% Mizar problem: t15_bvfunc14,bvfunc14,943,35 
fof(t15_bvfunc14,conjecture,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D,E] : 
          ( B != C
         => k1_funct_1(k1_funct_4(k1_funct_4(A,k3_cqc_lang(B,D)),k3_cqc_lang(C,E)),B) = D ) ) ),
    inference(mizar_bg_added,[status(thm)],[idempotence_k1_funct_4,dt_k1_funct_1,dt_k1_funct_4,dt_k3_cqc_lang,fc1_cqc_lang,l4_bvfunc14]),
    [file(bvfunc14,t15_bvfunc14)]).

fof(idempotence_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => k1_funct_4(A,A) = A ) ),
    file(funct_4,k1_funct_4),
    []).

fof(dt_k1_funct_1,axiom,(
    $true ),
    file(funct_1,k1_funct_1),
    []).

fof(dt_k1_funct_4,axiom,(
    ! [A,B] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_relat_1(B)
        & v1_funct_1(B) )
     => ( v1_relat_1(k1_funct_4(A,B))
        & v1_funct_1(k1_funct_4(A,B)) ) ) ),
    file(funct_4,k1_funct_4),
    []).

fof(dt_k3_cqc_lang,axiom,(
    $true ),
    file(cqc_lang,k3_cqc_lang),
    []).

fof(fc1_cqc_lang,axiom,(
    ! [A,B] : 
      ( v1_relat_1(k3_cqc_lang(A,B))
      & v1_funct_1(k3_cqc_lang(A,B)) ) ),
    file(cqc_lang,fc1_cqc_lang),
    []).

fof(l4_bvfunc14,axiom,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C,D,E] : 
          ( B != C
         => k1_funct_1(k1_funct_4(k1_funct_4(A,k3_cqc_lang(B,D)),k3_cqc_lang(C,E)),B) = D ) ) ),
    file(bvfunc14,l4_bvfunc14),
    []).