% Mizar problem: t8_algstr_3,algstr_3,338,19 
fof(t8_algstr_3,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_algstr_3(A)
        & l1_algstr_3(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))
                             => ( ( k1_algstr_3(A,D,B,E) = k1_algstr_3(A,F,B,G)
                                  & k1_algstr_3(A,D,C,E) = k1_algstr_3(A,F,C,G) )
                               => ( B = C
                                  | ( D = F
                                    & E = G ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc10_membered,cc11_membered,cc12_membered,cc13_membered,cc14_membered,cc15_membered,cc16_membered,cc17_membered,cc18_membered,cc19_membered,cc1_membered,cc20_membered,cc2_membered,cc3_membered,cc4_membered,d1_algstr_3,d3_algstr_3,d7_algstr_3,dt_k1_algstr_3,dt_k1_multop_1,dt_k1_rlvect_1,dt_k1_zfmisc_1,dt_k2_algstr_3,dt_k2_multop_1,dt_k2_zfmisc_1,dt_k3_zfmisc_1,dt_l1_algstr_3,dt_l1_struct_0,dt_l2_struct_0,dt_m1_relset_1,dt_m1_subset_1,dt_m2_relset_1,dt_u1_algstr_3,dt_u1_struct_0,dt_u2_algstr_3,existence_l1_algstr_3,existence_l1_struct_0,existence_l2_struct_0,existence_m1_relset_1,existence_m1_subset_1,existence_m2_relset_1,fc1_struct_0,rc1_membered,rc2_algstr_3,rc3_struct_0,rc4_struct_0,rc5_struct_0,redefinition_k2_multop_1,redefinition_m2_relset_1,reflexivity_r1_tarski,t1_subset,t2_subset,t3_subset,t4_subset,t5_subset]),
    [file(algstr_3,t8_algstr_3)]).

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

fof(cc10_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => v1_xcmplx_0(B) ) ) ),
    file(membered,cc10_membered),
    []).

fof(cc11_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B) ) ) ) ),
    file(membered,cc11_membered),
    []).

fof(cc12_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc12_membered),
    []).

fof(cc13_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc13_membered),
    []).

fof(cc14_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ( v1_xcmplx_0(B)
            & v4_ordinal2(B)
            & v1_xreal_0(B)
            & v1_int_1(B)
            & v1_rat_1(B) ) ) ) ),
    file(membered,cc14_membered),
    []).

fof(cc15_membered,axiom,(
    ! [A] : 
      ( v1_xboole_0(A)
     => ( v1_membered(A)
        & v2_membered(A)
        & v3_membered(A)
        & v4_membered(A)
        & v5_membered(A) ) ) ),
    file(membered,cc15_membered),
    []).

fof(cc16_membered,axiom,(
    ! [A] : 
      ( v1_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => v1_membered(B) ) ) ),
    file(membered,cc16_membered),
    []).

fof(cc17_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B) ) ) ) ),
    file(membered,cc17_membered),
    []).

fof(cc18_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B) ) ) ) ),
    file(membered,cc18_membered),
    []).

fof(cc19_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B) ) ) ) ),
    file(membered,cc19_membered),
    []).

fof(cc1_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => v4_membered(A) ) ),
    file(membered,cc1_membered),
    []).

fof(cc20_membered,axiom,(
    ! [A] : 
      ( v5_membered(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(A))
         => ( v1_membered(B)
            & v2_membered(B)
            & v3_membered(B)
            & v4_membered(B)
            & v5_membered(B) ) ) ) ),
    file(membered,cc20_membered),
    []).

fof(cc2_membered,axiom,(
    ! [A] : 
      ( v4_membered(A)
     => v3_membered(A) ) ),
    file(membered,cc2_membered),
    []).

fof(cc3_membered,axiom,(
    ! [A] : 
      ( v3_membered(A)
     => v2_membered(A) ) ),
    file(membered,cc3_membered),
    []).

fof(cc4_membered,axiom,(
    ! [A] : 
      ( v2_membered(A)
     => v1_membered(A) ) ),
    file(membered,cc4_membered),
    []).

fof(d1_algstr_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_algstr_3(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_algstr_3(A,B,C,D) = k2_multop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u2_algstr_3(A),B,C,D) ) ) ) ) ),
    file(algstr_3,d1_algstr_3),
    []).

fof(d3_algstr_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_algstr_3(A) )
     => k2_algstr_3(A) = u1_algstr_3(A) ) ),
    file(algstr_3,d3_algstr_3),
    []).

fof(d7_algstr_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_algstr_3(A) )
     => ( v2_algstr_3(A)
      <=> ( k1_rlvect_1(A) != k2_algstr_3(A)
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => k1_algstr_3(A,B,k2_algstr_3(A),k1_rlvect_1(A)) = B )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => k1_algstr_3(A,k2_algstr_3(A),B,k1_rlvect_1(A)) = B )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k1_algstr_3(A,B,k1_rlvect_1(A),C) = C ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k1_algstr_3(A,k1_rlvect_1(A),B,C) = C ) )
          & ! [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_algstr_3(A,B,C,E) = D ) ) ) )
          & ! [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_algstr_3(A,B,C,D) = k1_algstr_3(A,B,C,E)
                           => D = E ) ) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(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))
                                    & k1_algstr_3(A,F,B,G) = D
                                    & k1_algstr_3(A,F,C,G) = E ) ) ) ) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(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))
                                & k1_algstr_3(A,B,F,D) = k1_algstr_3(A,C,F,E) ) ) ) ) ) )
          & ! [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))
                                 => ~ ( k1_algstr_3(A,D,B,F) = k1_algstr_3(A,E,B,G)
                                      & k1_algstr_3(A,D,C,F) = k1_algstr_3(A,E,C,G)
                                      & B != C
                                      & D != E ) ) ) ) ) ) ) ) ) ) ),
    file(algstr_3,d7_algstr_3),
    []).

fof(dt_k1_algstr_3,axiom,(
    ! [A,B,C,D] : 
      ( ( ~ v3_struct_0(A)
        & l1_algstr_3(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(k1_algstr_3(A,B,C,D),u1_struct_0(A)) ) ),
    file(algstr_3,k1_algstr_3),
    []).

fof(dt_k1_multop_1,axiom,(
    $true ),
    file(multop_1,k1_multop_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_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_algstr_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_algstr_3(A) )
     => m1_subset_1(k2_algstr_3(A),u1_struct_0(A)) ) ),
    file(algstr_3,k2_algstr_3),
    []).

fof(dt_k2_multop_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)
        & v1_funct_1(E)
        & v1_funct_2(E,k3_zfmisc_1(A,B,C),D)
        & m1_relset_1(E,k3_zfmisc_1(A,B,C),D)
        & m1_subset_1(F,A)
        & m1_subset_1(G,B)
        & m1_subset_1(H,C) )
     => m1_subset_1(k2_multop_1(A,B,C,D,E,F,G,H),D) ) ),
    file(multop_1,k2_multop_1),
    []).

fof(dt_k2_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k2_zfmisc_1),
    []).

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

fof(dt_l1_algstr_3,axiom,(
    ! [A] : 
      ( l1_algstr_3(A)
     => l2_struct_0(A) ) ),
    file(algstr_3,l1_algstr_3),
    []).

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_relset_1,axiom,(
    $true ),
    file(relset_1,m1_relset_1),
    []).

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

fof(dt_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(dt_u1_algstr_3,axiom,(
    ! [A] : 
      ( l1_algstr_3(A)
     => m1_subset_1(u1_algstr_3(A),u1_struct_0(A)) ) ),
    file(algstr_3,u1_algstr_3),
    []).

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

fof(dt_u2_algstr_3,axiom,(
    ! [A] : 
      ( l1_algstr_3(A)
     => ( v1_funct_1(u2_algstr_3(A))
        & v1_funct_2(u2_algstr_3(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u2_algstr_3(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) ),
    file(algstr_3,u2_algstr_3),
    []).

fof(existence_l1_algstr_3,axiom,(
    ? [A] : l1_algstr_3(A) ),
    file(algstr_3,l1_algstr_3),
    []).

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_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m1_relset_1(C,A,B) ),
    file(relset_1,m1_relset_1),
    []).

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

fof(existence_m2_relset_1,axiom,(
    ! [A,B] : 
    ? [C] : m2_relset_1(C,A,B) ),
    file(relset_1,m2_relset_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(rc1_membered,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v1_membered(A)
      & v2_membered(A)
      & v3_membered(A)
      & v4_membered(A)
      & v5_membered(A) ) ),
    file(membered,rc1_membered),
    []).

fof(rc2_algstr_3,axiom,(
    ? [A] : 
      ( l1_algstr_3(A)
      & ~ v3_struct_0(A) ) ),
    file(algstr_3,rc2_algstr_3),
    []).

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(rc5_struct_0,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ? [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
          & ~ v1_xboole_0(B) ) ) ),
    file(struct_0,rc5_struct_0),
    []).

fof(redefinition_k2_multop_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)
        & v1_funct_1(E)
        & v1_funct_2(E,k3_zfmisc_1(A,B,C),D)
        & m1_relset_1(E,k3_zfmisc_1(A,B,C),D)
        & m1_subset_1(F,A)
        & m1_subset_1(G,B)
        & m1_subset_1(H,C) )
     => k2_multop_1(A,B,C,D,E,F,G,H) = k1_multop_1(E,F,G,H) ) ),
    file(multop_1,k2_multop_1),
    []).

fof(redefinition_m2_relset_1,axiom,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
    <=> m1_relset_1(C,A,B) ) ),
    file(relset_1,m2_relset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

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(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).