SET007 Axioms: SET007+381.ax
%------------------------------------------------------------------------------
% File : SET007+381 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Two Programs for bf SCM. Part II - Programs
% 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_fusc [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 12 ( 5 unt; 0 def)
% Number of atoms : 65 ( 27 equ)
% Maximal formula atoms : 14 ( 5 avg)
% Number of connectives : 62 ( 9 ~; 2 |; 20 &)
% ( 1 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 7 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-6 aty)
% Number of functors : 41 ( 41 usr; 13 con; 0-3 aty)
% Number of variables : 21 ( 20 !; 1 ?)
% 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(d1_fib_fusc,axiom,
k1_fib_fusc = k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k10_ami_3(k16_ami_3(np__2),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(np__3),k15_ami_3(np__0)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_3(k15_ami_3(np__1),k15_ami_3(np__0)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k9_ami_3(k16_ami_3(np__1),k15_ami_3(np__1)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(np__4),k15_ami_3(np__2)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(np__2),k15_ami_3(np__3)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k4_ami_3(k15_ami_3(np__3),k15_ami_3(np__4)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_ami_3(k16_ami_3(np__3)))) ).
fof(t1_fib_fusc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m1_scm_1(B,k1_fib_fusc,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(np__1),k1_scm_1(A)),k1_scm_1(np__0)),k1_scm_1(np__0)),np__0,np__0,np__0)
=> ( v9_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& ( A = np__0
=> k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,B) = np__1 )
& ( ~ r1_xreal_0(A,np__0)
=> k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,B) = k6_xcmplx_0(k2_nat_1(np__6,A),np__2) )
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),k15_ami_3(np__3)) = k3_pre_ff(A) ) ) ) ).
fof(d2_fib_fusc,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( B = k2_fib_fusc(A)
<=> ~ ( ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( A = C
& B = k5_pre_ff(C) ) )
& ~ ( ~ m2_subset_1(A,k1_numbers,k5_numbers)
& B = np__0 ) ) ) ) ) ).
fof(d3_fib_fusc,axiom,
k3_fib_fusc = k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k9_ami_3(k16_ami_3(np__8),k15_ami_3(np__1))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k3_ami_3(k15_ami_3(np__4),k15_ami_3(np__0)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k7_ami_3(k15_ami_3(np__1),k15_ami_3(np__4)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k9_ami_3(k16_ami_3(np__6),k15_ami_3(np__4)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k4_ami_3(k15_ami_3(np__3),k15_ami_3(np__2)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_ami_3(k16_ami_3(np__0)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k4_ami_3(k15_ami_3(np__2),k15_ami_3(np__3)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k8_ami_3(k16_ami_3(np__0)))),k12_finseq_1(u4_ami_1(k1_tarski(k4_numbers),k1_ami_3),k5_ami_1(k1_tarski(k4_numbers),k1_ami_3))) ).
fof(t2_fib_fusc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> ! [B] :
( m1_scm_1(B,k3_fib_fusc,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(np__2),k1_scm_1(A)),k1_scm_1(np__1)),k1_scm_1(np__0)),np__0,np__0,np__0)
=> ( v9_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),k15_ami_3(np__3)) = k5_pre_ff(A)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,B) = k2_xcmplx_0(k3_xcmplx_0(np__6,k2_xcmplx_0(k1_int_1(k6_power(np__2,A)),np__1)),np__1) ) ) ) ) ).
fof(t3_fib_fusc,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] :
( m1_scm_1(E,k1_fib_fusc,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(np__1),k1_scm_1(A)),k1_scm_1(C)),k1_scm_1(D)),np__3,np__0,np__0)
=> ( ( C = k3_pre_ff(B)
& D = k3_pre_ff(k1_nat_1(B,np__1)) )
=> ( r1_xreal_0(A,np__0)
| ( v9_ami_1(E,k1_tarski(k4_numbers),k1_ami_3)
& k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,E) = k6_xcmplx_0(k2_nat_1(np__6,A),np__4)
& ? [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
& F = k6_xcmplx_0(k1_nat_1(B,A),np__1)
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),k15_ami_3(np__2)) = k3_pre_ff(F)
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),k15_ami_3(np__3)) = k3_pre_ff(k1_nat_1(F,np__1)) ) ) ) ) ) ) ) ) ) ).
fof(t4_fib_fusc,axiom,
$true ).
fof(t5_fib_fusc,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] :
( m1_scm_1(E,k3_fib_fusc,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(np__2),k1_scm_1(A)),k1_scm_1(C)),k1_scm_1(D)),np__0,np__0,np__0)
=> ( k5_pre_ff(B) = k1_nat_1(k2_nat_1(C,k5_pre_ff(A)),k2_nat_1(D,k5_pre_ff(k1_nat_1(A,np__1))))
=> ( r1_xreal_0(B,np__0)
| ( v9_ami_1(E,k1_tarski(k4_numbers),k1_ami_3)
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,E),k15_ami_3(np__3)) = k5_pre_ff(B)
& ( A = np__0
=> k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,E) = np__1 )
& ( ~ r1_xreal_0(A,np__0)
=> k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,E) = k2_xcmplx_0(k3_xcmplx_0(np__6,k2_xcmplx_0(k1_int_1(k6_power(np__2,A)),np__1)),np__1) ) ) ) ) ) ) ) ) ) ).
fof(t6_fib_fusc,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(A,np__0)
=> ! [B] :
( m1_scm_1(B,k3_fib_fusc,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k8_finseq_1(k4_numbers,k1_scm_1(np__2),k1_scm_1(A)),k1_scm_1(np__1)),k1_scm_1(np__0)),np__0,np__0,np__0)
=> ( v9_ami_1(B,k1_tarski(k4_numbers),k1_ami_3)
& k2_ami_3(k12_ami_1(k1_tarski(k4_numbers),k1_ami_3,B),k15_ami_3(np__3)) = k5_pre_ff(A)
& ( A = np__0
=> k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,B) = np__1 )
& ( ~ r1_xreal_0(A,np__0)
=> k2_scm_1(k1_tarski(k4_numbers),k1_ami_3,B) = k2_xcmplx_0(k3_xcmplx_0(np__6,k2_xcmplx_0(k1_int_1(k6_power(np__2,A)),np__1)),np__1) ) ) ) ) ) ).
fof(dt_k1_fib_fusc,axiom,
m2_finseq_1(k1_fib_fusc,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ).
fof(dt_k2_fib_fusc,axiom,
! [A] :
( v1_int_1(A)
=> m2_subset_1(k2_fib_fusc(A),k1_numbers,k5_numbers) ) ).
fof(dt_k3_fib_fusc,axiom,
m2_finseq_1(k3_fib_fusc,u4_ami_1(k1_tarski(k4_numbers),k1_ami_3)) ).
%------------------------------------------------------------------------------