SET007 Axioms: SET007+840.ax
%------------------------------------------------------------------------------
% File : SET007+840 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Some Properties of 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_num2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 99 ( 16 unt; 0 def)
% Number of atoms : 380 ( 79 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 349 ( 68 ~; 5 |; 143 &)
% ( 5 <=>; 128 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 avg)
% Maximal term depth : 7 ( 2 avg)
% Number of predicates : 37 ( 36 usr; 0 prp; 1-3 aty)
% Number of functors : 57 ( 57 usr; 17 con; 0-4 aty)
% Number of variables : 131 ( 127 !; 4 ?)
% 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_num2,axiom,
! [A] :
( ( v1_int_1(A)
& ~ v1_abian(A) )
=> ( v1_xcmplx_0(k4_xcmplx_0(A))
& v1_xreal_0(k4_xcmplx_0(A))
& v1_int_1(k4_xcmplx_0(A))
& ~ v1_abian(k4_xcmplx_0(A)) ) ) ).
fof(fc2_fib_num2,axiom,
! [A] :
( ( v1_int_1(A)
& v1_abian(A) )
=> ( v1_xcmplx_0(k4_xcmplx_0(A))
& v1_xreal_0(k4_xcmplx_0(A))
& v1_int_1(k4_xcmplx_0(A))
& v1_abian(k4_xcmplx_0(A)) ) ) ).
fof(rc1_fib_num2,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_finset_1(A)
& v1_membered(A)
& v2_membered(A)
& v3_membered(A)
& v4_membered(A)
& v5_membered(A)
& v1_setfam_1(A) ) ).
fof(fc3_fib_num2,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k5_numbers)
& m1_relset_1(A,k5_numbers,k5_numbers)
& v1_finset_1(B)
& v5_membered(B)
& v1_setfam_1(B) )
=> ( v1_relat_1(k7_relat_1(A,B))
& v1_funct_1(k7_relat_1(A,B))
& v1_finset_1(k7_relat_1(A,B))
& v2_finseq_1(k7_relat_1(A,B)) ) ) ).
fof(fc4_fib_num2,axiom,
( ~ v1_xboole_0(k5_ordinal2)
& v1_ordinal1(k5_ordinal2)
& v2_ordinal1(k5_ordinal2)
& v3_ordinal1(k5_ordinal2)
& v1_membered(k5_ordinal2)
& v2_membered(k5_ordinal2)
& v3_membered(k5_ordinal2)
& v4_membered(k5_ordinal2)
& v5_membered(k5_ordinal2)
& v2_seq_4(k5_ordinal2) ) ).
fof(fc5_fib_num2,axiom,
( v1_finset_1(k1_enumset1(np__1,np__2,np__3))
& v1_membered(k1_enumset1(np__1,np__2,np__3))
& v2_membered(k1_enumset1(np__1,np__2,np__3))
& v3_membered(k1_enumset1(np__1,np__2,np__3))
& v4_membered(k1_enumset1(np__1,np__2,np__3))
& v5_membered(k1_enumset1(np__1,np__2,np__3))
& v1_setfam_1(k1_enumset1(np__1,np__2,np__3)) ) ).
fof(fc6_fib_num2,axiom,
( v1_finset_1(k2_enumset1(np__1,np__2,np__3,np__4))
& v1_membered(k2_enumset1(np__1,np__2,np__3,np__4))
& v2_membered(k2_enumset1(np__1,np__2,np__3,np__4))
& v3_membered(k2_enumset1(np__1,np__2,np__3,np__4))
& v4_membered(k2_enumset1(np__1,np__2,np__3,np__4))
& v5_membered(k2_enumset1(np__1,np__2,np__3,np__4))
& v1_setfam_1(k2_enumset1(np__1,np__2,np__3,np__4)) ) ).
fof(fc7_fib_num2,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> ( v1_finset_1(k1_finseq_1(A))
& v1_setfam_1(k1_finseq_1(A)) ) ) ).
fof(cc1_fib_num2,axiom,
! [A] :
( v1_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_setfam_1(B) ) ) ).
fof(fc8_fib_num2,axiom,
! [A,B] :
( v1_setfam_1(A)
=> v1_setfam_1(k3_xboole_0(A,B)) ) ).
fof(fc9_fib_num2,axiom,
! [A,B] :
( v1_setfam_1(A)
=> v1_setfam_1(k3_xboole_0(B,A)) ) ).
fof(t1_fib_num2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> k1_nat_1(k5_binarith(A,np__1),np__2) = k1_nat_1(A,np__1) ) ).
fof(t2_fib_num2,axiom,
! [A] :
( ( v1_int_1(A)
& ~ v1_abian(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_xreal_0(B) )
=> k3_power(k4_xcmplx_0(B),A) = k4_xcmplx_0(k3_power(B,A)) ) ) ).
fof(t3_fib_num2,axiom,
! [A] :
( ( v1_int_1(A)
& ~ v1_abian(A) )
=> k3_power(k4_xcmplx_0(np__1),A) = k4_xcmplx_0(np__1) ) ).
fof(t4_fib_num2,axiom,
! [A] :
( ( v1_int_1(A)
& v1_abian(A) )
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_xreal_0(B) )
=> k3_power(k4_xcmplx_0(B),A) = k3_power(B,A) ) ) ).
fof(t5_fib_num2,axiom,
! [A] :
( ( v1_int_1(A)
& v1_abian(A) )
=> k3_power(k4_xcmplx_0(np__1),A) = np__1 ) ).
fof(t6_fib_num2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_xreal_0(A) )
=> ! [B] :
( v1_int_1(B)
=> k3_power(k3_xcmplx_0(k4_xcmplx_0(np__1),A),B) = k3_xcmplx_0(k3_power(k4_xcmplx_0(np__1),B),k3_power(A,B)) ) ) ).
fof(t7_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_xreal_0(C) )
=> k3_power(C,k1_nat_1(A,B)) = k3_xcmplx_0(k3_power(C,A),k3_power(C,B)) ) ) ) ).
fof(t8_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_xreal_0(B) )
=> ! [C] :
( ( v1_int_1(C)
& ~ v1_abian(C) )
=> k3_power(k3_power(B,C),A) = k3_power(B,k3_xcmplx_0(C,A)) ) ) ) ).
fof(t9_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k5_square_1(k3_power(k4_xcmplx_0(np__1),k4_xcmplx_0(A))) = np__1 ) ).
fof(t10_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_xreal_0(C) )
=> k3_xcmplx_0(k3_power(C,k4_xcmplx_0(A)),k3_power(C,k4_xcmplx_0(B))) = k3_power(C,k6_xcmplx_0(k4_xcmplx_0(A),B)) ) ) ) ).
fof(t11_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_power(k4_xcmplx_0(np__1),k4_xcmplx_0(k2_nat_1(np__2,A))) = np__1 ) ).
fof(t12_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& v1_xreal_0(B) )
=> k3_xcmplx_0(k3_power(B,A),k3_power(B,k4_xcmplx_0(A))) = np__1 ) ) ).
fof(t13_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_power(k4_xcmplx_0(np__1),k4_xcmplx_0(A)) = k3_power(k4_xcmplx_0(np__1),A) ) ).
fof(t14_fib_num2,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)
=> ( ( r1_nat_1(B,C)
& r1_nat_1(B,A) )
=> r1_nat_1(B,k1_nat_1(k2_nat_1(C,D),k2_nat_1(A,E))) ) ) ) ) ) ) ).
fof(t15_fib_num2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_finseq_1(A) )
=> r1_tarski(k2_relat_1(k15_finseq_1(A)),k2_relat_1(A)) ) ).
fof(d1_fib_num2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k5_numbers)
& m2_relset_1(A,k5_numbers,k5_numbers) )
=> ! [B] :
( ( v1_finset_1(B)
& v5_membered(B)
& v1_setfam_1(B) )
=> k1_fib_num2(A,B) = k15_finseq_1(k7_relat_1(A,B)) ) ) ).
fof(t16_fib_num2,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)
=> ~ ( C != np__0
& r1_xreal_0(k1_nat_1(C,A),B)
& r1_xreal_0(B,A) ) ) ) ) ).
fof(t17_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C,D] :
~ ( ~ r1_xreal_0(A,np__0)
& ~ r1_xreal_0(B,A)
& ~ ( v1_relat_1(k2_tarski(k4_tarski(A,C),k4_tarski(B,D)))
& v1_funct_1(k2_tarski(k4_tarski(A,C),k4_tarski(B,D)))
& v2_finseq_1(k2_tarski(k4_tarski(A,C),k4_tarski(B,D))) ) ) ) ) ).
fof(t18_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C,D,E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v2_finseq_1(E) )
=> ( E = k2_tarski(k4_tarski(A,C),k4_tarski(B,D))
=> ( r1_xreal_0(B,A)
| k15_finseq_1(E) = k10_finseq_1(C,D) ) ) ) ) ) ).
fof(t19_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( r1_xreal_0(np__1,A)
=> ( v1_relat_1(k1_tarski(k4_tarski(A,B)))
& v1_funct_1(k1_tarski(k4_tarski(A,B)))
& v2_finseq_1(k1_tarski(k4_tarski(A,B))) ) ) ) ).
fof(t20_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B,C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v2_finseq_1(C) )
=> ( C = k1_tarski(k4_tarski(np__1,B))
=> k14_pnproc_1(C,A) = k1_tarski(k4_tarski(k1_nat_1(np__1,A),B)) ) ) ) ).
fof(t21_fib_num2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_finseq_1(A) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_tarski(k1_relat_1(A),k2_finseq_1(B))
& ~ r1_xreal_0(C,B)
& ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D)
& v1_finseq_1(D) )
=> ~ ( r1_tarski(A,D)
& k4_finseq_1(D) = k2_finseq_1(C) ) ) ) ) ) ) ).
fof(t22_fib_num2,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v2_finseq_1(A) )
=> ? [B] :
( v1_relat_1(B)
& v1_funct_1(B)
& v1_finseq_1(B)
& r1_tarski(A,B) ) ) ).
fof(t23_fib_num2,axiom,
k3_pre_ff(np__2) = np__1 ).
fof(t24_fib_num2,axiom,
k3_pre_ff(np__3) = np__2 ).
fof(t25_fib_num2,axiom,
k3_pre_ff(np__4) = np__3 ).
fof(t26_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(k1_nat_1(A,np__2)) = k1_nat_1(k3_pre_ff(A),k3_pre_ff(k1_nat_1(A,np__1))) ) ).
fof(t27_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(k1_nat_1(A,np__3)) = k1_nat_1(k3_pre_ff(k1_nat_1(A,np__2)),k3_pre_ff(k1_nat_1(A,np__1))) ) ).
fof(t28_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(k1_nat_1(A,np__4)) = k1_nat_1(k3_pre_ff(k1_nat_1(A,np__2)),k3_pre_ff(k1_nat_1(A,np__3))) ) ).
fof(t29_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(k1_nat_1(A,np__5)) = k1_nat_1(k3_pre_ff(k1_nat_1(A,np__3)),k3_pre_ff(k1_nat_1(A,np__4))) ) ).
fof(t30_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(k1_nat_1(A,np__2)) = k6_xcmplx_0(k3_pre_ff(k1_nat_1(A,np__3)),k3_pre_ff(k1_nat_1(A,np__1))) ) ).
fof(t31_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(k1_nat_1(A,np__1)) = k6_xcmplx_0(k3_pre_ff(k1_nat_1(A,np__2)),k3_pre_ff(A)) ) ).
fof(t32_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_pre_ff(A) = k6_xcmplx_0(k3_pre_ff(k1_nat_1(A,np__2)),k3_pre_ff(k1_nat_1(A,np__1))) ) ).
fof(t33_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k6_xcmplx_0(k2_nat_1(k3_pre_ff(A),k3_pre_ff(k1_nat_1(A,np__2))),k2_pepin(k3_pre_ff(k1_nat_1(A,np__1)))) = k2_newton(k4_xcmplx_0(np__1),k1_nat_1(A,np__1)) ) ).
fof(t34_fib_num2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> k6_xcmplx_0(k2_nat_1(k3_pre_ff(k5_binarith(A,np__1)),k3_pre_ff(k1_nat_1(A,np__1))),k2_pepin(k3_pre_ff(A))) = k2_newton(k4_xcmplx_0(np__1),A) ) ).
fof(t35_fib_num2,axiom,
~ r1_xreal_0(k1_fib_num,np__0) ).
fof(t36_fib_num2,axiom,
k2_fib_num = k3_power(k4_xcmplx_0(k1_fib_num),k4_xcmplx_0(np__1)) ).
fof(t37_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k3_power(k4_xcmplx_0(k1_fib_num),k3_xcmplx_0(k4_xcmplx_0(np__1),A)) = k3_power(k3_power(k4_xcmplx_0(k1_fib_num),k4_xcmplx_0(np__1)),A) ) ).
fof(t38_fib_num2,axiom,
k4_xcmplx_0(k7_xcmplx_0(np__1,k1_fib_num)) = k2_fib_num ).
fof(t39_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_xcmplx_0(k6_xcmplx_0(k5_square_1(k3_power(k1_fib_num,A)),k3_xcmplx_0(np__2,k3_power(k4_xcmplx_0(np__1),A))),k5_square_1(k3_power(k1_fib_num,k4_xcmplx_0(A)))) = k5_square_1(k6_xcmplx_0(k3_power(k1_fib_num,A),k3_power(k2_fib_num,A))) ) ).
fof(t40_fib_num2,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) )
=> ( r1_xreal_0(B,A)
=> k6_xcmplx_0(k2_pepin(k3_pre_ff(A)),k2_nat_1(k3_pre_ff(k1_nat_1(A,B)),k3_pre_ff(k5_binarith(A,B)))) = k3_xcmplx_0(k2_newton(k4_xcmplx_0(np__1),k5_binarith(A,B)),k2_pepin(k3_pre_ff(B))) ) ) ) ).
fof(t41_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_nat_1(k2_pepin(k3_pre_ff(A)),k2_pepin(k3_pre_ff(k1_nat_1(A,np__1)))) = k3_pre_ff(k1_nat_1(k2_nat_1(np__2,A),np__1)) ) ).
fof(t42_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> k3_pre_ff(k1_nat_1(A,B)) = k1_nat_1(k2_nat_1(k3_pre_ff(B),k3_pre_ff(k1_nat_1(A,np__1))),k2_nat_1(k3_pre_ff(k5_binarith(B,np__1)),k3_pre_ff(A))) ) ) ).
fof(t43_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> r1_nat_1(k3_pre_ff(B),k3_pre_ff(k2_nat_1(B,A))) ) ) ).
fof(t44_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> ( r1_nat_1(B,A)
=> r1_nat_1(k3_pre_ff(B),k3_pre_ff(A)) ) ) ) ).
fof(t45_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> r1_xreal_0(k3_pre_ff(A),k3_pre_ff(k1_nat_1(A,np__1))) ) ).
fof(t46_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(A,np__1)
& r1_xreal_0(k3_pre_ff(k1_nat_1(A,np__1)),k3_pre_ff(A)) ) ) ).
fof(t47_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_xreal_0(B,A)
=> r1_xreal_0(k3_pre_ff(B),k3_pre_ff(A)) ) ) ) ).
fof(t48_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,np__1)
& ~ r1_xreal_0(A,B)
& r1_xreal_0(k3_pre_ff(A),k3_pre_ff(B)) ) ) ) ).
fof(t49_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( k3_pre_ff(A) = np__1
<=> ( A = np__1
| A = np__2 ) ) ) ).
fof(t50_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,np__1)
& A != np__0
& A != np__1
& ( ( A != np__1
& B != np__2 )
| ( A != np__2
& B != np__1 ) )
& ~ ( k3_pre_ff(A) = k3_pre_ff(B)
<=> A = B ) ) ) ) ).
fof(t51_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(A,np__1)
& A != np__4
& ~ v1_int_2(A)
& ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> ~ ( B != np__1
& B != np__2
& B != A
& r1_nat_1(B,A) ) ) ) ) ).
fof(t52_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( v1_int_2(k3_pre_ff(A))
=> ( r1_xreal_0(A,np__1)
| A = np__4
| v1_int_2(A) ) ) ) ).
fof(d2_fib_num2,axiom,
! [A] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k5_numbers)
& m2_relset_1(A,k5_numbers,k5_numbers) )
=> ( A = k2_fib_num2
<=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k8_funct_2(k5_numbers,k5_numbers,A,B) = k3_pre_ff(B) ) ) ) ).
fof(t53_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r2_hidden(k2_nat_1(np__2,A),k3_fib_num2)
& ~ r2_hidden(k1_nat_1(k2_nat_1(np__2,A),np__1),k3_fib_num2) ) ) ).
fof(t54_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r2_hidden(k1_nat_1(k2_nat_1(np__2,A),np__1),k4_fib_num2)
& ~ r2_hidden(k2_nat_1(np__2,A),k4_fib_num2) ) ) ).
fof(d5_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k5_fib_num2(A) = k1_fib_num2(k2_fib_num2,k3_xboole_0(k3_fib_num2,k2_finseq_1(A))) ) ).
fof(d6_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k6_fib_num2(A) = k1_fib_num2(k2_fib_num2,k3_xboole_0(k4_fib_num2,k2_finseq_1(A))) ) ).
fof(t55_fib_num2,axiom,
k5_fib_num2(np__0) = k1_xboole_0 ).
fof(t56_fib_num2,axiom,
k15_finseq_1(k7_relat_1(k2_fib_num2,k1_seq_4(np__2))) = k13_binarith(k5_numbers,np__1) ).
fof(t57_fib_num2,axiom,
k5_fib_num2(np__2) = k13_binarith(k5_numbers,np__1) ).
fof(t58_fib_num2,axiom,
k5_fib_num2(np__4) = k10_finseq_1(np__1,np__3) ).
fof(t59_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_xboole_0(k3_xboole_0(k3_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(np__2,A),np__2))),k1_seq_4(k1_nat_1(k2_nat_1(np__2,A),np__4))) = k3_xboole_0(k3_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(np__2,A),np__4))) ) ).
fof(t60_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_xboole_0(k7_relat_1(k2_fib_num2,k3_xboole_0(k3_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(np__2,A),np__2)))),k1_tarski(k1_domain_1(k5_numbers,k5_numbers,k1_nat_1(k2_nat_1(np__2,A),np__4),k8_funct_2(k5_numbers,k5_numbers,k2_fib_num2,k1_nat_1(k2_nat_1(np__2,A),np__4))))) = k7_relat_1(k2_fib_num2,k3_xboole_0(k3_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(np__2,A),np__4)))) ) ).
fof(t61_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k5_fib_num2(k1_nat_1(k2_nat_1(np__2,A),np__2)) = k4_wsierp_1(k1_numbers,k5_numbers,k5_fib_num2(k2_nat_1(np__2,A)),k13_binarith(k5_numbers,k3_pre_ff(k1_nat_1(k2_nat_1(np__2,A),np__2)))) ) ).
fof(t62_fib_num2,axiom,
k6_fib_num2(np__1) = k13_binarith(k5_numbers,np__1) ).
fof(t63_fib_num2,axiom,
k6_fib_num2(np__3) = k10_finseq_1(np__1,np__2) ).
fof(t64_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_xboole_0(k3_xboole_0(k4_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(np__2,A),np__3))),k1_seq_4(k1_nat_1(k2_nat_1(np__2,A),np__5))) = k3_xboole_0(k4_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(np__2,A),np__5))) ) ).
fof(t65_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k2_xboole_0(k7_relat_1(k2_fib_num2,k3_xboole_0(k4_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(np__2,A),np__3)))),k1_tarski(k1_domain_1(k5_numbers,k5_numbers,k1_nat_1(k2_nat_1(np__2,A),np__5),k8_funct_2(k5_numbers,k5_numbers,k2_fib_num2,k1_nat_1(k2_nat_1(np__2,A),np__5))))) = k7_relat_1(k2_fib_num2,k3_xboole_0(k4_fib_num2,k2_finseq_1(k1_nat_1(k2_nat_1(np__2,A),np__5)))) ) ).
fof(t66_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k6_fib_num2(k1_nat_1(k2_nat_1(np__2,A),np__3)) = k4_wsierp_1(k1_numbers,k5_numbers,k6_fib_num2(k1_nat_1(k2_nat_1(np__2,A),np__1)),k13_binarith(k5_numbers,k3_pre_ff(k1_nat_1(k2_nat_1(np__2,A),np__3)))) ) ).
fof(t67_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k9_wsierp_1(k5_fib_num2(k1_nat_1(k2_nat_1(np__2,A),np__2))) = k6_xcmplx_0(k3_pre_ff(k1_nat_1(k2_nat_1(np__2,A),np__3)),np__1) ) ).
fof(t68_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k9_wsierp_1(k6_fib_num2(k1_nat_1(k2_nat_1(np__2,A),np__1))) = k3_pre_ff(k1_nat_1(k2_nat_1(np__2,A),np__2)) ) ).
fof(t69_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> r2_int_2(k3_pre_ff(A),k3_pre_ff(k1_nat_1(A,np__1))) ) ).
fof(t70_fib_num2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( B != np__1
& r1_nat_1(B,k3_pre_ff(A))
& r1_nat_1(B,k3_pre_ff(k5_binarith(A,np__1))) ) ) ) ).
fof(t71_fib_num2,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( ( ~ v1_xboole_0(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> ( ( v1_int_2(A)
& v1_int_2(B)
& r1_nat_1(A,k3_pre_ff(B)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(B,C)
& C != np__0
& r1_nat_1(A,k3_pre_ff(C)) ) ) ) ) ) ).
fof(t72_fib_num2,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> m1_pythtrip(k8_domain_1(k5_numbers,k2_nat_1(k3_pre_ff(A),k3_pre_ff(k1_nat_1(A,np__3))),k2_nat_1(k2_nat_1(np__2,k3_pre_ff(k1_nat_1(A,np__1))),k3_pre_ff(k1_nat_1(A,np__2))),k1_nat_1(k2_pepin(k3_pre_ff(k1_nat_1(A,np__1))),k2_pepin(k3_pre_ff(k1_nat_1(A,np__2)))))) ) ).
fof(s1_fib_num2,axiom,
( ( p1_s1_fib_num2(np__1)
& p1_s1_fib_num2(np__2)
& ! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ( ( p1_s1_fib_num2(A)
& p1_s1_fib_num2(k1_nat_1(A,np__1)) )
=> p1_s1_fib_num2(k1_nat_1(A,np__2)) ) ) )
=> ! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> p1_s1_fib_num2(A) ) ) ).
fof(s2_fib_num2,axiom,
( ( p1_s2_fib_num2(np__2)
& p1_s2_fib_num2(np__3)
& ! [A] :
( ( ~ v1_realset1(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ( ( p1_s2_fib_num2(A)
& p1_s2_fib_num2(k1_nat_1(A,np__1)) )
=> p1_s2_fib_num2(k1_nat_1(A,np__2)) ) ) )
=> ! [A] :
( ( ~ v1_realset1(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> p1_s2_fib_num2(A) ) ) ).
fof(dt_k1_fib_num2,axiom,
! [A,B] :
( ( v1_funct_1(A)
& v1_funct_2(A,k5_numbers,k5_numbers)
& m1_relset_1(A,k5_numbers,k5_numbers)
& v1_finset_1(B)
& v5_membered(B)
& v1_setfam_1(B) )
=> m2_finseq_1(k1_fib_num2(A,B),k5_numbers) ) ).
fof(dt_k2_fib_num2,axiom,
( v1_funct_1(k2_fib_num2)
& v1_funct_2(k2_fib_num2,k5_numbers,k5_numbers)
& m2_relset_1(k2_fib_num2,k5_numbers,k5_numbers) ) ).
fof(dt_k3_fib_num2,axiom,
m1_subset_1(k3_fib_num2,k1_zfmisc_1(k5_numbers)) ).
fof(dt_k4_fib_num2,axiom,
m1_subset_1(k4_fib_num2,k1_zfmisc_1(k5_numbers)) ).
fof(dt_k5_fib_num2,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m2_finseq_1(k5_fib_num2(A),k5_numbers) ) ).
fof(dt_k6_fib_num2,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m2_finseq_1(k6_fib_num2(A),k5_numbers) ) ).
fof(d3_fib_num2,axiom,
k3_fib_num2 = a_0_0_fib_num2 ).
fof(d4_fib_num2,axiom,
k4_fib_num2 = a_0_1_fib_num2 ).
fof(fraenkel_a_0_0_fib_num2,axiom,
! [A] :
( r2_hidden(A,a_0_0_fib_num2)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k2_nat_1(np__2,B) ) ) ).
fof(fraenkel_a_0_1_fib_num2,axiom,
! [A] :
( r2_hidden(A,a_0_1_fib_num2)
<=> ? [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
& A = k1_nat_1(k2_nat_1(np__2,B),np__1) ) ) ).
%------------------------------------------------------------------------------