% Mizar problem: t109_pboole,pboole,1376,41 
fof(t109_pboole,conjecture,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r4_pboole(A,B,C)
                  & r2_pboole(A,B,D) )
               => r4_pboole(A,D,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_m1_pboole,existence_m1_pboole,rc1_funct_1,reflexivity_r2_pboole,symmetry_r4_pboole,t10_pboole,t11_pboole,t9_pboole]),
    [file(pboole,t109_pboole)]).

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

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

fof(rc1_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc1_funct_1),
    []).

fof(reflexivity_r2_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r2_pboole(A,B,B) ) ),
    file(pboole,r2_pboole),
    []).

fof(symmetry_r4_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r4_pboole(A,B,C)
       => r4_pboole(A,C,B) ) ) ),
    file(pboole,r4_pboole),
    []).

fof(t10_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  & r1_pboole(A,B,D) )
               => r4_pboole(A,C,D) ) ) ) ) ),
    file(pboole,t10_pboole),
    []).

fof(t11_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ~ ( r4_pboole(A,B,C)
              & ! [D] : 
                  ( m1_pboole(D,A)
                 => ~ ( r1_pboole(A,D,B)
                      & r1_pboole(A,D,C) ) ) ) ) ) ),
    file(pboole,t11_pboole),
    []).

fof(t9_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m1_pboole(D,A)
             => ( ( r1_pboole(A,B,C)
                  & r2_pboole(A,C,D) )
               => r1_pboole(A,B,D) ) ) ) ) ),
    file(pboole,t9_pboole),
    []).