SET007 Axioms: SET007+927.ax
%------------------------------------------------------------------------------
% File : SET007+927 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Several Differentiable Formulas of Special Functions - Part II
% 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 : fdiff_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 50 ( 0 unt; 0 def)
% Number of atoms : 697 ( 132 equ)
% Maximal formula atoms : 21 ( 13 avg)
% Number of connectives : 673 ( 26 ~; 20 |; 257 &)
% ( 0 <=>; 370 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 13 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 0 prp; 1-3 aty)
% Number of functors : 39 ( 39 usr; 11 con; 0-6 aty)
% Number of variables : 230 ( 230 !; 0 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(t1_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,k4_real_1(B,k6_power(k8_power,A))) = k13_prepower(A,B) ) ) ) ).
fof(t2_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,k1_real_1(k4_real_1(B,k6_power(k8_power,A)))) = k13_prepower(A,k1_real_1(B)) ) ) ) ).
fof(t3_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k7_seq_1(k1_numbers,k1_numbers,C,D)))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> k2_seq_1(k1_numbers,k1_numbers,C,E) = k7_square_1(A) ) )
& D = k1_taylor_1(np__2) )
=> ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,C,D),B)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,C,D),B),E) = k1_real_1(k4_real_1(np__2,E)) ) ) ) ) ) ) ) ) ).
fof(t4_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D))))
& D = k1_taylor_1(np__2)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k7_square_1(A)
& k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,C,D),E) != np__0 ) ) ) )
=> ( r2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D)),B)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,D),k7_seq_1(k1_numbers,k1_numbers,C,D)),B),E) = k6_real_1(k4_real_1(k4_real_1(np__4,k7_square_1(A)),E),k7_square_1(k5_real_1(k7_square_1(A),k3_prepower(E,np__2)))) ) ) ) ) ) ) ) ) ).
fof(t5_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(C))
& C = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,D,E),k7_seq_1(k1_numbers,k1_numbers,D,E)),k2_taylor_1(k8_power))
& E = k1_taylor_1(np__2)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,B)
=> ( k2_seq_1(k1_numbers,k1_numbers,D,F) = k7_square_1(A)
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,D,E),F),np__0)
& A != np__0 ) ) ) )
=> ( r2_fdiff_1(C,B)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(C,B),F) = k6_real_1(k4_real_1(k4_real_1(np__4,k7_square_1(A)),F),k5_real_1(k3_prepower(A,np__4),k3_prepower(F,np__4))) ) ) ) ) ) ) ) ) ) ).
fof(t6_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ! [E] :
( ( v1_funct_1(E)
& m2_relset_1(E,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,C,k6_real_1(np__1,k4_real_1(np__4,k7_square_1(A))))))
& C = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,D,E),k7_seq_1(k1_numbers,k1_numbers,D,E)),k2_taylor_1(k8_power))
& E = k1_taylor_1(np__2)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,B)
=> ( k2_seq_1(k1_numbers,k1_numbers,D,F) = k7_square_1(A)
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,D,E),F),np__0)
& A != np__0 ) ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,C,k6_real_1(np__1,k4_real_1(np__4,k7_square_1(A)))),B)
& ! [F] :
( m1_subset_1(F,k1_numbers)
=> ( r2_hidden(F,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,C,k6_real_1(np__1,k4_real_1(np__4,k7_square_1(A)))),B),F) = k6_real_1(F,k5_real_1(k3_prepower(A,np__4),k3_prepower(F,np__4))) ) ) ) ) ) ) ) ) ) ).
fof(t7_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k2_rfunct_1(k1_numbers,k1_numbers,B,k6_seq_1(k1_numbers,k1_numbers,C,B))))
& B = k1_taylor_1(np__2)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1
& D != np__0 ) ) ) )
=> ( r2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,B,k6_seq_1(k1_numbers,k1_numbers,C,B)),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k2_rfunct_1(k1_numbers,k1_numbers,B,k6_seq_1(k1_numbers,k1_numbers,C,B)),A),D) = k6_real_1(k4_real_1(np__2,D),k7_square_1(k3_real_1(np__1,k7_square_1(D)))) ) ) ) ) ) ) ) ).
fof(t8_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,B,k6_real_1(np__1,np__2))))
& B = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,C,k6_seq_1(k1_numbers,k1_numbers,D,C)),k2_taylor_1(k8_power))
& C = k1_taylor_1(np__2)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,D,E) = np__1
& E != np__0 ) ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,B,k6_real_1(np__1,np__2)),A)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,B,k6_real_1(np__1,np__2)),A),E) = k6_real_1(np__1,k4_real_1(E,k3_real_1(np__1,k7_square_1(E)))) ) ) ) ) ) ) ) ) ).
fof(t9_fdiff_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( ( r1_tarski(B,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_taylor_1(A),k2_taylor_1(k8_power))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ~ ( r2_hidden(C,B)
& r1_xreal_0(C,np__0) ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_taylor_1(A),k2_taylor_1(k8_power)),B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k1_taylor_1(A),k2_taylor_1(k8_power)),B),C) = k6_real_1(A,C) ) ) ) ) ) ) ).
fof(t10_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k6_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,C,B),k2_taylor_1(k8_power)))))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,B,D) = D
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),np__0)
& k2_seq_1(k1_numbers,k1_numbers,C,D) = k5_real_1(D,np__1)
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,C,D),np__0) ) ) ) )
=> ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,C,B),k2_taylor_1(k8_power))),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k4_rfunct_1(k1_numbers,k1_numbers,B),k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,C,B),k2_taylor_1(k8_power))),A),D) = k6_real_1(np__1,k4_real_1(k7_square_1(D),k5_real_1(D,np__1))) ) ) ) ) ) ) ) ).
fof(t11_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(D,k6_power(k8_power,A)) ) ) )
=> ( r1_xreal_0(A,np__0)
| ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),B),D) = k4_real_1(k13_prepower(A,D),k6_power(k8_power,A)) ) ) ) ) ) ) ) ) ).
fof(t12_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),D),k6_real_1(np__1,k6_power(k8_power,A)))))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k4_real_1(E,k6_power(k8_power,A))
& k2_seq_1(k1_numbers,k1_numbers,D,E) = k5_real_1(E,k6_real_1(np__1,k6_power(k8_power,A))) ) ) ) )
=> ( r1_xreal_0(A,np__0)
| A = np__1
| ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),D),k6_real_1(np__1,k6_power(k8_power,A))),B)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),D),k6_real_1(np__1,k6_power(k8_power,A))),B),E) = k4_real_1(E,k13_prepower(A,E)) ) ) ) ) ) ) ) ) ) ).
fof(t13_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),k26_sin_cos),k6_real_1(np__1,k3_real_1(np__1,k6_power(k8_power,A))))))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(D,k6_power(k8_power,A)) ) ) )
=> ( r1_xreal_0(A,np__0)
| A = k6_real_1(np__1,k8_power)
| ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),k26_sin_cos),k6_real_1(np__1,k3_real_1(np__1,k6_power(k8_power,A)))),B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),k26_sin_cos),k6_real_1(np__1,k3_real_1(np__1,k6_power(k8_power,A)))),B),D) = k4_real_1(k13_prepower(A,D),k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D)) ) ) ) ) ) ) ) ) ).
fof(t14_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k26_sin_cos)))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = k1_real_1(C) ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k26_sin_cos),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k26_sin_cos),A),C) = k1_real_1(k28_sin_cos(k1_real_1(C))) ) ) ) ) ) ) ).
fof(t15_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos))))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,B,D) = k5_real_1(k1_real_1(D),np__1)
& k2_seq_1(k1_numbers,k1_numbers,C,D) = k1_real_1(D) ) ) ) )
=> ( r2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k8_seq_1(k1_numbers,k1_numbers,B,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),A),D) = k6_real_1(D,k28_sin_cos(D)) ) ) ) ) ) ) ) ).
fof(t16_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos))))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = k1_real_1(k4_real_1(D,k6_power(k8_power,A))) ) ) )
=> ( r1_xreal_0(A,np__0)
| ( r2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),B),D) = k4_real_1(k13_prepower(A,k1_real_1(D)),k6_power(k8_power,A)) ) ) ) ) ) ) ) ) ).
fof(t17_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),D),k6_real_1(np__1,k6_power(k8_power,A)))))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k1_real_1(k4_real_1(E,k6_power(k8_power,A)))
& k2_seq_1(k1_numbers,k1_numbers,D,E) = k3_real_1(E,k6_real_1(np__1,k6_power(k8_power,A))) ) ) ) )
=> ( r1_xreal_0(A,np__0)
| A = np__1
| ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),D),k6_real_1(np__1,k6_power(k8_power,A))),B)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k8_seq_1(k1_numbers,k1_numbers,k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),D),k6_real_1(np__1,k6_power(k8_power,A))),B),E) = k6_real_1(E,k13_prepower(A,E)) ) ) ) ) ) ) ) ) ) ).
fof(t18_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),k26_sin_cos),k6_real_1(np__1,k5_real_1(k6_power(k8_power,A),np__1)))))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(D,k6_power(k8_power,A)) ) ) )
=> ( r1_xreal_0(A,np__0)
| A = k8_power
| ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),k26_sin_cos),k6_real_1(np__1,k5_real_1(k6_power(k8_power,A),np__1))),B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos),k26_sin_cos),k6_real_1(np__1,k5_real_1(k6_power(k8_power,A),np__1))),B),D) = k6_real_1(k13_prepower(A,D),k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D)) ) ) ) ) ) ) ) ) ).
fof(t19_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k26_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),k6_real_1(np__1,k5_real_1(np__1,k6_power(k8_power,A))))))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(D,k6_power(k8_power,A)) ) ) )
=> ( r1_xreal_0(A,np__0)
| A = k8_power
| ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k26_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),k6_real_1(np__1,k5_real_1(np__1,k6_power(k8_power,A)))),B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k26_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos)),k6_real_1(np__1,k5_real_1(np__1,k6_power(k8_power,A)))),B),D) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D),k13_prepower(A,D)) ) ) ) ) ) ) ) ) ).
fof(t20_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k2_taylor_1(k8_power))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1 ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k2_taylor_1(k8_power)),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k2_taylor_1(k8_power)),A),C) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),k3_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),np__1)) ) ) ) ) ) ) ).
fof(t21_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k2_taylor_1(k8_power))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),C),np__0) ) ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k2_taylor_1(k8_power)),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k2_taylor_1(k8_power)),A),C) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),k5_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),np__1)) ) ) ) ) ) ) ).
fof(t22_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k2_taylor_1(k8_power)))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),C),np__0) ) ) ) )
=> ( r2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k2_taylor_1(k8_power))),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k2_taylor_1(k8_power))),A),C) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),k5_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C))) ) ) ) ) ) ) ).
fof(t23_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(np__2)),B)))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1 ) ) )
=> ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(np__2)),B),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(np__2)),B),A),C) = k4_real_1(np__2,k28_sin_cos(k4_real_1(np__2,C))) ) ) ) ) ) ) ).
fof(t24_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2))))
& B = k6_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(np__2)),C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1 ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2)),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2)),A),D) = k6_real_1(k28_sin_cos(D),k3_real_1(k28_sin_cos(D),k28_sin_cos(k1_real_1(D)))) ) ) ) ) ) ) ) ).
fof(t25_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(np__2)),B)))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1 ) ) )
=> ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(np__2)),B),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(np__2)),B),A),C) = k4_real_1(np__2,k28_sin_cos(k4_real_1(np__2,C))) ) ) ) ) ) ) ).
fof(t26_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2))))
& B = k7_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k26_sin_cos,k1_taylor_1(np__2)),C)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),np__0) ) ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2)),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2)),A),D) = k6_real_1(k28_sin_cos(D),k5_real_1(k28_sin_cos(D),k28_sin_cos(k1_real_1(D)))) ) ) ) ) ) ) ) ).
fof(t27_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k1_taylor_1(np__2))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1 ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k1_taylor_1(np__2)),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k1_taylor_1(np__2)),A),C) = k4_real_1(k4_real_1(np__2,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C)),k5_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),np__1)) ) ) ) ) ) ) ).
fof(t28_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(B))
& B = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),k1_taylor_1(np__2)),k26_sin_cos),k2_taylor_1(k8_power))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),D),np__0) ) ) ) )
=> ( r2_fdiff_1(B,A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(B,A),D) = k6_real_1(k3_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D),np__1),k5_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D),np__1)) ) ) ) ) ) ) ) ).
fof(t29_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k1_taylor_1(np__2))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1 ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k1_taylor_1(np__2)),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,B),k1_taylor_1(np__2)),A),C) = k4_real_1(k4_real_1(np__2,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C)),k3_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),np__1)) ) ) ) ) ) ) ).
fof(t30_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(B))
& B = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),k1_taylor_1(np__2)),k26_sin_cos),k2_taylor_1(k8_power))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1 ) ) )
=> ( r2_fdiff_1(B,A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(B,A),D) = k6_real_1(k5_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D),np__1),k3_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D),np__1)) ) ) ) ) ) ) ) ).
fof(t31_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k1_taylor_1(np__2))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1 ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k1_taylor_1(np__2)),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k1_taylor_1(np__2)),A),C) = k1_real_1(k4_real_1(k4_real_1(np__2,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C)),k5_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C)))) ) ) ) ) ) ) ).
fof(t32_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(B))
& B = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k26_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,C,k26_sin_cos),k1_taylor_1(np__2))),k2_taylor_1(k8_power))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,C,k26_sin_cos),D),np__0) ) ) ) )
=> ( r2_fdiff_1(B,A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(B,A),D) = k6_real_1(k3_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D)),k5_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D))) ) ) ) ) ) ) ) ).
fof(t33_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(B))
& B = k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_rfunct_1(k1_numbers,k1_numbers,k26_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,k26_sin_cos),k1_taylor_1(np__2))),k2_taylor_1(k8_power))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1 ) ) )
=> ( r2_fdiff_1(B,A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(B,A),D) = k6_real_1(k5_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D)),k3_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,D))) ) ) ) ) ) ) ) ).
fof(t34_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power))))
& B = k6_seq_1(k1_numbers,k1_numbers,k26_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = k1_real_1(D) ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),A),D) = k6_real_1(k5_real_1(k28_sin_cos(D),k28_sin_cos(k1_real_1(D))),k3_real_1(k28_sin_cos(D),k28_sin_cos(k1_real_1(D)))) ) ) ) ) ) ) ) ).
fof(t35_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power))))
& B = k7_seq_1(k1_numbers,k1_numbers,k26_sin_cos,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k26_sin_cos))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,D) = k1_real_1(D)
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),np__0) ) ) ) )
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),A),D) = k6_real_1(k3_real_1(k28_sin_cos(D),k28_sin_cos(k1_real_1(D))),k5_real_1(k28_sin_cos(D),k28_sin_cos(k1_real_1(D)))) ) ) ) ) ) ) ) ).
fof(t36_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,np__3))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1 ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,np__3)),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,B,k26_sin_cos),k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,np__3)),A),C) = k4_real_1(k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C),k13_prepower(k3_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k26_sin_cos,C)),k6_real_1(np__1,np__2))) ) ) ) ) ) ) ).
fof(t37_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k26_sin_cos)),k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,k4_real_1(np__3,k6_power(k8_power,A))))))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,E) = np__1
& k2_seq_1(k1_numbers,k1_numbers,D,E) = k4_real_1(E,k6_power(k8_power,A)) ) ) ) )
=> ( r1_xreal_0(A,np__0)
| A = np__1
| ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k26_sin_cos)),k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,k4_real_1(np__3,k6_power(k8_power,A)))),B)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,C,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k26_sin_cos)),k3_taylor_1(k6_real_1(np__3,np__2))),k6_real_1(np__2,k4_real_1(np__3,k6_power(k8_power,A)))),B),E) = k4_real_1(k13_prepower(A,E),k13_prepower(k3_real_1(np__1,k13_prepower(A,E)),k6_real_1(np__1,np__2))) ) ) ) ) ) ) ) ) ) ).
fof(t38_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k21_sin_cos),k1_real_1(k6_real_1(np__1,np__2)))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,B,C) = k4_real_1(np__2,C) ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k21_sin_cos),k1_real_1(k6_real_1(np__1,np__2))),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k21_sin_cos),k1_real_1(k6_real_1(np__1,np__2))),A),C) = k20_sin_cos(k4_real_1(np__2,C)) ) ) ) ) ) ) ).
fof(t39_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k21_sin_cos),k3_taylor_1(k6_real_1(np__1,np__2))),np__2)))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,C),np__0)
& ~ r1_xreal_0(np__1,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C))
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C),k1_real_1(np__1)) ) ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k21_sin_cos),k3_taylor_1(k6_real_1(np__1,np__2))),np__2),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k7_seq_1(k1_numbers,k1_numbers,B,k21_sin_cos),k3_taylor_1(k6_real_1(np__1,np__2))),np__2),A),C) = k13_prepower(k3_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C)),k6_real_1(np__1,np__2)) ) ) ) ) ) ) ).
fof(t40_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,B,k21_sin_cos),k3_taylor_1(k6_real_1(np__1,np__2))),k1_real_1(np__2))))
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,B,C) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,C),np__0)
& ~ r1_xreal_0(np__1,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C))
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C),k1_real_1(np__1)) ) ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,B,k21_sin_cos),k3_taylor_1(k6_real_1(np__1,np__2))),k1_real_1(np__2)),A)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k6_seq_1(k1_numbers,k1_numbers,B,k21_sin_cos),k3_taylor_1(k6_real_1(np__1,np__2))),k1_real_1(np__2)),A),C) = k13_prepower(k5_real_1(np__1,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C)),k6_real_1(np__1,np__2)) ) ) ) ) ) ) ).
fof(t41_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2))))
& B = k6_seq_1(k1_numbers,k1_numbers,C,k13_seq_1(k1_numbers,k1_numbers,k18_sin_cos,np__2))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),np__0) ) ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2)),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k6_real_1(np__1,np__2)),A),D) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,D),k3_real_1(np__1,k4_real_1(np__2,k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,D)))) ) ) ) ) ) ) ) ).
fof(t42_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ! [B] :
( ( v1_funct_1(B)
& m2_relset_1(B,k1_numbers,k1_numbers) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(A,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k1_real_1(k6_real_1(np__1,np__2)))))
& B = k6_seq_1(k1_numbers,k1_numbers,C,k13_seq_1(k1_numbers,k1_numbers,k21_sin_cos,np__2))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,D) = np__1
& ~ r1_xreal_0(k2_seq_1(k1_numbers,k1_numbers,B,D),np__0) ) ) ) )
=> ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k1_real_1(k6_real_1(np__1,np__2))),A)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,B,k2_taylor_1(k8_power)),k1_real_1(k6_real_1(np__1,np__2))),A),D) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,D),k3_real_1(np__1,k4_real_1(np__2,k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,D)))) ) ) ) ) ) ) ) ).
fof(t43_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A)))))
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,C,D) = k4_real_1(k4_real_1(np__2,A),D) ) ) )
=> ( A = np__0
| ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A))),B)
& ! [D] :
( m1_subset_1(D,k1_numbers)
=> ( r2_hidden(D,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,C,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A))),B),D) = k4_real_1(k6_real_1(np__1,np__2),k23_sin_cos(k4_real_1(k4_real_1(np__2,A),D))) ) ) ) ) ) ) ) ) ).
fof(t44_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k7_seq_1(k1_numbers,k1_numbers,C,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A))))))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k6_real_1(E,np__2)
& k2_seq_1(k1_numbers,k1_numbers,D,E) = k4_real_1(k4_real_1(np__2,A),E) ) ) ) )
=> ( A = np__0
| ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,C,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A)))),B)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,C,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A)))),B),E) = k7_square_1(k20_sin_cos(k4_real_1(A,E))) ) ) ) ) ) ) ) ) ) ).
fof(t45_fdiff_6,axiom,
! [A] :
( m1_subset_1(A,k1_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ! [C] :
( ( v1_funct_1(C)
& m2_relset_1(C,k1_numbers,k1_numbers) )
=> ! [D] :
( ( v1_funct_1(D)
& m2_relset_1(D,k1_numbers,k1_numbers) )
=> ( ( r1_tarski(B,k1_relat_1(k6_seq_1(k1_numbers,k1_numbers,C,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A))))))
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> ( k2_seq_1(k1_numbers,k1_numbers,C,E) = k6_real_1(E,np__2)
& k2_seq_1(k1_numbers,k1_numbers,D,E) = k4_real_1(k4_real_1(np__2,A),E) ) ) ) )
=> ( A = np__0
| ( r2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,C,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A)))),B)
& ! [E] :
( m1_subset_1(E,k1_numbers)
=> ( r2_hidden(E,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k6_seq_1(k1_numbers,k1_numbers,C,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,D,k18_sin_cos),k6_real_1(np__1,k4_real_1(np__4,A)))),B),E) = k7_square_1(k23_sin_cos(k4_real_1(A,E))) ) ) ) ) ) ) ) ) ) ).
fof(t46_fdiff_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( r1_tarski(B,k1_relat_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A)),k6_real_1(np__1,A))))
=> ( r1_xreal_0(A,np__0)
| ( r2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A)),k6_real_1(np__1,A)),B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(A)),k6_real_1(np__1,A)),B),C) = k1_real_1(k4_real_1(k7_prepower(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C),k5_real_1(A,np__1)),k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,C))) ) ) ) ) ) ) ) ).
fof(t47_fdiff_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( r1_tarski(B,k1_relat_1(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(np__3)),k6_real_1(np__1,np__3)),k21_sin_cos)))
=> ( r1_xreal_0(A,np__0)
| ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(np__3)),k6_real_1(np__1,np__3)),k21_sin_cos),B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k21_sin_cos,k1_taylor_1(np__3)),k6_real_1(np__1,np__3)),k21_sin_cos),B),C) = k3_prepower(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,C),np__3) ) ) ) ) ) ) ) ).
fof(t48_fdiff_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( v3_rcomp_1(B)
& m1_subset_1(B,k1_zfmisc_1(k1_numbers)) )
=> ( r1_tarski(B,k1_relat_1(k7_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__3)),k6_real_1(np__1,np__3)))))
=> ( r1_xreal_0(A,np__0)
| ( r2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__3)),k6_real_1(np__1,np__3))),B)
& ! [C] :
( m1_subset_1(C,k1_numbers)
=> ( r2_hidden(C,B)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k7_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k13_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k18_sin_cos,k1_taylor_1(np__3)),k6_real_1(np__1,np__3))),B),C) = k3_prepower(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,C),np__3) ) ) ) ) ) ) ) ).
fof(t49_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( r1_tarski(A,k1_relat_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_taylor_1(k8_power),k18_sin_cos)))
=> ( r2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_taylor_1(k8_power),k18_sin_cos),A)
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(B,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_taylor_1(k8_power),k18_sin_cos),A),B) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k21_sin_cos,k6_power(k8_power,B)),B) ) ) ) ) ) ).
fof(t50_fdiff_6,axiom,
! [A] :
( ( v3_rcomp_1(A)
& m1_subset_1(A,k1_zfmisc_1(k1_numbers)) )
=> ( r1_tarski(A,k1_relat_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_taylor_1(k8_power),k21_sin_cos))))
=> ( r2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_taylor_1(k8_power),k21_sin_cos)),A)
& ! [B] :
( m1_subset_1(B,k1_numbers)
=> ( r2_hidden(B,A)
=> k2_seq_1(k1_numbers,k1_numbers,k2_fdiff_1(k16_seq_1(k1_numbers,k1_numbers,k1_partfun1(k1_numbers,k1_numbers,k1_numbers,k1_numbers,k2_taylor_1(k8_power),k21_sin_cos)),A),B) = k6_real_1(k2_seq_1(k1_numbers,k1_numbers,k18_sin_cos,k6_power(k8_power,B)),B) ) ) ) ) ) ).
%------------------------------------------------------------------------------