% Mizar problem: t222_xcmplx_1,xcmplx_1,1535,22 
fof(t222_xcmplx_1,conjecture,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => k3_xcmplx_0(k5_xcmplx_0(A),k7_xcmplx_0(B,C)) = k7_xcmplx_0(B,k3_xcmplx_0(A,C)) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k3_xcmplx_0,d9_xcmplx_0,dt_k3_xcmplx_0,dt_k5_xcmplx_0,dt_k7_xcmplx_0,fc3_xcmplx_0,fc5_xcmplx_0,involutiveness_k5_xcmplx_0,l25_xcmplx_1,rc1_xcmplx_0]),
    [file(xcmplx_1,t222_xcmplx_1)]).

fof(commutativity_k3_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k3_xcmplx_0(A,B) = k3_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(d9_xcmplx_0,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k7_xcmplx_0(A,B) = k3_xcmplx_0(A,k5_xcmplx_0(B)) ) ) ),
    file(xcmplx_0,d9_xcmplx_0),
    []).

fof(dt_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_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(dt_k7_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k7_xcmplx_0),
    []).

fof(fc3_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k3_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc3_xcmplx_0),
    []).

fof(fc5_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k7_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc5_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(l25_xcmplx_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k3_xcmplx_0(k5_xcmplx_0(A),k5_xcmplx_0(B)) = k5_xcmplx_0(k3_xcmplx_0(A,B)) ) ) ),
    file(xcmplx_1,l25_xcmplx_1),
    []).

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