k3_finseq_1(D) = k1_nat_1(k3_finseq_1(C),np__1)
& k1_funct_1(D,np__1) = B
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m1_subset_1(F,u1_abcmiz_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( r2_hidden(E,k4_finseq_1(C))
& F = k1_funct_1(C,E)
& G = k1_funct_1(D,E) )
=> k1_funct_1(D,k1_nat_1(E,np__1)) = k5_abcmiz_0(A,G,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t29_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) = k12_finseq_1(u1_struct_0(A),B) ) ) ).
fof(t30_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> k7_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) = k10_finseq_1(B,k5_abcmiz_0(A,B,C)) ) ) ) ).
fof(d20_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> k8_abcmiz_0(A,B,C) = k1_funct_1(k7_abcmiz_0(A,B,C),k1_nat_1(k3_finseq_1(C),np__1)) ) ) ) ).
fof(t31_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k8_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) = B ) ) ).
fof(t32_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> k8_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) = k5_abcmiz_0(A,B,C) ) ) ) ).
fof(t33_abcmiz_0,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( v4_ordinal2(C)
=> ( r1_xreal_0(np__1,C)
=> ( r1_xreal_0(k3_finseq_1(A),C)
| k1_funct_1(k1_rewrite1(A,B),C) = k1_funct_1(A,C) ) ) ) ) ) ).
fof(t34_abcmiz_0,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_relat_1(A)
& v1_funct_1(A)
& v1_finseq_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B) )
=> ! [C] :
( v4_ordinal2(C)
=> ( ~ r1_xreal_0(k3_finseq_1(B),C)
=> k1_funct_1(k1_rewrite1(A,B),k2_xcmplx_0(k3_finseq_1(A),C)) = k1_funct_1(B,k2_xcmplx_0(C,np__1)) ) ) ) ) ).
fof(t35_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) = k1_rewrite1(k7_abcmiz_0(A,B,C),k7_abcmiz_0(A,k8_abcmiz_0(A,B,C),D)) ) ) ) ) ).
fof(t36_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> ! [E] :
( v4_ordinal2(E)
=> ( r2_hidden(E,k4_finseq_1(C))
=> k1_funct_1(k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)),E) = k1_funct_1(k7_abcmiz_0(A,B,C),E) ) ) ) ) ) ) ).
fof(t37_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> k1_funct_1(k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)),k1_nat_1(k3_finseq_1(C),np__1)) = k8_abcmiz_0(A,B,C) ) ) ) ) ).
fof(t38_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> k8_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) = k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) ) ) ) ) ).
fof(d21_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,C)
<=> ! [D] :
( v4_ordinal2(D)
=> ! [E] :
( m1_subset_1(E,u1_abcmiz_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(D,k4_finseq_1(C))
& E = k1_funct_1(C,D)
& F = k1_funct_1(k7_abcmiz_0(A,B,C),D) )
=> r1_abcmiz_0(A,F,E) ) ) ) ) ) ) ) ) ).
fof(t39_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r3_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) ) ) ).
fof(t40_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r1_abcmiz_0(A,B,C)
<=> r3_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) ) ) ) ) ).
fof(t41_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
=> ( r3_abcmiz_0(A,B,C)
& r3_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) ) ) ) ) ) ) ).
fof(t42_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,C)
=> ! [D] :
( v4_ordinal2(D)
=> ! [E] :
( v4_ordinal2(E)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k1_nat_1(k3_finseq_1(C),np__1)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ! [G] :
( m1_subset_1(G,u1_struct_0(A))
=> ( ( F = k1_funct_1(k7_abcmiz_0(A,B,C),D)
& G = k1_funct_1(k7_abcmiz_0(A,B,C),E) )
=> r3_orders_2(A,G,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,C)
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(D,k2_relat_1(k7_abcmiz_0(A,B,C)))
=> ( r3_orders_2(A,k8_abcmiz_0(A,B,C),D)
& r3_orders_2(A,D,B) ) ) ) ) ) ) ) ).
fof(t44_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,C)
=> r3_orders_2(A,k8_abcmiz_0(A,B,C),B) ) ) ) ) ).
fof(t45_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,C)
=> r1_tarski(k2_relat_1(C),k2_abcmiz_0(A,k8_abcmiz_0(A,B,C))) ) ) ) ) ).
fof(t46_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,C)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( D = k2_relat_1(C)
=> r2_abcmiz_0(A,B,D) ) ) ) ) ) ) ).
fof(t47_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> ( ( r3_abcmiz_0(A,B,C)
& r1_tarski(k2_relat_1(D),k2_relat_1(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ( r2_hidden(E,k2_relat_1(k7_abcmiz_0(A,B,D)))
=> r3_orders_2(A,k8_abcmiz_0(A,B,C),E) ) ) ) ) ) ) ) ).
fof(t48_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
=> r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),D,C)) ) ) ) ) ) ).
fof(t49_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
=> k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) = k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),D,C)) ) ) ) ) ) ).
fof(t50_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( r2_abcmiz_0(A,B,C)
=> r3_orders_2(A,k6_abcmiz_0(A,B,C),B) ) ) ) ) ).
fof(t51_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( r2_abcmiz_0(A,B,C)
=> r1_tarski(C,k2_abcmiz_0(A,k6_abcmiz_0(A,B,C))) ) ) ) ) ).
fof(t52_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( r2_abcmiz_0(A,B,C)
=> r2_hidden(k6_abcmiz_0(A,B,C),k4_abcmiz_0(A,C)) ) ) ) ) ).
fof(t53_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r3_orders_2(A,D,B)
& r1_tarski(C,k2_abcmiz_0(A,D)) )
=> ( r2_abcmiz_0(A,B,C)
& r3_orders_2(A,D,k6_abcmiz_0(A,B,C)) ) ) ) ) ) ) ).
fof(t54_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( r1_tarski(C,k2_abcmiz_0(A,B))
=> ( r2_abcmiz_0(A,B,C)
& k6_abcmiz_0(A,B,C) = B ) ) ) ) ) ).
fof(t55_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( ( r2_abcmiz_0(A,B,C)
& r1_tarski(D,C) )
=> r2_abcmiz_0(A,B,D) ) ) ) ) ) ).
fof(t56_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( ( E = k2_xboole_0(D,k1_tarski(C))
& r2_abcmiz_0(A,B,E) )
=> k5_abcmiz_0(A,k6_abcmiz_0(A,B,D),C) = k6_abcmiz_0(A,B,E) ) ) ) ) ) ) ).
fof(t57_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r3_abcmiz_0(A,B,C)
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( D = k2_relat_1(C)
=> k8_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) ) ) ) ) ) ) ).
fof(d22_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_abcmiz_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_abcmiz_0(A),u1_struct_0(A)) )
=> ( B = k9_abcmiz_0(A)
<=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> k8_funct_2(u1_abcmiz_0(A),u1_struct_0(A),B,C) = k1_yellow_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,C),k3_abcmiz_0(A,k1_abcmiz_0(A,C)))) ) ) ) ) ).
fof(d23_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> k10_abcmiz_0(A,B) = k8_funct_2(u1_abcmiz_0(A),u1_struct_0(A),u4_abcmiz_0(A),B) ) ) ).
fof(d24_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ( v12_abcmiz_0(A)
<=> k7_funct_2(u1_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A),u2_abcmiz_0(A),u4_abcmiz_0(A)) = u4_abcmiz_0(A) ) ) ).
fof(d25_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ( v13_abcmiz_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> ( r2_lattice3(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B))),k10_abcmiz_0(A,B))
& ~ ( k3_abcmiz_0(A,B) != k1_xboole_0
& k3_abcmiz_0(A,k1_abcmiz_0(A,B)) != k1_xboole_0
& k10_abcmiz_0(A,B) != k1_yellow_0(A,k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B)))) ) ) ) ) ) ).
fof(d26_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ( v12_abcmiz_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> k10_abcmiz_0(A,k1_abcmiz_0(A,B)) = k10_abcmiz_0(A,B) ) ) ) ).
fof(d27_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r4_abcmiz_0(A,B,C)
<=> ( r1_orders_2(A,B,k10_abcmiz_0(A,C))
& r1_abcmiz_0(A,B,C) ) ) ) ) ) ).
fof(d28_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r5_abcmiz_0(A,B,C)
<=> ! [D] :
( v4_ordinal2(D)
=> ! [E] :
( m1_subset_1(E,u1_abcmiz_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( ( r2_hidden(D,k4_finseq_1(C))
& E = k1_funct_1(C,D)
& F = k1_funct_1(k7_abcmiz_0(A,B,C),D) )
=> r4_abcmiz_0(A,F,E) ) ) ) ) ) ) ) ) ).
fof(t58_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ( r5_abcmiz_0(A,B,C)
=> r3_abcmiz_0(A,B,C) ) ) ) ) ).
fof(t59_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r5_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) ) ) ).
fof(t60_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r4_abcmiz_0(A,B,C)
<=> r5_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) ) ) ) ) ).
fof(t61_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> ( r5_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
=> ( r5_abcmiz_0(A,B,C)
& r5_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) ) ) ) ) ) ) ).
fof(t62_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m2_finseq_1(C,u1_abcmiz_0(A))
=> ! [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
=> ( ( r5_abcmiz_0(A,B,C)
& r5_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) )
=> r5_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) ) ) ) ) ) ).
fof(d29_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( r6_abcmiz_0(A,B,C)
<=> ? [D] :
( m2_finseq_1(D,u1_abcmiz_0(A))
& k2_relat_1(D) = C
& r5_abcmiz_0(A,B,D) ) ) ) ) ) ).
fof(t63_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( r6_abcmiz_0(A,B,C)
=> v1_finset_1(C) ) ) ) ) ).
fof(t64_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r6_abcmiz_0(A,B,k1_subset_1(u1_abcmiz_0(A))) ) ) ).
fof(t65_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ~ ( r6_abcmiz_0(A,B,C)
& ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ~ ( r1_tarski(D,C)
& r6_abcmiz_0(A,B,D)
& k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D)
& ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( ( r1_tarski(E,D)
& r6_abcmiz_0(A,B,E)
& k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,E) )
=> E = D ) ) ) ) ) ) ) ) ).
fof(d30_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ( v14_abcmiz_0(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_abcmiz_0(A))
=> ~ ( r4_abcmiz_0(A,B,D)
& r3_orders_2(A,k5_abcmiz_0(A,B,D),C)
& ! [E] :
( ( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A))) )
=> ~ ( r6_abcmiz_0(A,k10_lattice3(A,B,C),E)
& k6_abcmiz_0(A,k10_lattice3(A,B,C),E) = C ) ) ) ) ) ) ) ) ).
fof(t66_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ~ ( r6_abcmiz_0(A,B,C)
& ! [D] :
( ( v2_funct_1(D)
& m2_finseq_1(D,u1_abcmiz_0(A)) )
=> ~ ( k2_relat_1(D) = C
& r5_abcmiz_0(A,B,D) ) ) ) ) ) ) ).
fof(d31_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( B = k11_abcmiz_0(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r2_hidden(k4_tarski(C,D),B)
<=> ? [E] :
( m1_subset_1(E,u1_abcmiz_0(A))
& ~ r2_hidden(E,k2_abcmiz_0(A,D))
& r4_abcmiz_0(A,D,E)
& k5_abcmiz_0(A,D,E) = C ) ) ) ) ) ) ) ).
fof(t67_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> r1_tarski(k11_abcmiz_0(A),u1_orders_2(A)) ) ).
fof(t68_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_rewrite1(k11_abcmiz_0(A),B,C)
=> r3_orders_2(A,B,C) ) ) ) ) ).
fof(t69_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> v2_relat_2(k11_abcmiz_0(A)) ) ).
fof(t70_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> v3_rewrite1(k11_abcmiz_0(A)) ) ).
fof(t71_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
=> ( ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( ( r1_tarski(D,C)
& r6_abcmiz_0(A,B,D)
& k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) )
=> D = C ) )
=> ! [D] :
( ( v2_funct_1(D)
& m2_finseq_1(D,u1_abcmiz_0(A)) )
=> ( ( k2_relat_1(D) = C
& r5_abcmiz_0(A,B,D) )
=> ! [E] :
( v4_ordinal2(E)
=> ( ( r1_xreal_0(np__1,E)
& r1_xreal_0(E,k3_finseq_1(D)) )
=> r2_hidden(k4_tarski(k1_funct_1(k7_abcmiz_0(A,B,D),k2_xcmplx_0(E,np__1)),k1_funct_1(k7_abcmiz_0(A,B,D),E)),k11_abcmiz_0(A)) ) ) ) ) ) ) ) ) ).
fof(t72_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
=> ( ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
=> ( ( r1_tarski(D,C)
& r6_abcmiz_0(A,B,D)
& k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) )
=> D = C ) )
=> ! [D] :
( ( v2_funct_1(D)
& m2_finseq_1(D,u1_abcmiz_0(A)) )
=> ( ( k2_relat_1(D) = C
& r5_abcmiz_0(A,B,D) )
=> m1_rewrite1(k4_finseq_5(u1_struct_0(A),k7_abcmiz_0(A,B,D)),k11_abcmiz_0(A)) ) ) ) ) ) ) ).
fof(t73_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_finset_1(C)
& m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
=> ( r6_abcmiz_0(A,B,C)
=> r1_rewrite1(k11_abcmiz_0(A),k6_abcmiz_0(A,B,C),B) ) ) ) ) ).
fof(t74_abcmiz_0,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,A,A)
=> ! [C] :
( m1_rewrite1(C,B)
=> ( r2_hidden(k1_funct_1(C,np__1),A)
=> m2_finseq_1(C,A) ) ) ) ) ).
fof(t75_abcmiz_0,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,A,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( r1_rewrite1(B,C,D)
=> r2_hidden(D,A) ) ) ) ) ).
fof(t76_abcmiz_0,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( m2_relset_1(B,A,A)
=> ( ( v4_rewrite1(B)
& v2_rewrite1(B) )
=> ! [C] :
( m1_subset_1(C,A)
=> r2_hidden(k2_rewrite1(B,C),A) ) ) ) ) ).
fof(t77_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ~ ( r1_rewrite1(k11_abcmiz_0(A),B,C)
& ! [D] :
( ( v1_finset_1(D)
& m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A))) )
=> ~ ( r6_abcmiz_0(A,C,D)
& B = k6_abcmiz_0(A,C,D) ) ) ) ) ) ) ).
fof(t78_abcmiz_0,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ( v8_rewrite1(k11_abcmiz_0(A))
& v4_rewrite1(k11_abcmiz_0(A)) ) ) ).
fof(d32_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k12_abcmiz_0(A,B) = k2_rewrite1(k11_abcmiz_0(A),B) ) ) ).
fof(t79_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r1_rewrite1(k11_abcmiz_0(A),B,k12_abcmiz_0(A,B)) ) ) ).
fof(t80_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r3_orders_2(A,B,k12_abcmiz_0(A,B)) ) ) ).
fof(t82_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_abcmiz_0(A))
=> ( ( r4_abcmiz_0(A,B,D)
& r3_orders_2(A,k5_abcmiz_0(A,B,D),k12_abcmiz_0(A,C)) )
=> r3_orders_2(A,B,k12_abcmiz_0(A,C)) ) ) ) ) ) ).
fof(t83_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> r3_orders_2(A,k12_abcmiz_0(A,B),k12_abcmiz_0(A,C)) ) ) ) ) ).
fof(t84_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_abcmiz_0(A))
=> ( r4_abcmiz_0(A,B,C)
=> k12_abcmiz_0(A,k5_abcmiz_0(A,B,C)) = k12_abcmiz_0(A,B) ) ) ) ) ).
fof(s1_abcmiz_0,axiom,
( ? [A] :
( v1_finset_1(A)
& p1_s1_abcmiz_0(A) )
=> ? [A] :
( v1_finset_1(A)
& p1_s1_abcmiz_0(A)
& ! [B] :
( ( r1_tarski(B,A)
& p1_s1_abcmiz_0(B) )
=> B = A ) ) ) ).
fof(s2_abcmiz_0,axiom,
( ( ! [A] :
( m1_subset_1(A,f1_s2_abcmiz_0)
=> ! [B] :
( m1_subset_1(B,f1_s2_abcmiz_0)
=> ( r2_hidden(k4_tarski(A,B),f2_s2_abcmiz_0)
=> p1_s2_abcmiz_0(A,B) ) ) )
& ! [A] :
( m1_subset_1(A,f1_s2_abcmiz_0)
=> p1_s2_abcmiz_0(A,A) )
& ! [A] :
( m1_subset_1(A,f1_s2_abcmiz_0)
=> ! [B] :
( m1_subset_1(B,f1_s2_abcmiz_0)
=> ! [C] :
( m1_subset_1(C,f1_s2_abcmiz_0)
=> ( ( p1_s2_abcmiz_0(A,B)
& p1_s2_abcmiz_0(B,C) )
=> p1_s2_abcmiz_0(A,C) ) ) ) ) )
=> ! [A] :
( m1_subset_1(A,f1_s2_abcmiz_0)
=> ! [B] :
( m1_subset_1(B,f1_s2_abcmiz_0)
=> ( r1_rewrite1(f2_s2_abcmiz_0,A,B)
=> p1_s2_abcmiz_0(A,B) ) ) ) ) ).
fof(dt_l1_abcmiz_0,axiom,
$true ).
fof(existence_l1_abcmiz_0,axiom,
? [A] : l1_abcmiz_0(A) ).
fof(dt_l2_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ( l1_orders_2(A)
& l1_abcmiz_0(A) ) ) ).
fof(existence_l2_abcmiz_0,axiom,
? [A] : l2_abcmiz_0(A) ).
fof(dt_l3_abcmiz_0,axiom,
! [A] :
( l3_abcmiz_0(A)
=> l2_abcmiz_0(A) ) ).
fof(existence_l3_abcmiz_0,axiom,
? [A] : l3_abcmiz_0(A) ).
fof(abstractness_v3_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ( v3_abcmiz_0(A)
=> A = g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) ) ) ).
fof(abstractness_v7_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ( v7_abcmiz_0(A)
=> A = g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) ) ) ).
fof(abstractness_v11_abcmiz_0,axiom,
! [A] :
( l3_abcmiz_0(A)
=> ( v11_abcmiz_0(A)
=> A = g3_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A),u4_abcmiz_0(A)) ) ) ).
fof(dt_k1_abcmiz_0,axiom,
! [A,B] :
( ( l1_abcmiz_0(A)
& m1_subset_1(B,u1_abcmiz_0(A)) )
=> m1_subset_1(k1_abcmiz_0(A,B),u1_abcmiz_0(A)) ) ).
fof(dt_k2_abcmiz_0,axiom,
! [A,B] :
( ( l2_abcmiz_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k2_abcmiz_0(A,B),k1_zfmisc_1(u1_abcmiz_0(A))) ) ).
fof(dt_k3_abcmiz_0,axiom,
! [A,B] :
( ( l2_abcmiz_0(A)
& m1_subset_1(B,u1_abcmiz_0(A)) )
=> m1_subset_1(k3_abcmiz_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k4_abcmiz_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_abcmiz_0(A)
& m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A))) )
=> m1_subset_1(k4_abcmiz_0(A,B),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k5_abcmiz_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l2_abcmiz_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_abcmiz_0(A)) )
=> m1_subset_1(k5_abcmiz_0(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k6_abcmiz_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l2_abcmiz_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
=> m1_subset_1(k6_abcmiz_0(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k7_abcmiz_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_finseq_1(C,u1_abcmiz_0(A)) )
=> m2_finseq_1(k7_abcmiz_0(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k8_abcmiz_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_finseq_1(C,u1_abcmiz_0(A)) )
=> m1_subset_1(k8_abcmiz_0(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k9_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ( v1_funct_1(k9_abcmiz_0(A))
& v1_funct_2(k9_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A))
& m2_relset_1(k9_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k10_abcmiz_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A)
& m1_subset_1(B,u1_abcmiz_0(A)) )
=> m1_subset_1(k10_abcmiz_0(A,B),u1_struct_0(A)) ) ).
fof(dt_k11_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& ~ v4_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> m2_relset_1(k11_abcmiz_0(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_k12_abcmiz_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k12_abcmiz_0(A,B),u1_struct_0(A)) ) ).
fof(dt_u1_abcmiz_0,axiom,
$true ).
fof(dt_u2_abcmiz_0,axiom,
! [A] :
( l1_abcmiz_0(A)
=> ( v1_funct_1(u2_abcmiz_0(A))
& v1_funct_2(u2_abcmiz_0(A),u1_abcmiz_0(A),u1_abcmiz_0(A))
& m2_relset_1(u2_abcmiz_0(A),u1_abcmiz_0(A),u1_abcmiz_0(A)) ) ) ).
fof(dt_u3_abcmiz_0,axiom,
! [A] :
( l2_abcmiz_0(A)
=> ( v1_funct_1(u3_abcmiz_0(A))
& v1_funct_2(u3_abcmiz_0(A),u1_struct_0(A),k5_finsub_1(u1_abcmiz_0(A)))
& m2_relset_1(u3_abcmiz_0(A),u1_struct_0(A),k5_finsub_1(u1_abcmiz_0(A))) ) ) ).
fof(dt_u4_abcmiz_0,axiom,
! [A] :
( l3_abcmiz_0(A)
=> ( v1_funct_1(u4_abcmiz_0(A))
& v1_funct_2(u4_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A))
& m2_relset_1(u4_abcmiz_0(A),u1_abcmiz_0(A),u1_struct_0(A)) ) ) ).
fof(dt_g1_abcmiz_0,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A) )
=> ( v3_abcmiz_0(g1_abcmiz_0(A,B))
& l1_abcmiz_0(g1_abcmiz_0(A,B)) ) ) ).
fof(free_g1_abcmiz_0,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A) )
=> ! [C,D] :
( g1_abcmiz_0(A,B) = g1_abcmiz_0(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(dt_g2_abcmiz_0,axiom,
! [A,B,C,D,E] :
( ( m1_relset_1(C,A,A)
& v1_funct_1(D)
& v1_funct_2(D,B,B)
& m1_relset_1(D,B,B)
& v1_funct_1(E)
& v1_funct_2(E,A,k5_finsub_1(B))
& m1_relset_1(E,A,k5_finsub_1(B)) )
=> ( v7_abcmiz_0(g2_abcmiz_0(A,B,C,D,E))
& l2_abcmiz_0(g2_abcmiz_0(A,B,C,D,E)) ) ) ).
fof(free_g2_abcmiz_0,axiom,
! [A,B,C,D,E] :
( ( m1_relset_1(C,A,A)
& v1_funct_1(D)
& v1_funct_2(D,B,B)
& m1_relset_1(D,B,B)
& v1_funct_1(E)
& v1_funct_2(E,A,k5_finsub_1(B))
& m1_relset_1(E,A,k5_finsub_1(B)) )
=> ! [F,G,H,I,J] :
( g2_abcmiz_0(A,B,C,D,E) = g2_abcmiz_0(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
fof(dt_g3_abcmiz_0,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(C,A,A)
& v1_funct_1(D)
& v1_funct_2(D,B,B)
& m1_relset_1(D,B,B)
& v1_funct_1(E)
& v1_funct_2(E,A,k5_finsub_1(B))
& m1_relset_1(E,A,k5_finsub_1(B))
& v1_funct_1(F)
& v1_funct_2(F,B,A)
& m1_relset_1(F,B,A) )
=> ( v11_abcmiz_0(g3_abcmiz_0(A,B,C,D,E,F))
& l3_abcmiz_0(g3_abcmiz_0(A,B,C,D,E,F)) ) ) ).
fof(free_g3_abcmiz_0,axiom,
! [A,B,C,D,E,F] :
( ( m1_relset_1(C,A,A)
& v1_funct_1(D)
& v1_funct_2(D,B,B)
& m1_relset_1(D,B,B)
& v1_funct_1(E)
& v1_funct_2(E,A,k5_finsub_1(B))
& m1_relset_1(E,A,k5_finsub_1(B))
& v1_funct_1(F)
& v1_funct_2(F,B,A)
& m1_relset_1(F,B,A) )
=> ! [G,H,I,J,K,L] :
( g3_abcmiz_0(A,B,C,D,E,F) = g3_abcmiz_0(G,H,I,J,K,L)
=> ( A = G
& B = H
& C = I
& D = J
& E = K
& F = L ) ) ) ).
fof(t12_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_abcmiz_0(A))
=> k3_abcmiz_0(A,B) = a_2_0_abcmiz_0(A,B) ) ) ).
fof(t15_abcmiz_0,axiom,
! [A] :
( ( ~ v4_abcmiz_0(A)
& l2_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k2_abcmiz_0(A,B) = a_2_1_abcmiz_0(A,B) ) ) ).
fof(t81_abcmiz_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_abcmiz_0(A)
& ~ v4_abcmiz_0(A)
& v9_abcmiz_0(A)
& v14_abcmiz_0(A)
& l3_abcmiz_0(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( C = a_2_2_abcmiz_0(A,B)
=> ( r1_yellow_0(A,C)
& k12_abcmiz_0(A,B) = k1_yellow_0(A,C) ) ) ) ) ).
fof(fraenkel_a_2_0_abcmiz_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l2_abcmiz_0(B)
& m1_subset_1(C,u1_abcmiz_0(B)) )
=> ( r2_hidden(A,a_2_0_abcmiz_0(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& r2_hidden(C,k2_abcmiz_0(B,D)) ) ) ) ).
fof(fraenkel_a_2_1_abcmiz_0,axiom,
! [A,B,C] :
( ( ~ v4_abcmiz_0(B)
& l2_abcmiz_0(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_1_abcmiz_0(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_abcmiz_0(B))
& A = D
& r2_hidden(C,k3_abcmiz_0(B,D)) ) ) ) ).
fof(fraenkel_a_2_2_abcmiz_0,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v1_abcmiz_0(B)
& ~ v4_abcmiz_0(B)
& v9_abcmiz_0(B)
& v14_abcmiz_0(B)
& l3_abcmiz_0(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( r2_hidden(A,a_2_2_abcmiz_0(B,C))
<=> ? [D] :
( m1_subset_1(D,u1_struct_0(B))
& A = D
& ? [E] :
( v1_finset_1(E)
& m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(B)))
& r6_abcmiz_0(B,D,E)
& k6_abcmiz_0(B,D,E) = C ) ) ) ) ).
%------------------------------------------------------------------------------