% Mizar problem: t9_polyeq_1,polyeq_1,298,7 
fof(t9_polyeq_1,conjecture,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_polyeq_1(0,0,0,A) = 0 ) ),
    inference(mizar_bg_added,[status(thm)],[commutativity_k2_xcmplx_0,commutativity_k3_xcmplx_0,dt_k2_xcmplx_0,dt_k3_xcmplx_0,dt_k5_square_1,fc1_square_1,fc2_xcmplx_0,fc3_xcmplx_0,t1_arithm,t2_arithm,d3_square_1,dt_k3_polyeq_1,fc4_polyeq_1,rc1_xcmplx_0,d2_polyeq_1]),
    [file(polyeq_1,t9_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(dt_k5_square_1,axiom,(
    $true ),
    file(square_1,k5_square_1),
    []).

fof(fc1_square_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => v1_xcmplx_0(k5_square_1(A)) ) ),
    file(square_1,fc1_square_1),
    []).

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(d3_square_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k5_square_1(A) = k3_xcmplx_0(A,A) ) ),
    file(square_1,d3_square_1),
    []).

fof(dt_k3_polyeq_1,axiom,(
    $true ),
    file(polyeq_1,k3_polyeq_1),
    []).

fof(fc4_polyeq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( v1_xcmplx_0(A)
        & v1_xcmplx_0(B)
        & v1_xcmplx_0(C)
        & v1_xcmplx_0(D) )
     => v1_xcmplx_0(k3_polyeq_1(A,B,C,D)) ) ),
    file(polyeq_1,fc4_polyeq_1),
    []).

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

fof(d2_polyeq_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ! [C] : 
              ( v1_xcmplx_0(C)
             => ! [D] : 
                  ( v1_xcmplx_0(D)
                 => k3_polyeq_1(A,B,C,D) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k5_square_1(D)),k3_xcmplx_0(B,D)),C) ) ) ) ) ),
    file(polyeq_1,d2_polyeq_1),
    []).