% Mizar problem: t39_pasch,pasch,1612,54 
fof(t39_pasch,conjecture,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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_diraf(A,B,C,D)
                                  & r2_analoaf(A,B,C,E,F)
                                  & r3_diraf(A,E,F,G)
                                  & r2_analoaf(A,B,E,C,F)
                                  & r2_analoaf(A,B,E,D,G) )
                               => ( r3_diraf(A,B,C,E)
                                  | r1_diraf(A,E,F,G) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d4_diraf,d5_analoaf,d5_diraf,dt_l1_analoaf,dt_l1_struct_0,dt_m1_subset_1,dt_u1_struct_0,existence_l1_analoaf,existence_l1_struct_0,existence_m1_subset_1,t11_diraf,t12_diraf,t13_diraf,t14_diraf,t26_pasch,t34_diraf,t36_diraf,t37_diraf,t38_diraf,t39_diraf,t5_diraf,t6_diraf]),
    [file(pasch,t39_pasch)]).

fof(d4_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(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_diraf(A,B,C,D,E)
                      <=> ( r2_analoaf(A,B,C,D,E)
                          | r2_analoaf(A,B,C,E,D) ) ) ) ) ) ) ) ),
    file(diraf,d4_diraf),
    []).

fof(d5_analoaf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_analoaf(A) )
     => ( v2_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,u1_struct_0(A))
                                         => ( r2_analoaf(A,B,C,D,D)
                                            & ( r2_analoaf(A,B,C,C,B)
                                             => B = C )
                                            & ( ( r2_analoaf(A,B,C,F,G)
                                                & r2_analoaf(A,B,C,H,I) )
                                             => ( B = C
                                                | r2_analoaf(A,F,G,H,I) ) )
                                            & ( r2_analoaf(A,B,C,D,E)
                                             => r2_analoaf(A,C,B,E,D) )
                                            & ( r2_analoaf(A,B,C,C,D)
                                             => r2_analoaf(A,B,C,B,D) )
                                            & ~ ( r2_analoaf(A,B,C,B,D)
                                                & ~ r2_analoaf(A,B,C,C,D)
                                                & ~ r2_analoaf(A,B,D,D,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))
                          & ~ r2_analoaf(A,B,C,D,E)
                          & ~ r2_analoaf(A,B,C,E,D) ) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ? [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r2_analoaf(A,B,C,D,E)
                          & 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))
                         => ~ ( B != D
                              & r2_analoaf(A,D,B,B,E)
                              & ! [F] : 
                                  ( m1_subset_1(F,u1_struct_0(A))
                                 => ~ ( r2_analoaf(A,C,B,B,F)
                                      & r2_analoaf(A,C,D,E,F) ) ) ) ) ) ) ) ) ) ) ),
    file(analoaf,d5_analoaf),
    []).

fof(d5_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(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))
                 => ( r3_diraf(A,B,C,D)
                  <=> r2_diraf(A,B,C,B,D) ) ) ) ) ) ),
    file(diraf,d5_diraf),
    []).

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

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

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

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

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

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

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

fof(t11_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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,B,D)
                  <=> ( r1_diraf(A,B,C,D)
                      | r1_diraf(A,B,D,C) ) ) ) ) ) ) ),
    file(diraf,t11_diraf),
    []).

fof(t12_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_diraf(A,B,C,B)
               => B = C ) ) ) ) ),
    file(diraf,t12_diraf),
    []).

fof(t13_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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_diraf(A,B,C,D)
                   => r1_diraf(A,D,C,B) ) ) ) ) ) ),
    file(diraf,t13_diraf),
    []).

fof(t14_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_diraf(A,B,B,C)
                & r1_diraf(A,B,C,C) ) ) ) ) ),
    file(diraf,t14_diraf),
    []).

fof(t26_pasch,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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_diraf(A,B,C,D)
                          & ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ~ ( r1_diraf(A,B,F,E)
                                  & r2_analoaf(A,D,E,C,F) ) ) ) ) ) ) ) ) ),
    file(pasch,t26_pasch),
    []).

fof(t34_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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_diraf(A,B,C,D)
                   => r3_diraf(A,B,C,D) ) ) ) ) ) ),
    file(diraf,t34_diraf),
    []).

fof(t36_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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))
                 => ( r3_diraf(A,B,C,D)
                   => ( r3_diraf(A,B,D,C)
                      & r3_diraf(A,C,B,D)
                      & r3_diraf(A,C,D,B)
                      & r3_diraf(A,D,B,C)
                      & r3_diraf(A,D,C,B) ) ) ) ) ) ) ),
    file(diraf,t36_diraf),
    []).

fof(t37_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(A)
        & l1_analoaf(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_diraf(A,B,B,C)
                & r3_diraf(A,B,C,C)
                & r3_diraf(A,B,C,B) ) ) ) ) ),
    file(diraf,t37_diraf),
    []).

fof(t38_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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))
                         => ( ( r3_diraf(A,B,C,D)
                              & r3_diraf(A,B,C,E)
                              & r3_diraf(A,B,C,F) )
                           => ( B = C
                              | r3_diraf(A,D,E,F) ) ) ) ) ) ) ) ) ),
    file(diraf,t38_diraf),
    []).

fof(t39_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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))
                     => ( ( r3_diraf(A,B,C,D)
                          & r2_diraf(A,B,C,D,E) )
                       => ( B = C
                          | r3_diraf(A,B,C,E) ) ) ) ) ) ) ) ),
    file(diraf,t39_diraf),
    []).

fof(t5_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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,C,B,E,D)
                          & r2_analoaf(A,D,E,B,C)
                          & r2_analoaf(A,E,D,C,B) ) ) ) ) ) ) ) ),
    file(diraf,t5_diraf),
    []).

fof(t6_diraf,axiom,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v3_realset2(A)
        & v2_analoaf(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))
                             => ( ( r2_analoaf(A,D,E,B,C)
                                  & r2_analoaf(A,B,C,F,G) )
                               => ( B = C
                                  | r2_analoaf(A,D,E,F,G) ) ) ) ) ) ) ) ) ) ),
    file(diraf,t6_diraf),
    []).