% Mizar problem: t20_parsp_1,parsp_1,410,52 
fof(t20_parsp_1,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) )
     => ! [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)
                      <=> ( r2_hidden(k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E),k6_parsp_1(A))
                          & ? [F] : 
                              ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                              & ? [G] : 
                                  ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                  & ? [H] : 
                                      ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                      & ? [I] : 
                                          ( m1_subset_1(I,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                          & k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E) = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),F,G,H,I)
                                          & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)),k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))),k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I)),k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))) = k1_rlvect_1(A)
                                          & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))),k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))) = k1_rlvect_1(A)
                                          & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))),k10_group_1(A,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[abstractness_v1_parsp_1,antisymmetry_r2_hidden,cc1_vectsp_1,cc2_vectsp_1,cc3_vectsp_1,cc4_vectsp_1,cc5_vectsp_1,commutativity_k10_group_1,d10_parsp_1,d11_parsp_1,d7_parsp_1,d8_parsp_1,dt_g1_parsp_1,dt_k10_group_1,dt_k1_group_1,dt_k1_rlvect_1,dt_k1_xboole_0,dt_k3_zfmisc_1,dt_k4_mcart_1,dt_k4_zfmisc_1,dt_k5_domain_1,dt_k5_mcart_1,dt_k5_parsp_1,dt_k6_mcart_1,dt_k6_parsp_1,dt_k6_rlvect_1,dt_k7_mcart_1,dt_k7_parsp_1,dt_k8_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_parsp_1,fc1_struct_0,fc1_xboole_0,fc2_parsp_1,fc3_parsp_1,fc5_subset_1,fc6_subset_1,free_g1_parsp_1,rc1_parsp_1,rc1_xboole_0,rc2_parsp_1,rc2_xboole_0,rc3_struct_0,rc4_struct_0,rc8_vectsp_1,rc9_vectsp_1,redefinition_k10_group_1,redefinition_k5_domain_1,t18_parsp_1,t19_parsp_1,t1_subset,t2_subset,t6_boole,t7_boole,t8_boole]),
    [file(parsp_1,t20_parsp_1)]).

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(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

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(commutativity_k10_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k10_group_1(A,B,C) = k10_group_1(A,C,B) ) ),
    file(group_1,k10_group_1),
    []).

fof(d10_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) )
     => k8_parsp_1(A) = k7_parsp_1(A) ) ),
    file(parsp_1,d10_parsp_1),
    []).

fof(d11_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) )
     => k9_parsp_1(A) = g1_parsp_1(k5_parsp_1(A),k8_parsp_1(A)) ) ),
    file(parsp_1,d11_parsp_1),
    []).

fof(d7_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) )
     => k5_parsp_1(A) = k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)) ) ),
    file(parsp_1,d7_parsp_1),
    []).

fof(d8_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) )
     => k6_parsp_1(A) = k4_zfmisc_1(k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A),k5_parsp_1(A)) ) ),
    file(parsp_1,d8_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_k10_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k10_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k10_group_1),
    []).

fof(dt_k1_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_group_1(A,B,C),u1_struct_0(A)) ) ),
    file(group_1,k1_group_1),
    []).

fof(dt_k1_rlvect_1,axiom,(
    ! [A] : 
      ( l2_struct_0(A)
     => m1_subset_1(k1_rlvect_1(A),u1_struct_0(A)) ) ),
    file(rlvect_1,k1_rlvect_1),
    []).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    []).

fof(dt_k3_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k3_zfmisc_1),
    []).

fof(dt_k4_mcart_1,axiom,(
    $true ),
    file(mcart_1,k4_mcart_1),
    []).

fof(dt_k4_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k4_zfmisc_1),
    []).

fof(dt_k5_domain_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B)
        & m1_subset_1(G,C)
        & m1_subset_1(H,D) )
     => m1_subset_1(k5_domain_1(A,B,C,D,E,F,G,H),k4_zfmisc_1(A,B,C,D)) ) ),
    file(domain_1,k5_domain_1),
    []).

fof(dt_k5_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k5_mcart_1(A,B,C,D),A) ) ),
    file(mcart_1,k5_mcart_1),
    []).

fof(dt_k5_parsp_1,axiom,(
    $true ),
    file(parsp_1,k5_parsp_1),
    []).

fof(dt_k6_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k6_mcart_1(A,B,C,D),B) ) ),
    file(mcart_1,k6_mcart_1),
    []).

fof(dt_k6_parsp_1,axiom,(
    $true ),
    file(parsp_1,k6_parsp_1),
    []).

fof(dt_k6_rlvect_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & l1_rlvect_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k6_rlvect_1(A,B,C),u1_struct_0(A)) ) ),
    file(rlvect_1,k6_rlvect_1),
    []).

fof(dt_k7_mcart_1,axiom,(
    ! [A,B,C,D] : 
      ( m1_subset_1(D,k3_zfmisc_1(A,B,C))
     => m1_subset_1(k7_mcart_1(A,B,C,D),C) ) ),
    file(mcart_1,k7_mcart_1),
    []).

fof(dt_k7_parsp_1,axiom,(
    $true ),
    file(parsp_1,k7_parsp_1),
    []).

fof(dt_k8_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) )
     => m1_parsp_1(k8_parsp_1(A),k5_parsp_1(A)) ) ),
    file(parsp_1,k8_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_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) )
     => ~ v1_xboole_0(k5_parsp_1(A)) ) ),
    file(parsp_1,fc1_parsp_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(fc1_xboole_0,axiom,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    []).

fof(fc2_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) )
     => ~ v1_xboole_0(k6_parsp_1(A)) ) ),
    file(parsp_1,fc2_parsp_1),
    []).

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(fc5_subset_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C) )
     => ~ v1_xboole_0(k3_zfmisc_1(A,B,C)) ) ),
    file(subset_1,fc5_subset_1),
    []).

fof(fc6_subset_1,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D) )
     => ~ v1_xboole_0(k4_zfmisc_1(A,B,C,D)) ) ),
    file(subset_1,fc6_subset_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_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(redefinition_k10_group_1,axiom,(
    ! [A,B,C] : 
      ( ( ~ v3_struct_0(A)
        & v7_group_1(A)
        & l1_group_1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k10_group_1(A,B,C) = k1_group_1(A,B,C) ) ),
    file(group_1,k10_group_1),
    []).

fof(redefinition_k5_domain_1,axiom,(
    ! [A,B,C,D,E,F,G,H] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & ~ v1_xboole_0(C)
        & ~ v1_xboole_0(D)
        & m1_subset_1(E,A)
        & m1_subset_1(F,B)
        & m1_subset_1(G,C)
        & m1_subset_1(H,D) )
     => k5_domain_1(A,B,C,D,E,F,G,H) = k4_mcart_1(E,F,G,H) ) ),
    file(domain_1,k5_domain_1),
    []).

fof(t18_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)
                      <=> r2_hidden(k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E),k8_parsp_1(A)) ) ) ) ) ) ) ),
    file(parsp_1,t18_parsp_1),
    []).

fof(t19_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)))
                     => ( r2_hidden(k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E),k8_parsp_1(A))
                      <=> ( r2_hidden(k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E),k6_parsp_1(A))
                          & ? [F] : 
                              ( m1_subset_1(F,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                              & ? [G] : 
                                  ( m1_subset_1(G,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                  & ? [H] : 
                                      ( m1_subset_1(H,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                      & ? [I] : 
                                          ( m1_subset_1(I,k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)))
                                          & k5_domain_1(u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),u1_struct_0(k9_parsp_1(A)),B,C,D,E) = k5_domain_1(k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),F,G,H,I)
                                          & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)),k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))),k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I)),k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))) = k1_rlvect_1(A)
                                          & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))),k10_group_1(A,k6_rlvect_1(A,k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k5_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))) = k1_rlvect_1(A)
                                          & k6_rlvect_1(A,k10_group_1(A,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I))),k10_group_1(A,k6_rlvect_1(A,k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),H),k6_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),I)),k6_rlvect_1(A,k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),F),k7_mcart_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),G)))) = k1_rlvect_1(A) ) ) ) ) ) ) ) ) ) ) ) ),
    file(parsp_1,t19_parsp_1),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t6_boole,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    []).

fof(t7_boole,axiom,(
    ! [A,B] : ~ ( r2_hidden(A,B)
      & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    []).

fof(t8_boole,axiom,(
    ! [A,B] : ~ ( v1_xboole_0(A)
      & A != B
      & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    []).