% Mizar problem: t22_projpl_1,projpl_1,547,70 
fof(t22_projpl_1,conjecture,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ( ( v1_projpl_1(A)
          & ! [B] : 
              ( m1_subset_1(B,u1_incsp_1(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_incsp_1(A))
                 => ? [D] : 
                      ( m1_subset_1(D,u2_incsp_1(A))
                      & r3_incproj(A,B,C,D) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,u2_incsp_1(A))
             => ! [C] : 
                  ( m1_subset_1(C,u2_incsp_1(A))
                 => ? [D] : 
                      ( m1_subset_1(D,u1_incsp_1(A))
                      & r2_projpl_1(A,D,B,C) ) ) ) )
       => ( ! [B] : 
              ( m1_subset_1(B,u1_incsp_1(A))
             => ! [C] : 
                  ( m1_subset_1(C,u1_incsp_1(A))
                 => ! [D] : 
                      ( m1_subset_1(D,u1_incsp_1(A))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_incsp_1(A))
                         => ~ r5_projpl_1(A,B,C,D,E) ) ) ) )
          | ! [B] : 
              ( m1_subset_1(B,u2_incsp_1(A))
             => ? [C] : 
                  ( m1_subset_1(C,u1_incsp_1(A))
                  & ? [D] : 
                      ( m1_subset_1(D,u1_incsp_1(A))
                      & ? [E] : 
                          ( m1_subset_1(E,u1_incsp_1(A))
                          & r1_incproj(C,D,E)
                          & r4_incproj(A,C,D,B,E) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d2_projpl_1,d3_projpl_1,d6_projpl_1,d7_incproj,d8_incproj,dt_l1_incsp_1,dt_m1_subset_1,dt_u1_incsp_1,dt_u2_incsp_1,existence_l1_incsp_1,existence_m1_subset_1,rc1_xboole_0,rc2_xboole_0,t13_projpl_1,t20_projpl_1,t21_projpl_1,t5_projpl_1]),
    [file(projpl_1,t22_projpl_1)]).

fof(d2_projpl_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_incsp_1(A))
                 => ( r2_projpl_1(A,B,C,D)
                  <=> ( r1_incsp_1(A,B,C)
                      & r1_incsp_1(A,B,D) ) ) ) ) ) ) ),
    file(projpl_1,d2_projpl_1),
    []).

fof(d3_projpl_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_incsp_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u2_incsp_1(A))
                     => ( r3_projpl_1(A,B,C,D,E)
                      <=> ( r1_incsp_1(A,B,C)
                          & r1_incsp_1(A,B,D)
                          & r1_incsp_1(A,B,E) ) ) ) ) ) ) ) ),
    file(projpl_1,d3_projpl_1),
    []).

fof(d6_projpl_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_incsp_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_incsp_1(A))
                     => ( r5_projpl_1(A,B,C,D,E)
                      <=> ( ~ r4_projpl_1(A,B,C,D)
                          & ~ r4_projpl_1(A,C,D,E)
                          & ~ r4_projpl_1(A,D,E,B)
                          & ~ r4_projpl_1(A,E,B,C) ) ) ) ) ) ) ) ),
    file(projpl_1,d6_projpl_1),
    []).

fof(d7_incproj,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_incsp_1(A))
                 => ( r3_incproj(A,B,C,D)
                  <=> ( r1_incsp_1(A,B,D)
                      & r1_incsp_1(A,C,D) ) ) ) ) ) ) ),
    file(incproj,d7_incproj),
    []).

fof(d8_incproj,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u2_incsp_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_incsp_1(A))
                     => ( r4_incproj(A,B,C,D,E)
                      <=> ( r1_incsp_1(A,B,D)
                          & r1_incsp_1(A,C,D)
                          & r1_incsp_1(A,E,D) ) ) ) ) ) ) ) ),
    file(incproj,d8_incproj),
    []).

fof(dt_l1_incsp_1,axiom,(
    $true ),
    file(incsp_1,l1_incsp_1),
    []).

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

fof(dt_u1_incsp_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ~ v1_xboole_0(u1_incsp_1(A)) ) ),
    file(incsp_1,u1_incsp_1),
    []).

fof(dt_u2_incsp_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ~ v1_xboole_0(u2_incsp_1(A)) ) ),
    file(incsp_1,u2_incsp_1),
    []).

fof(existence_l1_incsp_1,axiom,(
    ? [A] : l1_incsp_1(A) ),
    file(incsp_1,l1_incsp_1),
    []).

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

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

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

fof(t13_projpl_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_incsp_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_incsp_1(A))
                     => ( r5_projpl_1(A,B,C,D,E)
                       => ( r5_projpl_1(A,B,D,C,E)
                          & r5_projpl_1(A,C,B,D,E)
                          & r5_projpl_1(A,C,D,B,E)
                          & r5_projpl_1(A,D,B,C,E)
                          & r5_projpl_1(A,D,C,B,E)
                          & r5_projpl_1(A,B,C,E,D)
                          & r5_projpl_1(A,B,D,E,C)
                          & r5_projpl_1(A,C,B,E,D)
                          & r5_projpl_1(A,C,D,E,B)
                          & r5_projpl_1(A,D,B,E,C)
                          & r5_projpl_1(A,D,C,E,B)
                          & r5_projpl_1(A,B,E,C,D)
                          & r5_projpl_1(A,B,E,D,C)
                          & r5_projpl_1(A,C,E,B,D)
                          & r5_projpl_1(A,C,E,D,B)
                          & r5_projpl_1(A,D,E,B,C)
                          & r5_projpl_1(A,D,E,C,B)
                          & r5_projpl_1(A,E,B,C,D)
                          & r5_projpl_1(A,E,B,D,C)
                          & r5_projpl_1(A,E,C,B,D)
                          & r5_projpl_1(A,E,C,D,B)
                          & r5_projpl_1(A,E,D,B,C)
                          & r5_projpl_1(A,E,D,C,B) ) ) ) ) ) ) ) ),
    file(projpl_1,t13_projpl_1),
    []).

fof(t20_projpl_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_incsp_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_incsp_1(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u2_incsp_1(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u2_incsp_1(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u2_incsp_1(A))
                                 => ( ( r5_projpl_1(A,B,C,D,E)
                                      & r3_incproj(A,B,C,F)
                                      & r3_incproj(A,B,D,G)
                                      & r3_incproj(A,B,E,H) )
                                   => r1_incproj(F,G,H) ) ) ) ) ) ) ) ) ) ),
    file(projpl_1,t20_projpl_1),
    []).

fof(t21_projpl_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_incsp_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_incsp_1(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u2_incsp_1(A))
                         => ! [G] : 
                              ( m1_subset_1(G,u2_incsp_1(A))
                             => ! [H] : 
                                  ( m1_subset_1(H,u2_incsp_1(A))
                                 => ! [I] : 
                                      ( m1_subset_1(I,u2_incsp_1(A))
                                     => ( ( v1_projpl_1(A)
                                          & r3_projpl_1(A,B,F,G,H)
                                          & r1_incproj(F,G,H)
                                          & r2_projpl_1(A,C,I,F)
                                          & r2_projpl_1(A,D,I,G)
                                          & r2_projpl_1(A,E,I,H) )
                                       => ( r1_incsp_1(A,B,I)
                                          | r1_incproj(C,D,E) ) ) ) ) ) ) ) ) ) ) ) ),
    file(projpl_1,t21_projpl_1),
    []).

fof(t5_projpl_1,axiom,(
    ! [A] : 
      ( l1_incsp_1(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_incsp_1(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_incsp_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_incsp_1(A))
                 => ( r4_projpl_1(A,B,C,D)
                  <=> ? [E] : 
                        ( m1_subset_1(E,u2_incsp_1(A))
                        & r1_incsp_1(A,B,E)
                        & r1_incsp_1(A,C,E)
                        & r1_incsp_1(A,D,E) ) ) ) ) ) ) ),
    file(projpl_1,t5_projpl_1),
    []).