SET007 Axioms: SET007+831.ax
%------------------------------------------------------------------------------
% File : SET007+831 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Roots of the Special Polynomial Equation with Real Coefficients
% 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_4 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 30 ( 4 unt; 0 def)
% Number of atoms : 312 ( 143 equ)
% Maximal formula atoms : 29 ( 10 avg)
% Number of connectives : 379 ( 97 ~; 21 |; 145 &)
% ( 0 <=>; 116 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 14 avg)
% Maximal term depth : 9 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 25 ( 25 usr; 8 con; 0-7 aty)
% Number of variables : 118 ( 107 !; 11 ?)
% 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(t1_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(np__0,k2_quin_1(A,B,C))
=> ( A = np__0
| r1_xreal_0(np__0,k6_real_1(B,A))
| r1_xreal_0(k6_real_1(C,A),np__0)
| ( ~ r1_xreal_0(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)),np__0)
& ~ r1_xreal_0(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)),np__0) ) ) ) ) ) ) ).
fof(t2_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r1_xreal_0(np__0,k2_quin_1(A,B,C))
=> ( A = np__0
| r1_xreal_0(k6_real_1(B,A),np__0)
| r1_xreal_0(k6_real_1(C,A),np__0)
| ( ~ r1_xreal_0(np__0,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)))
& ~ r1_xreal_0(np__0,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))) ) ) ) ) ) ) ).
fof(t3_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( A != np__0
& ~ r1_xreal_0(np__0,k6_real_1(B,A))
& ~ ( ~ r1_xreal_0(k6_real_1(k3_real_1(k1_real_1(C),k9_square_1(k2_quin_1(A,C,B))),k4_real_1(np__2,A)),np__0)
& ~ r1_xreal_0(np__0,k6_real_1(k5_real_1(k1_real_1(C),k9_square_1(k2_quin_1(A,C,B))),k4_real_1(np__2,A))) )
& ~ ( ~ r1_xreal_0(np__0,k6_real_1(k3_real_1(k1_real_1(C),k9_square_1(k2_quin_1(A,C,B))),k4_real_1(np__2,A)))
& ~ r1_xreal_0(k6_real_1(k5_real_1(k1_real_1(C),k9_square_1(k2_quin_1(A,C,B))),k4_real_1(np__2,A)),np__0) ) ) ) ) ) ).
fof(t4_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& C = k2_nat_1(np__2,D)
& r1_xreal_0(np__1,D) )
& k3_newton(B,C) = A
& B != k2_power(C,A)
& B != k1_real_1(k2_power(C,A)) ) ) ) ) ).
fof(t5_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( A != np__0
& k4_polyeq_1(A,B,np__0,C) = np__0
& C != np__0
& C != k1_real_1(k6_real_1(B,A)) ) ) ) ) ).
fof(t6_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( k4_polyeq_1(A,np__0,np__0,B) = np__0
=> ( A = np__0
| B = np__0 ) ) ) ) ).
fof(t7_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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( A != np__0
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& E = k1_nat_1(k2_nat_1(np__2,F),np__1) )
& r1_xreal_0(np__0,k2_quin_1(A,B,C))
& k4_polyeq_1(A,B,C,k3_newton(D,E)) = np__0
& D != k2_power(E,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 != k2_power(E,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))) ) ) ) ) ) ) ).
fof(t8_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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( A != np__0
& ~ r1_xreal_0(np__0,k6_real_1(B,A))
& ~ r1_xreal_0(k6_real_1(C,A),np__0)
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& E = k2_nat_1(np__2,F)
& r1_xreal_0(np__1,F) )
& r1_xreal_0(np__0,k2_quin_1(A,B,C))
& k4_polyeq_1(A,B,C,k3_newton(D,E)) = np__0
& D != k2_power(E,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 != k1_real_1(k2_power(E,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 != k2_power(E,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(k2_power(E,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)))) ) ) ) ) ) ) ).
fof(t9_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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( A != np__0
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& D = k1_nat_1(k2_nat_1(np__2,E),np__1) )
& k4_polyeq_1(A,B,np__0,k3_newton(C,D)) = np__0
& C != np__0
& C != k2_power(D,k1_real_1(k6_real_1(B,A))) ) ) ) ) ) ).
fof(t10_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] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( A != np__0
& ~ r1_xreal_0(np__0,k6_real_1(B,A))
& ? [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
& D = k2_nat_1(np__2,E)
& r1_xreal_0(np__1,E) )
& k4_polyeq_1(A,B,np__0,k3_newton(C,D)) = np__0
& C != np__0
& C != k2_power(D,k1_real_1(k6_real_1(B,A)))
& C != k1_real_1(k2_power(D,k1_real_1(k6_real_1(B,A)))) ) ) ) ) ) ).
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,np__3),k3_newton(B,np__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,np__5),k3_newton(B,np__5)) = k4_real_1(k3_real_1(A,B),k3_real_1(k5_real_1(k3_real_1(k5_real_1(k3_newton(A,np__4),k4_real_1(k3_newton(A,np__3),B)),k4_real_1(k3_newton(A,np__2),k3_newton(B,np__2))),k4_real_1(A,k3_newton(B,np__3))),k3_newton(B,np__4))) ) ) ) ).
fof(t12_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( A != np__0
& r1_xreal_0(np__0,k5_real_1(k5_real_1(k7_square_1(B),k4_real_1(k4_real_1(np__2,A),B)),k4_real_1(np__3,k7_square_1(A))))
& k8_polyeq_1(A,B,B,A,C) = np__0
& C != k1_real_1(np__1)
& C != k6_real_1(k3_real_1(k5_real_1(A,B),k9_square_1(k5_real_1(k5_real_1(k7_square_1(B),k4_real_1(k4_real_1(np__2,A),B)),k4_real_1(np__3,k7_square_1(A))))),k4_real_1(np__2,A))
& C != k6_real_1(k5_real_1(k5_real_1(A,B),k9_square_1(k5_real_1(k5_real_1(k7_square_1(B),k4_real_1(k4_real_1(np__2,A),B)),k4_real_1(np__3,k7_square_1(A))))),k4_real_1(np__2,A)) ) ) ) ) ).
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,np__5)),k4_real_1(B,k3_newton(G,np__4))),k4_real_1(C,k3_newton(G,np__3))),k4_real_1(D,k7_square_1(G))),k4_real_1(E,G)),F) ) ) ) ) ) ) ) ).
fof(t13_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)
=> ( k1_polyeq_4(A,B,C,C,B,A,D) = np__0
=> ( A = np__0
| r1_xreal_0(k5_real_1(k3_real_1(k3_real_1(k7_square_1(B),k4_real_1(k4_real_1(np__2,A),B)),k4_real_1(np__5,k7_square_1(A))),k4_real_1(k4_real_1(np__4,A),C)),np__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(np__2,A),B)),k4_real_1(np__5,k7_square_1(A))),k4_real_1(k4_real_1(np__4,A),C)))),k4_real_1(np__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(np__2,A),B)),k4_real_1(np__5,k7_square_1(A))),k4_real_1(k4_real_1(np__4,A),C)))),k4_real_1(np__2,A))
& D != k1_real_1(np__1)
& D != k6_real_1(k3_real_1(E,k9_square_1(k2_quin_1(np__1,k1_real_1(E),np__1))),np__2)
& D != k6_real_1(k3_real_1(F,k9_square_1(k2_quin_1(np__1,k1_real_1(F),np__1))),np__2)
& D != k6_real_1(k5_real_1(E,k9_square_1(k2_quin_1(np__1,k1_real_1(E),np__1))),np__2)
& D != k6_real_1(k5_real_1(F,k9_square_1(k2_quin_1(np__1,k1_real_1(F),np__1))),np__2) ) ) ) ) ) ) ) ) ) ).
fof(t14_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)
=> ~ ( k3_real_1(A,B) = C
& k4_real_1(A,B) = D
& r1_xreal_0(np__0,k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))
& ~ ( A = k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)
& B = k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2) )
& ~ ( A = k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)
& B = k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2) ) ) ) ) ) ) ).
fof(t15_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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( k3_real_1(k3_newton(A,E),k3_newton(B,E)) = C
& k4_real_1(k3_newton(A,E),k3_newton(B,E)) = D
& r1_xreal_0(np__0,k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& E = k1_nat_1(k2_nat_1(np__2,F),np__1) )
& ~ ( A = k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))
& B = k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)) )
& ~ ( A = k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))
& B = k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)) ) ) ) ) ) ) ) ).
fof(t16_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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( k3_real_1(k3_newton(A,E),k3_newton(B,E)) = C
& k4_real_1(k3_newton(A,E),k3_newton(B,E)) = D
& r1_xreal_0(np__0,k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))
& ~ r1_xreal_0(C,np__0)
& ~ r1_xreal_0(D,np__0)
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& E = k2_nat_1(np__2,F)
& r1_xreal_0(np__1,F) )
& ~ ( A = k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))
& B = k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)) )
& ~ ( A = k1_real_1(k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)))
& B = k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)) )
& ~ ( A = k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))
& B = k1_real_1(k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))) )
& ~ ( A = k1_real_1(k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)))
& B = k1_real_1(k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))) )
& ~ ( A = k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))
& B = k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)) )
& ~ ( A = k1_real_1(k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)))
& B = k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)) )
& ~ ( A = k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))
& B = k1_real_1(k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))) )
& ~ ( A = k1_real_1(k2_power(E,k6_real_1(k5_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2)))
& B = k1_real_1(k2_power(E,k6_real_1(k3_real_1(C,k9_square_1(k5_real_1(k7_square_1(C),k4_real_1(np__4,D)))),np__2))) ) ) ) ) ) ) ) ).
fof(t17_polyeq_4,axiom,
$true ).
fof(t18_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] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( k3_real_1(k3_newton(A,E),k3_newton(B,E)) = C
& k5_real_1(k3_newton(A,E),k3_newton(B,E)) = D
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& E = k2_nat_1(np__2,F)
& r1_xreal_0(np__1,F) )
& ~ r1_xreal_0(C,np__0)
& ~ r1_xreal_0(k3_real_1(C,D),np__0)
& ~ r1_xreal_0(k5_real_1(C,D),np__0)
& ~ ( A = k2_power(E,k6_real_1(k3_real_1(C,D),np__2))
& B = k2_power(E,k6_real_1(k5_real_1(C,D),np__2)) )
& ~ ( A = k2_power(E,k6_real_1(k3_real_1(C,D),np__2))
& B = k1_real_1(k2_power(E,k6_real_1(k5_real_1(C,D),np__2))) )
& ~ ( A = k1_real_1(k2_power(E,k6_real_1(k3_real_1(C,D),np__2)))
& B = k2_power(E,k6_real_1(k5_real_1(C,D),np__2)) )
& ~ ( A = k1_real_1(k2_power(E,k6_real_1(k3_real_1(C,D),np__2)))
& B = k1_real_1(k2_power(E,k6_real_1(k5_real_1(C,D),np__2))) ) ) ) ) ) ) ) ).
fof(t19_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] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( k3_real_1(k4_real_1(A,k3_newton(B,F)),k4_real_1(C,k3_newton(D,F))) = E
& k4_real_1(B,D) = np__0
& ? [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
& F = k1_nat_1(k2_nat_1(np__2,G),np__1) )
& k4_real_1(A,C) != np__0
& ~ ( B = np__0
& D = k2_power(F,k6_real_1(E,C)) )
& ~ ( B = k2_power(F,k6_real_1(E,A))
& D = np__0 ) ) ) ) ) ) ) ) ).
fof(t20_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] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( k3_real_1(k4_real_1(A,k3_newton(B,F)),k4_real_1(C,k3_newton(D,F))) = E
& k4_real_1(B,D) = np__0
& ? [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
& F = k2_nat_1(np__2,G)
& r1_xreal_0(np__1,G) )
& ~ r1_xreal_0(k6_real_1(E,C),np__0)
& ~ r1_xreal_0(k6_real_1(E,A),np__0)
& k4_real_1(A,C) != np__0
& ~ ( B = np__0
& D = k2_power(F,k6_real_1(E,C)) )
& ~ ( B = np__0
& D = k1_real_1(k2_power(F,k6_real_1(E,C))) )
& ~ ( B = k2_power(F,k6_real_1(E,A))
& D = np__0 )
& ~ ( B = k1_real_1(k2_power(F,k6_real_1(E,A)))
& D = np__0 ) ) ) ) ) ) ) ) ).
fof(t21_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] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( ( k4_real_1(A,k3_newton(B,F)) = C
& k4_real_1(B,D) = E )
=> ( ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> F != k1_nat_1(k2_nat_1(np__2,G),np__1) )
| k4_real_1(C,A) = np__0
| ( B = k2_power(F,k6_real_1(C,A))
& D = k4_real_1(E,k2_power(F,k6_real_1(A,C))) ) ) ) ) ) ) ) ) ) ).
fof(t22_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] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ~ ( k4_real_1(A,k3_newton(B,F)) = C
& k4_real_1(B,D) = E
& ? [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
& F = k2_nat_1(np__2,G)
& r1_xreal_0(np__1,G) )
& ~ r1_xreal_0(k6_real_1(C,A),np__0)
& A != np__0
& ~ ( B = k2_power(F,k6_real_1(C,A))
& D = k4_real_1(E,k2_power(F,k6_real_1(A,C))) )
& ~ ( B = k1_real_1(k2_power(F,k6_real_1(C,A)))
& D = k1_real_1(k4_real_1(E,k2_power(F,k6_real_1(A,C)))) ) ) ) ) ) ) ) ) ).
fof(t23_polyeq_4,axiom,
$true ).
fof(t24_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( k4_power(A,B) = np__1
=> ( r1_xreal_0(A,np__0)
| A = np__1
| B = np__0 ) ) ) ) ).
fof(t25_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( k4_power(A,B) = A
=> ( r1_xreal_0(A,np__0)
| A = np__1
| B = np__1 ) ) ) ) ).
fof(t26_polyeq_4,axiom,
$true ).
fof(t27_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( k6_power(A,C) = np__0
=> ( r1_xreal_0(A,np__0)
| A = np__1
| r1_xreal_0(C,np__0)
| C = np__1 ) ) ) ) ) ).
fof(t28_polyeq_4,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( k6_power(A,C) = np__1
=> ( r1_xreal_0(A,np__0)
| A = np__1
| r1_xreal_0(C,np__0)
| C = A ) ) ) ) ) ).
fof(dt_k1_polyeq_4,axiom,
$true ).
%------------------------------------------------------------------------------