SET007 Axioms: SET007+797.ax
%------------------------------------------------------------------------------
% File : SET007+797 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : High Speed Modulo Calculation Algorithm with Radix-2^k SD Number
% 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 : radix_6 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 42 ( 0 unt; 0 def)
% Number of atoms : 288 ( 30 equ)
% Maximal formula atoms : 11 ( 6 avg)
% Number of connectives : 279 ( 33 ~; 1 |; 73 &)
% ( 7 <=>; 165 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 11 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 0 prp; 1-4 aty)
% Number of functors : 34 ( 34 usr; 6 con; 0-4 aty)
% Number of variables : 152 ( 152 !; 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_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(np__2,C) )
=> k8_radix_1(k1_nat_1(B,A),C,k6_radix_5(k1_nat_1(B,A),B,C)) = k8_radix_1(B,C,k6_radix_5(B,B,C)) ) ) ) ) ) ).
fof(t2_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B)
& r1_xreal_0(k8_radix_1(A,B,k6_radix_5(A,A,B)),np__0) ) ) ) ).
fof(d1_radix_6,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_finseq_2(D,k3_radix_1(C),k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C)))
=> ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__2)))
=> ( ( r1_xreal_0(B,A)
=> k1_radix_6(A,B,C,D) = k1_funct_1(D,A) )
& ( ~ r1_xreal_0(B,A)
=> k1_radix_6(A,B,C,D) = np__0 ) ) ) ) ) ) ) ).
fof(d2_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ! [D] :
( m2_finseq_2(D,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ( D = k2_radix_6(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k2_finseq_1(k1_nat_1(A,np__2)))
=> k4_radix_1(E,B,k1_nat_1(A,np__2),D) = k1_radix_6(E,A,B,C) ) ) ) ) ) ) ) ).
fof(d3_radix_6,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_finseq_2(D,k3_radix_1(C),k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C)))
=> ( ( r1_xreal_0(np__2,C)
& r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__2))) )
=> ( ( r1_xreal_0(B,A)
=> k3_radix_6(A,B,C,D) = k1_funct_1(D,A) )
& ( ~ r1_xreal_0(B,A)
=> k3_radix_6(A,B,C,D) = k6_xcmplx_0(k1_radix_1(C),np__1) ) ) ) ) ) ) ) ).
fof(d4_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ! [D] :
( m2_finseq_2(D,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ( D = k4_radix_6(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k2_finseq_1(k1_nat_1(A,np__2)))
=> k4_radix_1(E,B,k1_nat_1(A,np__2),D) = k3_radix_6(E,A,B,C) ) ) ) ) ) ) ) ).
fof(d5_radix_6,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_finseq_2(D,k3_radix_1(C),k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C)))
=> ( ( r1_xreal_0(np__2,C)
& r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__2))) )
=> ( ( r1_xreal_0(B,A)
=> k5_radix_6(A,B,C,D) = k1_funct_1(D,A) )
& ( ~ r1_xreal_0(B,A)
=> k5_radix_6(A,B,C,D) = k2_xcmplx_0(k4_xcmplx_0(k1_radix_1(C)),np__1) ) ) ) ) ) ) ) ).
fof(d6_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ! [D] :
( m2_finseq_2(D,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ( D = k6_radix_6(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k2_finseq_1(k1_nat_1(A,np__2)))
=> k4_radix_1(E,B,k1_nat_1(A,np__2),D) = k5_radix_6(E,A,B,C) ) ) ) ) ) ) ) ).
fof(t3_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B) )
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),B,C),k8_radix_1(k1_nat_1(A,np__2),B,k4_radix_6(A,B,C))) ) ) ) ) ).
fof(t4_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B) )
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),B,k6_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,C)) ) ) ) ) ).
fof(d7_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( v1_int_1(C)
=> ( r1_radix_6(A,B,C)
<=> ( ~ r1_xreal_0(k2_wsierp_1(k1_radix_1(B),A),C)
& r1_xreal_0(k2_wsierp_1(k1_radix_1(B),k5_binarith(A,np__1)),C) ) ) ) ) ) ).
fof(t5_radix_6,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)
=> ( r2_hidden(D,k2_finseq_1(B))
=> r1_xreal_0(np__0,k4_radix_1(D,C,B,k10_radix_1(C,B,A))) ) ) ) ) ) ).
fof(t6_radix_6,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)
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B)
& r1_radix_6(A,B,C)
& r1_xreal_0(k4_radix_1(A,B,A,k10_radix_1(B,A,C)),np__0) ) ) ) ) ).
fof(t7_radix_6,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)
=> ( ( r1_xreal_0(np__1,B)
& r1_xreal_0(np__2,C)
& r1_radix_6(B,C,A) )
=> r1_xreal_0(k8_radix_1(k1_nat_1(B,np__2),C,k6_radix_5(k1_nat_1(B,np__2),B,C)),A) ) ) ) ) ).
fof(t8_radix_6,axiom,
! [A] :
( v1_int_1(A)
=> ! [B] :
( v1_int_1(B)
=> ! [C] :
( v1_int_1(C)
=> ~ ( ~ r1_xreal_0(k2_xcmplx_0(A,C),B)
& ~ r1_xreal_0(C,np__0)
& ! [D] :
( v1_int_1(D)
=> ~ ( ~ r1_xreal_0(k6_xcmplx_0(A,k3_xcmplx_0(D,C)),k4_xcmplx_0(C))
& ~ r1_xreal_0(C,k6_xcmplx_0(B,k3_xcmplx_0(D,C))) ) ) ) ) ) ) ).
fof(t9_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B) )
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k4_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k10_radix_1(B,k1_nat_1(A,np__2),np__0))) = k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k4_radix_5(k1_nat_1(A,np__2),A,B))) ) ) ) ) ).
fof(t10_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B) )
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ~ r1_xreal_0(k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k6_radix_5(k1_nat_1(A,np__2),A,B))),k8_radix_1(k1_nat_1(A,np__2),B,k4_radix_6(A,B,C))) ) ) ) ) ).
fof(t11_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B) )
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k6_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k10_radix_1(B,k1_nat_1(A,np__2),np__0))) = k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_5(k1_nat_1(A,np__2),A,B))) ) ) ) ) ).
fof(t12_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B) )
=> k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k10_radix_1(B,k1_nat_1(A,np__2),np__0))) = k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k6_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k4_radix_5(k1_nat_1(A,np__2),A,B))) ) ) ) ) ).
fof(t13_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B) )
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ~ r1_xreal_0(k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k6_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k6_radix_5(k1_nat_1(A,np__2),A,B))),k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C))) ) ) ) ) ).
fof(t14_radix_6,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_finseq_2(D,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B)
& r1_radix_6(A,B,C)
& ! [E] :
( v1_int_1(E)
=> ~ ( ~ r1_xreal_0(k6_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,D)),k3_xcmplx_0(E,C)),k4_xcmplx_0(C))
& ~ r1_xreal_0(C,k6_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k4_radix_6(A,B,D)),k3_xcmplx_0(E,C))) ) ) ) ) ) ) ) ).
fof(t15_radix_6,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_finseq_2(D,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B)
& r1_radix_6(A,B,C)
& ! [E] :
( v1_int_1(E)
=> ~ ( ~ r1_xreal_0(k6_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k6_radix_6(A,B,D)),k3_xcmplx_0(E,C)),k4_xcmplx_0(C))
& ~ r1_xreal_0(C,k6_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,D)),k3_xcmplx_0(E,C))) ) ) ) ) ) ) ) ).
fof(t16_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B)
& ~ ( r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,C))
& r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),B,C),k8_radix_1(k1_nat_1(A,np__2),B,k4_radix_6(A,B,C))) )
& ~ ( r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),B,k6_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,C))
& ~ r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,C)) ) ) ) ) ) ).
fof(d8_radix_6,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_finseq_2(D,k3_radix_1(C),k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C)))
=> ( r2_hidden(A,k2_finseq_1(k1_nat_1(B,np__2)))
=> ( ( ~ r1_xreal_0(B,A)
=> k7_radix_6(A,B,C,D) = k1_funct_1(D,A) )
& ( r1_xreal_0(B,A)
=> k7_radix_6(A,B,C,D) = np__0 ) ) ) ) ) ) ) ).
fof(d9_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ! [D] :
( m2_finseq_2(D,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ( D = k8_radix_6(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k2_finseq_1(k1_nat_1(A,np__2)))
=> k4_radix_1(E,B,k1_nat_1(A,np__2),D) = k7_radix_6(E,A,B,C) ) ) ) ) ) ) ) ).
fof(t17_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ( ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B) )
=> k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C)),k8_radix_1(k1_nat_1(A,np__2),B,k8_radix_6(A,B,C))) = k2_xcmplx_0(k8_radix_1(k1_nat_1(A,np__2),B,C),k8_radix_1(k1_nat_1(A,np__2),B,k10_radix_1(B,k1_nat_1(A,np__2),np__0))) ) ) ) ) ).
fof(t18_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_finseq_2(C,k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B)))
=> ~ ( r1_xreal_0(np__1,A)
& r1_xreal_0(np__2,B)
& ~ r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),B,k8_radix_6(A,B,C)),np__0)
& r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),B,C),k8_radix_1(k1_nat_1(A,np__2),B,k2_radix_6(A,B,C))) ) ) ) ) ).
fof(d10_radix_6,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)
=> ( r1_xreal_0(np__2,C)
=> ( ( ~ r1_xreal_0(A,B)
=> k9_radix_6(A,B,C) = np__0 )
& ( A = B
=> k9_radix_6(A,B,C) = np__1 )
& ( r1_xreal_0(A,B)
=> ( A = B
| k9_radix_6(A,B,C) = k2_xcmplx_0(k4_xcmplx_0(k1_radix_1(C)),np__1) ) ) ) ) ) ) ) ).
fof(d11_radix_6,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_finseq_2(D,k3_radix_1(C),k4_finseq_2(A,k3_radix_1(C)))
=> ( D = k10_radix_6(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k2_finseq_1(A))
=> k4_radix_1(E,C,A,D) = k9_radix_6(E,B,C) ) ) ) ) ) ) ) ).
fof(t19_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r2_hidden(B,k2_finseq_1(A))
& r1_xreal_0(np__2,C) )
=> k8_radix_1(A,C,k10_radix_6(A,B,C)) = np__1 ) ) ) ) ) ).
fof(d12_radix_6,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_finseq_2(D,k3_radix_1(C),k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C)))
=> ( r2_radix_6(A,B,C,D)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(E,A)
=> k4_radix_1(E,C,k1_nat_1(B,np__2),D) = np__0 ) ) ) ) ) ) ) ).
fof(t20_radix_6,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ( r1_xreal_0(np__1,A)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_finseq_2(D,k3_radix_1(C),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(C)))
=> ~ ( r1_xreal_0(np__2,C)
& r2_hidden(B,k2_finseq_1(k1_nat_1(A,np__2)))
& r2_radix_6(B,A,C,k8_radix_6(A,C,D))
& ~ r1_xreal_0(k4_radix_1(B,C,k1_nat_1(A,np__2),k8_radix_6(A,C,D)),np__0)
& r1_xreal_0(k8_radix_1(k1_nat_1(A,np__2),C,k8_radix_6(A,C,D)),np__0) ) ) ) ) ) ) ).
fof(dt_k1_radix_6,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C))) )
=> m2_subset_1(k1_radix_6(A,B,C,D),k6_wsierp_1,k3_radix_1(C)) ) ).
fof(dt_k2_radix_6,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B))) )
=> m2_finseq_2(k2_radix_6(A,B,C),k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B))) ) ).
fof(dt_k3_radix_6,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C))) )
=> m2_subset_1(k3_radix_6(A,B,C,D),k6_wsierp_1,k3_radix_1(C)) ) ).
fof(dt_k4_radix_6,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B))) )
=> m2_finseq_2(k4_radix_6(A,B,C),k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B))) ) ).
fof(dt_k5_radix_6,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C))) )
=> m2_subset_1(k5_radix_6(A,B,C,D),k6_wsierp_1,k3_radix_1(C)) ) ).
fof(dt_k6_radix_6,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B))) )
=> m2_finseq_2(k6_radix_6(A,B,C),k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B))) ) ).
fof(dt_k7_radix_6,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k4_finseq_2(k1_nat_1(B,np__2),k3_radix_1(C))) )
=> m2_subset_1(k7_radix_6(A,B,C,D),k6_wsierp_1,k3_radix_1(C)) ) ).
fof(dt_k8_radix_6,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B))) )
=> m2_finseq_2(k8_radix_6(A,B,C),k3_radix_1(B),k4_finseq_2(k1_nat_1(A,np__2),k3_radix_1(B))) ) ).
fof(dt_k9_radix_6,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(k9_radix_6(A,B,C),k6_wsierp_1,k3_radix_1(C)) ) ).
fof(dt_k10_radix_6,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& m1_subset_1(C,k5_numbers) )
=> m2_finseq_2(k10_radix_6(A,B,C),k3_radix_1(C),k4_finseq_2(A,k3_radix_1(C))) ) ).
%------------------------------------------------------------------------------