SET007 Axioms: SET007+368.ax


%------------------------------------------------------------------------------
% File     : SET007+368 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Subspaces of Real Linear Space Generated by Vectors
% 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    : rlvect_4 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   43 (   2 unit)
%            Number of atoms       :  535 (  94 equality)
%            Maximal formula depth :   19 (  12 average)
%            Number of connectives :  566 (  74 ~  ;  34  |; 283  &)
%                                         (   7 <=>; 168 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   19 (   1 propositional; 0-3 arity)
%            Number of functors    :   41 (  26 constant; 0-4 arity)
%            Number of variables   :  169 (   0 singleton; 153 !;  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(t1_rlvect_4,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))
             => ( k6_rlvect_1(A,k4_rlvect_1(A,B,C),B) = C
                & k6_rlvect_1(A,k4_rlvect_1(A,C,B),B) = C
                & k4_rlvect_1(A,k6_rlvect_1(A,B,B),C) = C
                & k4_rlvect_1(A,k6_rlvect_1(A,C,B),B) = C
                & k4_rlvect_1(A,B,k6_rlvect_1(A,C,B)) = C
                & k4_rlvect_1(A,C,k6_rlvect_1(A,B,B)) = C
                & k6_rlvect_1(A,B,k6_rlvect_1(A,B,C)) = C ) ) ) ) )).

fof(t2_rlvect_4,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))
                 => k6_rlvect_1(A,k4_rlvect_1(A,B,C),D) = k4_rlvect_1(A,k6_rlvect_1(A,B,D),C) ) ) ) ) )).

fof(t3_rlvect_4,axiom,(
    $true )).

fof(t4_rlvect_4,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))
                 => ( k6_rlvect_1(A,B,C) = k6_rlvect_1(A,D,C)
                   => B = D ) ) ) ) ) )).

fof(t5_rlvect_4,axiom,(
    $true )).

fof(t6_rlvect_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => k5_rlvect_1(B,k3_rlvect_1(B,C,A)) = k3_rlvect_1(B,C,k1_real_1(A)) ) ) ) )).

fof(t7_rlvect_4,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_rlsub_1(C,A)
             => ! [D] :
                  ( m1_rlsub_1(D,A)
                 => ( m1_rlsub_1(C,D)
                   => r1_tarski(k3_rlsub_1(A,B,C),k3_rlsub_1(A,B,D)) ) ) ) ) ) )).

fof(t8_rlvect_4,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_rlsub_1(D,A)
                 => ( r2_hidden(B,k3_rlsub_1(A,C,D))
                   => k3_rlsub_1(A,C,D) = k3_rlsub_1(A,B,D) ) ) ) ) ) )).

fof(t9_rlvect_4,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] :
                      ( m2_rlvect_2(E,A,k9_rlvect_2(A,B,C,D))
                     => ~ ( B != C
                          & B != D
                          & C != D
                          & k13_rlvect_2(A,E) != k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,k8_funct_2(u1_struct_0(A),k1_numbers,E,B)),k3_rlvect_1(A,C,k8_funct_2(u1_struct_0(A),k1_numbers,E,C))),k3_rlvect_1(A,D,k8_funct_2(u1_struct_0(A),k1_numbers,E,D))) ) ) ) ) ) ) )).

fof(t10_rlvect_4,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))
                 => ( ( B != C
                      & B != D
                      & C != D
                      & v1_rlvect_3(k9_rlvect_2(A,B,C,D),A) )
                  <=> ! [E] :
                        ( m1_subset_1(E,k1_numbers)
                       => ! [F] :
                            ( m1_subset_1(F,k1_numbers)
                           => ! [G] :
                                ( m1_subset_1(G,k1_numbers)
                               => ( k4_rlvect_1(A,k4_rlvect_1(A,k3_rlvect_1(A,B,E),k3_rlvect_1(A,C,F)),k3_rlvect_1(A,D,G)) = k1_rlvect_1(A)
                                 => ( E = np__0
                                    & F = np__0
                                    & G = np__0 ) ) ) ) ) ) ) ) ) ) )).

fof(t11_rlvect_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r1_rlvect_1(k1_rlvect_3(B,k7_rlvect_2(B,C)),A)
          <=> ? [D] :
                ( m1_subset_1(D,k1_numbers)
                & A = k3_rlvect_1(B,C,D) ) ) ) ) )).

fof(t12_rlvect_4,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))
         => r1_rlvect_1(k1_rlvect_3(A,k7_rlvect_2(A,B)),B) ) ) )).

fof(t13_rlvect_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k7_rlvect_2(B,D))))
              <=> ? [E] :
                    ( m1_subset_1(E,k1_numbers)
                    & A = k4_rlvect_1(B,C,k3_rlvect_1(B,D,E)) ) ) ) ) ) )).

fof(t14_rlvect_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r1_rlvect_1(k1_rlvect_3(B,k8_rlvect_2(B,C,D)),A)
              <=> ? [E] :
                    ( m1_subset_1(E,k1_numbers)
                    & ? [F] :
                        ( m1_subset_1(F,k1_numbers)
                        & A = k4_rlvect_1(B,k3_rlvect_1(B,C,E),k3_rlvect_1(B,D,F)) ) ) ) ) ) ) )).

fof(t15_rlvect_4,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_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,B,C)),B)
                & r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,B,C)),C) ) ) ) ) )).

fof(t16_rlvect_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_struct_0(B))
                 => ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k8_rlvect_2(B,D,E))))
                  <=> ? [F] :
                        ( m1_subset_1(F,k1_numbers)
                        & ? [G] :
                            ( m1_subset_1(G,k1_numbers)
                            & A = k4_rlvect_1(B,k4_rlvect_1(B,C,k3_rlvect_1(B,D,F)),k3_rlvect_1(B,E,G)) ) ) ) ) ) ) ) )).

fof(t17_rlvect_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_struct_0(B))
                 => ( r1_rlvect_1(k1_rlvect_3(B,k9_rlvect_2(B,C,D,E)),A)
                  <=> ? [F] :
                        ( m1_subset_1(F,k1_numbers)
                        & ? [G] :
                            ( m1_subset_1(G,k1_numbers)
                            & ? [H] :
                                ( m1_subset_1(H,k1_numbers)
                                & A = k4_rlvect_1(B,k4_rlvect_1(B,k3_rlvect_1(B,C,F),k3_rlvect_1(B,D,G)),k3_rlvect_1(B,E,H)) ) ) ) ) ) ) ) ) )).

fof(t18_rlvect_4,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_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),B)
                    & r1_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),C)
                    & r1_rlvect_1(k1_rlvect_3(A,k9_rlvect_2(A,B,C,D)),D) ) ) ) ) ) )).

fof(t19_rlvect_4,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(B)
        & v3_rlvect_1(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & v7_rlvect_1(B)
        & l2_rlvect_1(B) )
     => ! [C] :
          ( m1_subset_1(C,u1_struct_0(B))
         => ! [D] :
              ( m1_subset_1(D,u1_struct_0(B))
             => ! [E] :
                  ( m1_subset_1(E,u1_struct_0(B))
                 => ! [F] :
                      ( m1_subset_1(F,u1_struct_0(B))
                     => ( r2_hidden(A,k3_rlsub_1(B,C,k1_rlvect_3(B,k9_rlvect_2(B,D,E,F))))
                      <=> ? [G] :
                            ( m1_subset_1(G,k1_numbers)
                            & ? [H] :
                                ( m1_subset_1(H,k1_numbers)
                                & ? [I] :
                                    ( m1_subset_1(I,k1_numbers)
                                    & A = k4_rlvect_1(B,k4_rlvect_1(B,k4_rlvect_1(B,C,k3_rlvect_1(B,D,G)),k3_rlvect_1(B,E,H)),k3_rlvect_1(B,F,I)) ) ) ) ) ) ) ) ) ) )).

fof(t20_rlvect_4,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))
             => ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
               => ( B = C
                  | v1_rlvect_3(k8_rlvect_2(A,B,k6_rlvect_1(A,C,B)),A) ) ) ) ) ) )).

fof(t21_rlvect_4,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))
             => ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
               => ( B = C
                  | v1_rlvect_3(k8_rlvect_2(A,B,k4_rlvect_1(A,C,B)),A) ) ) ) ) ) )).

fof(t22_rlvect_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( v1_rlvect_3(k8_rlvect_2(B,C,D),B)
                   => ( C = D
                      | A = np__0
                      | v1_rlvect_3(k8_rlvect_2(B,C,k3_rlvect_1(B,D,A)),B) ) ) ) ) ) ) )).

fof(t23_rlvect_4,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))
             => ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
               => ( B = C
                  | v1_rlvect_3(k8_rlvect_2(A,B,k5_rlvect_1(A,C)),A) ) ) ) ) ) )).

fof(t24_rlvect_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ~ ( A != B
                      & v1_rlvect_3(k8_rlvect_2(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B)),C) ) ) ) ) ) )).

fof(t25_rlvect_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ~ ( A != np__1
                  & v1_rlvect_3(k8_rlvect_2(B,C,k3_rlvect_1(B,C,A)),B) ) ) ) ) )).

fof(t26_rlvect_4,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))
                 => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
                   => ( B = D
                      | B = C
                      | D = C
                      | v1_rlvect_3(k9_rlvect_2(A,B,C,k6_rlvect_1(A,D,B)),A) ) ) ) ) ) ) )).

fof(t27_rlvect_4,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))
                 => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
                   => ( B = D
                      | B = C
                      | D = C
                      | v1_rlvect_3(k9_rlvect_2(A,B,k6_rlvect_1(A,C,B),k6_rlvect_1(A,D,B)),A) ) ) ) ) ) ) )).

fof(t28_rlvect_4,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))
                 => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
                   => ( B = D
                      | B = C
                      | D = C
                      | v1_rlvect_3(k9_rlvect_2(A,B,C,k4_rlvect_1(A,D,B)),A) ) ) ) ) ) ) )).

fof(t29_rlvect_4,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))
                 => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
                   => ( B = D
                      | B = C
                      | D = C
                      | v1_rlvect_3(k9_rlvect_2(A,B,k4_rlvect_1(A,C,B),k4_rlvect_1(A,D,B)),A) ) ) ) ) ) ) )).

fof(t30_rlvect_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( v1_rlvect_3(k9_rlvect_2(B,C,D,E),B)
                       => ( C = E
                          | C = D
                          | E = D
                          | A = np__0
                          | v1_rlvect_3(k9_rlvect_2(B,C,D,k3_rlvect_1(B,E,A)),B) ) ) ) ) ) ) ) )).

fof(t31_rlvect_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ! [F] :
                          ( m1_subset_1(F,u1_struct_0(C))
                         => ( v1_rlvect_3(k9_rlvect_2(C,D,E,F),C)
                           => ( D = F
                              | D = E
                              | F = E
                              | A = np__0
                              | B = np__0
                              | v1_rlvect_3(k9_rlvect_2(C,D,k3_rlvect_1(C,E,A),k3_rlvect_1(C,F,B)),C) ) ) ) ) ) ) ) ) )).

fof(t32_rlvect_4,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))
                 => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
                   => ( B = D
                      | B = C
                      | D = C
                      | v1_rlvect_3(k9_rlvect_2(A,B,C,k5_rlvect_1(A,D)),A) ) ) ) ) ) ) )).

fof(t33_rlvect_4,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))
                 => ( v1_rlvect_3(k9_rlvect_2(A,B,C,D),A)
                   => ( B = D
                      | B = C
                      | D = C
                      | v1_rlvect_3(k9_rlvect_2(A,B,k5_rlvect_1(A,C),k5_rlvect_1(A,D)),A) ) ) ) ) ) ) )).

fof(t34_rlvect_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( m1_subset_1(B,k1_numbers)
         => ! [C] :
              ( ( ~ v3_struct_0(C)
                & v3_rlvect_1(C)
                & v4_rlvect_1(C)
                & v5_rlvect_1(C)
                & v6_rlvect_1(C)
                & v7_rlvect_1(C)
                & l2_rlvect_1(C) )
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] :
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ~ ( A != B
                          & v1_rlvect_3(k9_rlvect_2(C,k3_rlvect_1(C,D,A),k3_rlvect_1(C,D,B),E),C) ) ) ) ) ) ) )).

fof(t35_rlvect_4,axiom,(
    ! [A] :
      ( m1_subset_1(A,k1_numbers)
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v3_rlvect_1(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & v7_rlvect_1(B)
            & l2_rlvect_1(B) )
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] :
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ~ ( A != np__1
                      & v1_rlvect_3(k9_rlvect_2(B,C,k3_rlvect_1(B,C,A),D),B) ) ) ) ) ) )).

fof(t36_rlvect_4,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_rlvect_1(k1_rlvect_3(A,k7_rlvect_2(A,C)),B)
               => ( B = k1_rlvect_1(A)
                  | k1_rlvect_3(A,k7_rlvect_2(A,B)) = k1_rlvect_3(A,k7_rlvect_2(A,C)) ) ) ) ) ) )).

fof(t37_rlvect_4,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))
                     => ( ( v1_rlvect_3(k8_rlvect_2(A,B,C),A)
                          & r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,D,E)),B)
                          & r1_rlvect_1(k1_rlvect_3(A,k8_rlvect_2(A,D,E)),C) )
                       => ( B = C
                          | ( k1_rlvect_3(A,k8_rlvect_2(A,D,E)) = k1_rlvect_3(A,k8_rlvect_2(A,B,C))
                            & v1_rlvect_3(k8_rlvect_2(A,D,E),A)
                            & D != E ) ) ) ) ) ) ) ) )).

fof(t38_rlvect_4,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))
             => ~ ( B != k1_rlvect_1(A)
                  & ~ v1_rlvect_3(k8_rlvect_2(A,C,B),A)
                  & ! [D] :
                      ( m1_subset_1(D,k1_numbers)
                     => C != k3_rlvect_1(A,B,D) ) ) ) ) ) )).

fof(t39_rlvect_4,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))
                 => ~ ( B != C
                      & v1_rlvect_3(k8_rlvect_2(A,B,C),A)
                      & ~ v1_rlvect_3(k9_rlvect_2(A,D,B,C),A)
                      & ! [E] :
                          ( m1_subset_1(E,k1_numbers)
                         => ! [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(s1_rlvect_4,axiom,
    ( ( f3_s1_rlvect_4 != f4_s1_rlvect_4
      & f3_s1_rlvect_4 != f5_s1_rlvect_4
      & f4_s1_rlvect_4 != f5_s1_rlvect_4 )
   => ? [A] :
        ( v1_funct_1(A)
        & v1_funct_2(A,f1_s1_rlvect_4,f2_s1_rlvect_4)
        & m2_relset_1(A,f1_s1_rlvect_4,f2_s1_rlvect_4)
        & k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f3_s1_rlvect_4) = f6_s1_rlvect_4
        & k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f4_s1_rlvect_4) = f7_s1_rlvect_4
        & k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,f5_s1_rlvect_4) = f8_s1_rlvect_4
        & ! [B] :
            ( m1_subset_1(B,f1_s1_rlvect_4)
           => ~ ( B != f3_s1_rlvect_4
                & B != f4_s1_rlvect_4
                & B != f5_s1_rlvect_4
                & k8_funct_2(f1_s1_rlvect_4,f2_s1_rlvect_4,A,B) != f9_s1_rlvect_4(B) ) ) ) )).

fof(s2_rlvect_4,axiom,(
    ? [A] :
      ( m2_rlvect_2(A,f1_s2_rlvect_4,k7_rlvect_2(f1_s2_rlvect_4,f2_s2_rlvect_4))
      & k8_funct_2(u1_struct_0(f1_s2_rlvect_4),k1_numbers,A,f2_s2_rlvect_4) = f3_s2_rlvect_4 ) )).

fof(s3_rlvect_4,axiom,
    ( f2_s3_rlvect_4 != f3_s3_rlvect_4
   => ? [A] :
        ( m2_rlvect_2(A,f1_s3_rlvect_4,k8_rlvect_2(f1_s3_rlvect_4,f2_s3_rlvect_4,f3_s3_rlvect_4))
        & k8_funct_2(u1_struct_0(f1_s3_rlvect_4),k1_numbers,A,f2_s3_rlvect_4) = f4_s3_rlvect_4
        & k8_funct_2(u1_struct_0(f1_s3_rlvect_4),k1_numbers,A,f3_s3_rlvect_4) = f5_s3_rlvect_4 ) )).

fof(s4_rlvect_4,axiom,
    ( ( f2_s4_rlvect_4 != f3_s4_rlvect_4
      & f2_s4_rlvect_4 != f4_s4_rlvect_4
      & f3_s4_rlvect_4 != f4_s4_rlvect_4 )
   => ? [A] :
        ( m2_rlvect_2(A,f1_s4_rlvect_4,k9_rlvect_2(f1_s4_rlvect_4,f2_s4_rlvect_4,f3_s4_rlvect_4,f4_s4_rlvect_4))
        & k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f2_s4_rlvect_4) = f5_s4_rlvect_4
        & k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f3_s4_rlvect_4) = f6_s4_rlvect_4
        & k8_funct_2(u1_struct_0(f1_s4_rlvect_4),k1_numbers,A,f4_s4_rlvect_4) = f7_s4_rlvect_4 ) )).
%------------------------------------------------------------------------------