SET007 Axioms: SET007+146.ax
%------------------------------------------------------------------------------
% File : SET007+146 : TPTP v8.2.0. 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 unt; 0 def)
% Number of atoms : 336 ( 105 equ)
% Maximal formula atoms : 18 ( 6 avg)
% Number of connectives : 320 ( 34 ~; 9 |; 107 &)
% ( 0 <=>; 170 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 6 con; 0-5 aty)
% Number of variables : 204 ( 203 !; 1 ?)
% 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) ) ).
%------------------------------------------------------------------------------