% Mizar problem: t39_altcat_4,altcat_4,1107,28 
fof(t39_altcat_4,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v2_altcat_2(B,A)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ! [H] : 
                                  ( m1_subset_1(H,k1_altcat_1(B,E,F))
                                 => ( ( E = C
                                      & F = D
                                      & G = H )
                                   => ( k1_altcat_1(B,E,F) = k1_xboole_0
                                      | k1_altcat_1(B,F,E) = k1_xboole_0
                                      | ( ( v1_altcat_3(G,A,C,D)
                                         => v1_altcat_3(H,B,E,F) )
                                        & ( v2_altcat_3(G,A,C,D)
                                         => v2_altcat_3(H,B,E,F) )
                                        & ( v3_altcat_3(G,A,C,D)
                                         => v3_altcat_3(H,B,E,F) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_altcat_2,cc2_altcat_2,cc2_functor0,cc3_altcat_2,cc4_altcat_2,commutativity_k2_tarski,d1_binop_1,d2_altcat_1,d2_altcat_3,d3_altcat_3,d5_tarski,dt_k1_altcat_1,dt_k1_binop_1,dt_k1_funct_1,dt_k1_tarski,dt_k1_xboole_0,dt_k2_tarski,dt_k2_zfmisc_1,dt_k4_tarski,dt_l1_altcat_1,dt_l1_struct_0,dt_l2_altcat_1,dt_m1_altcat_2,dt_m1_pboole,dt_m1_subset_1,dt_u1_altcat_1,dt_u1_struct_0,existence_l1_altcat_1,existence_l1_struct_0,existence_l2_altcat_1,existence_m1_altcat_2,existence_m1_pboole,existence_m1_subset_1,fc1_altcat_4,fc1_struct_0,fc1_xboole_0,fc2_altcat_1,fc2_subset_1,fc3_subset_1,fc4_subset_1,rc10_altcat_2,rc1_xboole_0,rc2_altcat_2,rc2_xboole_0,rc3_altcat_2,rc3_struct_0,rc7_functor0,t1_subset,t29_altcat_2,t2_subset,t38_altcat_4,t5_altcat_3,t6_altcat_3,t6_boole,t7_boole,t8_boole]),
    [file(altcat_4,t39_altcat_4)]).

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

fof(cc1_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v12_altcat_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_altcat_2(A) ) ) ) ),
    file(altcat_2,cc1_altcat_2),
    []).

fof(cc2_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_2(B,A) )
           => v2_altcat_1(B) ) ) ) ),
    file(altcat_2,cc2_altcat_2),
    []).

fof(cc2_functor0,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ( ( ~ v3_struct_0(A)
          & v12_altcat_1(A) )
       => ( ~ v3_struct_0(A)
          & v1_altcat_2(A) ) ) ) ),
    file(functor0,cc2_functor0),
    []).

fof(cc3_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B) )
           => ( ~ v3_struct_0(B)
              & v11_altcat_1(B) ) ) ) ) ),
    file(altcat_2,cc3_altcat_2),
    []).

fof(cc4_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => ( ( ~ v3_struct_0(B)
              & v2_altcat_1(B)
              & v3_altcat_2(B,A) )
           => ( ~ v3_struct_0(B)
              & v12_altcat_1(B)
              & v1_altcat_2(B) ) ) ) ) ),
    file(altcat_2,cc4_altcat_2),
    []).

fof(commutativity_k2_tarski,axiom,(
    ! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ),
    file(tarski,k2_tarski),
    []).

fof(d1_binop_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ),
    file(binop_1,d1_binop_1),
    []).

fof(d2_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_altcat_1(A,B,C) = k1_binop_1(u1_altcat_1(A),B,C) ) ) ) ),
    file(altcat_1,d2_altcat_1),
    []).

fof(d2_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_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,k1_altcat_1(A,B,C))
                 => ( v1_altcat_3(D,A,B,C)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_altcat_1(A,C,B))
                        & r1_altcat_3(A,B,C,D,E) ) ) ) ) ) ) ),
    file(altcat_3,d2_altcat_3),
    []).

fof(d3_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_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,k1_altcat_1(A,B,C))
                 => ( v2_altcat_3(D,A,B,C)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_altcat_1(A,C,B))
                        & r1_altcat_3(A,C,B,E,D) ) ) ) ) ) ) ),
    file(altcat_3,d3_altcat_3),
    []).

fof(d5_tarski,axiom,(
    ! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ),
    file(tarski,d5_tarski),
    []).

fof(dt_k1_altcat_1,axiom,(
    $true ),
    file(altcat_1,k1_altcat_1),
    []).

fof(dt_k1_binop_1,axiom,(
    $true ),
    file(binop_1,k1_binop_1),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_tarski,axiom,(
    $true ),
    file(tarski,k1_tarski),
    []).

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

fof(dt_k2_tarski,axiom,(
    $true ),
    file(tarski,k2_tarski),
    []).

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

fof(dt_k4_tarski,axiom,(
    $true ),
    file(tarski,k4_tarski),
    []).

fof(dt_l1_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => l1_struct_0(A) ) ),
    file(altcat_1,l1_altcat_1),
    []).

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

fof(dt_l2_altcat_1,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => l1_altcat_1(A) ) ),
    file(altcat_1,l2_altcat_1),
    []).

fof(dt_m1_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ! [B] : 
          ( m1_altcat_2(B,A)
         => l2_altcat_1(B) ) ) ),
    file(altcat_2,m1_altcat_2),
    []).

fof(dt_m1_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(B)
        & v1_funct_1(B) ) ) ),
    file(pboole,m1_pboole),
    []).

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

fof(dt_u1_altcat_1,axiom,(
    ! [A] : 
      ( l1_altcat_1(A)
     => m1_pboole(u1_altcat_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ),
    file(altcat_1,u1_altcat_1),
    []).

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

fof(existence_l1_altcat_1,axiom,(
    ? [A] : l1_altcat_1(A) ),
    file(altcat_1,l1_altcat_1),
    []).

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

fof(existence_l2_altcat_1,axiom,(
    ? [A] : l2_altcat_1(A) ),
    file(altcat_1,l2_altcat_1),
    []).

fof(existence_m1_altcat_2,axiom,(
    ! [A] : 
      ( l2_altcat_1(A)
     => ? [B] : m1_altcat_2(B,A) ) ),
    file(altcat_2,m1_altcat_2),
    []).

fof(existence_m1_pboole,axiom,(
    ! [A] : 
    ? [B] : m1_pboole(B,A) ),
    file(pboole,m1_pboole),
    []).

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

fof(fc1_altcat_4,axiom,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => ~ v1_xboole_0(k1_altcat_1(A,B,B)) ) ),
    file(altcat_4,fc1_altcat_4),
    []).

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_altcat_1,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( ~ v1_xboole_0(k1_tarski(A))
        & v1_finset_1(k1_tarski(A))
        & v1_fraenkel(k1_tarski(A))
        & v1_realset1(k1_tarski(A)) ) ) ),
    file(altcat_1,fc2_altcat_1),
    []).

fof(fc2_subset_1,axiom,(
    ! [A] : ~ v1_xboole_0(k1_tarski(A)) ),
    file(subset_1,fc2_subset_1),
    []).

fof(fc3_subset_1,axiom,(
    ! [A,B] : ~ v1_xboole_0(k2_tarski(A,B)) ),
    file(subset_1,fc3_subset_1),
    []).

fof(fc4_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B) )
     => ~ v1_xboole_0(k2_zfmisc_1(A,B)) ) ),
    file(subset_1,fc4_subset_1),
    []).

fof(rc10_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ? [B] : 
          ( m1_altcat_2(B,A)
          & ~ v3_struct_0(B)
          & v2_altcat_1(B)
          & v11_altcat_1(B)
          & v12_altcat_1(B)
          & v1_altcat_2(B)
          & v3_altcat_2(B,A) ) ) ),
    file(altcat_2,rc10_altcat_2),
    []).

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

fof(rc2_altcat_2,axiom,(
    ? [A] : 
      ( l1_altcat_1(A)
      & ~ v3_struct_0(A)
      & v1_altcat_2(A) ) ),
    file(altcat_2,rc2_altcat_2),
    []).

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

fof(rc3_altcat_2,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v1_altcat_2(A) ) ),
    file(altcat_2,rc3_altcat_2),
    []).

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

fof(rc7_functor0,axiom,(
    ? [A] : 
      ( l2_altcat_1(A)
      & ~ v3_struct_0(A)
      & v1_altcat_2(A) ) ),
    file(functor0,rc7_functor0),
    []).

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

fof(t29_altcat_2,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_2(B,A)
            & m1_altcat_2(B,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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( C = E
                              & D = F )
                           => k1_altcat_1(A,C,D) = k1_altcat_1(B,E,F) ) ) ) ) ) ) ) ),
    file(altcat_2,t29_altcat_2),
    []).

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

fof(t38_altcat_4,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v2_altcat_1(B)
            & v3_altcat_2(B,A)
            & m1_altcat_2(B,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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_altcat_1(A,C,D))
                             => ! [H] : 
                                  ( m1_subset_1(H,k1_altcat_1(A,D,C))
                                 => ! [I] : 
                                      ( m1_subset_1(I,k1_altcat_1(B,E,F))
                                     => ! [J] : 
                                          ( m1_subset_1(J,k1_altcat_1(B,F,E))
                                         => ( ( E = C
                                              & F = D
                                              & G = I
                                              & H = J )
                                           => ( k1_altcat_1(B,E,F) = k1_xboole_0
                                              | k1_altcat_1(B,F,E) = k1_xboole_0
                                              | ( ( r1_altcat_3(A,C,D,G,H)
                                                 => r1_altcat_3(B,E,F,I,J) )
                                                & ( r1_altcat_3(B,E,F,I,J)
                                                 => r1_altcat_3(A,C,D,G,H) )
                                                & ( r1_altcat_3(A,D,C,H,G)
                                                 => r1_altcat_3(B,F,E,J,I) )
                                                & ( r1_altcat_3(B,F,E,J,I)
                                                 => r1_altcat_3(A,D,C,H,G) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(altcat_4,t38_altcat_4),
    []).

fof(t5_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_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,k1_altcat_1(A,B,C))
                 => ( v3_altcat_3(D,A,B,C)
                   => ( v1_altcat_3(D,A,B,C)
                      & v2_altcat_3(D,A,B,C) ) ) ) ) ) ) ),
    file(altcat_3,t5_altcat_3),
    []).

fof(t6_altcat_3,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_altcat_1(A)
        & v11_altcat_1(A)
        & v12_altcat_1(A)
        & l2_altcat_1(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( k1_altcat_1(A,B,C) != k1_xboole_0
                  & k1_altcat_1(A,C,B) != k1_xboole_0
                  & ~ ! [D] : 
                        ( m1_subset_1(D,k1_altcat_1(A,B,C))
                       => ( v3_altcat_3(D,A,B,C)
                        <=> ( v1_altcat_3(D,A,B,C)
                            & v2_altcat_3(D,A,B,C) ) ) ) ) ) ) ) ),
    file(altcat_3,t6_altcat_3),
    []).

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),
    []).