SET007 Axioms: SET007+313.ax
%------------------------------------------------------------------------------
% File : SET007+313 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Rings and Modules - Part II
% 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 : mod_2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 101 ( 18 unt; 0 def)
% Number of atoms : 1574 ( 137 equ)
% Maximal formula atoms : 49 ( 15 avg)
% Number of connectives : 1636 ( 163 ~; 0 |;1228 &)
% ( 7 <=>; 238 =>; 0 <=; 0 <~>)
% Maximal formula depth : 40 ( 12 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 43 ( 41 usr; 1 prp; 0-4 aty)
% Number of functors : 52 ( 52 usr; 12 con; 0-6 aty)
% Number of variables : 261 ( 249 !; 12 ?)
% 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_mod_2,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] :
( l1_mod_2(B,A)
& v2_mod_2(B,A) ) ) ).
fof(rc2_mod_2,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] :
( l1_mod_2(B,A)
& v2_mod_2(B,A)
& v3_mod_2(B,A) ) ) ).
fof(fc1_mod_2,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) )
=> ( v2_mod_2(k5_mod_2(A,B,C),A)
& v3_mod_2(k5_mod_2(A,B,C),A) ) ) ).
fof(rc3_mod_2,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] :
( m1_mod_2(D,A,B,C)
& v2_mod_2(D,A)
& v3_mod_2(D,A) ) ) ).
fof(fc2_mod_2,axiom,
! [A,B,C] : ~ v1_xboole_0(k1_enumset1(A,B,C)) ).
fof(fc3_mod_2,axiom,
( ~ v3_struct_0(k18_mod_2)
& v3_vectsp_1(k18_mod_2) ) ).
fof(fc4_mod_2,axiom,
( ~ v3_struct_0(k18_mod_2)
& v2_group_1(k18_mod_2)
& v3_vectsp_1(k18_mod_2)
& v6_vectsp_1(k18_mod_2)
& v8_vectsp_1(k18_mod_2) ) ).
fof(fc5_mod_2,axiom,
( ~ v3_struct_0(k18_mod_2)
& v4_rlvect_1(k18_mod_2)
& v5_rlvect_1(k18_mod_2)
& v6_rlvect_1(k18_mod_2)
& v2_group_1(k18_mod_2)
& v3_vectsp_1(k18_mod_2)
& v6_vectsp_1(k18_mod_2)
& v8_vectsp_1(k18_mod_2)
& v1_algstr_1(k18_mod_2)
& v2_algstr_1(k18_mod_2)
& v3_algstr_1(k18_mod_2)
& v4_algstr_1(k18_mod_2)
& v5_algstr_1(k18_mod_2)
& v6_algstr_1(k18_mod_2) ) ).
fof(fc6_mod_2,axiom,
( ~ v3_struct_0(k18_mod_2)
& v3_rlvect_1(k18_mod_2)
& v4_rlvect_1(k18_mod_2)
& v5_rlvect_1(k18_mod_2)
& v6_rlvect_1(k18_mod_2)
& v2_group_1(k18_mod_2)
& v4_group_1(k18_mod_2)
& v7_group_1(k18_mod_2)
& v3_vectsp_1(k18_mod_2)
& v4_vectsp_1(k18_mod_2)
& v5_vectsp_1(k18_mod_2)
& v6_vectsp_1(k18_mod_2)
& v7_vectsp_1(k18_mod_2)
& v8_vectsp_1(k18_mod_2)
& v9_vectsp_1(k18_mod_2)
& v13_vectsp_1(k18_mod_2)
& v1_algstr_1(k18_mod_2)
& v2_algstr_1(k18_mod_2)
& v3_algstr_1(k18_mod_2)
& v4_algstr_1(k18_mod_2)
& v5_algstr_1(k18_mod_2)
& v6_algstr_1(k18_mod_2) ) ).
fof(d1_mod_2,axiom,
$true ).
fof(d2_mod_2,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) )
=> k1_mod_2(A) = g4_vectsp_1(A,k1_tarski(k1_xboole_0),k2_midsp_1,k8_vectsp_2,k10_funct_3(u1_struct_0(A),k1_tarski(k1_xboole_0))) ) ).
fof(t1_mod_2,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_subset_1(B,u1_struct_0(k1_mod_2(A)))
=> B = k1_rlvect_1(k1_mod_2(A)) ) ) ).
fof(d3_mod_2,axiom,
$true ).
fof(d4_mod_2,axiom,
$true ).
fof(d5_mod_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_vectsp_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_mod_2(D,A,B,C)
<=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,k2_rlvect_1(B,E,F)) = k2_rlvect_1(C,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,E),k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,F)) ) )
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,k6_vectsp_1(A,B,E,F)) = k6_vectsp_1(A,C,E,k8_funct_2(u1_struct_0(B),u1_struct_0(C),D,F)) ) ) ) ) ) ) ) ) ).
fof(t2_mod_2,axiom,
$true ).
fof(t3_mod_2,axiom,
$true ).
fof(t4_mod_2,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)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_mod_2(D,A,B,C)
=> v1_grcat_1(D,B,C) ) ) ) ) ) ).
fof(t5_mod_2,axiom,
$true ).
fof(t6_mod_2,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)
& l4_vectsp_1(B,A) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l4_vectsp_1(C,A) )
=> ! [D] :
( ( ~ v3_struct_0(D)
& l4_vectsp_1(D,A) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
=> ( ( v1_mod_2(E,A,B,C)
& v1_mod_2(F,A,C,D) )
=> v1_mod_2(k7_funct_2(u1_struct_0(B),u1_struct_0(C),u1_struct_0(D),E,F),A,B,D) ) ) ) ) ) ) ) ).
fof(t7_mod_2,axiom,
$true ).
fof(t8_mod_2,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) )
=> v1_mod_2(k8_grcat_1(B,C),A,B,C) ) ) ) ).
fof(d6_mod_2,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] :
( l1_mod_2(B,A)
=> k2_mod_2(A,B) = u1_mod_2(A,B) ) ) ).
fof(d7_mod_2,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] :
( l1_mod_2(B,A)
=> k3_mod_2(A,B) = u2_mod_2(A,B) ) ) ).
fof(d8_mod_2,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] :
( l1_mod_2(B,A)
=> k4_mod_2(A,B) = u3_mod_2(A,B) ) ) ).
fof(t9_mod_2,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] :
( l1_mod_2(D,A)
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C)) )
=> ( D = g1_mod_2(A,B,C,E)
=> ( k2_mod_2(A,D) = B
& k3_mod_2(A,D) = C
& k4_mod_2(A,D) = E ) ) ) ) ) ) ) ).
fof(d9_mod_2,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) )
=> k5_mod_2(A,B,C) = g1_mod_2(A,B,C,k8_grcat_1(B,C)) ) ) ) ).
fof(d10_mod_2,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] :
( l1_mod_2(B,A)
=> ( v3_mod_2(B,A)
<=> v1_mod_2(k4_mod_2(A,B),A,k2_mod_2(A,B),k3_mod_2(A,B)) ) ) ) ).
fof(t10_mod_2,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_mod_2(B,A)
& l1_mod_2(B,A) )
=> v1_mod_2(u3_mod_2(A,B),A,u1_mod_2(A,B),u2_mod_2(A,B)) ) ) ).
fof(d11_mod_2,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] :
( ( v3_mod_2(D,A)
& l1_mod_2(D,A) )
=> ( m1_mod_2(D,A,B,C)
<=> ( k2_mod_2(A,D) = B
& k3_mod_2(A,D) = C ) ) ) ) ) ) ).
fof(t11_mod_2,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] :
( l1_mod_2(D,A)
=> ( ( k2_mod_2(A,D) = B
& k3_mod_2(A,D) = C
& v1_mod_2(k4_mod_2(A,D),A,k2_mod_2(A,D),k3_mod_2(A,D)) )
=> m1_mod_2(D,A,B,C) ) ) ) ) ) ).
fof(t12_mod_2,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] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( v1_mod_2(D,A,B,C)
=> ( v2_mod_2(g1_mod_2(A,B,C,D),A)
& m1_mod_2(g1_mod_2(A,B,C,D),A,B,C) ) ) ) ) ) ) ).
fof(t13_mod_2,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) )
=> v1_mod_2(k7_grcat_1(B),A,B,B) ) ) ).
fof(d12_mod_2,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) )
=> k6_mod_2(A,B) = g1_mod_2(A,B,B,k7_grcat_1(B)) ) ) ).
fof(t14_mod_2,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] :
( m1_mod_2(D,A,B,C)
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C))
& g1_mod_2(A,u1_mod_2(A,D),u2_mod_2(A,D),u3_mod_2(A,D)) = g1_mod_2(A,B,C,E)
& v1_mod_2(E,A,B,C) ) ) ) ) ) ).
fof(t15_mod_2,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) )
=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(C))
& D = g1_mod_2(A,B,C,E) ) ) ) ) ) ).
fof(t16_mod_2,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_mod_2(B,A)
& l1_mod_2(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] :
( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& l4_vectsp_1(D,A)
& m1_mod_2(B,A,C,D) ) ) ) ) ).
fof(t17_mod_2,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) )
=> ? [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] :
( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& l4_vectsp_1(D,A)
& ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(C),u1_struct_0(D))
& m2_relset_1(E,u1_struct_0(C),u1_struct_0(D))
& v2_mod_2(B,A)
& m1_mod_2(B,A,C,D)
& B = g1_mod_2(A,C,D,E)
& v1_mod_2(E,A,C,D) ) ) ) ) ) ).
fof(t18_mod_2,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_mod_2(B,A)
& l1_mod_2(B,A) )
=> ! [C] :
( ( v3_mod_2(C,A)
& l1_mod_2(C,A) )
=> ~ ( k2_mod_2(A,B) = k3_mod_2(A,C)
& ! [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,A)
& l4_vectsp_1(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v3_rlvect_1(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& v12_vectsp_1(E,A)
& l4_vectsp_1(E,A) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v3_rlvect_1(F)
& v4_rlvect_1(F)
& v5_rlvect_1(F)
& v6_rlvect_1(F)
& v12_vectsp_1(F,A)
& l4_vectsp_1(F,A) )
=> ~ ( m1_mod_2(B,A,E,F)
& m1_mod_2(C,A,D,E) ) ) ) ) ) ) ) ) ).
fof(d13_mod_2,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_mod_2(B,A)
& l1_mod_2(B,A) )
=> ! [C] :
( ( v3_mod_2(C,A)
& l1_mod_2(C,A) )
=> ( k2_mod_2(A,B) = k3_mod_2(A,C)
=> ! [D] :
( ( v2_mod_2(D,A)
& v3_mod_2(D,A)
& l1_mod_2(D,A) )
=> ( D = k8_mod_2(A,B,C)
<=> ! [E] :
( ( ~ v3_struct_0(E)
& v3_rlvect_1(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& v12_vectsp_1(E,A)
& l4_vectsp_1(E,A) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v3_rlvect_1(F)
& v4_rlvect_1(F)
& v5_rlvect_1(F)
& v6_rlvect_1(F)
& v12_vectsp_1(F,A)
& l4_vectsp_1(F,A) )
=> ! [G] :
( ( ~ v3_struct_0(G)
& v3_rlvect_1(G)
& v4_rlvect_1(G)
& v5_rlvect_1(G)
& v6_rlvect_1(G)
& v12_vectsp_1(G,A)
& l4_vectsp_1(G,A) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(F),u1_struct_0(G))
& m2_relset_1(H,u1_struct_0(F),u1_struct_0(G)) )
=> ! [I] :
( ( v1_funct_1(I)
& v1_funct_2(I,u1_struct_0(E),u1_struct_0(F))
& m2_relset_1(I,u1_struct_0(E),u1_struct_0(F)) )
=> ( ( g1_mod_2(A,u1_mod_2(A,B),u2_mod_2(A,B),u3_mod_2(A,B)) = g1_mod_2(A,F,G,H)
& g1_mod_2(A,u1_mod_2(A,C),u2_mod_2(A,C),u3_mod_2(A,C)) = g1_mod_2(A,E,F,I) )
=> D = g1_mod_2(A,E,G,k7_funct_2(u1_struct_0(E),u1_struct_0(F),u1_struct_0(G),I,H)) ) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t19_mod_2,axiom,
$true ).
fof(t20_mod_2,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] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& l4_vectsp_1(D,A) )
=> ! [E] :
( m1_mod_2(E,A,B,C)
=> ! [F] :
( m1_mod_2(F,A,D,B)
=> ( v2_mod_2(k8_mod_2(A,E,F),A)
& m1_mod_2(k8_mod_2(A,E,F),A,D,C) ) ) ) ) ) ) ) ).
fof(d14_mod_2,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] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& l4_vectsp_1(D,A) )
=> ! [E] :
( m1_mod_2(E,A,C,D)
=> ! [F] :
( m1_mod_2(F,A,B,C)
=> k9_mod_2(A,B,C,D,E,F) = k8_mod_2(A,E,F) ) ) ) ) ) ) ).
fof(t21_mod_2,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] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& l4_vectsp_1(D,A) )
=> ! [E] :
( m1_mod_2(E,A,B,C)
=> ! [F] :
( m1_mod_2(F,A,D,B)
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(G,u1_struct_0(B),u1_struct_0(C)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(H,u1_struct_0(D),u1_struct_0(B)) )
=> ( ( E = g1_mod_2(A,B,C,G)
& F = g1_mod_2(A,D,B,H) )
=> ( k9_mod_2(A,D,B,C,E,F) = g1_mod_2(A,D,C,k7_funct_2(u1_struct_0(D),u1_struct_0(B),u1_struct_0(C),H,G))
& k8_mod_2(A,E,F) = g1_mod_2(A,D,C,k7_funct_2(u1_struct_0(D),u1_struct_0(B),u1_struct_0(C),H,G)) ) ) ) ) ) ) ) ) ) ) ).
fof(t22_mod_2,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) )
=> ! [C] :
( ( v2_mod_2(C,A)
& v3_mod_2(C,A)
& l1_mod_2(C,A) )
=> ~ ( k2_mod_2(A,C) = k3_mod_2(A,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,A)
& l4_vectsp_1(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v3_rlvect_1(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& v12_vectsp_1(E,A)
& l4_vectsp_1(E,A) )
=> ! [F] :
( ( ~ v3_struct_0(F)
& v3_rlvect_1(F)
& v4_rlvect_1(F)
& v5_rlvect_1(F)
& v6_rlvect_1(F)
& v12_vectsp_1(F,A)
& l4_vectsp_1(F,A) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(E),u1_struct_0(F))
& m2_relset_1(H,u1_struct_0(E),u1_struct_0(F)) )
=> ~ ( B = g1_mod_2(A,D,E,G)
& C = g1_mod_2(A,E,F,H)
& k8_mod_2(A,C,B) = g1_mod_2(A,D,F,k7_funct_2(u1_struct_0(D),u1_struct_0(E),u1_struct_0(F),G,H)) ) ) ) ) ) ) ) ) ) ) ).
fof(t23_mod_2,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) )
=> ! [C] :
( ( v2_mod_2(C,A)
& v3_mod_2(C,A)
& l1_mod_2(C,A) )
=> ( k2_mod_2(A,C) = k3_mod_2(A,B)
=> ( k2_mod_2(A,k8_mod_2(A,C,B)) = k2_mod_2(A,B)
& k3_mod_2(A,k8_mod_2(A,C,B)) = k3_mod_2(A,C) ) ) ) ) ) ).
fof(t24_mod_2,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] :
( ( ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& l4_vectsp_1(D,A) )
=> ! [E] :
( ( ~ v3_struct_0(E)
& v3_rlvect_1(E)
& v4_rlvect_1(E)
& v5_rlvect_1(E)
& v6_rlvect_1(E)
& v12_vectsp_1(E,A)
& l4_vectsp_1(E,A) )
=> ! [F] :
( ( v2_mod_2(F,A)
& m1_mod_2(F,A,B,C) )
=> ! [G] :
( ( v2_mod_2(G,A)
& m1_mod_2(G,A,C,D) )
=> ! [H] :
( ( v2_mod_2(H,A)
& m1_mod_2(H,A,D,E) )
=> k8_mod_2(A,H,k8_mod_2(A,G,F)) = k8_mod_2(A,k8_mod_2(A,H,G),F) ) ) ) ) ) ) ) ) ).
fof(t25_mod_2,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) )
=> ! [C] :
( ( v2_mod_2(C,A)
& v3_mod_2(C,A)
& l1_mod_2(C,A) )
=> ! [D] :
( ( v2_mod_2(D,A)
& v3_mod_2(D,A)
& l1_mod_2(D,A) )
=> ( ( k2_mod_2(A,D) = k3_mod_2(A,C)
& k2_mod_2(A,C) = k3_mod_2(A,B) )
=> k8_mod_2(A,D,k8_mod_2(A,C,B)) = k8_mod_2(A,k8_mod_2(A,D,C),B) ) ) ) ) ) ).
fof(t26_mod_2,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) )
=> ( k2_mod_2(A,k6_mod_2(A,B)) = B
& k3_mod_2(A,k6_mod_2(A,B)) = B
& ! [C] :
( ( v2_mod_2(C,A)
& v3_mod_2(C,A)
& l1_mod_2(C,A) )
=> ( k3_mod_2(A,C) = B
=> k8_mod_2(A,k6_mod_2(A,B),C) = C ) )
& ! [C] :
( ( v2_mod_2(C,A)
& v3_mod_2(C,A)
& l1_mod_2(C,A) )
=> ( k2_mod_2(A,C) = B
=> k8_mod_2(A,C,k6_mod_2(A,B)) = C ) ) ) ) ) ).
fof(t27_mod_2,axiom,
$true ).
fof(t28_mod_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,A)
=> ! [C] :
( m1_subset_1(C,A)
=> ! [D] :
( m1_subset_1(D,A)
=> m1_subset_1(k1_enumset1(B,C,D),A) ) ) ) ) ).
fof(t29_mod_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ! [B] :
( m1_subset_1(B,A)
=> m1_subset_1(k1_ordinal1(B),A) ) ) ).
fof(t30_mod_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ( m1_subset_1(np__0,A)
& m1_subset_1(np__1,A)
& m1_subset_1(np__2,A) ) ) ).
fof(d15_mod_2,axiom,
! [A] :
( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
=> ( ( A = np__0
=> k10_mod_2(A) = np__0 )
& ( A = np__1
=> k10_mod_2(A) = np__2 )
& ( A = np__2
=> k10_mod_2(A) = np__1 ) ) ) ).
fof(d16_mod_2,axiom,
! [A] :
( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
=> ! [B] :
( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
=> ( ( A = np__0
=> k11_mod_2(A,B) = B )
& ( B = np__0
=> k11_mod_2(A,B) = A )
& ( ( A = np__1
& B = np__1 )
=> k11_mod_2(A,B) = np__2 )
& ( ( A = np__1
& B = np__2 )
=> k11_mod_2(A,B) = np__0 )
& ( ( A = np__2
& B = np__1 )
=> k11_mod_2(A,B) = np__0 )
& ( ( A = np__2
& B = np__2 )
=> k11_mod_2(A,B) = np__1 ) ) ) ) ).
fof(d17_mod_2,axiom,
! [A] :
( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
=> ! [B] :
( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
=> ( ( B = np__0
=> k12_mod_2(A,B) = np__0 )
& ( A = np__0
=> k12_mod_2(A,B) = np__0 )
& ( B = np__1
=> k12_mod_2(A,B) = A )
& ( A = np__1
=> k12_mod_2(A,B) = B )
& ( ( A = np__2
& B = np__2 )
=> k12_mod_2(A,B) = np__1 ) ) ) ) ).
fof(d18_mod_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2))
& m2_relset_1(A,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2)) )
=> ( A = k13_mod_2
<=> ! [B] :
( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
=> ! [C] :
( m1_subset_1(C,k1_enumset1(np__0,np__1,np__2))
=> k2_binop_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),A,B,C) = k11_mod_2(B,C) ) ) ) ) ).
fof(d19_mod_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2))
& m2_relset_1(A,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2)) )
=> ( A = k14_mod_2
<=> ! [B] :
( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
=> ! [C] :
( m1_subset_1(C,k1_enumset1(np__0,np__1,np__2))
=> k2_binop_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),A,B,C) = k12_mod_2(B,C) ) ) ) ) ).
fof(d20_mod_2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2))
& m2_relset_1(A,k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)) )
=> ( A = k15_mod_2
<=> ! [B] :
( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
=> k8_funct_2(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2),A,B) = k10_mod_2(B) ) ) ) ).
fof(d21_mod_2,axiom,
k16_mod_2 = np__1 ).
fof(d22_mod_2,axiom,
k17_mod_2 = np__0 ).
fof(d23_mod_2,axiom,
k18_mod_2 = g3_vectsp_1(k1_enumset1(np__0,np__1,np__2),k13_mod_2,k14_mod_2,k16_mod_2,k17_mod_2) ).
fof(t31_mod_2,axiom,
$true ).
fof(t32_mod_2,axiom,
( k1_rlvect_1(k18_mod_2) = np__0
& k2_group_1(k18_mod_2) = np__1
& m1_subset_1(k1_rlvect_1(k18_mod_2),k1_enumset1(np__0,np__1,np__2))
& m1_subset_1(k2_group_1(k18_mod_2),k1_enumset1(np__0,np__1,np__2))
& u1_rlvect_1(k18_mod_2) = k13_mod_2
& u1_group_1(k18_mod_2) = k14_mod_2 ) ).
fof(t33_mod_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k18_mod_2))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k18_mod_2))
=> ! [C] :
( m1_subset_1(C,k1_enumset1(np__0,np__1,np__2))
=> ! [D] :
( m1_subset_1(D,k1_enumset1(np__0,np__1,np__2))
=> ( ( C = A
& D = B )
=> ( k2_rlvect_1(k18_mod_2,A,B) = k11_mod_2(C,D)
& k1_group_1(k18_mod_2,A,B) = k12_mod_2(C,D)
& k5_rlvect_1(k18_mod_2,A) = k10_mod_2(C) ) ) ) ) ) ) ).
fof(t34_mod_2,axiom,
! [A] :
( m1_subset_1(A,u1_struct_0(k18_mod_2))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k18_mod_2))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k18_mod_2))
=> ! [D] :
( m1_subset_1(D,k1_enumset1(np__0,np__1,np__2))
=> ! [E] :
( m1_subset_1(E,k1_enumset1(np__0,np__1,np__2))
=> ! [F] :
( m1_subset_1(F,k1_enumset1(np__0,np__1,np__2))
=> ( ( D = A
& E = B
& F = C )
=> ( k2_rlvect_1(k18_mod_2,k2_rlvect_1(k18_mod_2,A,B),C) = k11_mod_2(k11_mod_2(D,E),F)
& k2_rlvect_1(k18_mod_2,A,k2_rlvect_1(k18_mod_2,B,C)) = k11_mod_2(D,k11_mod_2(E,F))
& k1_group_1(k18_mod_2,k1_group_1(k18_mod_2,A,B),C) = k12_mod_2(k12_mod_2(D,E),F)
& k1_group_1(k18_mod_2,A,k1_group_1(k18_mod_2,B,C)) = k12_mod_2(D,k12_mod_2(E,F)) ) ) ) ) ) ) ) ) ).
fof(t35_mod_2,axiom,
! [A] :
( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
=> ! [B] :
( m1_subset_1(B,k1_enumset1(np__0,np__1,np__2))
=> ! [C] :
( m1_subset_1(C,k1_enumset1(np__0,np__1,np__2))
=> ! [D] :
( m1_subset_1(D,k1_enumset1(np__0,np__1,np__2))
=> ! [E] :
( m1_subset_1(E,k1_enumset1(np__0,np__1,np__2))
=> ( ( D = np__0
& E = np__1 )
=> ( k11_mod_2(A,B) = k11_mod_2(B,A)
& k11_mod_2(k11_mod_2(A,B),C) = k11_mod_2(A,k11_mod_2(B,C))
& k11_mod_2(A,D) = A
& k11_mod_2(A,k10_mod_2(A)) = D
& k12_mod_2(A,B) = k12_mod_2(B,A)
& k12_mod_2(k12_mod_2(A,B),C) = k12_mod_2(A,k12_mod_2(B,C))
& k12_mod_2(E,A) = A
& ~ ( A != D
& ! [F] :
( m1_subset_1(F,k1_enumset1(np__0,np__1,np__2))
=> k12_mod_2(A,F) != E ) )
& D != E
& k12_mod_2(A,k11_mod_2(B,C)) = k11_mod_2(k12_mod_2(A,B),k12_mod_2(A,C)) ) ) ) ) ) ) ) ).
fof(t36_mod_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_vectsp_1(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_struct_0(A))
=> ( k2_rlvect_1(A,B,C) = k2_rlvect_1(A,C,B)
& k2_rlvect_1(A,k2_rlvect_1(A,B,C),D) = k2_rlvect_1(A,B,k2_rlvect_1(A,C,D))
& k2_rlvect_1(A,B,k1_rlvect_1(A)) = B
& k2_rlvect_1(A,B,k5_rlvect_1(A,B)) = k1_rlvect_1(A)
& k1_group_1(A,B,C) = k1_group_1(A,C,B)
& k1_group_1(A,k1_group_1(A,B,C),D) = k1_group_1(A,B,k1_group_1(A,C,D))
& k1_group_1(A,k2_group_1(A),B) = B
& ~ ( B != k1_rlvect_1(A)
& ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_group_1(A,B,E) != k2_group_1(A) ) )
& k1_rlvect_1(A) != k2_group_1(A)
& k1_group_1(A,B,k2_rlvect_1(A,C,D)) = k2_rlvect_1(A,k1_group_1(A,B,C),k1_group_1(A,B,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)
& v7_group_1(A)
& v7_vectsp_1(A)
& v8_vectsp_1(A)
& v9_vectsp_1(A)
& ~ v10_vectsp_1(A)
& l3_vectsp_1(A) ) ) ) ).
fof(t37_mod_2,axiom,
( ~ v3_struct_0(k18_mod_2)
& v3_rlvect_1(k18_mod_2)
& v4_rlvect_1(k18_mod_2)
& v5_rlvect_1(k18_mod_2)
& v6_rlvect_1(k18_mod_2)
& v4_group_1(k18_mod_2)
& v7_group_1(k18_mod_2)
& v7_vectsp_1(k18_mod_2)
& v8_vectsp_1(k18_mod_2)
& v9_vectsp_1(k18_mod_2)
& ~ v10_vectsp_1(k18_mod_2)
& v13_vectsp_1(k18_mod_2)
& l3_vectsp_1(k18_mod_2) ) ).
fof(t38_mod_2,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_classes2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m2_relset_1(D,A,B) )
=> ( ( r2_hidden(A,C)
& r2_hidden(B,C) )
=> r2_hidden(D,C) ) ) ) ) ) ).
fof(t39_mod_2,axiom,
$true ).
fof(t40_mod_2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_classes2(A) )
=> ( r2_hidden(u1_struct_0(k18_mod_2),A)
& m1_subset_1(u1_rlvect_1(k18_mod_2),A)
& m1_subset_1(k7_vectsp_1(k18_mod_2),A)
& m1_subset_1(u2_struct_0(k18_mod_2),A)
& m1_subset_1(u1_group_1(k18_mod_2),A)
& m1_subset_1(u1_vectsp_1(k18_mod_2),A) ) ) ).
fof(dt_m1_mod_2,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] :
( m1_mod_2(D,A,B,C)
=> ( v3_mod_2(D,A)
& l1_mod_2(D,A) ) ) ) ).
fof(existence_m1_mod_2,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] : m1_mod_2(D,A,B,C) ) ).
fof(dt_l1_mod_2,axiom,
$true ).
fof(existence_l1_mod_2,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] : l1_mod_2(B,A) ) ).
fof(abstractness_v2_mod_2,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)
& l1_mod_2(B,A) )
=> ( v2_mod_2(B,A)
=> B = g1_mod_2(A,u1_mod_2(A,B),u2_mod_2(A,B),u3_mod_2(A,B)) ) ) ).
fof(dt_k1_mod_2,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) )
=> ( ~ v3_struct_0(k1_mod_2(A))
& v3_rlvect_1(k1_mod_2(A))
& v4_rlvect_1(k1_mod_2(A))
& v5_rlvect_1(k1_mod_2(A))
& v6_rlvect_1(k1_mod_2(A))
& v11_vectsp_1(k1_mod_2(A),A)
& v12_vectsp_1(k1_mod_2(A),A)
& l4_vectsp_1(k1_mod_2(A),A) ) ) ).
fof(dt_k2_mod_2,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)
& l1_mod_2(B,A) )
=> ( ~ v3_struct_0(k2_mod_2(A,B))
& v3_rlvect_1(k2_mod_2(A,B))
& v4_rlvect_1(k2_mod_2(A,B))
& v5_rlvect_1(k2_mod_2(A,B))
& v6_rlvect_1(k2_mod_2(A,B))
& v12_vectsp_1(k2_mod_2(A,B),A)
& l4_vectsp_1(k2_mod_2(A,B),A) ) ) ).
fof(dt_k3_mod_2,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)
& l1_mod_2(B,A) )
=> ( ~ v3_struct_0(k3_mod_2(A,B))
& v3_rlvect_1(k3_mod_2(A,B))
& v4_rlvect_1(k3_mod_2(A,B))
& v5_rlvect_1(k3_mod_2(A,B))
& v6_rlvect_1(k3_mod_2(A,B))
& v12_vectsp_1(k3_mod_2(A,B),A)
& l4_vectsp_1(k3_mod_2(A,B),A) ) ) ).
fof(dt_k4_mod_2,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)
& l1_mod_2(B,A) )
=> ( v1_funct_1(k4_mod_2(A,B))
& v1_funct_2(k4_mod_2(A,B),u1_struct_0(k2_mod_2(A,B)),u1_struct_0(k3_mod_2(A,B)))
& m2_relset_1(k4_mod_2(A,B),u1_struct_0(k2_mod_2(A,B)),u1_struct_0(k3_mod_2(A,B))) ) ) ).
fof(dt_k5_mod_2,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) )
=> ( v2_mod_2(k5_mod_2(A,B,C),A)
& l1_mod_2(k5_mod_2(A,B,C),A) ) ) ).
fof(dt_k6_mod_2,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)
& ~ 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) )
=> ( v2_mod_2(k6_mod_2(A,B),A)
& m1_mod_2(k6_mod_2(A,B),A,B,B) ) ) ).
fof(dt_k7_mod_2,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) )
=> ( v2_mod_2(k7_mod_2(A,B,C),A)
& m1_mod_2(k7_mod_2(A,B,C),A,B,C) ) ) ).
fof(redefinition_k7_mod_2,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) )
=> k7_mod_2(A,B,C) = k5_mod_2(A,B,C) ) ).
fof(dt_k8_mod_2,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_mod_2(B,A)
& l1_mod_2(B,A)
& v3_mod_2(C,A)
& l1_mod_2(C,A) )
=> ( v2_mod_2(k8_mod_2(A,B,C),A)
& v3_mod_2(k8_mod_2(A,B,C),A)
& l1_mod_2(k8_mod_2(A,B,C),A) ) ) ).
fof(dt_k9_mod_2,axiom,
! [A,B,C,D,E,F] :
( ( ~ 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)
& ~ v3_struct_0(D)
& v3_rlvect_1(D)
& v4_rlvect_1(D)
& v5_rlvect_1(D)
& v6_rlvect_1(D)
& v12_vectsp_1(D,A)
& l4_vectsp_1(D,A)
& m1_mod_2(E,A,C,D)
& m1_mod_2(F,A,B,C) )
=> ( v2_mod_2(k9_mod_2(A,B,C,D,E,F),A)
& m1_mod_2(k9_mod_2(A,B,C,D,E,F),A,B,D) ) ) ).
fof(dt_k10_mod_2,axiom,
! [A] :
( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
=> m1_subset_1(k10_mod_2(A),k1_enumset1(np__0,np__1,np__2)) ) ).
fof(dt_k11_mod_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
& m1_subset_1(B,k1_enumset1(np__0,np__1,np__2)) )
=> m1_subset_1(k11_mod_2(A,B),k1_enumset1(np__0,np__1,np__2)) ) ).
fof(dt_k12_mod_2,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_enumset1(np__0,np__1,np__2))
& m1_subset_1(B,k1_enumset1(np__0,np__1,np__2)) )
=> m1_subset_1(k12_mod_2(A,B),k1_enumset1(np__0,np__1,np__2)) ) ).
fof(dt_k13_mod_2,axiom,
( v1_funct_1(k13_mod_2)
& v1_funct_2(k13_mod_2,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2))
& m2_relset_1(k13_mod_2,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2)) ) ).
fof(dt_k14_mod_2,axiom,
( v1_funct_1(k14_mod_2)
& v1_funct_2(k14_mod_2,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2))
& m2_relset_1(k14_mod_2,k2_zfmisc_1(k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)),k1_enumset1(np__0,np__1,np__2)) ) ).
fof(dt_k15_mod_2,axiom,
( v1_funct_1(k15_mod_2)
& v1_funct_2(k15_mod_2,k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2))
& m2_relset_1(k15_mod_2,k1_enumset1(np__0,np__1,np__2),k1_enumset1(np__0,np__1,np__2)) ) ).
fof(dt_k16_mod_2,axiom,
m1_subset_1(k16_mod_2,k1_enumset1(np__0,np__1,np__2)) ).
fof(dt_k17_mod_2,axiom,
m1_subset_1(k17_mod_2,k1_enumset1(np__0,np__1,np__2)) ).
fof(dt_k18_mod_2,axiom,
( v3_vectsp_1(k18_mod_2)
& l3_vectsp_1(k18_mod_2) ) ).
fof(dt_u1_mod_2,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)
& l1_mod_2(B,A) )
=> ( ~ v3_struct_0(u1_mod_2(A,B))
& v3_rlvect_1(u1_mod_2(A,B))
& v4_rlvect_1(u1_mod_2(A,B))
& v5_rlvect_1(u1_mod_2(A,B))
& v6_rlvect_1(u1_mod_2(A,B))
& v12_vectsp_1(u1_mod_2(A,B),A)
& l4_vectsp_1(u1_mod_2(A,B),A) ) ) ).
fof(dt_u2_mod_2,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)
& l1_mod_2(B,A) )
=> ( ~ v3_struct_0(u2_mod_2(A,B))
& v3_rlvect_1(u2_mod_2(A,B))
& v4_rlvect_1(u2_mod_2(A,B))
& v5_rlvect_1(u2_mod_2(A,B))
& v6_rlvect_1(u2_mod_2(A,B))
& v12_vectsp_1(u2_mod_2(A,B),A)
& l4_vectsp_1(u2_mod_2(A,B),A) ) ) ).
fof(dt_u3_mod_2,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)
& l1_mod_2(B,A) )
=> ( v1_funct_1(u3_mod_2(A,B))
& v1_funct_2(u3_mod_2(A,B),u1_struct_0(u1_mod_2(A,B)),u1_struct_0(u2_mod_2(A,B)))
& m2_relset_1(u3_mod_2(A,B),u1_struct_0(u1_mod_2(A,B)),u1_struct_0(u2_mod_2(A,B))) ) ) ).
fof(dt_g1_mod_2,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)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ( v2_mod_2(g1_mod_2(A,B,C,D),A)
& l1_mod_2(g1_mod_2(A,B,C,D),A) ) ) ).
fof(free_g1_mod_2,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)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& m1_relset_1(D,u1_struct_0(B),u1_struct_0(C)) )
=> ! [E,F,G,H] :
( g1_mod_2(A,B,C,D) = g1_mod_2(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
%------------------------------------------------------------------------------