% Mizar problem: t1_parsp_2,parsp_2,83,20 
fof(t1_parsp_2,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k9_parsp_1(A))
        & v2_parsp_1(k9_parsp_1(A))
        & l1_parsp_1(k9_parsp_1(A)) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_parsp_1,cc1_vectsp_1,cc2_vectsp_1,cc3_vectsp_1,cc4_vectsp_1,cc5_vectsp_1,d12_parsp_1,dt_g1_parsp_1,dt_k9_parsp_1,dt_l1_group_1,dt_l1_parsp_1,dt_l1_rlvect_1,dt_l1_struct_0,dt_l1_vectsp_1,dt_l2_struct_0,dt_l2_vectsp_1,dt_l3_vectsp_1,dt_m1_parsp_1,dt_m1_subset_1,dt_u1_parsp_1,dt_u1_struct_0,existence_l1_group_1,existence_l1_parsp_1,existence_l1_rlvect_1,existence_l1_struct_0,existence_l1_vectsp_1,existence_l2_struct_0,existence_l2_vectsp_1,existence_l3_vectsp_1,existence_m1_parsp_1,existence_m1_subset_1,fc1_struct_0,fc3_parsp_1,free_g1_parsp_1,rc1_parsp_1,rc1_xboole_0,rc2_parsp_1,rc2_xboole_0,rc3_parsp_1,rc3_struct_0,rc4_struct_0,rc8_vectsp_1,rc9_vectsp_1,t24_parsp_1,t25_parsp_1,t26_parsp_1,t27_parsp_1,t28_parsp_1]),
    [file(parsp_2,t1_parsp_2)]).

fof(abstractness_v1_parsp_1,axiom,(
    ! [A] : 
      ( l1_parsp_1(A)
     => ( v1_parsp_1(A)
       => A = g1_parsp_1(u1_struct_0(A),u1_parsp_1(A)) ) ) ),
    file(parsp_1,v1_parsp_1),
    []).

fof(cc1_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc1_vectsp_1),
    []).

fof(cc2_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v4_vectsp_1(A)
          & v5_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v7_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc2_vectsp_1),
    []).

fof(cc3_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v2_group_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc3_vectsp_1),
    []).

fof(cc4_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v6_vectsp_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v2_group_1(A) ) ) ) ),
    file(vectsp_1,cc4_vectsp_1),
    []).

fof(cc5_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => ( ( ~ v3_struct_0(A)
          & v7_group_1(A)
          & v8_vectsp_1(A) )
       => ( ~ v3_struct_0(A)
          & v6_vectsp_1(A) ) ) ) ),
    file(vectsp_1,cc5_vectsp_1),
    []).

fof(d12_parsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_parsp_1(A) )
     => ( v2_parsp_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_parsp_1(A,B,C,C,B)
                                          & r1_parsp_1(A,B,C,D,D)
                                          & ~ ( r1_parsp_1(A,B,C,F,G)
                                              & r1_parsp_1(A,B,C,H,I)
                                              & ~ r1_parsp_1(A,F,G,H,I)
                                              & B != C )
                                          & ( r1_parsp_1(A,B,C,B,D)
                                           => r1_parsp_1(A,C,B,C,D) )
                                          & ? [J] : 
                                              ( m1_subset_1(J,u1_struct_0(A))
                                              & r1_parsp_1(A,B,C,D,J)
                                              & r1_parsp_1(A,B,D,C,J) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(parsp_1,d12_parsp_1),
    []).

fof(dt_g1_parsp_1,axiom,(
    ! [A,B] : 
      ( m1_parsp_1(B,A)
     => ( v1_parsp_1(g1_parsp_1(A,B))
        & l1_parsp_1(g1_parsp_1(A,B)) ) ) ),
    file(parsp_1,g1_parsp_1),
    []).

fof(dt_k9_parsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => l1_parsp_1(k9_parsp_1(A)) ) ),
    file(parsp_1,k9_parsp_1),
    []).

fof(dt_l1_group_1,axiom,(
    ! [A] : 
      ( l1_group_1(A)
     => l1_struct_0(A) ) ),
    file(group_1,l1_group_1),
    []).

fof(dt_l1_parsp_1,axiom,(
    ! [A] : 
      ( l1_parsp_1(A)
     => l1_struct_0(A) ) ),
    file(parsp_1,l1_parsp_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_l1_vectsp_1,axiom,(
    ! [A] : 
      ( l1_vectsp_1(A)
     => l1_group_1(A) ) ),
    file(vectsp_1,l1_vectsp_1),
    []).

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

fof(dt_l2_vectsp_1,axiom,(
    ! [A] : 
      ( l2_vectsp_1(A)
     => ( l1_vectsp_1(A)
        & l2_struct_0(A) ) ) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(dt_l3_vectsp_1,axiom,(
    ! [A] : 
      ( l3_vectsp_1(A)
     => ( l1_rlvect_1(A)
        & l2_vectsp_1(A) ) ) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(dt_m1_parsp_1,axiom,(
    $true ),
    file(parsp_1,m1_parsp_1),
    []).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(dt_u1_parsp_1,axiom,(
    ! [A] : 
      ( l1_parsp_1(A)
     => m1_parsp_1(u1_parsp_1(A),u1_struct_0(A)) ) ),
    file(parsp_1,u1_parsp_1),
    []).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    []).

fof(existence_l1_group_1,axiom,(
    ? [A] : l1_group_1(A) ),
    file(group_1,l1_group_1),
    []).

fof(existence_l1_parsp_1,axiom,(
    ? [A] : l1_parsp_1(A) ),
    file(parsp_1,l1_parsp_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_l1_vectsp_1,axiom,(
    ? [A] : l1_vectsp_1(A) ),
    file(vectsp_1,l1_vectsp_1),
    []).

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

fof(existence_l2_vectsp_1,axiom,(
    ? [A] : l2_vectsp_1(A) ),
    file(vectsp_1,l2_vectsp_1),
    []).

fof(existence_l3_vectsp_1,axiom,(
    ? [A] : l3_vectsp_1(A) ),
    file(vectsp_1,l3_vectsp_1),
    []).

fof(existence_m1_parsp_1,axiom,(
    ! [A] : 
    ? [B] : m1_parsp_1(B,A) ),
    file(parsp_1,m1_parsp_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(fc1_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    []).

fof(fc3_parsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ( ~ v3_struct_0(k9_parsp_1(A))
        & v1_parsp_1(k9_parsp_1(A)) ) ) ),
    file(parsp_1,fc3_parsp_1),
    []).

fof(free_g1_parsp_1,axiom,(
    ! [A,B] : 
      ( m1_parsp_1(B,A)
     => ! [C,D] : 
          ( g1_parsp_1(A,B) = g1_parsp_1(C,D)
         => ( A = C
            & B = D ) ) ) ),
    file(parsp_1,g1_parsp_1),
    []).

fof(rc1_parsp_1,axiom,(
    ? [A] : 
      ( l1_parsp_1(A)
      & v1_parsp_1(A) ) ),
    file(parsp_1,rc1_parsp_1),
    []).

fof(rc1_xboole_0,axiom,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    []).

fof(rc2_parsp_1,axiom,(
    ? [A] : 
      ( l1_parsp_1(A)
      & ~ v3_struct_0(A) ) ),
    file(parsp_1,rc2_parsp_1),
    []).

fof(rc2_xboole_0,axiom,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    []).

fof(rc3_parsp_1,axiom,(
    ? [A] : 
      ( l1_parsp_1(A)
      & ~ v3_struct_0(A)
      & v1_parsp_1(A)
      & v2_parsp_1(A) ) ),
    file(parsp_1,rc3_parsp_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(rc8_vectsp_1,axiom,(
    ? [A] : 
      ( l1_group_1(A)
      & ~ v3_struct_0(A)
      & v4_group_1(A)
      & v7_group_1(A) ) ),
    file(vectsp_1,rc8_vectsp_1),
    []).

fof(rc9_vectsp_1,axiom,(
    ? [A] : 
      ( l1_vectsp_1(A)
      & ~ v3_struct_0(A)
      & v2_group_1(A)
      & v4_group_1(A)
      & v7_group_1(A)
      & v6_vectsp_1(A)
      & v8_vectsp_1(A) ) ),
    file(vectsp_1,rc9_vectsp_1),
    []).

fof(t24_parsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => r1_parsp_1(k9_parsp_1(A),B,C,C,B) ) ) ) ),
    file(parsp_1,t24_parsp_1),
    []).

fof(t25_parsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => r1_parsp_1(k9_parsp_1(A),B,C,D,D) ) ) ) ) ),
    file(parsp_1,t25_parsp_1),
    []).

fof(t26_parsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(k9_parsp_1(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(k9_parsp_1(A)))
                             => ~ ( r1_parsp_1(k9_parsp_1(A),B,C,D,E)
                                  & r1_parsp_1(k9_parsp_1(A),B,C,F,G)
                                  & ~ r1_parsp_1(k9_parsp_1(A),D,E,F,G)
                                  & B != C ) ) ) ) ) ) ) ) ),
    file(parsp_1,t26_parsp_1),
    []).

fof(t27_parsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ( r1_parsp_1(k9_parsp_1(A),B,C,B,D)
                   => r1_parsp_1(k9_parsp_1(A),C,B,C,D) ) ) ) ) ) ),
    file(parsp_1,t27_parsp_1),
    []).

fof(t28_parsp_1,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_rlvect_1(A)
        & v4_rlvect_1(A)
        & v5_rlvect_1(A)
        & v6_rlvect_1(A)
        & v4_group_1(A)
        & v7_group_1(A)
        & v7_vectsp_1(A)
        & v8_vectsp_1(A)
        & v9_vectsp_1(A)
        & ~ v10_vectsp_1(A)
        & l3_vectsp_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k9_parsp_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k9_parsp_1(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(k9_parsp_1(A)))
                 => ? [E] : 
                      ( m1_subset_1(E,u1_struct_0(k9_parsp_1(A)))
                      & r1_parsp_1(k9_parsp_1(A),B,C,D,E)
                      & r1_parsp_1(k9_parsp_1(A),B,D,C,E) ) ) ) ) ) ),
    file(parsp_1,t28_parsp_1),
    []).