SET007 Axioms: SET007+282.ax


%------------------------------------------------------------------------------
% File     : SET007+282 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : A Construction of Analytical Ordered Trapezium 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    : geomtrap [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   94 (   5 unit)
%            Number of atoms       : 1230 ( 114 equality)
%            Maximal formula depth :   42 (  14 average)
%            Number of connectives : 1257 ( 121 ~  ;  16  |; 613  &)
%                                         (  22 <=>; 485 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   34 (   1 propositional; 0-7 arity)
%            Number of functors    :   31 (   3 constant; 0-6 arity)
%            Number of variables   :  479 (   0 singleton; 463 !;  16 ?)
%            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_geomtrap,axiom,(
    ? [A] :
      ( l1_geomtrap(A)
      & v1_geomtrap(A) ) )).

fof(rc2_geomtrap,axiom,(
    ? [A] :
      ( l1_geomtrap(A)
      & ~ v3_struct_0(A)
      & v1_geomtrap(A) ) )).

fof(fc1_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( ~ v3_struct_0(k7_geomtrap(A,B,C))
        & v1_geomtrap(k7_geomtrap(A,B,C)) ) ) )).

fof(fc2_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_geomtrap(A) )
     => ( ~ v3_struct_0(k8_geomtrap(A))
        & v1_analoaf(k8_geomtrap(A)) ) ) )).

fof(rc3_geomtrap,axiom,(
    ? [A] :
      ( l1_geomtrap(A)
      & ~ v3_struct_0(A)
      & v1_geomtrap(A)
      & v2_geomtrap(A) ) )).

fof(rc4_geomtrap,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_analoaf(A)
      & v3_geomtrap(A) ) )).

fof(fc3_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_geomtrap(A)
        & l1_geomtrap(A) )
     => ( ~ v3_struct_0(k8_geomtrap(A))
        & v1_analoaf(k8_geomtrap(A))
        & v3_geomtrap(k8_geomtrap(A)) ) ) )).

fof(rc5_geomtrap,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_analoaf(A)
      & v4_geomtrap(A) ) )).

fof(fc4_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ( ~ v3_struct_0(k2_diraf(A))
        & v1_analoaf(k2_diraf(A))
        & v4_geomtrap(k2_diraf(A)) ) ) )).

fof(rc6_geomtrap,axiom,(
    ? [A] :
      ( l1_analoaf(A)
      & ~ v3_struct_0(A)
      & v1_analoaf(A)
      & v3_geomtrap(A)
      & v5_geomtrap(A) ) )).

fof(fc5_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_geomtrap(A)
        & l1_geomtrap(A) )
     => ( ~ v3_struct_0(k8_geomtrap(A))
        & v1_analoaf(k8_geomtrap(A))
        & v3_geomtrap(k8_geomtrap(A))
        & v5_geomtrap(k8_geomtrap(A)) ) ) )).

fof(d1_geomtrap,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_geomtrap(A,B,C,D,E)
                      <=> ( r1_analoaf(A,B,C,D,E)
                          | r1_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) )).

fof(t1_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ( ~ v3_struct_0(k2_analoaf(A))
                  & ~ v3_realset2(k2_analoaf(A))
                  & v2_analoaf(k2_analoaf(A))
                  & l1_analoaf(k2_analoaf(A)) ) ) ) ) ) )).

fof(t2_geomtrap,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,u1_struct_0(k2_analoaf(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_analoaf(A)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_analoaf(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k2_analoaf(A)))
                                     => ( ( F = B
                                          & G = C
                                          & H = D
                                          & I = E )
                                       => ( r2_analoaf(k2_analoaf(A),F,G,H,I)
                                        <=> r1_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t3_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( r1_analmetr(A,B,C)
                               => ! [H] :
                                    ( m1_subset_1(H,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(k2_diraf(k2_analoaf(A))))
                                               => ( ( H = D
                                                    & I = E
                                                    & J = F
                                                    & K = G )
                                                 => ( r2_analoaf(k2_diraf(k2_analoaf(A)),H,I,J,K)
                                                  <=> r1_geomtrap(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t4_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_analmetr(A,B,C)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k2_analmetr(A,B,C)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(k2_analmetr(A,B,C)))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(k2_analmetr(A,B,C)))
                                             => ( ( H = D
                                                  & I = E
                                                  & J = F
                                                  & K = G )
                                               => ( r4_analmetr(k2_analmetr(A,B,C),H,I,J,K)
                                                <=> r1_geomtrap(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d2_geomtrap,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))
                 => ( D = k1_geomtrap(A,B,C)
                  <=> k4_rlvect_1(A,D,D) = k4_rlvect_1(A,B,C) ) ) ) ) ) )).

fof(t5_geomtrap,axiom,(
    $true )).

fof(t6_geomtrap,axiom,(
    $true )).

fof(t7_geomtrap,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))
                  & k1_geomtrap(A,B,D) = C ) ) ) ) )).

fof(t8_geomtrap,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))
                     => k1_geomtrap(A,k1_geomtrap(A,B,C),k1_geomtrap(A,D,E)) = k1_geomtrap(A,k1_geomtrap(A,B,D),k1_geomtrap(A,C,E)) ) ) ) ) ) )).

fof(t9_geomtrap,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))
                 => ( k1_geomtrap(A,B,C) = k1_geomtrap(A,B,D)
                   => C = D ) ) ) ) ) )).

fof(t10_geomtrap,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))
                 => r1_analoaf(A,B,C,k1_geomtrap(A,D,B),k1_geomtrap(A,D,C)) ) ) ) ) )).

fof(t11_geomtrap,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))
                 => r1_geomtrap(A,B,C,k1_geomtrap(A,D,B),k1_geomtrap(A,D,C)) ) ) ) ) )).

fof(t12_geomtrap,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))
             => ( k3_rlvect_1(A,k6_rlvect_1(A,k1_geomtrap(A,B,C),B),np__2) = k6_rlvect_1(A,C,B)
                & k3_rlvect_1(A,k6_rlvect_1(A,C,k1_geomtrap(A,B,C)),np__2) = k6_rlvect_1(A,C,B) ) ) ) ) )).

fof(t13_geomtrap,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))
             => r1_analoaf(A,B,k1_geomtrap(A,B,C),k1_geomtrap(A,B,C),C) ) ) ) )).

fof(t14_geomtrap,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))
             => ( r1_analoaf(A,B,C,B,k1_geomtrap(A,B,C))
                & r1_analoaf(A,B,C,k1_geomtrap(A,B,C),C) ) ) ) ) )).

fof(t15_geomtrap,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))
                 => ( r1_analoaf(A,B,C,C,D)
                   => r1_analoaf(A,k1_geomtrap(A,B,C),C,C,k1_geomtrap(A,C,D)) ) ) ) ) ) )).

fof(t16_geomtrap,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_analoaf(A,B,C,D,E)
                       => r1_analoaf(A,B,C,k1_geomtrap(A,B,D),k1_geomtrap(A,C,E)) ) ) ) ) ) ) )).

fof(d3_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( r2_geomtrap(A,B,C,D,E,F,G)
                              <=> ( r1_analoaf(A,D,E,F,G)
                                  & r3_analmetr(A,D,E,k1_geomtrap(A,D,E),k1_geomtrap(A,F,G),B,C)
                                  & r3_analmetr(A,F,G,k1_geomtrap(A,D,E),k1_geomtrap(A,F,G),B,C) ) ) ) ) ) ) ) ) ) )).

fof(t17_geomtrap,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)
                       => r2_geomtrap(A,B,C,D,D,E,E) ) ) ) ) ) ) )).

fof(t18_geomtrap,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)
                       => r2_geomtrap(A,B,C,D,E,D,E) ) ) ) ) ) ) )).

fof(t19_geomtrap,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))
                     => ( r2_geomtrap(A,D,E,B,C,C,B)
                       => B = C ) ) ) ) ) ) )).

fof(t20_geomtrap,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,u1_struct_0(A))
                         => ( ( r1_analmetr(A,B,C)
                              & r2_geomtrap(A,B,C,D,E,E,F) )
                           => ( D = E
                              & E = F ) ) ) ) ) ) ) ) )).

fof(t21_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ( ( r1_analmetr(A,B,C)
                                          & r2_geomtrap(A,B,C,D,E,F,G)
                                          & r2_geomtrap(A,B,C,D,E,H,I) )
                                       => ( D = E
                                          | r2_geomtrap(A,B,C,F,G,H,I) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_geomtrap,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,u1_struct_0(A))
                         => ~ ( r1_analmetr(A,B,C)
                              & ! [G] :
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ~ r2_geomtrap(A,B,C,D,E,F,G)
                                    & ~ r2_geomtrap(A,B,C,D,E,G,F) ) ) ) ) ) ) ) ) ) )).

fof(t23_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_analmetr(A,B,C)
                                  & r2_geomtrap(A,B,C,D,E,F,G) )
                               => r2_geomtrap(A,B,C,F,G,D,E) ) ) ) ) ) ) ) ) )).

fof(t24_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_analmetr(A,B,C)
                                  & r2_geomtrap(A,B,C,D,E,F,G) )
                               => r2_geomtrap(A,B,C,E,D,G,F) ) ) ) ) ) ) ) ) )).

fof(t25_geomtrap,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,u1_struct_0(A))
                         => ( ( r1_analmetr(A,B,C)
                              & r2_geomtrap(A,B,C,D,E,D,F) )
                           => E = F ) ) ) ) ) ) ) )).

fof(t26_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ~ ( r1_analmetr(A,B,C)
                                      & r2_geomtrap(A,B,C,D,E,F,G)
                                      & r2_geomtrap(A,B,C,D,E,F,H)
                                      & D != E
                                      & G != H ) ) ) ) ) ) ) ) ) )).

fof(t27_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ( ( r1_analmetr(A,B,C)
                                      & r2_geomtrap(A,B,C,D,E,F,G) )
                                   => ( D = E
                                      | ( ~ r2_geomtrap(A,B,C,D,E,F,H)
                                        & ~ r2_geomtrap(A,B,C,D,E,H,F) )
                                      | G = H ) ) ) ) ) ) ) ) ) ) )).

fof(t28_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_analmetr(A,B,C)
                                  & r2_geomtrap(A,B,C,D,E,F,G) )
                               => r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,D,F),k1_geomtrap(A,E,G)) ) ) ) ) ) ) ) ) )).

fof(t29_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ~ ( r1_analmetr(A,B,C)
                                  & r2_geomtrap(A,B,C,D,E,F,G)
                                  & ~ r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,D,G),k1_geomtrap(A,E,F))
                                  & ~ r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,E,F),k1_geomtrap(A,D,G)) ) ) ) ) ) ) ) ) )).

fof(t30_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(A))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(A))
                                             => ! [L] :
                                                  ( m1_subset_1(L,u1_struct_0(A))
                                                 => ( ( r1_analmetr(A,B,C)
                                                      & D = k1_geomtrap(A,E,I)
                                                      & D = k1_geomtrap(A,F,J)
                                                      & D = k1_geomtrap(A,G,K)
                                                      & D = k1_geomtrap(A,H,L)
                                                      & r2_geomtrap(A,B,C,E,F,G,H) )
                                                   => r2_geomtrap(A,B,C,I,J,K,L) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d4_geomtrap,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))
                 => ( r1_analmetr(A,B,C)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( E = k2_geomtrap(A,B,C,D)
                        <=> ? [F] :
                              ( m1_subset_1(F,k1_numbers)
                              & D = k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)) ) ) ) ) ) ) ) ) )).

fof(d5_geomtrap,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))
                 => ( r1_analmetr(A,B,C)
                   => ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ( E = k3_geomtrap(A,B,C,D)
                        <=> ? [F] :
                              ( m1_subset_1(F,k1_numbers)
                              & D = k4_rlvect_1(A,k3_rlvect_1(A,B,F),k3_rlvect_1(A,C,E)) ) ) ) ) ) ) ) ) )).

fof(d6_geomtrap,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))
                     => k4_geomtrap(A,B,C,D,E) = k3_real_1(k4_real_1(k2_geomtrap(A,B,C,D),k2_geomtrap(A,B,C,E)),k4_real_1(k3_geomtrap(A,B,C,D),k3_geomtrap(A,B,C,E))) ) ) ) ) ) )).

fof(t31_geomtrap,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))
                     => k4_geomtrap(A,B,C,D,E) = k4_geomtrap(A,B,C,E,D) ) ) ) ) ) )).

fof(t32_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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))
                           => ( k4_geomtrap(A,B,C,D,k4_rlvect_1(A,E,F)) = k3_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F))
                              & k4_geomtrap(A,B,C,D,k6_rlvect_1(A,E,F)) = k5_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F))
                              & k4_geomtrap(A,B,C,k6_rlvect_1(A,E,F),D) = k5_real_1(k4_geomtrap(A,B,C,E,D),k4_geomtrap(A,B,C,F,D))
                              & k4_geomtrap(A,B,C,k4_rlvect_1(A,E,F),D) = k3_real_1(k4_geomtrap(A,B,C,E,D),k4_geomtrap(A,B,C,F,D)) ) ) ) ) ) ) ) ) )).

fof(t33_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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)
                           => ( k4_geomtrap(A,B,C,k3_rlvect_1(A,D,F),E) = k4_real_1(F,k4_geomtrap(A,B,C,D,E))
                              & k4_geomtrap(A,B,C,D,k3_rlvect_1(A,E,F)) = k4_real_1(F,k4_geomtrap(A,B,C,D,E))
                              & k4_geomtrap(A,B,C,k3_rlvect_1(A,D,F),E) = k4_real_1(k4_geomtrap(A,B,C,D,E),F)
                              & k4_geomtrap(A,B,C,D,k3_rlvect_1(A,E,F)) = k4_real_1(k4_geomtrap(A,B,C,D,E),F) ) ) ) ) ) ) ) ) )).

fof(t34_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_analmetr(A,D,E,B,C)
                        <=> k4_geomtrap(A,B,C,D,E) = np__0 ) ) ) ) ) ) ) )).

fof(t35_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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))
                               => ( r3_analmetr(A,D,E,F,G,B,C)
                                <=> k4_geomtrap(A,B,C,k6_rlvect_1(A,E,D),k6_rlvect_1(A,G,F)) = np__0 ) ) ) ) ) ) ) ) ) )).

fof(t36_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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))
                           => k4_real_1(np__2,k4_geomtrap(A,B,C,D,k1_geomtrap(A,E,F))) = k3_real_1(k4_geomtrap(A,B,C,D,E),k4_geomtrap(A,B,C,D,F)) ) ) ) ) ) ) ) )).

fof(t37_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] :
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( D != E
                            & k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E)) = np__0 ) ) ) ) ) ) ) )).

fof(t38_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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))
                                   => ! [I] :
                                        ( m1_subset_1(I,k1_numbers)
                                       => ( ( r2_geomtrap(A,B,C,D,E,F,G)
                                            & I = k4_real_1(k5_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k4_rlvect_1(A,D,E)),k4_real_1(np__2,k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),F))),k2_real_1(k4_geomtrap(A,B,C,k6_rlvect_1(A,D,E),k6_rlvect_1(A,D,E))))
                                            & H = k4_rlvect_1(A,F,k3_rlvect_1(A,k6_rlvect_1(A,D,E),I)) )
                                         => ( D = E
                                            | G = H ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t39_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u1_struct_0(A))
                                                       => ( ( r2_geomtrap(A,B,C,D,E,F,J)
                                                            & r2_geomtrap(A,B,C,D,E,G,K)
                                                            & r2_geomtrap(A,B,C,D,E,H,L)
                                                            & r2_geomtrap(A,B,C,D,E,I,M)
                                                            & r1_analoaf(A,F,G,H,I) )
                                                         => ( D = E
                                                            | r1_analoaf(A,J,K,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t40_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_geomtrap(A,B,C,D,E,F,I)
                                                    & r2_geomtrap(A,B,C,D,E,G,J)
                                                    & r2_geomtrap(A,B,C,D,E,H,K)
                                                    & H = k1_geomtrap(A,F,G) )
                                                 => ( D = E
                                                    | K = k1_geomtrap(A,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t41_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ( ( r2_geomtrap(A,B,C,D,E,F,H)
                                            & r2_geomtrap(A,B,C,D,E,G,I) )
                                         => ( D = E
                                            | r2_geomtrap(A,B,C,D,E,k1_geomtrap(A,F,G),k1_geomtrap(A,H,I)) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t42_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ! [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))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ! [L] :
                                                    ( m1_subset_1(L,u1_struct_0(A))
                                                   => ! [M] :
                                                        ( m1_subset_1(M,u1_struct_0(A))
                                                       => ( ( r2_geomtrap(A,B,C,D,E,F,J)
                                                            & r2_geomtrap(A,B,C,D,E,G,K)
                                                            & r2_geomtrap(A,B,C,D,E,H,L)
                                                            & r2_geomtrap(A,B,C,D,E,I,M)
                                                            & r3_analmetr(A,F,G,H,I,B,C) )
                                                         => ( D = E
                                                            | r3_analmetr(A,J,K,L,M,B,C) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t43_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(A))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(A))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(A))
                                             => ! [L] :
                                                  ( m1_subset_1(L,u1_struct_0(A))
                                                 => ! [M] :
                                                      ( m1_subset_1(M,u1_struct_0(A))
                                                     => ( ( r1_analmetr(A,B,C)
                                                          & r2_geomtrap(A,B,C,D,E,F,J)
                                                          & r2_geomtrap(A,B,C,D,E,G,K)
                                                          & r2_geomtrap(A,B,C,D,E,H,L)
                                                          & r2_geomtrap(A,B,C,D,E,I,M)
                                                          & r2_geomtrap(A,B,C,F,G,H,I) )
                                                       => ( D = E
                                                          | r2_geomtrap(A,B,C,J,K,L,M) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d7_geomtrap,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] :
                  ( m2_relset_1(D,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)))
                 => ( D = k5_geomtrap(A,B,C)
                  <=> ! [E,F] :
                        ( r2_hidden(k4_tarski(E,F),D)
                      <=> ? [G] :
                            ( m1_subset_1(G,u1_struct_0(A))
                            & ? [H] :
                                ( m1_subset_1(H,u1_struct_0(A))
                                & ? [I] :
                                    ( m1_subset_1(I,u1_struct_0(A))
                                    & ? [J] :
                                        ( m1_subset_1(J,u1_struct_0(A))
                                        & E = k1_domain_1(u1_struct_0(A),u1_struct_0(A),G,H)
                                        & F = k1_domain_1(u1_struct_0(A),u1_struct_0(A),I,J)
                                        & r2_geomtrap(A,B,C,G,H,I,J) ) ) ) ) ) ) ) ) ) ) )).

fof(t44_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( r2_hidden(k1_domain_1(k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k1_domain_1(u1_struct_0(A),u1_struct_0(A),B,C),k1_domain_1(u1_struct_0(A),u1_struct_0(A),D,E)),k5_geomtrap(A,F,G))
                              <=> r2_geomtrap(A,F,G,B,C,D,E) ) ) ) ) ) ) ) ) )).

fof(d8_geomtrap,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] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
            & m2_relset_1(B,k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) )
         => ( B = k6_geomtrap(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] :
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),B,C,D) = k1_geomtrap(A,C,D) ) ) ) ) ) )).

fof(d9_geomtrap,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))
             => k7_geomtrap(A,B,C) = g1_geomtrap(u1_struct_0(A),k6_geomtrap(A),k5_geomtrap(A,B,C)) ) ) ) )).

fof(d10_geomtrap,axiom,(
    ! [A] :
      ( l1_geomtrap(A)
     => k8_geomtrap(A) = g1_analoaf(u1_struct_0(A),u1_analoaf(A)) ) )).

fof(d11_geomtrap,axiom,(
    $true )).

fof(d12_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_geomtrap(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k9_geomtrap(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_midsp_1(A),B,C) ) ) ) )).

fof(t45_geomtrap,axiom,(
    $true )).

fof(t46_geomtrap,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(k7_geomtrap(A,B,C)))
                <=> m1_subset_1(D,u1_struct_0(A)) ) ) ) ) )).

fof(t47_geomtrap,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,u1_struct_0(A))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k7_geomtrap(A,B,C)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k7_geomtrap(A,B,C)))
                                     => ! [J] :
                                          ( m1_subset_1(J,u1_struct_0(k7_geomtrap(A,B,C)))
                                         => ! [K] :
                                              ( m1_subset_1(K,u1_struct_0(k7_geomtrap(A,B,C)))
                                             => ( ( r1_analmetr(A,B,C)
                                                  & D = H
                                                  & E = I
                                                  & F = J
                                                  & G = K )
                                               => ( r2_analoaf(k7_geomtrap(A,B,C),H,I,J,K)
                                                <=> r2_geomtrap(A,B,C,D,E,F,G) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t48_geomtrap,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,u1_struct_0(k7_geomtrap(A,B,C)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k7_geomtrap(A,B,C)))
                             => ( ( r1_analmetr(A,B,C)
                                  & D = F
                                  & E = G )
                               => k1_geomtrap(A,D,E) = k9_geomtrap(k7_geomtrap(A,B,C),F,G) ) ) ) ) ) ) ) ) )).

fof(d13_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_geomtrap(A) )
     => ( v2_geomtrap(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))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( k9_geomtrap(A,B,C) = k9_geomtrap(A,C,B)
                                                  & k9_geomtrap(A,B,B) = B
                                                  & k9_geomtrap(A,k9_geomtrap(A,B,C),k9_geomtrap(A,D,E)) = k9_geomtrap(A,k9_geomtrap(A,B,D),k9_geomtrap(A,C,E))
                                                  & ? [L] :
                                                      ( m1_subset_1(L,u1_struct_0(A))
                                                      & k9_geomtrap(A,L,B) = C )
                                                  & ( k9_geomtrap(A,B,C) = k9_geomtrap(A,B,D)
                                                   => C = D )
                                                  & ( r2_analoaf(A,B,C,D,E)
                                                   => r2_analoaf(A,B,C,k9_geomtrap(A,B,D),k9_geomtrap(A,C,E)) )
                                                  & ~ ( r2_analoaf(A,B,C,D,E)
                                                      & ~ r2_analoaf(A,B,C,k9_geomtrap(A,B,E),k9_geomtrap(A,C,D))
                                                      & ~ r2_analoaf(A,B,C,k9_geomtrap(A,C,D),k9_geomtrap(A,B,E)) )
                                                  & ( ( r2_analoaf(A,B,C,D,E)
                                                      & k9_geomtrap(A,B,F) = J
                                                      & k9_geomtrap(A,C,G) = J
                                                      & k9_geomtrap(A,D,H) = J
                                                      & k9_geomtrap(A,E,I) = J )
                                                   => r2_analoaf(A,F,G,H,I) )
                                                  & ( ( r2_analoaf(A,J,K,B,F)
                                                      & r2_analoaf(A,J,K,C,G)
                                                      & r2_analoaf(A,J,K,D,H)
                                                      & r2_analoaf(A,J,K,E,I)
                                                      & r2_analoaf(A,B,C,D,E) )
                                                   => ( J = K
                                                      | r2_analoaf(A,F,G,H,I) ) )
                                                  & ( r2_analoaf(A,B,C,C,D)
                                                   => ( B = C
                                                      & C = D ) )
                                                  & ( ( r2_analoaf(A,B,C,F,G)
                                                      & r2_analoaf(A,B,C,H,I) )
                                                   => ( B = C
                                                      | r2_analoaf(A,F,G,H,I) ) )
                                                  & ( r2_analoaf(A,B,C,D,E)
                                                   => ( r2_analoaf(A,D,E,B,C)
                                                      & r2_analoaf(A,C,B,E,D) ) )
                                                  & ~ ! [L] :
                                                        ( m1_subset_1(L,u1_struct_0(A))
                                                       => ( ~ r2_analoaf(A,B,C,D,L)
                                                          & ~ r2_analoaf(A,B,C,L,D) ) )
                                                  & ~ ( r2_analoaf(A,B,C,D,J)
                                                      & r2_analoaf(A,B,C,D,K)
                                                      & B != C
                                                      & J != K ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t49_geomtrap,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))
             => ( r1_analmetr(A,B,C)
               => ( ~ v3_struct_0(k7_geomtrap(A,B,C))
                  & v2_geomtrap(k7_geomtrap(A,B,C))
                  & l1_geomtrap(k7_geomtrap(A,B,C)) ) ) ) ) ) )).

fof(d14_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v3_geomtrap(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))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_analoaf(A,B,C,C,D)
                                                   => ( B = C
                                                      & C = D ) )
                                                  & ( ( r2_analoaf(A,B,C,F,G)
                                                      & r2_analoaf(A,B,C,H,I) )
                                                   => ( B = C
                                                      | r2_analoaf(A,F,G,H,I) ) )
                                                  & ( r2_analoaf(A,B,C,D,E)
                                                   => ( r2_analoaf(A,D,E,B,C)
                                                      & r2_analoaf(A,C,B,E,D) ) )
                                                  & ~ ! [L] :
                                                        ( m1_subset_1(L,u1_struct_0(A))
                                                       => ( ~ r2_analoaf(A,B,C,D,L)
                                                          & ~ r2_analoaf(A,B,C,L,D) ) )
                                                  & ~ ( r2_analoaf(A,B,C,D,J)
                                                      & r2_analoaf(A,B,C,D,K)
                                                      & B != C
                                                      & J != K ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t50_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(A)
        & l1_analoaf(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
        <=> m1_subset_1(B,u1_struct_0(k2_diraf(A))) ) ) )).

fof(t51_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_geomtrap(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(k2_diraf(A)))
                         => ! [G] :
                              ( m1_subset_1(G,u1_struct_0(k2_diraf(A)))
                             => ! [H] :
                                  ( m1_subset_1(H,u1_struct_0(k2_diraf(A)))
                                 => ! [I] :
                                      ( m1_subset_1(I,u1_struct_0(k2_diraf(A)))
                                     => ( ( B = F
                                          & C = G
                                          & D = H
                                          & E = I )
                                       => ( r2_analoaf(k2_diraf(A),F,G,H,I)
                                        <=> ( r2_analoaf(A,B,C,D,E)
                                            | r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(d15_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v4_geomtrap(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,C,B)
                                  & ~ ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,B,C,D,G)
                                      & B != C
                                      & E != G )
                                  & ( ( r2_analoaf(A,F,G,B,C)
                                      & r2_analoaf(A,F,G,D,E) )
                                   => ( F = G
                                      | r2_analoaf(A,B,C,D,E) ) )
                                  & ( r2_analoaf(A,B,C,D,E)
                                   => r2_analoaf(A,D,E,B,C) )
                                  & ? [H] :
                                      ( m1_subset_1(H,u1_struct_0(A))
                                      & r2_analoaf(A,B,C,D,H) ) ) ) ) ) ) ) ) ) ) )).

fof(d16_geomtrap,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v5_geomtrap(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))
                                   => ! [I] :
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] :
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] :
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_analoaf(A,B,C,D,E)
                                                    & r2_analoaf(A,B,C,F,G)
                                                    & r2_analoaf(A,B,C,H,I)
                                                    & r2_analoaf(A,B,C,J,K)
                                                    & r2_analoaf(A,D,F,H,J) )
                                                 => ( B = C
                                                    | r2_analoaf(A,E,G,I,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(dt_l1_geomtrap,axiom,(
    ! [A] :
      ( l1_geomtrap(A)
     => ( l1_analoaf(A)
        & l1_midsp_1(A) ) ) )).

fof(existence_l1_geomtrap,axiom,(
    ? [A] : l1_geomtrap(A) )).

fof(abstractness_v1_geomtrap,axiom,(
    ! [A] :
      ( l1_geomtrap(A)
     => ( v1_geomtrap(A)
       => A = g1_geomtrap(u1_struct_0(A),u1_midsp_1(A),u1_analoaf(A)) ) ) )).

fof(dt_k1_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_geomtrap(A,B,C),u1_struct_0(A)) ) )).

fof(commutativity_k1_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k1_geomtrap(A,B,C) = k1_geomtrap(A,C,B) ) )).

fof(idempotence_k1_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k1_geomtrap(A,B,B) = B ) )).

fof(dt_k2_geomtrap,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k2_geomtrap(A,B,C,D),k1_numbers) ) )).

fof(dt_k3_geomtrap,axiom,(
    ! [A,B,C,D] :
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v7_rlvect_1(A)
        & l2_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A)) )
     => m1_subset_1(k3_geomtrap(A,B,C,D),k1_numbers) ) )).

fof(dt_k4_geomtrap,axiom,(
    ! [A,B,C,D,E] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A))
        & m1_subset_1(D,u1_struct_0(A))
        & m1_subset_1(E,u1_struct_0(A)) )
     => m1_subset_1(k4_geomtrap(A,B,C,D,E),k1_numbers) ) )).

fof(dt_k5_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m2_relset_1(k5_geomtrap(A,B,C),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) )).

fof(dt_k6_geomtrap,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) )
     => ( v1_funct_1(k6_geomtrap(A))
        & v1_funct_2(k6_geomtrap(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(k6_geomtrap(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_k7_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( ~ 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)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( v1_geomtrap(k7_geomtrap(A,B,C))
        & l1_geomtrap(k7_geomtrap(A,B,C)) ) ) )).

fof(dt_k8_geomtrap,axiom,(
    ! [A] :
      ( l1_geomtrap(A)
     => ( v1_analoaf(k8_geomtrap(A))
        & l1_analoaf(k8_geomtrap(A)) ) ) )).

fof(dt_k9_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_geomtrap(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k9_geomtrap(A,B,C),u1_struct_0(A)) ) )).

fof(dt_g1_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
     => ( v1_geomtrap(g1_geomtrap(A,B,C))
        & l1_geomtrap(g1_geomtrap(A,B,C)) ) ) )).

fof(free_g1_geomtrap,axiom,(
    ! [A,B,C] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),k2_zfmisc_1(A,A)) )
     => ! [D,E,F] :
          ( g1_geomtrap(A,B,C) = g1_geomtrap(D,E,F)
         => ( A = D
            & B = E
            & C = F ) ) ) )).
%------------------------------------------------------------------------------