SET007 Axioms: SET007+294.ax


%------------------------------------------------------------------------------
% File     : SET007+294 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Fundamental Types of Metric Affine Spaces
% 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    : euclmetr [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   45 (   1 unit)
%            Number of atoms       :  462 (  22 equality)
%            Maximal formula depth :   26 (  11 average)
%            Number of connectives :  516 (  99 ~  ;   9  |; 260  &)
%                                         (  13 <=>; 135 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   43 (   1 propositional; 0-5 arity)
%            Number of functors    :   12 (   2 constant; 0-3 arity)
%            Number of variables   :  124 (   0 singleton; 122 !;   2 ?)
%            Maximal term depth    :    6 (   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(rc1_euclmetr,axiom,(
    ? [A] :
      ( l1_analmetr(A)
      & ~ v3_struct_0(A)
      & v2_analmetr(A)
      & v3_analmetr(A)
      & v1_euclmetr(A)
      & v2_euclmetr(A)
      & v3_euclmetr(A)
      & v4_euclmetr(A)
      & v5_euclmetr(A)
      & v6_euclmetr(A)
      & v7_euclmetr(A) ) )).

fof(rc2_euclmetr,axiom,(
    ? [A] :
      ( l1_analmetr(A)
      & ~ v3_struct_0(A)
      & v2_analmetr(A)
      & v1_euclmetr(A)
      & v2_euclmetr(A)
      & v3_euclmetr(A)
      & v4_euclmetr(A)
      & v5_euclmetr(A)
      & v6_euclmetr(A)
      & v7_euclmetr(A) ) )).

fof(fc1_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & v2_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A))
        & v2_aff_2(k3_analmetr(A)) ) ) )).

fof(fc2_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & v3_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A))
        & v4_aff_2(k3_analmetr(A)) ) ) )).

fof(fc3_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & v5_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A))
        & v7_aff_2(k3_analmetr(A)) ) ) )).

fof(fc4_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & v6_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A))
        & v11_aff_2(k3_analmetr(A)) ) ) )).

fof(fc5_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & v4_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A))
        & v1_translac(k3_analmetr(A)) ) ) )).

fof(fc6_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & v7_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A))
        & v4_aff_2(k3_analmetr(A)) ) ) )).

fof(fc7_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & v1_euclmetr(A)
        & v3_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_diraf(k3_analmetr(A))
        & v2_aff_2(k3_analmetr(A))
        & v4_aff_2(k3_analmetr(A)) ) ) )).

fof(fc8_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & v2_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v2_aff_2(k3_analmetr(A)) ) ) )).

fof(fc9_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & v3_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v4_aff_2(k3_analmetr(A)) ) ) )).

fof(fc10_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & v5_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v7_aff_2(k3_analmetr(A)) ) ) )).

fof(fc11_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & v6_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v11_aff_2(k3_analmetr(A)) ) ) )).

fof(fc12_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & v4_euclmetr(A)
        & l1_analmetr(A) )
     => ( ~ v3_struct_0(k3_analmetr(A))
        & ~ v3_realset2(k3_analmetr(A))
        & v1_analoaf(k3_analmetr(A))
        & v1_diraf(k3_analmetr(A))
        & v1_translac(k3_analmetr(A)) ) ) )).

fof(d1_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v1_euclmetr(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))
                       => ( ( r5_analmetr(A,B,C,D,E)
                            & r5_analmetr(A,C,D,B,E) )
                         => r5_analmetr(A,C,E,B,D) ) ) ) ) ) ) ) )).

fof(d2_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v2_euclmetr(A)
      <=> v2_aff_2(k3_analmetr(A)) ) ) )).

fof(d3_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v3_euclmetr(A)
      <=> v4_aff_2(k3_analmetr(A)) ) ) )).

fof(d4_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v4_euclmetr(A)
      <=> v1_translac(k3_analmetr(A)) ) ) )).

fof(d5_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v5_euclmetr(A)
      <=> v7_aff_2(k3_analmetr(A)) ) ) )).

fof(d6_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v6_euclmetr(A)
      <=> v11_aff_2(k3_analmetr(A)) ) ) )).

fof(d7_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(A) )
     => ( v7_euclmetr(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))
                       => ! [F] :
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] :
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ( ( r5_analmetr(A,B,C,B,D)
                                        & r5_analmetr(A,B,E,B,F)
                                        & r5_analmetr(A,B,G,B,H)
                                        & r5_analmetr(A,C,E,D,F)
                                        & r5_analmetr(A,C,G,D,H) )
                                     => ( r4_analmetr(A,B,G,B,C)
                                        | r4_analmetr(A,B,C,B,E)
                                        | r5_analmetr(A,E,G,F,H) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t1_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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))
                 => ( ~ r6_analmetr(A,B,C,D)
                   => ( B != C
                      & C != D
                      & B != D ) ) ) ) ) ) )).

fof(t2_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                     => ! [F] :
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( r7_analmetr(A,B,C,F)
                              & r7_analmetr(A,D,E,F) )
                           => ( r4_analmetr(A,B,C,D,E)
                              & r4_analmetr(A,B,C,E,D) ) ) ) ) ) ) ) ) )).

fof(t3_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] :
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( B != C
                          & ( r7_analmetr(A,B,C,E)
                            | r7_analmetr(A,C,B,E) )
                          & ( r7_analmetr(A,B,C,D)
                            | r7_analmetr(A,C,B,D) )
                          & ~ r10_analmetr(A,E,D) ) ) ) ) ) ) )).

fof(t4_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_analmetr(A)
        & l1_analmetr(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))
                 => ( r6_analmetr(A,B,C,D)
                   => ( r6_analmetr(A,B,D,C)
                      & r6_analmetr(A,C,B,D)
                      & r6_analmetr(A,C,D,B)
                      & r6_analmetr(A,D,B,C)
                      & r6_analmetr(A,D,C,B) ) ) ) ) ) ) )).

fof(t5_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                 => ~ ( ~ r6_analmetr(A,B,C,D)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r5_analmetr(A,E,B,C,D)
                              & r5_analmetr(A,E,C,B,D) ) ) ) ) ) ) ) )).

fof(t6_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r5_analmetr(A,E,B,C,D)
                              & r5_analmetr(A,E,C,B,D)
                              & r5_analmetr(A,F,B,C,D)
                              & r5_analmetr(A,F,C,B,D) )
                           => ( r6_analmetr(A,B,C,D)
                              | E = F ) ) ) ) ) ) ) ) )).

fof(t7_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                     => ~ ( r5_analmetr(A,B,C,D,E)
                          & r5_analmetr(A,C,D,B,E)
                          & r6_analmetr(A,B,C,D)
                          & B != D
                          & B != C
                          & C != D ) ) ) ) ) ) )).

fof(t8_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v1_euclmetr(A)
      <=> v3_conaffm(A) ) ) )).

fof(t9_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v7_euclmetr(A)
      <=> v4_conaffm(A) ) ) )).

fof(t10_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v2_euclmetr(A)
      <=> v2_conmetr(A) ) ) )).

fof(t11_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v3_euclmetr(A)
      <=> v1_conaffm(A) ) ) )).

fof(t12_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v5_euclmetr(A)
      <=> v5_conmetr(A) ) ) )).

fof(t13_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v6_euclmetr(A)
      <=> v8_conmetr(A) ) ) )).

fof(t14_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( v7_euclmetr(A)
       => v3_euclmetr(A) ) ) )).

fof(t15_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ( ( v1_euclmetr(A)
          & v3_euclmetr(A) )
       => v2_euclmetr(A) ) ) )).

fof(t16_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r5_analmetr(A,B,C,B,D)
                                  & r5_analmetr(A,B,E,B,F)
                                  & r5_analmetr(A,B,E,B,G)
                                  & r5_analmetr(A,C,E,D,F)
                                  & r5_analmetr(A,C,E,D,G) )
                               => ( r6_analmetr(A,B,C,E)
                                  | B = D
                                  | F = G ) ) ) ) ) ) ) ) ) )).

fof(t17_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                     => ~ ( ~ r6_analmetr(A,B,C,E)
                          & B != D
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r5_analmetr(A,B,E,B,F)
                                  & r5_analmetr(A,C,E,D,F) ) ) ) ) ) ) ) ) )).

fof(t18_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_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))
                     => ! [F] :
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] :
                              ( m1_subset_1(G,k1_numbers)
                             => ~ ( r1_analmetr(A,B,C)
                                  & k1_rlvect_1(A) != D
                                  & k1_rlvect_1(A) != E
                                  & r2_analmetr(A,D,E,B,C)
                                  & D = k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,G))
                                  & ! [H] :
                                      ( m1_subset_1(H,k1_numbers)
                                     => ~ ( H != np__0
                                          & E = k4_rlvect_1(A,k3_rlvect_1(A,B,k4_real_1(H,G)),k3_rlvect_1(A,C,k1_real_1(k4_real_1(H,F)))) ) ) ) ) ) ) ) ) ) ) )).

fof(t19_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_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_analmetr(A,B,C)
                          & k1_rlvect_1(A) != D
                          & k1_rlvect_1(A) != E
                          & r2_analmetr(A,D,E,B,C)
                          & ! [F] :
                              ( m1_subset_1(F,k1_numbers)
                             => ~ ! [G] :
                                    ( m1_subset_1(G,k1_numbers)
                                   => ! [H] :
                                        ( m1_subset_1(H,k1_numbers)
                                       => ( r2_analmetr(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),k4_rlvect_1(A,k3_rlvect_1(A,B,k4_real_1(F,H)),k3_rlvect_1(A,C,k1_real_1(k4_real_1(F,G)))),B,C)
                                          & r2_analmetr(A,k6_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,G),k3_rlvect_1(A,C,H)),D),k6_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,k4_real_1(F,H)),k3_rlvect_1(A,C,k1_real_1(k4_real_1(F,G)))),E),B,C) ) ) ) ) ) ) ) ) ) ) )).

fof(t20_euclmetr,axiom,(
    $true )).

fof(t21_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r1_analmetr(B,C,D)
                      & A = k2_analmetr(B,C,D) )
                   => v5_conaffm(A) ) ) ) ) ) )).

fof(t22_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(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))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ( ( r5_analmetr(A,B,C,B,D)
                                      & r5_analmetr(A,B,E,B,F)
                                      & r5_analmetr(A,B,G,B,H)
                                      & r5_analmetr(A,C,E,D,F)
                                      & r5_analmetr(A,C,G,D,H)
                                      & B = D )
                                   => ( r4_analmetr(A,B,G,B,C)
                                      | r4_analmetr(A,B,C,B,E)
                                      | r5_analmetr(A,E,G,F,H) ) ) ) ) ) ) ) ) ) ) )).

fof(t23_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r1_analmetr(B,C,D)
                      & A = k2_analmetr(B,C,D) )
                   => v7_euclmetr(A) ) ) ) ) ) )).

fof(t24_euclmetr,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_analmetr(A)
        & l1_analmetr(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r1_analmetr(B,C,D)
                      & A = k2_analmetr(B,C,D) )
                   => ( ~ v3_struct_0(A)
                      & v3_analmetr(A)
                      & v1_euclmetr(A)
                      & v2_euclmetr(A)
                      & v3_euclmetr(A)
                      & v4_euclmetr(A)
                      & v5_euclmetr(A)
                      & v6_euclmetr(A)
                      & v7_euclmetr(A)
                      & l1_analmetr(A) ) ) ) ) ) ) )).
%------------------------------------------------------------------------------