SET007 Axioms: SET007+648.ax


%------------------------------------------------------------------------------
% File     : SET007+648 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Properties of Instructions of SCM over Ring
% 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    : scmring3 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  116 (   0 unit)
%            Number of atoms       : 1756 (  87 equality)
%            Maximal formula depth :   21 (  14 average)
%            Number of connectives : 1843 ( 203 ~  ;   0  |;1386  &)
%                                         (   0 <=>; 254 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   72 (   0 propositional; 1-3 arity)
%            Number of functors    :   65 (  14 constant; 0-5 arity)
%            Number of variables   :  309 (   0 singleton; 307 !;   2 ?)
%            Maximal term depth    :    7 (   2 average)
% 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(fc1_scmring3,axiom,
    ( ~ v1_xboole_0(k4_numbers)
    & ~ v1_finset_1(k4_numbers)
    & ~ v1_realset1(k4_numbers)
    & v1_membered(k4_numbers)
    & v2_membered(k4_numbers)
    & v3_membered(k4_numbers)
    & v4_membered(k4_numbers) )).

fof(fc2_scmring3,axiom,
    ( ~ v3_struct_0(k1_int_3)
    & v2_group_1(k1_int_3)
    & v4_group_1(k1_int_3)
    & ~ v6_group_1(k1_int_3)
    & v7_group_1(k1_int_3)
    & v3_rlvect_1(k1_int_3)
    & v4_rlvect_1(k1_int_3)
    & v5_rlvect_1(k1_int_3)
    & v6_rlvect_1(k1_int_3)
    & v3_vectsp_1(k1_int_3)
    & v4_vectsp_1(k1_int_3)
    & v5_vectsp_1(k1_int_3)
    & v6_vectsp_1(k1_int_3)
    & v7_vectsp_1(k1_int_3)
    & v8_vectsp_1(k1_int_3)
    & ~ v10_vectsp_1(k1_int_3)
    & v1_scmring1(k1_int_3)
    & ~ v3_realset2(k1_int_3)
    & v1_int_3(k1_int_3)
    & v2_vectsp_2(k1_int_3)
    & v3_gcd_1(k1_int_3) )).

fof(rc1_scmring3,axiom,(
    ? [A] :
      ( l1_struct_0(A)
      & v1_struct_0(A)
      & ~ v3_struct_0(A)
      & ~ v6_group_1(A)
      & ~ v3_realset2(A) ) )).

fof(rc2_scmring3,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & ~ v6_group_1(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v3_vectsp_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & v1_scmring1(A)
      & ~ v3_realset2(A) ) )).

fof(fc3_scmring3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v1_xboole_0(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))
        & v1_fraenkel(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B)) ) ) )).

fof(fc4_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
        & v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
        & v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
        & v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
        & v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
        & v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
        & v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
        & v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
        & v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))) ) ) )).

fof(fc5_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
        & v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
        & v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
        & v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C))) ) ) )).

fof(fc6_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
        & v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
        & v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
        & v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C))) ) ) )).

fof(fc7_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
        & v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
        & v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
        & v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C))) ) ) )).

fof(fc8_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
        & v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
        & v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
        & v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C))) ) ) )).

fof(fc9_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_relat_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
        & v1_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
        & v2_funct_1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
        & v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
        & v1_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
        & v2_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
        & v3_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
        & v4_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)))
        & v5_membered(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C))) ) ) )).

fof(fc10_scmring3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)))
        & v1_realset1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B))) ) ) )).

fof(fc11_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v1_xboole_0(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)))
        & v1_realset1(k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B))) ) ) )).

fof(fc12_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_scmring2(A))
        & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) )).

fof(fc13_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(fc14_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( ~ v1_xboole_0(k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
        & v3_ami_1(k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v2_amistd_1(k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v12_amistd_2(k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc15_scmring3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(fc16_scmring3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v3_ami_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v2_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc17_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(fc18_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v3_ami_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v2_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc19_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(fc20_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( ~ v3_ami_1(k4_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v2_amistd_1(k4_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc21_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(fc22_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( ~ v3_ami_1(k5_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v2_amistd_1(k5_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc23_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(fc24_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( ~ v3_ami_1(k6_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v2_amistd_1(k6_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc25_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(fc26_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( ~ v3_ami_1(k7_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v2_amistd_1(k7_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc27_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => ~ v1_amistd_1(k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,B,C)),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(fc28_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v3_ami_1(k8_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v2_amistd_1(k8_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc29_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( ~ v3_ami_1(k4_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v5_amistd_1(k4_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc30_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( ~ v3_ami_1(k5_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v5_amistd_1(k5_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc31_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( ~ v3_ami_1(k6_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v5_amistd_1(k6_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc32_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A) )
     => ( ~ v3_ami_1(k7_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v5_amistd_1(k7_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc33_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v3_ami_1(k8_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v5_amistd_1(k8_scmring2(A,B,C),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc34_scmring3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v3_ami_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v2_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v5_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc35_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v3_ami_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v2_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v5_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc36_scmring3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v3_ami_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v2_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v5_amistd_1(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v9_amistd_2(k9_scmring2(A,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc37_scmring3,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_subset_1(C,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
     => ( ~ v3_ami_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & v2_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v5_amistd_1(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A))
        & ~ v9_amistd_2(k10_scmring2(A,C,B),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(fc38_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_scmring2(A))
        & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) )).

fof(fc39_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_scmring2(A))
        & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v8_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) )).

fof(fc40_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k1_scmring2(A))
        & v1_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & ~ v2_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v4_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v5_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v6_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v7_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v8_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v10_ami_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v4_amistd_1(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v2_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v5_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v6_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v7_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v8_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v11_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A)))
        & v13_amistd_2(k1_scmring2(A),k1_tarski(u1_struct_0(A))) ) ) )).

fof(t1_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => k3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = u1_struct_0(A) ) ) )).

fof(t2_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ~ r2_hidden(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) ) ) )).

fof(t3_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => B != k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(t4_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => k2_ami_2 != u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(t5_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k1_scmring2(A)))
         => ~ ( B != k2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))
              & ~ r2_hidden(B,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
              & ~ m1_scmring2(B,A) ) ) ) )).

fof(t6_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => ~ ( B != C
                  & k11_scmring2(A,B) = k11_scmring2(A,C) ) ) ) ) )).

fof(t7_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_subset_1(C,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
             => ! [D] :
                  ( m1_subset_1(D,k4_card_3(u5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))))
                 => ( r1_funct_7(C,D,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                   => k3_scmring2(A,C,B) = k3_scmring2(A,D,B) ) ) ) ) ) )).

fof(t8_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = np__0 ) )).

fof(t9_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)) = np__1 ) ) ) )).

fof(t10_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)) = np__2 ) ) ) )).

fof(t11_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)) = np__3 ) ) ) )).

fof(t12_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)) = np__4 ) ) ) )).

fof(t13_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B)) = np__5 ) ) ) )).

fof(t14_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)) = np__6 ) ) )).

fof(t15_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)) = np__7 ) ) ) )).

fof(t16_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__0
           => B = k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ) )).

fof(t17_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__1
              & ! [C] :
                  ( m1_scmring2(C,A)
                 => ! [D] :
                      ( m1_scmring2(D,A)
                     => B != k4_scmring2(A,C,D) ) ) ) ) ) )).

fof(t18_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__2
              & ! [C] :
                  ( m1_scmring2(C,A)
                 => ! [D] :
                      ( m1_scmring2(D,A)
                     => B != k5_scmring2(A,C,D) ) ) ) ) ) )).

fof(t19_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__3
              & ! [C] :
                  ( m1_scmring2(C,A)
                 => ! [D] :
                      ( m1_scmring2(D,A)
                     => B != k6_scmring2(A,C,D) ) ) ) ) ) )).

fof(t20_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__4
              & ! [C] :
                  ( m1_scmring2(C,A)
                 => ! [D] :
                      ( m1_scmring2(D,A)
                     => B != k7_scmring2(A,C,D) ) ) ) ) ) )).

fof(t21_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__5
              & ! [C] :
                  ( m1_scmring2(C,A)
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => B != k8_scmring2(A,C,D) ) ) ) ) ) )).

fof(t22_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__6
              & ! [C] :
                  ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                 => B != k9_scmring2(A,C) ) ) ) ) )).

fof(t23_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k2_zfmisc_1(u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),k13_finseq_1(k2_xboole_0(k3_tarski(k1_tarski(u1_struct_0(A))),u1_struct_0(k1_scmring2(A))))),u4_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ~ ( k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = np__7
              & ! [C] :
                  ( m1_scmring2(C,A)
                 => ! [D] :
                      ( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                     => B != k10_scmring2(A,D,C) ) ) ) ) ) )).

fof(t24_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k1_xboole_0 ) )).

fof(t25_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)) = k10_finseq_1(B,C) ) ) ) )).

fof(t26_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)) = k10_finseq_1(B,C) ) ) ) )).

fof(t27_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)) = k10_finseq_1(B,C) ) ) ) )).

fof(t28_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)) = k10_finseq_1(B,C) ) ) ) )).

fof(t29_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_scmring2(C,A)
             => k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B)) = k10_finseq_1(C,B) ) ) ) )).

fof(t30_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)) = k12_finseq_1(u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B) ) ) )).

fof(t31_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => k4_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)) = k10_finseq_1(C,B) ) ) ) )).

fof(t32_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( B = np__0
           => k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = k5_realset1(k5_numbers,np__0) ) ) ) )).

fof(t33_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( B = np__1
           => k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) )).

fof(t34_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( B = np__2
           => k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) )).

fof(t35_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( B = np__3
           => k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) )).

fof(t36_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( B = np__4
           => k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) )).

fof(t37_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( B = np__5
           => k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) )).

fof(t38_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( B = np__6
           => k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k5_realset1(k5_numbers,np__1) ) ) ) )).

fof(t39_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u3_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ( B = np__7
           => k1_relat_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B))) = k2_tarski(np__1,np__2) ) ) ) )).

fof(t40_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))),np__1) = k2_ami_2 ) ) ) )).

fof(t41_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k4_scmring2(A,B,C)))),np__2) = k2_ami_2 ) ) ) )).

fof(t42_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))),np__1) = k2_ami_2 ) ) ) )).

fof(t43_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k5_scmring2(A,B,C)))),np__2) = k2_ami_2 ) ) ) )).

fof(t44_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))),np__1) = k2_ami_2 ) ) ) )).

fof(t45_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k6_scmring2(A,B,C)))),np__2) = k2_ami_2 ) ) ) )).

fof(t46_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))),np__1) = k2_ami_2 ) ) ) )).

fof(t47_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k7_scmring2(A,B,C)))),np__2) = k2_ami_2 ) ) ) )).

fof(t48_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B)))),np__1) = k2_ami_2 ) ) ) )).

fof(t49_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_scmring2(C,A)
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_scmring2(A,C,B)))),np__2) = u1_struct_0(A) ) ) ) )).

fof(t50_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)))),np__1) = u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) )).

fof(t51_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)))),np__1) = u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) ) ) )).

fof(t52_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => k1_funct_1(k1_amistd_2(k5_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k1_ami_5(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)))),np__2) = k2_ami_2 ) ) ) )).

fof(t53_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B,k5_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) = k1_struct_0(k1_scmring2(A),B) ) ) )).

fof(t54_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => ! [D] :
                  ( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                 => k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k4_scmring2(A,B,C)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) )).

fof(t55_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => ! [D] :
                  ( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                 => k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k5_scmring2(A,B,C)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) )).

fof(t56_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => ! [D] :
                  ( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                 => k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k6_scmring2(A,B,C)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) )).

fof(t57_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_scmring2(C,A)
             => ! [D] :
                  ( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                 => k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k7_scmring2(A,B,C)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) )).

fof(t58_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_scmring2(C,A)
             => ! [D] :
                  ( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                 => k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k8_scmring2(A,C,B)) = k1_struct_0(k1_scmring2(A),k11_scmring2(A,D)) ) ) ) ) )).

fof(t59_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),C,k9_scmring2(A,B)) = k1_struct_0(k1_scmring2(A),B) ) ) ) )).

fof(t60_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B)) = k1_struct_0(k1_scmring2(A),B) ) ) )).

fof(t61_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => ! [D] :
                  ( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                 => ( r2_hidden(C,k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k10_scmring2(A,C,B)))
                    & r1_tarski(k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),D,k10_scmring2(A,C,B)),k2_struct_0(k1_scmring2(A),C,k11_scmring2(A,D))) ) ) ) ) ) )).

fof(t62_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & ~ v3_realset2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => ! [D] :
                  ( m1_struct_0(D,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
                 => k1_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),C,k10_scmring2(A,D,B)) = k2_struct_0(k1_scmring2(A),D,k11_scmring2(A,C)) ) ) ) ) )).

fof(t63_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => k2_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B)) = k1_struct_0(k1_scmring2(A),C) ) ) ) )).

fof(t64_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => k3_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = k2_struct_0(k1_scmring2(A),B,k11_scmring2(A,B)) ) ) )).

fof(t65_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
            & m2_relset_1(B,k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A))) )
         => ( ! [C] :
                ( m2_subset_1(C,k1_numbers,k5_numbers)
               => k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,C) = k16_ami_3(C) )
           => ( v3_funct_2(B,k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
              & ! [C] :
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,k1_nat_1(C,np__1)),k3_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,C)))
                    & ! [D] :
                        ( m2_subset_1(D,k1_numbers,k5_numbers)
                       => ( r2_hidden(k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,D),k3_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k8_funct_2(k5_numbers,u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)),B,C)))
                         => r1_xreal_0(C,D) ) ) ) ) ) ) ) ) )).

fof(t66_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( v4_ordinal2(B)
         => k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) = k16_ami_3(B) ) ) )).

fof(t67_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( v4_ordinal2(B)
         => k11_scmring2(A,k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B)) = k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k2_xcmplx_0(B,np__1)) ) ) )).

fof(t68_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => k11_scmring2(A,B) = k9_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B) ) ) )).

fof(d1_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => k2_scmring3(A,B) = k15_ami_3(B) ) ) )).

fof(t69_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_struct_0(B,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
         => ! [C] :
              ( v4_ordinal2(C)
             => k8_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k9_scmring2(A,B),C) = k9_scmring2(A,k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k2_xcmplx_0(k7_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),B),C))) ) ) ) )).

fof(t70_scmring3,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_scmring2(B,A)
         => ! [C] :
              ( m1_struct_0(C,k1_scmring2(A),u2_ami_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A)))
             => ! [D] :
                  ( v4_ordinal2(D)
                 => k8_amistd_2(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k10_scmring2(A,C,B),D) = k10_scmring2(A,k5_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),k2_xcmplx_0(k7_amistd_1(k1_tarski(u1_struct_0(A)),k1_scmring2(A),C),D)),B) ) ) ) ) )).

fof(dt_k1_scmring3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A)
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A)) )
     => m1_ami_1(k1_scmring3(A,B,C,D,E),k1_tarski(u1_struct_0(A)),k1_scmring2(A)) ) )).

fof(redefinition_k1_scmring3,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_scmring2(B,A)
        & m1_scmring2(C,A)
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A)) )
     => k1_scmring3(A,B,C,D,E) = k4_funct_4(B,C,D,E) ) )).

fof(dt_k2_scmring3,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v1_scmring1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,k5_numbers) )
     => m1_scmring2(k2_scmring3(A,B),A) ) )).
%------------------------------------------------------------------------------