SET007 Axioms: SET007+904.ax
%------------------------------------------------------------------------------
% File : SET007+904 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Formulas And Identities of Inverse Hyperbolic Functions
% 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 : sin_cos7 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 89 ( 0 unt; 0 def)
% Number of atoms : 308 ( 69 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 315 ( 96 ~; 7 |; 64 &)
% ( 0 <=>; 148 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 8 ( 2 avg)
% Number of predicates : 3 ( 2 usr; 0 prp; 1-2 aty)
% Number of functors : 40 ( 40 usr; 11 con; 0-4 aty)
% Number of variables : 111 ( 111 !; 0 ?)
% 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_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(A,np__0)
=> k7_xcmplx_0(np__1,A) = k3_power(A,k7_binop_2(np__1)) ) ) ).
fof(t2_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__1)
& r1_xreal_0(np__1,k5_square_1(k7_xcmplx_0(k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1)),A))) ) ) ).
fof(t3_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ r1_xreal_0(np__1,k5_square_1(k7_xcmplx_0(A,k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1))))) ) ).
fof(t4_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ r1_xreal_0(k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1)),np__0) ) ).
fof(t5_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ r1_xreal_0(k2_xcmplx_0(k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1)),A),np__0) ) ).
fof(t6_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(np__1,B) )
=> r1_xreal_0(np__0,k7_xcmplx_0(k2_xcmplx_0(B,np__1),A)) ) ) ) ).
fof(t7_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(np__1,B) )
=> r1_xreal_0(np__0,k7_xcmplx_0(k6_xcmplx_0(B,np__1),A)) ) ) ) ).
fof(t8_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,A)
=> r1_xreal_0(np__1,k8_square_1(k7_xcmplx_0(k2_xcmplx_0(A,np__1),np__2))) ) ) ).
fof(t9_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(np__1,B) )
=> r1_xreal_0(np__0,k7_xcmplx_0(k6_xcmplx_0(k5_square_1(B),np__1),A)) ) ) ) ).
fof(t10_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(k2_xcmplx_0(k8_square_1(k7_xcmplx_0(k2_xcmplx_0(A,np__1),np__2)),k8_square_1(k7_xcmplx_0(k6_xcmplx_0(A,np__1),np__2))),np__0) ) ) ).
fof(t11_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(np__1,k5_square_1(A))
=> ( ~ r1_xreal_0(k2_xcmplx_0(A,np__1),np__0)
& ~ r1_xreal_0(k6_xcmplx_0(np__1,A),np__0) ) ) ) ).
fof(t12_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( A != np__1
& r1_xreal_0(k5_square_1(k6_xcmplx_0(np__1,A)),np__0) ) ) ).
fof(t13_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(np__1,k5_square_1(A))
=> r1_xreal_0(np__0,k7_xcmplx_0(k2_xcmplx_0(k5_square_1(A),np__1),k6_xcmplx_0(np__1,k5_square_1(A)))) ) ) ).
fof(t14_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(np__1,k5_square_1(A))
& r1_xreal_0(np__1,k5_square_1(k7_xcmplx_0(k3_xcmplx_0(np__2,A),k2_xcmplx_0(np__1,k5_square_1(A))))) ) ) ).
fof(t15_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A)
& r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(np__1,A),k6_xcmplx_0(np__1,A)),np__0) ) ) ).
fof(t16_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,k5_square_1(A)) ) ) ).
fof(t17_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A)
& r1_xreal_0(k7_xcmplx_0(np__1,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A)))),np__1) ) ) ).
fof(t18_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A)
& r1_xreal_0(k7_xcmplx_0(k3_xcmplx_0(np__2,A),k6_xcmplx_0(np__1,k5_square_1(A))),np__0) ) ) ).
fof(t19_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A)
& r1_xreal_0(k5_square_1(k6_xcmplx_0(np__1,k5_square_1(A))),np__0) ) ) ).
fof(t20_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A)
& r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(np__1,k5_square_1(A)),k6_xcmplx_0(np__1,k5_square_1(A))),np__1) ) ) ).
fof(t21_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(k5_square_1(A),np__1)
& r1_xreal_0(np__1,k5_square_1(k7_xcmplx_0(np__1,A))) ) ) ).
fof(t22_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(A,np__1)
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(np__0,k6_xcmplx_0(np__1,k5_square_1(A))) ) ) ) ).
fof(t23_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(k2_xcmplx_0(A,k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1))),np__0) ) ) ).
fof(t24_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B) )
=> r1_xreal_0(np__0,k2_xcmplx_0(k3_xcmplx_0(A,k8_square_1(k6_xcmplx_0(k5_square_1(B),np__1))),k3_xcmplx_0(B,k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1))))) ) ) ) ).
fof(t25_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(k18_complex1(B),k18_complex1(A))
& r1_xreal_0(k6_xcmplx_0(B,k8_square_1(k6_xcmplx_0(k5_square_1(B),np__1))),np__0) ) ) ) ).
fof(t26_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(k18_complex1(B),k18_complex1(A)) )
=> r1_xreal_0(np__0,k6_xcmplx_0(k3_xcmplx_0(B,k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1))),k3_xcmplx_0(A,k8_square_1(k6_xcmplx_0(k5_square_1(B),np__1))))) ) ) ) ).
fof(t27_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__1,k5_square_1(A))
& ~ r1_xreal_0(np__1,k5_square_1(B))
& k3_xcmplx_0(A,B) = k7_binop_2(np__1) ) ) ) ).
fof(t28_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__1,k5_square_1(A))
& ~ r1_xreal_0(np__1,k5_square_1(B))
& k3_xcmplx_0(A,B) = np__1 ) ) ) ).
fof(t29_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( A != np__0
& k27_sin_cos(A) = np__1 ) ) ).
fof(t30_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( np__0 != A
& k6_xcmplx_0(k5_square_1(k27_sin_cos(A)),np__1) = np__0 ) ) ).
fof(t31_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& r1_xreal_0(np__1,k7_xcmplx_0(k6_xcmplx_0(k5_square_1(A),np__1),k2_xcmplx_0(k5_square_1(A),np__1))) ) ) ).
fof(t32_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,k7_binop_2(np__1))
& ~ r1_xreal_0(np__1,A)
& r1_xreal_0(k7_xcmplx_0(k2_xcmplx_0(A,np__1),k6_xcmplx_0(np__1,A)),np__0) ) ) ).
fof(d1_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k1_sin_cos7(A) = k5_power(k8_power,k2_xcmplx_0(A,k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1)))) ) ).
fof(d2_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k2_sin_cos7(A) = k5_power(k8_power,k2_xcmplx_0(A,k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1)))) ) ).
fof(d3_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k3_sin_cos7(A) = k4_xcmplx_0(k5_power(k8_power,k2_xcmplx_0(A,k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1))))) ) ).
fof(d4_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k4_sin_cos7(A) = k3_xcmplx_0(k12_binop_2(np__1,np__2),k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(np__1,A),k6_xcmplx_0(np__1,A)))) ) ).
fof(d5_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k5_sin_cos7(A) = k3_xcmplx_0(k12_binop_2(np__1,np__2),k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(A,np__1),k6_xcmplx_0(A,np__1)))) ) ).
fof(d6_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k6_sin_cos7(A) = k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(np__1,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A)))),A)) ) ).
fof(d7_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k7_sin_cos7(A) = k4_xcmplx_0(k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(np__1,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A)))),A))) ) ).
fof(d8_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( ~ r1_xreal_0(A,np__0)
=> k8_sin_cos7(A) = k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(np__1,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),A)) )
& ( ~ r1_xreal_0(np__0,A)
=> k8_sin_cos7(A) = k5_power(k8_power,k7_xcmplx_0(k6_xcmplx_0(np__1,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),A)) ) ) ) ).
fof(t33_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__0,A)
=> k1_sin_cos7(A) = k2_sin_cos7(k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1))) ) ) ).
fof(t34_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(np__0,A)
=> k1_sin_cos7(A) = k3_sin_cos7(k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1))) ) ) ).
fof(t35_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k1_sin_cos7(A) = k4_sin_cos7(k7_xcmplx_0(A,k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1)))) ) ).
fof(t36_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,A)
=> k2_sin_cos7(A) = k1_sin_cos7(k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1))) ) ) ).
fof(t37_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(A,np__1)
=> k2_sin_cos7(A) = k4_sin_cos7(k7_xcmplx_0(k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1)),A)) ) ) ).
fof(t38_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,A)
=> k2_sin_cos7(A) = k3_xcmplx_0(np__2,k2_sin_cos7(k8_square_1(k7_xcmplx_0(k2_xcmplx_0(A,np__1),np__2)))) ) ) ).
fof(t39_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,A)
=> k3_sin_cos7(A) = k3_xcmplx_0(np__2,k3_sin_cos7(k8_square_1(k7_xcmplx_0(k2_xcmplx_0(A,np__1),np__2)))) ) ) ).
fof(t40_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,A)
=> k2_sin_cos7(A) = k3_xcmplx_0(np__2,k1_sin_cos7(k8_square_1(k7_xcmplx_0(k6_xcmplx_0(A,np__1),np__2)))) ) ) ).
fof(t41_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(np__1,k5_square_1(A))
=> k4_sin_cos7(A) = k1_sin_cos7(k7_xcmplx_0(A,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A))))) ) ) ).
fof(t42_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A)
& k4_sin_cos7(A) != k2_sin_cos7(k7_xcmplx_0(np__1,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A))))) ) ) ).
fof(t43_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(np__1,k5_square_1(A))
=> k4_sin_cos7(A) = k3_xcmplx_0(k12_binop_2(np__1,np__2),k1_sin_cos7(k7_xcmplx_0(k3_xcmplx_0(np__2,A),k6_xcmplx_0(np__1,k5_square_1(A))))) ) ) ).
fof(t44_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,A)
& k4_sin_cos7(A) != k3_xcmplx_0(k12_binop_2(np__1,np__2),k2_sin_cos7(k7_xcmplx_0(k2_xcmplx_0(np__1,k5_square_1(A)),k6_xcmplx_0(np__1,k5_square_1(A))))) ) ) ).
fof(t45_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(np__1,k5_square_1(A))
=> k4_sin_cos7(A) = k3_xcmplx_0(k12_binop_2(np__1,np__2),k4_sin_cos7(k7_xcmplx_0(k3_xcmplx_0(np__2,A),k2_xcmplx_0(np__1,k5_square_1(A))))) ) ) ).
fof(t46_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(k5_square_1(A),np__1)
=> k5_sin_cos7(A) = k4_sin_cos7(k7_xcmplx_0(np__1,A)) ) ) ).
fof(t47_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(A,np__1)
=> ( r1_xreal_0(A,np__0)
| k6_sin_cos7(A) = k2_sin_cos7(k7_xcmplx_0(np__1,A)) ) ) ) ).
fof(t48_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(A,np__1)
=> ( r1_xreal_0(A,np__0)
| k7_sin_cos7(A) = k3_sin_cos7(k7_xcmplx_0(np__1,A)) ) ) ) ).
fof(t49_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(A,np__0)
=> k8_sin_cos7(A) = k1_sin_cos7(k7_xcmplx_0(np__1,A)) ) ) ).
fof(t50_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(np__0,k2_xcmplx_0(k3_xcmplx_0(A,B),k3_xcmplx_0(k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1)),k8_square_1(k2_xcmplx_0(k5_square_1(B),np__1)))))
=> k2_xcmplx_0(k1_sin_cos7(A),k1_sin_cos7(B)) = k1_sin_cos7(k2_xcmplx_0(k3_xcmplx_0(A,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B)))),k3_xcmplx_0(B,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))))) ) ) ) ).
fof(t51_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k6_xcmplx_0(k1_sin_cos7(A),k1_sin_cos7(B)) = k1_sin_cos7(k6_xcmplx_0(k3_xcmplx_0(A,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(B)))),k3_xcmplx_0(B,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))))) ) ) ).
fof(t52_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B) )
=> k2_xcmplx_0(k2_sin_cos7(A),k2_sin_cos7(B)) = k2_sin_cos7(k2_xcmplx_0(k3_xcmplx_0(A,B),k8_square_1(k3_xcmplx_0(k6_xcmplx_0(k5_square_1(A),np__1),k6_xcmplx_0(k5_square_1(B),np__1))))) ) ) ) ).
fof(t53_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B) )
=> k2_xcmplx_0(k3_sin_cos7(A),k3_sin_cos7(B)) = k3_sin_cos7(k2_xcmplx_0(k3_xcmplx_0(A,B),k8_square_1(k3_xcmplx_0(k6_xcmplx_0(k5_square_1(A),np__1),k6_xcmplx_0(k5_square_1(B),np__1))))) ) ) ) ).
fof(t54_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(k18_complex1(B),k18_complex1(A)) )
=> k6_xcmplx_0(k2_sin_cos7(A),k2_sin_cos7(B)) = k2_sin_cos7(k6_xcmplx_0(k3_xcmplx_0(A,B),k8_square_1(k3_xcmplx_0(k6_xcmplx_0(k5_square_1(A),np__1),k6_xcmplx_0(k5_square_1(B),np__1))))) ) ) ) ).
fof(t55_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__1,B)
& r1_xreal_0(k18_complex1(B),k18_complex1(A)) )
=> k6_xcmplx_0(k3_sin_cos7(A),k3_sin_cos7(B)) = k3_sin_cos7(k6_xcmplx_0(k3_xcmplx_0(A,B),k8_square_1(k3_xcmplx_0(k6_xcmplx_0(k5_square_1(A),np__1),k6_xcmplx_0(k5_square_1(B),np__1))))) ) ) ) ).
fof(t56_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__1,k5_square_1(A))
& ~ r1_xreal_0(np__1,k5_square_1(B))
& k2_xcmplx_0(k4_sin_cos7(A),k4_sin_cos7(B)) != k4_sin_cos7(k7_xcmplx_0(k2_xcmplx_0(A,B),k2_xcmplx_0(np__1,k3_xcmplx_0(A,B)))) ) ) ) ).
fof(t57_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( ~ r1_xreal_0(np__1,k5_square_1(A))
& ~ r1_xreal_0(np__1,k5_square_1(B))
& k6_xcmplx_0(k4_sin_cos7(A),k4_sin_cos7(B)) != k4_sin_cos7(k7_xcmplx_0(k6_xcmplx_0(A,B),k6_xcmplx_0(np__1,k3_xcmplx_0(A,B)))) ) ) ) ).
fof(t58_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(A,np__1),k2_xcmplx_0(A,np__1))))
& k5_power(k8_power,A) != k3_xcmplx_0(np__2,k4_sin_cos7(k7_xcmplx_0(k6_xcmplx_0(A,np__1),k2_xcmplx_0(A,np__1)))) ) ) ).
fof(t59_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(np__1,k5_square_1(k7_xcmplx_0(k6_xcmplx_0(k5_square_1(A),np__1),k2_xcmplx_0(k5_square_1(A),np__1))))
& k5_power(k8_power,A) != k4_sin_cos7(k7_xcmplx_0(k6_xcmplx_0(k5_square_1(A),np__1),k2_xcmplx_0(k5_square_1(A),np__1))) ) ) ).
fof(t60_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,k7_xcmplx_0(k2_xcmplx_0(k5_square_1(A),np__1),k3_xcmplx_0(np__2,A)))
=> ( r1_xreal_0(A,np__1)
| k5_power(k8_power,A) = k2_sin_cos7(k7_xcmplx_0(k2_xcmplx_0(k5_square_1(A),np__1),k3_xcmplx_0(np__2,A))) ) ) ) ).
fof(t61_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r1_xreal_0(np__1,k7_xcmplx_0(k2_xcmplx_0(k5_square_1(A),np__1),k3_xcmplx_0(np__2,A)))
=> ( r1_xreal_0(A,np__0)
| r1_xreal_0(np__1,A)
| k5_power(k8_power,A) = k3_sin_cos7(k7_xcmplx_0(k2_xcmplx_0(k5_square_1(A),np__1),k3_xcmplx_0(np__2,A))) ) ) ) ).
fof(t62_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ~ r1_xreal_0(A,np__0)
=> k5_power(k8_power,A) = k1_sin_cos7(k7_xcmplx_0(k6_xcmplx_0(k5_square_1(A),np__1),k3_xcmplx_0(np__2,A))) ) ) ).
fof(t63_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k3_xcmplx_0(k12_binop_2(np__1,np__2),k6_xcmplx_0(k27_sin_cos(B),k27_sin_cos(k4_xcmplx_0(B))))
=> B = k5_power(k8_power,k2_xcmplx_0(A,k8_square_1(k2_xcmplx_0(k5_square_1(A),np__1)))) ) ) ) ).
fof(t64_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( A = k3_xcmplx_0(k12_binop_2(np__1,np__2),k2_xcmplx_0(k27_sin_cos(B),k27_sin_cos(k4_xcmplx_0(B))))
& r1_xreal_0(np__1,A)
& B != k5_power(k8_power,k2_xcmplx_0(A,k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1))))
& B != k4_xcmplx_0(k5_power(k8_power,k2_xcmplx_0(A,k8_square_1(k6_xcmplx_0(k5_square_1(A),np__1))))) ) ) ) ).
fof(t65_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k7_xcmplx_0(k6_xcmplx_0(k27_sin_cos(B),k27_sin_cos(k4_xcmplx_0(B))),k2_xcmplx_0(k27_sin_cos(B),k27_sin_cos(k4_xcmplx_0(B))))
=> B = k3_xcmplx_0(k12_binop_2(np__1,np__2),k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(np__1,A),k6_xcmplx_0(np__1,A)))) ) ) ) ).
fof(t66_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( A = k7_xcmplx_0(k2_xcmplx_0(k27_sin_cos(B),k27_sin_cos(k4_xcmplx_0(B))),k6_xcmplx_0(k27_sin_cos(B),k27_sin_cos(k4_xcmplx_0(B))))
=> ( B = np__0
| B = k3_xcmplx_0(k12_binop_2(np__1,np__2),k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(A,np__1),k6_xcmplx_0(A,np__1)))) ) ) ) ) ).
fof(t67_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( A = k7_xcmplx_0(np__1,k7_xcmplx_0(k2_xcmplx_0(k27_sin_cos(B),k27_sin_cos(k4_xcmplx_0(B))),np__2))
& B != k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(np__1,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A)))),A))
& B != k4_xcmplx_0(k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(np__1,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A)))),A))) ) ) ) ).
fof(t68_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ~ ( A = k7_xcmplx_0(np__1,k7_xcmplx_0(k6_xcmplx_0(k27_sin_cos(B),k27_sin_cos(k4_xcmplx_0(B))),np__2))
& B != np__0
& B != k5_power(k8_power,k7_xcmplx_0(k2_xcmplx_0(np__1,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),A))
& B != k5_power(k8_power,k7_xcmplx_0(k6_xcmplx_0(np__1,k8_square_1(k2_xcmplx_0(np__1,k5_square_1(A)))),A)) ) ) ) ).
fof(t69_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k2_seq_1(k1_numbers,k1_numbers,k4_sin_cos2,k3_xcmplx_0(np__2,A)) = k9_binop_2(np__1,k11_binop_2(np__2,k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k1_sin_cos2,A)))) ) ).
fof(t70_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k4_sin_cos2,A)) = k9_binop_2(np__1,k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k1_sin_cos2,A))) ) ).
fof(t71_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k1_sin_cos2,A)) = k10_binop_2(k7_square_1(k2_seq_1(k1_numbers,k1_numbers,k4_sin_cos2,A)),np__1) ) ).
fof(t72_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k3_sin_cos2(k3_xcmplx_0(np__5,A)) = k9_binop_2(k9_binop_2(k11_binop_2(np__5,k3_sin_cos2(A)),k11_binop_2(np__20,k3_newton(k3_sin_cos2(A),np__3))),k11_binop_2(np__16,k3_newton(k3_sin_cos2(A),np__5))) ) ).
fof(t73_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> k6_sin_cos2(k3_xcmplx_0(np__5,A)) = k9_binop_2(k10_binop_2(k11_binop_2(np__5,k6_sin_cos2(A)),k11_binop_2(np__20,k3_newton(k6_sin_cos2(A),np__3))),k11_binop_2(np__16,k3_newton(k6_sin_cos2(A),np__5))) ) ).
fof(dt_k1_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> v1_xreal_0(k1_sin_cos7(A)) ) ).
fof(dt_k2_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> v1_xreal_0(k2_sin_cos7(A)) ) ).
fof(dt_k3_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> v1_xreal_0(k3_sin_cos7(A)) ) ).
fof(dt_k4_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> v1_xreal_0(k4_sin_cos7(A)) ) ).
fof(dt_k5_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> v1_xreal_0(k5_sin_cos7(A)) ) ).
fof(dt_k6_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> v1_xreal_0(k6_sin_cos7(A)) ) ).
fof(dt_k7_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> v1_xreal_0(k7_sin_cos7(A)) ) ).
fof(dt_k8_sin_cos7,axiom,
! [A] :
( v1_xreal_0(A)
=> v1_xreal_0(k8_sin_cos7(A)) ) ).
%------------------------------------------------------------------------------