SET007 Axioms: SET007+807.ax
%------------------------------------------------------------------------------
% File : SET007+807 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Solving Roots of Polynomial Equations
% Version : [Urb08] axioms.
% English : Solving Roots of Polynomial Equations of Degree 2 and 3 with
% Complex Coefficients
% 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_3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 85 ( 5 unt; 0 def)
% Number of atoms : 492 ( 207 equ)
% Maximal formula atoms : 18 ( 5 avg)
% Number of connectives : 529 ( 122 ~; 14 |; 148 &)
% ( 1 <=>; 244 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 9 avg)
% Maximal term depth : 15 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 58 ( 58 usr; 17 con; 0-5 aty)
% Number of variables : 246 ( 245 !; 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(d1_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k3_polyeq_3(A) = k2_polyeq_3(k5_real_1(k7_square_1(k3_complex1(A)),k7_square_1(k4_complex1(A))),k1_polyeq_3(k4_real_1(np__2,k4_real_1(k3_complex1(A),k4_complex1(A))),k7_complex1)) ) ).
fof(t1_polyeq_3,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)
=> k9_complex1(k2_polyeq_3(A,k1_polyeq_3(B,k7_complex1)),k2_polyeq_3(C,k1_polyeq_3(D,k7_complex1))) = k2_polyeq_3(k5_real_1(k4_real_1(A,C),k4_real_1(B,D)),k1_polyeq_3(k3_real_1(k4_real_1(A,D),k4_real_1(C,B)),k7_complex1)) ) ) ) ) ).
fof(t2_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> k3_polyeq_3(k5_arytm_0(A,B)) = k2_polyeq_3(k5_real_1(k7_square_1(A),k7_square_1(B)),k1_polyeq_3(k4_real_1(k4_real_1(np__2,A),B),k7_complex1)) ) ) ).
fof(t3_polyeq_3,axiom,
$true ).
fof(t4_polyeq_3,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,k2_numbers)
=> ~ ( A != np__0
& r1_xreal_0(np__0,k2_quin_1(A,B,C))
& k4_polyeq_3(A,B,C,D) = np__0
& D != k6_real_1(k3_real_1(k1_real_1(B),k9_square_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))
& D != k6_real_1(k5_real_1(k1_real_1(B),k9_square_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))
& D != k1_real_1(k6_real_1(B,k4_real_1(np__2,A))) ) ) ) ) ) ).
fof(t5_polyeq_3,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,k2_numbers)
=> ~ ( A != np__0
& ~ r1_xreal_0(np__0,k2_quin_1(A,B,C))
& k4_polyeq_3(A,B,C,D) = np__0
& D != k2_polyeq_3(k1_real_1(k6_real_1(B,k4_real_1(np__2,A))),k1_polyeq_3(k6_real_1(k9_square_1(k1_real_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A)),k7_complex1))
& D != k2_polyeq_3(k1_real_1(k6_real_1(B,k4_real_1(np__2,A))),k1_polyeq_3(k1_real_1(k6_real_1(k9_square_1(k1_real_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))),k7_complex1)) ) ) ) ) ) ).
fof(t6_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( ! [D] :
( m1_subset_1(D,k2_numbers)
=> k4_polyeq_3(np__0,A,B,D) = np__0 )
=> ( A = np__0
| C = k1_real_1(k6_real_1(B,A)) ) ) ) ) ) ).
fof(t7_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ! [D] :
( v1_xcmplx_0(D)
=> ! [E] :
( v1_xcmplx_0(E)
=> ! [F] :
( v1_xcmplx_0(F)
=> ( ! [G] :
( v1_xcmplx_0(G)
=> k3_polyeq_1(A,B,C,G) = k5_polyeq_1(A,G,E,F) )
=> ( A = np__0
| ( k6_real_1(B,A) = k4_xcmplx_0(k2_xcmplx_0(E,F))
& k6_real_1(C,A) = k3_xcmplx_0(E,F) ) ) ) ) ) ) ) ) ) ).
fof(d2_polyeq_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> k5_polyeq_3(A) = k3_xcmplx_0(k5_square_1(A),A) ) ).
fof(d3_polyeq_3,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] :
( v1_xcmplx_0(E)
=> k6_polyeq_3(A,B,C,D,E) = k2_xcmplx_0(k2_xcmplx_0(k2_xcmplx_0(k1_polyeq_3(A,k5_polyeq_3(E)),k3_xcmplx_0(B,k5_square_1(E))),k3_xcmplx_0(C,E)),D) ) ) ) ) ) ).
fof(t8_polyeq_3,axiom,
k5_polyeq_3(k5_complex1) = np__0 ).
fof(t9_polyeq_3,axiom,
k5_polyeq_3(np__1) = np__1 ).
fof(t10_polyeq_3,axiom,
k5_polyeq_3(k1_real_1(np__1)) = k1_real_1(np__1) ).
fof(t11_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ( k3_complex1(k5_polyeq_3(A)) = k5_real_1(k3_prepower(k3_complex1(A),np__3),k4_real_1(k4_real_1(np__3,k3_complex1(A)),k7_square_1(k4_complex1(A))))
& k4_complex1(k5_polyeq_3(A)) = k3_real_1(k1_real_1(k3_prepower(k4_complex1(A),np__3)),k4_real_1(k4_real_1(np__3,k7_square_1(k3_complex1(A))),k4_complex1(A))) ) ) ).
fof(t12_polyeq_3,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)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ( ! [I] :
( v1_xcmplx_0(I)
=> k6_polyeq_3(A,B,C,D,I) = k6_polyeq_3(E,F,G,H,I) )
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ) ) ) ) ) ) ) ).
fof(t13_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k5_polyeq_3(k8_complex1(A,B)) = k8_complex1(k8_complex1(k8_complex1(k5_polyeq_3(A),k9_complex1(k1_polyeq_3(np__3,B),k3_polyeq_3(A))),k9_complex1(k1_polyeq_3(np__3,k3_polyeq_3(B)),A)),k5_polyeq_3(B)) ) ) ).
fof(t14_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k5_polyeq_3(k9_complex1(A,B)) = k9_complex1(k5_polyeq_3(A),k5_polyeq_3(B)) ) ) ).
fof(t15_polyeq_3,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,k2_numbers)
=> ~ ( A != np__0
& k6_polyeq_3(np__0,A,B,C,D) = np__0
& r1_xreal_0(np__0,k2_quin_1(A,B,C))
& D != k6_real_1(k3_real_1(k1_real_1(B),k9_square_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))
& D != k6_real_1(k5_real_1(k1_real_1(B),k9_square_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))
& D != k1_real_1(k6_real_1(B,k4_real_1(np__2,A))) ) ) ) ) ) ).
fof(t16_polyeq_3,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,k2_numbers)
=> ~ ( A != np__0
& k6_polyeq_3(np__0,A,B,C,D) = np__0
& ~ r1_xreal_0(np__0,k2_quin_1(A,B,C))
& D != k2_polyeq_3(k1_real_1(k6_real_1(B,k4_real_1(np__2,A))),k1_polyeq_3(k6_real_1(k9_square_1(k1_real_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A)),k7_complex1))
& D != k2_polyeq_3(k1_real_1(k6_real_1(B,k4_real_1(np__2,A))),k1_polyeq_3(k1_real_1(k6_real_1(k9_square_1(k1_real_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))),k7_complex1)) ) ) ) ) ) ).
fof(t17_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ~ ( A != np__0
& k6_polyeq_3(A,np__0,B,np__0,C) = np__0
& r1_xreal_0(k4_real_1(k4_real_1(np__4,A),B),np__0)
& C != k6_real_1(k9_square_1(k1_real_1(k4_real_1(k4_real_1(np__4,A),B))),k4_real_1(np__2,A))
& C != k6_real_1(k1_real_1(k9_square_1(k1_real_1(k4_real_1(k4_real_1(np__4,A),B)))),k4_real_1(np__2,A))
& C != np__0 ) ) ) ) ).
fof(t18_polyeq_3,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,k2_numbers)
=> ~ ( A != np__0
& k6_polyeq_3(A,B,C,np__0,D) = np__0
& r1_xreal_0(np__0,k2_quin_1(A,B,C))
& D != k6_real_1(k3_real_1(k1_real_1(B),k9_square_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))
& D != k6_real_1(k5_real_1(k1_real_1(B),k9_square_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))
& D != k1_real_1(k6_real_1(B,k4_real_1(np__2,A)))
& D != np__0 ) ) ) ) ) ).
fof(t19_polyeq_3,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,k2_numbers)
=> ~ ( A != np__0
& k6_polyeq_3(A,B,C,np__0,D) = np__0
& ~ r1_xreal_0(np__0,k2_quin_1(A,B,C))
& D != k2_polyeq_3(k1_real_1(k6_real_1(B,k4_real_1(np__2,A))),k1_polyeq_3(k6_real_1(k9_square_1(k1_real_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A)),k7_complex1))
& D != k2_polyeq_3(k1_real_1(k6_real_1(B,k4_real_1(np__2,A))),k1_polyeq_3(k1_real_1(k6_real_1(k9_square_1(k1_real_1(k2_quin_1(A,B,C))),k4_real_1(np__2,A))),k7_complex1))
& D != np__0 ) ) ) ) ) ).
fof(t20_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ~ ( k7_square_1(A) = B
& A != k9_square_1(B)
& A != k1_real_1(k9_square_1(B)) ) ) ) ).
fof(t21_polyeq_3,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,k2_numbers)
=> ( ( k6_polyeq_3(A,np__0,B,C,D) = np__0
& k4_complex1(D) = np__0 )
=> ( A = np__0
| ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ ( k3_complex1(D) = k3_real_1(E,F)
& k3_real_1(k4_real_1(k4_real_1(np__3,F),E),k6_real_1(B,A)) = np__0
& D != k3_real_1(k2_power(np__3,k3_real_1(k1_real_1(k6_real_1(C,k4_real_1(np__2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(np__4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3))))),k2_power(np__3,k5_real_1(k1_real_1(k6_real_1(C,k4_real_1(np__2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(np__4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3))))))
& D != k3_real_1(k2_power(np__3,k3_real_1(k1_real_1(k6_real_1(C,k4_real_1(np__2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(np__4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3))))),k2_power(np__3,k3_real_1(k1_real_1(k6_real_1(C,k4_real_1(np__2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(np__4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3))))))
& D != k3_real_1(k2_power(np__3,k5_real_1(k1_real_1(k6_real_1(C,k4_real_1(np__2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(np__4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3))))),k2_power(np__3,k5_real_1(k1_real_1(k6_real_1(C,k4_real_1(np__2,A))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(C),k4_real_1(np__4,k7_square_1(A))),k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)))))) ) ) ) ) ) ) ) ) ) ).
fof(t22_polyeq_3,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,k2_numbers)
=> ( k6_polyeq_3(A,np__0,B,C,D) = np__0
=> ( A = np__0
| k4_complex1(D) = np__0
| ! [E] :
( m1_subset_1(E,k1_numbers)
=> ! [F] :
( m1_subset_1(F,k1_numbers)
=> ~ ( k3_complex1(D) = k3_real_1(E,F)
& k3_real_1(k4_real_1(k4_real_1(np__3,F),E),k6_real_1(B,k4_real_1(np__4,A))) = np__0
& r1_xreal_0(np__0,k6_real_1(B,A))
& D != k2_polyeq_3(k3_real_1(k2_power(np__3,k3_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3))))),k2_power(np__3,k5_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))),k1_polyeq_3(k9_square_1(k3_real_1(k4_real_1(np__3,k7_square_1(k3_real_1(k2_power(np__3,k3_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3))))),k2_power(np__3,k5_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))))),k6_real_1(B,A))),k7_complex1))
& D != k6_xcmplx_0(k3_real_1(k2_power(np__3,k3_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3))))),k2_power(np__3,k5_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))),k1_polyeq_3(k9_square_1(k3_real_1(k4_real_1(np__3,k7_square_1(k3_real_1(k2_power(np__3,k3_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3))))),k2_power(np__3,k5_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))))),k6_real_1(B,A))),k7_complex1))
& D != k2_polyeq_3(k4_real_1(np__2,k2_power(np__3,k3_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))),k1_polyeq_3(k9_square_1(k3_real_1(k4_real_1(np__3,k7_square_1(k4_real_1(np__2,k2_power(np__3,k3_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))))),k6_real_1(B,A))),k7_complex1))
& D != k6_xcmplx_0(k4_real_1(np__2,k2_power(np__3,k3_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))),k1_polyeq_3(k9_square_1(k3_real_1(k4_real_1(np__3,k7_square_1(k4_real_1(np__2,k2_power(np__3,k3_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))))),k6_real_1(B,A))),k7_complex1))
& D != k2_polyeq_3(k4_real_1(np__2,k2_power(np__3,k5_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))),k1_polyeq_3(k9_square_1(k3_real_1(k4_real_1(np__3,k7_square_1(k4_real_1(np__2,k2_power(np__3,k5_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))))),k6_real_1(B,A))),k7_complex1))
& D != k6_xcmplx_0(k4_real_1(np__2,k2_power(np__3,k5_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))),k1_polyeq_3(k9_square_1(k3_real_1(k4_real_1(np__3,k7_square_1(k4_real_1(np__2,k2_power(np__3,k5_real_1(k6_real_1(C,k4_real_1(np__16,A)),k9_square_1(k3_real_1(k7_square_1(k6_real_1(C,k4_real_1(np__16,A))),k3_prepower(k6_real_1(B,k4_real_1(np__12,A)),np__3)))))))),k6_real_1(B,A))),k7_complex1)) ) ) ) ) ) ) ) ) ) ).
fof(t23_polyeq_3,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,k2_numbers)
=> ( ( k6_polyeq_3(A,B,C,D,E) = np__0
& k4_complex1(E) = np__0 )
=> ( A = np__0
| ! [F] :
( m1_subset_1(F,k1_numbers)
=> ! [G] :
( m1_subset_1(G,k1_numbers)
=> ! [H] :
( m1_subset_1(H,k1_numbers)
=> ~ ( H = k3_real_1(k3_complex1(E),k6_real_1(B,k4_real_1(np__3,A)))
& k3_complex1(E) = k5_real_1(k3_real_1(F,G),k6_real_1(B,k4_real_1(np__3,A)))
& k3_real_1(k4_real_1(k4_real_1(np__3,F),G),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),C),k7_square_1(B)),k4_real_1(np__3,k7_square_1(A)))) = np__0
& E != k2_polyeq_3(k5_real_1(k3_real_1(k2_power(np__3,k3_real_1(k5_real_1(k1_real_1(k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__6,k7_square_1(A)))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(k3_real_1(k4_real_1(np__2,k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__3,k7_square_1(A))))),np__4),k3_prepower(k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),C),k7_square_1(B)),k4_real_1(np__9,k7_square_1(A))),np__3))))),k2_power(np__3,k5_real_1(k5_real_1(k1_real_1(k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__6,k7_square_1(A)))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(k3_real_1(k4_real_1(np__2,k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__3,k7_square_1(A))))),np__4),k3_prepower(k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),C),k7_square_1(B)),k4_real_1(np__9,k7_square_1(A))),np__3)))))),k6_real_1(B,k4_real_1(np__3,A))),k1_polyeq_3(np__0,k7_complex1))
& E != k2_polyeq_3(k5_real_1(k3_real_1(k2_power(np__3,k3_real_1(k5_real_1(k1_real_1(k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__6,k7_square_1(A)))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(k3_real_1(k4_real_1(np__2,k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__3,k7_square_1(A))))),np__4),k3_prepower(k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),C),k7_square_1(B)),k4_real_1(np__9,k7_square_1(A))),np__3))))),k2_power(np__3,k3_real_1(k5_real_1(k1_real_1(k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__6,k7_square_1(A)))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(k3_real_1(k4_real_1(np__2,k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__3,k7_square_1(A))))),np__4),k3_prepower(k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),C),k7_square_1(B)),k4_real_1(np__9,k7_square_1(A))),np__3)))))),k6_real_1(B,k4_real_1(np__3,A))),k1_polyeq_3(np__0,k7_complex1))
& E != k2_polyeq_3(k5_real_1(k3_real_1(k2_power(np__3,k5_real_1(k5_real_1(k1_real_1(k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__6,k7_square_1(A)))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(k3_real_1(k4_real_1(np__2,k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__3,k7_square_1(A))))),np__4),k3_prepower(k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),C),k7_square_1(B)),k4_real_1(np__9,k7_square_1(A))),np__3))))),k2_power(np__3,k5_real_1(k5_real_1(k1_real_1(k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__6,k7_square_1(A)))),k9_square_1(k3_real_1(k6_real_1(k7_square_1(k3_real_1(k4_real_1(np__2,k3_prepower(k6_real_1(B,k4_real_1(np__3,A)),np__3)),k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),D),k4_real_1(B,C)),k4_real_1(np__3,k7_square_1(A))))),np__4),k3_prepower(k6_real_1(k5_real_1(k4_real_1(k4_real_1(np__3,A),C),k7_square_1(B)),k4_real_1(np__9,k7_square_1(A))),np__3)))))),k6_real_1(B,k4_real_1(np__3,A))),k1_polyeq_3(np__0,k7_complex1)) ) ) ) ) ) ) ) ) ) ) ) ).
fof(t24_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( k1_polyeq_1(A,B,C) = np__0
=> ( A = np__0
| C = k10_complex1(k13_complex1(B,A)) ) ) ) ) ) ).
fof(t25_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ( A != np__0
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k1_polyeq_1(np__0,A,B) != np__0 ) ) ) ).
fof(d4_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> k7_polyeq_3(A,B,C,D) = k8_complex1(k8_complex1(k9_complex1(A,k3_polyeq_3(D)),k9_complex1(B,D)),C) ) ) ) ) ).
fof(t26_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> ! [F] :
( m1_subset_1(F,k2_numbers)
=> ( ! [G] :
( m1_subset_1(G,k2_numbers)
=> k7_polyeq_3(A,B,C,G) = k7_polyeq_3(D,E,F,G) )
=> ( A = D
& B = E
& C = F ) ) ) ) ) ) ) ) ).
fof(t27_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r1_xreal_0(np__0,k6_real_1(k3_real_1(k1_real_1(A),k9_square_1(k3_real_1(k7_square_1(A),k7_square_1(B)))),np__2))
& r1_xreal_0(np__0,k6_real_1(k3_real_1(A,k9_square_1(k3_real_1(k7_square_1(A),k7_square_1(B)))),np__2)) ) ) ) ).
fof(t28_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ~ ( k3_polyeq_3(A) = B
& r1_xreal_0(np__0,k4_complex1(B))
& A != k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(B),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2)),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(B)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2)),k7_complex1))
& A != k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(B),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2))),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(B)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2))),k7_complex1)) ) ) ) ).
fof(t29_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ~ ( k3_polyeq_3(A) = B
& k4_complex1(B) = np__0
& ~ r1_xreal_0(k3_complex1(B),np__0)
& A != k9_square_1(k3_complex1(B))
& A != k1_real_1(k9_square_1(k3_complex1(B))) ) ) ) ).
fof(t30_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ~ ( k3_polyeq_3(A) = B
& k4_complex1(B) = np__0
& ~ r1_xreal_0(np__0,k3_complex1(B))
& A != k1_polyeq_3(k9_square_1(k1_real_1(k3_complex1(B))),k7_complex1)
& A != k10_complex1(k1_polyeq_3(k9_square_1(k1_real_1(k3_complex1(B))),k7_complex1)) ) ) ) ).
fof(t31_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ~ ( k3_polyeq_3(A) = B
& ~ r1_xreal_0(np__0,k4_complex1(B))
& A != k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(B),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2)),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(B)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2))),k7_complex1))
& A != k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(B),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2))),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(B)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2)),k7_complex1)) ) ) ) ).
fof(t32_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ~ ( k3_polyeq_3(A) = B
& A != k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(B),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2)),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(B)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2)),k7_complex1))
& A != k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(B),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2))),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(B)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2))),k7_complex1))
& A != k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(B),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2)),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(B)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2))),k7_complex1))
& A != k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(B),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2))),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(B)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(B)),k7_square_1(k4_complex1(B))))),np__2)),k7_complex1)) ) ) ) ).
fof(t33_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k7_polyeq_3(k5_complex1,k5_complex1,k5_complex1,A) = np__0 ) ).
fof(t34_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ( k7_polyeq_3(A,k5_complex1,k5_complex1,B) = np__0
=> ( A = np__0
| B = np__0 ) ) ) ) ).
fof(t35_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ~ ( A != np__0
& k7_polyeq_3(A,B,k5_complex1,C) = np__0
& C != k10_complex1(k13_complex1(B,A))
& C != np__0 ) ) ) ) ).
fof(t36_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( k7_polyeq_3(A,k5_complex1,B,C) = np__0
=> ( A = np__0
| ! [D] :
( m1_subset_1(D,k2_numbers)
=> ~ ( D = k10_complex1(k13_complex1(B,A))
& C != k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(D),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2)),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(D)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2)),k7_complex1))
& C != k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(D),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2))),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(D)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2))),k7_complex1))
& C != k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(D),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2)),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(D)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2))),k7_complex1))
& C != k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(D),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2))),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(D)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2)),k7_complex1)) ) ) ) ) ) ) ) ).
fof(t37_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ( k7_polyeq_3(A,B,C,D) = np__0
=> ( A = np__0
| ! [E] :
( m1_subset_1(E,k2_numbers)
=> ! [F] :
( m1_subset_1(F,k2_numbers)
=> ~ ( E = k11_complex1(k3_polyeq_3(k13_complex1(B,k1_polyeq_3(np__2,A))),k13_complex1(C,A))
& F = k13_complex1(B,k1_polyeq_3(np__2,A))
& D != k11_complex1(k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(E),k9_square_1(k3_real_1(k7_square_1(k3_complex1(E)),k7_square_1(k4_complex1(E))))),np__2)),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(E)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(E)),k7_square_1(k4_complex1(E))))),np__2)),k7_complex1)),F)
& D != k11_complex1(k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(E),k9_square_1(k3_real_1(k7_square_1(k3_complex1(E)),k7_square_1(k4_complex1(E))))),np__2))),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(E)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(E)),k7_square_1(k4_complex1(E))))),np__2))),k7_complex1)),F)
& D != k11_complex1(k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(E),k9_square_1(k3_real_1(k7_square_1(k3_complex1(E)),k7_square_1(k4_complex1(E))))),np__2)),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(E)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(E)),k7_square_1(k4_complex1(E))))),np__2))),k7_complex1)),F)
& D != k11_complex1(k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(E),k9_square_1(k3_real_1(k7_square_1(k3_complex1(E)),k7_square_1(k4_complex1(E))))),np__2))),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(E)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(E)),k7_square_1(k4_complex1(E))))),np__2)),k7_complex1)),F) ) ) ) ) ) ) ) ) ) ).
fof(d5_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> k8_polyeq_3(A,B,C,D,E) = k8_complex1(k8_complex1(k8_complex1(k9_complex1(A,k5_polyeq_3(E)),k9_complex1(B,k3_polyeq_3(E))),k9_complex1(C,E)),D) ) ) ) ) ) ).
fof(t38_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ~ ( k3_polyeq_3(A) = np__1
& A != np__1
& A != k1_real_1(np__1) ) ) ).
fof(t39_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ( k2_comseq_3(A,np__3) = k9_complex1(k9_complex1(A,A),A)
& k2_comseq_3(A,np__3) = k9_complex1(k3_polyeq_3(A),A)
& k2_comseq_3(A,np__3) = k5_polyeq_3(A) ) ) ).
fof(t40_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ~ ( A != np__0
& k8_polyeq_3(A,B,k5_complex1,k5_complex1,C) = np__0
& C != k10_complex1(k13_complex1(B,A))
& C != np__0 ) ) ) ) ).
fof(t41_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( k8_polyeq_3(A,k5_complex1,B,k5_complex1,C) = np__0
=> ( A = np__0
| ! [D] :
( m1_subset_1(D,k2_numbers)
=> ~ ( D = k10_complex1(k13_complex1(B,A))
& C != np__0
& C != k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(D),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2)),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(D)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2)),k7_complex1))
& C != k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(D),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2))),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(D)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2))),k7_complex1))
& C != k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(D),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2)),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(D)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2))),k7_complex1))
& C != k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(D),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2))),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(D)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(D)),k7_square_1(k4_complex1(D))))),np__2)),k7_complex1)) ) ) ) ) ) ) ) ).
fof(t42_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ( k8_polyeq_3(A,B,C,k5_complex1,D) = np__0
=> ( A = np__0
| ! [E] :
( m1_subset_1(E,k2_numbers)
=> ! [F] :
( m1_subset_1(F,k2_numbers)
=> ! [G] :
( m1_subset_1(G,k2_numbers)
=> ~ ( E = k10_complex1(k13_complex1(C,A))
& F = k11_complex1(k3_polyeq_3(k13_complex1(B,k1_polyeq_3(np__2,A))),k13_complex1(C,A))
& G = k13_complex1(B,k1_polyeq_3(np__2,A))
& D != np__0
& D != k11_complex1(k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(F),k9_square_1(k3_real_1(k7_square_1(k3_complex1(F)),k7_square_1(k4_complex1(F))))),np__2)),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(F)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(F)),k7_square_1(k4_complex1(F))))),np__2)),k7_complex1)),G)
& D != k11_complex1(k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(F),k9_square_1(k3_real_1(k7_square_1(k3_complex1(F)),k7_square_1(k4_complex1(F))))),np__2))),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(F)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(F)),k7_square_1(k4_complex1(F))))),np__2))),k7_complex1)),G)
& D != k11_complex1(k2_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k3_complex1(F),k9_square_1(k3_real_1(k7_square_1(k3_complex1(F)),k7_square_1(k4_complex1(F))))),np__2)),k1_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(F)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(F)),k7_square_1(k4_complex1(F))))),np__2))),k7_complex1)),G)
& D != k11_complex1(k2_polyeq_3(k1_real_1(k9_square_1(k6_real_1(k3_real_1(k3_complex1(F),k9_square_1(k3_real_1(k7_square_1(k3_complex1(F)),k7_square_1(k4_complex1(F))))),np__2))),k1_polyeq_3(k9_square_1(k6_real_1(k3_real_1(k1_real_1(k3_complex1(F)),k9_square_1(k3_real_1(k7_square_1(k3_complex1(F)),k7_square_1(k4_complex1(F))))),np__2)),k7_complex1)),G) ) ) ) ) ) ) ) ) ) ) ).
fof(t43_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> k3_polyeq_3(k11_complex1(A,k1_polyeq_3(k6_real_1(np__1,np__3),B))) = k8_complex1(k8_complex1(k3_polyeq_3(A),k9_complex1(k1_polyeq_3(k1_real_1(k6_real_1(np__2,np__3)),B),A)),k1_polyeq_3(k6_real_1(np__1,np__9),k3_polyeq_3(B))) ) ) ).
fof(t44_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( A = k11_complex1(B,k1_polyeq_3(k6_real_1(np__1,np__3),C))
=> k5_polyeq_3(A) = k11_complex1(k8_complex1(k11_complex1(k5_polyeq_3(B),k9_complex1(C,k3_polyeq_3(B))),k9_complex1(k1_polyeq_3(k6_real_1(np__1,np__3),k3_polyeq_3(C)),B)),k1_polyeq_3(k6_real_1(np__1,np__27),k5_polyeq_3(C))) ) ) ) ) ).
fof(t45_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ! [D] :
( m1_subset_1(D,k2_numbers)
=> ( k8_polyeq_3(k6_complex1,A,B,C,D) = np__0
=> ! [E] :
( m1_subset_1(E,k2_numbers)
=> ! [F] :
( m1_subset_1(F,k2_numbers)
=> ! [G] :
( m1_subset_1(G,k2_numbers)
=> ( ( D = k11_complex1(G,k1_polyeq_3(k6_real_1(np__1,np__3),A))
& E = k8_complex1(k10_complex1(k1_polyeq_3(k6_real_1(np__1,np__3),k3_polyeq_3(A))),B)
& F = k8_complex1(k11_complex1(k1_polyeq_3(k6_real_1(np__2,np__27),k5_polyeq_3(A)),k9_complex1(k1_polyeq_3(k6_real_1(np__1,np__3),A),B)),C) )
=> k8_polyeq_3(k6_complex1,k5_complex1,E,F,G) = np__0 ) ) ) ) ) ) ) ) ) ).
fof(t46_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k5_arytm_0(k4_real_1(k17_complex1(A),k23_sin_cos(k1_comptrig(A))),k4_real_1(k17_complex1(A),k20_sin_cos(k1_comptrig(A)))) = k9_complex1(k5_arytm_0(k17_complex1(A),np__0),k5_arytm_0(k23_sin_cos(k1_comptrig(A)),k20_sin_cos(k1_comptrig(A)))) ) ).
fof(t47_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_comseq_3(A,k1_nat_1(B,np__1)) = k9_complex1(k2_comseq_3(A,B),A) ) ) ).
fof(t48_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k2_comseq_3(A,np__1) = A ) ).
fof(t49_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k2_comseq_3(A,np__2) = k9_complex1(A,A) ) ).
fof(t50_polyeq_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> k2_comseq_3(k5_complex1,A) = np__0 ) ) ).
fof(t51_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_comseq_3(k9_complex1(A,B),C) = k9_complex1(k2_comseq_3(A,C),k2_comseq_3(B,C)) ) ) ) ).
fof(t52_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_comseq_3(k5_arytm_0(A,np__0),B) = k4_power(A,B) ) ) ) ).
fof(t53_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_comseq_3(k5_arytm_0(k23_sin_cos(A),k20_sin_cos(A)),B) = k2_polyeq_3(k23_sin_cos(k4_real_1(B,A)),k1_polyeq_3(k20_sin_cos(k4_real_1(B,A)),k7_complex1)) ) ) ).
fof(t54_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ~ ( A = np__0
& r1_xreal_0(B,np__0) )
=> k2_comseq_3(A,B) = k2_polyeq_3(k4_real_1(k4_power(k17_complex1(A),B),k23_sin_cos(k4_real_1(B,k1_comptrig(A)))),k1_polyeq_3(k4_real_1(k4_power(k17_complex1(A),B),k20_sin_cos(k4_real_1(B,k1_comptrig(A)))),k7_complex1)) ) ) ) ).
fof(t55_polyeq_3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( A != np__0
=> k2_comseq_3(k5_arytm_0(k23_sin_cos(k6_real_1(k3_real_1(C,k4_real_1(k4_real_1(np__2,k32_sin_cos),B)),A)),k20_sin_cos(k6_real_1(k3_real_1(C,k4_real_1(k4_real_1(np__2,k32_sin_cos),B)),A))),A) = k2_polyeq_3(k23_sin_cos(C),k1_polyeq_3(k20_sin_cos(C),k7_complex1)) ) ) ) ) ).
fof(t56_polyeq_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( B != np__0
=> A = k2_comseq_3(k5_arytm_0(k4_real_1(k2_power(B,k17_complex1(A)),k23_sin_cos(k6_real_1(k3_real_1(k1_comptrig(A),k4_real_1(k4_real_1(np__2,k32_sin_cos),C)),B))),k4_real_1(k2_power(B,k17_complex1(A)),k20_sin_cos(k6_real_1(k3_real_1(k1_comptrig(A),k4_real_1(k4_real_1(np__2,k32_sin_cos),C)),B)))),B) ) ) ) ) ).
fof(d6_polyeq_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> ! [C] :
( m1_subset_1(C,k2_numbers)
=> ( m1_polyeq_3(C,A,B)
<=> k2_comseq_3(C,B) = A ) ) ) ) ).
fof(t57_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> m1_polyeq_3(k5_arytm_0(k4_real_1(k2_power(B,k17_complex1(A)),k23_sin_cos(k6_real_1(k3_real_1(k1_comptrig(A),k4_real_1(k4_real_1(np__2,k32_sin_cos),C)),B))),k4_real_1(k2_power(B,k17_complex1(A)),k20_sin_cos(k6_real_1(k3_real_1(k1_comptrig(A),k4_real_1(k4_real_1(np__2,k32_sin_cos),C)),B)))),A,B) ) ) ) ).
fof(t58_polyeq_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> ! [B] :
( m1_polyeq_3(B,A,np__1)
=> B = A ) ) ).
fof(t59_polyeq_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m1_polyeq_3(B,np__0,A)
=> B = np__0 ) ) ).
fof(t60_polyeq_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( v1_xcmplx_0(B)
=> ! [C] :
( m1_polyeq_3(C,B,A)
=> ( C = np__0
=> B = np__0 ) ) ) ) ).
fof(t61_polyeq_3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> m1_polyeq_3(k2_polyeq_3(k23_sin_cos(k6_real_1(k4_real_1(k4_real_1(np__2,k32_sin_cos),B),A)),k1_polyeq_3(k20_sin_cos(k6_real_1(k4_real_1(k4_real_1(np__2,k32_sin_cos),B),A)),k7_complex1)),np__1,A) ) ) ).
fof(t62_polyeq_3,axiom,
$true ).
fof(t63_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> ! [B] :
( m1_subset_1(B,k2_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,C)
& k2_comseq_3(B,C) = k2_comseq_3(A,C) )
=> ( B = np__0
| A = np__0
| k17_complex1(B) = k17_complex1(A) ) ) ) ) ) ).
fof(dt_m1_polyeq_3,axiom,
! [A,B] :
( ( v1_xcmplx_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k5_numbers) )
=> ! [C] :
( m1_polyeq_3(C,A,B)
=> m1_subset_1(C,k2_numbers) ) ) ).
fof(existence_m1_polyeq_3,axiom,
! [A,B] :
( ( v1_xcmplx_0(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k5_numbers) )
=> ? [C] : m1_polyeq_3(C,A,B) ) ).
fof(dt_k1_polyeq_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k2_numbers) )
=> m1_subset_1(k1_polyeq_3(A,B),k2_numbers) ) ).
fof(commutativity_k1_polyeq_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k2_numbers) )
=> k1_polyeq_3(A,B) = k1_polyeq_3(B,A) ) ).
fof(redefinition_k1_polyeq_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k2_numbers) )
=> k1_polyeq_3(A,B) = k3_xcmplx_0(A,B) ) ).
fof(dt_k2_polyeq_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k2_numbers) )
=> m1_subset_1(k2_polyeq_3(A,B),k2_numbers) ) ).
fof(commutativity_k2_polyeq_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k2_numbers) )
=> k2_polyeq_3(A,B) = k2_polyeq_3(B,A) ) ).
fof(redefinition_k2_polyeq_3,axiom,
! [A,B] :
( ( m1_subset_1(A,k1_numbers)
& m1_subset_1(B,k2_numbers) )
=> k2_polyeq_3(A,B) = k2_xcmplx_0(A,B) ) ).
fof(dt_k3_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> m1_subset_1(k3_polyeq_3(A),k2_numbers) ) ).
fof(redefinition_k3_polyeq_3,axiom,
! [A] :
( m1_subset_1(A,k2_numbers)
=> k3_polyeq_3(A) = k5_square_1(A) ) ).
fof(dt_k4_polyeq_3,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,k2_numbers) )
=> m1_subset_1(k4_polyeq_3(A,B,C,D),k2_numbers) ) ).
fof(redefinition_k4_polyeq_3,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,k2_numbers) )
=> k4_polyeq_3(A,B,C,D) = k3_polyeq_1(A,B,C,D) ) ).
fof(dt_k5_polyeq_3,axiom,
! [A] :
( v1_xcmplx_0(A)
=> m1_subset_1(k5_polyeq_3(A),k2_numbers) ) ).
fof(dt_k6_polyeq_3,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)
& v1_xcmplx_0(E) )
=> m1_subset_1(k6_polyeq_3(A,B,C,D,E),k2_numbers) ) ).
fof(dt_k7_polyeq_3,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers)
& m1_subset_1(C,k2_numbers)
& m1_subset_1(D,k2_numbers) )
=> m1_subset_1(k7_polyeq_3(A,B,C,D),k2_numbers) ) ).
fof(dt_k8_polyeq_3,axiom,
! [A,B,C,D,E] :
( ( m1_subset_1(A,k2_numbers)
& m1_subset_1(B,k2_numbers)
& m1_subset_1(C,k2_numbers)
& m1_subset_1(D,k2_numbers)
& m1_subset_1(E,k2_numbers) )
=> m1_subset_1(k8_polyeq_3(A,B,C,D,E),k2_numbers) ) ).
%------------------------------------------------------------------------------