SET007 Axioms: SET007+515.ax


%------------------------------------------------------------------------------
% File     : SET007+515 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : The Correctness of the Generic Algorithms of Brown and Henrici
% Version  : [Urb08] axioms.
% English  : The Correctness of the Generic Algorithms of Brown and Henrici
%            Concerning Addition and Multiplication in Fraction Fields

% 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    : gcd_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  106 (   4 unit)
%            Number of atoms       : 1520 ( 158 equality)
%            Maximal formula depth :   27 (  13 average)
%            Number of connectives : 1606 ( 192 ~  ;  21  |; 997  &)
%                                         (  26 <=>; 370 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   41 (   1 propositional; 0-4 arity)
%            Number of functors    :   19 (   1 constant; 0-6 arity)
%            Number of variables   :  363 (   0 singleton; 349 !;  14 ?)
%            Maximal term depth    :    7 (   1 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(cc1_gcd_1,axiom,(
    ! [A] :
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v6_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v8_vectsp_1(A) ) ) ) )).

fof(cc2_gcd_1,axiom,(
    ! [A] :
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v4_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v7_vectsp_1(A) ) ) ) )).

fof(cc3_gcd_1,axiom,(
    ! [A] :
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v5_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v7_vectsp_1(A) ) ) ) )).

fof(cc4_gcd_1,axiom,(
    ! [A] :
      ( l3_vectsp_1(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) )
       => ( ~ v3_struct_0(A)
          & v3_rlvect_1(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v2_group_1(A)
          & v4_group_1(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v6_vectsp_1(A)
          & v7_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) )).

fof(fc1_gcd_1,axiom,
    ( ~ v3_struct_0(k3_vectsp_1)
    & v3_rlvect_1(k3_vectsp_1)
    & v4_rlvect_1(k3_vectsp_1)
    & v5_rlvect_1(k3_vectsp_1)
    & v6_rlvect_1(k3_vectsp_1)
    & v2_group_1(k3_vectsp_1)
    & v4_group_1(k3_vectsp_1)
    & v7_group_1(k3_vectsp_1)
    & v3_vectsp_1(k3_vectsp_1)
    & v4_vectsp_1(k3_vectsp_1)
    & v5_vectsp_1(k3_vectsp_1)
    & v6_vectsp_1(k3_vectsp_1)
    & v7_vectsp_1(k3_vectsp_1)
    & v8_vectsp_1(k3_vectsp_1)
    & v9_vectsp_1(k3_vectsp_1)
    & ~ v10_vectsp_1(k3_vectsp_1)
    & v2_vectsp_2(k3_vectsp_1) )).

fof(rc1_gcd_1,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_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)
      & v9_vectsp_1(A)
      & ~ v10_vectsp_1(A)
      & v2_vectsp_2(A) ) )).

fof(fc2_gcd_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k2_gcd_1(A,B)) ) )).

fof(fc3_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ~ v1_xboole_0(k3_gcd_1(A)) ) )).

fof(rc2_gcd_1,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & ~ v10_vectsp_1(A)
      & v2_vectsp_2(A)
      & v3_gcd_1(A) ) )).

fof(rc3_gcd_1,axiom,(
    ? [A] :
      ( l1_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v6_vectsp_1(A)
      & v8_vectsp_1(A)
      & v3_gcd_1(A) ) )).

fof(rc4_gcd_1,axiom,(
    ? [A] :
      ( l2_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v6_vectsp_1(A)
      & v8_vectsp_1(A)
      & v3_gcd_1(A) ) )).

fof(cc5_gcd_1,axiom,(
    ! [A] :
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v7_group_1(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A)
          & v9_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A)
          & v2_group_1(A)
          & v7_group_1(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A)
          & v6_vectsp_1(A)
          & v7_vectsp_1(A)
          & v8_vectsp_1(A)
          & v9_vectsp_1(A)
          & v3_gcd_1(A) ) ) ) )).

fof(rc5_gcd_1,axiom,(
    ? [A] :
      ( l3_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v3_rlvect_1(A)
      & v4_rlvect_1(A)
      & v5_rlvect_1(A)
      & v6_rlvect_1(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v4_vectsp_1(A)
      & v5_vectsp_1(A)
      & v6_vectsp_1(A)
      & v7_vectsp_1(A)
      & v8_vectsp_1(A)
      & ~ v10_vectsp_1(A)
      & v2_vectsp_2(A)
      & v3_gcd_1(A) ) )).

fof(t1_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(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))
                 => ( B != k1_rlvect_1(A)
                   => ( ( k10_group_1(A,B,C) = k10_group_1(A,B,D)
                       => C = D )
                      & ( k10_group_1(A,C,B) = k10_group_1(A,D,B)
                       => C = D ) ) ) ) ) ) ) )).

fof(d1_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_gcd_1(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C = k1_group_1(A,B,D) ) ) ) ) ) )).

fof(d2_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_gcd_1(B,A)
          <=> r1_gcd_1(A,B,k2_group_1(A)) ) ) ) )).

fof(d3_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_gcd_1(A,B,C)
              <=> ( r1_gcd_1(A,B,C)
                  & r1_gcd_1(A,C,B) ) ) ) ) ) )).

fof(d4_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_gcd_1(A,C,B)
               => ( C = k1_rlvect_1(A)
                  | ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( D = k1_gcd_1(A,B,C)
                      <=> k10_group_1(A,D,C) = B ) ) ) ) ) ) ) )).

fof(t2_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_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))
                 => ( ( r1_gcd_1(A,B,C)
                      & r1_gcd_1(A,C,D) )
                   => r1_gcd_1(A,B,D) ) ) ) ) ) )).

fof(t3_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & l1_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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r1_gcd_1(A,C,B)
                          & r1_gcd_1(A,E,D) )
                       => r1_gcd_1(A,k10_group_1(A,C,E),k10_group_1(A,B,D)) ) ) ) ) ) ) )).

fof(t4_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_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))
                 => ( ( r3_gcd_1(A,B,C)
                      & r3_gcd_1(A,C,D) )
                   => r3_gcd_1(A,B,D) ) ) ) ) ) )).

fof(t5_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_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))
                 => ( r1_gcd_1(A,B,C)
                   => r1_gcd_1(A,k1_group_1(A,D,B),k1_group_1(A,D,C)) ) ) ) ) ) )).

fof(t6_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_gcd_1(A,B,k1_group_1(A,B,C))
                & ( v7_group_1(A)
                 => r1_gcd_1(A,C,k1_group_1(A,B,C)) ) ) ) ) ) )).

fof(t7_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_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))
                 => ( r1_gcd_1(A,B,C)
                   => r1_gcd_1(A,B,k1_group_1(A,C,D)) ) ) ) ) ) )).

fof(t8_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_gcd_1(A,C,B)
               => ( C = k1_rlvect_1(A)
                  | ( k1_gcd_1(A,B,C) = k1_rlvect_1(A)
                  <=> B = k1_rlvect_1(A) ) ) ) ) ) ) )).

fof(t9_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( B != k1_rlvect_1(A)
           => k1_gcd_1(A,B,B) = k2_group_1(A) ) ) ) )).

fof(t10_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_gcd_1(A,B,k2_group_1(A)) = B ) ) )).

fof(t11_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(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))
                 => ( D != k1_rlvect_1(A)
                   => ( ( ( r2_gcd_1(A,D,k10_group_1(A,B,C))
                          & r2_gcd_1(A,D,B) )
                       => k1_gcd_1(A,k10_group_1(A,B,C),D) = k10_group_1(A,k1_gcd_1(A,B,D),C) )
                      & ( ( r2_gcd_1(A,D,k10_group_1(A,B,C))
                          & r2_gcd_1(A,D,C) )
                       => k1_gcd_1(A,k10_group_1(A,B,C),D) = k10_group_1(A,B,k1_gcd_1(A,C,D)) ) ) ) ) ) ) ) )).

fof(t12_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(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))
                 => ( ( r2_gcd_1(A,D,B)
                      & r2_gcd_1(A,D,C)
                      & r2_gcd_1(A,D,k4_rlvect_1(A,B,C)) )
                   => ( D = k1_rlvect_1(A)
                      | k4_rlvect_1(A,k1_gcd_1(A,B,D),k1_gcd_1(A,C,D)) = k1_gcd_1(A,k4_rlvect_1(A,B,C),D) ) ) ) ) ) ) )).

fof(t13_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(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))
                 => ( ( r2_gcd_1(A,D,B)
                      & r2_gcd_1(A,D,C) )
                   => ( D = k1_rlvect_1(A)
                      | ( k1_gcd_1(A,B,D) = k1_gcd_1(A,C,D)
                      <=> B = C ) ) ) ) ) ) ) )).

fof(t14_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(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))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r2_gcd_1(A,C,B)
                          & r2_gcd_1(A,E,D) )
                       => ( C = k1_rlvect_1(A)
                          | E = k1_rlvect_1(A)
                          | k10_group_1(A,k1_gcd_1(A,B,C),k1_gcd_1(A,D,E)) = k1_gcd_1(A,k10_group_1(A,B,D),k10_group_1(A,C,E)) ) ) ) ) ) ) ) )).

fof(t15_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(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))
                 => ( r2_gcd_1(A,k10_group_1(A,B,C),k10_group_1(A,B,D))
                   => ( B = k1_rlvect_1(A)
                      | r2_gcd_1(A,C,D) ) ) ) ) ) ) )).

fof(t16_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r4_gcd_1(A,B,k1_rlvect_1(A))
           => B = k1_rlvect_1(A) ) ) ) )).

fof(t17_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k10_group_1(A,B,C) = B
               => ( B = k1_rlvect_1(A)
                  | C = k2_group_1(A) ) ) ) ) ) )).

fof(t18_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r4_gcd_1(A,B,C)
              <=> ? [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                    & v1_gcd_1(D,A)
                    & k10_group_1(A,B,D) = C ) ) ) ) ) )).

fof(t19_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(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))
                 => ( r4_gcd_1(A,k10_group_1(A,D,B),k10_group_1(A,D,C))
                   => ( D = k1_rlvect_1(A)
                      | r4_gcd_1(A,B,C) ) ) ) ) ) ) )).

fof(d5_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = k2_gcd_1(A,B)
              <=> ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> r3_gcd_1(A,D,B) ) ) ) ) ) ) )).

fof(t20_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ~ r1_xboole_0(k2_gcd_1(A,B),k2_gcd_1(A,C))
               => k2_gcd_1(A,B) = k2_gcd_1(A,C) ) ) ) ) )).

fof(d6_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( B = k3_gcd_1(A)
          <=> ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                <=> ? [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                      & C = k2_gcd_1(A,D) ) ) ) ) ) ) )).

fof(t21_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( r2_hidden(B,k3_gcd_1(A))
              & v1_xboole_0(B) ) ) ) )).

fof(d7_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( m1_gcd_1(B,A)
          <=> ( ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ? [D] :
                      ( m1_struct_0(D,A,B)
                      & r4_gcd_1(A,D,C) ) )
              & ! [C] :
                  ( m1_struct_0(C,A,B)
                 => ! [D] :
                      ( m1_struct_0(D,A,B)
                     => ~ ( C != D
                          & r3_gcd_1(A,C,D) ) ) ) ) ) ) ) )).

fof(d8_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( m2_gcd_1(B,A)
          <=> ( m1_gcd_1(B,A)
              & r2_hidden(k2_group_1(A),B) ) ) ) ) )).

fof(t22_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ( r2_hidden(k2_group_1(A),B)
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] :
                    ( m1_struct_0(D,A,B)
                    & r4_gcd_1(A,D,C) ) )
            & ! [C] :
                ( m1_struct_0(C,A,B)
               => ! [D] :
                    ( m1_struct_0(D,A,B)
                   => ~ ( C != D
                        & r3_gcd_1(A,C,D) ) ) ) ) ) ) )).

fof(t23_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_struct_0(C,A,B)
             => ! [D] :
                  ( m1_struct_0(D,A,B)
                 => ( r4_gcd_1(A,C,D)
                   => C = D ) ) ) ) ) )).

fof(t24_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => m1_struct_0(k1_rlvect_1(A),A,B) ) ) )).

fof(d9_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( D = k4_gcd_1(A,B,C)
                  <=> ( r2_hidden(D,B)
                      & r4_gcd_1(A,D,C) ) ) ) ) ) ) )).

fof(t25_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ( k4_gcd_1(A,B,k1_rlvect_1(A)) = k1_rlvect_1(A)
            & k4_gcd_1(A,B,k2_group_1(A)) = k2_group_1(A) ) ) ) )).

fof(t26_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,B)
              <=> C = k4_gcd_1(A,B,C) ) ) ) ) )).

fof(d10_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ( v2_gcd_1(B,A)
          <=> ! [C] :
                ( m1_struct_0(C,A,B)
               => ! [D] :
                    ( m1_struct_0(D,A,B)
                   => r2_hidden(k1_group_1(A,C,D),B) ) ) ) ) ) )).

fof(t27_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ( v2_gcd_1(B,A)
           => ! [C] :
                ( m1_struct_0(C,A,B)
               => ! [D] :
                    ( m1_struct_0(D,A,B)
                   => ( r2_gcd_1(A,D,C)
                     => ( D = k1_rlvect_1(A)
                        | r2_hidden(k1_gcd_1(A,C,D),B) ) ) ) ) ) ) ) )).

fof(d11_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => ( v3_gcd_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))
                    & r1_gcd_1(A,D,B)
                    & r1_gcd_1(A,D,C)
                    & ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r1_gcd_1(A,E,B)
                            & r1_gcd_1(A,E,C) )
                         => r1_gcd_1(A,E,D) ) ) ) ) ) ) ) )).

fof(d12_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v3_gcd_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( E = k5_gcd_1(A,B,C,D)
                      <=> ( r2_hidden(E,B)
                          & r2_gcd_1(A,E,C)
                          & r2_gcd_1(A,E,D)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ( ( r2_gcd_1(A,F,C)
                                  & r2_gcd_1(A,F,D) )
                               => r2_gcd_1(A,F,E) ) ) ) ) ) ) ) ) ) )).

fof(t28_gcd_1,axiom,(
    $true )).

fof(t29_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r2_gcd_1(A,E,k5_gcd_1(A,B,C,D))
                       => ( r2_gcd_1(A,E,C)
                          & r2_gcd_1(A,E,D) ) ) ) ) ) ) ) )).

fof(t30_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => k5_gcd_1(A,B,C,D) = k5_gcd_1(A,B,D,C) ) ) ) ) )).

fof(t31_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k5_gcd_1(A,B,C,k1_rlvect_1(A)) = k4_gcd_1(A,B,C)
                & k5_gcd_1(A,B,k1_rlvect_1(A),C) = k4_gcd_1(A,B,C) ) ) ) ) )).

fof(t32_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => k5_gcd_1(A,B,k1_rlvect_1(A),k1_rlvect_1(A)) = k1_rlvect_1(A) ) ) )).

fof(t33_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k5_gcd_1(A,B,C,k2_group_1(A)) = k2_group_1(A)
                & k5_gcd_1(A,B,k2_group_1(A),C) = k2_group_1(A) ) ) ) ) )).

fof(t34_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( k5_gcd_1(A,B,C,D) = k1_rlvect_1(A)
                  <=> ( C = k1_rlvect_1(A)
                      & D = k1_rlvect_1(A) ) ) ) ) ) ) )).

fof(t35_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r4_gcd_1(A,D,E)
                       => ( r4_gcd_1(A,k5_gcd_1(A,B,C,D),k5_gcd_1(A,B,C,E))
                          & r4_gcd_1(A,k5_gcd_1(A,B,D,C),k5_gcd_1(A,B,E,C)) ) ) ) ) ) ) ) )).

fof(t36_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k5_gcd_1(A,B,k5_gcd_1(A,B,C,D),E) = k5_gcd_1(A,B,C,k5_gcd_1(A,B,D,E)) ) ) ) ) ) )).

fof(t37_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => r4_gcd_1(A,k5_gcd_1(A,B,k10_group_1(A,C,E),k10_group_1(A,D,E)),k10_group_1(A,E,k5_gcd_1(A,B,C,D))) ) ) ) ) ) )).

fof(t38_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( k5_gcd_1(A,B,C,D) = k2_group_1(A)
                       => k5_gcd_1(A,B,C,k10_group_1(A,D,E)) = k5_gcd_1(A,B,C,E) ) ) ) ) ) ) )).

fof(t39_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( E = k5_gcd_1(A,B,C,D)
                       => ( E = k1_rlvect_1(A)
                          | k5_gcd_1(A,B,k1_gcd_1(A,C,E),k1_gcd_1(A,D,E)) = k2_group_1(A) ) ) ) ) ) ) ) )).

fof(t40_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => k5_gcd_1(A,B,k4_rlvect_1(A,C,k10_group_1(A,D,E)),E) = k5_gcd_1(A,B,C,E) ) ) ) ) ) )).

fof(t41_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( k5_gcd_1(A,B,C,D) = k2_group_1(A)
                              & k5_gcd_1(A,B,E,F) = k2_group_1(A) )
                           => ( D = k1_rlvect_1(A)
                              | F = k1_rlvect_1(A)
                              | k5_gcd_1(A,B,k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))),k10_group_1(A,D,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F)))) = k5_gcd_1(A,B,k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))),k5_gcd_1(A,B,D,F)) ) ) ) ) ) ) ) ) )).

fof(t42_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( k5_gcd_1(A,B,C,D) = k2_group_1(A)
                              & k5_gcd_1(A,B,E,F) = k2_group_1(A) )
                           => ( D = k1_rlvect_1(A)
                              | F = k1_rlvect_1(A)
                              | k5_gcd_1(A,B,k10_group_1(A,k1_gcd_1(A,C,k5_gcd_1(A,B,C,F)),k1_gcd_1(A,E,k5_gcd_1(A,B,E,D))),k10_group_1(A,k1_gcd_1(A,D,k5_gcd_1(A,B,E,D)),k1_gcd_1(A,F,k5_gcd_1(A,B,C,F)))) = k2_group_1(A) ) ) ) ) ) ) ) ) )).

fof(d13_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v3_gcd_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r5_gcd_1(A,B,C,D)
                  <=> k5_gcd_1(A,B,C,D) = k2_group_1(A) ) ) ) ) ) )).

fof(t43_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m2_gcd_1(C,A)
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( r5_gcd_1(A,B,D,E)
                      <=> r5_gcd_1(A,C,D,E) ) ) ) ) ) ) )).

fof(d14_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v3_gcd_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r6_gcd_1(A,B,C)
              <=> ? [D] :
                    ( m2_gcd_1(D,A)
                    & k5_gcd_1(A,D,B,C) = k2_group_1(A) ) ) ) ) ) )).

fof(t44_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r7_gcd_1(A,C,D)
                   => k5_gcd_1(A,B,C,D) = k2_group_1(A) ) ) ) ) ) )).

fof(d15_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v3_gcd_1(A)
        & l2_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r8_gcd_1(A,B,C,D)
                  <=> ( k5_gcd_1(A,B,C,D) = k2_group_1(A)
                      & r2_hidden(D,B)
                      & D != k1_rlvect_1(A) ) ) ) ) ) ) )).

fof(d16_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r7_gcd_1(A,C,D)
                              & r7_gcd_1(A,E,F)
                              & D = k4_gcd_1(A,B,D)
                              & F = k4_gcd_1(A,B,F) )
                           => ( ( C = k1_rlvect_1(A)
                               => k6_gcd_1(A,B,C,D,E,F) = E )
                              & ( E = k1_rlvect_1(A)
                               => k6_gcd_1(A,B,C,D,E,F) = C )
                              & ( k5_gcd_1(A,B,D,F) = k2_group_1(A)
                               => k6_gcd_1(A,B,C,D,E,F) = k4_rlvect_1(A,k10_group_1(A,C,F),k10_group_1(A,D,E)) )
                              & ( k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))) = k1_rlvect_1(A)
                               => k6_gcd_1(A,B,C,D,E,F) = k1_rlvect_1(A) )
                              & ~ ( C != k1_rlvect_1(A)
                                  & E != k1_rlvect_1(A)
                                  & k5_gcd_1(A,B,D,F) != k2_group_1(A)
                                  & k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))) != k1_rlvect_1(A)
                                  & k6_gcd_1(A,B,C,D,E,F) != k1_gcd_1(A,k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))),k5_gcd_1(A,B,k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))),k5_gcd_1(A,B,D,F))) ) ) ) ) ) ) ) ) ) )).

fof(d17_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r7_gcd_1(A,C,D)
                              & r7_gcd_1(A,E,F)
                              & D = k4_gcd_1(A,B,D)
                              & F = k4_gcd_1(A,B,F) )
                           => ( ( C = k1_rlvect_1(A)
                               => k7_gcd_1(A,B,C,D,E,F) = F )
                              & ( E = k1_rlvect_1(A)
                               => k7_gcd_1(A,B,C,D,E,F) = D )
                              & ( k5_gcd_1(A,B,D,F) = k2_group_1(A)
                               => k7_gcd_1(A,B,C,D,E,F) = k10_group_1(A,D,F) )
                              & ( k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))) = k1_rlvect_1(A)
                               => k7_gcd_1(A,B,C,D,E,F) = k2_group_1(A) )
                              & ~ ( C != k1_rlvect_1(A)
                                  & E != k1_rlvect_1(A)
                                  & k5_gcd_1(A,B,D,F) != k2_group_1(A)
                                  & k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))) != k1_rlvect_1(A)
                                  & k7_gcd_1(A,B,C,D,E,F) != k1_gcd_1(A,k10_group_1(A,D,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k5_gcd_1(A,B,k4_rlvect_1(A,k10_group_1(A,C,k1_gcd_1(A,F,k5_gcd_1(A,B,D,F))),k10_group_1(A,E,k1_gcd_1(A,D,k5_gcd_1(A,B,D,F)))),k5_gcd_1(A,B,D,F))) ) ) ) ) ) ) ) ) ) )).

fof(t45_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( v2_gcd_1(B,A)
                              & r8_gcd_1(A,B,C,D)
                              & r8_gcd_1(A,B,E,F) )
                           => r8_gcd_1(A,B,k6_gcd_1(A,B,C,D,E,F),k7_gcd_1(A,B,C,D,E,F)) ) ) ) ) ) ) ) )).

fof(t46_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( v2_gcd_1(B,A)
                              & r8_gcd_1(A,B,C,D)
                              & r8_gcd_1(A,B,E,F) )
                           => k10_group_1(A,k6_gcd_1(A,B,C,D,E,F),k10_group_1(A,D,F)) = k10_group_1(A,k7_gcd_1(A,B,C,D,E,F),k4_rlvect_1(A,k10_group_1(A,C,F),k10_group_1(A,E,D))) ) ) ) ) ) ) ) )).

fof(d18_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( ( C = k1_rlvect_1(A)
                                | E = k1_rlvect_1(A) )
                             => k8_gcd_1(A,B,C,D,E,F) = k1_rlvect_1(A) )
                            & ( ( D = k2_group_1(A)
                                & F = k2_group_1(A) )
                             => k8_gcd_1(A,B,C,D,E,F) = k10_group_1(A,C,E) )
                            & ( D = k2_group_1(A)
                             => ( F = k1_rlvect_1(A)
                                | k8_gcd_1(A,B,C,D,E,F) = k1_gcd_1(A,k10_group_1(A,C,E),k5_gcd_1(A,B,C,F)) ) )
                            & ( F = k2_group_1(A)
                             => ( D = k1_rlvect_1(A)
                                | k8_gcd_1(A,B,C,D,E,F) = k1_gcd_1(A,k10_group_1(A,C,E),k5_gcd_1(A,B,E,D)) ) )
                            & ~ ( C != k1_rlvect_1(A)
                                & E != k1_rlvect_1(A)
                                & ~ ( D = k2_group_1(A)
                                    & F = k2_group_1(A) )
                                & ~ ( F != k1_rlvect_1(A)
                                    & D = k2_group_1(A) )
                                & ~ ( D != k1_rlvect_1(A)
                                    & F = k2_group_1(A) )
                                & k8_gcd_1(A,B,C,D,E,F) != k10_group_1(A,k1_gcd_1(A,C,k5_gcd_1(A,B,C,F)),k1_gcd_1(A,E,k5_gcd_1(A,B,E,D))) ) ) ) ) ) ) ) ) )).

fof(d19_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r7_gcd_1(A,C,D)
                              & r7_gcd_1(A,E,F)
                              & D = k4_gcd_1(A,B,D)
                              & F = k4_gcd_1(A,B,F) )
                           => ( ( ( C = k1_rlvect_1(A)
                                  | E = k1_rlvect_1(A) )
                               => k9_gcd_1(A,B,C,D,E,F) = k2_group_1(A) )
                              & ( ( D = k2_group_1(A)
                                  & F = k2_group_1(A) )
                               => k9_gcd_1(A,B,C,D,E,F) = k2_group_1(A) )
                              & ( D = k2_group_1(A)
                               => ( F = k1_rlvect_1(A)
                                  | k9_gcd_1(A,B,C,D,E,F) = k1_gcd_1(A,F,k5_gcd_1(A,B,C,F)) ) )
                              & ( F = k2_group_1(A)
                               => ( D = k1_rlvect_1(A)
                                  | k9_gcd_1(A,B,C,D,E,F) = k1_gcd_1(A,D,k5_gcd_1(A,B,E,D)) ) )
                              & ~ ( C != k1_rlvect_1(A)
                                  & E != k1_rlvect_1(A)
                                  & ~ ( D = k2_group_1(A)
                                      & F = k2_group_1(A) )
                                  & ~ ( F != k1_rlvect_1(A)
                                      & D = k2_group_1(A) )
                                  & ~ ( D != k1_rlvect_1(A)
                                      & F = k2_group_1(A) )
                                  & k9_gcd_1(A,B,C,D,E,F) != k10_group_1(A,k1_gcd_1(A,D,k5_gcd_1(A,B,E,D)),k1_gcd_1(A,F,k5_gcd_1(A,B,C,F))) ) ) ) ) ) ) ) ) ) )).

fof(t47_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( v2_gcd_1(B,A)
                              & r8_gcd_1(A,B,C,D)
                              & r8_gcd_1(A,B,E,F) )
                           => r8_gcd_1(A,B,k8_gcd_1(A,B,C,D,E,F),k9_gcd_1(A,B,C,D,E,F)) ) ) ) ) ) ) ) )).

fof(t48_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( v2_gcd_1(B,A)
                              & r8_gcd_1(A,B,C,D)
                              & r8_gcd_1(A,B,E,F) )
                           => k10_group_1(A,k8_gcd_1(A,B,C,D,E,F),k10_group_1(A,D,F)) = k10_group_1(A,k9_gcd_1(A,B,C,D,E,F),k10_group_1(A,C,E)) ) ) ) ) ) ) ) )).

fof(t49_gcd_1,axiom,(
    $true )).

fof(t50_gcd_1,axiom,(
    $true )).

fof(t51_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_group_1(A,k5_rlvect_1(A,B),C) = k5_rlvect_1(A,k1_group_1(A,B,C))
                & k1_group_1(A,B,k5_rlvect_1(A,C)) = k5_rlvect_1(A,k1_group_1(A,B,C)) ) ) ) ) )).

fof(t52_gcd_1,axiom,(
    $true )).

fof(t53_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( B != k1_rlvect_1(A)
                  & C != k1_rlvect_1(A)
                  & k10_group_1(A,k4_vectsp_1(A,B),k4_vectsp_1(A,C)) != k4_vectsp_1(A,k10_group_1(A,C,B)) ) ) ) ) )).

fof(dt_m1_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m1_gcd_1(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(existence_m1_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ? [B] : m1_gcd_1(B,A) ) )).

fof(dt_m2_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ! [B] :
          ( m2_gcd_1(B,A)
         => ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(existence_m2_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A) )
     => ? [B] : m2_gcd_1(B,A) ) )).

fof(reflexivity_r2_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r2_gcd_1(A,B,B) ) )).

fof(redefinition_r2_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r2_gcd_1(A,B,C)
      <=> r1_gcd_1(A,B,C) ) ) )).

fof(symmetry_r3_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r3_gcd_1(A,B,C)
       => r3_gcd_1(A,C,B) ) ) )).

fof(symmetry_r4_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r4_gcd_1(A,B,C)
       => r4_gcd_1(A,C,B) ) ) )).

fof(reflexivity_r4_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => r4_gcd_1(A,B,B) ) )).

fof(redefinition_r4_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & l1_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r4_gcd_1(A,B,C)
      <=> r3_gcd_1(A,B,C) ) ) )).

fof(symmetry_r7_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r7_gcd_1(A,B,C)
       => r7_gcd_1(A,C,B) ) ) )).

fof(redefinition_r7_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r7_gcd_1(A,B,C)
      <=> r6_gcd_1(A,B,C) ) ) )).

fof(dt_k1_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v2_vectsp_2(A)
        & l3_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_gcd_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k2_gcd_1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k2_gcd_1(A,B),k1_zfmisc_1(u1_struct_0(A))) ) )).

fof(dt_k3_gcd_1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_vectsp_1(A) )
     => m1_subset_1(k3_gcd_1(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) )).

fof(dt_k4_gcd_1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & l1_vectsp_1(A)
        & m2_gcd_1(B,A)
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k4_gcd_1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k5_gcd_1,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v2_group_1(A)
        & v4_group_1(A)
        & v3_gcd_1(A)
        & l1_vectsp_1(A)
        & m2_gcd_1(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k5_gcd_1(A,B,C,D),u1_struct_0(A)) ) )).

fof(dt_k6_gcd_1,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)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A)
        & m2_gcd_1(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A))
        & m1_subset_1(F,u1_struct_0(A)) )
     => m1_subset_1(k6_gcd_1(A,B,C,D,E,F),u1_struct_0(A)) ) )).

fof(dt_k7_gcd_1,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)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A)
        & m2_gcd_1(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A))
        & m1_subset_1(F,u1_struct_0(A)) )
     => m1_subset_1(k7_gcd_1(A,B,C,D,E,F),u1_struct_0(A)) ) )).

fof(dt_k8_gcd_1,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)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A)
        & m2_gcd_1(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A))
        & m1_subset_1(F,u1_struct_0(A)) )
     => m1_subset_1(k8_gcd_1(A,B,C,D,E,F),u1_struct_0(A)) ) )).

fof(dt_k9_gcd_1,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)
        & v7_group_1(A)
        & v6_vectsp_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & v2_vectsp_2(A)
        & v3_gcd_1(A)
        & l3_vectsp_1(A)
        & m2_gcd_1(B,A)
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A))
        & m1_subset_1(F,u1_struct_0(A)) )
     => m1_subset_1(k9_gcd_1(A,B,C,D,E,F),u1_struct_0(A)) ) )).
%------------------------------------------------------------------------------