SET007 Axioms: SET007+843.ax
%------------------------------------------------------------------------------
% File : SET007+843 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Lucas Numbers and Generalized Fibonacci Numbers
% 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 : fib_num3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 3 unt; 0 def)
% Number of atoms : 220 ( 66 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 174 ( 16 ~; 0 |; 44 &)
% ( 2 <=>; 112 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 18 ( 17 usr; 0 prp; 1-3 aty)
% Number of functors : 31 ( 31 usr; 11 con; 0-5 aty)
% Number of variables : 115 ( 113 !; 2 ?)
% 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_fib_num3,axiom,
( ~ v1_xboole_0(k1_fib_num)
& v1_xcmplx_0(k1_fib_num)
& v1_xreal_0(k1_fib_num)
& v2_xreal_0(k1_fib_num)
& ~ v3_xreal_0(k1_fib_num) ) ).
fof(fc2_fib_num3,axiom,
( ~ v1_xboole_0(k2_fib_num)
& v1_xcmplx_0(k2_fib_num)
& v1_xreal_0(k2_fib_num)
& ~ v2_xreal_0(k2_fib_num)
& v3_xreal_0(k2_fib_num) ) ).
fof(fc3_fib_num3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( ~ v1_xboole_0(k1_fib_num3(A))
& v1_ordinal1(k1_fib_num3(A))
& v2_ordinal1(k1_fib_num3(A))
& v3_ordinal1(k1_fib_num3(A))
& v4_ordinal2(k1_fib_num3(A))
& v1_xcmplx_0(k1_fib_num3(A))
& v1_xreal_0(k1_fib_num3(A))
& v2_xreal_0(k1_fib_num3(A))
& ~ v3_xreal_0(k1_fib_num3(A))
& v1_int_1(k1_fib_num3(A))
& v1_rat_1(k1_fib_num3(A)) ) ) ).
fof(t1_fib_num3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k3_power(A,B) = np__0
=> A = np__0 ) ) ) ).
fof(t2_fib_num3,axiom,
! [A] :
( ( v1_xreal_0(A)
& ~ v3_xreal_0(A) )
=> k3_xcmplx_0(k8_square_1(A),k8_square_1(A)) = A ) ).
fof(t3_fib_num3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_xreal_0(A) )
=> k3_power(A,np__2) = k3_power(k4_xcmplx_0(A),np__2) ) ).
fof(t4_fib_num3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> k1_nat_1(k5_binarith(A,np__1),np__2) = k5_binarith(k1_nat_1(A,np__2),np__1) ) ).
fof(t5_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k3_prepower(k1_nat_1(A,B),np__2) = k1_nat_1(k1_nat_1(k1_nat_1(k2_nat_1(A,A),k2_nat_1(A,B)),k2_nat_1(A,B)),k2_nat_1(B,B)) ) ) ).
fof(t6_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_xreal_0(B) )
=> k3_power(k3_power(B,A),np__2) = k3_power(B,k2_nat_1(np__2,A)) ) ) ).
fof(t7_fib_num3,axiom,
! [A] :
( v1_xreal_0(A)
=> ! [B] :
( v1_xreal_0(B)
=> k3_xcmplx_0(k2_xcmplx_0(A,B),k6_xcmplx_0(A,B)) = k6_xcmplx_0(k3_power(A,np__2),k3_power(B,np__2)) ) ) ).
fof(t8_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_xreal_0(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_xreal_0(C) )
=> k3_power(k3_xcmplx_0(B,C),A) = k3_xcmplx_0(k3_power(B,A),k3_power(C,A)) ) ) ) ).
fof(t9_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_xcmplx_0(k3_power(k1_fib_num,A),k3_power(k1_fib_num,k1_nat_1(A,np__1))) = k3_power(k1_fib_num,k1_nat_1(A,np__2)) ) ).
fof(t10_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_xcmplx_0(k3_power(k2_fib_num,A),k3_power(k2_fib_num,k1_nat_1(A,np__1))) = k3_power(k2_fib_num,k1_nat_1(A,np__2)) ) ).
fof(d1_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( B = k1_fib_num3(A)
<=> ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m2_relset_1(C,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& B = k1_pre_ff(k1_numbers,k1_numbers,k5_numbers,k5_numbers,k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),C,A))
& k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),C,np__0) = k1_domain_1(k5_numbers,k5_numbers,np__2,np__1)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),C,k1_nat_1(D,np__1)) = k1_domain_1(k5_numbers,k5_numbers,k2_pre_ff(k1_numbers,k1_numbers,k5_numbers,k5_numbers,k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),C,D)),k1_nat_1(k1_pre_ff(k1_numbers,k1_numbers,k5_numbers,k5_numbers,k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),C,D)),k2_pre_ff(k1_numbers,k1_numbers,k5_numbers,k5_numbers,k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),C,D)))) ) ) ) ) ) ).
fof(t11_fib_num3,axiom,
( k1_fib_num3(np__0) = np__2
& k1_fib_num3(np__1) = np__1
& ! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_fib_num3(k1_nat_1(k1_nat_1(A,np__1),np__1)) = k1_nat_1(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,np__1))) ) ) ).
fof(t12_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_fib_num3(k1_nat_1(A,np__2)) = k1_nat_1(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,np__1))) ) ).
fof(t13_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_nat_1(k1_fib_num3(k1_nat_1(A,np__1)),k1_fib_num3(k1_nat_1(A,np__2))) = k1_fib_num3(k1_nat_1(A,np__3)) ) ).
fof(t14_fib_num3,axiom,
k1_fib_num3(np__2) = np__3 ).
fof(t15_fib_num3,axiom,
k1_fib_num3(np__3) = np__4 ).
fof(t16_fib_num3,axiom,
k1_fib_num3(np__4) = np__7 ).
fof(t17_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> r1_xreal_0(A,k1_fib_num3(A)) ) ).
fof(t18_fib_num3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> r1_xreal_0(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,np__1))) ) ).
fof(t19_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_nat_1(np__2,k1_fib_num3(k1_nat_1(A,np__2))) = k1_nat_1(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,np__3))) ) ).
fof(t20_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_fib_num3(k1_nat_1(A,np__1)) = k1_nat_1(k3_pre_ff(A),k3_pre_ff(k1_nat_1(A,np__2))) ) ).
fof(t21_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_fib_num3(A) = k2_xcmplx_0(k3_power(k1_fib_num,A),k3_power(k2_fib_num,A)) ) ).
fof(t22_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_nat_1(k2_nat_1(np__2,k1_fib_num3(A)),k1_fib_num3(k1_nat_1(A,np__1))) = k2_nat_1(np__5,k3_pre_ff(k1_nat_1(A,np__1))) ) ).
fof(t23_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k6_xcmplx_0(k1_fib_num3(k1_nat_1(A,np__3)),k2_nat_1(np__2,k1_fib_num3(A))) = k2_nat_1(np__5,k3_pre_ff(A)) ) ).
fof(t24_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_nat_1(k1_fib_num3(A),k3_pre_ff(A)) = k2_nat_1(np__2,k3_pre_ff(k1_nat_1(A,np__1))) ) ).
fof(t25_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_nat_1(k2_nat_1(np__3,k3_pre_ff(A)),k1_fib_num3(A)) = k2_nat_1(np__2,k3_pre_ff(k1_nat_1(A,np__2))) ) ).
fof(t26_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_nat_1(np__2,k1_fib_num3(k1_nat_1(A,B))) = k1_nat_1(k2_nat_1(k1_fib_num3(A),k1_fib_num3(B)),k2_nat_1(k2_nat_1(np__5,k3_pre_ff(A)),k3_pre_ff(B))) ) ) ).
fof(t27_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_nat_1(k1_fib_num3(k1_nat_1(A,np__3)),k1_fib_num3(A)) = k6_xcmplx_0(k3_prepower(k1_fib_num3(k1_nat_1(A,np__2)),np__2),k3_prepower(k1_fib_num3(k1_nat_1(A,np__1)),np__2)) ) ).
fof(t28_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(k2_nat_1(np__2,A)) = k2_nat_1(k3_pre_ff(A),k1_fib_num3(A)) ) ).
fof(t29_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_nat_1(np__2,k3_pre_ff(k1_nat_1(k2_nat_1(np__2,A),np__1))) = k1_nat_1(k2_nat_1(k1_fib_num3(k1_nat_1(A,np__1)),k3_pre_ff(A)),k2_nat_1(k1_fib_num3(A),k3_pre_ff(k1_nat_1(A,np__1)))) ) ).
fof(t30_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k6_xcmplx_0(k3_xcmplx_0(np__5,k3_prepower(k3_pre_ff(A),np__2)),k3_prepower(k1_fib_num3(A),np__2)) = k3_xcmplx_0(np__4,k3_power(k4_xcmplx_0(np__1),k1_nat_1(A,np__1))) ) ).
fof(t31_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(k1_nat_1(k2_nat_1(np__2,A),np__1)) = k6_xcmplx_0(k2_nat_1(k3_pre_ff(k1_nat_1(A,np__1)),k1_fib_num3(k1_nat_1(A,np__1))),k2_nat_1(k3_pre_ff(A),k1_fib_num3(A))) ) ).
fof(d2_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D = k2_fib_num3(A,B,C)
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& m2_relset_1(E,k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers))
& D = k1_pre_ff(k1_numbers,k1_numbers,k5_numbers,k5_numbers,k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),E,C))
& k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),E,np__0) = k1_domain_1(k5_numbers,k5_numbers,A,B)
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),E,k1_nat_1(F,np__1)) = k1_domain_1(k5_numbers,k5_numbers,k2_pre_ff(k1_numbers,k1_numbers,k5_numbers,k5_numbers,k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),E,F)),k1_nat_1(k1_pre_ff(k1_numbers,k1_numbers,k5_numbers,k5_numbers,k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),E,F)),k2_pre_ff(k1_numbers,k1_numbers,k5_numbers,k5_numbers,k8_funct_2(k5_numbers,k12_mcart_1(k1_numbers,k1_numbers,k5_numbers,k5_numbers),E,F)))) ) ) ) ) ) ) ) ).
fof(t32_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k2_fib_num3(A,B,np__0) = A
& k2_fib_num3(A,B,np__1) = B
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_fib_num3(A,B,k1_nat_1(k1_nat_1(C,np__1),np__1)) = k1_nat_1(k2_fib_num3(A,B,C),k2_fib_num3(A,B,k1_nat_1(C,np__1))) ) ) ) ) ).
fof(t33_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k3_prepower(k1_nat_1(k2_fib_num3(A,B,k1_nat_1(C,np__1)),k2_fib_num3(A,B,k1_nat_1(k1_nat_1(C,np__1),np__1))),np__2) = k2_xcmplx_0(k2_xcmplx_0(k3_prepower(k2_fib_num3(A,B,k1_nat_1(C,np__1)),np__2),k2_nat_1(k2_nat_1(np__2,k2_fib_num3(A,B,k1_nat_1(C,np__1))),k2_fib_num3(A,B,k1_nat_1(k1_nat_1(C,np__1),np__1)))),k3_prepower(k2_fib_num3(A,B,k1_nat_1(k1_nat_1(C,np__1),np__1)),np__2)) ) ) ) ).
fof(t34_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_nat_1(k2_fib_num3(A,B,C),k2_fib_num3(A,B,k1_nat_1(C,np__1))) = k2_fib_num3(A,B,k1_nat_1(C,np__2)) ) ) ) ).
fof(t35_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_nat_1(k2_fib_num3(A,B,k1_nat_1(C,np__1)),k2_fib_num3(A,B,k1_nat_1(C,np__2))) = k2_fib_num3(A,B,k1_nat_1(C,np__3)) ) ) ) ).
fof(t36_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_nat_1(k2_fib_num3(A,B,k1_nat_1(C,np__2)),k2_fib_num3(A,B,k1_nat_1(C,np__3))) = k2_fib_num3(A,B,k1_nat_1(C,np__4)) ) ) ) ).
fof(t37_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_fib_num3(np__0,np__1,A) = k3_pre_ff(A) ) ).
fof(t38_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_fib_num3(np__2,np__1,A) = k1_fib_num3(A) ) ).
fof(t39_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_nat_1(k2_fib_num3(A,B,C),k2_fib_num3(A,B,k1_nat_1(C,np__3))) = k2_nat_1(np__2,k2_fib_num3(A,B,k1_nat_1(C,np__2))) ) ) ) ).
fof(t40_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k1_nat_1(k2_fib_num3(A,B,C),k2_fib_num3(A,B,k1_nat_1(C,np__4))) = k2_nat_1(np__3,k2_fib_num3(A,B,k1_nat_1(C,np__2))) ) ) ) ).
fof(t41_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k6_xcmplx_0(k2_fib_num3(A,B,k1_nat_1(C,np__3)),k2_fib_num3(A,B,C)) = k2_nat_1(np__2,k2_fib_num3(A,B,k1_nat_1(C,np__1))) ) ) ) ).
fof(t42_fib_num3,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> k2_fib_num3(A,B,C) = k1_nat_1(k2_nat_1(k2_fib_num3(A,B,np__0),k3_pre_ff(k5_binarith(C,np__1))),k2_nat_1(k2_fib_num3(A,B,np__1),k3_pre_ff(C))) ) ) ) ).
fof(t43_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k1_nat_1(k2_nat_1(k3_pre_ff(B),k1_fib_num3(A)),k2_nat_1(k1_fib_num3(B),k3_pre_ff(A))) = k2_fib_num3(k3_pre_ff(np__0),k1_fib_num3(np__0),k1_nat_1(A,B)) ) ) ).
fof(t44_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_nat_1(k1_fib_num3(A),k1_fib_num3(k1_nat_1(A,np__3))) = k2_nat_1(np__2,k1_fib_num3(k1_nat_1(A,np__2))) ) ).
fof(t45_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_fib_num3(A,A,B) = k3_xcmplx_0(k7_xcmplx_0(k2_fib_num3(A,A,np__0),np__2),k1_nat_1(k3_pre_ff(B),k1_fib_num3(B))) ) ) ).
fof(t46_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_fib_num3(B,k1_nat_1(A,B),C) = k2_fib_num3(A,B,k1_nat_1(C,np__1)) ) ) ) ).
fof(t47_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k6_xcmplx_0(k2_nat_1(k2_fib_num3(A,B,k1_nat_1(C,np__2)),k2_fib_num3(A,B,C)),k3_prepower(k2_fib_num3(A,B,k1_nat_1(C,np__1)),np__2)) = k3_xcmplx_0(k3_power(k4_xcmplx_0(np__1),C),k6_xcmplx_0(k3_prepower(k2_fib_num3(A,B,np__2),np__2),k2_nat_1(k2_fib_num3(A,B,np__1),k2_fib_num3(A,B,np__3)))) ) ) ) ).
fof(t48_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_fib_num3(k2_fib_num3(A,B,C),k2_fib_num3(A,B,k1_nat_1(C,np__1)),D) = k2_fib_num3(A,B,k1_nat_1(D,C)) ) ) ) ) ).
fof(t49_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_fib_num3(A,B,k1_nat_1(C,np__1)) = k1_nat_1(k2_nat_1(A,k3_pre_ff(C)),k2_nat_1(B,k3_pre_ff(k1_nat_1(C,np__1)))) ) ) ) ).
fof(t50_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_fib_num3(np__0,A,B) = k2_nat_1(A,k3_pre_ff(B)) ) ) ).
fof(t51_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_fib_num3(A,np__0,k1_nat_1(B,np__1)) = k2_nat_1(A,k3_pre_ff(B)) ) ) ).
fof(t52_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k1_nat_1(k2_fib_num3(A,B,E),k2_fib_num3(C,D,E)) = k2_fib_num3(k1_nat_1(A,C),k1_nat_1(B,D),E) ) ) ) ) ) ).
fof(t53_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k2_fib_num3(k2_nat_1(C,A),k2_nat_1(C,B),D) = k2_nat_1(C,k2_fib_num3(A,B,D)) ) ) ) ) ).
fof(t54_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k2_fib_num3(A,B,C) = k7_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(k2_xcmplx_0(k3_xcmplx_0(A,k4_xcmplx_0(k2_fib_num)),B),k3_power(k1_fib_num,C)),k3_xcmplx_0(k6_xcmplx_0(k3_xcmplx_0(A,k1_fib_num),B),k3_power(k2_fib_num,C))),k9_square_1(np__5)) ) ) ) ).
fof(t55_fib_num3,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k2_fib_num3(k1_nat_1(k2_nat_1(np__2,A),np__1),k1_nat_1(k2_nat_1(np__2,A),np__1),k1_nat_1(B,np__1)) = k2_nat_1(k1_nat_1(k2_nat_1(np__2,A),np__1),k3_pre_ff(k1_nat_1(B,np__2))) ) ) ).
fof(dt_k1_fib_num3,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m2_subset_1(k1_fib_num3(A),k1_numbers,k5_numbers) ) ).
fof(dt_k2_fib_num3,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m2_subset_1(k2_fib_num3(A,B,C),k1_numbers,k5_numbers) ) ).
%------------------------------------------------------------------------------