SET007 Axioms: SET007+870.ax


%------------------------------------------------------------------------------
% File     : SET007+870 : TPTP v7.5.0. 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 unit)
%            Number of atoms       :  470 (  98 equality)
%            Maximal formula depth :   11 (   4 average)
%            Number of connectives :  392 (  75 ~  ;   3  |; 169  &)
%                                         (   0 <=>; 145 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   20 (   1 propositional; 0-3 arity)
%            Number of functors    :   47 (  12 constant; 0-6 arity)
%            Number of variables   :  114 (   0 singleton; 114 !;   0 ?)
%            Maximal term depth    :    6 (   2 average)
% 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) )).
%------------------------------------------------------------------------------