% Mizar problem: t33_mssubfam,mssubfam,1093,37 
fof(t33_mssubfam,conjecture,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m4_pboole(D,A,k1_mboolean(A,C))
             => ( r1_pboole(A,B,D)
               => m4_pboole(B,A,C) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[d23_pboole,dt_k1_mboolean,dt_k3_mssubfam,dt_m1_pboole,dt_m4_pboole,existence_m1_pboole,existence_m4_pboole,fc1_mboolean,rc1_funct_1,rc2_mssubfam,rc3_pboole,rc5_funct_1,rc5_pboole,redefinition_k3_mssubfam,reflexivity_r2_pboole,t19_mboolean,t9_pboole]),
    [file(mssubfam,t33_mssubfam)]).

fof(d23_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( m4_pboole(C,A,B)
          <=> r2_pboole(A,C,B) ) ) ) ),
    file(pboole,d23_pboole),
    []).

fof(dt_k1_mboolean,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m1_pboole(k1_mboolean(A,B),A) ) ),
    file(mboolean,k1_mboolean),
    []).

fof(dt_k3_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m4_pboole(k3_mssubfam(A,B),A,k1_mboolean(A,B)) ) ),
    file(mssubfam,k3_mssubfam),
    []).

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

fof(dt_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m4_pboole(C,A,B)
         => m1_pboole(C,A) ) ) ),
    file(pboole,m4_pboole),
    []).

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

fof(existence_m4_pboole,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : m4_pboole(C,A,B) ) ),
    file(pboole,m4_pboole),
    []).

fof(fc1_mboolean,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ( v1_relat_1(k1_mboolean(A,B))
        & v2_relat_1(k1_mboolean(A,B))
        & v1_funct_1(k1_mboolean(A,B)) ) ) ),
    file(mboolean,fc1_mboolean),
    []).

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

fof(rc2_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ? [C] : 
          ( m4_pboole(C,A,k1_mboolean(A,B))
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(mssubfam,rc2_mssubfam),
    []).

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(rc5_pboole,axiom,(
    ! [A,B] : 
      ( ( v2_relat_1(B)
        & m1_pboole(B,A) )
     => ? [C] : 
          ( m4_pboole(C,A,B)
          & v1_relat_1(C)
          & v2_relat_1(C)
          & v1_funct_1(C) ) ) ),
    file(pboole,rc5_pboole),
    []).

fof(redefinition_k3_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => k3_mssubfam(A,B) = k1_mboolean(A,B) ) ),
    file(mssubfam,k3_mssubfam),
    []).

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(t19_mboolean,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ( r2_pboole(A,B,C)
          <=> r1_pboole(A,B,k1_mboolean(A,C)) ) ) ) ),
    file(mboolean,t19_mboolean),
    []).

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),
    []).