% Mizar problem: t13_polyeq_4,polyeq_4,476,33 
fof(t13_polyeq_4,conjecture,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_subset_1(D,k1_numbers)
                 => ( k1_polyeq_4(A,B,C,C,B,A,D) = 0
                   => ( A = 0
                      | r1_xreal_0(k5_real_1(k3_real_1(k3_real_1(k7_square_1(B),k4_real_1(k4_real_1(2,A),B)),k4_real_1(5,k7_square_1(A))),k4_real_1(k4_real_1(4,A),C)),0)
                      | ! [E] : 
                          ( m1_subset_1(E,k1_numbers)
                         => ! [F] : 
                              ( m1_subset_1(F,k1_numbers)
                             => ~ ( E = k6_real_1(k3_real_1(k5_real_1(A,B),k9_square_1(k5_real_1(k3_real_1(k3_real_1(k7_square_1(B),k4_real_1(k4_real_1(2,A),B)),k4_real_1(5,k7_square_1(A))),k4_real_1(k4_real_1(4,A),C)))),k4_real_1(2,A))
                                  & F = k6_real_1(k5_real_1(k5_real_1(A,B),k9_square_1(k5_real_1(k3_real_1(k3_real_1(k7_square_1(B),k4_real_1(k4_real_1(2,A),B)),k4_real_1(5,k7_square_1(A))),k4_real_1(k4_real_1(4,A),C)))),k4_real_1(2,A))
                                  & D != k1_real_1(1)
                                  & D != k6_real_1(k3_real_1(E,k9_square_1(k2_quin_1(1,k1_real_1(E),1))),2)
                                  & D != k6_real_1(k3_real_1(F,k9_square_1(k2_quin_1(1,k1_real_1(F),1))),2)
                                  & D != k6_real_1(k5_real_1(E,k9_square_1(k2_quin_1(1,k1_real_1(E),1))),2)
                                  & D != k6_real_1(k5_real_1(F,k9_square_1(k2_quin_1(1,k1_real_1(F),1))),2) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_bg_added,[status(thm)],[antisymmetry_r2_hidden,cc1_nat_1,cc1_real_1,cc2_nat_1,cc3_nat_1,commutativity_k1_nat_1,commutativity_k2_xcmplx_0,commutativity_k3_real_1,commutativity_k3_xcmplx_0,commutativity_k4_real_1,connectedness_r1_xreal_0,d1_polyeq_2,d1_polyeq_4,d3_square_1,dt_k1_nat_1,dt_k1_numbers,dt_k1_polyeq_2,dt_k1_polyeq_4,dt_k1_quin_1,dt_k1_real_1,dt_k1_zfmisc_1,dt_k2_newton,dt_k2_quin_1,dt_k2_xcmplx_0,dt_k3_newton,dt_k3_real_1,dt_k3_xcmplx_0,dt_k4_real_1,dt_k4_xcmplx_0,dt_k5_numbers,dt_k5_ordinal2,dt_k5_real_1,dt_k5_square_1,dt_k6_real_1,dt_k6_xcmplx_0,dt_k7_square_1,dt_k7_xcmplx_0,dt_k8_square_1,dt_k9_square_1,dt_m1_subset_1,dt_m2_subset_1,existence_m1_subset_1,existence_m2_subset_1,fc1_nat_1,fc2_nat_1,fc3_nat_1,fc4_nat_1,involutiveness_k1_real_1,involutiveness_k4_xcmplx_0,rc1_nat_1,rc2_nat_1,rc3_nat_1,redefinition_k1_nat_1,redefinition_k1_real_1,redefinition_k2_quin_1,redefinition_k3_newton,redefinition_k3_real_1,redefinition_k4_real_1,redefinition_k5_numbers,redefinition_k5_real_1,redefinition_k6_real_1,redefinition_k7_square_1,redefinition_k9_square_1,redefinition_m2_subset_1,reflexivity_r1_tarski,reflexivity_r1_xreal_0,spc1_numerals,spc2_numerals,spc3_numerals,spc4_numerals,spc5_numerals,spc8_numerals,t10_newton,t11_newton,t11_polyeq_4,t15_newton,t1_arithm,t1_numerals,t1_real,t1_subset,t2_arithm,t2_real,t2_subset,t3_arithm,t3_polyeq_2,t3_real,t3_subset,t4_arithm,t4_real,t4_subset,t5_arithm,t5_real,t5_subset,t6_arithm,t6_real,t6_xcmplx_1,t7_real,t8_real]),
    [file(polyeq_4,t13_polyeq_4)]).

fof(antisymmetry_r2_hidden,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => ~ r2_hidden(B,A) ) ),
    file(hidden,r2_hidden),
    []).

fof(cc1_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A) ) ) ),
    file(nat_1,cc1_nat_1),
    []).

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(cc2_nat_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k5_numbers)
     => ( v1_ordinal1(A)
        & v2_ordinal1(A)
        & v3_ordinal1(A)
        & v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc2_nat_1),
    []).

fof(cc3_nat_1,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ( v4_ordinal2(A)
        & v1_xcmplx_0(A)
        & v1_xreal_0(A)
        & ~ v3_xreal_0(A) ) ) ),
    file(nat_1,cc3_nat_1),
    []).

fof(commutativity_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k1_nat_1(B,A) ) ),
    file(nat_1,k1_nat_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(connectedness_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => ( r1_xreal_0(A,B)
        | r1_xreal_0(B,A) ) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(d1_polyeq_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ! [E] : 
                      ( v1_xreal_0(E)
                     => ! [F] : 
                          ( v1_xreal_0(F)
                         => k1_polyeq_2(A,B,C,D,E,F) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k2_newton(F,4)),k3_xcmplx_0(B,k2_newton(F,3))),k3_xcmplx_0(C,k5_square_1(F))),k3_xcmplx_0(D,F)),E) ) ) ) ) ) ) ),
    file(polyeq_2,d1_polyeq_2),
    []).

fof(d1_polyeq_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ! [C] : 
              ( m1_subset_1(C,k1_numbers)
             => ! [D] : 
                  ( m1_subset_1(D,k1_numbers)
                 => ! [E] : 
                      ( m1_subset_1(E,k1_numbers)
                     => ! [F] : 
                          ( m1_subset_1(F,k1_numbers)
                         => ! [G] : 
                              ( m1_subset_1(G,k1_numbers)
                             => k1_polyeq_4(A,B,C,D,E,F,G) = k3_real_1(k3_real_1(k3_real_1(k3_real_1(k3_real_1(k4_real_1(A,k3_newton(G,5)),k4_real_1(B,k3_newton(G,4))),k4_real_1(C,k3_newton(G,3))),k4_real_1(D,k7_square_1(G))),k4_real_1(E,G)),F) ) ) ) ) ) ) ) ),
    file(polyeq_4,d1_polyeq_4),
    []).

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_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => m2_subset_1(k1_nat_1(A,B),k1_numbers,k5_numbers) ) ),
    file(nat_1,k1_nat_1),
    []).

fof(dt_k1_numbers,axiom,(
    $true ),
    file(numbers,k1_numbers),
    []).

fof(dt_k1_polyeq_2,axiom,(
    $true ),
    file(polyeq_2,k1_polyeq_2),
    []).

fof(dt_k1_polyeq_4,axiom,(
    $true ),
    file(polyeq_4,k1_polyeq_4),
    []).

fof(dt_k1_quin_1,axiom,(
    $true ),
    file(quin_1,k1_quin_1),
    []).

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_k1_zfmisc_1,axiom,(
    $true ),
    file(zfmisc_1,k1_zfmisc_1),
    []).

fof(dt_k2_newton,axiom,(
    $true ),
    file(newton,k2_newton),
    []).

fof(dt_k2_quin_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => m1_subset_1(k2_quin_1(A,B,C),k1_numbers) ) ),
    file(quin_1,k2_quin_1),
    []).

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

fof(dt_k3_newton,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & v4_ordinal2(B) )
     => m1_subset_1(k3_newton(A,B),k1_numbers) ) ),
    file(newton,k3_newton),
    []).

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_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_numbers,axiom,(
    m1_subset_1(k5_numbers,k1_zfmisc_1(k1_numbers)) ),
    file(numbers,k5_numbers),
    []).

fof(dt_k5_ordinal2,axiom,(
    $true ),
    file(ordinal2,k5_ordinal2),
    []).

fof(dt_k5_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => m1_subset_1(k5_real_1(A,B),k1_numbers) ) ),
    file(real_1,k5_real_1),
    []).

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_k6_xcmplx_0,axiom,(
    $true ),
    file(xcmplx_0,k6_xcmplx_0),
    []).

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_k8_square_1,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => v1_xreal_0(k8_square_1(A)) ) ),
    file(square_1,k8_square_1),
    []).

fof(dt_k9_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => m1_subset_1(k9_square_1(A),k1_numbers) ) ),
    file(square_1,k9_square_1),
    []).

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

fof(dt_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
         => m1_subset_1(C,A) ) ) ),
    file(subset_1,m2_subset_1),
    []).

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

fof(existence_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ? [C] : m2_subset_1(C,A,B) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(fc1_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc1_nat_1),
    []).

fof(fc2_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & v4_ordinal2(B) )
     => ( v4_ordinal2(k3_xcmplx_0(A,B))
        & v1_xcmplx_0(k3_xcmplx_0(A,B))
        & v1_xreal_0(k3_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc2_nat_1),
    []).

fof(fc3_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(A,B))
        & v4_ordinal2(k2_xcmplx_0(A,B))
        & v1_xcmplx_0(k2_xcmplx_0(A,B))
        & v1_xreal_0(k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,fc3_nat_1),
    []).

fof(fc4_nat_1,axiom,(
    ! [A,B] : 
      ( ( v4_ordinal2(A)
        & ~ v1_xboole_0(B)
        & v4_ordinal2(B) )
     => ( ~ v1_xboole_0(k2_xcmplx_0(B,A))
        & v4_ordinal2(k2_xcmplx_0(B,A))
        & v1_xcmplx_0(k2_xcmplx_0(B,A))
        & v1_xreal_0(k2_xcmplx_0(B,A)) ) ) ),
    file(nat_1,fc4_nat_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(rc1_nat_1,axiom,(
    ? [A] : 
      ( ~ v1_xboole_0(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc1_nat_1),
    []).

fof(rc2_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k1_zfmisc_1(k1_numbers))
      & ~ v1_xboole_0(A)
      & v3_ordinal1(A) ) ),
    file(nat_1,rc2_nat_1),
    []).

fof(rc3_nat_1,axiom,(
    ? [A] : 
      ( m1_subset_1(A,k5_numbers)
      & ~ v1_xboole_0(A)
      & v1_ordinal1(A)
      & v2_ordinal1(A)
      & v3_ordinal1(A)
      & v4_ordinal2(A)
      & v1_xcmplx_0(A)
      & v1_xreal_0(A) ) ),
    file(nat_1,rc3_nat_1),
    []).

fof(redefinition_k1_nat_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k5_numbers)
        & m1_subset_1(B,k5_numbers) )
     => k1_nat_1(A,B) = k2_xcmplx_0(A,B) ) ),
    file(nat_1,k1_nat_1),
    []).

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_k2_quin_1,axiom,(
    ! [A,B,C] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => k2_quin_1(A,B,C) = k1_quin_1(A,B,C) ) ),
    file(quin_1,k2_quin_1),
    []).

fof(redefinition_k3_newton,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & v4_ordinal2(B) )
     => k3_newton(A,B) = k2_newton(A,B) ) ),
    file(newton,k3_newton),
    []).

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_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_k5_numbers,axiom,(
    k5_numbers = k5_ordinal2 ),
    file(numbers,k5_numbers),
    []).

fof(redefinition_k5_real_1,axiom,(
    ! [A,B] : 
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers) )
     => k5_real_1(A,B) = k6_xcmplx_0(A,B) ) ),
    file(real_1,k5_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(redefinition_k9_square_1,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => k9_square_1(A) = k8_square_1(A) ) ),
    file(square_1,k9_square_1),
    []).

fof(redefinition_m2_subset_1,axiom,(
    ! [A,B] : 
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & m1_subset_1(B,k1_zfmisc_1(A)) )
     => ! [C] : 
          ( m2_subset_1(C,A,B)
        <=> m1_subset_1(C,B) ) ) ),
    file(subset_1,m2_subset_1),
    []).

fof(reflexivity_r1_tarski,axiom,(
    ! [A,B] : r1_tarski(A,A) ),
    file(tarski,r1_tarski),
    []).

fof(reflexivity_r1_xreal_0,axiom,(
    ! [A,B] : 
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B) )
     => r1_xreal_0(A,A) ) ),
    file(xreal_0,r1_xreal_0),
    []).

fof(spc1_numerals,axiom,
    ( v2_xreal_0(1)
    & m1_subset_1(1,k5_numbers) ),
    file(numerals,spc1_numerals),
    []).

fof(spc2_numerals,axiom,
    ( v2_xreal_0(2)
    & m1_subset_1(2,k5_numbers) ),
    file(numerals,spc2_numerals),
    []).

fof(spc3_numerals,axiom,
    ( v2_xreal_0(3)
    & m1_subset_1(3,k5_numbers) ),
    file(numerals,spc3_numerals),
    []).

fof(spc4_numerals,axiom,
    ( v2_xreal_0(4)
    & m1_subset_1(4,k5_numbers) ),
    file(numerals,spc4_numerals),
    []).

fof(spc5_numerals,axiom,
    ( v2_xreal_0(5)
    & m1_subset_1(5,k5_numbers) ),
    file(numerals,spc5_numerals),
    []).

fof(spc8_numerals,axiom,
    ( v2_xreal_0(8)
    & m1_subset_1(8,k5_numbers) ),
    file(numerals,spc8_numerals),
    []).

fof(t10_newton,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => k2_newton(A,1) = A ) ),
    file(newton,t10_newton),
    []).

fof(t11_newton,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => k2_newton(B,k2_xcmplx_0(A,1)) = k3_xcmplx_0(k2_newton(B,A),B) ) ) ),
    file(newton,t11_newton),
    []).

fof(t11_polyeq_4,axiom,(
    ! [A] : 
      ( m1_subset_1(A,k1_numbers)
     => ! [B] : 
          ( m1_subset_1(B,k1_numbers)
         => ( k3_real_1(k3_newton(A,3),k3_newton(B,3)) = k4_real_1(k3_real_1(A,B),k3_real_1(k5_real_1(k7_square_1(A),k4_real_1(A,B)),k7_square_1(B)))
            & k3_real_1(k3_newton(A,5),k3_newton(B,5)) = k4_real_1(k3_real_1(A,B),k3_real_1(k5_real_1(k3_real_1(k5_real_1(k3_newton(A,4),k4_real_1(k3_newton(A,3),B)),k4_real_1(k3_newton(A,2),k3_newton(B,2))),k4_real_1(A,k3_newton(B,3))),k3_newton(B,4))) ) ) ) ),
    file(polyeq_4,t11_polyeq_4),
    []).

fof(t15_newton,axiom,(
    ! [A] : 
      ( v4_ordinal2(A)
     => k3_newton(1,A) = 1 ) ),
    file(newton,t15_newton),
    []).

fof(t1_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k2_xcmplx_0(A,0) = A ) ),
    file(arithm,t1_arithm),
    []).

fof(t1_numerals,axiom,(
    m1_subset_1(0,k5_numbers) ),
    file(numerals,t1_numerals),
    []).

fof(t1_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v2_xreal_0(A) )
           => v2_xreal_0(B) ) ) ) ),
    file(real,t1_real),
    []).

fof(t1_subset,axiom,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => m1_subset_1(A,B) ) ),
    file(subset,t1_subset),
    []).

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

fof(t2_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & v3_xreal_0(B) )
           => v3_xreal_0(A) ) ) ) ),
    file(real,t2_real),
    []).

fof(t2_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,B)
     => ( v1_xboole_0(B)
        | r2_hidden(A,B) ) ) ),
    file(subset,t2_subset),
    []).

fof(t3_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k3_xcmplx_0(1,A) = A ) ),
    file(arithm,t3_arithm),
    []).

fof(t3_polyeq_2,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ! [E] : 
                      ( v1_xreal_0(E)
                     => ( ( E = k2_xcmplx_0(D,k7_xcmplx_0(1,D))
                          & k1_polyeq_2(A,B,C,B,A,D) = 0 )
                       => ( A = 0
                          | r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(k5_square_1(B),k3_xcmplx_0(k3_xcmplx_0(4,A),C)),k3_xcmplx_0(8,k5_square_1(A))),0)
                          | ! [F] : 
                              ( v1_xreal_0(F)
                             => ! [G] : 
                                  ( v1_xreal_0(G)
                                 => ( ( F = k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k2_xcmplx_0(k6_xcmplx_0(k5_square_1(B),k3_xcmplx_0(k3_xcmplx_0(4,A),C)),k3_xcmplx_0(8,k5_square_1(A))))),k3_xcmplx_0(2,A))
                                      & G = k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k2_xcmplx_0(k6_xcmplx_0(k5_square_1(B),k3_xcmplx_0(k3_xcmplx_0(4,A),C)),k3_xcmplx_0(8,k5_square_1(A))))),k3_xcmplx_0(2,A)) )
                                   => ( D != 0
                                      & ~ ( D != k7_xcmplx_0(k2_xcmplx_0(F,k8_square_1(k1_quin_1(1,k4_xcmplx_0(F),1))),2)
                                          & D != k7_xcmplx_0(k2_xcmplx_0(G,k8_square_1(k1_quin_1(1,k4_xcmplx_0(G),1))),2)
                                          & D != k7_xcmplx_0(k6_xcmplx_0(F,k8_square_1(k1_quin_1(1,k4_xcmplx_0(F),1))),2)
                                          & D != k7_xcmplx_0(k6_xcmplx_0(G,k8_square_1(k1_quin_1(1,k4_xcmplx_0(G),1))),2) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(polyeq_2,t3_polyeq_2),
    []).

fof(t3_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v3_xreal_0(A)
              & v3_xreal_0(B) ) ) ) ),
    file(real,t3_real),
    []).

fof(t3_subset,axiom,(
    ! [A,B] : 
      ( m1_subset_1(A,k1_zfmisc_1(B))
    <=> r1_tarski(A,B) ) ),
    file(subset,t3_subset),
    []).

fof(t4_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k6_xcmplx_0(A,0) = A ) ),
    file(arithm,t4_arithm),
    []).

fof(t4_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( r1_xreal_0(A,B)
              & ~ v2_xreal_0(B)
              & v2_xreal_0(A) ) ) ) ),
    file(real,t4_real),
    []).

fof(t4_subset,axiom,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & m1_subset_1(B,k1_zfmisc_1(C)) )
     => m1_subset_1(A,C) ) ),
    file(subset,t4_subset),
    []).

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

fof(t5_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(B)
              | v3_xreal_0(A)
              | v2_xreal_0(B) ) ) ) ) ),
    file(real,t5_real),
    []).

fof(t5_subset,axiom,(
    ! [A,B,C] : ~ ( r2_hidden(A,B)
      & m1_subset_1(B,k1_zfmisc_1(C))
      & v1_xboole_0(C) ) ),
    file(subset,t5_subset),
    []).

fof(t6_arithm,axiom,(
    ! [A] : 
      ( v1_xcmplx_0(A)
     => k7_xcmplx_0(A,1) = A ) ),
    file(arithm,t6_arithm),
    []).

fof(t6_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
           => ( v1_xboole_0(A)
              | v2_xreal_0(B)
              | v3_xreal_0(A) ) ) ) ) ),
    file(real,t6_real),
    []).

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(t7_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v2_xreal_0(A)
              & ~ v3_xreal_0(B) ) ) ) ),
    file(real,t7_real),
    []).

fof(t8_real,axiom,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,B)
              & ~ v3_xreal_0(B)
              & ~ v2_xreal_0(A) ) ) ) ),
    file(real,t8_real),
    []).