% Mizar problem: t224_xcmplx_1,xcmplx_1,1552,17 
fof(t224_xcmplx_1,conjecture,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_xcmplx_0(k4_xcmplx_0(A)) = k4_xcmplx_0(k5_xcmplx_0(A)) ) ),
    inference(mizar_bg_added,[status(thm)],[involutiveness_k4_xcmplx_0,involutiveness_k5_xcmplx_0,dt_k4_xcmplx_0,dt_k5_xcmplx_0,rc1_xcmplx_0,l233_xcmplx_1]),
    [file(xcmplx_1,t224_xcmplx_1)]).

fof(involutiveness_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k4_xcmplx_0(k4_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

fof(involutiveness_k5_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_xcmplx_0(k5_xcmplx_0(A)) = A ) ),
    file(xcmplx_0,k5_xcmplx_0),
    []).

fof(dt_k4_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k4_xcmplx_0(A)) ) ),
    file(xcmplx_0,k4_xcmplx_0),
    []).

fof(dt_k5_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k5_xcmplx_0(A)) ) ),
    file(xcmplx_0,k5_xcmplx_0),
    []).

fof(rc1_xcmplx_0,axiom,(
    ? [A] : v1_xcmplx_0(A) ),
    file(xcmplx_0,rc1_xcmplx_0),
    []).

fof(l233_xcmplx_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_xcmplx_0(k4_xcmplx_0(A)) = k4_xcmplx_0(k5_xcmplx_0(A)) ) ),
    file(xcmplx_1,l233_xcmplx_1),
    []).