% Mizar problem: t16_equation,equation,403,43 
fof(t16_equation,conjecture,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => r6_pboole(A,k14_pboole(A,B,k2_msualg_3(A,B)),B) ) ),
    inference(mizar_bg_added,[status(thm)],[cc3_pboole,dt_k14_pboole,dt_k1_extens_1,dt_k1_mssubfam,dt_k2_extens_1,dt_k2_funct_6,dt_k2_mssubfam,dt_k2_msualg_3,dt_k3_funct_6,dt_m1_pboole,dt_m3_pboole,existence_m1_pboole,existence_m3_pboole,rc1_funcop_1,rc1_funct_1,rc4_pboole,redefinition_k1_extens_1,redefinition_k1_mssubfam,redefinition_k2_extens_1,redefinition_k2_mssubfam,redefinition_r6_pboole,reflexivity_r1_pzfmisc1,reflexivity_r2_pboole,reflexivity_r6_pboole,symmetry_r6_pboole,t13_extens_1,t14_equation,t17_mssubfam,t24_autalg_1]),
    [file(equation,t16_equation)]).

fof(cc3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => v1_funcop_1(D) ) ) ),
    file(pboole,cc3_pboole),
    []).

fof(dt_k14_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & v1_funcop_1(C)
        & m1_pboole(C,A) )
     => m1_pboole(k14_pboole(A,B,C),A) ) ),
    file(pboole,k14_pboole),
    []).

fof(dt_k1_extens_1,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k1_extens_1(A,B),A) ) ),
    file(extens_1,k1_extens_1),
    []).

fof(dt_k1_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k1_mssubfam(A,B),A) ) ),
    file(mssubfam,k1_mssubfam),
    []).

fof(dt_k2_extens_1,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k2_extens_1(A,B),A) ) ),
    file(extens_1,k2_extens_1),
    []).

fof(dt_k2_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k2_funct_6(A))
        & v1_funct_1(k2_funct_6(A)) ) ) ),
    file(funct_6,k2_funct_6),
    []).

fof(dt_k2_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => m1_pboole(k2_mssubfam(A,B),A) ) ),
    file(mssubfam,k2_mssubfam),
    []).

fof(dt_k2_msualg_3,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => m3_pboole(k2_msualg_3(A,B),A,B,B) ) ),
    file(msualg_3,k2_msualg_3),
    []).

fof(dt_k3_funct_6,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_relat_1(k3_funct_6(A))
        & v1_funct_1(k3_funct_6(A)) ) ) ),
    file(funct_6,k3_funct_6),
    []).

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_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ! [D] : 
          ( m3_pboole(D,A,B,C)
         => m1_pboole(D,A) ) ) ),
    file(pboole,m3_pboole),
    []).

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

fof(existence_m3_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ? [D] : m3_pboole(D,A,B,C) ) ),
    file(pboole,m3_pboole),
    []).

fof(rc1_funcop_1,axiom,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & v1_funcop_1(A) ) ),
    file(funcop_1,rc1_funcop_1),
    []).

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

fof(rc4_pboole,axiom,(
    ! [A] : 
    ? [B] : 
      ( m1_pboole(B,A)
      & v1_relat_1(B)
      & v1_funct_1(B)
      & v1_funcop_1(B) ) ),
    file(pboole,rc4_pboole),
    []).

fof(redefinition_k1_extens_1,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => k1_extens_1(A,B) = k2_funct_6(B) ) ),
    file(extens_1,k1_extens_1),
    []).

fof(redefinition_k1_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => k1_mssubfam(A,B) = k2_funct_6(B) ) ),
    file(mssubfam,k1_mssubfam),
    []).

fof(redefinition_k2_extens_1,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => k2_extens_1(A,B) = k3_funct_6(B) ) ),
    file(extens_1,k2_extens_1),
    []).

fof(redefinition_k2_mssubfam,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => k2_mssubfam(A,B) = k3_funct_6(B) ) ),
    file(mssubfam,k2_mssubfam),
    []).

fof(redefinition_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
      <=> B = C ) ) ),
    file(pboole,r6_pboole),
    []).

fof(reflexivity_r1_pzfmisc1,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r1_pzfmisc1(A,B,B) ) ),
    file(pzfmisc1,r1_pzfmisc1),
    []).

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_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => r6_pboole(A,B,B) ) ),
    file(pboole,r6_pboole),
    []).

fof(symmetry_r6_pboole,axiom,(
    ! [A,B,C] : 
      ( ( m1_pboole(B,A)
        & m1_pboole(C,A) )
     => ( r6_pboole(A,B,C)
       => r6_pboole(A,C,B) ) ) ),
    file(pboole,r6_pboole),
    []).

fof(t13_extens_1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( m3_pboole(D,A,B,C)
             => ( v2_msualg_3(D,A,B,C)
              <=> r6_pboole(A,k2_extens_1(A,D),C) ) ) ) ) ),
    file(extens_1,t13_extens_1),
    []).

fof(t14_equation,axiom,(
    ! [A,B] : 
      ( ( v1_funcop_1(B)
        & m1_pboole(B,A) )
     => r6_pboole(A,k14_pboole(A,k1_extens_1(A,B),B),k2_extens_1(A,B)) ) ),
    file(equation,t14_equation),
    []).

fof(t17_mssubfam,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => ! [C] : 
          ( m1_pboole(C,A)
         => ! [D] : 
              ( ( v1_funcop_1(D)
                & m1_pboole(D,A) )
             => ( ( r1_pzfmisc1(A,B,C)
                  & m3_pboole(D,A,B,C) )
               => ( r6_pboole(A,k1_mssubfam(A,D),B)
                  & r2_pboole(A,k2_mssubfam(A,D),C) ) ) ) ) ) ),
    file(mssubfam,t17_mssubfam),
    []).

fof(t24_autalg_1,axiom,(
    ! [A,B] : 
      ( m1_pboole(B,A)
     => v2_msualg_3(k2_msualg_3(A,B),A,B,B) ) ),
    file(autalg_1,t24_autalg_1),
    []).