fof(t50_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( ~ ( ~ v3_struct_0(A)
            & ~ v3_realset2(A)
            & v1_diraf(A)
            & v2_diraf(A)
            & l1_analoaf(A) )
       => v4_aff_2(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_aff_4,d4_aff_2]),
    [file(aff_4,t50_aff_4),interesting(1.00)]).

fof(t67_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,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v1_aff_4(D,A)
                   => k3_aff_4(A,B,D) = k3_aff_4(A,B,k3_aff_4(A,C,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_aff_4,d6_aff_4,t61_aff_4,t61_aff_4,l80_aff_4]),
    [file(aff_4,t67_aff_4),interesting(1.00)]).

fof(t57_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_aff_4(B,A)
           => r1_aff_4(A,B,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t28_aff_4,d4_aff_4]),
    [file(aff_4,t57_aff_4),interesting(0.99)]).

fof(t52_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( ~ ( ~ v3_struct_0(A)
            & ~ v3_realset2(A)
            & v1_diraf(A)
            & v2_diraf(A)
            & l1_analoaf(A) )
       => v11_aff_2(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t51_aff_4,d11_aff_2]),
    [file(aff_4,t52_aff_4),interesting(0.98)]).

fof(t69_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_4(C,A)
                      & v1_aff_4(D,A)
                      & r1_aff_4(A,C,D) )
                   => k3_aff_4(A,B,C) = k3_aff_4(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_aff_4,t61_aff_4,t61_aff_4,l80_aff_4]),
    [file(aff_4,t69_aff_4),interesting(0.88)]).

fof(t58_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_aff_4(B,A)
                  & v1_aff_4(C,A)
                  & r1_aff_4(A,B,C) )
               => r1_aff_4(A,C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_aff_4,t58_aff_1,t58_aff_1,t55_aff_4]),
    [file(aff_4,t58_aff_4),interesting(0.85)]).

fof(t65_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,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_4(C,A)
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(B,D)
                          & r1_aff_4(A,C,D)
                          & v1_aff_4(D,A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_aff_4,t16_aff_1,t26_aff_1,d3_aff_1,d3_aff_4,t27_aff_4,t38_aff_4,t19_aff_4,t59_aff_1,t33_aff_1,t55_aff_4]),
    [file(aff_4,t65_aff_4),interesting(0.75)]).

fof(t40_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_aff_1(B,A)
                  & v1_aff_1(C,A) )
               => ( r4_aff_1(A,B,C)
                <=> r1_aff_4(A,B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_aff_4,t33_aff_4,d4_aff_4,t31_aff_1,d4_aff_4,t27_aff_4,t33_aff_4,d3_aff_4]),
    [file(aff_4,t40_aff_4),interesting(0.70)]).

fof(t33_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_tarski(B,C)
               => ( ( ~ ( v1_aff_1(B,A)
                        & v1_aff_1(C,A) )
                    & ~ ( v1_aff_4(B,A)
                        & v1_aff_4(C,A) ) )
                  | B = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_aff_1,t26_aff_1,t71_aff_1,d2_aff_4,t31_aff_1,d3_aff_4,t27_aff_4,t14_aff_4,t14_aff_4,t1_xboole_1,l24_aff_4,t1_xboole_1,t26_aff_4]),
    [file(aff_4,t33_aff_4),interesting(0.68)]).

fof(t66_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,k1_zfmisc_1(u1_struct_0(A)))
             => ( v1_aff_4(C,A)
               => ( r2_hidden(B,C)
                <=> k3_aff_4(A,B,C) = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t57_aff_4,d6_aff_4,d6_aff_4]),
    [file(aff_4,t66_aff_4),interesting(0.66)]).

fof(t42_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_aff_1(B,A)
                  & v1_aff_4(C,A)
                  & r1_tarski(B,C) )
               => r1_aff_4(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_aff_1,t41_aff_4]),
    [file(aff_4,t42_aff_4),interesting(0.62)]).

fof(t41_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_aff_1(B,A)
                  & v1_aff_4(C,A) )
               => ( r1_aff_4(A,B,C)
                <=> ? [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                      & r1_tarski(D,C)
                      & ( r4_aff_1(A,B,D)
                        | r4_aff_1(A,D,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_aff_4,d4_aff_4,d3_aff_4,d3_aff_4,t33_aff_4,d3_aff_4,t58_aff_1,t23_aff_4,d4_aff_4]),
    [file(aff_4,t41_aff_4),interesting(0.57)]).

fof(t28_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_4(C,A)
                      & v1_aff_1(D,A)
                      & r2_hidden(B,C)
                      & r1_tarski(D,C) )
                   => r1_tarski(k2_aff_4(A,B,D),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_aff_4,t23_aff_4]),
    [file(aff_4,t28_aff_4),interesting(0.55)]).

fof(t19_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,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_4(D,A)
                      & r2_hidden(B,D)
                      & r2_hidden(C,D) )
                   => ( B = C
                      | r1_tarski(k2_aff_1(A,B,C),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_aff_1,t26_aff_1,d2_aff_4,l25_aff_4]),
    [file(aff_4,t19_aff_4),interesting(0.52)]).

fof(t20_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_1(B,A)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & r1_tarski(D,k1_aff_4(A,B,C)) )
                   => ( r4_aff_1(A,B,C)
                      | r4_aff_1(A,B,D)
                      | k1_aff_4(A,B,D) = k1_aff_4(A,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l27_aff_4,t31_aff_1,l17_aff_4,l17_aff_4,t63_aff_1,t50_aff_1,t3_aff_4,t2_aff_4,t30_aff_1,t48_aff_1,l25_aff_4,l27_aff_4,d10_xboole_0]),
    [file(aff_4,t20_aff_4),interesting(0.46)]).

fof(t43_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_1(C,A)
                      & v1_aff_4(D,A)
                      & r2_hidden(B,C)
                      & r2_hidden(B,D)
                      & r1_aff_4(A,C,D) )
                   => r1_tarski(C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t41_aff_4,t50_aff_1,l42_aff_4,t32_aff_4,t28_aff_4]),
    [file(aff_4,t43_aff_4),interesting(0.45)]).

fof(t46_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(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(B,A)
                          & v1_aff_1(C,A)
                          & v1_aff_4(D,A)
                          & r1_tarski(B,D)
                          & r1_tarski(C,D) )
                       => ( B = C
                          | ( r2_aff_4(A,B,C,E)
                          <=> r1_tarski(E,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_aff_4,t26_aff_4,d5_aff_4]),
    [file(aff_4,t46_aff_4),interesting(0.45)]).

fof(t22_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( v1_aff_4(B,A)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & r1_tarski(C,B)
                      & r1_tarski(D,B)
                      & ~ r4_aff_1(A,C,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(E,C)
                              & r2_hidden(E,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_aff_4,t20_aff_4,t21_aff_4,t20_aff_4,t21_aff_4,t58_aff_1]),
    [file(aff_4,t22_aff_4),interesting(0.43)]).

fof(l70_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)))
                             => ~ ( ~ r1_aff_1(A,B,C,D)
                                  & E != F
                                  & r2_analoaf(A,B,C,E,F)
                                  & r2_hidden(B,G)
                                  & r2_hidden(C,G)
                                  & r2_hidden(D,G)
                                  & v1_aff_4(G,A)
                                  & r2_hidden(E,G)
                                  & ! [H] : 
                                      ( m1_subset_1(H,u1_struct_0(A))
                                     => ~ ( r2_analoaf(A,B,D,E,H)
                                          & r2_analoaf(A,C,D,F,H) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_aff_1,t29_aff_4,t26_aff_1,d3_aff_1,d3_aff_4,t27_aff_4,d3_aff_4,t58_aff_1,t58_aff_1,t59_aff_1,t33_aff_1,t19_aff_4,t28_aff_4,t22_aff_4,t53_aff_1]),
    [file(aff_4,l70_aff_4),interesting(0.35)]).

fof(t68_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_1(C,A)
                      & v1_aff_4(D,A)
                      & r1_aff_4(A,C,D) )
                   => r1_tarski(k2_aff_4(A,B,C),k3_aff_4(A,B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t41_aff_4,t32_aff_4,t50_aff_1,d6_aff_4,d4_aff_4]),
    [file(aff_4,t68_aff_4),interesting(0.34)]).

fof(l66_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,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                         => ( ( r4_aff_1(A,H,I)
                                              & r4_aff_1(A,H,J)
                                              & r2_hidden(B,H)
                                              & r2_hidden(C,H)
                                              & r2_hidden(D,I)
                                              & r2_hidden(E,I)
                                              & r2_hidden(F,J)
                                              & r2_hidden(G,J)
                                              & v1_aff_1(H,A)
                                              & v1_aff_1(I,A)
                                              & v1_aff_1(J,A)
                                              & r2_analoaf(A,B,D,C,E)
                                              & r2_analoaf(A,B,F,C,G) )
                                           => ( r2_aff_4(A,H,I,J)
                                              | H = I
                                              | H = J
                                              | r2_analoaf(A,D,F,E,G) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t58_aff_1,t39_aff_4,t39_aff_4,d5_aff_4,t59_aff_1,t10_aff_4,t10_aff_4,t11_aff_1,t59_aff_1,d3_aff_1,t26_aff_1,t26_aff_1,t51_aff_1,t19_aff_4,t19_aff_4,t53_aff_1,t22_aff_4,t27_aff_4,d3_aff_4,t58_aff_1,t33_aff_1,t1_aff_4,t1_aff_4,t13_aff_1,d4_aff_1,t3_aff_4,t2_aff_4,t13_aff_1,d4_aff_1,t3_aff_4,t2_aff_4,t39_aff_1,t59_aff_1,t30_aff_1,t59_aff_1,t71_aff_1,t19_aff_4,t23_aff_4,d3_aff_4,t28_aff_4,d5_aff_4]),
    [file(aff_4,l66_aff_4),interesting(0.28)]).

fof(t63_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,k1_zfmisc_1(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)))
                                 => ( ( v1_aff_4(F,A)
                                      & v1_aff_4(G,A)
                                      & v1_aff_4(H,A)
                                      & r1_aff_4(A,F,G)
                                      & r2_hidden(B,k5_subset_1(u1_struct_0(A),F,H))
                                      & r2_hidden(C,k5_subset_1(u1_struct_0(A),F,H))
                                      & r2_hidden(D,k5_subset_1(u1_struct_0(A),G,H))
                                      & r2_hidden(E,k5_subset_1(u1_struct_0(A),G,H)) )
                                   => ( F = G
                                      | r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,l80_aff_4,l80_aff_4,t24_aff_4,d3_aff_4,t27_aff_4,t17_xboole_1,t17_xboole_1,d4_aff_4,t28_aff_4,t26_aff_4,t53_aff_1,t12_aff_1]),
    [file(aff_4,t63_aff_4),interesting(0.28)]).

fof(t51_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,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(A)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                         => ( ( r4_aff_1(A,H,I)
                                              & r4_aff_1(A,H,J)
                                              & r2_hidden(B,H)
                                              & r2_hidden(C,H)
                                              & r2_hidden(D,I)
                                              & r2_hidden(E,I)
                                              & r2_hidden(F,J)
                                              & r2_hidden(G,J)
                                              & v1_aff_1(H,A)
                                              & v1_aff_1(I,A)
                                              & v1_aff_1(J,A)
                                              & r2_analoaf(A,B,D,C,E)
                                              & r2_analoaf(A,B,F,C,G) )
                                           => ( ( ~ v3_struct_0(A)
                                                & ~ v3_realset2(A)
                                                & v1_diraf(A)
                                                & v2_diraf(A)
                                                & l1_analoaf(A) )
                                              | H = I
                                              | H = J
                                              | r2_analoaf(A,D,F,E,G) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_aff_4,t48_aff_4,d3_aff_4,t58_aff_1,t27_aff_4,t47_diraf,t13_aff_1,t41_aff_1,t3_aff_4,t2_aff_4,d3_aff_4,t11_aff_1,t44_aff_4,t46_aff_4,t44_aff_4,t46_aff_4,t44_aff_4,t46_aff_4,l66_aff_4,l66_aff_4,l66_aff_4,t65_aff_1,l66_aff_4]),
    [file(aff_4,t51_aff_4),interesting(0.20)]).

fof(t40_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r2_aff_1(A,C,D,B) ) )
           => v1_aff_1(B,A) ) ) ) ),
    file(aff_1,t40_aff_1),
    [interesting(0.00)]).

fof(t13_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ~ v1_aff_1(B,A)
               => k1_aff_4(A,B,C) = k1_xboole_0 ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t40_aff_1]),
    [file(aff_4,t13_aff_4),interesting(0.00)]).

fof(t50_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r3_aff_1(A,B,C)
               => ( v1_aff_1(B,A)
                  & v1_aff_1(C,A) ) ) ) ) ) ),
    file(aff_1,t50_aff_1),
    [interesting(0.00)]).

fof(t47_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,k1_zfmisc_1(u1_struct_0(A)))
             => ( v1_aff_1(C,A)
               => r2_aff_1(A,B,B,C) ) ) ) ) ),
    file(aff_1,t47_aff_1),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(t14_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( v1_aff_1(B,A)
               => r1_tarski(C,k1_aff_4(A,B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_aff_1,d3_tarski]),
    [file(aff_4,t14_aff_4),interesting(0.00)]).

fof(t57_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)))
                     => ( ( r2_aff_1(A,B,C,D)
                          & r4_aff_1(A,D,E) )
                       => r2_aff_1(A,B,C,E) ) ) ) ) ) ) ),
    file(aff_1,t57_aff_1),
    [interesting(0.00)]).

fof(t48_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)))
                 => ( r2_aff_1(A,B,C,D)
                   => r2_aff_1(A,C,B,D) ) ) ) ) ) ),
    file(aff_1,t48_aff_1),
    [interesting(0.00)]).

fof(t37_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)))
                 => ( ( v1_aff_1(D,A)
                      & r2_hidden(B,D) )
                   => ( r2_hidden(C,D)
                    <=> r2_aff_1(A,B,C,D) ) ) ) ) ) ) ),
    file(aff_1,t37_aff_1),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(t15_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r4_aff_1(A,B,C)
               => k1_aff_4(A,B,C) = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_aff_1,t14_aff_4,t57_aff_1,t48_aff_1,t37_aff_1,d3_tarski,d10_xboole_0]),
    [file(aff_4,t15_aff_4),interesting(0.00)]).

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(0.00)]).

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(0.00)]).

fof(t15_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)
                   => ( r1_aff_1(A,B,D,C)
                      & r1_aff_1(A,C,B,D)
                      & r1_aff_1(A,C,D,B)
                      & r1_aff_1(A,D,B,C)
                      & r1_aff_1(A,D,C,B) ) ) ) ) ) ) ),
    file(aff_1,t15_aff_1),
    [interesting(0.00)]).

fof(d1_aff_1,definition,(
    ! [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)
                  <=> r2_analoaf(A,B,C,B,D) ) ) ) ) ) ),
    file(aff_1,d1_aff_1),
    [interesting(0.00)]).

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(0.00)]).

fof(t47_diraf,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))
                 => B = 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))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ( r2_analoaf(A,B,C,C,B)
                                  & r2_analoaf(A,B,C,D,D)
                                  & ( ( r2_analoaf(A,B,C,D,E)
                                      & r2_analoaf(A,B,C,F,G) )
                                   => ( B = C
                                      | r2_analoaf(A,D,E,F,G) ) )
                                  & ( r2_analoaf(A,B,C,B,D)
                                   => r2_analoaf(A,C,B,C,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))
                     => r2_analoaf(A,B,C,B,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))
                        & r2_analoaf(A,B,D,C,E)
                        & C != 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))
                        & r2_analoaf(A,B,C,D,E)
                        & r2_analoaf(A,B,D,C,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))
                       => ~ ( r2_analoaf(A,D,B,B,E)
                            & B != D
                            & ! [F] : 
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_analoaf(A,C,B,B,F)
                                    & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ),
    file(diraf,t47_diraf),
    [interesting(0.00)]).

fof(t1_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))
                     => ~ ( ( r1_aff_1(A,B,C,D)
                            | r1_aff_1(A,B,D,C) )
                          & B != C
                          & ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_aff_1(A,B,E,F)
                                  & r2_analoaf(A,C,E,D,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_aff_1,d1_aff_1,t13_aff_1,t47_diraf,t13_aff_1,t13_aff_1,d1_aff_1]),
    [file(aff_4,t1_aff_4),interesting(0.00)]).

fof(t39_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,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v1_aff_1(E,A)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & r1_aff_1(A,B,C,D) )
                       => ( B = C
                          | r2_hidden(D,E) ) ) ) ) ) ) ) ),
    file(aff_1,t39_aff_1),
    [interesting(0.00)]).

fof(d3_aff_1,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_aff_1(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & C != D
                    & B = k2_aff_1(A,C,D) ) ) ) ) ) ),
    file(aff_1,d3_aff_1),
    [interesting(0.00)]).

fof(t26_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))
             => ( r2_hidden(B,k2_aff_1(A,B,C))
                & r2_hidden(C,k2_aff_1(A,B,C)) ) ) ) ) ),
    file(aff_1,t26_aff_1),
    [interesting(0.00)]).

fof(t14_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))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ~ ( B != C
                                  & ~ ( ~ ( r2_analoaf(A,B,C,D,E)
                                          & r2_analoaf(A,B,C,F,G) )
                                      & ~ ( r2_analoaf(A,B,C,D,E)
                                          & r2_analoaf(A,F,G,B,C) )
                                      & ~ ( r2_analoaf(A,D,E,B,C)
                                          & r2_analoaf(A,F,G,B,C) )
                                      & ~ ( r2_analoaf(A,D,E,B,C)
                                          & r2_analoaf(A,B,C,F,G) ) )
                                  & ~ r2_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ),
    file(aff_1,t14_aff_1),
    [interesting(0.00)]).

fof(t52_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( v1_aff_1(F,A)
                                  & v1_aff_1(G,A)
                                  & r2_hidden(B,F)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,G)
                                  & r2_hidden(E,G) )
                               => ( B = C
                                  | D = E
                                  | ( r3_aff_1(A,F,G)
                                  <=> r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ) ) ),
    file(aff_1,t52_aff_1),
    [interesting(0.00)]).

fof(t17_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)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                         => ~ ( r2_hidden(B,G)
                                              & r2_hidden(C,G)
                                              & r2_hidden(D,G)
                                              & r2_hidden(B,H)
                                              & r2_hidden(E,H)
                                              & r2_hidden(F,H)
                                              & ~ r2_hidden(B,I)
                                              & ~ r2_hidden(B,J)
                                              & G != H
                                              & r2_hidden(C,I)
                                              & r2_hidden(E,I)
                                              & r2_hidden(D,J)
                                              & r2_hidden(F,J)
                                              & v1_aff_1(G,A)
                                              & v1_aff_1(H,A)
                                              & v1_aff_1(I,A)
                                              & v1_aff_1(J,A)
                                              & ~ r4_aff_1(A,I,J)
                                              & ! [K] : 
                                                  ( m1_subset_1(K,u1_struct_0(A))
                                                 => ~ ( r2_hidden(K,I)
                                                      & r2_hidden(K,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_aff_1,t30_aff_1,t33_aff_1,t1_aff_4,t39_aff_1,t30_aff_1,d3_aff_1,t26_aff_1,t30_aff_1,t33_aff_1,t1_aff_4,t39_aff_1,t13_aff_1,t14_aff_1,d1_aff_1,t39_aff_1,t52_aff_1]),
    [file(aff_4,t17_aff_4),interesting(0.00)]).

fof(t55_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_aff_1(B,A)
           => r3_aff_1(A,B,B) ) ) ) ),
    file(aff_1,t55_aff_1),
    [interesting(0.00)]).

fof(d3_aff_4,definition,(
    ! [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,k1_zfmisc_1(u1_struct_0(A)))
             => ( v1_aff_1(C,A)
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( D = k2_aff_4(A,B,C)
                    <=> ( r2_hidden(B,D)
                        & r4_aff_1(A,C,D) ) ) ) ) ) ) ) ),
    file(aff_4,d3_aff_4),
    [interesting(0.00)]).

fof(t30_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,k1_zfmisc_1(u1_struct_0(A)))
             => ( v1_aff_1(C,A)
               => ( r2_hidden(B,C)
                <=> k2_aff_4(A,B,C) = C ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_aff_1,d3_aff_4,d3_aff_4]),
    [file(aff_4,t30_aff_4),interesting(0.00)]).

fof(d2_aff_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_aff_4(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                & ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & v1_aff_1(C,A)
                    & v1_aff_1(D,A)
                    & ~ r4_aff_1(A,C,D)
                    & B = k1_aff_4(A,C,D) ) ) ) ) ) ),
    file(aff_4,d2_aff_4),
    [interesting(0.00)]).

fof(t31_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_aff_1(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(C,B)
                          & r2_hidden(D,B)
                          & C != D ) ) ) ) ) ) ),
    file(aff_1,t31_aff_1),
    [interesting(0.00)]).

fof(t27_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,k1_zfmisc_1(u1_struct_0(A)))
             => ( v1_aff_1(C,A)
               => v1_aff_1(k2_aff_4(A,B,C),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_aff_4,t50_aff_1]),
    [file(aff_4,t27_aff_4),interesting(0.00)]).

fof(t32_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,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_1(C,A)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( B != D
                          & r2_hidden(D,C) ) ) ) ) ) ) ),
    file(aff_1,t32_aff_1),
    [interesting(0.00)]).

fof(l17_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_hidden(D,k1_aff_4(A,B,C))
                  <=> ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & r2_aff_1(A,D,E,B)
                        & r2_hidden(E,C) ) ) ) ) ) ) ),
    file(aff_4,l17_aff_4),
    [interesting(0.00)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

fof(t16_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r4_aff_1(A,B,C)
                   => k1_aff_4(A,B,D) = k1_aff_4(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t57_aff_1,t57_aff_1,t2_tarski]),
    [file(aff_4,t16_aff_4),interesting(0.00)]).

fof(l24_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,k1_zfmisc_1(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(C,A)
                          & v1_aff_1(D,A)
                          & r2_hidden(B,E)
                          & r2_hidden(B,k1_aff_4(A,C,D))
                          & r4_aff_1(A,C,E) )
                       => r1_tarski(E,k1_aff_4(A,C,D)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l17_aff_4,t16_aff_4,t50_aff_1,t57_aff_1,t37_aff_1,t37_aff_1,d3_tarski]),
    [file(aff_4,l24_aff_4),interesting(0.00)]).

fof(t34_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_aff_4(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(A))
                         => ~ ( r2_hidden(C,B)
                              & r2_hidden(D,B)
                              & r2_hidden(E,B)
                              & ~ r1_aff_1(A,C,D,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_aff_4,t31_aff_1,d3_aff_4,t27_aff_4,t32_aff_1,t14_aff_4,l24_aff_4,t39_aff_1,t30_aff_1]),
    [file(aff_4,t34_aff_4),interesting(0.00)]).

fof(t35_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_1(B,A)
                  & v1_aff_4(C,A)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ~ r2_hidden(D,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_aff_4,t33_aff_1]),
    [file(aff_4,t35_aff_4),interesting(0.00)]).

fof(t71_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)))
                 => ( ( v1_aff_1(D,A)
                      & r2_hidden(B,D)
                      & r2_hidden(C,D) )
                   => ( B = C
                      | D = k2_aff_1(A,B,C) ) ) ) ) ) ) ),
    file(aff_1,t71_aff_1),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

fof(t59_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r4_aff_1(A,C,D)
                      & r2_hidden(B,C)
                      & r2_hidden(B,D) )
                   => C = D ) ) ) ) ) ),
    file(aff_1,t59_aff_1),
    [interesting(0.00)]).

fof(l34_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,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( v1_aff_1(E,A)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E)
                          & B != C
                          & ~ r2_hidden(D,E)
                          & r1_aff_1(A,B,C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t33_aff_1,t30_aff_1]),
    [file(aff_4,l34_aff_4),interesting(0.00)]).

fof(t16_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))
             => ( r1_aff_1(A,B,B,C)
                & r1_aff_1(A,B,C,C)
                & r1_aff_1(A,B,C,B) ) ) ) ) ),
    file(aff_1,t16_aff_1),
    [interesting(0.00)]).

fof(t63_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,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_1(C,A)
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(B,D)
                          & r4_aff_1(A,C,D) ) ) ) ) ) ) ),
    file(aff_1,t63_aff_1),
    [interesting(0.00)]).

fof(t58_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ~ ( ~ ( r4_aff_1(A,B,C)
                            & r4_aff_1(A,C,D) )
                        & ~ ( r4_aff_1(A,B,C)
                            & r4_aff_1(A,D,C) )
                        & ~ ( r4_aff_1(A,C,B)
                            & r4_aff_1(A,C,D) )
                        & ~ ( r4_aff_1(A,C,B)
                            & r4_aff_1(A,D,C) ) )
                   => r4_aff_1(A,B,D) ) ) ) ) ) ),
    file(aff_1,t58_aff_1),
    [interesting(0.00)]).

fof(t2_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,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_hidden(B,D)
                   => ( ( ~ r2_aff_1(A,B,C,D)
                        & ~ r2_aff_1(A,C,B,D) )
                      | r2_hidden(C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t40_aff_1,t48_aff_1,t37_aff_1]),
    [file(aff_4,t2_aff_4),interesting(0.00)]).

fof(t66_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)))
                 => ( ( v1_aff_1(D,A)
                      & r2_hidden(B,D)
                      & r2_hidden(C,D) )
                   => r2_aff_1(A,B,C,D) ) ) ) ) ) ),
    file(aff_1,t66_aff_1),
    [interesting(0.00)]).

fof(t46_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( r2_aff_1(A,B,C,F)
                              & r2_analoaf(A,B,C,D,E) )
                           => ( B = C
                              | r2_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) ),
    file(aff_1,t46_aff_1),
    [interesting(0.00)]).

fof(t18_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,k1_zfmisc_1(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)))
                                 => ! [I] : 
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ~ ( r2_hidden(B,F)
                                          & r2_hidden(C,F)
                                          & r2_hidden(D,G)
                                          & r2_hidden(E,G)
                                          & r2_hidden(B,H)
                                          & r2_hidden(D,H)
                                          & r2_hidden(C,I)
                                          & r2_hidden(E,I)
                                          & F != G
                                          & r4_aff_1(A,F,G)
                                          & v1_aff_1(H,A)
                                          & v1_aff_1(I,A)
                                          & ~ r4_aff_1(A,H,I)
                                          & ! [J] : 
                                              ( m1_subset_1(J,u1_struct_0(A))
                                             => ~ ( r2_hidden(J,H)
                                                  & r2_hidden(J,I) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_aff_1,t59_aff_1,t47_diraf,t66_aff_1,t57_aff_1,t46_aff_1,t37_aff_1,t59_aff_1,d3_aff_1,t26_aff_1,t30_aff_1,t33_aff_1,t1_aff_4,t39_aff_1,t13_aff_1,t14_aff_1,d1_aff_1,t39_aff_1,t52_aff_1]),
    [file(aff_4,t18_aff_4),interesting(0.00)]).

fof(t67_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)))
                     => ( ( r2_aff_1(A,B,C,D)
                          & r2_aff_1(A,B,C,E) )
                       => ( B = C
                          | r4_aff_1(A,D,E) ) ) ) ) ) ) ) ),
    file(aff_1,t67_aff_1),
    [interesting(0.00)]).

fof(l25_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,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_1(D,A)
                              & v1_aff_1(E,A)
                              & v1_aff_1(F,A)
                              & r2_hidden(B,k1_aff_4(A,D,E))
                              & r2_hidden(C,k1_aff_4(A,D,E))
                              & r2_hidden(B,F)
                              & r2_hidden(C,F) )
                           => ( B = C
                              | r1_tarski(F,k1_aff_4(A,D,E)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l17_aff_4,l17_aff_4,t63_aff_1,t63_aff_1,t58_aff_1,t57_aff_1,t2_aff_4,t40_aff_1,t30_aff_1,l24_aff_4,t18_aff_4,t47_aff_1,t59_aff_1,t47_diraf,t37_aff_1,t46_aff_1,t57_aff_1,t2_aff_4,t46_aff_1,t55_aff_1,t30_aff_1,t37_aff_1,t67_aff_1,l24_aff_4,t33_aff_1,t1_aff_4,d1_aff_1,t37_aff_1,t46_aff_1,t2_aff_4,t46_aff_1,t30_aff_1,t37_aff_1,t67_aff_1,l24_aff_4,t33_aff_1,t1_aff_4,d1_aff_1,t37_aff_1,t46_aff_1,t2_aff_4,t46_aff_1,d3_tarski]),
    [file(aff_4,l25_aff_4),interesting(0.00)]).

fof(t19_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(A,k3_xboole_0(B,C)) ) ),
    file(xboole_1,t19_xboole_1),
    [interesting(0.00)]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t54_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)))
                     => ( ( r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & r3_aff_1(A,D,E) )
                       => r2_aff_1(A,B,C,E) ) ) ) ) ) ) ),
    file(aff_1,t54_aff_1),
    [interesting(0.00)]).

fof(l27_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_1(B,A)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & r1_tarski(D,k1_aff_4(A,B,C)) )
                   => r1_tarski(k1_aff_4(A,B,D),k1_aff_4(A,B,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l17_aff_4,t63_aff_1,t57_aff_1,t2_aff_4,t54_aff_1,d3_tarski]),
    [file(aff_4,l27_aff_4),interesting(0.00)]).

fof(t3_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,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( ( r2_aff_1(A,B,C,D)
                            | r2_aff_1(A,C,B,D) )
                          & ( r4_aff_1(A,D,E)
                            | r4_aff_1(A,E,D) )
                          & ~ ( r2_aff_1(A,B,C,E)
                              & r2_aff_1(A,C,B,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_aff_1,t57_aff_1,t48_aff_1]),
    [file(aff_4,t3_aff_4),interesting(0.00)]).

fof(t4_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( ( r2_aff_1(A,B,C,F)
                                | r2_aff_1(A,C,B,F) )
                              & ( r2_analoaf(A,B,C,D,E)
                                | r2_analoaf(A,D,E,B,C) )
                              & B != C
                              & ~ ( r2_aff_1(A,D,E,F)
                                  & r2_aff_1(A,E,D,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_aff_1,t48_aff_1,t46_aff_1,t48_aff_1]),
    [file(aff_4,t4_aff_4),interesting(0.00)]).

fof(t23_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,k1_zfmisc_1(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_4(C,A)
                          & r2_hidden(B,C)
                          & r1_tarski(D,C)
                          & r2_hidden(B,E) )
                       => ( ( ~ r4_aff_1(A,D,E)
                            & ~ r4_aff_1(A,E,D) )
                          | r1_tarski(E,C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_aff_1,d2_aff_4,t58_aff_1,l24_aff_4,t20_aff_4,t20_aff_4,l17_aff_4,t32_aff_1,t47_diraf,t59_aff_1,t13_aff_1,d1_aff_1,t15_aff_1,t39_aff_1,t59_aff_1,t66_aff_1,t46_aff_1,t3_aff_4,t2_aff_4,t4_aff_4,l25_aff_4]),
    [file(aff_4,t23_aff_4),interesting(0.00)]).

fof(t21_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( v1_aff_1(B,A)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & r1_tarski(D,k1_aff_4(A,B,C))
                      & ~ r4_aff_1(A,C,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(E,C)
                              & r2_hidden(E,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_aff_1,l17_aff_4,l17_aff_4,t63_aff_1,t63_aff_1,t3_aff_4,t58_aff_1,t2_aff_4,t50_aff_1,t2_aff_4,t30_aff_1,t18_aff_4]),
    [file(aff_4,t21_aff_4),interesting(0.00)]).

fof(t24_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,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ( ( v1_aff_4(D,A)
                          & v1_aff_4(E,A)
                          & r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & r2_hidden(B,E)
                          & r2_hidden(C,E) )
                       => ( D = E
                          | B = C
                          | v1_aff_1(k5_subset_1(u1_struct_0(A),D,E),A) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t26_aff_1,d3_aff_1,t19_aff_4,t19_xboole_1,d3_tarski,d3_xboole_0,t26_aff_1,d3_aff_1,t19_aff_4,t23_aff_4,t22_aff_4,t71_aff_1,t19_aff_4,d3_xboole_0,t26_aff_1,d3_aff_1,t19_aff_4,t23_aff_4,t22_aff_4,t71_aff_1,t19_aff_4,d3_xboole_0,t2_tarski,d10_xboole_0]),
    [file(aff_4,t24_aff_4),interesting(0.00)]).

fof(t25_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,k1_zfmisc_1(u1_struct_0(A)))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_4(E,A)
                              & v1_aff_4(F,A)
                              & r2_hidden(B,E)
                              & r2_hidden(C,E)
                              & r2_hidden(D,E)
                              & r2_hidden(B,F)
                              & r2_hidden(C,F)
                              & r2_hidden(D,F) )
                           => ( r1_aff_1(A,B,C,D)
                              | E = F ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_aff_1,t24_aff_4,d3_xboole_0,t33_aff_1]),
    [file(aff_4,t25_aff_4),interesting(0.00)]).

fof(t26_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(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_4(B,A)
                          & v1_aff_4(C,A)
                          & v1_aff_1(D,A)
                          & v1_aff_1(E,A)
                          & r1_tarski(D,B)
                          & r1_tarski(E,B)
                          & r1_tarski(D,C)
                          & r1_tarski(E,C) )
                       => ( D = E
                          | B = C ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_aff_1,t31_aff_1,t59_aff_1,l34_aff_4,t25_aff_4,t32_aff_1,t30_aff_1,l34_aff_4,t25_aff_4,l34_aff_4,t25_aff_4,t22_aff_4]),
    [file(aff_4,t26_aff_4),interesting(0.00)]).

fof(d4_aff_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r1_aff_4(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                       => ( ( r2_hidden(D,C)
                            & v1_aff_1(E,A)
                            & r1_tarski(E,B) )
                         => r1_tarski(k2_aff_4(A,D,E),C) ) ) ) ) ) ) ) ),
    file(aff_4,d4_aff_4),
    [interesting(0.00)]).

fof(l42_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,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_aff_1(C,A)
                  & r2_hidden(B,C) )
               => k2_aff_4(A,B,C) = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_aff_1,d3_aff_4]),
    [file(aff_4,l42_aff_4),interesting(0.00)]).

fof(t32_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r4_aff_1(A,C,D)
                   => k2_aff_4(A,B,C) = k2_aff_4(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_aff_1,d3_aff_4,t58_aff_1,t58_aff_1,t59_aff_1]),
    [file(aff_4,t32_aff_4),interesting(0.00)]).

fof(d5_aff_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_aff_4(A,B,C,D)
                  <=> ? [E] : 
                        ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                        & r1_tarski(B,E)
                        & r1_tarski(C,E)
                        & r1_tarski(D,E)
                        & v1_aff_4(E,A) ) ) ) ) ) ) ),
    file(aff_4,d5_aff_4),
    [interesting(0.00)]).

fof(t45_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(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(B,A)
                          & v1_aff_1(C,A)
                          & v1_aff_1(D,A)
                          & v1_aff_1(E,A)
                          & r2_aff_4(A,D,E,C)
                          & r2_aff_4(A,D,E,B) )
                       => ( D = E
                          | r2_aff_4(A,D,C,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_aff_4,d5_aff_4,t26_aff_4,d5_aff_4]),
    [file(aff_4,t45_aff_4),interesting(0.00)]).

fof(t12_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))
                 => ( r2_analoaf(A,B,C,D,D)
                    & r2_analoaf(A,D,D,B,C) ) ) ) ) ) ),
    file(aff_1,t12_aff_1),
    [interesting(0.00)]).

fof(t53_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( r2_hidden(B,F)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,G)
                                  & r2_hidden(E,G)
                                  & r3_aff_1(A,F,G) )
                               => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ) ),
    file(aff_1,t53_aff_1),
    [interesting(0.00)]).

fof(d8_diraf,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v2_diraf(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)
                            & ! [F] : 
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_analoaf(A,B,C,B,F)
                                    & r2_analoaf(A,D,E,D,F) ) ) ) ) ) ) ) ) ) ),
    file(diraf,d8_diraf),
    [interesting(0.00)]).

fof(t48_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( ~ ( ~ v3_struct_0(A)
                  & ~ v3_realset2(A)
                  & v1_diraf(A)
                  & v2_diraf(A)
                  & l1_analoaf(A) )
              & v1_aff_4(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => r2_hidden(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t12_aff_1,d3_tarski,t19_aff_4,d3_aff_1,t22_aff_4,t26_aff_1,t53_aff_1,t33_aff_1,d1_aff_1,d8_diraf]),
    [file(aff_4,t48_aff_4),interesting(0.00)]).

fof(t44_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_aff_4(A,B,C,D)
                   => ( r2_aff_4(A,B,D,C)
                      & r2_aff_4(A,C,B,D)
                      & r2_aff_4(A,C,D,B)
                      & r2_aff_4(A,D,B,C)
                      & r2_aff_4(A,D,C,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_aff_4,d5_aff_4]),
    [file(aff_4,t44_aff_4),interesting(0.00)]).

fof(t38_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)))
                 => ( ( D = k2_aff_1(A,B,C)
                     => ( B = C
                        | ( v1_aff_1(D,A)
                          & r2_hidden(B,D)
                          & r2_hidden(C,D)
                          & B != C ) ) )
                    & ( ( v1_aff_1(D,A)
                        & r2_hidden(B,D)
                        & r2_hidden(C,D) )
                     => ( B = C
                        | ( B != C
                          & D = k2_aff_1(A,B,C) ) ) ) ) ) ) ) ) ),
    file(aff_1,t38_aff_1),
    [interesting(0.00)]).

fof(t11_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,k1_zfmisc_1(u1_struct_0(A)))
                  & r2_hidden(B,D)
                  & r2_hidden(C,D)
                  & v1_aff_1(D,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_aff_1,t33_aff_1]),
    [file(aff_4,t11_aff_4),interesting(0.00)]).

fof(t22_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))
             => ~ ( B != C
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => r1_aff_1(A,B,C,D) ) ) ) ) ) ),
    file(aff_1,t22_aff_1),
    [interesting(0.00)]).

fof(t12_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_aff_1(B,A)
              & ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => r2_hidden(C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_aff_1,t22_aff_1,t33_aff_1]),
    [file(aff_4,t12_aff_4),interesting(0.00)]).

fof(t36_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,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_1(C,A)
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(B,D)
                          & r1_tarski(C,D)
                          & v1_aff_4(D,A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_aff_1,t11_aff_4,t59_aff_1,d2_aff_4,t14_aff_4,t55_aff_1,l24_aff_4,t12_aff_4,t11_aff_4,t59_aff_1,d2_aff_4,t14_aff_4]),
    [file(aff_4,t36_aff_4),interesting(0.00)]).

fof(t38_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ~ ( r2_hidden(B,C)
                      & r2_hidden(B,D)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A)
                      & ! [E] : 
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( r1_tarski(C,E)
                              & r1_tarski(D,E)
                              & v1_aff_4(E,A) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t32_aff_1,t38_aff_1,t36_aff_4,t19_aff_4]),
    [file(aff_4,t38_aff_4),interesting(0.00)]).

fof(t47_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r2_hidden(B,C)
                      & r2_hidden(B,D)
                      & v1_aff_1(C,A)
                      & v1_aff_1(D,A) )
                   => ( r2_aff_4(A,C,D,D)
                      & r2_aff_4(A,D,C,D)
                      & r2_aff_4(A,D,D,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_aff_4,d5_aff_4]),
    [file(aff_4,t47_aff_4),interesting(0.00)]).

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(0.00)]).

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(mizar_proof,[status(thm)],[t33_aff_1,t33_aff_1,t30_aff_1,t13_aff_1,t69_aff_1]),
    [file(aff_4,t8_aff_4),interesting(0.00)]).

fof(t11_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))
             => ( r2_analoaf(A,B,C,C,B)
                & r2_analoaf(A,B,C,B,C) ) ) ) ) ),
    file(aff_1,t11_aff_1),
    [interesting(0.00)]).

fof(t70_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))
                         => ! [G] : 
                              ( m1_subset_1(G,u1_struct_0(A))
                             => ( ( r1_aff_1(A,B,C,E)
                                  & r1_aff_1(A,B,D,F)
                                  & r1_aff_1(A,B,D,G)
                                  & r2_analoaf(A,C,D,E,F)
                                  & r2_analoaf(A,C,D,E,G) )
                               => ( r1_aff_1(A,B,C,D)
                                  | F = G ) ) ) ) ) ) ) ) ) ),
    file(aff_1,t70_aff_1),
    [interesting(0.00)]).

fof(t9_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)
                                      & C = D )
                                   => ( B = C
                                      | B = E
                                      | G = H
                                      | ( ~ r2_analoaf(A,C,E,D,F)
                                        & ~ r2_analoaf(A,E,C,F,D) )
                                      | E = F ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t33_aff_1,t33_aff_1,t30_aff_1,t11_aff_1,t16_aff_1,t13_aff_1,t70_aff_1]),
    [file(aff_4,t9_aff_4),interesting(0.00)]).

fof(t51_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( r3_aff_1(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))
                                & D != E
                                & F != G
                                & r2_analoaf(A,D,E,F,G)
                                & B = k2_aff_1(A,D,E)
                                & C = k2_aff_1(A,F,G) ) ) ) ) ) ) ) ) ),
    file(aff_1,t51_aff_1),
    [interesting(0.00)]).

fof(d4_aff_1,definition,(
    ! [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)))
                 => ( r2_aff_1(A,B,C,D)
                  <=> ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & ? [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                            & E != F
                            & D = k2_aff_1(A,E,F)
                            & r2_analoaf(A,B,C,E,F) ) ) ) ) ) ) ) ),
    file(aff_1,d4_aff_1),
    [interesting(0.00)]).

fof(l63_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,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                         => ! [K] : 
                                              ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A)))
                                             => ( ( r2_hidden(B,I)
                                                  & r2_hidden(B,J)
                                                  & r2_hidden(B,K)
                                                  & r2_hidden(C,I)
                                                  & r2_hidden(F,I)
                                                  & r2_hidden(D,J)
                                                  & r2_hidden(G,J)
                                                  & r2_hidden(E,K)
                                                  & r2_hidden(H,K)
                                                  & v1_aff_1(I,A)
                                                  & v1_aff_1(J,A)
                                                  & v1_aff_1(K,A)
                                                  & r2_analoaf(A,C,D,F,G)
                                                  & r2_analoaf(A,C,E,F,H) )
                                               => ( r2_aff_4(A,I,J,K)
                                                  | B = C
                                                  | B = D
                                                  | B = E
                                                  | I = J
                                                  | I = K
                                                  | r2_analoaf(A,D,E,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_aff_4,t38_aff_4,t47_aff_4,t30_aff_1,t8_aff_4,t8_aff_4,t12_aff_1,t8_aff_4,t9_aff_4,t9_aff_4,t11_aff_1,t30_aff_1,d3_aff_1,t26_aff_1,t26_aff_1,t51_aff_1,t19_aff_4,t19_aff_4,t53_aff_1,t22_aff_4,t27_aff_4,d3_aff_4,t58_aff_1,t33_aff_1,t1_aff_4,t1_aff_4,t13_aff_1,d4_aff_1,t3_aff_4,t2_aff_4,t13_aff_1,d4_aff_1,t3_aff_4,t2_aff_4,t39_aff_1,t59_aff_1,t30_aff_1,t30_aff_1,t71_aff_1,t19_aff_4,t23_aff_4,t71_aff_1,t19_aff_4,d5_aff_4]),
    [file(aff_4,l63_aff_4),interesting(0.00)]).

fof(t65_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_1(F,A)
                              & r2_hidden(B,F)
                              & r2_hidden(C,F)
                              & r2_hidden(D,F)
                              & r2_hidden(E,F) )
                           => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ),
    file(aff_1,t65_aff_1),
    [interesting(0.00)]).

fof(t49_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,u1_struct_0(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u1_struct_0(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,k1_zfmisc_1(u1_struct_0(A)))
                                     => ! [J] : 
                                          ( m1_subset_1(J,k1_zfmisc_1(u1_struct_0(A)))
                                         => ! [K] : 
                                              ( m1_subset_1(K,k1_zfmisc_1(u1_struct_0(A)))
                                             => ( ( r2_hidden(B,I)
                                                  & r2_hidden(B,J)
                                                  & r2_hidden(B,K)
                                                  & r2_hidden(C,I)
                                                  & r2_hidden(F,I)
                                                  & r2_hidden(D,J)
                                                  & r2_hidden(G,J)
                                                  & r2_hidden(E,K)
                                                  & r2_hidden(H,K)
                                                  & v1_aff_1(I,A)
                                                  & v1_aff_1(J,A)
                                                  & v1_aff_1(K,A)
                                                  & r2_analoaf(A,C,D,F,G)
                                                  & r2_analoaf(A,C,E,F,H) )
                                               => ( ( ~ v3_struct_0(A)
                                                    & ~ v3_realset2(A)
                                                    & v1_diraf(A)
                                                    & v2_diraf(A)
                                                    & l1_analoaf(A) )
                                                  | B = C
                                                  | B = D
                                                  | B = E
                                                  | I = J
                                                  | I = K
                                                  | r2_analoaf(A,D,E,G,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_aff_4,t48_aff_4,t26_aff_1,d3_aff_1,t33_aff_1,t1_aff_4,t39_aff_1,t44_aff_4,t46_aff_4,t44_aff_4,t46_aff_4,t44_aff_4,t46_aff_4,l63_aff_4,l63_aff_4,l63_aff_4,t65_aff_1,l63_aff_4]),
    [file(aff_4,t49_aff_4),interesting(0.00)]).

fof(d4_aff_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v4_aff_2(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ! [K] : 
                                                ( m1_subset_1(K,u1_struct_0(A))
                                               => ( ( r2_hidden(E,B)
                                                    & r2_hidden(E,C)
                                                    & r2_hidden(E,D)
                                                    & r2_hidden(F,B)
                                                    & r2_hidden(I,B)
                                                    & r2_hidden(G,C)
                                                    & r2_hidden(J,C)
                                                    & r2_hidden(H,D)
                                                    & r2_hidden(K,D)
                                                    & v1_aff_1(B,A)
                                                    & v1_aff_1(C,A)
                                                    & v1_aff_1(D,A)
                                                    & r2_analoaf(A,F,G,I,J)
                                                    & r2_analoaf(A,F,H,I,K) )
                                                 => ( E = F
                                                    | E = G
                                                    | E = H
                                                    | B = C
                                                    | B = D
                                                    | r2_analoaf(A,G,H,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(aff_2,d4_aff_2),
    [interesting(0.00)]).

fof(t41_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( r2_hidden(B,F)
                              & r2_hidden(C,F)
                              & v1_aff_1(F,A) )
                           => ( B = C
                              | ( r2_aff_1(A,D,E,F)
                              <=> r2_analoaf(A,D,E,B,C) ) ) ) ) ) ) ) ) ) ),
    file(aff_1,t41_aff_1),
    [interesting(0.00)]).

fof(t39_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( r4_aff_1(A,B,C)
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r1_tarski(B,D)
                          & r1_tarski(C,D)
                          & v1_aff_4(D,A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_aff_1,t31_aff_1,t36_aff_4,d3_aff_4,t28_aff_4]),
    [file(aff_4,t39_aff_4),interesting(0.00)]).

fof(t10_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( r2_hidden(B,F)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,G)
                                  & r2_hidden(E,G)
                                  & B = C )
                               => ( ( ~ r4_aff_1(A,F,G)
                                    & ~ r4_aff_1(A,G,F) )
                                  | F = G
                                  | ( ~ r2_analoaf(A,B,D,C,E)
                                    & ~ r2_analoaf(A,D,B,E,C) )
                                  | D = E ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_aff_1,d1_aff_1,t15_aff_1,t50_aff_1,t39_aff_1,t59_aff_1]),
    [file(aff_4,t10_aff_4),interesting(0.00)]).

fof(d11_aff_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ( v11_aff_2(A)
      <=> ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ! [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                               => ! [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                   => ! [I] : 
                                        ( m1_subset_1(I,u1_struct_0(A))
                                       => ! [J] : 
                                            ( m1_subset_1(J,u1_struct_0(A))
                                           => ( ( r4_aff_1(A,B,C)
                                                & r4_aff_1(A,B,D)
                                                & r2_hidden(E,B)
                                                & r2_hidden(H,B)
                                                & r2_hidden(F,C)
                                                & r2_hidden(I,C)
                                                & r2_hidden(G,D)
                                                & r2_hidden(J,D)
                                                & v1_aff_1(B,A)
                                                & v1_aff_1(C,A)
                                                & v1_aff_1(D,A)
                                                & r2_analoaf(A,E,F,H,I)
                                                & r2_analoaf(A,E,G,H,J) )
                                             => ( B = C
                                                | B = D
                                                | r2_analoaf(A,F,G,I,J) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(aff_2,d11_aff_2),
    [interesting(0.00)]).

fof(t31_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,k1_zfmisc_1(u1_struct_0(A)))
                 => ( v1_aff_1(D,A)
                   => k2_aff_4(A,B,D) = k2_aff_4(A,B,k2_aff_4(A,C,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_aff_4,d3_aff_4,t58_aff_1,t58_aff_1,t59_aff_1]),
    [file(aff_4,t31_aff_4),interesting(0.00)]).

fof(t56_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r4_aff_1(A,B,C)
                      & r1_aff_4(A,C,D) )
                   => r1_aff_4(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_aff_1,t33_aff_4,t31_aff_1,d3_aff_4,t31_aff_4,d4_aff_4,d4_aff_4]),
    [file(aff_4,t56_aff_4),interesting(0.00)]).

fof(t5_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,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( ( r2_aff_1(A,B,C,D)
                            | r2_aff_1(A,C,B,D) )
                          & ( r2_aff_1(A,B,C,E)
                            | r2_aff_1(A,C,B,E) )
                          & B != C
                          & ~ ( r4_aff_1(A,D,E)
                              & r4_aff_1(A,E,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_aff_1,t67_aff_1,t67_aff_1]),
    [file(aff_4,t5_aff_4),interesting(0.00)]).

fof(t17_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,D)
                              & r1_aff_1(A,B,C,E)
                              & r1_aff_1(A,B,C,F) )
                           => ( B = C
                              | r1_aff_1(A,D,E,F) ) ) ) ) ) ) ) ) ),
    file(aff_1,t17_aff_1),
    [interesting(0.00)]).

fof(l47_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,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_4(C,A)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(D,C)
                              & r2_hidden(E,C)
                              & ~ r1_aff_1(A,B,D,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_aff_4,t16_aff_1,t17_aff_1,t15_aff_1]),
    [file(aff_4,l47_aff_4),interesting(0.00)]).

fof(l80_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_aff_4(B,A)
                  & v1_aff_4(C,A)
                  & r1_aff_4(A,B,C) )
               => ( B = C
                  | ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,B)
                          & r2_hidden(D,C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l47_aff_4,t16_aff_1,t26_aff_1,d3_aff_1,t19_aff_4,d4_aff_4,l42_aff_4,t26_aff_1,t33_aff_1,t26_aff_4]),
    [file(aff_4,l80_aff_4),interesting(0.00)]).

fof(t62_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,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_4(C,A)
                      & v1_aff_4(D,A)
                      & r2_hidden(B,C)
                      & r2_hidden(B,D)
                      & r1_aff_4(A,C,D) )
                   => C = D ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l80_aff_4]),
    [file(aff_4,t62_aff_4),interesting(0.00)]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(t64_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,k1_zfmisc_1(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)))
                                 => ( ( v1_aff_4(F,A)
                                      & v1_aff_4(G,A)
                                      & v1_aff_4(H,A)
                                      & r1_aff_4(A,F,G)
                                      & r2_hidden(B,k5_subset_1(u1_struct_0(A),F,H))
                                      & r2_hidden(C,k5_subset_1(u1_struct_0(A),F,H))
                                      & r2_hidden(D,k5_subset_1(u1_struct_0(A),G,H))
                                      & r2_hidden(E,k5_subset_1(u1_struct_0(A),G,H)) )
                                   => ( F = G
                                      | B = C
                                      | D = E
                                      | r4_aff_1(A,k5_subset_1(u1_struct_0(A),F,H),k5_subset_1(u1_struct_0(A),G,H)) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t63_aff_4,d3_xboole_0,l80_aff_4,l80_aff_4,t24_aff_4,t52_aff_1]),
    [file(aff_4,t64_aff_4),interesting(0.00)]).

fof(t37_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,k1_zfmisc_1(u1_struct_0(A)))
                      & r2_hidden(B,E)
                      & r2_hidden(C,E)
                      & r2_hidden(D,E)
                      & v1_aff_4(E,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_aff_4,t36_aff_4]),
    [file(aff_4,t37_aff_4),interesting(0.00)]).

fof(l9_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,k1_zfmisc_1(u1_struct_0(A)))
                     => ! [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( r4_aff_1(A,E,F)
                              & r2_hidden(B,E)
                              & r2_hidden(C,E)
                              & r2_hidden(D,F)
                              & ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( r2_hidden(G,F)
                                      & r2_analoaf(A,B,D,C,G) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_aff_1,t47_diraf,t13_aff_1,t41_aff_1,t3_aff_4,t2_aff_4,t11_aff_1]),
    [file(aff_4,l9_aff_4),interesting(0.00)]).

fof(t7_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ! [G] : 
                              ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                             => ( ( r2_hidden(B,F)
                                  & r2_hidden(C,F)
                                  & r2_hidden(D,G) )
                               => ( ( ~ r4_aff_1(A,F,G)
                                    & ~ r4_aff_1(A,G,F) )
                                  | B = C
                                  | ( ~ r2_analoaf(A,B,C,D,E)
                                    & ~ r2_analoaf(A,D,E,B,C) )
                                  | r2_hidden(E,G) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t50_aff_1,t66_aff_1,t4_aff_4,t3_aff_4,t2_aff_4]),
    [file(aff_4,t7_aff_4),interesting(0.00)]).

fof(t29_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_4(F,A)
                              & r2_hidden(B,F)
                              & r2_hidden(C,F)
                              & r2_hidden(D,F)
                              & r2_analoaf(A,B,C,D,E) )
                           => ( B = C
                              | r2_hidden(E,F) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_aff_1,d3_aff_4,t26_aff_1,t7_aff_4,t19_aff_4,t28_aff_4]),
    [file(aff_4,t29_aff_4),interesting(0.00)]).

fof(t72_aff_1,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & v2_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ~ ( v1_aff_1(B,A)
                  & v1_aff_1(C,A)
                  & ~ r4_aff_1(A,B,C)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,B)
                          & r2_hidden(D,C) ) ) ) ) ) ) ),
    file(aff_1,t72_aff_1),
    [interesting(0.00)]).

fof(t53_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))
                         => ~ ( ~ v3_struct_0(A)
                              & ~ v3_realset2(A)
                              & v1_diraf(A)
                              & v2_diraf(A)
                              & l1_analoaf(A)
                              & ~ r1_aff_1(A,B,C,D)
                              & ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,B,D,E,G)
                                      & r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t11_aff_4,t11_aff_4,t63_aff_1,t63_aff_1,t50_aff_1,t58_aff_1,t58_aff_1,t59_aff_1,t33_aff_1,t72_aff_1,t53_aff_1]),
    [file(aff_4,t53_aff_4),interesting(0.00)]).

fof(t54_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))
                         => ~ ( ~ r1_aff_1(A,B,C,D)
                              & E != F
                              & r2_analoaf(A,B,C,E,F)
                              & ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,B,D,E,G)
                                      & r2_analoaf(A,C,D,F,G) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_aff_4,t16_aff_1,t26_aff_1,t51_aff_1,d3_aff_1,t19_aff_4,t23_aff_4,t39_aff_4,t26_aff_1,d3_aff_1,t19_aff_4,t30_aff_1,d3_aff_4,t27_aff_4,l9_aff_4,t71_aff_1,t19_aff_4,t51_aff_4,t30_aff_1,t30_aff_1,t25_aff_4,t26_aff_1,d3_aff_1,t33_aff_1,t1_aff_4,t39_aff_1,t71_aff_1,t19_aff_4,t49_aff_4,t22_aff_4,l70_aff_4,t53_aff_4]),
    [file(aff_4,t54_aff_4),interesting(0.00)]).

fof(t55_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v1_aff_4(B,A)
                  & v1_aff_4(C,A) )
               => ( r1_aff_4(A,B,C)
                <=> ? [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                      & ? [E] : 
                          ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                          & ? [F] : 
                              ( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
                              & ? [G] : 
                                  ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                                  & ~ r4_aff_1(A,D,E)
                                  & r1_tarski(D,B)
                                  & r1_tarski(E,B)
                                  & r1_tarski(F,C)
                                  & r1_tarski(G,C)
                                  & ( r4_aff_1(A,D,F)
                                    | r4_aff_1(A,F,D) )
                                  & ( r4_aff_1(A,E,G)
                                    | r4_aff_1(A,G,E) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_aff_4,t16_aff_1,t26_aff_1,d3_aff_1,t34_aff_4,t59_aff_1,t33_aff_1,t19_aff_4,d3_aff_4,d4_aff_4,t50_aff_1,t22_aff_4,t58_aff_1,t58_aff_1,t22_aff_4,d3_aff_4,t58_aff_1,t58_aff_1,t23_aff_4,t58_aff_1,t58_aff_1,t23_aff_4,t32_aff_1,d3_aff_4,t27_aff_4,d3_aff_4,t58_aff_1,t28_aff_4,t22_aff_4,t30_aff_1,t32_aff_1,t53_aff_1,t55_aff_1,t39_aff_1,t30_aff_1,t54_aff_4,t16_aff_1,t7_aff_4,t66_aff_1,t4_aff_4,t3_aff_4,t2_aff_4,t30_aff_1,t26_aff_1,d3_aff_1,t52_aff_1,t58_aff_1,t19_aff_4,t58_aff_1,t23_aff_4,d4_aff_4]),
    [file(aff_4,t55_aff_4),interesting(0.00)]).

fof(d6_aff_4,definition,(
    ! [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,k1_zfmisc_1(u1_struct_0(A)))
             => ( v1_aff_4(C,A)
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( D = k3_aff_4(A,B,C)
                    <=> ( r2_hidden(B,D)
                        & r1_aff_4(A,C,D)
                        & v1_aff_4(D,A) ) ) ) ) ) ) ) ),
    file(aff_4,d6_aff_4),
    [interesting(0.00)]).

fof(t59_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ~ ( v1_aff_4(B,A)
              & B = k1_xboole_0 ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_aff_4]),
    [file(aff_4,t59_aff_4),interesting(0.00)]).

fof(l1_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( r2_hidden(C,B)
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) ),
    file(aff_4,l1_aff_4),
    [interesting(0.00)]).

fof(t60_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( r1_aff_4(A,B,C)
                      & r1_aff_4(A,C,D) )
                   => ( C = k1_xboole_0
                      | r1_aff_4(A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[l1_aff_4,d4_aff_4,t27_aff_4,d4_aff_4,t31_aff_4,d4_aff_4]),
    [file(aff_4,t60_aff_4),interesting(0.00)]).

fof(l78_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_4(B,A)
                      & v1_aff_4(C,A)
                      & v1_aff_4(D,A)
                      & r1_aff_4(A,B,C)
                      & r1_aff_4(A,C,D) )
                   => r1_aff_4(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t59_aff_4,t60_aff_4]),
    [file(aff_4,l78_aff_4),interesting(0.00)]).

fof(t61_aff_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v1_diraf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( ( v1_aff_4(B,A)
                      & v1_aff_4(C,A)
                      & v1_aff_4(D,A) )
                   => ( ( ~ ( r1_aff_4(A,B,C)
                            & r1_aff_4(A,C,D) )
                        & ~ ( r1_aff_4(A,B,C)
                            & r1_aff_4(A,D,C) )
                        & ~ ( r1_aff_4(A,C,B)
                            & r1_aff_4(A,C,D) )
                        & ~ ( r1_aff_4(A,C,B)
                            & r1_aff_4(A,D,C) ) )
                      | ( r1_aff_4(A,B,D)
                        & r1_aff_4(A,D,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t58_aff_4,l78_aff_4,t58_aff_4]),
    [file(aff_4,t61_aff_4),interesting(0.00)]).

fof(t45_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ( ( v1_aff_1(F,A)
                              & r2_aff_1(A,B,C,F)
                              & r2_aff_1(A,D,E,F) )
                           => r2_analoaf(A,B,C,D,E) ) ) ) ) ) ) ) ),
    file(aff_1,t45_aff_1),
    [interesting(0.00)]).

fof(t6_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,k1_zfmisc_1(u1_struct_0(A)))
                         => ~ ( ( r2_aff_1(A,B,C,F)
                                | r2_aff_1(A,C,B,F) )
                              & ( r2_aff_1(A,D,E,F)
                                | r2_aff_1(A,E,D,F) )
                              & ~ ( r2_analoaf(A,B,C,D,E)
                                  & r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_aff_1,t40_aff_1,t45_aff_1,t13_aff_1]),
    [file(aff_4,t6_aff_4),interesting(0.00)]).