% Mizar problem: t5_polyeq_4,polyeq_4,266,53 
fof(t5_polyeq_4,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ~ ( A != 0
                  & k4_polyeq_1(A,B,0,C) = 0
                  & C != 0
                  & C != k1_real_1(k6_real_1(B,A)) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[cc1_real_1,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,d2_polyeq_1,d3_square_1,dt_k1_numbers,dt_k1_real_1,dt_k2_xcmplx_0,dt_k3_polyeq_1,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_polyeq_1,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_square_1,dt_k6_real_1,dt_k7_square_1,dt_k7_xcmplx_0,dt_m1_subset_1,existence_m1_subset_1,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,redefinition_k1_real_1,redefinition_k3_real_1,redefinition_k4_polyeq_1,redefinition_k4_real_1,redefinition_k6_real_1,redefinition_k7_square_1,t188_xcmplx_1,t1_arithm,t2_arithm,t5_arithm,t6_xcmplx_1,t90_xcmplx_1]),
    [file(polyeq_4,t5_polyeq_4)]).

fof(cc1_real_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ( v1_xreal_0(A)
        & v1_xcmplx_0(A) ) ) ),
    file(real_1,cc1_real_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_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k3_real_1(B,A) ) ),
    file(real_1,k3_real_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(commutativity_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k4_real_1(B,A) ) ),
    file(real_1,k4_real_1),
    []).

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),
    []).

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_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_real_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(k1_real_1(A),k1_numbers) ) ),
    file(real_1,k1_real_1),
    []).

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

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

fof(dt_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k3_real_1(A,B),k1_numbers) ) ),
    file(real_1,k3_real_1),
    []).

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

fof(dt_k4_polyeq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers)
        & m1_subset_1(D,k1_numbers) )
     => m1_subset_1(k4_polyeq_1(A,B,C,D),k1_numbers) ) ),
    file(polyeq_1,k4_polyeq_1),
    []).

fof(dt_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k4_real_1(A,B),k1_numbers) ) ),
    file(real_1,k4_real_1),
    []).

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_square_1,axiom,(
    $true ),
    file(square_1,k5_square_1),
    []).

fof(dt_k6_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k6_real_1(A,B),k1_numbers) ) ),
    file(real_1,k6_real_1),
    []).

fof(dt_k7_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(k7_square_1(A),k1_numbers) ) ),
    file(square_1,k7_square_1),
    []).

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

fof(dt_m1_subset_1,axiom,(
    $true ),
    file(subset_1,m1_subset_1),
    []).

fof(existence_m1_subset_1,axiom,(
    ! [A] : 
    ? [B] : m1_subset_1(B,A) ),
    file(subset_1,m1_subset_1),
    []).

fof(involutiveness_k1_real_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k1_real_1(k1_real_1(A)) = A ) ),
    file(real_1,k1_real_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(redefinition_k1_real_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k1_real_1(A) = k4_xcmplx_0(A) ) ),
    file(real_1,k1_real_1),
    []).

fof(redefinition_k3_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k3_real_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(real_1,k3_real_1),
    []).

fof(redefinition_k4_polyeq_1,axiom,(
    ! [A,B,C,D] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers)
        & m1_subset_1(D,k1_numbers) )
     => k4_polyeq_1(A,B,C,D) = k3_polyeq_1(A,B,C,D) ) ),
    file(polyeq_1,k4_polyeq_1),
    []).

fof(redefinition_k4_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k4_real_1(A,B) = k3_xcmplx_0(A,B) ) ),
    file(real_1,k4_real_1),
    []).

fof(redefinition_k6_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k6_real_1(A,B) = k7_xcmplx_0(A,B) ) ),
    file(real_1,k6_real_1),
    []).

fof(redefinition_k7_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k7_square_1(A) = k5_square_1(A) ) ),
    file(square_1,k7_square_1),
    []).

fof(t188_xcmplx_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => k4_xcmplx_0(k7_xcmplx_0(A,B)) = k7_xcmplx_0(k4_xcmplx_0(A),B) ) ) ),
    file(xcmplx_1,t188_xcmplx_1),
    []).

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(t5_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(0,A) = 0 ) ),
    file(arithm,t5_arithm),
    []).

fof(t6_xcmplx_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ~ ( k3_xcmplx_0(A,B) = 0
              & A != 0
              & B != 0 ) ) ) ),
    file(xcmplx_1,t6_xcmplx_1),
    []).

fof(t90_xcmplx_1,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => ! [B] : 
          ( v1_xcmplx_0(B)
         => ( A != 0
           => B = k7_xcmplx_0(k3_xcmplx_0(B,A),A) ) ) ) ),
    file(xcmplx_1,t90_xcmplx_1),
    []).