SET007 Axioms: SET007+564.ax
%------------------------------------------------------------------------------
% File : SET007+564 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Algebraic Group on Fixed-length Bit Integer
% Version : [Urb08] axioms.
% English : Algebraic Group on Fixed-length Bit Integer and its Adaptation
% to IDEA Cryptography
% 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 : idea_1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 100 ( 4 unt; 0 def)
% Number of atoms : 783 ( 163 equ)
% Maximal formula atoms : 59 ( 7 avg)
% Number of connectives : 755 ( 72 ~; 2 |; 351 &)
% ( 14 <=>; 316 =>; 0 <=; 0 <~>)
% Maximal formula depth : 50 ( 10 avg)
% Maximal term depth : 12 ( 1 avg)
% Number of predicates : 24 ( 22 usr; 1 prp; 0-4 aty)
% Number of functors : 61 ( 61 usr; 12 con; 0-5 aty)
% Number of variables : 306 ( 306 !; 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(fc1_idea_1,axiom,
~ v1_xboole_0(k14_idea_1) ).
fof(fc2_idea_1,axiom,
( ~ v1_xboole_0(k14_idea_1)
& v1_fraenkel(k14_idea_1) ) ).
fof(cc1_idea_1,axiom,
! [A] :
( m1_subset_1(A,k14_idea_1)
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(A)
& v1_finseq_1(A) ) ) ).
fof(fc3_idea_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k5_numbers)
& m1_matrix_1(D,k5_numbers,B,np__6) )
=> ( v1_relat_1(k17_idea_1(A,B,C,D))
& v1_funct_1(k17_idea_1(A,B,C,D))
& v1_finset_1(k17_idea_1(A,B,C,D))
& v1_finseq_1(k17_idea_1(A,B,C,D))
& v1_funcop_1(k17_idea_1(A,B,C,D)) ) ) ).
fof(fc4_idea_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k5_numbers)
& m1_matrix_1(D,k5_numbers,B,np__6) )
=> ( v1_relat_1(k18_idea_1(A,B,C,D))
& v1_funct_1(k18_idea_1(A,B,C,D))
& v1_finset_1(k18_idea_1(A,B,C,D))
& v1_finseq_1(k18_idea_1(A,B,C,D))
& v1_funcop_1(k18_idea_1(A,B,C,D)) ) ) ).
fof(t1_idea_1,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)
=> ~ ( v1_int_2(B)
& ~ r1_xreal_0(B,A)
& ~ r1_xreal_0(B,C)
& A != np__0
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( k4_nat_1(k2_nat_1(D,A),B) = C
& ~ r1_xreal_0(B,D) ) ) ) ) ) ) ).
fof(t2_idea_1,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)
=> ~ ( A != np__0
& k4_nat_1(B,A) = k4_nat_1(C,A)
& r1_xreal_0(B,C)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k6_xcmplx_0(C,B) != k2_nat_1(A,D) ) ) ) ) ) ).
fof(t3_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_xreal_0(k6_xcmplx_0(A,B),A) ) ) ).
fof(t4_idea_1,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(B,C)
=> r1_xreal_0(k6_xcmplx_0(B,A),C) ) ) ) ) ).
fof(t5_idea_1,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(A,np__0)
& ~ r1_xreal_0(B,np__0)
& ~ r1_xreal_0(C,A)
& ~ r1_xreal_0(C,B)
& v1_int_2(C)
& k4_nat_1(k2_nat_1(A,B),C) = np__0 ) ) ) ) ).
fof(d1_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_idea_1(A) = k2_finseq_2(A,k7_margrel1) ) ).
fof(d2_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> ! [C] :
( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> ! [D] :
( m2_finseq_2(D,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> ( D = k2_idea_1(A,B,C)
<=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k2_finseq_1(A))
=> k4_finseq_4(k5_numbers,k6_margrel1,D,E) = k4_binarith(k4_finseq_4(k5_numbers,k6_margrel1,B,E),k4_finseq_4(k5_numbers,k6_margrel1,C,E)) ) ) ) ) ) ) ) ).
fof(t6_idea_1,axiom,
$true ).
fof(t7_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> k2_idea_1(A,B,B) = k1_idea_1(A) ) ) ).
fof(t8_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> ! [C] :
( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> k2_idea_1(A,B,C) = k2_idea_1(A,C,B) ) ) ) ).
fof(t9_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> k3_idea_1(A,k1_idea_1(A),B) = B ) ) ).
fof(t10_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_2(B,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> ! [C] :
( m2_finseq_2(C,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> ! [D] :
( m2_finseq_2(D,k6_margrel1,k4_finseq_2(A,k6_margrel1))
=> k3_idea_1(A,k3_idea_1(A,B,C),D) = k3_idea_1(A,B,k3_idea_1(A,C,D)) ) ) ) ) ).
fof(d3_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_idea_1(A,B)
<=> ~ r1_xreal_0(k3_series_1(np__2,A),B) ) ) ) ).
fof(t11_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> k1_binari_3(A,np__0) = k1_idea_1(A) ) ).
fof(d4_idea_1,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)
=> k4_idea_1(A,B,C) = k4_nat_1(k1_nat_1(B,C),k3_series_1(np__2,A)) ) ) ) ).
fof(d5_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_idea_1(A,B)
=> k5_idea_1(A,B) = k6_xcmplx_0(k3_series_1(np__2,A),B) ) ) ) ).
fof(d6_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> k6_idea_1(A,B) = k4_nat_1(k5_idea_1(A,B),k3_series_1(np__2,A)) ) ) ).
fof(t12_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_idea_1(B,A)
=> k4_idea_1(B,A,k6_idea_1(B,A)) = np__0 ) ) ) ).
fof(t13_idea_1,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)
=> k4_idea_1(C,A,B) = k4_idea_1(C,B,A) ) ) ) ).
fof(t14_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_idea_1(B,A)
=> k4_idea_1(B,np__0,A) = A ) ) ) ).
fof(t15_idea_1,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)
=> k4_idea_1(C,k4_idea_1(C,A,B),D) = k4_idea_1(C,A,k4_idea_1(C,B,D)) ) ) ) ) ).
fof(t16_idea_1,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_idea_1(C,k4_idea_1(C,A,B)) ) ) ) ).
fof(t17_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> r1_idea_1(B,k6_idea_1(B,A)) ) ) ).
fof(d7_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( B = np__0
=> k7_idea_1(A,B) = k3_series_1(np__2,A) )
& ( B != np__0
=> k7_idea_1(A,B) = B ) ) ) ) ).
fof(t18_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_idea_1(B,A)
=> ( r1_xreal_0(k7_idea_1(B,A),k3_series_1(np__2,B))
& ~ r1_xreal_0(k7_idea_1(B,A),np__0) ) ) ) ) ).
fof(t19_idea_1,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_idea_1(A,B)
& r1_idea_1(A,C)
& k7_idea_1(A,B) = k7_idea_1(A,C) )
=> B = C ) ) ) ) ).
fof(d8_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( B = k3_series_1(np__2,A)
=> k8_idea_1(A,B) = np__0 )
& ( B != k3_series_1(np__2,A)
=> k8_idea_1(A,B) = B ) ) ) ) ).
fof(t20_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_idea_1(B,A)
=> r1_idea_1(B,k8_idea_1(B,A)) ) ) ) ).
fof(t21_idea_1,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)
=> ( k8_idea_1(A,B) = k8_idea_1(A,C)
=> ( B = np__0
| C = np__0
| B = C ) ) ) ) ) ).
fof(d9_idea_1,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)
=> k9_idea_1(A,B,C) = k8_idea_1(A,k4_nat_1(k2_nat_1(k7_idea_1(A,B),k7_idea_1(A,C)),k1_nat_1(k3_series_1(np__2,A),np__1))) ) ) ) ).
fof(d10_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( ( r1_idea_1(A,B)
& v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1)) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( C = k10_idea_1(A,B)
<=> ( k9_idea_1(A,B,C) = np__1
& r1_idea_1(A,C) ) ) ) ) ) ) ).
fof(t22_idea_1,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)
=> k9_idea_1(C,A,B) = k9_idea_1(C,B,A) ) ) ) ).
fof(t23_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_idea_1(B,A)
=> k9_idea_1(B,np__1,A) = A ) ) ) ).
fof(t24_idea_1,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)
=> ( ( v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_idea_1(A,B)
& r1_idea_1(A,C)
& r1_idea_1(A,D) )
=> k9_idea_1(A,k9_idea_1(A,B,C),D) = k9_idea_1(A,B,k9_idea_1(A,C,D)) ) ) ) ) ) ).
fof(t25_idea_1,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_idea_1(C,k9_idea_1(C,A,B)) ) ) ) ).
fof(t26_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( k8_idea_1(B,A) = np__1
=> A = np__1 ) ) ) ).
fof(d11_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( D = k11_idea_1(A,B,C)
<=> ( k3_finseq_1(D) = k3_finseq_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(B))
=> ( ( E = np__1
=> k3_wsierp_1(D,E) = k9_idea_1(A,k3_wsierp_1(B,np__1),k3_wsierp_1(C,np__1)) )
& ( E = np__2
=> k3_wsierp_1(D,E) = k4_idea_1(A,k3_wsierp_1(B,np__2),k3_wsierp_1(C,np__2)) )
& ( E = np__3
=> k3_wsierp_1(D,E) = k4_idea_1(A,k3_wsierp_1(B,np__3),k3_wsierp_1(C,np__3)) )
& ( E = np__4
=> k3_wsierp_1(D,E) = k9_idea_1(A,k3_wsierp_1(B,np__4),k3_wsierp_1(C,np__4)) )
& ~ ( E != np__1
& E != np__2
& E != np__3
& E != np__4
& k3_wsierp_1(D,E) != k3_wsierp_1(B,E) ) ) ) ) ) ) ) ) ) ) ).
fof(d12_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( D = k12_idea_1(A,B,C)
<=> ( k3_finseq_1(D) = k3_finseq_1(B)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_finseq_1(B))
=> ( ( E = np__1
=> k3_wsierp_1(D,E) = k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__1)),k1_binari_3(A,k9_idea_1(A,k4_idea_1(A,k9_idea_1(A,k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__1)),k1_binari_3(A,k3_wsierp_1(B,np__3)))),k3_wsierp_1(C,np__5)),k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__2)),k1_binari_3(A,k3_wsierp_1(B,np__4))))),k3_wsierp_1(C,np__6))))) )
& ( E = np__2
=> k3_wsierp_1(D,E) = k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__2)),k1_binari_3(A,k4_idea_1(A,k9_idea_1(A,k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__1)),k1_binari_3(A,k3_wsierp_1(B,np__3)))),k3_wsierp_1(C,np__5)),k9_idea_1(A,k4_idea_1(A,k9_idea_1(A,k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__1)),k1_binari_3(A,k3_wsierp_1(B,np__3)))),k3_wsierp_1(C,np__5)),k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__2)),k1_binari_3(A,k3_wsierp_1(B,np__4))))),k3_wsierp_1(C,np__6)))))) )
& ( E = np__3
=> k3_wsierp_1(D,E) = k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__3)),k1_binari_3(A,k9_idea_1(A,k4_idea_1(A,k9_idea_1(A,k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__1)),k1_binari_3(A,k3_wsierp_1(B,np__3)))),k3_wsierp_1(C,np__5)),k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__2)),k1_binari_3(A,k3_wsierp_1(B,np__4))))),k3_wsierp_1(C,np__6))))) )
& ( E = np__4
=> k3_wsierp_1(D,E) = k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__4)),k1_binari_3(A,k4_idea_1(A,k9_idea_1(A,k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__1)),k1_binari_3(A,k3_wsierp_1(B,np__3)))),k3_wsierp_1(C,np__5)),k9_idea_1(A,k4_idea_1(A,k9_idea_1(A,k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__1)),k1_binari_3(A,k3_wsierp_1(B,np__3)))),k3_wsierp_1(C,np__5)),k9_binarith(A,k3_idea_1(A,k1_binari_3(A,k3_wsierp_1(B,np__2)),k1_binari_3(A,k3_wsierp_1(B,np__4))))),k3_wsierp_1(C,np__6)))))) )
& ~ ( E != np__1
& E != np__2
& E != np__3
& E != np__4
& k3_wsierp_1(D,E) != k3_wsierp_1(B,E) ) ) ) ) ) ) ) ) ) ) ).
fof(d13_idea_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ( B = k13_idea_1(A)
<=> ( k3_finseq_1(B) = k3_finseq_1(A)
& ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_finseq_1(A))
=> k3_wsierp_1(B,C) = k2_cqc_lang(k5_numbers,C,np__2,k3_wsierp_1(A,np__3),k2_cqc_lang(k5_numbers,C,np__3,k3_wsierp_1(A,np__2),k3_wsierp_1(A,C))) ) ) ) ) ) ) ).
fof(t27_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ( r1_xreal_0(np__4,k3_finseq_1(B))
=> ( r1_idea_1(A,k3_wsierp_1(k11_idea_1(A,B,C),np__1))
& r1_idea_1(A,k3_wsierp_1(k11_idea_1(A,B,C),np__2))
& r1_idea_1(A,k3_wsierp_1(k11_idea_1(A,B,C),np__3))
& r1_idea_1(A,k3_wsierp_1(k11_idea_1(A,B,C),np__4)) ) ) ) ) ) ).
fof(t28_idea_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(np__4,k3_finseq_1(A))
=> ( r1_idea_1(C,k3_wsierp_1(k12_idea_1(C,A,B),np__1))
& r1_idea_1(C,k3_wsierp_1(k12_idea_1(C,A,B),np__2))
& r1_idea_1(C,k3_wsierp_1(k12_idea_1(C,A,B),np__3))
& r1_idea_1(C,k3_wsierp_1(k12_idea_1(C,A,B),np__4)) ) ) ) ) ) ).
fof(t29_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ( ( r1_xreal_0(np__4,k3_finseq_1(B))
& r1_idea_1(A,k3_wsierp_1(B,np__1))
& r1_idea_1(A,k3_wsierp_1(B,np__2))
& r1_idea_1(A,k3_wsierp_1(B,np__3))
& r1_idea_1(A,k3_wsierp_1(B,np__4)) )
=> ( r1_idea_1(A,k3_wsierp_1(k13_idea_1(B),np__1))
& r1_idea_1(A,k3_wsierp_1(k13_idea_1(B),np__2))
& r1_idea_1(A,k3_wsierp_1(k13_idea_1(B),np__3))
& r1_idea_1(A,k3_wsierp_1(k13_idea_1(B),np__4)) ) ) ) ) ).
fof(t30_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_xreal_0(np__4,k3_finseq_1(B))
& r1_idea_1(A,k3_wsierp_1(B,np__1))
& r1_idea_1(A,k3_wsierp_1(B,np__2))
& r1_idea_1(A,k3_wsierp_1(B,np__3))
& r1_idea_1(A,k3_wsierp_1(B,np__4))
& r1_idea_1(A,k3_wsierp_1(C,np__1))
& r1_idea_1(A,k3_wsierp_1(C,np__2))
& r1_idea_1(A,k3_wsierp_1(C,np__3))
& r1_idea_1(A,k3_wsierp_1(C,np__4))
& k3_wsierp_1(D,np__1) = k10_idea_1(A,k3_wsierp_1(C,np__1))
& k3_wsierp_1(D,np__2) = k6_idea_1(A,k3_wsierp_1(C,np__2))
& k3_wsierp_1(D,np__3) = k6_idea_1(A,k3_wsierp_1(C,np__3))
& k3_wsierp_1(D,np__4) = k10_idea_1(A,k3_wsierp_1(C,np__4)) )
=> k11_idea_1(A,k11_idea_1(A,B,C),D) = B ) ) ) ) ) ).
fof(t31_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_xreal_0(np__4,k3_finseq_1(B))
& r1_idea_1(A,k3_wsierp_1(B,np__1))
& r1_idea_1(A,k3_wsierp_1(B,np__2))
& r1_idea_1(A,k3_wsierp_1(B,np__3))
& r1_idea_1(A,k3_wsierp_1(B,np__4))
& r1_idea_1(A,k3_wsierp_1(C,np__1))
& r1_idea_1(A,k3_wsierp_1(C,np__2))
& r1_idea_1(A,k3_wsierp_1(C,np__3))
& r1_idea_1(A,k3_wsierp_1(C,np__4))
& k3_wsierp_1(D,np__1) = k10_idea_1(A,k3_wsierp_1(C,np__1))
& k3_wsierp_1(D,np__2) = k6_idea_1(A,k3_wsierp_1(C,np__3))
& k3_wsierp_1(D,np__3) = k6_idea_1(A,k3_wsierp_1(C,np__2))
& k3_wsierp_1(D,np__4) = k10_idea_1(A,k3_wsierp_1(C,np__4)) )
=> k11_idea_1(A,k13_idea_1(k11_idea_1(A,k13_idea_1(B),C)),D) = B ) ) ) ) ) ).
fof(t32_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_xreal_0(np__4,k3_finseq_1(B))
& r1_idea_1(A,k3_wsierp_1(B,np__1))
& r1_idea_1(A,k3_wsierp_1(B,np__2))
& r1_idea_1(A,k3_wsierp_1(B,np__3))
& r1_idea_1(A,k3_wsierp_1(B,np__4))
& r1_idea_1(A,k3_wsierp_1(C,np__5))
& r1_idea_1(A,k3_wsierp_1(C,np__6))
& k3_wsierp_1(D,np__5) = k3_wsierp_1(C,np__5)
& k3_wsierp_1(D,np__6) = k3_wsierp_1(C,np__6) )
=> k12_idea_1(A,k12_idea_1(A,B,C),D) = B ) ) ) ) ) ).
fof(t33_idea_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ( r1_xreal_0(np__4,k3_finseq_1(A))
=> k13_idea_1(k13_idea_1(A)) = A ) ) ).
fof(d14_idea_1,axiom,
k14_idea_1 = k3_finseq_2(k5_numbers) ).
fof(d15_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_idea_1,k14_idea_1)
& m2_relset_1(C,k14_idea_1,k14_idea_1) )
=> ( C = k15_idea_1(A,B)
<=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> k1_funct_1(C,D) = k11_idea_1(A,k13_idea_1(k12_idea_1(A,D,B)),B) ) ) ) ) ) ).
fof(d16_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_idea_1,k14_idea_1)
& m2_relset_1(C,k14_idea_1,k14_idea_1) )
=> ( C = k16_idea_1(A,B)
<=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> k1_funct_1(C,D) = k12_idea_1(A,k11_idea_1(A,k13_idea_1(D),B),B) ) ) ) ) ) ).
fof(d17_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( m1_matrix_1(D,k5_numbers,B,np__6)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ( E = k17_idea_1(A,B,C,D)
<=> ( k3_finseq_1(E) = A
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k4_finseq_1(E))
=> k1_funct_1(E,F) = k15_idea_1(C,k7_matrix_1(k5_numbers,D,F)) ) ) ) ) ) ) ) ) ) ).
fof(d18_idea_1,axiom,
! [A] :
( m2_subset_1(A,k1_numbers,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( m1_matrix_1(D,k5_numbers,B,np__6)
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E)
& v1_finseq_1(E) )
=> ( E = k18_idea_1(A,B,C,D)
<=> ( k3_finseq_1(E) = A
& ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r2_hidden(F,k4_finseq_1(E))
=> k1_funct_1(E,F) = k16_idea_1(C,k7_matrix_1(k5_numbers,D,k1_nat_1(k5_binarith(A,F),np__1))) ) ) ) ) ) ) ) ) ) ).
fof(d19_idea_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_idea_1,k14_idea_1)
& m2_relset_1(C,k14_idea_1,k14_idea_1) )
=> ( C = k19_idea_1(A,B)
<=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> k1_funct_1(C,D) = k11_idea_1(B,D,A) ) ) ) ) ) ).
fof(d20_idea_1,axiom,
! [A] :
( m2_finseq_1(A,k5_numbers)
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_idea_1,k14_idea_1)
& m2_relset_1(C,k14_idea_1,k14_idea_1) )
=> ( C = k20_idea_1(A,B)
<=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> k1_funct_1(C,D) = k11_idea_1(B,D,A) ) ) ) ) ) ).
fof(d21_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_idea_1,k14_idea_1)
& m2_relset_1(C,k14_idea_1,k14_idea_1) )
=> ( C = k21_idea_1(A,B)
<=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> k1_funct_1(C,D) = k11_idea_1(A,k12_idea_1(A,D,B),B) ) ) ) ) ) ).
fof(d22_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k14_idea_1,k14_idea_1)
& m2_relset_1(C,k14_idea_1,k14_idea_1) )
=> ( C = k22_idea_1(A,B)
<=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> k1_funct_1(C,D) = k12_idea_1(A,k11_idea_1(A,D,B),B) ) ) ) ) ) ).
fof(t34_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_xreal_0(np__4,k3_finseq_1(B))
& r1_idea_1(A,k3_wsierp_1(B,np__1))
& r1_idea_1(A,k3_wsierp_1(B,np__2))
& r1_idea_1(A,k3_wsierp_1(B,np__3))
& r1_idea_1(A,k3_wsierp_1(B,np__4))
& r1_idea_1(A,k3_wsierp_1(C,np__1))
& r1_idea_1(A,k3_wsierp_1(C,np__2))
& r1_idea_1(A,k3_wsierp_1(C,np__3))
& r1_idea_1(A,k3_wsierp_1(C,np__4))
& r1_idea_1(A,k3_wsierp_1(C,np__5))
& r1_idea_1(A,k3_wsierp_1(C,np__6))
& k3_wsierp_1(D,np__1) = k10_idea_1(A,k3_wsierp_1(C,np__1))
& k3_wsierp_1(D,np__2) = k6_idea_1(A,k3_wsierp_1(C,np__3))
& k3_wsierp_1(D,np__3) = k6_idea_1(A,k3_wsierp_1(C,np__2))
& k3_wsierp_1(D,np__4) = k10_idea_1(A,k3_wsierp_1(C,np__4))
& k3_wsierp_1(D,np__5) = k3_wsierp_1(C,np__5)
& k3_wsierp_1(D,np__6) = k3_wsierp_1(C,np__6) )
=> k1_funct_1(k7_funct_2(k14_idea_1,k14_idea_1,k14_idea_1,k15_idea_1(A,C),k16_idea_1(A,D)),B) = B ) ) ) ) ) ).
fof(t35_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_xreal_0(np__4,k3_finseq_1(B))
& r1_idea_1(A,k3_wsierp_1(B,np__1))
& r1_idea_1(A,k3_wsierp_1(B,np__2))
& r1_idea_1(A,k3_wsierp_1(B,np__3))
& r1_idea_1(A,k3_wsierp_1(B,np__4))
& r1_idea_1(A,k3_wsierp_1(C,np__1))
& r1_idea_1(A,k3_wsierp_1(C,np__2))
& r1_idea_1(A,k3_wsierp_1(C,np__3))
& r1_idea_1(A,k3_wsierp_1(C,np__4))
& k3_wsierp_1(D,np__1) = k10_idea_1(A,k3_wsierp_1(C,np__1))
& k3_wsierp_1(D,np__2) = k6_idea_1(A,k3_wsierp_1(C,np__2))
& k3_wsierp_1(D,np__3) = k6_idea_1(A,k3_wsierp_1(C,np__3))
& k3_wsierp_1(D,np__4) = k10_idea_1(A,k3_wsierp_1(C,np__4)) )
=> k1_funct_1(k7_funct_2(k14_idea_1,k14_idea_1,k14_idea_1,k19_idea_1(C,A),k20_idea_1(D,A)),B) = B ) ) ) ) ) ).
fof(t36_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_xreal_0(np__4,k3_finseq_1(B))
& r1_idea_1(A,k3_wsierp_1(B,np__1))
& r1_idea_1(A,k3_wsierp_1(B,np__2))
& r1_idea_1(A,k3_wsierp_1(B,np__3))
& r1_idea_1(A,k3_wsierp_1(B,np__4))
& r1_idea_1(A,k3_wsierp_1(C,np__1))
& r1_idea_1(A,k3_wsierp_1(C,np__2))
& r1_idea_1(A,k3_wsierp_1(C,np__3))
& r1_idea_1(A,k3_wsierp_1(C,np__4))
& r1_idea_1(A,k3_wsierp_1(C,np__5))
& r1_idea_1(A,k3_wsierp_1(C,np__6))
& k3_wsierp_1(D,np__1) = k10_idea_1(A,k3_wsierp_1(C,np__1))
& k3_wsierp_1(D,np__2) = k6_idea_1(A,k3_wsierp_1(C,np__2))
& k3_wsierp_1(D,np__3) = k6_idea_1(A,k3_wsierp_1(C,np__3))
& k3_wsierp_1(D,np__4) = k10_idea_1(A,k3_wsierp_1(C,np__4))
& k3_wsierp_1(D,np__5) = k3_wsierp_1(C,np__5)
& k3_wsierp_1(D,np__6) = k3_wsierp_1(C,np__6) )
=> k1_funct_1(k7_funct_2(k14_idea_1,k14_idea_1,k14_idea_1,k21_idea_1(A,C),k22_idea_1(A,D)),B) = B ) ) ) ) ) ).
fof(t37_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k17_idea_1(k1_nat_1(D,np__1),B,A,C) = k7_finseq_1(k17_idea_1(D,B,A,C),k9_finseq_1(k15_idea_1(A,k7_matrix_1(k5_numbers,C,k1_nat_1(D,np__1))))) ) ) ) ) ).
fof(t38_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> k18_idea_1(k1_nat_1(D,np__1),B,A,C) = k7_finseq_1(k9_finseq_1(k16_idea_1(A,k7_matrix_1(k5_numbers,C,k1_nat_1(D,np__1)))),k18_idea_1(D,B,A,C)) ) ) ) ) ).
fof(t39_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v1_relat_1(k17_idea_1(D,B,A,C))
& v1_funct_1(k17_idea_1(D,B,A,C))
& v1_finseq_1(k17_idea_1(D,B,A,C))
& v1_funct_7(k17_idea_1(D,B,A,C)) ) ) ) ) ) ).
fof(t40_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( v1_relat_1(k18_idea_1(D,B,A,C))
& v1_funct_1(k18_idea_1(D,B,A,C))
& v1_finseq_1(k18_idea_1(D,B,A,C))
& v1_funct_7(k18_idea_1(D,B,A,C)) ) ) ) ) ) ).
fof(t41_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D != np__0
=> m1_funct_7(k17_idea_1(D,B,A,C),k14_idea_1,k14_idea_1) ) ) ) ) ) ).
fof(t42_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( D != np__0
=> m1_funct_7(k18_idea_1(D,B,A,C),k14_idea_1,k14_idea_1) ) ) ) ) ) ).
fof(t43_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_finseq_1(C,k5_numbers)
=> ! [D] :
( m2_finseq_1(D,k5_numbers)
=> ( ( B = k1_funct_1(k15_idea_1(A,D),C)
& r1_xreal_0(np__4,k3_finseq_1(C)) )
=> ( r1_xreal_0(np__4,k3_finseq_1(B))
& r1_idea_1(A,k3_wsierp_1(B,np__1))
& r1_idea_1(A,k3_wsierp_1(B,np__2))
& r1_idea_1(A,k3_wsierp_1(B,np__3))
& r1_idea_1(A,k3_wsierp_1(B,np__4)) ) ) ) ) ) ) ).
fof(t44_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_tarski(k2_relat_1(k4_funct_7(k14_idea_1,k17_idea_1(D,B,A,C))),k14_idea_1)
& k1_relat_1(k4_funct_7(k14_idea_1,k17_idea_1(D,B,A,C))) = k14_idea_1 ) ) ) ) ) ).
fof(t45_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_tarski(k2_relat_1(k4_funct_7(k14_idea_1,k18_idea_1(D,B,A,C))),k14_idea_1)
& k1_relat_1(k4_funct_7(k14_idea_1,k18_idea_1(D,B,A,C))) = k14_idea_1 ) ) ) ) ) ).
fof(t46_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_finseq_1(B,k5_numbers)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m1_matrix_1(D,k5_numbers,C,np__6)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_finseq_1(F,k5_numbers)
=> ( ( F = k1_funct_1(k4_funct_7(k14_idea_1,k17_idea_1(E,C,A,D)),B)
& r1_xreal_0(np__4,k3_finseq_1(B)) )
=> r1_xreal_0(np__4,k3_finseq_1(F)) ) ) ) ) ) ) ) ).
fof(t47_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ! [E] :
( m2_finseq_1(E,k5_numbers)
=> ! [F] :
( m2_finseq_1(F,k5_numbers)
=> ( ( E = k1_funct_1(k4_funct_7(k14_idea_1,k17_idea_1(D,B,A,C)),F)
& r1_xreal_0(np__4,k3_finseq_1(F))
& r1_idea_1(A,k3_wsierp_1(F,np__1))
& r1_idea_1(A,k3_wsierp_1(F,np__2))
& r1_idea_1(A,k3_wsierp_1(F,np__3))
& r1_idea_1(A,k3_wsierp_1(F,np__4)) )
=> ( r1_xreal_0(np__4,k3_finseq_1(E))
& r1_idea_1(A,k3_wsierp_1(E,np__1))
& r1_idea_1(A,k3_wsierp_1(E,np__2))
& r1_idea_1(A,k3_wsierp_1(E,np__3))
& r1_idea_1(A,k3_wsierp_1(E,np__4)) ) ) ) ) ) ) ) ) ).
fof(t48_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m1_matrix_1(D,k5_numbers,B,np__6)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_finseq_1(F,k5_numbers)
=> ( ( r1_xreal_0(E,B)
& v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_xreal_0(np__4,k3_finseq_1(F))
& r1_idea_1(A,k3_wsierp_1(F,np__1))
& r1_idea_1(A,k3_wsierp_1(F,np__2))
& r1_idea_1(A,k3_wsierp_1(F,np__3))
& r1_idea_1(A,k3_wsierp_1(F,np__4))
& ! [G] :
( m2_subset_1(G,k1_numbers,k5_numbers)
=> ( r1_xreal_0(G,E)
=> ( r1_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__1))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__2))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__3))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__4))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__5))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__6))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,G,np__1))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,G,np__2))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,G,np__3))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,G,np__4))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,G,np__5))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,G,np__6))
& k3_matrix_1(k5_numbers,D,G,np__1) = k10_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__1))
& k3_matrix_1(k5_numbers,D,G,np__2) = k6_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__3))
& k3_matrix_1(k5_numbers,D,G,np__3) = k6_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__2))
& k3_matrix_1(k5_numbers,D,G,np__4) = k10_idea_1(A,k3_matrix_1(k5_numbers,C,G,np__4))
& k3_matrix_1(k5_numbers,C,G,np__5) = k3_matrix_1(k5_numbers,D,G,np__5)
& k3_matrix_1(k5_numbers,C,G,np__6) = k3_matrix_1(k5_numbers,D,G,np__6) ) ) ) )
=> k1_funct_1(k4_funct_7(k14_idea_1,k7_finseq_1(k17_idea_1(E,B,A,C),k18_idea_1(E,B,A,D))),F) = F ) ) ) ) ) ) ) ).
fof(t49_idea_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ! [C] :
( m1_matrix_1(C,k5_numbers,B,np__6)
=> ! [D] :
( m1_matrix_1(D,k5_numbers,B,np__6)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_finseq_1(F,k5_numbers)
=> ! [G] :
( m2_finseq_1(G,k5_numbers)
=> ! [H] :
( m2_finseq_1(H,k5_numbers)
=> ! [I] :
( m2_finseq_1(I,k5_numbers)
=> ! [J] :
( m2_finseq_1(J,k5_numbers)
=> ( ( r1_xreal_0(E,B)
& v1_int_2(k1_nat_1(k3_series_1(np__2,A),np__1))
& r1_xreal_0(np__4,k3_finseq_1(J))
& r1_idea_1(A,k3_wsierp_1(J,np__1))
& r1_idea_1(A,k3_wsierp_1(J,np__2))
& r1_idea_1(A,k3_wsierp_1(J,np__3))
& r1_idea_1(A,k3_wsierp_1(J,np__4))
& ! [K] :
( m2_subset_1(K,k1_numbers,k5_numbers)
=> ( r1_xreal_0(K,E)
=> ( r1_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__1))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__2))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__3))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__4))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__5))
& r1_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__6))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,K,np__1))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,K,np__2))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,K,np__3))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,K,np__4))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,K,np__5))
& r1_idea_1(A,k3_matrix_1(k5_numbers,D,K,np__6))
& k3_matrix_1(k5_numbers,D,K,np__1) = k10_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__1))
& k3_matrix_1(k5_numbers,D,K,np__2) = k6_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__3))
& k3_matrix_1(k5_numbers,D,K,np__3) = k6_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__2))
& k3_matrix_1(k5_numbers,D,K,np__4) = k10_idea_1(A,k3_matrix_1(k5_numbers,C,K,np__4))
& k3_matrix_1(k5_numbers,C,K,np__5) = k3_matrix_1(k5_numbers,D,K,np__5)
& k3_matrix_1(k5_numbers,C,K,np__6) = k3_matrix_1(k5_numbers,D,K,np__6) ) ) )
& r1_idea_1(A,k3_wsierp_1(F,np__1))
& r1_idea_1(A,k3_wsierp_1(F,np__2))
& r1_idea_1(A,k3_wsierp_1(F,np__3))
& r1_idea_1(A,k3_wsierp_1(F,np__4))
& k3_wsierp_1(G,np__1) = k10_idea_1(A,k3_wsierp_1(F,np__1))
& k3_wsierp_1(G,np__2) = k6_idea_1(A,k3_wsierp_1(F,np__2))
& k3_wsierp_1(G,np__3) = k6_idea_1(A,k3_wsierp_1(F,np__3))
& k3_wsierp_1(G,np__4) = k10_idea_1(A,k3_wsierp_1(F,np__4))
& r1_idea_1(A,k3_wsierp_1(H,np__1))
& r1_idea_1(A,k3_wsierp_1(H,np__2))
& r1_idea_1(A,k3_wsierp_1(H,np__3))
& r1_idea_1(A,k3_wsierp_1(H,np__4))
& r1_idea_1(A,k3_wsierp_1(H,np__5))
& r1_idea_1(A,k3_wsierp_1(H,np__6))
& k3_wsierp_1(I,np__1) = k10_idea_1(A,k3_wsierp_1(H,np__1))
& k3_wsierp_1(I,np__2) = k6_idea_1(A,k3_wsierp_1(H,np__2))
& k3_wsierp_1(I,np__3) = k6_idea_1(A,k3_wsierp_1(H,np__3))
& k3_wsierp_1(I,np__4) = k10_idea_1(A,k3_wsierp_1(H,np__4))
& k3_wsierp_1(I,np__5) = k3_wsierp_1(H,np__5)
& k3_wsierp_1(I,np__6) = k3_wsierp_1(H,np__6) )
=> k1_funct_1(k5_relat_1(k5_relat_1(k5_relat_1(k5_relat_1(k5_relat_1(k19_idea_1(F,A),k4_funct_7(k14_idea_1,k17_idea_1(E,B,A,C))),k21_idea_1(A,H)),k22_idea_1(A,I)),k4_funct_7(k14_idea_1,k18_idea_1(E,B,A,D))),k20_idea_1(G,A)),J) = J ) ) ) ) ) ) ) ) ) ) ) ).
fof(dt_k1_idea_1,axiom,
! [A] :
( m1_subset_1(A,k5_numbers)
=> m2_finseq_2(k1_idea_1(A),k6_margrel1,k4_finseq_2(A,k6_margrel1)) ) ).
fof(dt_k2_idea_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k4_finseq_2(A,k6_margrel1))
& m1_subset_1(C,k4_finseq_2(A,k6_margrel1)) )
=> m2_finseq_2(k2_idea_1(A,B,C),k6_margrel1,k4_finseq_2(A,k6_margrel1)) ) ).
fof(dt_k3_idea_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k4_finseq_2(A,k6_margrel1))
& m1_subset_1(C,k4_finseq_2(A,k6_margrel1)) )
=> m2_finseq_2(k3_idea_1(A,B,C),k6_margrel1,k4_finseq_2(A,k6_margrel1)) ) ).
fof(commutativity_k3_idea_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k4_finseq_2(A,k6_margrel1))
& m1_subset_1(C,k4_finseq_2(A,k6_margrel1)) )
=> k3_idea_1(A,B,C) = k3_idea_1(A,C,B) ) ).
fof(redefinition_k3_idea_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k4_finseq_2(A,k6_margrel1))
& m1_subset_1(C,k4_finseq_2(A,k6_margrel1)) )
=> k3_idea_1(A,B,C) = k2_idea_1(A,B,C) ) ).
fof(dt_k4_idea_1,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(k4_idea_1(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k5_idea_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k5_idea_1(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k6_idea_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k6_idea_1(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k7_idea_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k7_idea_1(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k8_idea_1,axiom,
! [A,B] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k8_idea_1(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k9_idea_1,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_idea_1(A,B,C),k1_numbers,k5_numbers) ) ).
fof(dt_k10_idea_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> m2_subset_1(k10_idea_1(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k11_idea_1,axiom,
! [A,B,C] :
( ( m1_subset_1(A,k5_numbers)
& m1_finseq_1(B,k5_numbers)
& m1_finseq_1(C,k5_numbers) )
=> m2_finseq_1(k11_idea_1(A,B,C),k5_numbers) ) ).
fof(dt_k12_idea_1,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers)
& m1_finseq_1(B,k5_numbers)
& m1_finseq_1(C,k5_numbers) )
=> m2_finseq_1(k12_idea_1(A,B,C),k5_numbers) ) ).
fof(dt_k13_idea_1,axiom,
! [A] :
( m1_finseq_1(A,k5_numbers)
=> m2_finseq_1(k13_idea_1(A),k5_numbers) ) ).
fof(dt_k14_idea_1,axiom,
$true ).
fof(dt_k15_idea_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers)
& m1_finseq_1(B,k5_numbers) )
=> ( v1_funct_1(k15_idea_1(A,B))
& v1_funct_2(k15_idea_1(A,B),k14_idea_1,k14_idea_1)
& m2_relset_1(k15_idea_1(A,B),k14_idea_1,k14_idea_1) ) ) ).
fof(dt_k16_idea_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers)
& m1_finseq_1(B,k5_numbers) )
=> ( v1_funct_1(k16_idea_1(A,B))
& v1_funct_2(k16_idea_1(A,B),k14_idea_1,k14_idea_1)
& m2_relset_1(k16_idea_1(A,B),k14_idea_1,k14_idea_1) ) ) ).
fof(dt_k17_idea_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k5_numbers)
& m1_matrix_1(D,k5_numbers,B,np__6) )
=> ( v1_relat_1(k17_idea_1(A,B,C,D))
& v1_funct_1(k17_idea_1(A,B,C,D))
& v1_finseq_1(k17_idea_1(A,B,C,D)) ) ) ).
fof(dt_k18_idea_1,axiom,
! [A,B,C,D] :
( ( m1_subset_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers)
& ~ v1_xboole_0(C)
& m1_subset_1(C,k5_numbers)
& m1_matrix_1(D,k5_numbers,B,np__6) )
=> ( v1_relat_1(k18_idea_1(A,B,C,D))
& v1_funct_1(k18_idea_1(A,B,C,D))
& v1_finseq_1(k18_idea_1(A,B,C,D)) ) ) ).
fof(dt_k19_idea_1,axiom,
! [A,B] :
( ( m1_finseq_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_funct_1(k19_idea_1(A,B))
& v1_funct_2(k19_idea_1(A,B),k14_idea_1,k14_idea_1)
& m2_relset_1(k19_idea_1(A,B),k14_idea_1,k14_idea_1) ) ) ).
fof(dt_k20_idea_1,axiom,
! [A,B] :
( ( m1_finseq_1(A,k5_numbers)
& m1_subset_1(B,k5_numbers) )
=> ( v1_funct_1(k20_idea_1(A,B))
& v1_funct_2(k20_idea_1(A,B),k14_idea_1,k14_idea_1)
& m2_relset_1(k20_idea_1(A,B),k14_idea_1,k14_idea_1) ) ) ).
fof(dt_k21_idea_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers)
& m1_finseq_1(B,k5_numbers) )
=> ( v1_funct_1(k21_idea_1(A,B))
& v1_funct_2(k21_idea_1(A,B),k14_idea_1,k14_idea_1)
& m2_relset_1(k21_idea_1(A,B),k14_idea_1,k14_idea_1) ) ) ).
fof(dt_k22_idea_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& m1_subset_1(A,k5_numbers)
& m1_finseq_1(B,k5_numbers) )
=> ( v1_funct_1(k22_idea_1(A,B))
& v1_funct_2(k22_idea_1(A,B),k14_idea_1,k14_idea_1)
& m2_relset_1(k22_idea_1(A,B),k14_idea_1,k14_idea_1) ) ) ).
%------------------------------------------------------------------------------