% Mizar ND problem: t8_aff_4,aff_4,84,10 
fof(dh_c1_9__aff_4,definition,
    ( ( ( ~ v3_struct_0(c1_9__aff_4)
        & ~ v3_realset2(c1_9__aff_4)
        & v1_diraf(c1_9__aff_4)
        & l1_analoaf(c1_9__aff_4) )
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(c1_9__aff_4))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(c1_9__aff_4))
                         => ! [F] : 
                              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                                 => ( ( r2_hidden(A,F)
                                      & r2_hidden(A,G)
                                      & r2_hidden(B,F)
                                      & r2_hidden(C,F)
                                      & r2_hidden(D,G)
                                      & r2_hidden(E,G)
                                      & v1_aff_1(F,c1_9__aff_4)
                                      & v1_aff_1(G,c1_9__aff_4)
                                      & A = C )
                                   => ( A = B
                                      | A = D
                                      | F = G
                                      | ( ~ r2_analoaf(c1_9__aff_4,B,D,C,E)
                                        & ~ r2_analoaf(c1_9__aff_4,D,B,E,C) )
                                      | A = E ) ) ) ) ) ) ) ) ) )
   => ! [H] : 
        ( ( ~ v3_struct_0(H)
          & ~ v3_realset2(H)
          & v1_diraf(H)
          & l1_analoaf(H) )
       => ! [I] : 
            ( m1_subset_1(I,u1_struct_0(H))
           => ! [J] : 
                ( m1_subset_1(J,u1_struct_0(H))
               => ! [K] : 
                    ( m1_subset_1(K,u1_struct_0(H))
                   => ! [L] : 
                        ( m1_subset_1(L,u1_struct_0(H))
                       => ! [M] : 
                            ( m1_subset_1(M,u1_struct_0(H))
                           => ! [N] : 
                                ( m1_subset_1(N,k1_zfmisc_1(u1_struct_0(H)))
                               => ! [O] : 
                                    ( m1_subset_1(O,k1_zfmisc_1(u1_struct_0(H)))
                                   => ( ( r2_hidden(I,N)
                                        & r2_hidden(I,O)
                                        & r2_hidden(J,N)
                                        & r2_hidden(K,N)
                                        & r2_hidden(L,O)
                                        & r2_hidden(M,O)
                                        & v1_aff_1(N,H)
                                        & v1_aff_1(O,H)
                                        & I = K )
                                     => ( I = J
                                        | I = L
                                        | N = O
                                        | ( ~ r2_analoaf(H,J,L,K,M)
                                          & ~ r2_analoaf(H,L,J,M,K) )
                                        | I = M ) ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c1_9__aff_4),file(aff_4,c1_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c1_9__aff_4)]).

fof(dh_c2_9__aff_4,definition,
    ( ( m1_subset_1(c2_9__aff_4,u1_struct_0(c1_9__aff_4))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(c1_9__aff_4))
                     => ! [E] : 
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                         => ! [F] : 
                              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                             => ( ( r2_hidden(c2_9__aff_4,E)
                                  & r2_hidden(c2_9__aff_4,F)
                                  & r2_hidden(A,E)
                                  & r2_hidden(B,E)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,F)
                                  & v1_aff_1(E,c1_9__aff_4)
                                  & v1_aff_1(F,c1_9__aff_4)
                                  & c2_9__aff_4 = B )
                               => ( c2_9__aff_4 = A
                                  | c2_9__aff_4 = C
                                  | E = F
                                  | ( ~ r2_analoaf(c1_9__aff_4,A,C,B,D)
                                    & ~ r2_analoaf(c1_9__aff_4,C,A,D,B) )
                                  | c2_9__aff_4 = D ) ) ) ) ) ) ) ) )
   => ! [G] : 
        ( m1_subset_1(G,u1_struct_0(c1_9__aff_4))
       => ! [H] : 
            ( m1_subset_1(H,u1_struct_0(c1_9__aff_4))
           => ! [I] : 
                ( m1_subset_1(I,u1_struct_0(c1_9__aff_4))
               => ! [J] : 
                    ( m1_subset_1(J,u1_struct_0(c1_9__aff_4))
                   => ! [K] : 
                        ( m1_subset_1(K,u1_struct_0(c1_9__aff_4))
                       => ! [L] : 
                            ( m1_subset_1(L,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                           => ! [M] : 
                                ( m1_subset_1(M,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                               => ( ( r2_hidden(G,L)
                                    & r2_hidden(G,M)
                                    & r2_hidden(H,L)
                                    & r2_hidden(I,L)
                                    & r2_hidden(J,M)
                                    & r2_hidden(K,M)
                                    & v1_aff_1(L,c1_9__aff_4)
                                    & v1_aff_1(M,c1_9__aff_4)
                                    & G = I )
                                 => ( G = H
                                    | G = J
                                    | L = M
                                    | ( ~ r2_analoaf(c1_9__aff_4,H,J,I,K)
                                      & ~ r2_analoaf(c1_9__aff_4,J,H,K,I) )
                                    | G = K ) ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c2_9__aff_4),file(aff_4,c2_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c2_9__aff_4)]).

fof(dh_c3_9__aff_4,definition,
    ( ( m1_subset_1(c3_9__aff_4,u1_struct_0(c1_9__aff_4))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
                 => ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                     => ! [E] : 
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                         => ( ( r2_hidden(c2_9__aff_4,D)
                              & r2_hidden(c2_9__aff_4,E)
                              & r2_hidden(c3_9__aff_4,D)
                              & r2_hidden(A,D)
                              & r2_hidden(B,E)
                              & r2_hidden(C,E)
                              & v1_aff_1(D,c1_9__aff_4)
                              & v1_aff_1(E,c1_9__aff_4)
                              & c2_9__aff_4 = A )
                           => ( c2_9__aff_4 = c3_9__aff_4
                              | c2_9__aff_4 = B
                              | D = E
                              | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,B,A,C)
                                & ~ r2_analoaf(c1_9__aff_4,B,c3_9__aff_4,C,A) )
                              | c2_9__aff_4 = C ) ) ) ) ) ) ) )
   => ! [F] : 
        ( m1_subset_1(F,u1_struct_0(c1_9__aff_4))
       => ! [G] : 
            ( m1_subset_1(G,u1_struct_0(c1_9__aff_4))
           => ! [H] : 
                ( m1_subset_1(H,u1_struct_0(c1_9__aff_4))
               => ! [I] : 
                    ( m1_subset_1(I,u1_struct_0(c1_9__aff_4))
                   => ! [J] : 
                        ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                       => ! [K] : 
                            ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                           => ( ( r2_hidden(c2_9__aff_4,J)
                                & r2_hidden(c2_9__aff_4,K)
                                & r2_hidden(F,J)
                                & r2_hidden(G,J)
                                & r2_hidden(H,K)
                                & r2_hidden(I,K)
                                & v1_aff_1(J,c1_9__aff_4)
                                & v1_aff_1(K,c1_9__aff_4)
                                & c2_9__aff_4 = G )
                             => ( c2_9__aff_4 = F
                                | c2_9__aff_4 = H
                                | J = K
                                | ( ~ r2_analoaf(c1_9__aff_4,F,H,G,I)
                                  & ~ r2_analoaf(c1_9__aff_4,H,F,I,G) )
                                | c2_9__aff_4 = I ) ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c3_9__aff_4),file(aff_4,c3_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c3_9__aff_4)]).

fof(dh_c4_9__aff_4,definition,
    ( ( m1_subset_1(c4_9__aff_4,u1_struct_0(c1_9__aff_4))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
         => ! [B] : 
              ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                 => ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                     => ( ( r2_hidden(c2_9__aff_4,C)
                          & r2_hidden(c2_9__aff_4,D)
                          & r2_hidden(c3_9__aff_4,C)
                          & r2_hidden(c4_9__aff_4,C)
                          & r2_hidden(A,D)
                          & r2_hidden(B,D)
                          & v1_aff_1(C,c1_9__aff_4)
                          & v1_aff_1(D,c1_9__aff_4)
                          & c2_9__aff_4 = c4_9__aff_4 )
                       => ( c2_9__aff_4 = c3_9__aff_4
                          | c2_9__aff_4 = A
                          | C = D
                          | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,A,c4_9__aff_4,B)
                            & ~ r2_analoaf(c1_9__aff_4,A,c3_9__aff_4,B,c4_9__aff_4) )
                          | c2_9__aff_4 = B ) ) ) ) ) ) )
   => ! [E] : 
        ( m1_subset_1(E,u1_struct_0(c1_9__aff_4))
       => ! [F] : 
            ( m1_subset_1(F,u1_struct_0(c1_9__aff_4))
           => ! [G] : 
                ( m1_subset_1(G,u1_struct_0(c1_9__aff_4))
               => ! [H] : 
                    ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                   => ! [I] : 
                        ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                       => ( ( r2_hidden(c2_9__aff_4,H)
                            & r2_hidden(c2_9__aff_4,I)
                            & r2_hidden(c3_9__aff_4,H)
                            & r2_hidden(E,H)
                            & r2_hidden(F,I)
                            & r2_hidden(G,I)
                            & v1_aff_1(H,c1_9__aff_4)
                            & v1_aff_1(I,c1_9__aff_4)
                            & c2_9__aff_4 = E )
                         => ( c2_9__aff_4 = c3_9__aff_4
                            | c2_9__aff_4 = F
                            | H = I
                            | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,F,E,G)
                              & ~ r2_analoaf(c1_9__aff_4,F,c3_9__aff_4,G,E) )
                            | c2_9__aff_4 = G ) ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c4_9__aff_4),file(aff_4,c4_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c4_9__aff_4)]).

fof(dh_c5_9__aff_4,definition,
    ( ( m1_subset_1(c5_9__aff_4,u1_struct_0(c1_9__aff_4))
     => ! [A] : 
          ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
             => ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                 => ( ( r2_hidden(c2_9__aff_4,B)
                      & r2_hidden(c2_9__aff_4,C)
                      & r2_hidden(c3_9__aff_4,B)
                      & r2_hidden(c4_9__aff_4,B)
                      & r2_hidden(c5_9__aff_4,C)
                      & r2_hidden(A,C)
                      & v1_aff_1(B,c1_9__aff_4)
                      & v1_aff_1(C,c1_9__aff_4)
                      & c2_9__aff_4 = c4_9__aff_4 )
                   => ( c2_9__aff_4 = c3_9__aff_4
                      | c2_9__aff_4 = c5_9__aff_4
                      | B = C
                      | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,A)
                        & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,A,c4_9__aff_4) )
                      | c2_9__aff_4 = A ) ) ) ) ) )
   => ! [D] : 
        ( m1_subset_1(D,u1_struct_0(c1_9__aff_4))
       => ! [E] : 
            ( m1_subset_1(E,u1_struct_0(c1_9__aff_4))
           => ! [F] : 
                ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
               => ! [G] : 
                    ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                   => ( ( r2_hidden(c2_9__aff_4,F)
                        & r2_hidden(c2_9__aff_4,G)
                        & r2_hidden(c3_9__aff_4,F)
                        & r2_hidden(c4_9__aff_4,F)
                        & r2_hidden(D,G)
                        & r2_hidden(E,G)
                        & v1_aff_1(F,c1_9__aff_4)
                        & v1_aff_1(G,c1_9__aff_4)
                        & c2_9__aff_4 = c4_9__aff_4 )
                     => ( c2_9__aff_4 = c3_9__aff_4
                        | c2_9__aff_4 = D
                        | F = G
                        | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,D,c4_9__aff_4,E)
                          & ~ r2_analoaf(c1_9__aff_4,D,c3_9__aff_4,E,c4_9__aff_4) )
                        | c2_9__aff_4 = E ) ) ) ) ) ) ),
    introduced(definition,[new_symbol(c5_9__aff_4),file(aff_4,c5_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c5_9__aff_4)]).

fof(dh_c6_9__aff_4,definition,
    ( ( m1_subset_1(c6_9__aff_4,u1_struct_0(c1_9__aff_4))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
         => ! [B] : 
              ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
             => ( ( r2_hidden(c2_9__aff_4,A)
                  & r2_hidden(c2_9__aff_4,B)
                  & r2_hidden(c3_9__aff_4,A)
                  & r2_hidden(c4_9__aff_4,A)
                  & r2_hidden(c5_9__aff_4,B)
                  & r2_hidden(c6_9__aff_4,B)
                  & v1_aff_1(A,c1_9__aff_4)
                  & v1_aff_1(B,c1_9__aff_4)
                  & c2_9__aff_4 = c4_9__aff_4 )
               => ( c2_9__aff_4 = c3_9__aff_4
                  | c2_9__aff_4 = c5_9__aff_4
                  | A = B
                  | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
                    & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
                  | c2_9__aff_4 = c6_9__aff_4 ) ) ) ) )
   => ! [C] : 
        ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
       => ! [D] : 
            ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
           => ! [E] : 
                ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
               => ( ( r2_hidden(c2_9__aff_4,D)
                    & r2_hidden(c2_9__aff_4,E)
                    & r2_hidden(c3_9__aff_4,D)
                    & r2_hidden(c4_9__aff_4,D)
                    & r2_hidden(c5_9__aff_4,E)
                    & r2_hidden(C,E)
                    & v1_aff_1(D,c1_9__aff_4)
                    & v1_aff_1(E,c1_9__aff_4)
                    & c2_9__aff_4 = c4_9__aff_4 )
                 => ( c2_9__aff_4 = c3_9__aff_4
                    | c2_9__aff_4 = c5_9__aff_4
                    | D = E
                    | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,C)
                      & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,C,c4_9__aff_4) )
                    | c2_9__aff_4 = C ) ) ) ) ) ),
    introduced(definition,[new_symbol(c6_9__aff_4),file(aff_4,c6_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c6_9__aff_4)]).

fof(dh_c7_9__aff_4,definition,
    ( ( m1_subset_1(c7_9__aff_4,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
     => ! [A] : 
          ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
         => ( ( r2_hidden(c2_9__aff_4,c7_9__aff_4)
              & r2_hidden(c2_9__aff_4,A)
              & r2_hidden(c3_9__aff_4,c7_9__aff_4)
              & r2_hidden(c4_9__aff_4,c7_9__aff_4)
              & r2_hidden(c5_9__aff_4,A)
              & r2_hidden(c6_9__aff_4,A)
              & v1_aff_1(c7_9__aff_4,c1_9__aff_4)
              & v1_aff_1(A,c1_9__aff_4)
              & c2_9__aff_4 = c4_9__aff_4 )
           => ( c2_9__aff_4 = c3_9__aff_4
              | c2_9__aff_4 = c5_9__aff_4
              | c7_9__aff_4 = A
              | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
                & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
              | c2_9__aff_4 = c6_9__aff_4 ) ) ) )
   => ! [B] : 
        ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
       => ! [C] : 
            ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
           => ( ( r2_hidden(c2_9__aff_4,B)
                & r2_hidden(c2_9__aff_4,C)
                & r2_hidden(c3_9__aff_4,B)
                & r2_hidden(c4_9__aff_4,B)
                & r2_hidden(c5_9__aff_4,C)
                & r2_hidden(c6_9__aff_4,C)
                & v1_aff_1(B,c1_9__aff_4)
                & v1_aff_1(C,c1_9__aff_4)
                & c2_9__aff_4 = c4_9__aff_4 )
             => ( c2_9__aff_4 = c3_9__aff_4
                | c2_9__aff_4 = c5_9__aff_4
                | B = C
                | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
                  & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
                | c2_9__aff_4 = c6_9__aff_4 ) ) ) ) ),
    introduced(definition,[new_symbol(c7_9__aff_4),file(aff_4,c7_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c7_9__aff_4)]).

fof(dh_c8_9__aff_4,definition,
    ( ( m1_subset_1(c8_9__aff_4,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
     => ( ( r2_hidden(c2_9__aff_4,c7_9__aff_4)
          & r2_hidden(c2_9__aff_4,c8_9__aff_4)
          & r2_hidden(c3_9__aff_4,c7_9__aff_4)
          & r2_hidden(c4_9__aff_4,c7_9__aff_4)
          & r2_hidden(c5_9__aff_4,c8_9__aff_4)
          & r2_hidden(c6_9__aff_4,c8_9__aff_4)
          & v1_aff_1(c7_9__aff_4,c1_9__aff_4)
          & v1_aff_1(c8_9__aff_4,c1_9__aff_4)
          & c2_9__aff_4 = c4_9__aff_4 )
       => ( c2_9__aff_4 = c3_9__aff_4
          | c2_9__aff_4 = c5_9__aff_4
          | c7_9__aff_4 = c8_9__aff_4
          | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
            & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
          | c2_9__aff_4 = c6_9__aff_4 ) ) )
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
       => ( ( r2_hidden(c2_9__aff_4,c7_9__aff_4)
            & r2_hidden(c2_9__aff_4,A)
            & r2_hidden(c3_9__aff_4,c7_9__aff_4)
            & r2_hidden(c4_9__aff_4,c7_9__aff_4)
            & r2_hidden(c5_9__aff_4,A)
            & r2_hidden(c6_9__aff_4,A)
            & v1_aff_1(c7_9__aff_4,c1_9__aff_4)
            & v1_aff_1(A,c1_9__aff_4)
            & c2_9__aff_4 = c4_9__aff_4 )
         => ( c2_9__aff_4 = c3_9__aff_4
            | c2_9__aff_4 = c5_9__aff_4
            | c7_9__aff_4 = A
            | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
              & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
            | c2_9__aff_4 = c6_9__aff_4 ) ) ) ),
    introduced(definition,[new_symbol(c8_9__aff_4),file(aff_4,c8_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c8_9__aff_4)]).

fof(e1_9__aff_4,assumption,
    ( r2_hidden(c2_9__aff_4,c7_9__aff_4)
    & r2_hidden(c2_9__aff_4,c8_9__aff_4)
    & r2_hidden(c3_9__aff_4,c7_9__aff_4)
    & r2_hidden(c4_9__aff_4,c7_9__aff_4)
    & r2_hidden(c5_9__aff_4,c8_9__aff_4)
    & r2_hidden(c6_9__aff_4,c8_9__aff_4) ),
    introduced(assumption,[file(aff_4,e1_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,e1_9__aff_4)]).

fof(e2_9__aff_4,assumption,
    ( c2_9__aff_4 != c3_9__aff_4
    & c2_9__aff_4 != c5_9__aff_4
    & c7_9__aff_4 != c8_9__aff_4 ),
    introduced(assumption,[file(aff_4,e2_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,e2_9__aff_4)]).

fof(e3_9__aff_4,assumption,
    ( r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
    | r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) ),
    introduced(assumption,[file(aff_4,e3_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,e3_9__aff_4)]).

fof(e4_9__aff_4,assumption,
    ( v1_aff_1(c7_9__aff_4,c1_9__aff_4)
    & v1_aff_1(c8_9__aff_4,c1_9__aff_4) ),
    introduced(assumption,[file(aff_4,e4_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,e4_9__aff_4)]).

fof(e5_9__aff_4,assumption,(
    c2_9__aff_4 = c4_9__aff_4 ),
    introduced(assumption,[file(aff_4,e5_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,e5_9__aff_4)]).

fof(antisymmetry_r2_hidden,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    [interesting(0.9),axiom,file(hidden,r2_hidden)]).

fof(dt_k1_xboole_0,axiom,(
    $true ),
    file(xboole_0,k1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,k1_xboole_0)]).

fof(fc1_xboole_0,theorem,(
    v1_xboole_0(k1_xboole_0) ),
    file(xboole_0,fc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,fc1_xboole_0)]).

fof(t1_subset,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    [interesting(0.9),axiom,file(subset,t1_subset)]).

fof(rc1_xboole_0,theorem,(
    ? [A] : v1_xboole_0(A) ),
    file(xboole_0,rc1_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc1_xboole_0)]).

fof(rc2_xboole_0,theorem,(
    ? [A] : ~ v1_xboole_0(A) ),
    file(xboole_0,rc2_xboole_0),
    [interesting(0.9),axiom,file(xboole_0,rc2_xboole_0)]).

fof(t2_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    [interesting(0.9),axiom,file(subset,t2_subset)]).

fof(t6_boole,theorem,(
    ! [A] : 
      ( v1_xboole_0(A)
     => A = k1_xboole_0 ) ),
    file(boole,t6_boole),
    [interesting(0.9),axiom,file(boole,t6_boole)]).

fof(t7_boole,theorem,(
    ! [A,B] : 
      ~ ( r2_hidden(A,B)
        & v1_xboole_0(B) ) ),
    file(boole,t7_boole),
    [interesting(0.9),axiom,file(boole,t7_boole)]).

fof(t8_boole,theorem,(
    ! [A,B] : 
      ~ ( v1_xboole_0(A)
        & A != B
        & v1_xboole_0(B) ) ),
    file(boole,t8_boole),
    [interesting(0.9),axiom,file(boole,t8_boole)]).

fof(existence_l1_struct_0,axiom,(
    ? [A] : l1_struct_0(A) ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(dt_l1_struct_0,axiom,(
    $true ),
    file(struct_0,l1_struct_0),
    [interesting(0.9),axiom,file(struct_0,l1_struct_0)]).

fof(fc1_struct_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ~ v1_xboole_0(u1_struct_0(A)) ) ),
    file(struct_0,fc1_struct_0),
    [interesting(0.9),axiom,file(struct_0,fc1_struct_0)]).

fof(rc3_struct_0,theorem,(
    ? [A] : 
      ( l1_struct_0(A)
      & ~ v3_struct_0(A) ) ),
    file(struct_0,rc3_struct_0),
    [interesting(0.9),axiom,file(struct_0,rc3_struct_0)]).

fof(existence_l1_analoaf,axiom,(
    ? [A] : l1_analoaf(A) ),
    file(analoaf,l1_analoaf),
    [interesting(0.9),axiom,file(analoaf,l1_analoaf)]).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_l1_analoaf,axiom,(
    ! [A] : 
      ( l1_analoaf(A)
     => l1_struct_0(A) ) ),
    file(analoaf,l1_analoaf),
    [interesting(0.9),axiom,file(analoaf,l1_analoaf)]).

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    [interesting(0.9),axiom,file(subset_1,m1_subset_1)]).

fof(dt_u1_struct_0,axiom,(
    $true ),
    file(struct_0,u1_struct_0),
    [interesting(0.9),axiom,file(struct_0,u1_struct_0)]).

fof(dt_c1_9__aff_4,assumption,
    ( ~ v3_struct_0(c1_9__aff_4)
    & ~ v3_realset2(c1_9__aff_4)
    & v1_diraf(c1_9__aff_4)
    & l1_analoaf(c1_9__aff_4) ),
    introduced(assumption,[file(aff_4,c1_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c1_9__aff_4)]).

fof(dt_c2_9__aff_4,assumption,(
    m1_subset_1(c2_9__aff_4,u1_struct_0(c1_9__aff_4)) ),
    introduced(assumption,[file(aff_4,c2_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c2_9__aff_4)]).

fof(dt_c3_9__aff_4,assumption,(
    m1_subset_1(c3_9__aff_4,u1_struct_0(c1_9__aff_4)) ),
    introduced(assumption,[file(aff_4,c3_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c3_9__aff_4)]).

fof(dt_c4_9__aff_4,assumption,(
    m1_subset_1(c4_9__aff_4,u1_struct_0(c1_9__aff_4)) ),
    introduced(assumption,[file(aff_4,c4_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c4_9__aff_4)]).

fof(dt_c5_9__aff_4,assumption,(
    m1_subset_1(c5_9__aff_4,u1_struct_0(c1_9__aff_4)) ),
    introduced(assumption,[file(aff_4,c5_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c5_9__aff_4)]).

fof(dt_c6_9__aff_4,assumption,(
    m1_subset_1(c6_9__aff_4,u1_struct_0(c1_9__aff_4)) ),
    introduced(assumption,[file(aff_4,c6_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c6_9__aff_4)]).

fof(t13_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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))
                     => ( r2_analoaf(A,B,C,D,E)
                       => ( r2_analoaf(A,B,C,E,D)
                          & r2_analoaf(A,C,B,D,E)
                          & r2_analoaf(A,C,B,E,D)
                          & r2_analoaf(A,D,E,B,C)
                          & r2_analoaf(A,D,E,C,B)
                          & r2_analoaf(A,E,D,B,C)
                          & r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) ),
    file(aff_1,t13_aff_1),
    [interesting(0.9),axiom,file(aff_1,t13_aff_1)]).

fof(e8_9__aff_4,plain,(
    r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__aff_4,dt_c3_9__aff_4,dt_c4_9__aff_4,dt_c5_9__aff_4,dt_c6_9__aff_4,e3_9__aff_4])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t8_boole,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_l1_analoaf,existence_m1_subset_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_9__aff_4,dt_c3_9__aff_4,dt_c4_9__aff_4,dt_c5_9__aff_4,dt_c6_9__aff_4,e3_9__aff_4,t13_aff_1]),
    [interesting(0.8),file(aff_4,e8_9__aff_4),[file(aff_4,e8_9__aff_4)]]).

fof(reflexivity_r1_tarski,theorem,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    [interesting(0.9),axiom,file(tarski,r1_tarski)]).

fof(rc5_struct_0,theorem,(
    ! [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),
    [interesting(0.9),axiom,file(struct_0,rc5_struct_0)]).

fof(t5_subset,theorem,(
    ! [A,B,C] : 
      ~ ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C))
        & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    [interesting(0.9),axiom,file(subset,t5_subset)]).

fof(dt_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    [interesting(0.9),axiom,file(zfmisc_1,k1_zfmisc_1)]).

fof(dt_c7_9__aff_4,assumption,(
    m1_subset_1(c7_9__aff_4,k1_zfmisc_1(u1_struct_0(c1_9__aff_4))) ),
    introduced(assumption,[file(aff_4,c7_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c7_9__aff_4)]).

fof(dt_c8_9__aff_4,assumption,(
    m1_subset_1(c8_9__aff_4,k1_zfmisc_1(u1_struct_0(c1_9__aff_4))) ),
    introduced(assumption,[file(aff_4,c8_9__aff_4)]),
    [interesting(0.8),axiom,file(aff_4,c8_9__aff_4)]).

fof(t3_subset,theorem,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    [interesting(0.9),axiom,file(subset,t3_subset)]).

fof(t4_subset,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    [interesting(0.9),axiom,file(subset,t4_subset)]).

fof(t33_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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))
                 => ( r1_aff_1(A,B,C,D)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                        & v1_aff_1(E,A)
                        & r2_hidden(B,E)
                        & r2_hidden(C,E)
                        & r2_hidden(D,E) ) ) ) ) ) ) ),
    file(aff_1,t33_aff_1),
    [interesting(0.9),axiom,file(aff_1,t33_aff_1)]).

fof(e6_9__aff_4,plain,
    ( r1_aff_1(c1_9__aff_4,c2_9__aff_4,c3_9__aff_4,c4_9__aff_4)
    & r1_aff_1(c1_9__aff_4,c2_9__aff_4,c5_9__aff_4,c6_9__aff_4) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c4_9__aff_4,dt_c5_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,e1_9__aff_4,e4_9__aff_4])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_l1_analoaf,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c4_9__aff_4,dt_c5_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,t1_subset,t3_subset,t4_subset,t7_boole,e1_9__aff_4,e4_9__aff_4,t33_aff_1]),
    [interesting(0.8),file(aff_4,e6_9__aff_4),[file(aff_4,e6_9__aff_4)]]).

fof(e1_9_1__aff_4,assumption,(
    r1_aff_1(c1_9__aff_4,c2_9__aff_4,c3_9__aff_4,c5_9__aff_4) ),
    introduced(assumption,[file(aff_4,e1_9_1__aff_4)]),
    [interesting(0.65),axiom,file(aff_4,e1_9_1__aff_4)]).

fof(dh_c1_9_1__aff_4,definition,
    ( ? [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
        & v1_aff_1(A,c1_9__aff_4)
        & r2_hidden(c2_9__aff_4,A)
        & r2_hidden(c3_9__aff_4,A)
        & r2_hidden(c5_9__aff_4,A) )
   => ( m1_subset_1(c1_9_1__aff_4,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
      & v1_aff_1(c1_9_1__aff_4,c1_9__aff_4)
      & r2_hidden(c2_9__aff_4,c1_9_1__aff_4)
      & r2_hidden(c3_9__aff_4,c1_9_1__aff_4)
      & r2_hidden(c5_9__aff_4,c1_9_1__aff_4) ) ),
    introduced(definition,[new_symbol(c1_9_1__aff_4),file(aff_4,c1_9_1__aff_4)]),
    [interesting(0.65),axiom,file(aff_4,c1_9_1__aff_4)]).

fof(e2_9_1__aff_4,plain,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
      & v1_aff_1(A,c1_9__aff_4)
      & r2_hidden(c2_9__aff_4,A)
      & r2_hidden(c3_9__aff_4,A)
      & r2_hidden(c5_9__aff_4,A) ) ),
    inference(mizar_by,[status(thm),assumptions([dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e1_9_1__aff_4])],[dt_k1_xboole_0,fc1_xboole_0,t8_boole,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,antisymmetry_r2_hidden,existence_l1_analoaf,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,t1_subset,t3_subset,t4_subset,t7_boole,e1_9_1__aff_4,t33_aff_1]),
    [interesting(0.65),file(aff_4,e2_9_1__aff_4),[file(aff_4,e2_9_1__aff_4)]]).

fof(dt_c1_9_1__aff_4,plain,(
    m1_subset_1(c1_9_1__aff_4,k1_zfmisc_1(u1_struct_0(c1_9__aff_4))) ),
    inference(consider,[status(thm),assumptions([dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e1_9_1__aff_4])],[dh_c1_9_1__aff_4,e2_9_1__aff_4]),
    [interesting(0.65),file(aff_4,c1_9_1__aff_4),[file(aff_4,c1_9_1__aff_4)]]).

fof(e3_9_1__aff_4,plain,
    ( v1_aff_1(c1_9_1__aff_4,c1_9__aff_4)
    & r2_hidden(c2_9__aff_4,c1_9_1__aff_4)
    & r2_hidden(c3_9__aff_4,c1_9_1__aff_4)
    & r2_hidden(c5_9__aff_4,c1_9_1__aff_4) ),
    inference(consider,[status(thm),assumptions([dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e1_9_1__aff_4])],[dh_c1_9_1__aff_4,e2_9_1__aff_4]),
    [interesting(0.65),file(aff_4,e3_9_1__aff_4),[file(aff_4,e3_9_1__aff_4)]]).

fof(t30_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v1_aff_1(D,A)
                          & v1_aff_1(E,A)
                          & r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & B != C
                          & D != E ) ) ) ) ) ) ),
    file(aff_1,t30_aff_1),
    [interesting(0.9),axiom,file(aff_1,t30_aff_1)]).

fof(e4_9_1__aff_4,plain,
    ( c7_9__aff_4 = c1_9_1__aff_4
    & c8_9__aff_4 = c1_9_1__aff_4 ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,e1_9__aff_4,e2_9__aff_4,e4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e1_9_1__aff_4])],[dt_k1_xboole_0,fc1_xboole_0,reflexivity_r1_tarski,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc1_xboole_0,rc2_xboole_0,rc3_struct_0,rc5_struct_0,t2_subset,t5_subset,t6_boole,t8_boole,antisymmetry_r2_hidden,existence_l1_analoaf,existence_m1_subset_1,dt_k1_zfmisc_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_9__aff_4,dt_c1_9_1__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c4_9__aff_4,dt_c5_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,t1_subset,t3_subset,t4_subset,t7_boole,e1_9__aff_4,e2_9__aff_4,e4_9__aff_4,e3_9_1__aff_4,t30_aff_1]),
    [interesting(0.65),file(aff_4,e4_9_1__aff_4),[file(aff_4,e4_9_1__aff_4)]]).

fof(e5_9_1__aff_4,plain,(
    ~ $true ),
    inference(mizar_by,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,e1_9__aff_4,e4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e1_9_1__aff_4,e2_9__aff_4])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,t4_subset,t5_subset,rc1_xboole_0,rc2_xboole_0,rc5_struct_0,t2_subset,t6_boole,t7_boole,t8_boole,reflexivity_r1_tarski,existence_l1_analoaf,existence_l1_struct_0,dt_l1_analoaf,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_m1_subset_1,dt_k1_zfmisc_1,dt_m1_subset_1,dt_u1_struct_0,dt_c1_9__aff_4,t3_subset,dt_c1_9_1__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,e4_9_1__aff_4,e2_9__aff_4]),
    [interesting(0.65),file(aff_4,e5_9_1__aff_4),[file(aff_4,e5_9_1__aff_4)]]).

fof(i2_9_1__aff_4,theorem,(
    $true ),
    introduced(tautology,[file(aff_4,i2_9_1__aff_4)]),
    [interesting(0.65),trivial,file(aff_4,i2_9_1__aff_4)]).

fof(i1_9_1__aff_4,plain,(
    ~ $true ),
    inference(conclusion,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,e1_9__aff_4,e4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e1_9_1__aff_4,e2_9__aff_4])],[e5_9_1__aff_4,i2_9_1__aff_4]),
    [interesting(0.65),file(aff_4,i1_9_1__aff_4),[file(aff_4,i1_9_1__aff_4)]]).

fof(e7_9__aff_4,plain,(
    ~ r1_aff_1(c1_9__aff_4,c2_9__aff_4,c3_9__aff_4,c5_9__aff_4) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,e1_9__aff_4,e4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e2_9__aff_4]),discharge_asm(discharge,[e1_9_1__aff_4])],[e1_9_1__aff_4,i1_9_1__aff_4]),
    [interesting(0.8),file(aff_4,e7_9__aff_4),[file(aff_4,e7_9__aff_4)]]).

fof(t69_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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))
                         => ( ( r1_aff_1(A,B,C,E)
                              & r1_aff_1(A,B,D,F)
                              & r2_analoaf(A,C,D,E,F)
                              & E = B )
                           => ( r1_aff_1(A,B,C,D)
                              | F = B ) ) ) ) ) ) ) ) ),
    file(aff_1,t69_aff_1),
    [interesting(0.9),axiom,file(aff_1,t69_aff_1)]).

fof(e9_9__aff_4,plain,(
    c2_9__aff_4 = c6_9__aff_4 ),
    inference(mizar_by,[status(thm),assumptions([e3_9__aff_4,e5_9__aff_4,dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,e1_9__aff_4,e4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e2_9__aff_4])],[antisymmetry_r2_hidden,dt_k1_xboole_0,fc1_xboole_0,t1_subset,rc1_xboole_0,rc2_xboole_0,t2_subset,t6_boole,t7_boole,t8_boole,existence_l1_struct_0,dt_l1_struct_0,fc1_struct_0,rc3_struct_0,existence_l1_analoaf,existence_m1_subset_1,dt_l1_analoaf,dt_m1_subset_1,dt_u1_struct_0,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c4_9__aff_4,dt_c5_9__aff_4,dt_c6_9__aff_4,e8_9__aff_4,e5_9__aff_4,e6_9__aff_4,e7_9__aff_4,t69_aff_1]),
    [interesting(0.8),file(aff_4,e9_9__aff_4),[file(aff_4,e9_9__aff_4)]]).

fof(i10_9__aff_4,theorem,(
    $true ),
    introduced(tautology,[file(aff_4,i10_9__aff_4)]),
    [interesting(0.8),trivial,file(aff_4,i10_9__aff_4)]).

fof(i9_9__aff_4,plain,(
    c2_9__aff_4 = c6_9__aff_4 ),
    inference(conclusion,[status(thm),assumptions([e3_9__aff_4,e5_9__aff_4,dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,e1_9__aff_4,e4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4,e2_9__aff_4])],[e9_9__aff_4,i10_9__aff_4]),
    [interesting(0.8),file(aff_4,i9_9__aff_4),[file(aff_4,i9_9__aff_4)]]).

fof(i8_9__aff_4,plain,
    ( ( r2_hidden(c2_9__aff_4,c7_9__aff_4)
      & r2_hidden(c2_9__aff_4,c8_9__aff_4)
      & r2_hidden(c3_9__aff_4,c7_9__aff_4)
      & r2_hidden(c4_9__aff_4,c7_9__aff_4)
      & r2_hidden(c5_9__aff_4,c8_9__aff_4)
      & r2_hidden(c6_9__aff_4,c8_9__aff_4)
      & v1_aff_1(c7_9__aff_4,c1_9__aff_4)
      & v1_aff_1(c8_9__aff_4,c1_9__aff_4)
      & c2_9__aff_4 = c4_9__aff_4 )
   => ( c2_9__aff_4 = c3_9__aff_4
      | c2_9__aff_4 = c5_9__aff_4
      | c7_9__aff_4 = c8_9__aff_4
      | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
        & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
      | c2_9__aff_4 = c6_9__aff_4 ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c8_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4]),discharge_asm(discharge,[e1_9__aff_4,e2_9__aff_4,e3_9__aff_4,e4_9__aff_4,e5_9__aff_4])],[e1_9__aff_4,e2_9__aff_4,e3_9__aff_4,e4_9__aff_4,e5_9__aff_4,i9_9__aff_4]),
    [interesting(0.8),file(aff_4,i8_9__aff_4),[file(aff_4,i8_9__aff_4)]]).

fof(i8_9_tmp__aff_4,plain,
    ( m1_subset_1(c8_9__aff_4,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
   => ( ( r2_hidden(c2_9__aff_4,c7_9__aff_4)
        & r2_hidden(c2_9__aff_4,c8_9__aff_4)
        & r2_hidden(c3_9__aff_4,c7_9__aff_4)
        & r2_hidden(c4_9__aff_4,c7_9__aff_4)
        & r2_hidden(c5_9__aff_4,c8_9__aff_4)
        & r2_hidden(c6_9__aff_4,c8_9__aff_4)
        & v1_aff_1(c7_9__aff_4,c1_9__aff_4)
        & v1_aff_1(c8_9__aff_4,c1_9__aff_4)
        & c2_9__aff_4 = c4_9__aff_4 )
     => ( c2_9__aff_4 = c3_9__aff_4
        | c2_9__aff_4 = c5_9__aff_4
        | c7_9__aff_4 = c8_9__aff_4
        | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
          & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
        | c2_9__aff_4 = c6_9__aff_4 ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4]),discharge_asm(discharge,[dt_c8_9__aff_4])],[dt_c8_9__aff_4,i8_9__aff_4]),
    [interesting(0.8),i7_9__aff_4]).

fof(i7_9__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
     => ( ( r2_hidden(c2_9__aff_4,c7_9__aff_4)
          & r2_hidden(c2_9__aff_4,A)
          & r2_hidden(c3_9__aff_4,c7_9__aff_4)
          & r2_hidden(c4_9__aff_4,c7_9__aff_4)
          & r2_hidden(c5_9__aff_4,A)
          & r2_hidden(c6_9__aff_4,A)
          & v1_aff_1(c7_9__aff_4,c1_9__aff_4)
          & v1_aff_1(A,c1_9__aff_4)
          & c2_9__aff_4 = c4_9__aff_4 )
       => ( c2_9__aff_4 = c3_9__aff_4
          | c2_9__aff_4 = c5_9__aff_4
          | c7_9__aff_4 = A
          | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
            & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
          | c2_9__aff_4 = c6_9__aff_4 ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c7_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4])],[i8_9_tmp__aff_4,dh_c8_9__aff_4]),
    [interesting(0.8),file(aff_4,i7_9__aff_4),[file(aff_4,i7_9__aff_4)]]).

fof(i7_9_tmp__aff_4,plain,
    ( m1_subset_1(c7_9__aff_4,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
       => ( ( r2_hidden(c2_9__aff_4,c7_9__aff_4)
            & r2_hidden(c2_9__aff_4,A)
            & r2_hidden(c3_9__aff_4,c7_9__aff_4)
            & r2_hidden(c4_9__aff_4,c7_9__aff_4)
            & r2_hidden(c5_9__aff_4,A)
            & r2_hidden(c6_9__aff_4,A)
            & v1_aff_1(c7_9__aff_4,c1_9__aff_4)
            & v1_aff_1(A,c1_9__aff_4)
            & c2_9__aff_4 = c4_9__aff_4 )
         => ( c2_9__aff_4 = c3_9__aff_4
            | c2_9__aff_4 = c5_9__aff_4
            | c7_9__aff_4 = A
            | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
              & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
            | c2_9__aff_4 = c6_9__aff_4 ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4]),discharge_asm(discharge,[dt_c7_9__aff_4])],[dt_c7_9__aff_4,i7_9__aff_4]),
    [interesting(0.8),i6_9__aff_4]).

fof(i6_9__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
         => ( ( r2_hidden(c2_9__aff_4,A)
              & r2_hidden(c2_9__aff_4,B)
              & r2_hidden(c3_9__aff_4,A)
              & r2_hidden(c4_9__aff_4,A)
              & r2_hidden(c5_9__aff_4,B)
              & r2_hidden(c6_9__aff_4,B)
              & v1_aff_1(A,c1_9__aff_4)
              & v1_aff_1(B,c1_9__aff_4)
              & c2_9__aff_4 = c4_9__aff_4 )
           => ( c2_9__aff_4 = c3_9__aff_4
              | c2_9__aff_4 = c5_9__aff_4
              | A = B
              | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
                & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
              | c2_9__aff_4 = c6_9__aff_4 ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_9__aff_4,dt_c6_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4])],[i7_9_tmp__aff_4,dh_c7_9__aff_4]),
    [interesting(0.8),file(aff_4,i6_9__aff_4),[file(aff_4,i6_9__aff_4)]]).

fof(i6_9_tmp__aff_4,plain,
    ( m1_subset_1(c6_9__aff_4,u1_struct_0(c1_9__aff_4))
   => ! [A] : 
        ( m1_subset_1(A,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
           => ( ( r2_hidden(c2_9__aff_4,A)
                & r2_hidden(c2_9__aff_4,B)
                & r2_hidden(c3_9__aff_4,A)
                & r2_hidden(c4_9__aff_4,A)
                & r2_hidden(c5_9__aff_4,B)
                & r2_hidden(c6_9__aff_4,B)
                & v1_aff_1(A,c1_9__aff_4)
                & v1_aff_1(B,c1_9__aff_4)
                & c2_9__aff_4 = c4_9__aff_4 )
             => ( c2_9__aff_4 = c3_9__aff_4
                | c2_9__aff_4 = c5_9__aff_4
                | A = B
                | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,c6_9__aff_4)
                  & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,c6_9__aff_4,c4_9__aff_4) )
                | c2_9__aff_4 = c6_9__aff_4 ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4]),discharge_asm(discharge,[dt_c6_9__aff_4])],[dt_c6_9__aff_4,i6_9__aff_4]),
    [interesting(0.8),i5_9__aff_4]).

fof(i5_9__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
             => ( ( r2_hidden(c2_9__aff_4,B)
                  & r2_hidden(c2_9__aff_4,C)
                  & r2_hidden(c3_9__aff_4,B)
                  & r2_hidden(c4_9__aff_4,B)
                  & r2_hidden(c5_9__aff_4,C)
                  & r2_hidden(A,C)
                  & v1_aff_1(B,c1_9__aff_4)
                  & v1_aff_1(C,c1_9__aff_4)
                  & c2_9__aff_4 = c4_9__aff_4 )
               => ( c2_9__aff_4 = c3_9__aff_4
                  | c2_9__aff_4 = c5_9__aff_4
                  | B = C
                  | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,A)
                    & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,A,c4_9__aff_4) )
                  | c2_9__aff_4 = A ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4,dt_c5_9__aff_4])],[i6_9_tmp__aff_4,dh_c6_9__aff_4]),
    [interesting(0.8),file(aff_4,i5_9__aff_4),[file(aff_4,i5_9__aff_4)]]).

fof(i5_9_tmp__aff_4,plain,
    ( m1_subset_1(c5_9__aff_4,u1_struct_0(c1_9__aff_4))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
               => ( ( r2_hidden(c2_9__aff_4,B)
                    & r2_hidden(c2_9__aff_4,C)
                    & r2_hidden(c3_9__aff_4,B)
                    & r2_hidden(c4_9__aff_4,B)
                    & r2_hidden(c5_9__aff_4,C)
                    & r2_hidden(A,C)
                    & v1_aff_1(B,c1_9__aff_4)
                    & v1_aff_1(C,c1_9__aff_4)
                    & c2_9__aff_4 = c4_9__aff_4 )
                 => ( c2_9__aff_4 = c3_9__aff_4
                    | c2_9__aff_4 = c5_9__aff_4
                    | B = C
                    | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,c5_9__aff_4,c4_9__aff_4,A)
                      & ~ r2_analoaf(c1_9__aff_4,c5_9__aff_4,c3_9__aff_4,A,c4_9__aff_4) )
                    | c2_9__aff_4 = A ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4]),discharge_asm(discharge,[dt_c5_9__aff_4])],[dt_c5_9__aff_4,i5_9__aff_4]),
    [interesting(0.8),i4_9__aff_4]).

fof(i4_9__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                 => ( ( r2_hidden(c2_9__aff_4,C)
                      & r2_hidden(c2_9__aff_4,D)
                      & r2_hidden(c3_9__aff_4,C)
                      & r2_hidden(c4_9__aff_4,C)
                      & r2_hidden(A,D)
                      & r2_hidden(B,D)
                      & v1_aff_1(C,c1_9__aff_4)
                      & v1_aff_1(D,c1_9__aff_4)
                      & c2_9__aff_4 = c4_9__aff_4 )
                   => ( c2_9__aff_4 = c3_9__aff_4
                      | c2_9__aff_4 = A
                      | C = D
                      | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,A,c4_9__aff_4,B)
                        & ~ r2_analoaf(c1_9__aff_4,A,c3_9__aff_4,B,c4_9__aff_4) )
                      | c2_9__aff_4 = B ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c4_9__aff_4,dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4])],[i5_9_tmp__aff_4,dh_c5_9__aff_4]),
    [interesting(0.8),file(aff_4,i4_9__aff_4),[file(aff_4,i4_9__aff_4)]]).

fof(i4_9_tmp__aff_4,plain,
    ( m1_subset_1(c4_9__aff_4,u1_struct_0(c1_9__aff_4))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                   => ( ( r2_hidden(c2_9__aff_4,C)
                        & r2_hidden(c2_9__aff_4,D)
                        & r2_hidden(c3_9__aff_4,C)
                        & r2_hidden(c4_9__aff_4,C)
                        & r2_hidden(A,D)
                        & r2_hidden(B,D)
                        & v1_aff_1(C,c1_9__aff_4)
                        & v1_aff_1(D,c1_9__aff_4)
                        & c2_9__aff_4 = c4_9__aff_4 )
                     => ( c2_9__aff_4 = c3_9__aff_4
                        | c2_9__aff_4 = A
                        | C = D
                        | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,A,c4_9__aff_4,B)
                          & ~ r2_analoaf(c1_9__aff_4,A,c3_9__aff_4,B,c4_9__aff_4) )
                        | c2_9__aff_4 = B ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4]),discharge_asm(discharge,[dt_c4_9__aff_4])],[dt_c4_9__aff_4,i4_9__aff_4]),
    [interesting(0.8),i3_9__aff_4]).

fof(i3_9__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                     => ( ( r2_hidden(c2_9__aff_4,D)
                          & r2_hidden(c2_9__aff_4,E)
                          & r2_hidden(c3_9__aff_4,D)
                          & r2_hidden(A,D)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & v1_aff_1(D,c1_9__aff_4)
                          & v1_aff_1(E,c1_9__aff_4)
                          & c2_9__aff_4 = A )
                       => ( c2_9__aff_4 = c3_9__aff_4
                          | c2_9__aff_4 = B
                          | D = E
                          | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,B,A,C)
                            & ~ r2_analoaf(c1_9__aff_4,B,c3_9__aff_4,C,A) )
                          | c2_9__aff_4 = C ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__aff_4,dt_c2_9__aff_4,dt_c3_9__aff_4])],[i4_9_tmp__aff_4,dh_c4_9__aff_4]),
    [interesting(0.8),file(aff_4,i3_9__aff_4),[file(aff_4,i3_9__aff_4)]]).

fof(i3_9_tmp__aff_4,plain,
    ( m1_subset_1(c3_9__aff_4,u1_struct_0(c1_9__aff_4))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                   => ! [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                       => ( ( r2_hidden(c2_9__aff_4,D)
                            & r2_hidden(c2_9__aff_4,E)
                            & r2_hidden(c3_9__aff_4,D)
                            & r2_hidden(A,D)
                            & r2_hidden(B,E)
                            & r2_hidden(C,E)
                            & v1_aff_1(D,c1_9__aff_4)
                            & v1_aff_1(E,c1_9__aff_4)
                            & c2_9__aff_4 = A )
                         => ( c2_9__aff_4 = c3_9__aff_4
                            | c2_9__aff_4 = B
                            | D = E
                            | ( ~ r2_analoaf(c1_9__aff_4,c3_9__aff_4,B,A,C)
                              & ~ r2_analoaf(c1_9__aff_4,B,c3_9__aff_4,C,A) )
                            | c2_9__aff_4 = C ) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__aff_4,dt_c2_9__aff_4]),discharge_asm(discharge,[dt_c3_9__aff_4])],[dt_c3_9__aff_4,i3_9__aff_4]),
    [interesting(0.8),i2_9__aff_4]).

fof(i2_9__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(c1_9__aff_4))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                         => ( ( r2_hidden(c2_9__aff_4,E)
                              & r2_hidden(c2_9__aff_4,F)
                              & r2_hidden(A,E)
                              & r2_hidden(B,E)
                              & r2_hidden(C,F)
                              & r2_hidden(D,F)
                              & v1_aff_1(E,c1_9__aff_4)
                              & v1_aff_1(F,c1_9__aff_4)
                              & c2_9__aff_4 = B )
                           => ( c2_9__aff_4 = A
                              | c2_9__aff_4 = C
                              | E = F
                              | ( ~ r2_analoaf(c1_9__aff_4,A,C,B,D)
                                & ~ r2_analoaf(c1_9__aff_4,C,A,D,B) )
                              | c2_9__aff_4 = D ) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__aff_4,dt_c2_9__aff_4])],[i3_9_tmp__aff_4,dh_c3_9__aff_4]),
    [interesting(0.8),file(aff_4,i2_9__aff_4),[file(aff_4,i2_9__aff_4)]]).

fof(i2_9_tmp__aff_4,plain,
    ( m1_subset_1(c2_9__aff_4,u1_struct_0(c1_9__aff_4))
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(c1_9__aff_4))
                   => ! [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                       => ! [F] : 
                            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                           => ( ( r2_hidden(c2_9__aff_4,E)
                                & r2_hidden(c2_9__aff_4,F)
                                & r2_hidden(A,E)
                                & r2_hidden(B,E)
                                & r2_hidden(C,F)
                                & r2_hidden(D,F)
                                & v1_aff_1(E,c1_9__aff_4)
                                & v1_aff_1(F,c1_9__aff_4)
                                & c2_9__aff_4 = B )
                             => ( c2_9__aff_4 = A
                                | c2_9__aff_4 = C
                                | E = F
                                | ( ~ r2_analoaf(c1_9__aff_4,A,C,B,D)
                                  & ~ r2_analoaf(c1_9__aff_4,C,A,D,B) )
                                | c2_9__aff_4 = D ) ) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([dt_c1_9__aff_4]),discharge_asm(discharge,[dt_c2_9__aff_4])],[dt_c2_9__aff_4,i2_9__aff_4]),
    [interesting(0.8),i1_9__aff_4]).

fof(i1_9__aff_4,plain,(
    ! [A] : 
      ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(c1_9__aff_4))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(c1_9__aff_4))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                             => ( ( r2_hidden(A,F)
                                  & r2_hidden(A,G)
                                  & r2_hidden(B,F)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,G)
                                  & r2_hidden(E,G)
                                  & v1_aff_1(F,c1_9__aff_4)
                                  & v1_aff_1(G,c1_9__aff_4)
                                  & A = C )
                               => ( A = B
                                  | A = D
                                  | F = G
                                  | ( ~ r2_analoaf(c1_9__aff_4,B,D,C,E)
                                    & ~ r2_analoaf(c1_9__aff_4,D,B,E,C) )
                                  | A = E ) ) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([dt_c1_9__aff_4])],[i2_9_tmp__aff_4,dh_c2_9__aff_4]),
    [interesting(0.8),file(aff_4,i1_9__aff_4),[file(aff_4,i1_9__aff_4)]]).

fof(i1_9_tmp__aff_4,plain,
    ( ( ~ v3_struct_0(c1_9__aff_4)
      & ~ v3_realset2(c1_9__aff_4)
      & v1_diraf(c1_9__aff_4)
      & l1_analoaf(c1_9__aff_4) )
   => ! [A] : 
        ( m1_subset_1(A,u1_struct_0(c1_9__aff_4))
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(c1_9__aff_4))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(c1_9__aff_4))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(c1_9__aff_4))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(c1_9__aff_4))
                       => ! [F] : 
                            ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                           => ! [G] : 
                                ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(c1_9__aff_4)))
                               => ( ( r2_hidden(A,F)
                                    & r2_hidden(A,G)
                                    & r2_hidden(B,F)
                                    & r2_hidden(C,F)
                                    & r2_hidden(D,G)
                                    & r2_hidden(E,G)
                                    & v1_aff_1(F,c1_9__aff_4)
                                    & v1_aff_1(G,c1_9__aff_4)
                                    & A = C )
                                 => ( A = B
                                    | A = D
                                    | F = G
                                    | ( ~ r2_analoaf(c1_9__aff_4,B,D,C,E)
                                      & ~ r2_analoaf(c1_9__aff_4,D,B,E,C) )
                                    | A = E ) ) ) ) ) ) ) ) ) ),
    inference(discharge_asm,[status(thm),assumptions([]),discharge_asm(discharge,[dt_c1_9__aff_4])],[dt_c1_9__aff_4,i1_9__aff_4]),
    [interesting(1),t8_aff_4]).

fof(t8_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(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,k1_zfmisc_1(u1_struct_0(A)))
                             => ! [H] : 
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ( ( r2_hidden(B,G)
                                      & r2_hidden(B,H)
                                      & r2_hidden(C,G)
                                      & r2_hidden(D,G)
                                      & r2_hidden(E,H)
                                      & r2_hidden(F,H)
                                      & v1_aff_1(G,A)
                                      & v1_aff_1(H,A)
                                      & B = D )
                                   => ( B = C
                                      | B = E
                                      | G = H
                                      | ( ~ r2_analoaf(A,C,E,D,F)
                                        & ~ r2_analoaf(A,E,C,F,D) )
                                      | B = F ) ) ) ) ) ) ) ) ) ) ),
    inference(let,[status(thm),assumptions([])],[i1_9_tmp__aff_4,dh_c1_9__aff_4]),
    [interesting(1),file(aff_4,t8_aff_4),[file(aff_4,t8_aff_4)]]).