SET007 Axioms: SET007+904.ax


%------------------------------------------------------------------------------
% File     : SET007+904 : TPTP v7.5.0. 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 unit)
%            Number of atoms       :  308 (  69 equality)
%            Maximal formula depth :   10 (   5 average)
%            Number of connectives :  315 (  96 ~  ;   7  |;  64  &)
%                                         (   0 <=>; 148 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :    3 (   0 propositional; 1-2 arity)
%            Number of functors    :   40 (  11 constant; 0-4 arity)
%            Number of variables   :  111 (   0 singleton; 111 !;   0 ?)
%            Maximal term depth    :    8 (   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(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)) ) )).
%------------------------------------------------------------------------------