% Mizar problem: t145_pboole,pboole,1799,50 
fof(t145_pboole,conjecture,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & r7_pboole(A,B,C) )
           => v2_relat_1(C) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[dt_m1_pboole,existence_m1_pboole,rc1_funct_1,rc3_pboole,rc5_funct_1,reflexivity_r2_pboole,reflexivity_r7_pboole,t143_pboole,t144_pboole]),
    [file(pboole,t145_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(rc3_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v2_relat_1(B)
      & v1_funct_1(B) ) ),
    file(pboole,rc3_pboole),
    []).

fof(rc5_funct_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v2_relat_1(A)
      & v1_funct_1(A) ) ),
    file(funct_1,rc5_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(reflexivity_r7_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r7_pboole(A,B,B) ) ),
    file(pboole,r7_pboole),
    []).

fof(t143_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & r2_pboole(A,B,C) )
           => v2_relat_1(C) ) ) ) ),
    file(pboole,t143_pboole),
    []).

fof(t144_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( ( v2_relat_1(B)
              & r7_pboole(A,B,C) )
           => r2_pboole(A,B,C) ) ) ) ),
    file(pboole,t144_pboole),
    []).