SET007 Axioms: SET007+146.ax


%------------------------------------------------------------------------------
% File     : SET007+146 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Solving Roots of Polynomial Equations of Degree 2 and 3
% Version  : [Urb08] axioms.
% English  :

% Refs     : [Mat90] Matuszewski (1990), Formalized Mathematics
%          : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
%          : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source   : [Urb08]
% Names    : polyeq_1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   50 (   5 unit)
%            Number of atoms       :  336 ( 105 equality)
%            Maximal formula depth :   28 (  11 average)
%            Number of connectives :  320 (  34 ~  ;   9  |; 107  &)
%                                         (   0 <=>; 170 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    6 (   1 propositional; 0-2 arity)
%            Number of functors    :   26 (   6 constant; 0-5 arity)
%            Number of variables   :  204 (   0 singleton; 203 !;   1 ?)
%            Maximal term depth    :    9 (   2 average)
% SPC      : 

% Comments : The individual reference can be found in [Mat90] by looking for
%            the name provided by [Urb08].
%          : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
%          : These set theory axioms are used in encodings of problems in
%            various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
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)) ) )).

fof(fc2_polyeq_1,axiom,(
    ! [A,B,C] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C) )
     => ( v1_xcmplx_0(k1_polyeq_1(A,B,C))
        & v1_xreal_0(k1_polyeq_1(A,B,C)) ) ) )).

fof(fc3_polyeq_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( v1_xcmplx_0(k3_polyeq_1(A,B,C,D))
        & v1_xreal_0(k3_polyeq_1(A,B,C,D)) ) ) )).

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)) ) )).

fof(fc5_polyeq_1,axiom,(
    ! [A,B,C,D] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D) )
     => ( v1_xcmplx_0(k5_polyeq_1(A,B,C,D))
        & v1_xreal_0(k5_polyeq_1(A,B,C,D)) ) ) )).

fof(fc6_polyeq_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D)
        & v1_xreal_0(E) )
     => ( v1_xcmplx_0(k7_polyeq_1(A,B,C,D,E))
        & v1_xreal_0(k7_polyeq_1(A,B,C,D,E)) ) ) )).

fof(fc7_polyeq_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_xreal_0(A)
        & v1_xreal_0(B)
        & v1_xreal_0(C)
        & v1_xreal_0(D)
        & v1_xreal_0(E) )
     => ( v1_xcmplx_0(k9_polyeq_1(A,B,C,D,E))
        & v1_xreal_0(k9_polyeq_1(A,B,C,D,E)) ) ) )).

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) ) ) ) )).

fof(t1_polyeq_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( k1_polyeq_1(A,B,C) = np__0
               => ( A = np__0
                  | C = k4_xcmplx_0(k7_xcmplx_0(B,A)) ) ) ) ) ) )).

fof(t2_polyeq_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k1_polyeq_1(np__0,np__0,A) = np__0 ) )).

fof(t3_polyeq_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ( A != np__0
       => ! [B] :
            ( v1_xcmplx_0(B)
           => k1_polyeq_1(np__0,A,B) != np__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) ) ) ) ) )).

fof(t4_polyeq_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ! [E] :
                      ( v1_xcmplx_0(E)
                     => ! [F] :
                          ( v1_xcmplx_0(F)
                         => ( ! [G] :
                                ( v1_xreal_0(G)
                               => k3_polyeq_1(A,B,C,G) = k3_polyeq_1(D,E,F,G) )
                           => ( A = D
                              & B = E
                              & C = F ) ) ) ) ) ) ) ) )).

fof(t5_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( r1_xreal_0(np__0,k1_quin_1(A,B,C))
               => ( A = np__0
                  | ! [D] :
                      ( v1_xreal_0(D)
                     => ~ ( k3_polyeq_1(A,B,C,D) = np__0
                          & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))
                          & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)) ) ) ) ) ) ) ) )).

fof(t6_polyeq_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ( ( k1_quin_1(A,B,C) = np__0
                      & k3_polyeq_1(A,B,C,D) = np__0 )
                   => ( A = np__0
                      | D = k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(np__2,A))) ) ) ) ) ) ) )).

fof(t7_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( A != np__0
                  & ~ r1_xreal_0(np__0,k1_quin_1(A,B,C))
                  & ? [D] :
                      ( v1_xreal_0(D)
                      & k3_polyeq_1(A,B,C,D) = np__0 ) ) ) ) ) )).

fof(t8_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ( ! [D] :
                    ( v1_xreal_0(D)
                   => k3_polyeq_1(np__0,B,C,D) = np__0 )
               => ( B = np__0
                  | A = k4_xcmplx_0(k7_xcmplx_0(C,B)) ) ) ) ) ) )).

fof(t9_polyeq_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => k3_polyeq_1(np__0,np__0,np__0,A) = np__0 ) )).

fof(t10_polyeq_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ( A != np__0
       => ! [B] :
            ( v1_xcmplx_0(B)
           => k3_polyeq_1(np__0,np__0,A,B) != np__0 ) ) ) )).

fof(d3_polyeq_1,axiom,(
    ! [A] :
      ( v1_xcmplx_0(A)
     => ! [B] :
          ( v1_xcmplx_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => k5_polyeq_1(A,B,C,D) = k3_xcmplx_0(A,k3_xcmplx_0(k6_xcmplx_0(B,C),k6_xcmplx_0(B,D))) ) ) ) ) )).

fof(t11_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xcmplx_0(C)
             => ! [D] :
                  ( v1_xcmplx_0(D)
                 => ! [E] :
                      ( v1_xcmplx_0(E)
                     => ( ! [F] :
                            ( v1_xreal_0(F)
                           => k3_polyeq_1(C,D,E,F) = k5_polyeq_1(C,F,A,B) )
                       => ( C = np__0
                          | ( k7_xcmplx_0(D,C) = k4_xcmplx_0(k2_xcmplx_0(A,B))
                            & k7_xcmplx_0(E,C) = k3_xcmplx_0(A,B) ) ) ) ) ) ) ) ) )).

fof(d4_polyeq_1,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)
                     => k7_polyeq_1(A,B,C,D,E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k2_newton(E,np__3)),k3_xcmplx_0(B,k5_square_1(E))),k3_xcmplx_0(C,E)),D) ) ) ) ) ) )).

fof(t12_polyeq_1,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)
                         => ! [G] :
                              ( v1_xreal_0(G)
                             => ! [H] :
                                  ( v1_xreal_0(H)
                                 => ( ! [I] :
                                        ( v1_xreal_0(I)
                                       => k7_polyeq_1(A,B,C,D,I) = k7_polyeq_1(E,F,G,H,I) )
                                   => ( A = E
                                      & B = F
                                      & C = G
                                      & D = H ) ) ) ) ) ) ) ) ) ) )).

fof(d5_polyeq_1,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)
                     => k9_polyeq_1(A,B,C,D,E) = k3_xcmplx_0(A,k3_xcmplx_0(k3_xcmplx_0(k6_xcmplx_0(B,C),k6_xcmplx_0(B,D)),k6_xcmplx_0(B,E))) ) ) ) ) ) )).

fof(t13_polyeq_1,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)
                         => ! [G] :
                              ( v1_xreal_0(G)
                             => ( ! [H] :
                                    ( v1_xreal_0(H)
                                   => k7_polyeq_1(A,B,C,D,H) = k9_polyeq_1(A,H,E,F,G) )
                               => ( A = np__0
                                  | ( k7_xcmplx_0(B,A) = k4_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(E,F),G))
                                    & k7_xcmplx_0(C,A) = k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(E,F),k3_xcmplx_0(F,G)),k3_xcmplx_0(E,G))
                                    & k7_xcmplx_0(D,A) = k4_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(E,F),G)) ) ) ) ) ) ) ) ) ) ) )).

fof(t14_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => k2_newton(k2_xcmplx_0(A,B),np__3) = k2_xcmplx_0(k2_xcmplx_0(k2_newton(A,np__3),k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,B),k5_square_1(A)),k3_xcmplx_0(k3_xcmplx_0(np__3,k5_square_1(B)),A))),k2_newton(B,np__3)) ) ) )).

fof(t15_polyeq_1,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)
                     => ( k7_polyeq_1(A,B,C,D,E) = np__0
                       => ( A = np__0
                          | ! [F] :
                              ( v1_xreal_0(F)
                             => ! [G] :
                                  ( v1_xreal_0(G)
                                 => ! [H] :
                                      ( v1_xreal_0(H)
                                     => ! [I] :
                                          ( v1_xreal_0(I)
                                         => ! [J] :
                                              ( v1_xreal_0(J)
                                             => ( ( J = k2_xcmplx_0(E,k7_xcmplx_0(B,k3_xcmplx_0(np__3,A)))
                                                  & I = k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(np__3,A)))
                                                  & F = k7_xcmplx_0(B,A)
                                                  & G = k7_xcmplx_0(C,A)
                                                  & H = k7_xcmplx_0(D,A) )
                                               => k2_xcmplx_0(k2_xcmplx_0(k2_newton(J,np__3),k2_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(np__3,I),F),k5_square_1(J)),k3_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(np__3,k5_square_1(I)),k3_xcmplx_0(np__2,k3_xcmplx_0(F,I))),G),J))),k2_xcmplx_0(k2_xcmplx_0(k2_newton(I,np__3),k3_xcmplx_0(F,k5_square_1(I))),k2_xcmplx_0(k3_xcmplx_0(G,I),H))) = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t16_polyeq_1,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)
                     => ( k7_polyeq_1(A,B,C,D,E) = np__0
                       => ( A = np__0
                          | ! [F] :
                              ( v1_xreal_0(F)
                             => ! [G] :
                                  ( v1_xreal_0(G)
                                 => ! [H] :
                                      ( v1_xreal_0(H)
                                     => ! [I] :
                                          ( v1_xreal_0(I)
                                         => ! [J] :
                                              ( v1_xreal_0(J)
                                             => ( ( J = k2_xcmplx_0(E,k7_xcmplx_0(B,k3_xcmplx_0(np__3,A)))
                                                  & I = k4_xcmplx_0(k7_xcmplx_0(B,k3_xcmplx_0(np__3,A)))
                                                  & F = k7_xcmplx_0(B,A)
                                                  & G = k7_xcmplx_0(C,A)
                                                  & H = k7_xcmplx_0(D,A) )
                                               => k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_newton(J,np__3),k3_xcmplx_0(np__0,k5_square_1(J))),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,A),C),k5_square_1(B)),k3_xcmplx_0(np__3,k5_square_1(A))),J)),k2_xcmplx_0(k3_xcmplx_0(np__2,k2_newton(k7_xcmplx_0(B,k3_xcmplx_0(np__3,A)),np__3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,A),D),k3_xcmplx_0(B,C)),k3_xcmplx_0(np__3,k5_square_1(A))))) = np__0 ) ) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t17_polyeq_1,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)
                     => ( k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k2_newton(A,np__3),k3_xcmplx_0(np__0,k5_square_1(A))),k3_xcmplx_0(k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,B),C),k5_square_1(D)),k3_xcmplx_0(np__3,k5_square_1(B))),A)),k2_xcmplx_0(k3_xcmplx_0(np__2,k2_newton(k7_xcmplx_0(D,k3_xcmplx_0(np__3,B)),np__3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,B),E),k3_xcmplx_0(D,C)),k3_xcmplx_0(np__3,k5_square_1(B))))) = np__0
                       => ! [F] :
                            ( v1_xreal_0(F)
                           => ! [G] :
                                ( v1_xreal_0(G)
                               => ( ( F = k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,B),C),k5_square_1(D)),k3_xcmplx_0(np__3,k5_square_1(B)))
                                    & G = k2_xcmplx_0(k3_xcmplx_0(np__2,k2_newton(k7_xcmplx_0(D,k3_xcmplx_0(np__3,B)),np__3)),k7_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,B),E),k3_xcmplx_0(D,C)),k3_xcmplx_0(np__3,k5_square_1(B)))) )
                                 => k7_polyeq_1(np__1,np__0,F,G,A) = np__0 ) ) ) ) ) ) ) ) ) )).

fof(t18_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( k7_polyeq_1(np__1,np__0,A,B,C) = np__0
               => ! [D] :
                    ( v1_xreal_0(D)
                   => ! [E] :
                        ( v1_xreal_0(E)
                       => ( ( C = k2_xcmplx_0(D,E)
                            & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,E),D),A) = np__0 )
                         => ( k2_xcmplx_0(k2_newton(D,np__3),k2_newton(E,np__3)) = k4_xcmplx_0(B)
                            & k3_xcmplx_0(k2_newton(D,np__3),k2_newton(E,np__3)) = k2_newton(k4_xcmplx_0(k7_xcmplx_0(A,np__3)),np__3) ) ) ) ) ) ) ) ) )).

fof(t19_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ( k7_polyeq_1(np__1,np__0,A,B,C) = np__0
               => ! [D] :
                    ( v1_xreal_0(D)
                   => ! [E] :
                        ( v1_xreal_0(E)
                       => ~ ( C = k2_xcmplx_0(D,E)
                            & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,E),D),A) = np__0
                            & C != k2_xcmplx_0(k1_power(np__3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,np__2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),np__4),k2_newton(k7_xcmplx_0(A,np__3),np__3))))),k1_power(np__3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,np__2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),np__4),k2_newton(k7_xcmplx_0(A,np__3),np__3))))))
                            & C != k2_xcmplx_0(k1_power(np__3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,np__2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),np__4),k2_newton(k7_xcmplx_0(A,np__3),np__3))))),k1_power(np__3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,np__2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),np__4),k2_newton(k7_xcmplx_0(A,np__3),np__3))))))
                            & C != k2_xcmplx_0(k1_power(np__3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,np__2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),np__4),k2_newton(k7_xcmplx_0(A,np__3),np__3))))),k1_power(np__3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(B,np__2)),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(B),np__4),k2_newton(k7_xcmplx_0(A,np__3),np__3)))))) ) ) ) ) ) ) ) )).

fof(t20_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( A != np__0
                      & ~ r1_xreal_0(k1_quin_1(A,B,C),np__0)
                      & k7_polyeq_1(np__0,A,B,C,D) = np__0
                      & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))
                      & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)) ) ) ) ) ) )).

fof(t21_polyeq_1,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)
                         => ( ( B = k7_xcmplx_0(C,A)
                              & D = k7_xcmplx_0(E,A)
                              & k7_polyeq_1(A,np__0,C,E,F) = np__0 )
                           => ( A = np__0
                              | ! [G] :
                                  ( v1_xreal_0(G)
                                 => ! [H] :
                                      ( v1_xreal_0(H)
                                     => ~ ( F = k2_xcmplx_0(G,H)
                                          & k2_xcmplx_0(k3_xcmplx_0(k3_xcmplx_0(np__3,H),G),B) = np__0
                                          & F != k2_xcmplx_0(k1_power(np__3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(E,k3_xcmplx_0(np__2,A))),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(E),k3_xcmplx_0(np__4,k5_square_1(A))),k2_newton(k7_xcmplx_0(C,k3_xcmplx_0(np__3,A)),np__3))))),k1_power(np__3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(E,k3_xcmplx_0(np__2,A))),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(E),k3_xcmplx_0(np__4,k5_square_1(A))),k2_newton(k7_xcmplx_0(C,k3_xcmplx_0(np__3,A)),np__3))))))
                                          & F != k2_xcmplx_0(k1_power(np__3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(E,k3_xcmplx_0(np__2,A))),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(E),k3_xcmplx_0(np__4,k5_square_1(A))),k2_newton(k7_xcmplx_0(C,k3_xcmplx_0(np__3,A)),np__3))))),k1_power(np__3,k2_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(E,k3_xcmplx_0(np__2,A))),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(E),k3_xcmplx_0(np__4,k5_square_1(A))),k2_newton(k7_xcmplx_0(C,k3_xcmplx_0(np__3,A)),np__3))))))
                                          & F != k2_xcmplx_0(k1_power(np__3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(E,k3_xcmplx_0(np__2,A))),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(E),k3_xcmplx_0(np__4,k5_square_1(A))),k2_newton(k7_xcmplx_0(C,k3_xcmplx_0(np__3,A)),np__3))))),k1_power(np__3,k6_xcmplx_0(k4_xcmplx_0(k7_xcmplx_0(E,k3_xcmplx_0(np__2,A))),k8_square_1(k2_xcmplx_0(k7_xcmplx_0(k5_square_1(E),k3_xcmplx_0(np__4,k5_square_1(A))),k2_newton(k7_xcmplx_0(C,k3_xcmplx_0(np__3,A)),np__3)))))) ) ) ) ) ) ) ) ) ) ) ) )).

fof(t22_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ! [D] :
                  ( v1_xreal_0(D)
                 => ~ ( A != np__0
                      & r1_xreal_0(np__0,k1_quin_1(A,B,C))
                      & k7_polyeq_1(A,B,C,np__0,D) = np__0
                      & D != np__0
                      & D != k7_xcmplx_0(k2_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A))
                      & D != k7_xcmplx_0(k6_xcmplx_0(k4_xcmplx_0(B),k8_square_1(k1_quin_1(A,B,C))),k3_xcmplx_0(np__2,A)) ) ) ) ) ) )).

fof(t23_polyeq_1,axiom,(
    ! [A] :
      ( v1_xreal_0(A)
     => ! [B] :
          ( v1_xreal_0(B)
         => ! [C] :
              ( v1_xreal_0(C)
             => ~ ( A != np__0
                  & ~ r1_xreal_0(np__0,k7_xcmplx_0(B,A))
                  & k7_polyeq_1(A,np__0,B,np__0,C) = np__0
                  & C != np__0
                  & C != k8_square_1(k4_xcmplx_0(k7_xcmplx_0(B,A)))
                  & C != k4_xcmplx_0(k8_square_1(k4_xcmplx_0(k7_xcmplx_0(B,A)))) ) ) ) ) )).

fof(dt_k1_polyeq_1,axiom,(
    $true )).

fof(dt_k2_polyeq_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_polyeq_1(A,B,C),k1_numbers) ) )).

fof(redefinition_k2_polyeq_1,axiom,(
    ! [A,B,C] :
      ( ( m1_subset_1(A,k1_numbers)
        & m1_subset_1(B,k1_numbers)
        & m1_subset_1(C,k1_numbers) )
     => k2_polyeq_1(A,B,C) = k1_polyeq_1(A,B,C) ) )).

fof(dt_k3_polyeq_1,axiom,(
    $true )).

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) ) )).

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) ) )).

fof(dt_k5_polyeq_1,axiom,(
    $true )).

fof(dt_k6_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(k6_polyeq_1(A,B,C,D),k1_numbers) ) )).

fof(redefinition_k6_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) )
     => k6_polyeq_1(A,B,C,D) = k5_polyeq_1(A,B,C,D) ) )).

fof(dt_k7_polyeq_1,axiom,(
    $true )).

fof(dt_k8_polyeq_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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(E,k1_numbers) )
     => m1_subset_1(k8_polyeq_1(A,B,C,D,E),k1_numbers) ) )).

fof(redefinition_k8_polyeq_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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(E,k1_numbers) )
     => k8_polyeq_1(A,B,C,D,E) = k7_polyeq_1(A,B,C,D,E) ) )).

fof(dt_k9_polyeq_1,axiom,(
    $true )).

fof(dt_k10_polyeq_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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(E,k1_numbers) )
     => m1_subset_1(k10_polyeq_1(A,B,C,D,E),k1_numbers) ) )).

fof(redefinition_k10_polyeq_1,axiom,(
    ! [A,B,C,D,E] :
      ( ( 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(E,k1_numbers) )
     => k10_polyeq_1(A,B,C,D,E) = k9_polyeq_1(A,B,C,D,E) ) )).
%------------------------------------------------------------------------------