% Mizar problem: t2_polyeq_1,polyeq_1,62,41 
fof(t2_polyeq_1,conjecture,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k1_polyeq_1(0,0,A) = 0 ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,dt_k2_xcmplx_0,dt_k3_xcmplx_0,fc2_xcmplx_0,fc3_xcmplx_0,t1_arithm,t2_arithm,dt_k1_polyeq_1,fc1_polyeq_1,rc1_xcmplx_0,d1_polyeq_1]),
    [file(polyeq_1,t2_polyeq_1)]).

fof(commutativity_k2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => k2_xcmplx_0(A,B) = k2_xcmplx_0(B,A) ) ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

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(dt_k2_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k2_xcmplx_0),
    []).

fof(dt_k3_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k3_xcmplx_0),
    []).

fof(fc2_xcmplx_0,axiom,(
    ! [A,B] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B) )
     => v1_xcmplx_0(k2_xcmplx_0(A,B)) ) ),
    file(xcmplx_0,fc2_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(t1_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    []).

fof(t2_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(A,0) = 0 ) ),
    file(arithm,t2_arithm),
    []).

fof(dt_k1_polyeq_1,axiom,(
    $true ),
    file(polyeq_1,k1_polyeq_1),
    []).

fof(fc1_polyeq_1,axiom,(
    ! [A,B,C] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C) )
     => v1_xcmplx_0(k1_polyeq_1(A,B,C)) ) ),
    file(polyeq_1,fc1_polyeq_1),
    []).

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

fof(d1_polyeq_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => k1_polyeq_1(A,B,C) = k2_xcmplx_0(k3_xcmplx_0(A,C),B) ) ) ) ),
    file(polyeq_1,d1_polyeq_1),
    []).