SET007 Axioms: SET007+236.ax


%------------------------------------------------------------------------------
% File     : SET007+236 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Transformations in 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    : transgeo [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :  134 (  24 unit)
%            Number of atoms       : 1406 (  82 equality)
%            Maximal formula depth :   25 (   9 average)
%            Number of connectives : 1479 ( 207 ~  ;  23  |; 738  &)
%                                         (  30 <=>; 481 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   39 (   1 propositional; 0-5 arity)
%            Number of functors    :   16 (   1 constant; 0-4 arity)
%            Number of variables   :  423 (   0 singleton; 417 !;   6 ?)
%            Maximal term depth    :    4 (   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_transgeo,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_analoaf(A)
      & v1_transgeo(A) ) )).

fof(t1_transgeo,axiom,(
    $true )).

fof(t2_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ? [D] :
                  ( m1_subset_1(D,A)
                  & k8_funct_2(A,A,C,D) = B ) ) ) ) )).

fof(t3_transgeo,axiom,(
    $true )).

fof(t4_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( m1_subset_1(C,A)
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & v3_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => ( k8_funct_2(A,A,D,B) = C
                  <=> k8_funct_2(A,A,k6_funct_2(A,D),C) = B ) ) ) ) ) )).

fof(d1_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => k2_transgeo(A,B,C) = k1_transgeo(A,k6_funct_2(A,C),k1_transgeo(A,B,C)) ) ) ) )).

fof(t5_transgeo,axiom,(
    $true )).

fof(t6_transgeo,axiom,(
    $true )).

fof(t7_transgeo,axiom,(
    $true )).

fof(t8_transgeo,axiom,(
    $true )).

fof(t9_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ( k8_funct_2(A,A,C,k8_funct_2(A,A,k6_funct_2(A,C),B)) = B
                & k8_funct_2(A,A,k6_funct_2(A,C),k8_funct_2(A,A,C,B)) = B ) ) ) ) )).

fof(t10_transgeo,axiom,(
    $true )).

fof(t11_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => k1_transgeo(A,k6_partfun1(A),B) = k1_transgeo(A,B,k6_partfun1(A)) ) ) )).

fof(t12_transgeo,axiom,(
    $true )).

fof(t13_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & v3_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => ( ( k1_transgeo(A,C,B) = k1_transgeo(A,C,D)
                      | k1_transgeo(A,B,C) = k1_transgeo(A,D,C) )
                   => B = D ) ) ) ) ) )).

fof(t14_transgeo,axiom,(
    $true )).

fof(t15_transgeo,axiom,(
    $true )).

fof(t16_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & v3_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => k2_transgeo(A,k1_transgeo(A,C,B),D) = k1_transgeo(A,k2_transgeo(A,C,D),k2_transgeo(A,B,D)) ) ) ) ) )).

fof(t17_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => k2_transgeo(A,k6_funct_2(A,B),C) = k6_funct_2(A,k2_transgeo(A,B,C)) ) ) ) )).

fof(t18_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & v3_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => k2_transgeo(A,B,k1_transgeo(A,D,C)) = k2_transgeo(A,k2_transgeo(A,B,D),C) ) ) ) ) )).

fof(t19_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => k2_transgeo(A,k6_partfun1(A),B) = k6_partfun1(A) ) ) )).

fof(t20_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => k2_transgeo(A,B,k6_partfun1(A)) = B ) ) )).

fof(t21_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m1_subset_1(B,A)
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,A,A)
                    & v3_funct_2(D,A,A)
                    & m2_relset_1(D,A,A) )
                 => ( k8_funct_2(A,A,C,B) = B
                   => k8_funct_2(A,A,k2_transgeo(A,C,D),k8_funct_2(A,A,D,B)) = k8_funct_2(A,A,D,B) ) ) ) ) ) )).

fof(d2_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
             => ( r1_transgeo(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => r2_hidden(k4_tarski(k4_tarski(D,E),k4_tarski(k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E))),C) ) ) ) ) ) ) )).

fof(t22_transgeo,axiom,(
    $true )).

fof(t23_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
         => ( r1_relat_2(B,k2_zfmisc_1(A,A))
           => r1_transgeo(A,k6_partfun1(A),B) ) ) ) )).

fof(t24_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
             => ( ( r3_relat_2(C,k2_zfmisc_1(A,A))
                  & r1_transgeo(A,B,C) )
               => r1_transgeo(A,k6_funct_2(A,B),C) ) ) ) ) )).

fof(t25_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
                 => ( ( r8_relat_2(D,k2_zfmisc_1(A,A))
                      & r1_transgeo(A,B,D)
                      & r1_transgeo(A,C,D) )
                   => r1_transgeo(A,k1_transgeo(A,C,B),D) ) ) ) ) ) )).

fof(t26_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
                 => ( ( ! [E] :
                          ( m1_subset_1(E,A)
                         => ! [F] :
                              ( m1_subset_1(F,A)
                             => ! [G] :
                                  ( m1_subset_1(G,A)
                                 => ! [H] :
                                      ( m1_subset_1(H,A)
                                     => ! [I] :
                                          ( m1_subset_1(I,A)
                                         => ! [J] :
                                              ( m1_subset_1(J,A)
                                             => ( ( r2_hidden(k4_tarski(k4_tarski(G,H),k4_tarski(E,F)),D)
                                                  & r2_hidden(k4_tarski(k4_tarski(E,F),k4_tarski(I,J)),D) )
                                               => ( E = F
                                                  | r2_hidden(k4_tarski(k4_tarski(G,H),k4_tarski(I,J)),D) ) ) ) ) ) ) ) )
                      & ! [E] :
                          ( m1_subset_1(E,A)
                         => ! [F] :
                              ( m1_subset_1(F,A)
                             => ! [G] :
                                  ( m1_subset_1(G,A)
                                 => r2_hidden(k4_tarski(k4_tarski(E,E),k4_tarski(F,G)),D) ) ) )
                      & r1_transgeo(A,B,D)
                      & r1_transgeo(A,C,D) )
                   => r1_transgeo(A,k1_transgeo(A,C,B),D) ) ) ) ) ) )).

fof(d3_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
             => ( r2_transgeo(A,B,C)
              <=> ! [D] :
                    ( m1_subset_1(D,A)
                   => ! [E] :
                        ( m1_subset_1(E,A)
                       => ! [F] :
                            ( m1_subset_1(F,A)
                           => ! [G] :
                                ( m1_subset_1(G,A)
                               => ( r2_hidden(k4_tarski(k4_tarski(D,E),k4_tarski(F,G)),C)
                                <=> r2_hidden(k4_tarski(k4_tarski(k8_funct_2(A,A,B,D),k8_funct_2(A,A,B,E)),k4_tarski(k8_funct_2(A,A,B,F),k8_funct_2(A,A,B,G))),C) ) ) ) ) ) ) ) ) ) )).

fof(t27_transgeo,axiom,(
    $true )).

fof(t28_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( m2_relset_1(B,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
         => r2_transgeo(A,k6_partfun1(A),B) ) ) )).

fof(t29_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
             => ( r2_transgeo(A,B,C)
               => r2_transgeo(A,k6_funct_2(A,B),C) ) ) ) ) )).

fof(t30_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
                 => ( ( r2_transgeo(A,B,D)
                      & r2_transgeo(A,C,D) )
                   => r2_transgeo(A,k1_transgeo(A,B,C),D) ) ) ) ) ) )).

fof(t31_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
             => ( ( r3_relat_2(C,k2_zfmisc_1(A,A))
                  & r8_relat_2(C,k2_zfmisc_1(A,A))
                  & r1_transgeo(A,B,C) )
               => r2_transgeo(A,B,C) ) ) ) ) )).

fof(t32_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( m2_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
             => ( ( ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => ! [F] :
                              ( m1_subset_1(F,A)
                             => ! [G] :
                                  ( m1_subset_1(G,A)
                                 => ! [H] :
                                      ( m1_subset_1(H,A)
                                     => ! [I] :
                                          ( m1_subset_1(I,A)
                                         => ( ( r2_hidden(k4_tarski(k4_tarski(F,G),k4_tarski(D,E)),C)
                                              & r2_hidden(k4_tarski(k4_tarski(D,E),k4_tarski(H,I)),C) )
                                           => ( D = E
                                              | r2_hidden(k4_tarski(k4_tarski(F,G),k4_tarski(H,I)),C) ) ) ) ) ) ) ) )
                  & ! [D] :
                      ( m1_subset_1(D,A)
                     => ! [E] :
                          ( m1_subset_1(E,A)
                         => ! [F] :
                              ( m1_subset_1(F,A)
                             => r2_hidden(k4_tarski(k4_tarski(D,D),k4_tarski(E,F)),C) ) ) )
                  & r3_relat_2(C,k2_zfmisc_1(A,A))
                  & r1_transgeo(A,B,C) )
               => r2_transgeo(A,B,C) ) ) ) ) )).

fof(t33_transgeo,axiom,(
    ! [A] :
      ( ~ v1_xboole_0(A)
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,A,A)
            & v3_funct_2(B,A,A)
            & m2_relset_1(B,A,A) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,A)
                & v3_funct_2(C,A,A)
                & m2_relset_1(C,A,A) )
             => ! [D] :
                  ( m2_relset_1(D,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A))
                 => ( ( r1_transgeo(A,B,D)
                      & r2_transgeo(A,C,D) )
                   => r1_transgeo(A,k2_transgeo(A,B,C),D) ) ) ) ) ) )).

fof(d4_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r3_transgeo(A,B)
          <=> r1_transgeo(u1_struct_0(A),B,u1_analoaf(A)) ) ) ) )).

fof(t34_transgeo,axiom,(
    $true )).

fof(t35_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r3_transgeo(A,B)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_analoaf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) )).

fof(d5_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v1_transgeo(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))
                                 => ( ( r2_analoaf(A,B,C,F,G)
                                      & r2_analoaf(A,F,G,D,E) )
                                   => ( F = G
                                      | r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) )
          & ! [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_analoaf(A,B,B,C,D) ) ) )
          & ! [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_analoaf(A,B,C,D,E)
                           => r2_analoaf(A,D,E,B,C) ) ) ) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => r2_analoaf(A,B,C,B,C) ) ) ) ) ) )).

fof(t36_transgeo,axiom,(
    $true )).

fof(t37_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_transgeo(A)
        & l1_analoaf(A) )
     => r3_transgeo(A,k6_partfun1(u1_struct_0(A))) ) )).

fof(t38_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_transgeo(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( r3_transgeo(A,B)
           => r3_transgeo(A,k6_funct_2(u1_struct_0(A),B)) ) ) ) )).

fof(t39_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v1_transgeo(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( r3_transgeo(A,B)
                  & r3_transgeo(A,C) )
               => r3_transgeo(A,k1_transgeo(u1_struct_0(A),C,B)) ) ) ) ) )).

fof(t40_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v1_transgeo(A) ) )).

fof(d6_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v2_transgeo(B,A)
          <=> r3_transgeo(A,B) ) ) ) )).

fof(t41_transgeo,axiom,(
    $true )).

fof(t42_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v2_transgeo(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_analoaf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) )).

fof(d7_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v3_transgeo(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_analoaf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C)) ) ) ) ) ) )).

fof(t43_transgeo,axiom,(
    $true )).

fof(t44_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v2_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).

fof(t45_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v2_transgeo(B,A)
           => v2_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) )).

fof(t46_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( v2_transgeo(B,A)
                  & v2_transgeo(C,A) )
               => v2_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) )).

fof(t47_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ~ ( v3_transgeo(B,A)
              & v2_transgeo(B,A) ) ) ) )).

fof(t48_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v3_transgeo(B,A)
           => v3_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) )).

fof(t49_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( v2_transgeo(B,A)
                  & v3_transgeo(C,A) )
               => ( v3_transgeo(k1_transgeo(u1_struct_0(A),C,B),A)
                  & v3_transgeo(k1_transgeo(u1_struct_0(A),B,C),A) ) ) ) ) ) )).

fof(d8_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v4_transgeo(B,A)
          <=> r1_transgeo(u1_struct_0(A),B,k1_diraf(u1_struct_0(A),u1_analoaf(A))) ) ) ) )).

fof(t50_transgeo,axiom,(
    $true )).

fof(t51_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v4_transgeo(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_diraf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) )).

fof(t52_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( ( v2_transgeo(B,A)
              | v3_transgeo(B,A) )
           => v4_transgeo(B,A) ) ) ) )).

fof(t53_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ~ ( v4_transgeo(B,A)
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
                    & v3_funct_2(C,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
                    & m2_relset_1(C,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A))) )
                 => ~ ( B = C
                      & r3_transgeo(k2_diraf(A),C) ) ) ) ) ) )).

fof(t54_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
            & v3_funct_2(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A)))
            & m2_relset_1(B,u1_struct_0(k2_diraf(A)),u1_struct_0(k2_diraf(A))) )
         => ~ ( r3_transgeo(k2_diraf(A),B)
              & ! [C] :
                  ( ( v1_funct_1(C)
                    & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => ~ ( B = C
                      & v4_transgeo(C,A) ) ) ) ) ) )).

fof(t55_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => v4_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).

fof(t56_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v4_transgeo(B,A)
           => v4_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) )).

fof(t57_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( v4_transgeo(B,A)
                  & v4_transgeo(C,A) )
               => v4_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) )).

fof(t58_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v4_transgeo(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))
                           => ( r2_diraf(A,C,D,E,F)
                            <=> r2_diraf(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F)) ) ) ) ) ) ) ) ) )).

fof(t59_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v4_transgeo(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))
                       => ( r3_diraf(A,C,D,E)
                        <=> r3_diraf(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)) ) ) ) ) ) ) ) )).

fof(t60_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( ( v4_transgeo(D,A)
                      & r3_diraf(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C) )
                   => r3_diraf(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) ) ) ) ) ) )).

fof(t61_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(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_diraf(A,B,C,D,E)
                          & ~ r2_diraf(A,B,D,C,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r3_diraf(A,B,D,F)
                                  & r3_diraf(A,C,E,F) ) ) ) ) ) ) ) ) )).

fof(t62_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v4_transgeo(B,A)
           => ( ( B = k6_partfun1(u1_struct_0(A))
                | ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) != C ) )
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r2_diraf(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ) )).

fof(t63_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(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] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ( ( v4_transgeo(E,A)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) = C )
                       => ( r3_diraf(A,B,C,D)
                          | k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D) = D ) ) ) ) ) ) ) )).

fof(t64_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( ( v4_transgeo(D,A)
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = B
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = C )
                   => ( B = C
                      | D = k6_partfun1(u1_struct_0(A)) ) ) ) ) ) ) )).

fof(t65_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ~ ( v4_transgeo(D,A)
                          & v4_transgeo(E,A)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C)
                          & B != C
                          & D != E ) ) ) ) ) ) )).

fof(d9_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v5_transgeo(B,A)
          <=> ( v4_transgeo(B,A)
              & ( B = k6_partfun1(u1_struct_0(A))
                | ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => C != k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) ) ) ) ) ) ) )).

fof(t66_transgeo,axiom,(
    $true )).

fof(t67_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v4_transgeo(B,A)
           => ( v5_transgeo(B,A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r2_diraf(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ) )).

fof(t68_transgeo,axiom,(
    $true )).

fof(t69_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ( ( v5_transgeo(D,A)
                          & v5_transgeo(E,A)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) )
                       => ( r3_diraf(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C)
                          | k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) ) ) ) ) ) ) ) )).

fof(t70_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( ( v5_transgeo(C,A)
                      & v5_transgeo(D,A)
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) )
                   => C = D ) ) ) ) ) )).

fof(t71_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v5_transgeo(B,A)
           => v5_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) )).

fof(t72_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( v5_transgeo(B,A)
                  & v5_transgeo(C,A) )
               => v5_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) )).

fof(t73_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v5_transgeo(B,A)
           => v2_transgeo(B,A) ) ) ) )).

fof(t74_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(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] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ( ( v4_transgeo(E,A)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
                          & r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C)) )
                       => ( r3_diraf(A,B,C,D)
                          | r1_diraf(A,D,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) )).

fof(t75_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(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] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ( ( v4_transgeo(E,A)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
                          & r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C)) )
                       => ( C = B
                          | r1_diraf(A,D,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) )).

fof(t76_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(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] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(A),u1_struct_0(A))
                            & v3_funct_2(F,u1_struct_0(A),u1_struct_0(A))
                            & m2_relset_1(F,u1_struct_0(A),u1_struct_0(A)) )
                         => ( ( v4_transgeo(F,A)
                              & k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,B) = B
                              & r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,C)) )
                           => ( C = B
                              | r3_diraf(A,B,D,E)
                              | r2_analoaf(A,D,E,k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,D)) ) ) ) ) ) ) ) ) )).

fof(t77_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(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] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(A),u1_struct_0(A))
                            & v3_funct_2(F,u1_struct_0(A),u1_struct_0(A))
                            & m2_relset_1(F,u1_struct_0(A),u1_struct_0(A)) )
                         => ( ( v4_transgeo(F,A)
                              & k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,B) = B
                              & r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,C))
                              & r3_diraf(A,B,D,E) )
                           => ( C = B
                              | r2_analoaf(A,D,E,k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),F,D)) ) ) ) ) ) ) ) ) )).

fof(t78_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( ( v4_transgeo(D,A)
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = B
                      & r1_diraf(A,C,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) )
                   => ( C = B
                      | v3_transgeo(D,A) ) ) ) ) ) ) )).

fof(t79_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( v4_transgeo(C,A)
                  & k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,B) = B
                  & ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r2_analoaf(A,B,D,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D)) ) )
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => r2_analoaf(A,D,E,k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E)) ) ) ) ) ) ) )).

fof(t80_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ~ ( v4_transgeo(B,A)
              & ~ v2_transgeo(B,A)
              & ~ v3_transgeo(B,A) ) ) ) )).

fof(t81_transgeo,axiom,(
    $true )).

fof(t82_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => v1_transgeo(A) ) )).

fof(t83_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & v1_transgeo(k2_diraf(A))
        & l1_analoaf(k2_diraf(A)) ) ) )).

fof(d10_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v6_transgeo(B,A)
          <=> r3_transgeo(A,B) ) ) ) )).

fof(t84_transgeo,axiom,(
    $true )).

fof(t85_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v6_transgeo(B,A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => r2_analoaf(A,C,D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) )).

fof(t86_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => v6_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).

fof(t87_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v6_transgeo(B,A)
           => v6_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) )).

fof(t88_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( v6_transgeo(B,A)
                  & v6_transgeo(C,A) )
               => v6_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) )).

fof(t89_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v6_transgeo(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))
                           => ( r2_analoaf(A,C,D,E,F)
                            <=> r2_analoaf(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F)) ) ) ) ) ) ) ) ) )).

fof(t90_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v6_transgeo(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))
                       => ( r1_aff_1(A,C,D,E)
                        <=> r1_aff_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E)) ) ) ) ) ) ) ) )).

fof(t91_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( ( v6_transgeo(D,A)
                      & r1_aff_1(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C) )
                   => r1_aff_1(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) ) ) ) ) ) )).

fof(t92_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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_analoaf(A,B,C,D,E)
                          & ~ r2_analoaf(A,B,D,C,E)
                          & ! [F] :
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_aff_1(A,B,D,F)
                                  & r1_aff_1(A,C,E,F) ) ) ) ) ) ) ) ) )).

fof(t93_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v6_transgeo(B,A)
           => ( ( B = k6_partfun1(u1_struct_0(A))
                | ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) != C ) )
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r2_analoaf(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ) )).

fof(t94_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ( ( v6_transgeo(E,A)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) = B
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) = C )
                       => ( r1_aff_1(A,B,C,D)
                          | k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D) = D ) ) ) ) ) ) ) )).

fof(t95_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( ( v6_transgeo(D,A)
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = B
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = C )
                   => ( B = C
                      | D = k6_partfun1(u1_struct_0(A)) ) ) ) ) ) ) )).

fof(t96_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ~ ( v6_transgeo(D,A)
                          & v6_transgeo(E,A)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C)
                          & B != C
                          & D != E ) ) ) ) ) ) )).

fof(t97_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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))
                         => ( ( r2_analoaf(A,B,C,D,E)
                              & r2_analoaf(A,B,C,D,F)
                              & r2_analoaf(A,B,D,C,E)
                              & r2_analoaf(A,B,D,C,F) )
                           => ( r1_aff_1(A,B,C,D)
                              | E = F ) ) ) ) ) ) ) ) )).

fof(d11_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v7_transgeo(B,A)
          <=> ( v6_transgeo(B,A)
              & ( B = k6_partfun1(u1_struct_0(A))
                | ! [C] :
                    ( m1_subset_1(C,u1_struct_0(A))
                   => C != k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) ) ) ) ) ) ) )).

fof(t98_transgeo,axiom,(
    $true )).

fof(t99_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => v7_transgeo(k6_partfun1(u1_struct_0(A)),A) ) )).

fof(t100_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v6_transgeo(B,A)
           => ( v7_transgeo(B,A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] :
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r2_analoaf(A,C,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),D,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) ) )).

fof(t101_transgeo,axiom,(
    $true )).

fof(t102_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ( ( v7_transgeo(D,A)
                          & v7_transgeo(E,A)
                          & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B) )
                       => ( r1_aff_1(A,B,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),C)
                          | k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C) ) ) ) ) ) ) ) )).

fof(t103_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( ( v7_transgeo(C,A)
                      & v7_transgeo(D,A)
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B) )
                   => C = D ) ) ) ) ) )).

fof(t104_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v7_transgeo(B,A)
           => v7_transgeo(k6_funct_2(u1_struct_0(A),B),A) ) ) ) )).

fof(t105_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( v7_transgeo(B,A)
                  & v7_transgeo(C,A) )
               => v7_transgeo(k1_transgeo(u1_struct_0(A),C,B),A) ) ) ) ) )).

fof(d12_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v8_transgeo(B,A)
          <=> r2_transgeo(u1_struct_0(A),B,u1_analoaf(A)) ) ) ) )).

fof(t106_transgeo,axiom,(
    $true )).

fof(t107_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v8_transgeo(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))
                           => ( r2_analoaf(A,C,D,E,F)
                            <=> r2_analoaf(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,D),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,E),k8_funct_2(u1_struct_0(A),u1_struct_0(A),B,F)) ) ) ) ) ) ) ) ) )).

fof(t108_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & v3_funct_2(E,u1_struct_0(A),u1_struct_0(A))
                        & m2_relset_1(E,u1_struct_0(A),u1_struct_0(A)) )
                     => ( v8_transgeo(E,A)
                       => ( r1_aff_1(A,B,C,D)
                        <=> r1_aff_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,B),k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,C),k8_funct_2(u1_struct_0(A),u1_struct_0(A),E,D)) ) ) ) ) ) ) ) )).

fof(t109_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( ( v8_transgeo(B,A)
                  & v8_transgeo(C,A) )
               => ( v8_transgeo(k6_funct_2(u1_struct_0(A),B),A)
                  & v8_transgeo(k1_transgeo(u1_struct_0(A),C,B),A)
                  & v8_transgeo(k6_partfun1(u1_struct_0(A)),A) ) ) ) ) ) )).

fof(t110_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_hidden(B,D)
                   => r2_hidden(k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,B),k2_funct_2(u1_struct_0(A),u1_struct_0(A),C,D)) ) ) ) ) ) )).

fof(t111_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & v3_funct_2(C,u1_struct_0(A),u1_struct_0(A))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_hidden(B,k2_funct_2(u1_struct_0(A),u1_struct_0(A),C,D))
                  <=> ? [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r2_hidden(E,D)
                        & k8_funct_2(u1_struct_0(A),u1_struct_0(A),C,E) = B ) ) ) ) ) ) )).

fof(t112_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,C) = k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)
                   => C = D ) ) ) ) ) )).

fof(t113_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( v8_transgeo(D,A)
                   => k2_funct_2(u1_struct_0(A),u1_struct_0(A),D,k2_aff_1(A,B,C)) = k2_aff_1(A,k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,B),k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C)) ) ) ) ) ) )).

fof(t114_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v8_transgeo(B,A)
                  & v1_aff_1(C,A) )
               => v1_aff_1(k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),A) ) ) ) ) )).

fof(t115_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] :
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v8_transgeo(B,A)
                      & r4_aff_1(A,C,D) )
                   => r4_aff_1(A,k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,D)) ) ) ) ) ) )).

fof(t116_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & v3_funct_2(B,u1_struct_0(A),u1_struct_0(A))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( ! [C] :
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( v1_aff_1(C,A)
                 => v1_aff_1(k2_funct_2(u1_struct_0(A),u1_struct_0(A),B,C),A) ) )
           => v8_transgeo(B,A) ) ) ) )).

fof(t117_transgeo,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & v3_funct_2(D,u1_struct_0(A),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ( ( v8_transgeo(D,A)
                      & v1_aff_1(B,A)
                      & ! [E] :
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_hidden(E,B)
                           => k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,E) = E ) )
                      & k8_funct_2(u1_struct_0(A),u1_struct_0(A),D,C) = C )
                   => ( r2_hidden(C,B)
                      | D = k6_partfun1(u1_struct_0(A)) ) ) ) ) ) ) )).

fof(s1_transgeo,axiom,
    ( ( ! [A] :
          ( m1_subset_1(A,f1_s1_transgeo)
         => ? [B] :
              ( m1_subset_1(B,f1_s1_transgeo)
              & p1_s1_transgeo(A,B) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_transgeo)
         => ? [B] :
              ( m1_subset_1(B,f1_s1_transgeo)
              & p1_s1_transgeo(B,A) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_transgeo)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_transgeo)
             => ! [C] :
                  ( m1_subset_1(C,f1_s1_transgeo)
                 => ( ( p1_s1_transgeo(A,B)
                      & p1_s1_transgeo(C,B) )
                   => A = C ) ) ) )
      & ! [A] :
          ( m1_subset_1(A,f1_s1_transgeo)
         => ! [B] :
              ( m1_subset_1(B,f1_s1_transgeo)
             => ! [C] :
                  ( m1_subset_1(C,f1_s1_transgeo)
                 => ( ( p1_s1_transgeo(A,B)
                      & p1_s1_transgeo(A,C) )
                   => B = C ) ) ) ) )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s1_transgeo,f1_s1_transgeo)
        & v3_funct_2(A,f1_s1_transgeo,f1_s1_transgeo)
        & m2_relset_1(A,f1_s1_transgeo,f1_s1_transgeo)
        & ! [B] :
            ( m1_subset_1(B,f1_s1_transgeo)
           => ! [C] :
                ( m1_subset_1(C,f1_s1_transgeo)
               => ( k8_funct_2(f1_s1_transgeo,f1_s1_transgeo,A,B) = C
                <=> p1_s1_transgeo(B,C) ) ) ) ) )).

fof(dt_k1_transgeo,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & v3_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v1_funct_1(k1_transgeo(A,B,C))
        & v1_funct_2(k1_transgeo(A,B,C),A,A)
        & v3_funct_2(k1_transgeo(A,B,C),A,A)
        & m2_relset_1(k1_transgeo(A,B,C),A,A) ) ) )).

fof(redefinition_k1_transgeo,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & v3_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => k1_transgeo(A,B,C) = k5_relat_1(B,C) ) )).

fof(dt_k2_transgeo,axiom,(
    ! [A,B,C] :
      ( ( ~ v1_xboole_0(A)
        & v1_funct_1(B)
        & v1_funct_2(B,A,A)
        & v3_funct_2(B,A,A)
        & m1_relset_1(B,A,A)
        & v1_funct_1(C)
        & v1_funct_2(C,A,A)
        & v3_funct_2(C,A,A)
        & m1_relset_1(C,A,A) )
     => ( v1_funct_1(k2_transgeo(A,B,C))
        & v1_funct_2(k2_transgeo(A,B,C),A,A)
        & v3_funct_2(k2_transgeo(A,B,C),A,A)
        & m2_relset_1(k2_transgeo(A,B,C),A,A) ) ) )).
%------------------------------------------------------------------------------