SET007 Axioms: SET007+324.ax
%------------------------------------------------------------------------------
% File : SET007+324 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Category of Left Modules
% 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 : modcat_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 67 ( 3 unt; 0 def)
% Number of atoms : 1111 ( 52 equ)
% Maximal formula atoms : 36 ( 16 avg)
% Number of connectives : 1158 ( 114 ~; 0 |; 853 &)
% ( 23 <=>; 168 =>; 0 <=; 0 <~>)
% Maximal formula depth : 30 ( 15 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 38 ( 36 usr; 1 prp; 0-5 aty)
% Number of functors : 41 ( 41 usr; 1 con; 0-6 aty)
% Number of variables : 226 ( 207 !; 19 ?)
% 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_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> ? [C] :
( m1_subset_1(C,B)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v11_vectsp_1(C,A)
& v12_vectsp_1(C,A) ) ) ).
fof(rc2_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m3_modcat_1(B,A) )
=> ? [C] :
( m1_subset_1(C,B)
& v2_mod_2(C,A)
& v3_mod_2(C,A) ) ) ).
fof(fc1_modcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ~ v1_xboole_0(k2_modcat_1(A,B)) ) ).
fof(fc2_modcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ( v1_cat_1(k12_modcat_1(A,B))
& v2_cat_1(k12_modcat_1(A,B)) ) ) ).
fof(d1_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ( m1_modcat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,B)
=> ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v11_vectsp_1(C,A)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) ) ) ) ) ) ).
fof(d2_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ( m3_modcat_1(B,A)
<=> ! [C] :
( m1_subset_1(C,B)
=> ( v2_mod_2(C,A)
& v3_mod_2(C,A)
& l1_mod_2(C,A) ) ) ) ) ) ).
fof(t1_modcat_1,axiom,
$true ).
fof(t2_modcat_1,axiom,
$true ).
fof(t3_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( v2_mod_2(B,A)
& v3_mod_2(B,A)
& l1_mod_2(B,A) )
=> m3_modcat_1(k1_tarski(B),A) ) ) ).
fof(d3_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m3_modcat_1(D,A)
=> ( m5_modcat_1(D,A,B,C)
<=> ! [E] :
( m4_modcat_1(E,A,D)
=> ( v2_mod_2(E,A)
& m1_mod_2(E,A,B,C) ) ) ) ) ) ) ) ).
fof(t4_modcat_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,B)
& l4_vectsp_1(C,B) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,B)
& l4_vectsp_1(D,B) )
=> ( m5_modcat_1(A,B,C,D)
<=> ! [E] :
( m1_subset_1(E,A)
=> ( v2_mod_2(E,B)
& m1_mod_2(E,B,C,D) ) ) ) ) ) ) ) ).
fof(t5_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v2_mod_2(D,A)
& m1_mod_2(D,A,B,C) )
=> m5_modcat_1(k1_tarski(D),A,B,C) ) ) ) ) ).
fof(d4_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m5_modcat_1(D,A,B,C)
=> ( D = k1_modcat_1(A,B,C)
<=> ! [E] :
( r2_hidden(E,D)
<=> ( v2_mod_2(E,A)
& m1_mod_2(E,A,B,C) ) ) ) ) ) ) ) ).
fof(d5_modcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& l3_vectsp_1(C) )
=> ( r1_modcat_1(A,B,C)
<=> ? [D,E] :
( A = k4_tarski(D,E)
& ? [F] :
( ~ v3_struct_0(F)
& v3_rlvect_1(F)
& v4_rlvect_1(F)
& v5_rlvect_1(F)
& v6_rlvect_1(F)
& v11_vectsp_1(F,C)
& v12_vectsp_1(F,C)
& l4_vectsp_1(F,C)
& B = F
& D = g1_rlvect_1(u1_struct_0(F),u1_rlvect_1(F),u2_struct_0(F))
& E = u2_vectsp_1(C,F) ) ) ) ) ).
fof(t6_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B,C,D] :
( ( r1_modcat_1(B,C,A)
& r1_modcat_1(B,D,A) )
=> C = D ) ) ).
fof(t8_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> r2_hidden(k1_mod_2(B),k2_modcat_1(A,B)) ) ) ).
fof(t9_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_subset_1(C,k2_modcat_1(A,B))
=> ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v11_vectsp_1(C,B)
& v12_vectsp_1(C,B)
& l4_vectsp_1(C,B) ) ) ) ) ).
fof(d7_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( m3_modcat_1(C,A)
=> ( C = k4_modcat_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( v11_vectsp_1(E,A)
& m2_modcat_1(E,A,B)
& ? [F] :
( v11_vectsp_1(F,A)
& m2_modcat_1(F,A,B)
& v2_mod_2(D,A)
& m1_mod_2(D,A,E,F) ) ) ) ) ) ) ) ).
fof(d8_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( m4_modcat_1(C,A,k4_modcat_1(A,B))
=> k5_modcat_1(A,B,C) = k2_mod_2(A,C) ) ) ) ).
fof(d9_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( m4_modcat_1(C,A,k4_modcat_1(A,B))
=> k6_modcat_1(A,B,C) = k3_mod_2(A,C) ) ) ) ).
fof(d10_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( m2_modcat_1(C,A,B)
=> k7_modcat_1(A,B,C) = k6_mod_2(A,C) ) ) ) ).
fof(d11_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_modcat_1(A,B),B)
& m2_relset_1(C,k4_modcat_1(A,B),B) )
=> ( C = k8_modcat_1(A,B)
<=> ! [D] :
( m4_modcat_1(D,A,k4_modcat_1(A,B))
=> k8_funct_2(k4_modcat_1(A,B),B,C,D) = k5_modcat_1(A,B,D) ) ) ) ) ) ).
fof(d12_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k4_modcat_1(A,B),B)
& m2_relset_1(C,k4_modcat_1(A,B),B) )
=> ( C = k9_modcat_1(A,B)
<=> ! [D] :
( m4_modcat_1(D,A,k4_modcat_1(A,B))
=> k8_funct_2(k4_modcat_1(A,B),B,C,D) = k6_modcat_1(A,B,D) ) ) ) ) ) ).
fof(d13_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,B,k4_modcat_1(A,B))
& m2_relset_1(C,B,k4_modcat_1(A,B)) )
=> ( C = k10_modcat_1(A,B)
<=> ! [D] :
( m2_modcat_1(D,A,B)
=> k8_funct_2(B,k4_modcat_1(A,B),C,D) = k7_modcat_1(A,B,D) ) ) ) ) ) ).
fof(t10_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( m4_modcat_1(C,A,k4_modcat_1(A,B))
=> ! [D] :
( m4_modcat_1(D,A,k4_modcat_1(A,B))
=> ~ ( k5_modcat_1(A,B,C) = k6_modcat_1(A,B,D)
& ! [E] :
( ( v11_vectsp_1(E,A)
& m2_modcat_1(E,A,B) )
=> ! [F] :
( ( v11_vectsp_1(F,A)
& m2_modcat_1(F,A,B) )
=> ! [G] :
( ( v11_vectsp_1(G,A)
& m2_modcat_1(G,A,B) )
=> ~ ( m1_mod_2(C,A,F,G)
& m1_mod_2(D,A,E,F) ) ) ) ) ) ) ) ) ) ).
fof(t11_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( m4_modcat_1(C,A,k4_modcat_1(A,B))
=> ! [D] :
( m4_modcat_1(D,A,k4_modcat_1(A,B))
=> ( k5_modcat_1(A,B,C) = k6_modcat_1(A,B,D)
=> r2_hidden(k8_mod_2(A,C,D),k4_modcat_1(A,B)) ) ) ) ) ) ).
fof(t12_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( m4_modcat_1(C,A,k4_modcat_1(A,B))
=> ! [D] :
( m4_modcat_1(D,A,k4_modcat_1(A,B))
=> ( k2_mod_2(A,C) = k3_mod_2(A,D)
=> r2_hidden(k8_mod_2(A,C,D),k4_modcat_1(A,B)) ) ) ) ) ) ).
fof(d14_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k2_zfmisc_1(k4_modcat_1(A,B),k4_modcat_1(A,B)),k4_modcat_1(A,B)) )
=> ( C = k11_modcat_1(A,B)
<=> ( ! [D] :
( m4_modcat_1(D,A,k4_modcat_1(A,B))
=> ! [E] :
( m4_modcat_1(E,A,k4_modcat_1(A,B))
=> ( r2_hidden(k4_tarski(D,E),k1_relat_1(C))
<=> k5_modcat_1(A,B,D) = k6_modcat_1(A,B,E) ) ) )
& ! [D] :
( m4_modcat_1(D,A,k4_modcat_1(A,B))
=> ! [E] :
( m4_modcat_1(E,A,k4_modcat_1(A,B))
=> ( r2_hidden(k4_tarski(D,E),k1_relat_1(C))
=> k1_funct_1(C,k4_tarski(D,E)) = k8_mod_2(A,D,E) ) ) ) ) ) ) ) ) ).
fof(t13_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ! [C] :
( m4_modcat_1(C,A,k4_modcat_1(A,B))
=> ! [D] :
( m4_modcat_1(D,A,k4_modcat_1(A,B))
=> ( r2_hidden(k4_tarski(C,D),k1_relat_1(k11_modcat_1(A,B)))
<=> k2_mod_2(A,C) = k3_mod_2(A,D) ) ) ) ) ) ).
fof(d15_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> k12_modcat_1(A,B) = g1_cat_1(k3_modcat_1(A,B),k4_modcat_1(B,k3_modcat_1(A,B)),k8_modcat_1(B,k3_modcat_1(A,B)),k9_modcat_1(B,k3_modcat_1(A,B)),k11_modcat_1(B,k3_modcat_1(A,B)),k10_modcat_1(B,k3_modcat_1(A,B))) ) ) ).
fof(t14_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k12_modcat_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k12_modcat_1(A,B)))
=> ( r2_hidden(k4_tarski(D,C),k1_relat_1(u5_cat_1(k12_modcat_1(A,B))))
<=> k2_cat_1(k12_modcat_1(A,B),D) = k3_cat_1(k12_modcat_1(A,B),C) ) ) ) ) ) ).
fof(t15_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k12_modcat_1(A,B)))
=> ! [D] :
( m4_modcat_1(D,B,k4_modcat_1(B,k3_modcat_1(A,B)))
=> ! [E] :
( m1_subset_1(E,u1_cat_1(k12_modcat_1(A,B)))
=> ! [F] :
( m2_modcat_1(F,B,k3_modcat_1(A,B))
=> ( v2_mod_2(C,B)
& m4_modcat_1(C,B,k4_modcat_1(B,k3_modcat_1(A,B)))
& m1_subset_1(D,u2_cat_1(k12_modcat_1(A,B)))
& v11_vectsp_1(E,B)
& m2_modcat_1(E,B,k3_modcat_1(A,B))
& m1_subset_1(F,u1_cat_1(k12_modcat_1(A,B))) ) ) ) ) ) ) ) ).
fof(t16_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_subset_1(C,u1_cat_1(k12_modcat_1(A,B)))
=> ! [D] :
( m2_modcat_1(D,B,k3_modcat_1(A,B))
=> ( C = D
=> k5_cat_1(k12_modcat_1(A,B),C) = k7_modcat_1(B,k3_modcat_1(A,B),D) ) ) ) ) ) ).
fof(t17_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k12_modcat_1(A,B)))
=> ! [D] :
( m4_modcat_1(D,B,k4_modcat_1(B,k3_modcat_1(A,B)))
=> ( C = D
=> ( k2_cat_1(k12_modcat_1(A,B),C) = k2_mod_2(B,D)
& k3_cat_1(k12_modcat_1(A,B),C) = k3_mod_2(B,D) ) ) ) ) ) ) ).
fof(t18_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( m1_subset_1(C,u2_cat_1(k12_modcat_1(A,B)))
=> ! [D] :
( m1_subset_1(D,u2_cat_1(k12_modcat_1(A,B)))
=> ! [E] :
( m4_modcat_1(E,B,k4_modcat_1(B,k3_modcat_1(A,B)))
=> ! [F] :
( m4_modcat_1(F,B,k4_modcat_1(B,k3_modcat_1(A,B)))
=> ( ( C = E
& D = F )
=> ( ( k2_cat_1(k12_modcat_1(A,B),D) = k3_cat_1(k12_modcat_1(A,B),C)
=> k2_mod_2(B,F) = k3_mod_2(B,E) )
& ( k2_mod_2(B,F) = k3_mod_2(B,E)
=> k2_cat_1(k12_modcat_1(A,B),D) = k3_cat_1(k12_modcat_1(A,B),C) )
& ( k2_cat_1(k12_modcat_1(A,B),D) = k3_cat_1(k12_modcat_1(A,B),C)
=> r2_hidden(k4_tarski(F,E),k1_relat_1(k11_modcat_1(B,k3_modcat_1(A,B)))) )
& ( r2_hidden(k4_tarski(F,E),k1_relat_1(k11_modcat_1(B,k3_modcat_1(A,B))))
=> k2_cat_1(k12_modcat_1(A,B),D) = k3_cat_1(k12_modcat_1(A,B),C) )
& ( k2_cat_1(k12_modcat_1(A,B),D) = k3_cat_1(k12_modcat_1(A,B),C)
=> k4_cat_1(k12_modcat_1(A,B),C,D) = k8_mod_2(B,F,E) )
& ( k2_cat_1(k12_modcat_1(A,B),C) = k2_cat_1(k12_modcat_1(A,B),D)
=> k2_mod_2(B,E) = k2_mod_2(B,F) )
& ( k2_mod_2(B,E) = k2_mod_2(B,F)
=> k2_cat_1(k12_modcat_1(A,B),C) = k2_cat_1(k12_modcat_1(A,B),D) )
& ( k3_cat_1(k12_modcat_1(A,B),C) = k3_cat_1(k12_modcat_1(A,B),D)
=> k3_mod_2(B,E) = k3_mod_2(B,F) )
& ( k3_mod_2(B,E) = k3_mod_2(B,F)
=> k3_cat_1(k12_modcat_1(A,B),C) = k3_cat_1(k12_modcat_1(A,B),D) ) ) ) ) ) ) ) ) ) ).
fof(dt_m1_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m1_modcat_1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(existence_m1_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ? [B] : m1_modcat_1(B,A) ) ).
fof(dt_m2_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> ! [C] :
( m2_modcat_1(C,A,B)
=> ( ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) ) ) ) ).
fof(existence_m2_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> ? [C] : m2_modcat_1(C,A,B) ) ).
fof(redefinition_m2_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> ! [C] :
( m2_modcat_1(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m3_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( m3_modcat_1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(existence_m3_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ? [B] : m3_modcat_1(B,A) ) ).
fof(dt_m4_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m3_modcat_1(B,A) )
=> ! [C] :
( m4_modcat_1(C,A,B)
=> ( v3_mod_2(C,A)
& l1_mod_2(C,A) ) ) ) ).
fof(existence_m4_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m3_modcat_1(B,A) )
=> ? [C] : m4_modcat_1(C,A,B) ) ).
fof(redefinition_m4_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m3_modcat_1(B,A) )
=> ! [C] :
( m4_modcat_1(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m5_modcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ! [D] :
( m5_modcat_1(D,A,B,C)
=> m3_modcat_1(D,A) ) ) ).
fof(existence_m5_modcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> ? [D] : m5_modcat_1(D,A,B,C) ) ).
fof(dt_m6_modcat_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& m5_modcat_1(D,A,B,C) )
=> ! [E] :
( m6_modcat_1(E,A,B,C,D)
=> m1_mod_2(E,A,B,C) ) ) ).
fof(existence_m6_modcat_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& m5_modcat_1(D,A,B,C) )
=> ? [E] : m6_modcat_1(E,A,B,C,D) ) ).
fof(redefinition_m6_modcat_1,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A)
& m5_modcat_1(D,A,B,C) )
=> ! [E] :
( m6_modcat_1(E,A,B,C,D)
<=> m1_subset_1(E,D) ) ) ).
fof(dt_k1_modcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v12_vectsp_1(B,A)
& l4_vectsp_1(B,A)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v12_vectsp_1(C,A)
& l4_vectsp_1(C,A) )
=> m5_modcat_1(k1_modcat_1(A,B,C),A,B,C) ) ).
fof(dt_k2_modcat_1,axiom,
$true ).
fof(dt_k3_modcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> m1_modcat_1(k3_modcat_1(A,B),B) ) ).
fof(redefinition_k3_modcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> k3_modcat_1(A,B) = k2_modcat_1(A,B) ) ).
fof(dt_k4_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> m3_modcat_1(k4_modcat_1(A,B),A) ) ).
fof(dt_k5_modcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A)
& m1_subset_1(C,k4_modcat_1(A,B)) )
=> m2_modcat_1(k5_modcat_1(A,B,C),A,B) ) ).
fof(dt_k6_modcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A)
& m1_subset_1(C,k4_modcat_1(A,B)) )
=> m2_modcat_1(k6_modcat_1(A,B,C),A,B) ) ).
fof(dt_k7_modcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A)
& m1_subset_1(C,B) )
=> ( v2_mod_2(k7_modcat_1(A,B,C),A)
& m4_modcat_1(k7_modcat_1(A,B,C),A,k4_modcat_1(A,B)) ) ) ).
fof(dt_k8_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> ( v1_funct_1(k8_modcat_1(A,B))
& v1_funct_2(k8_modcat_1(A,B),k4_modcat_1(A,B),B)
& m2_relset_1(k8_modcat_1(A,B),k4_modcat_1(A,B),B) ) ) ).
fof(dt_k9_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> ( v1_funct_1(k9_modcat_1(A,B))
& v1_funct_2(k9_modcat_1(A,B),k4_modcat_1(A,B),B)
& m2_relset_1(k9_modcat_1(A,B),k4_modcat_1(A,B),B) ) ) ).
fof(dt_k10_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> ( v1_funct_1(k10_modcat_1(A,B))
& v1_funct_2(k10_modcat_1(A,B),B,k4_modcat_1(A,B))
& m2_relset_1(k10_modcat_1(A,B),B,k4_modcat_1(A,B)) ) ) ).
fof(dt_k11_modcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A)
& m1_modcat_1(B,A) )
=> ( v1_funct_1(k11_modcat_1(A,B))
& m2_relset_1(k11_modcat_1(A,B),k2_zfmisc_1(k4_modcat_1(A,B),k4_modcat_1(A,B)),k4_modcat_1(A,B)) ) ) ).
fof(dt_k12_modcat_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A)
& ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ( v1_cat_1(k12_modcat_1(A,B))
& l1_cat_1(k12_modcat_1(A,B)) ) ) ).
fof(t7_modcat_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_rlvect_1(A)
& v4_rlvect_1(A)
& v5_rlvect_1(A)
& v6_rlvect_1(A)
& v4_group_1(A)
& v6_vectsp_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_classes2(B) )
=> ? [C] :
( r2_hidden(C,a_2_0_modcat_1(A,B))
& r1_modcat_1(C,k1_mod_2(A),A) ) ) ) ).
fof(d6_modcat_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B) )
=> ! [C] :
( C = k2_modcat_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E] :
( r2_hidden(E,a_2_1_modcat_1(A,B))
& r1_modcat_1(E,D,B) ) ) ) ) ) ).
fof(fraenkel_a_2_0_modcat_1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& v3_rlvect_1(B)
& v4_rlvect_1(B)
& v5_rlvect_1(B)
& v6_rlvect_1(B)
& v4_group_1(B)
& v6_vectsp_1(B)
& v7_vectsp_1(B)
& v8_vectsp_1(B)
& l3_vectsp_1(B)
& ~ v1_xboole_0(C)
& v1_classes2(C) )
=> ( r2_hidden(A,a_2_0_modcat_1(B,C))
<=> ? [D,E] :
( m2_grcat_1(D,k19_grcat_1(C))
& m2_fraenkel(E,k2_zfmisc_1(u1_struct_0(B),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0),k1_fraenkel(k2_zfmisc_1(u1_struct_0(B),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)))
& A = k4_tarski(D,E) ) ) ) ).
fof(fraenkel_a_2_1_modcat_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v1_classes2(B)
& ~ v3_struct_0(C)
& v3_rlvect_1(C)
& v4_rlvect_1(C)
& v5_rlvect_1(C)
& v6_rlvect_1(C)
& v4_group_1(C)
& v6_vectsp_1(C)
& v7_vectsp_1(C)
& v8_vectsp_1(C)
& l3_vectsp_1(C) )
=> ( r2_hidden(A,a_2_1_modcat_1(B,C))
<=> ? [D,E] :
( m2_grcat_1(D,k19_grcat_1(B))
& m2_fraenkel(E,k2_zfmisc_1(u1_struct_0(C),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0),k1_fraenkel(k2_zfmisc_1(u1_struct_0(C),k1_tarski(k1_xboole_0)),k1_tarski(k1_xboole_0)))
& A = k4_tarski(D,E) ) ) ) ).
%------------------------------------------------------------------------------