% Mizar problem: t26_grcat_1,grcat_1,542,50 
fof(t26_grcat_1,conjecture,(
    ! [A] : 
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ! [B] : 
          ( ( v3_grcat_1(B)
            & l1_grcat_1(B) )
         => ~ ( k9_grcat_1(A) = k10_grcat_1(B)
              & ! [C] : 
                  ( ( ~ v3_struct_0(C)
                    & v4_rlvect_1(C)
                    & v5_rlvect_1(C)
                    & v6_rlvect_1(C)
                    & l1_rlvect_1(C) )
                 => ! [D] : 
                      ( ( ~ v3_struct_0(D)
                        & v4_rlvect_1(D)
                        & v5_rlvect_1(D)
                        & v6_rlvect_1(D)
                        & l1_rlvect_1(D) )
                     => ! [E] : 
                          ( ( ~ v3_struct_0(E)
                            & v4_rlvect_1(E)
                            & v5_rlvect_1(E)
                            & v6_rlvect_1(E)
                            & l1_rlvect_1(E) )
                         => ~ ( m1_grcat_1(A,D,E)
                              & m1_grcat_1(B,C,D) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_algstr_1,cc2_algstr_1,cc3_algstr_1,cc4_algstr_1,d14_grcat_1,d15_grcat_1,d19_grcat_1,dt_k10_grcat_1,dt_k9_grcat_1,dt_l1_grcat_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l2_struct_0,dt_m1_grcat_1,dt_u1_grcat_1,dt_u2_grcat_1,existence_l1_grcat_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l2_struct_0,existence_m1_grcat_1,rc3_struct_0,rc4_struct_0,t24_grcat_1]),
    [file(grcat_1,t26_grcat_1)]).

fof(cc1_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) ) ) ) ),
    file(algstr_1,cc1_algstr_1),
    []).

fof(cc2_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc2_algstr_1),
    []).

fof(cc3_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_algstr_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_rlvect_1(A) ) ) ) ),
    file(algstr_1,cc3_algstr_1),
    []).

fof(cc4_algstr_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_rlvect_1(A)
          & v5_rlvect_1(A)
          & v6_rlvect_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_algstr_1(A)
          & v2_algstr_1(A)
          & v3_algstr_1(A)
          & v4_algstr_1(A)
          & v5_algstr_1(A)
          & v6_algstr_1(A) ) ) ) ),
    file(algstr_1,cc4_algstr_1),
    []).

fof(d14_grcat_1,axiom,(
    ! [A] : 
      ( l1_grcat_1(A)
     => k9_grcat_1(A) = u1_grcat_1(A) ) ),
    file(grcat_1,d14_grcat_1),
    []).

fof(d15_grcat_1,axiom,(
    ! [A] : 
      ( l1_grcat_1(A)
     => k10_grcat_1(A) = u2_grcat_1(A) ) ),
    file(grcat_1,d15_grcat_1),
    []).

fof(d19_grcat_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_rlvect_1(B)
            & v5_rlvect_1(B)
            & v6_rlvect_1(B)
            & l1_rlvect_1(B) )
         => ! [C] : 
              ( ( v3_grcat_1(C)
                & l1_grcat_1(C) )
             => ( m1_grcat_1(C,A,B)
              <=> ( k9_grcat_1(C) = A
                  & k10_grcat_1(C) = B ) ) ) ) ) ),
    file(grcat_1,d19_grcat_1),
    []).

fof(dt_k10_grcat_1,axiom,(
    ! [A] : 
      ( l1_grcat_1(A)
     => ( ~ v3_struct_0(k10_grcat_1(A))
        & v4_rlvect_1(k10_grcat_1(A))
        & v5_rlvect_1(k10_grcat_1(A))
        & v6_rlvect_1(k10_grcat_1(A))
        & l1_rlvect_1(k10_grcat_1(A)) ) ) ),
    file(grcat_1,k10_grcat_1),
    []).

fof(dt_k9_grcat_1,axiom,(
    ! [A] : 
      ( l1_grcat_1(A)
     => ( ~ v3_struct_0(k9_grcat_1(A))
        & v4_rlvect_1(k9_grcat_1(A))
        & v5_rlvect_1(k9_grcat_1(A))
        & v6_rlvect_1(k9_grcat_1(A))
        & l1_rlvect_1(k9_grcat_1(A)) ) ) ),
    file(grcat_1,k9_grcat_1),
    []).

fof(dt_l1_grcat_1,axiom,(
    $true ),
    file(grcat_1,l1_grcat_1),
    []).

fof(dt_l1_rlvect_1,axiom,(
    ! [A] : 
      ( l1_rlvect_1(A)
     => l2_struct_0(A) ) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    []).

fof(dt_l2_struct_0,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => l1_struct_0(A) ) ),
    file(struct_0,l2_struct_0),
    []).

fof(dt_m1_grcat_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ! [C] : 
          ( m1_grcat_1(C,A,B)
         => ( v3_grcat_1(C)
            & l1_grcat_1(C) ) ) ) ),
    file(grcat_1,m1_grcat_1),
    []).

fof(dt_u1_grcat_1,axiom,(
    ! [A] : 
      ( l1_grcat_1(A)
     => ( ~ v3_struct_0(u1_grcat_1(A))
        & v4_rlvect_1(u1_grcat_1(A))
        & v5_rlvect_1(u1_grcat_1(A))
        & v6_rlvect_1(u1_grcat_1(A))
        & l1_rlvect_1(u1_grcat_1(A)) ) ) ),
    file(grcat_1,u1_grcat_1),
    []).

fof(dt_u2_grcat_1,axiom,(
    ! [A] : 
      ( l1_grcat_1(A)
     => ( ~ v3_struct_0(u2_grcat_1(A))
        & v4_rlvect_1(u2_grcat_1(A))
        & v5_rlvect_1(u2_grcat_1(A))
        & v6_rlvect_1(u2_grcat_1(A))
        & l1_rlvect_1(u2_grcat_1(A)) ) ) ),
    file(grcat_1,u2_grcat_1),
    []).

fof(existence_l1_grcat_1,axiom,(
    ? [A] : l1_grcat_1(A) ),
    file(grcat_1,l1_grcat_1),
    []).

fof(existence_l1_rlvect_1,axiom,(
    ? [A] : l1_rlvect_1(A) ),
    file(rlvect_1,l1_rlvect_1),
    []).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    []).

fof(existence_l2_struct_0,axiom,(
    ? [A] : l2_struct_0(A) ),
    file(struct_0,l2_struct_0),
    []).

fof(existence_m1_grcat_1,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & l1_rlvect_1(A)
        & ~ v3_struct_0(B)
        & v4_rlvect_1(B)
        & v5_rlvect_1(B)
        & v6_rlvect_1(B)
        & l1_rlvect_1(B) )
     => ? [C] : m1_grcat_1(C,A,B) ) ),
    file(grcat_1,m1_grcat_1),
    []).

fof(rc3_struct_0,axiom,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    []).

fof(rc4_struct_0,axiom,(
    ? [A] : 
      ( l2_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc4_struct_0),
    []).

fof(t24_grcat_1,axiom,(
    ! [A] : 
      ( ( v3_grcat_1(A)
        & l1_grcat_1(A) )
     => ? [B] : 
          ( ~ v3_struct_0(B)
          & v4_rlvect_1(B)
          & v5_rlvect_1(B)
          & v6_rlvect_1(B)
          & l1_rlvect_1(B)
          & ? [C] : 
              ( ~ v3_struct_0(C)
              & v4_rlvect_1(C)
              & v5_rlvect_1(C)
              & v6_rlvect_1(C)
              & l1_rlvect_1(C)
              & m1_grcat_1(A,B,C) ) ) ) ),
    file(grcat_1,t24_grcat_1),
    []).