SET007 Axioms: SET007+870.ax
%------------------------------------------------------------------------------
% File : SET007+870 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Inverse Trigonometric Functions Arcsin and Arccos
% 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_cos6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 153 ( 42 unt; 0 def)
% Number of atoms : 470 ( 98 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 392 ( 75 ~; 3 |; 169 &)
% ( 0 <=>; 145 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 20 ( 18 usr; 1 prp; 0-3 aty)
% Number of functors : 47 ( 47 usr; 12 con; 0-6 aty)
% Number of variables : 114 ( 114 !; 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(fc1_sin_cos6,axiom,
( ~ v1_xboole_0(k31_sin_cos)
& v1_xcmplx_0(k31_sin_cos)
& v1_xreal_0(k31_sin_cos)
& v2_xreal_0(k31_sin_cos)
& ~ v3_xreal_0(k31_sin_cos) ) ).
fof(fc2_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2)))) ) ).
fof(fc3_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos)))) ) ).
fof(fc4_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),np__0)))
& v1_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),np__0)))
& v2_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),np__0))) ) ).
fof(fc5_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2)))) ) ).
fof(fc6_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos)))
& v1_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos)))
& v2_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos))) ) ).
fof(fc7_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos)))) ) ).
fof(fc8_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k1_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos)))) ) ).
fof(fc9_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2)))) ) ).
fof(fc10_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos)))) ) ).
fof(fc11_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),np__0)))
& v1_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),np__0)))
& v2_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),np__0))) ) ).
fof(fc12_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2)))) ) ).
fof(fc13_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos)))
& v1_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos)))
& v2_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos))) ) ).
fof(fc14_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos)))) ) ).
fof(fc15_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos))))
& v1_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos))))
& v2_funct_1(k7_relat_1(k18_sin_cos,k2_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos)))) ) ).
fof(fc16_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos)))
& v1_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos)))
& v2_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos))) ) ).
fof(fc17_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(np__2,k32_sin_cos))))
& v1_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(np__2,k32_sin_cos))))
& v2_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(np__2,k32_sin_cos)))) ) ).
fof(fc18_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2))))
& v1_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2))))
& v2_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2)))) ) ).
fof(fc19_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos)))
& v1_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos)))
& v2_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos))) ) ).
fof(fc20_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v1_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v2_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos)))) ) ).
fof(fc21_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos))))
& v1_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos))))
& v2_funct_1(k7_relat_1(k21_sin_cos,k1_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos)))) ) ).
fof(fc22_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(np__0,k32_sin_cos)))
& v1_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(np__0,k32_sin_cos)))
& v2_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(np__0,k32_sin_cos))) ) ).
fof(fc23_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(np__2,k32_sin_cos))))
& v1_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(np__2,k32_sin_cos))))
& v2_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(np__2,k32_sin_cos)))) ) ).
fof(fc24_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2))))
& v1_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2))))
& v2_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(np__0,k6_real_1(k32_sin_cos,np__2)))) ) ).
fof(fc25_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos)))
& v1_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos)))
& v2_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k32_sin_cos))) ) ).
fof(fc26_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v1_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))))
& v2_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos)))) ) ).
fof(fc27_sin_cos6,axiom,
( v1_relat_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos))))
& v1_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos))))
& v2_funct_1(k7_relat_1(k21_sin_cos,k2_rcomp_1(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k4_real_1(np__2,k32_sin_cos)))) ) ).
fof(fc28_sin_cos6,axiom,
( v1_relat_1(k1_sin_cos6)
& v1_funct_1(k1_sin_cos6)
& v2_funct_1(k1_sin_cos6) ) ).
fof(fc29_sin_cos6,axiom,
( v1_relat_1(k4_sin_cos6)
& v1_funct_1(k4_sin_cos6)
& v2_funct_1(k4_sin_cos6) ) ).
fof(t1_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( r1_xreal_0(np__0,A)
=> ( r1_xreal_0(B,A)
| k1_int_1(k7_xcmplx_0(A,B)) = np__0 ) ) ) ) ).
fof(t2_sin_cos6,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] :
( ( v2_funct_1(k7_relat_1(A,B))
& r1_tarski(C,B) )
=> v2_funct_1(k7_relat_1(A,C)) ) ) ).
fof(t3_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xreal_0(k1_real_1(np__1),k19_sin_cos(A)) ) ).
fof(t4_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xreal_0(k19_sin_cos(A),np__1) ) ).
fof(t5_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xreal_0(k1_real_1(np__1),k22_sin_cos(A)) ) ).
fof(t6_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> r1_xreal_0(k22_sin_cos(A),np__1) ) ).
fof(t7_sin_cos6,axiom,
( k20_sin_cos(k1_real_1(k6_real_1(k32_sin_cos,np__2))) = k1_real_1(np__1)
& k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k1_real_1(k6_real_1(k32_sin_cos,np__2))) = k1_real_1(np__1) ) ).
fof(t8_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,A) = k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k2_xcmplx_0(A,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))) ) ) ).
fof(t9_sin_cos6,axiom,
( k23_sin_cos(k1_real_1(k6_real_1(k32_sin_cos,np__2))) = np__0
& k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k1_real_1(k6_real_1(k32_sin_cos,np__2))) = np__0 ) ).
fof(t10_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,A) = k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k2_xcmplx_0(A,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))) ) ) ).
fof(t11_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))
& ~ r1_xreal_0(k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(k19_sin_cos(A),np__0) ) ) ) ).
fof(t12_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& ~ r1_xreal_0(k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(np__0,k19_sin_cos(A)) ) ) ) ).
fof(t13_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k2_xcmplx_0(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& ~ r1_xreal_0(k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(k22_sin_cos(A),np__0) ) ) ) ).
fof(t14_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& ~ r1_xreal_0(k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(np__0,k22_sin_cos(A)) ) ) ) ).
fof(t15_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& ~ r1_xreal_0(k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(k22_sin_cos(A),np__0) ) ) ) ).
fof(t16_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ( ( r1_xreal_0(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B),A)
& r1_xreal_0(A,k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))) )
=> r1_xreal_0(np__0,k19_sin_cos(A)) ) ) ) ).
fof(t17_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ( ( r1_xreal_0(k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(A,k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))) )
=> r1_xreal_0(k19_sin_cos(A),np__0) ) ) ) ).
fof(t18_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ( ( r1_xreal_0(k2_xcmplx_0(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(A,k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))) )
=> r1_xreal_0(np__0,k22_sin_cos(A)) ) ) ) ).
fof(t19_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ( ( r1_xreal_0(k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(A,k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))) )
=> r1_xreal_0(k22_sin_cos(A),np__0) ) ) ) ).
fof(t20_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ( ( r1_xreal_0(k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(A,k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))) )
=> r1_xreal_0(np__0,k22_sin_cos(A)) ) ) ) ).
fof(t21_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( r1_xreal_0(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B),A)
& ~ r1_xreal_0(k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& k19_sin_cos(A) = np__0
& A != k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)
& A != k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)) ) ) ) ).
fof(t22_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( r1_xreal_0(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B),A)
& ~ r1_xreal_0(k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& k22_sin_cos(A) = np__0
& A != k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))
& A != k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)) ) ) ) ).
fof(t23_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( k19_sin_cos(A) = k1_real_1(np__1)
=> A = k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k1_int_1(k7_xcmplx_0(A,k4_real_1(np__2,k32_sin_cos))))) ) ) ).
fof(t24_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( k19_sin_cos(A) = np__1
=> A = k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k1_int_1(k7_xcmplx_0(A,k4_real_1(np__2,k32_sin_cos))))) ) ) ).
fof(t25_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( k22_sin_cos(A) = k1_real_1(np__1)
=> A = k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k1_int_1(k7_xcmplx_0(A,k4_real_1(np__2,k32_sin_cos))))) ) ) ).
fof(t26_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( k22_sin_cos(A) = np__1
=> A = k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k1_int_1(k7_xcmplx_0(A,k4_real_1(np__2,k32_sin_cos)))) ) ) ).
fof(t27_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,k4_real_1(np__2,k32_sin_cos))
& k19_sin_cos(A) = k1_real_1(np__1) )
=> A = k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos) ) ) ).
fof(t28_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,k4_real_1(np__2,k32_sin_cos))
& k19_sin_cos(A) = np__1 )
=> A = k6_real_1(k32_sin_cos,np__2) ) ) ).
fof(t29_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,k4_real_1(np__2,k32_sin_cos))
& k22_sin_cos(A) = k1_real_1(np__1) )
=> A = k32_sin_cos ) ) ).
fof(t30_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( r1_xreal_0(np__0,A)
& ~ r1_xreal_0(k6_real_1(k32_sin_cos,np__2),A)
& r1_xreal_0(np__1,k19_sin_cos(A)) ) ) ).
fof(t31_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( r1_xreal_0(np__0,A)
& ~ r1_xreal_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),A)
& r1_xreal_0(k19_sin_cos(A),k1_real_1(np__1)) ) ) ).
fof(t32_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))
& r1_xreal_0(A,k4_real_1(np__2,k32_sin_cos))
& r1_xreal_0(k19_sin_cos(A),k1_real_1(np__1)) ) ) ).
fof(t33_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,k6_real_1(k32_sin_cos,np__2))
& r1_xreal_0(A,k4_real_1(np__2,k32_sin_cos))
& r1_xreal_0(np__1,k19_sin_cos(A)) ) ) ).
fof(t34_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(k4_real_1(np__2,k32_sin_cos),A)
& r1_xreal_0(np__1,k22_sin_cos(A)) ) ) ).
fof(t35_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( r1_xreal_0(np__0,A)
& ~ r1_xreal_0(k32_sin_cos,A)
& r1_xreal_0(k22_sin_cos(A),k1_real_1(np__1)) ) ) ).
fof(t36_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,k32_sin_cos)
& r1_xreal_0(A,k4_real_1(np__2,k32_sin_cos))
& r1_xreal_0(k22_sin_cos(A),k1_real_1(np__1)) ) ) ).
fof(t37_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( r1_xreal_0(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B),A)
& ~ r1_xreal_0(k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(np__1,k19_sin_cos(A)) ) ) ) ).
fof(t38_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( r1_xreal_0(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B),A)
& ~ r1_xreal_0(k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(k19_sin_cos(A),k1_real_1(np__1)) ) ) ) ).
fof(t39_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& r1_xreal_0(A,k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& r1_xreal_0(k19_sin_cos(A),k1_real_1(np__1)) ) ) ) ).
fof(t40_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& r1_xreal_0(A,k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& r1_xreal_0(np__1,k19_sin_cos(A)) ) ) ) ).
fof(t41_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B))
& ~ r1_xreal_0(k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(np__1,k22_sin_cos(A)) ) ) ) ).
fof(t42_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( r1_xreal_0(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B),A)
& ~ r1_xreal_0(k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)),A)
& r1_xreal_0(k22_sin_cos(A),k1_real_1(np__1)) ) ) ) ).
fof(t43_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_int_1(B)
=> ~ ( ~ r1_xreal_0(A,k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& r1_xreal_0(A,k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),B)))
& r1_xreal_0(k22_sin_cos(A),k1_real_1(np__1)) ) ) ) ).
fof(t44_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( k22_sin_cos(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)) = np__1
=> r2_hidden(A,k4_numbers) ) ) ).
fof(t45_sin_cos6,axiom,
k10_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))) = k1_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t46_sin_cos6,axiom,
k10_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))) = k2_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t47_sin_cos6,axiom,
k10_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k6_real_1(k32_sin_cos,np__2),k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))) = k1_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t48_sin_cos6,axiom,
k10_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k2_rcomp_1(k6_real_1(k32_sin_cos,np__2),k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos))) = k2_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t49_sin_cos6,axiom,
k10_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos)) = k1_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t50_sin_cos6,axiom,
k10_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k2_rcomp_1(np__0,k32_sin_cos)) = k2_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t51_sin_cos6,axiom,
k10_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(k32_sin_cos,k4_real_1(np__2,k32_sin_cos))) = k1_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t52_sin_cos6,axiom,
k10_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k2_rcomp_1(k32_sin_cos,k4_real_1(np__2,k32_sin_cos))) = k2_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t53_sin_cos6,axiom,
! [A] :
( v1_int_1(A)
=> r1_rfunct_2(k18_sin_cos,k1_rcomp_1(k2_xcmplx_0(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)),k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)))) ) ).
fof(t54_sin_cos6,axiom,
! [A] :
( v1_int_1(A)
=> r2_rfunct_2(k18_sin_cos,k1_rcomp_1(k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)),k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)))) ) ).
fof(t55_sin_cos6,axiom,
! [A] :
( v1_int_1(A)
=> r2_rfunct_2(k21_sin_cos,k1_rcomp_1(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A),k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)))) ) ).
fof(t56_sin_cos6,axiom,
! [A] :
( v1_int_1(A)
=> r1_rfunct_2(k21_sin_cos,k1_rcomp_1(k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)),k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)))) ) ).
fof(t57_sin_cos6,axiom,
! [A] :
( v1_int_1(A)
=> v2_funct_1(k8_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k2_xcmplx_0(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)),k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A))))) ) ).
fof(t58_sin_cos6,axiom,
! [A] :
( v1_int_1(A)
=> v2_funct_1(k8_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k2_xcmplx_0(k6_real_1(k32_sin_cos,np__2),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)),k2_xcmplx_0(k4_real_1(k6_real_1(np__3,np__2),k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A))))) ) ).
fof(t59_sin_cos6,axiom,
! [A] :
( v1_int_1(A)
=> v2_funct_1(k8_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A),k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A))))) ) ).
fof(t60_sin_cos6,axiom,
! [A] :
( v1_int_1(A)
=> v2_funct_1(k8_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(k2_xcmplx_0(k32_sin_cos,k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A)),k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),A))))) ) ).
fof(t61_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ! [C] :
( v1_int_1(C)
=> ( ( r1_xreal_0(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),C),A)
& r1_xreal_0(k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),C),B)
& k19_sin_cos(A) = k19_sin_cos(B)
& k22_sin_cos(A) = k22_sin_cos(B) )
=> ( r1_xreal_0(k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),C)),A)
| r1_xreal_0(k2_xcmplx_0(k4_real_1(np__2,k32_sin_cos),k3_xcmplx_0(k4_real_1(np__2,k32_sin_cos),C)),B)
| A = B ) ) ) ) ) ).
fof(d1_sin_cos6,axiom,
k1_sin_cos6 = k2_partfun2(k1_numbers,k1_numbers,k8_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2)))) ).
fof(d2_sin_cos6,axiom,
! [A] : k2_sin_cos6(A) = k2_seq_1(k1_numbers,k1_numbers,k1_sin_cos6,A) ).
fof(t62_sin_cos6,axiom,
k2_funct_1(k1_sin_cos6) = k8_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))) ).
fof(t63_sin_cos6,axiom,
k5_relset_1(k1_numbers,k1_numbers,k1_sin_cos6) = k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2)) ).
fof(t64_sin_cos6,axiom,
k4_relset_1(k1_numbers,k1_numbers,k1_sin_cos6) = k1_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t65_sin_cos6,axiom,
k5_relat_1(k1_sin_cos6,k8_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2)))) = k1_partfun2(k1_numbers,k1_rcomp_1(k1_real_1(np__1),np__1)) ).
fof(t66_sin_cos6,axiom,
k7_relset_1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_sin_cos6,k8_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2)))) = k1_partfun2(k1_numbers,k1_rcomp_1(k1_real_1(np__1),np__1)) ).
fof(t67_sin_cos6,axiom,
k7_relset_1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k8_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))),k1_sin_cos6) = k1_partfun2(k1_numbers,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))) ).
fof(t68_sin_cos6,axiom,
k5_relat_1(k8_relset_1(k1_numbers,k1_numbers,k18_sin_cos,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))),k1_sin_cos6) = k1_partfun2(k1_numbers,k1_rcomp_1(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k6_real_1(k32_sin_cos,np__2))) ).
fof(t69_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k20_sin_cos(k3_sin_cos6(A)) = A ) ) ).
fof(t70_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(k6_real_1(k32_sin_cos,np__2)),A)
& r1_xreal_0(A,k6_real_1(k32_sin_cos,np__2)) )
=> k3_sin_cos6(k19_sin_cos(A)) = A ) ) ).
fof(t71_sin_cos6,axiom,
k3_sin_cos6(k1_real_1(np__1)) = k1_real_1(k6_real_1(k32_sin_cos,np__2)) ).
fof(t72_sin_cos6,axiom,
k3_sin_cos6(np__0) = np__0 ).
fof(t73_sin_cos6,axiom,
k3_sin_cos6(np__1) = k6_real_1(k32_sin_cos,np__2) ).
fof(t74_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& k3_sin_cos6(A) = k1_real_1(k6_real_1(k32_sin_cos,np__2)) )
=> A = k1_real_1(np__1) ) ) ).
fof(t75_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& k3_sin_cos6(A) = np__0 )
=> A = np__0 ) ) ).
fof(t76_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& k3_sin_cos6(A) = k6_real_1(k32_sin_cos,np__2) )
=> A = np__1 ) ) ).
fof(t77_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> ( r1_xreal_0(k1_real_1(k6_real_1(k32_sin_cos,np__2)),k3_sin_cos6(A))
& r1_xreal_0(k3_sin_cos6(A),k6_real_1(k32_sin_cos,np__2)) ) ) ) ).
fof(t78_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ ( ~ r1_xreal_0(k3_sin_cos6(A),k1_real_1(k6_real_1(k32_sin_cos,np__2)))
& ~ r1_xreal_0(k6_real_1(k32_sin_cos,np__2),k3_sin_cos6(A)) ) ) ) ).
fof(t79_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k3_sin_cos6(A) = k1_real_1(k3_sin_cos6(k4_xcmplx_0(A))) ) ) ).
fof(t80_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& k2_xcmplx_0(k5_square_1(B),k5_square_1(A)) = np__1 )
=> k23_sin_cos(k3_sin_cos6(B)) = A ) ) ) ).
fof(t81_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(A,np__0)
& k2_xcmplx_0(k5_square_1(B),k5_square_1(A)) = np__1 )
=> k23_sin_cos(k3_sin_cos6(B)) = k4_xcmplx_0(A) ) ) ) ).
fof(t82_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k23_sin_cos(k3_sin_cos6(A)) = k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A))) ) ) ).
fof(t83_sin_cos6,axiom,
r1_rfunct_2(k1_sin_cos6,k1_rcomp_1(k1_real_1(np__1),np__1)) ).
fof(t84_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r2_fdiff_1(k1_sin_cos6,k2_rcomp_1(k1_real_1(np__1),np__1))
& ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& k1_fdiff_1(k1_sin_cos6,A) != k7_xcmplx_0(np__1,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A)))) ) ) ) ).
fof(t85_sin_cos6,axiom,
r2_fcont_1(k1_sin_cos6,k1_rcomp_1(k1_real_1(np__1),np__1)) ).
fof(d3_sin_cos6,axiom,
k4_sin_cos6 = k2_partfun2(k1_numbers,k1_numbers,k8_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos))) ).
fof(d4_sin_cos6,axiom,
! [A] : k5_sin_cos6(A) = k2_seq_1(k1_numbers,k1_numbers,k4_sin_cos6,A) ).
fof(t86_sin_cos6,axiom,
k2_funct_1(k4_sin_cos6) = k8_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos)) ).
fof(t87_sin_cos6,axiom,
k5_relset_1(k1_numbers,k1_numbers,k4_sin_cos6) = k1_rcomp_1(np__0,k32_sin_cos) ).
fof(t88_sin_cos6,axiom,
k4_relset_1(k1_numbers,k1_numbers,k4_sin_cos6) = k1_rcomp_1(k1_real_1(np__1),np__1) ).
fof(t89_sin_cos6,axiom,
k5_relat_1(k4_sin_cos6,k8_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos))) = k1_partfun2(k1_numbers,k1_rcomp_1(k1_real_1(np__1),np__1)) ).
fof(t90_sin_cos6,axiom,
k7_relset_1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k4_sin_cos6,k8_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos))) = k1_partfun2(k1_numbers,k1_rcomp_1(k1_real_1(np__1),np__1)) ).
fof(t91_sin_cos6,axiom,
k7_relset_1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k8_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos)),k4_sin_cos6) = k1_partfun2(k1_numbers,k1_rcomp_1(np__0,k32_sin_cos)) ).
fof(t92_sin_cos6,axiom,
k5_relat_1(k8_relset_1(k1_numbers,k1_numbers,k21_sin_cos,k1_rcomp_1(np__0,k32_sin_cos)),k4_sin_cos6) = k1_partfun2(k1_numbers,k1_rcomp_1(np__0,k32_sin_cos)) ).
fof(t93_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k23_sin_cos(k6_sin_cos6(A)) = A ) ) ).
fof(t94_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(np__0,A)
& r1_xreal_0(A,k32_sin_cos) )
=> k6_sin_cos6(k22_sin_cos(A)) = A ) ) ).
fof(t95_sin_cos6,axiom,
k6_sin_cos6(k1_real_1(np__1)) = k32_sin_cos ).
fof(t96_sin_cos6,axiom,
k6_sin_cos6(np__0) = k6_real_1(k32_sin_cos,np__2) ).
fof(t97_sin_cos6,axiom,
k6_sin_cos6(np__1) = np__0 ).
fof(t98_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& k6_sin_cos6(A) = np__0 )
=> A = np__1 ) ) ).
fof(t99_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& k6_sin_cos6(A) = k6_real_1(k32_sin_cos,np__2) )
=> A = np__0 ) ) ).
fof(t100_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1)
& k6_sin_cos6(A) = k32_sin_cos )
=> A = k1_real_1(np__1) ) ) ).
fof(t101_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> ( r1_xreal_0(np__0,k6_sin_cos6(A))
& r1_xreal_0(k6_sin_cos6(A),k32_sin_cos) ) ) ) ).
fof(t102_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& ~ ( ~ r1_xreal_0(k6_sin_cos6(A),np__0)
& ~ r1_xreal_0(k32_sin_cos,k6_sin_cos6(A)) ) ) ) ).
fof(t103_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k6_sin_cos6(A) = k5_real_1(k32_sin_cos,k6_sin_cos6(k4_xcmplx_0(A))) ) ) ).
fof(t104_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(np__0,A)
& k2_xcmplx_0(k5_square_1(B),k5_square_1(A)) = np__1 )
=> k20_sin_cos(k6_sin_cos6(B)) = A ) ) ) ).
fof(t105_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> ( ( r1_xreal_0(A,np__0)
& k2_xcmplx_0(k5_square_1(B),k5_square_1(A)) = np__1 )
=> k20_sin_cos(k6_sin_cos6(B)) = k4_xcmplx_0(A) ) ) ) ).
fof(t106_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k20_sin_cos(k6_sin_cos6(A)) = k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A))) ) ) ).
fof(t107_sin_cos6,axiom,
r2_rfunct_2(k4_sin_cos6,k1_rcomp_1(k1_real_1(np__1),np__1)) ).
fof(t108_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( r2_fdiff_1(k4_sin_cos6,k2_rcomp_1(k1_real_1(np__1),np__1))
& ~ ( ~ r1_xreal_0(A,k1_real_1(np__1))
& ~ r1_xreal_0(np__1,A)
& k1_fdiff_1(k4_sin_cos6,A) != k4_xcmplx_0(k7_xcmplx_0(np__1,k8_square_1(k6_xcmplx_0(np__1,k5_square_1(A))))) ) ) ) ).
fof(t109_sin_cos6,axiom,
r2_fcont_1(k4_sin_cos6,k1_rcomp_1(k1_real_1(np__1),np__1)) ).
fof(t110_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k3_real_1(k3_sin_cos6(A),k6_sin_cos6(A)) = k6_real_1(k32_sin_cos,np__2) ) ) ).
fof(t111_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k5_real_1(k6_sin_cos6(k4_xcmplx_0(A)),k3_sin_cos6(A)) = k6_real_1(k32_sin_cos,np__2) ) ) ).
fof(t112_sin_cos6,axiom,
! [A] :
( v1_xreal_0(A)
=> ( ( r1_xreal_0(k1_real_1(np__1),A)
& r1_xreal_0(A,np__1) )
=> k5_real_1(k6_sin_cos6(A),k3_sin_cos6(k4_xcmplx_0(A))) = k6_real_1(k32_sin_cos,np__2) ) ) ).
fof(dt_k1_sin_cos6,axiom,
( v1_funct_1(k1_sin_cos6)
& m2_relset_1(k1_sin_cos6,k1_numbers,k1_numbers) ) ).
fof(dt_k2_sin_cos6,axiom,
$true ).
fof(dt_k3_sin_cos6,axiom,
! [A] : m1_subset_1(k3_sin_cos6(A),k1_numbers) ).
fof(redefinition_k3_sin_cos6,axiom,
! [A] : k3_sin_cos6(A) = k2_sin_cos6(A) ).
fof(dt_k4_sin_cos6,axiom,
( v1_funct_1(k4_sin_cos6)
& m2_relset_1(k4_sin_cos6,k1_numbers,k1_numbers) ) ).
fof(dt_k5_sin_cos6,axiom,
$true ).
fof(dt_k6_sin_cos6,axiom,
! [A] : m1_subset_1(k6_sin_cos6(A),k1_numbers) ).
fof(redefinition_k6_sin_cos6,axiom,
! [A] : k6_sin_cos6(A) = k5_sin_cos6(A) ).
%------------------------------------------------------------------------------