SET007 Axioms: SET007+890.ax
%------------------------------------------------------------------------------
% File : SET007+890 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Walks in a Graph
% 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 : glib_001 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 311 ( 1 unt; 0 def)
% Number of atoms : 2326 ( 242 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 2205 ( 190 ~; 20 |;1007 &)
% ( 61 <=>; 927 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 9 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 48 ( 46 usr; 1 prp; 0-4 aty)
% Number of functors : 84 ( 84 usr; 7 con; 0-4 aty)
% Number of variables : 999 ( 970 !; 29 ?)
% 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_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> ( ~ v1_xboole_0(k1_card_1(B))
& v1_card_1(k1_card_1(B))
& ~ v1_abian(k1_card_1(B)) ) ) ).
fof(cc1_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v5_glib_001(B,A)
=> ( v1_relat_1(B)
& v4_glib_001(B,A) ) ) ) ) ).
fof(cc2_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v3_glib_001(B,A)
=> ( v1_relat_1(B)
& v5_glib_001(B,A) ) ) ) ) ).
fof(cc3_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v3_glib_001(B,A)
=> ( v1_relat_1(B)
& v6_glib_001(B,A) ) ) ) ) ).
fof(cc4_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v6_glib_001(B,A)
=> ( v1_relat_1(B)
& v5_glib_001(B,A) ) ) ) ) ).
fof(cc5_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v7_glib_001(B,A)
=> ( v1_relat_1(B)
& v1_glib_001(B,A)
& ~ v3_glib_001(B,A)
& v4_glib_001(B,A) ) ) ) ) ).
fof(cc6_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v8_glib_001(B,A)
=> ( v1_relat_1(B)
& v1_glib_001(B,A)
& ~ v3_glib_001(B,A)
& v5_glib_001(B,A) ) ) ) ) ).
fof(rc1_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ? [B] :
( m3_glib_001(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v2_finseq_1(B)
& v1_glib_001(B,A)
& v2_glib_001(B,A)
& v3_glib_001(B,A)
& v4_glib_001(B,A)
& v5_glib_001(B,A)
& v6_glib_001(B,A) ) ) ).
fof(rc2_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ? [B] :
( m3_glib_001(B,A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_finset_1(B)
& v1_finseq_1(B)
& v2_finseq_1(B)
& v4_glib_001(B,A)
& v5_glib_001(B,A)
& v6_glib_001(B,A) ) ) ).
fof(fc2_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m1_subset_1(B,k6_glib_000(A)) )
=> ( v1_relat_1(k1_glib_001(A,B))
& v1_funct_1(k1_glib_001(A,B))
& v1_finset_1(k1_glib_001(A,B))
& v1_finseq_1(k1_glib_001(A,B))
& v2_finseq_1(k1_glib_001(A,B))
& v1_glib_001(k1_glib_001(A,B),A)
& v2_glib_001(k1_glib_001(A,B),A)
& v3_glib_001(k1_glib_001(A,B),A)
& v4_glib_001(k1_glib_001(A,B),A)
& v5_glib_001(k1_glib_001(A,B),A)
& v6_glib_001(k1_glib_001(A,B),A) ) ) ).
fof(fc3_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ( v1_relat_1(k2_glib_001(A,B,D,C))
& v1_funct_1(k2_glib_001(A,B,D,C))
& v1_finset_1(k2_glib_001(A,B,D,C))
& v1_finseq_1(k2_glib_001(A,B,D,C))
& v2_finseq_1(k2_glib_001(A,B,D,C))
& v4_glib_001(k2_glib_001(A,B,D,C),A)
& v5_glib_001(k2_glib_001(A,B,D,C),A) ) ) ).
fof(fc4_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ( v1_relat_1(k2_glib_001(A,B,B,C))
& v1_funct_1(k2_glib_001(A,B,B,C))
& v1_finset_1(k2_glib_001(A,B,B,C))
& v1_finseq_1(k2_glib_001(A,B,B,C))
& v2_finseq_1(k2_glib_001(A,B,B,C))
& v1_glib_001(k2_glib_001(A,B,B,C),A)
& v4_glib_001(k2_glib_001(A,B,B,C),A)
& v5_glib_001(k2_glib_001(A,B,B,C),A) ) ) ).
fof(fc5_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v1_glib_001(B,A)
& m3_glib_001(B,A) )
=> ( v1_relat_1(k6_glib_001(A,B))
& v1_funct_1(k6_glib_001(A,B))
& v1_finset_1(k6_glib_001(A,B))
& v1_finseq_1(k6_glib_001(A,B))
& v2_finseq_1(k6_glib_001(A,B))
& v1_glib_001(k6_glib_001(A,B),A) ) ) ).
fof(fc6_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v3_glib_001(B,A)
& m3_glib_001(B,A) )
=> ( v1_relat_1(k6_glib_001(A,B))
& v1_funct_1(k6_glib_001(A,B))
& v1_finset_1(k6_glib_001(A,B))
& v1_finseq_1(k6_glib_001(A,B))
& v2_finseq_1(k6_glib_001(A,B))
& v3_glib_001(k6_glib_001(A,B),A)
& v4_glib_001(k6_glib_001(A,B),A)
& v5_glib_001(k6_glib_001(A,B),A)
& v6_glib_001(k6_glib_001(A,B),A) ) ) ).
fof(fc7_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v4_glib_001(B,A)
& m3_glib_001(B,A) )
=> ( v1_relat_1(k6_glib_001(A,B))
& v1_funct_1(k6_glib_001(A,B))
& v1_finset_1(k6_glib_001(A,B))
& v1_finseq_1(k6_glib_001(A,B))
& v2_finseq_1(k6_glib_001(A,B))
& v4_glib_001(k6_glib_001(A,B),A) ) ) ).
fof(fc8_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v5_glib_001(B,A)
& m3_glib_001(B,A) )
=> ( v1_relat_1(k6_glib_001(A,B))
& v1_funct_1(k6_glib_001(A,B))
& v1_finset_1(k6_glib_001(A,B))
& v1_finseq_1(k6_glib_001(A,B))
& v2_finseq_1(k6_glib_001(A,B))
& v4_glib_001(k6_glib_001(A,B),A)
& v5_glib_001(k6_glib_001(A,B),A) ) ) ).
fof(fc9_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v1_glib_001(B,A)
& m3_glib_001(B,A)
& v1_glib_001(C,A)
& m3_glib_001(C,A) )
=> ( v1_relat_1(k7_glib_001(A,B,C))
& v1_funct_1(k7_glib_001(A,B,C))
& v1_finset_1(k7_glib_001(A,B,C))
& v1_finseq_1(k7_glib_001(A,B,C))
& v2_finseq_1(k7_glib_001(A,B,C))
& v1_glib_001(k7_glib_001(A,B,C),A) ) ) ).
fof(fc10_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v2_glib_001(B,A)
& m3_glib_001(B,A)
& v2_glib_001(C,A)
& m3_glib_001(C,A) )
=> ( v1_relat_1(k7_glib_001(A,B,C))
& v1_funct_1(k7_glib_001(A,B,C))
& v1_finset_1(k7_glib_001(A,B,C))
& v1_finseq_1(k7_glib_001(A,B,C))
& v2_finseq_1(k7_glib_001(A,B,C))
& v2_glib_001(k7_glib_001(A,B,C),A) ) ) ).
fof(fc11_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v3_glib_001(B,A)
& m3_glib_001(B,A)
& v3_glib_001(C,A)
& m3_glib_001(C,A) )
=> ( v1_relat_1(k7_glib_001(A,B,C))
& v1_funct_1(k7_glib_001(A,B,C))
& v1_finset_1(k7_glib_001(A,B,C))
& v1_finseq_1(k7_glib_001(A,B,C))
& v2_finseq_1(k7_glib_001(A,B,C))
& v3_glib_001(k7_glib_001(A,B,C),A)
& v4_glib_001(k7_glib_001(A,B,C),A)
& v5_glib_001(k7_glib_001(A,B,C),A)
& v6_glib_001(k7_glib_001(A,B,C),A) ) ) ).
fof(fc12_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v2_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k8_glib_001(A,B,C,D))
& v1_funct_1(k8_glib_001(A,B,C,D))
& v1_finset_1(k8_glib_001(A,B,C,D))
& v1_finseq_1(k8_glib_001(A,B,C,D))
& v2_finseq_1(k8_glib_001(A,B,C,D))
& v2_glib_001(k8_glib_001(A,B,C,D),A) ) ) ).
fof(fc13_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v3_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k8_glib_001(A,B,C,D))
& v1_funct_1(k8_glib_001(A,B,C,D))
& v1_finset_1(k8_glib_001(A,B,C,D))
& v1_finseq_1(k8_glib_001(A,B,C,D))
& v2_finseq_1(k8_glib_001(A,B,C,D))
& v3_glib_001(k8_glib_001(A,B,C,D),A)
& v4_glib_001(k8_glib_001(A,B,C,D),A)
& v5_glib_001(k8_glib_001(A,B,C,D),A)
& v6_glib_001(k8_glib_001(A,B,C,D),A) ) ) ).
fof(fc14_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v4_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k8_glib_001(A,B,C,D))
& v1_funct_1(k8_glib_001(A,B,C,D))
& v1_finset_1(k8_glib_001(A,B,C,D))
& v1_finseq_1(k8_glib_001(A,B,C,D))
& v2_finseq_1(k8_glib_001(A,B,C,D))
& v4_glib_001(k8_glib_001(A,B,C,D),A) ) ) ).
fof(fc15_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v5_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k8_glib_001(A,B,C,D))
& v1_funct_1(k8_glib_001(A,B,C,D))
& v1_finset_1(k8_glib_001(A,B,C,D))
& v1_finseq_1(k8_glib_001(A,B,C,D))
& v2_finseq_1(k8_glib_001(A,B,C,D))
& v4_glib_001(k8_glib_001(A,B,C,D),A)
& v5_glib_001(k8_glib_001(A,B,C,D),A) ) ) ).
fof(fc16_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v6_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k8_glib_001(A,B,C,D))
& v1_funct_1(k8_glib_001(A,B,C,D))
& v1_finset_1(k8_glib_001(A,B,C,D))
& v1_finseq_1(k8_glib_001(A,B,C,D))
& v2_finseq_1(k8_glib_001(A,B,C,D))
& v4_glib_001(k8_glib_001(A,B,C,D),A)
& v5_glib_001(k8_glib_001(A,B,C,D),A)
& v6_glib_001(k8_glib_001(A,B,C,D),A) ) ) ).
fof(fc17_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v1_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k9_glib_001(A,B,C,D))
& v1_funct_1(k9_glib_001(A,B,C,D))
& v1_finset_1(k9_glib_001(A,B,C,D))
& v1_finseq_1(k9_glib_001(A,B,C,D))
& v2_finseq_1(k9_glib_001(A,B,C,D))
& v1_glib_001(k9_glib_001(A,B,C,D),A) ) ) ).
fof(fc18_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v2_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k9_glib_001(A,B,C,D))
& v1_funct_1(k9_glib_001(A,B,C,D))
& v1_finset_1(k9_glib_001(A,B,C,D))
& v1_finseq_1(k9_glib_001(A,B,C,D))
& v2_finseq_1(k9_glib_001(A,B,C,D))
& v2_glib_001(k9_glib_001(A,B,C,D),A) ) ) ).
fof(fc19_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v3_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k9_glib_001(A,B,C,D))
& v1_funct_1(k9_glib_001(A,B,C,D))
& v1_finset_1(k9_glib_001(A,B,C,D))
& v1_finseq_1(k9_glib_001(A,B,C,D))
& v2_finseq_1(k9_glib_001(A,B,C,D))
& v3_glib_001(k9_glib_001(A,B,C,D),A)
& v4_glib_001(k9_glib_001(A,B,C,D),A)
& v5_glib_001(k9_glib_001(A,B,C,D),A)
& v6_glib_001(k9_glib_001(A,B,C,D),A) ) ) ).
fof(fc20_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v4_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k9_glib_001(A,B,C,D))
& v1_funct_1(k9_glib_001(A,B,C,D))
& v1_finset_1(k9_glib_001(A,B,C,D))
& v1_finseq_1(k9_glib_001(A,B,C,D))
& v2_finseq_1(k9_glib_001(A,B,C,D))
& v4_glib_001(k9_glib_001(A,B,C,D),A) ) ) ).
fof(fc21_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v5_glib_001(B,A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> ( v1_relat_1(k9_glib_001(A,B,C,D))
& v1_funct_1(k9_glib_001(A,B,C,D))
& v1_finset_1(k9_glib_001(A,B,C,D))
& v1_finseq_1(k9_glib_001(A,B,C,D))
& v2_finseq_1(k9_glib_001(A,B,C,D))
& v4_glib_001(k9_glib_001(A,B,C,D),A)
& v5_glib_001(k9_glib_001(A,B,C,D),A) ) ) ).
fof(rc3_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> ? [C] :
( m4_glib_001(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_finseq_1(C)
& v2_finseq_1(C)
& v4_glib_001(C,A)
& v5_glib_001(C,A) ) ) ).
fof(rc4_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& v2_glib_001(B,A)
& m3_glib_001(B,A) )
=> ? [C] :
( m4_glib_001(C,A,B)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_finset_1(C)
& v1_finseq_1(C)
& v2_finseq_1(C)
& v2_glib_001(C,A)
& v4_glib_001(C,A)
& v5_glib_001(C,A) ) ) ).
fof(fc22_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& v2_glib_000(A)
& m1_glib_000(A) )
=> ( ~ v1_xboole_0(k22_glib_001(A))
& v1_finset_1(k22_glib_001(A)) ) ) ).
fof(t1_glib_001,axiom,
! [A] :
( ( ~ v1_abian(A)
& m2_subset_1(A,k1_numbers,k5_numbers) )
=> ! [B] :
( ( ~ v1_abian(B)
& m2_subset_1(B,k1_numbers,k5_numbers) )
=> ( ~ r1_xreal_0(B,A)
<=> r1_xreal_0(k1_nat_1(A,np__2),B) ) ) ) ).
fof(t2_glib_001,axiom,
! [A,B] :
( m2_subset_1(B,k1_numbers,k5_numbers)
=> ( r1_tarski(A,k2_finseq_1(B))
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(C,k4_relset_1(k5_numbers,k5_numbers,k14_finseq_1(A)))
& D = k1_funct_1(k14_finseq_1(A),C) )
=> r1_xreal_0(C,D) ) ) ) ) ) ).
fof(t3_glib_001,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_graph_2(C,A,B)
=> r1_xreal_0(k3_finseq_1(k15_finseq_1(C)),k3_finseq_1(B)) ) ) ).
fof(t4_glib_001,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_graph_2(C,A,B)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_finseq_1(k15_finseq_1(C)))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(E,k4_relset_1(k5_numbers,A,B))
& r1_xreal_0(D,E)
& k1_funct_1(k15_finseq_1(C),D) = k1_funct_1(B,E) ) ) ) ) ) ) ).
fof(t5_glib_001,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_graph_2(C,A,B)
=> k3_finseq_1(k15_finseq_1(C)) = k4_card_1(C) ) ) ).
fof(t6_glib_001,axiom,
! [A,B] :
( m2_finseq_1(B,A)
=> ! [C] :
( m1_graph_2(C,A,B)
=> k4_finseq_1(k15_finseq_1(C)) = k4_relset_1(k5_numbers,k5_numbers,k14_finseq_1(k1_relat_1(C))) ) ) ).
fof(d1_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_finseq_1(B,k6_glib_000(A))
=> ( m1_glib_001(B,A)
<=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(k3_finseq_1(B),C)
& ! [D] : ~ r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__1)),D) ) ) ) ) ) ).
fof(d2_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_finseq_1(B,k7_glib_000(A))
=> ( m2_glib_001(B,A)
<=> ? [C] :
( m2_finseq_1(C,k6_glib_000(A))
& k3_finseq_1(C) = k1_nat_1(k3_finseq_1(B),np__1)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> r1_glib_000(A,k1_funct_1(C,D),k1_funct_1(C,k1_nat_1(D,np__1)),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(d3_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_finseq_1(B,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)))
=> ( m3_glib_001(B,A)
<=> ( ~ v1_abian(k3_finseq_1(B))
& r2_hidden(k1_funct_1(B,np__1),k6_glib_000(A))
& ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( ~ r1_xreal_0(k3_finseq_1(B),C)
=> r1_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__2)),k1_funct_1(B,k1_nat_1(C,np__1))) ) ) ) ) ) ) ).
fof(d4_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m1_subset_1(B,k6_glib_000(A))
=> k1_glib_001(A,B) = k12_finseq_1(k6_glib_000(A),B) ) ) ).
fof(d5_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C,D] :
( ( r1_glib_000(A,B,C,D)
=> k2_glib_001(A,B,C,D) = k11_finseq_1(B,D,C) )
& ( ~ r1_glib_000(A,B,C,D)
=> k2_glib_001(A,B,C,D) = k1_glib_001(A,k8_subset_1(k6_glib_000(A))) ) ) ) ).
fof(d6_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k3_glib_001(A,B) = k1_funct_1(B,np__1) ) ) ).
fof(d7_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k4_glib_001(A,B) = k1_funct_1(B,k3_finseq_1(B)) ) ) ).
fof(d8_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(C,k3_finseq_1(B))
=> ( v1_abian(C)
| k5_glib_001(A,B,C) = k1_funct_1(B,C) ) )
& ( ~ ( ~ v1_abian(C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> k5_glib_001(A,B,C) = k3_glib_001(A,B) ) ) ) ) ) ).
fof(d9_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k6_glib_001(A,B) = k4_finseq_5(k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B) ) ) ).
fof(d10_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( ( k4_glib_001(A,B) = k3_glib_001(A,C)
=> k7_glib_001(A,B,C) = k4_graph_2(k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B,C) )
& ( k4_glib_001(A,B) != k3_glib_001(A,C)
=> k7_glib_001(A,B,C) = B ) ) ) ) ) ).
fof(d11_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( v1_abian(C)
| v1_abian(D)
| k8_glib_001(A,B,C,D) = k2_graph_2(k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B,C,D) ) )
& ( ~ ( ~ v1_abian(C)
& ~ v1_abian(D)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> k8_glib_001(A,B,C,D) = B ) ) ) ) ) ) ).
fof(d12_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> ( v1_abian(C)
| v1_abian(D)
| k9_glib_001(A,B,C,D) = k7_glib_001(A,k8_glib_001(A,B,np__1,C),k8_glib_001(A,B,D,k3_finseq_1(B))) ) )
& ( ~ ( ~ v1_abian(C)
& ~ v1_abian(D)
& r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> k9_glib_001(A,B,C,D) = B ) ) ) ) ) ) ).
fof(d13_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] : k10_glib_001(A,B,C) = k7_glib_001(A,B,k2_glib_001(A,k4_glib_001(A,B),k30_glib_000(A,k4_glib_001(A,B),C),C)) ) ) ).
fof(d14_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m1_glib_001(C,A)
=> ( C = k11_glib_001(A,B)
<=> ( k1_nat_1(k3_finseq_1(B),np__1) = k2_nat_1(np__2,k3_finseq_1(C))
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(C)) )
=> k1_funct_1(C,D) = k1_funct_1(B,k6_xcmplx_0(k2_nat_1(np__2,D),np__1)) ) ) ) ) ) ) ) ).
fof(d15_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_glib_001(C,A)
=> ( C = k12_glib_001(A,B)
<=> ( k3_finseq_1(B) = k1_nat_1(k2_nat_1(np__2,k3_finseq_1(C)),np__1)
& ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(C)) )
=> k1_funct_1(C,D) = k1_funct_1(B,k2_nat_1(np__2,D)) ) ) ) ) ) ) ) ).
fof(d16_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k13_glib_001(A,B) = k5_relset_1(k5_numbers,k6_glib_000(A),k11_glib_001(A,B)) ) ) ).
fof(d17_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k14_glib_001(A,B) = k5_relset_1(k5_numbers,k7_glib_000(A),k12_glib_001(A,B)) ) ) ).
fof(d18_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k15_glib_001(A,B) = k3_finseq_1(k12_glib_001(A,B)) ) ) ).
fof(d19_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r2_hidden(C,k13_glib_001(A,B))
=> ( D = k16_glib_001(A,B,C)
<=> ( r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,D) = C
& ! [E] :
( ( ~ v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(E,k3_finseq_1(B))
& k1_funct_1(B,E) = C )
=> r1_xreal_0(D,E) ) ) ) ) )
& ( ~ r2_hidden(C,k13_glib_001(A,B))
=> ( D = k16_glib_001(A,B,C)
<=> D = k3_finseq_1(B) ) ) ) ) ) ) ).
fof(d20_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,k3_finseq_1(B))
=> ( v1_abian(C)
| ( D = k17_glib_001(A,B,C)
<=> ( r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,D) = k1_funct_1(B,C)
& ! [E] :
( ( ~ v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(E,k3_finseq_1(B))
& k1_funct_1(B,E) = k1_funct_1(B,C) )
=> r1_xreal_0(D,E) ) ) ) ) ) )
& ( ~ ( ~ v1_abian(C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> ( D = k17_glib_001(A,B,C)
<=> D = k3_finseq_1(B) ) ) ) ) ) ) ) ).
fof(d21_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r2_hidden(C,k13_glib_001(A,B))
=> ( D = k18_glib_001(A,B,C)
<=> ( r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,D) = C
& ! [E] :
( ( ~ v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(E,k3_finseq_1(B))
& k1_funct_1(B,E) = C )
=> r1_xreal_0(E,D) ) ) ) ) )
& ( ~ r2_hidden(C,k13_glib_001(A,B))
=> ( D = k18_glib_001(A,B,C)
<=> D = k3_finseq_1(B) ) ) ) ) ) ) ).
fof(d22_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,k3_finseq_1(B))
=> ( v1_abian(C)
| ( D = k19_glib_001(A,B,C)
<=> ( r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,D) = k1_funct_1(B,C)
& ! [E] :
( ( ~ v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(E,k3_finseq_1(B))
& k1_funct_1(B,E) = k1_funct_1(B,C) )
=> r1_xreal_0(E,D) ) ) ) ) ) )
& ( ~ ( ~ v1_abian(C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> ( D = k19_glib_001(A,B,C)
<=> D = k3_finseq_1(B) ) ) ) ) ) ) ) ).
fof(d23_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C,D] :
( m3_glib_001(D,A)
=> ( r1_glib_001(A,B,C,D)
<=> ( k3_glib_001(A,D) = B
& k4_glib_001(A,D) = C ) ) ) ) ).
fof(d24_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v1_glib_001(B,A)
<=> k3_glib_001(A,B) = k4_glib_001(A,B) ) ) ) ).
fof(d25_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v2_glib_001(B,A)
<=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( ~ r1_xreal_0(k3_finseq_1(B),C)
=> k1_funct_1(k10_glib_000(A),k1_funct_1(B,k1_nat_1(C,np__1))) = k1_funct_1(B,C) ) ) ) ) ) ).
fof(d26_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v3_glib_001(B,A)
<=> k15_glib_001(A,B) = np__0 ) ) ) ).
fof(d27_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v4_glib_001(B,A)
<=> v2_funct_1(k12_glib_001(A,B)) ) ) ) ).
fof(d28_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v5_glib_001(B,A)
<=> ( v4_glib_001(B,A)
& ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> ( r1_xreal_0(D,C)
| ( C = np__1
& D = k3_finseq_1(B) ) ) ) ) ) ) ) ) ) ).
fof(d29_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v6_glib_001(B,A)
<=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> C = D ) ) ) ) ) ) ).
fof(d30_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v7_glib_001(B,A)
<=> ( v1_glib_001(B,A)
& v4_glib_001(B,A)
& ~ v3_glib_001(B,A) ) ) ) ) ).
fof(d31_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v8_glib_001(B,A)
<=> ( v1_glib_001(B,A)
& v5_glib_001(B,A)
& ~ v3_glib_001(B,A) ) ) ) ) ).
fof(d32_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( m4_glib_001(C,A,B)
<=> ( r1_glib_001(A,k3_glib_001(A,B),k4_glib_001(A,B),C)
& ? [D] :
( m1_graph_2(D,k7_glib_000(A),k12_glib_001(A,B))
& k12_glib_001(A,C) = k15_finseq_1(D) ) ) ) ) ) ) ).
fof(t7_glib_001,axiom,
$true ).
fof(t8_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> r2_hidden(k1_funct_1(B,C),k6_glib_000(A)) ) ) ) ) ).
fof(t9_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r2_hidden(C,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
=> r2_hidden(k1_funct_1(B,C),k7_glib_000(A)) ) ) ) ) ).
fof(t10_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ~ ( r2_hidden(C,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
& ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ~ ( D = k6_xcmplx_0(C,np__1)
& r2_hidden(k6_xcmplx_0(C,np__1),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
& r2_hidden(k1_nat_1(C,np__1),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
& r1_glib_000(A,k1_funct_1(B,D),k1_funct_1(B,k1_nat_1(C,np__1)),k1_funct_1(B,C)) ) ) ) ) ) ) ).
fof(t11_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( ~ r1_xreal_0(k3_finseq_1(B),C)
=> r2_hidden(k1_funct_1(B,k1_nat_1(C,np__1)),k29_glib_000(A,k5_glib_001(A,B,C))) ) ) ) ) ).
fof(t12_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> ( r1_xreal_0(C,np__1)
| r2_hidden(k1_funct_1(B,k6_xcmplx_0(C,np__1)),k29_glib_000(A,k5_glib_001(A,B,C))) ) ) ) ) ) ).
fof(t13_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( ~ r1_xreal_0(k3_finseq_1(B),C)
=> ( r2_hidden(C,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
& r2_hidden(k1_nat_1(C,np__1),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
& r2_hidden(k1_nat_1(C,np__2),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B)) ) ) ) ) ) ).
fof(t14_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m1_subset_1(B,k6_glib_000(A))
=> ( k3_finseq_1(k1_glib_001(A,B)) = np__1
& k1_funct_1(k1_glib_001(A,B),np__1) = B
& k3_glib_001(A,k1_glib_001(A,B)) = B
& k4_glib_001(A,k1_glib_001(A,B)) = B
& r1_glib_001(A,B,B,k1_glib_001(A,B)) ) ) ) ).
fof(t15_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C,D] :
( r1_glib_000(A,C,D,B)
=> k3_finseq_1(k2_glib_001(A,C,D,B)) = np__3 ) ) ).
fof(t16_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C,D] :
( r1_glib_000(A,C,D,B)
=> ( k3_glib_001(A,k2_glib_001(A,C,D,B)) = C
& k4_glib_001(A,k2_glib_001(A,C,D,B)) = D
& r1_glib_001(A,C,D,k2_glib_001(A,C,D,B)) ) ) ) ).
fof(t17_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> ( k3_glib_001(A,C) = k3_glib_001(B,D)
& k4_glib_001(A,C) = k4_glib_001(B,D) ) ) ) ) ) ) ).
fof(t18_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_001(A,C,D,B)
<=> ( k1_funct_1(B,np__1) = C
& k1_funct_1(B,k3_finseq_1(B)) = D ) ) ) ) ).
fof(t19_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_001(A,C,D,B)
=> ( m1_subset_1(C,k6_glib_000(A))
& m1_subset_1(D,k6_glib_000(A)) ) ) ) ) ).
fof(t20_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C,D,E] :
( m3_glib_001(E,A)
=> ! [F] :
( m3_glib_001(F,B)
=> ( E = F
=> ( r1_glib_001(A,C,D,E)
<=> r1_glib_001(B,C,D,F) ) ) ) ) ) ) ).
fof(t21_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> k5_glib_001(A,C,E) = k5_glib_001(B,D,E) ) ) ) ) ) ) ).
fof(t22_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( k3_finseq_1(B) = k3_finseq_1(k6_glib_001(A,B))
& k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B) = k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k6_glib_001(A,B))
& k5_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B) = k5_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k6_glib_001(A,B)) ) ) ) ).
fof(t23_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( k3_glib_001(A,B) = k4_glib_001(A,k6_glib_001(A,B))
& k4_glib_001(A,B) = k3_glib_001(A,k6_glib_001(A,B)) ) ) ) ).
fof(t24_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_001(A,C,D,B)
<=> r1_glib_001(A,D,C,k6_glib_001(A,B)) ) ) ) ).
fof(t25_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
=> ( k1_funct_1(B,C) = k1_funct_1(k6_glib_001(A,B),k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),C),np__1))
& r2_hidden(k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),C),np__1),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k6_glib_001(A,B))) ) ) ) ) ) ).
fof(t26_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k6_glib_001(A,B)))
=> ( k1_funct_1(k6_glib_001(A,B),C) = k1_funct_1(B,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),C),np__1))
& r2_hidden(k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(B),C),np__1),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B)) ) ) ) ) ) ).
fof(t27_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k6_glib_001(A,k6_glib_001(A,B)) = B ) ) ).
fof(t28_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> k6_glib_001(A,C) = k6_glib_001(B,D) ) ) ) ) ) ).
fof(t29_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( k4_glib_001(A,B) = k3_glib_001(A,C)
=> k1_nat_1(k3_finseq_1(k7_glib_001(A,B,C)),np__1) = k1_nat_1(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) ).
fof(t30_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( k4_glib_001(A,B) = k3_glib_001(A,C)
=> ( r1_xreal_0(k3_finseq_1(B),k3_finseq_1(k7_glib_001(A,B,C)))
& r1_xreal_0(k3_finseq_1(C),k3_finseq_1(k7_glib_001(A,B,C))) ) ) ) ) ) ).
fof(t31_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( k4_glib_001(A,B) = k3_glib_001(A,C)
=> ( k3_glib_001(A,k7_glib_001(A,B,C)) = k3_glib_001(A,B)
& k4_glib_001(A,k7_glib_001(A,B,C)) = k4_glib_001(A,C)
& r1_glib_001(A,k3_glib_001(A,B),k4_glib_001(A,C),k7_glib_001(A,B,C)) ) ) ) ) ) ).
fof(t32_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D,E,F] :
( ( r1_glib_001(A,D,E,B)
& r1_glib_001(A,E,F,C) )
=> r1_glib_001(A,D,F,k7_glib_001(A,B,C)) ) ) ) ) ).
fof(t33_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r2_hidden(D,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
=> ( k1_funct_1(k7_glib_001(A,B,C),D) = k1_funct_1(B,D)
& r2_hidden(D,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k7_glib_001(A,B,C))) ) ) ) ) ) ) ).
fof(t34_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( k4_glib_001(A,B) = k3_glib_001(A,C)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_finseq_1(C),D)
=> ( k1_funct_1(k7_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),D)) = k1_funct_1(C,k1_nat_1(D,np__1))
& r2_hidden(k1_nat_1(k3_finseq_1(B),D),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k7_glib_001(A,B,C))) ) ) ) ) ) ) ) ).
fof(t35_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ~ ( r2_hidden(D,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k7_glib_001(A,B,C)))
& ~ r2_hidden(D,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( ~ r1_xreal_0(k3_finseq_1(C),E)
& D = k1_nat_1(k3_finseq_1(B),E) ) ) ) ) ) ) ) ).
fof(t36_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,A)
=> ! [E] :
( m3_glib_001(E,B)
=> ! [F] :
( m3_glib_001(F,B)
=> ( ( C = E
& D = F )
=> k7_glib_001(A,C,D) = k7_glib_001(B,E,F) ) ) ) ) ) ) ) ).
fof(t37_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( k1_nat_1(k3_finseq_1(k8_glib_001(A,B,C,D)),C) = k1_nat_1(D,np__1)
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ~ r1_xreal_0(k3_finseq_1(k8_glib_001(A,B,C,D)),E)
=> ( k1_funct_1(k8_glib_001(A,B,C,D),k1_nat_1(E,np__1)) = k1_funct_1(B,k1_nat_1(C,E))
& r2_hidden(k1_nat_1(C,E),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B)) ) ) ) ) ) ) ) ) ) ).
fof(t38_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( k3_glib_001(A,k8_glib_001(A,B,C,D)) = k1_funct_1(B,C)
& k4_glib_001(A,k8_glib_001(A,B,C,D)) = k1_funct_1(B,D)
& r1_glib_001(A,k1_funct_1(B,C),k1_funct_1(B,D),k8_glib_001(A,B,C,D)) ) ) ) ) ) ) ).
fof(t39_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ! [E] :
( ( ~ v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(B)) )
=> k7_glib_001(A,k8_glib_001(A,B,C,D),k8_glib_001(A,B,D,E)) = k8_glib_001(A,B,C,E) ) ) ) ) ) ) ).
fof(t40_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k8_glib_001(A,B,np__1,k3_finseq_1(B)) = B ) ) ).
fof(t41_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( ~ r1_xreal_0(k3_finseq_1(B),C)
=> k2_glib_001(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__2)),k1_funct_1(B,k1_nat_1(C,np__1))) = k8_glib_001(A,B,C,k1_nat_1(C,np__2)) ) ) ) ) ).
fof(t42_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,D)
=> ( r1_xreal_0(k3_finseq_1(B),D)
| k10_glib_001(A,k8_glib_001(A,B,C,D),k1_funct_1(B,k1_nat_1(D,np__1))) = k8_glib_001(A,B,C,k1_nat_1(D,np__2)) ) ) ) ) ) ) ).
fof(t43_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> k8_glib_001(A,B,C,C) = k12_finseq_1(k6_glib_000(A),k5_glib_001(A,B,C)) ) ) ) ) ).
fof(t44_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( r1_xreal_0(C,D)
=> ( v1_abian(C)
| k8_glib_001(A,k8_glib_001(A,B,np__1,D),np__1,C) = k8_glib_001(A,B,np__1,C) ) ) ) ) ) ) ).
fof(t45_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ! [E] :
( ( ~ v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(B))
& k4_glib_001(A,B) = k3_glib_001(A,C) )
=> k8_glib_001(A,k7_glib_001(A,B,C),D,E) = k8_glib_001(A,B,D,E) ) ) ) ) ) ) ).
fof(t46_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> k3_finseq_1(k8_glib_001(A,B,np__1,C)) = C ) ) ) ) ).
fof(t47_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( ( r2_hidden(D,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k8_glib_001(A,B,np__1,C)))
& r1_xreal_0(C,k3_finseq_1(B)) )
=> k1_funct_1(k8_glib_001(A,B,np__1,C),D) = k1_funct_1(B,D) ) ) ) ) ) ).
fof(t48_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& r2_hidden(E,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k8_glib_001(A,B,C,D))) )
=> ( k1_funct_1(k8_glib_001(A,B,C,D),E) = k1_funct_1(B,k6_xcmplx_0(k1_nat_1(C,E),np__1))
& r2_hidden(k6_xcmplx_0(k1_nat_1(C,E),np__1),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B)) ) ) ) ) ) ) ) ).
fof(t49_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( C = D
=> k8_glib_001(A,C,E,F) = k8_glib_001(B,D,E,F) ) ) ) ) ) ) ) ).
fof(t50_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> k1_nat_1(k3_finseq_1(k20_glib_001(A,B,C,D)),D) = k1_nat_1(k3_finseq_1(B),C) ) ) ) ) ) ).
fof(t51_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D,E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( r1_glib_001(A,C,D,B)
=> r1_glib_001(A,C,D,k20_glib_001(A,B,E,F)) ) ) ) ) ) ).
fof(t52_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_xreal_0(k3_finseq_1(k20_glib_001(A,B,C,D)),k3_finseq_1(B)) ) ) ) ) ).
fof(t53_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> k20_glib_001(A,B,C,C) = B ) ) ) ).
fof(t54_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> k4_glib_001(A,k8_glib_001(A,B,np__1,C)) = k3_glib_001(A,k8_glib_001(A,B,D,k3_finseq_1(B))) ) ) ) ) ) ).
fof(t55_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k2_finseq_1(C))
=> k1_funct_1(k20_glib_001(A,B,C,D),E) = k1_funct_1(B,E) ) ) ) ) ) ) ) ).
fof(t56_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( ( r1_xreal_0(C,E)
& r1_xreal_0(E,k3_finseq_1(k20_glib_001(A,B,C,D))) )
=> ( k1_funct_1(k20_glib_001(A,B,C,D),E) = k1_funct_1(B,k2_xcmplx_0(k6_xcmplx_0(E,C),D))
& m2_subset_1(k2_xcmplx_0(k6_xcmplx_0(E,C),D),k1_numbers,k5_numbers)
& r1_xreal_0(k2_xcmplx_0(k6_xcmplx_0(E,C),D),k3_finseq_1(B)) ) ) ) ) ) ) ) ) ).
fof(t57_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> k3_finseq_1(k20_glib_001(A,B,C,D)) = k6_xcmplx_0(k1_nat_1(k3_finseq_1(B),C),D) ) ) ) ) ) ).
fof(t58_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k1_funct_1(B,C) = k4_glib_001(A,B)
=> k20_glib_001(A,B,C,k3_finseq_1(B)) = k8_glib_001(A,B,np__1,C) ) ) ) ) ).
fof(t59_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( k3_glib_001(A,B) = k1_funct_1(B,C)
=> k20_glib_001(A,B,np__1,C) = k8_glib_001(A,B,C,k3_finseq_1(B)) ) ) ) ) ).
fof(t60_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> ( k3_glib_001(A,k20_glib_001(A,B,C,D)) = k3_glib_001(A,B)
& k4_glib_001(A,k20_glib_001(A,B,C,D)) = k4_glib_001(A,B) ) ) ) ) ) ).
fof(t61_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ~ ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D)
& r2_hidden(E,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),k20_glib_001(A,B,C,D)))
& ~ r2_hidden(E,k2_finseq_1(C))
& ~ ( r1_xreal_0(C,E)
& r1_xreal_0(E,k3_finseq_1(k20_glib_001(A,B,C,D))) ) ) ) ) ) ) ) ).
fof(t62_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ! [F] :
( m2_subset_1(F,k1_numbers,k5_numbers)
=> ( C = D
=> k20_glib_001(A,C,E,F) = k20_glib_001(B,D,E,F) ) ) ) ) ) ) ) ).
fof(t63_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> k10_glib_001(A,B,C) = k7_finseq_1(B,k10_finseq_1(C,D)) ) ) ) ).
fof(t64_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> ( k3_glib_001(A,k10_glib_001(A,B,C)) = k3_glib_001(A,B)
& k4_glib_001(A,k10_glib_001(A,B,C)) = D
& r1_glib_001(A,k3_glib_001(A,B),D,k10_glib_001(A,B,C)) ) ) ) ) ).
fof(t65_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> k3_finseq_1(k10_glib_001(A,B,C)) = k1_nat_1(k3_finseq_1(B),np__2) ) ) ) ).
fof(t66_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> ( k1_funct_1(k10_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),np__1)) = C
& k1_funct_1(k10_glib_001(A,B,C),k1_nat_1(k3_finseq_1(B),np__2)) = D
& ! [E] :
( m2_subset_1(E,k1_numbers,k5_numbers)
=> ( r2_hidden(E,k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B))
=> k1_funct_1(k10_glib_001(A,B,C),E) = k1_funct_1(B,E) ) ) ) ) ) ) ).
fof(t67_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D,E,F] :
( ( r1_glib_001(A,C,D,B)
& r1_glib_000(A,D,F,E) )
=> r1_glib_001(A,C,F,k10_glib_001(A,B,E)) ) ) ) ).
fof(t68_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> r1_xreal_0(np__1,k3_finseq_1(k11_glib_001(A,B))) ) ) ).
fof(t69_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> ( k6_xcmplx_0(k2_nat_1(np__2,k3_nat_1(k1_nat_1(C,np__1),np__2)),np__1) = C
& r1_xreal_0(np__1,k3_nat_1(k1_nat_1(C,np__1),np__2))
& r1_xreal_0(k3_nat_1(k1_nat_1(C,np__1),np__2),k3_finseq_1(k11_glib_001(A,B))) ) ) ) ) ) ).
fof(t70_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m1_subset_1(B,k6_glib_000(A))
=> k11_glib_001(A,k1_glib_001(A,B)) = k12_finseq_1(k6_glib_000(A),B) ) ) ).
fof(t71_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C,D] :
( r1_glib_000(A,C,D,B)
=> k11_glib_001(A,k2_glib_001(A,C,D,B)) = k10_finseq_1(C,D) ) ) ).
fof(t72_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( k3_glib_001(A,B) = k1_funct_1(k11_glib_001(A,B),np__1)
& k4_glib_001(A,B) = k1_funct_1(k11_glib_001(A,B),k3_finseq_1(k11_glib_001(A,B))) ) ) ) ).
fof(t73_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> k5_glib_001(A,B,C) = k1_funct_1(k11_glib_001(A,B),k3_nat_1(k1_nat_1(C,np__1),np__2)) ) ) ) ) ).
fof(t74_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_relset_1(k5_numbers,k6_glib_000(A),k11_glib_001(A,B)))
<=> r2_hidden(k6_xcmplx_0(k2_nat_1(np__2,C),np__1),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B)) ) ) ) ) ).
fof(t75_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_tarski(k11_glib_001(A,k8_glib_001(A,B,np__1,C)),k11_glib_001(A,B)) ) ) ) ).
fof(t76_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> k11_glib_001(A,k10_glib_001(A,B,C)) = k7_finseq_1(k11_glib_001(A,B),k9_finseq_1(D)) ) ) ) ).
fof(t77_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> k11_glib_001(A,C) = k11_glib_001(B,D) ) ) ) ) ) ).
fof(t78_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(np__1,C)
& r1_xreal_0(C,k3_finseq_1(B)) )
=> ( r2_hidden(k3_nat_1(C,np__2),k4_relset_1(k5_numbers,k7_glib_000(A),k12_glib_001(A,B)))
& k1_funct_1(B,C) = k1_funct_1(k12_glib_001(A,B),k3_nat_1(C,np__2)) ) ) ) ) ) ).
fof(t79_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_relset_1(k5_numbers,k7_glib_000(A),k12_glib_001(A,B)))
<=> r2_hidden(k2_nat_1(np__2,C),k4_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B)) ) ) ) ) ).
fof(t80_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ( r2_hidden(C,k4_relset_1(k5_numbers,k7_glib_000(A),k12_glib_001(A,B)))
=> r2_hidden(k1_funct_1(k12_glib_001(A,B),C),k7_glib_000(A)) ) ) ) ) ).
fof(t81_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ? [C] :
( v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers)
& C = k6_xcmplx_0(k3_finseq_1(B),np__1)
& k3_finseq_1(k12_glib_001(A,B)) = k3_nat_1(C,np__2) ) ) ) ).
fof(t82_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> r1_tarski(k12_glib_001(A,k8_glib_001(A,B,np__1,C)),k12_glib_001(A,B)) ) ) ) ).
fof(t83_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> k12_glib_001(A,k10_glib_001(A,B,C)) = k7_finseq_1(k12_glib_001(A,B),k9_finseq_1(C)) ) ) ) ).
fof(t84_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C,D] :
( r1_glib_000(A,C,D,B)
<=> k12_glib_001(A,k2_glib_001(A,C,D,B)) = k9_finseq_1(B) ) ) ).
fof(t85_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k12_glib_001(A,k6_glib_001(A,B)) = k3_finseq_5(k12_glib_001(A,B)) ) ) ).
fof(t86_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( k4_glib_001(A,B) = k3_glib_001(A,C)
=> k12_glib_001(A,k7_glib_001(A,B,C)) = k8_finseq_1(k7_glib_000(A),k12_glib_001(A,B),k12_glib_001(A,C)) ) ) ) ) ).
fof(t87_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> k12_glib_001(A,C) = k12_glib_001(B,D) ) ) ) ) ) ).
fof(t88_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( r2_hidden(C,k13_glib_001(A,B))
<=> ? [D] :
( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,D) = C ) ) ) ) ).
fof(t89_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( r2_hidden(k3_glib_001(A,B),k13_glib_001(A,B))
& r2_hidden(k4_glib_001(A,B),k13_glib_001(A,B)) ) ) ) ).
fof(t90_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> r2_hidden(k5_glib_001(A,B,C),k13_glib_001(A,B)) ) ) ) ) ).
fof(t91_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m1_subset_1(B,k6_glib_000(A))
=> k13_glib_001(A,k1_glib_001(A,B)) = k6_domain_1(k6_glib_000(A),B) ) ) ).
fof(t92_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C,D] :
( r1_glib_000(A,C,D,B)
=> k13_glib_001(A,k2_glib_001(A,C,D,B)) = k2_tarski(C,D) ) ) ).
fof(t93_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k13_glib_001(A,B) = k13_glib_001(A,k6_glib_001(A,B)) ) ) ).
fof(t94_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( k4_glib_001(A,B) = k3_glib_001(A,C)
=> k13_glib_001(A,k7_glib_001(A,B,C)) = k4_subset_1(k6_glib_000(A),k13_glib_001(A,B),k13_glib_001(A,C)) ) ) ) ) ).
fof(t95_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> r1_tarski(k13_glib_001(A,k8_glib_001(A,B,C,D)),k13_glib_001(A,B)) ) ) ) ) ) ).
fof(t96_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> k13_glib_001(A,k10_glib_001(A,B,C)) = k2_xboole_0(k13_glib_001(A,B),k1_tarski(D)) ) ) ) ).
fof(t97_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& v2_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> ( r2_hidden(D,k13_glib_001(A,B))
| k4_card_1(k13_glib_001(A,k10_glib_001(A,B,C))) = k1_nat_1(k4_card_1(k13_glib_001(A,B)),np__1) ) ) ) ) ).
fof(t98_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
~ ( r2_hidden(C,k13_glib_001(A,B))
& r2_hidden(D,k13_glib_001(A,B))
& ! [E] :
( m3_glib_001(E,A)
=> ~ r1_glib_001(A,C,D,E) ) ) ) ) ).
fof(t99_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> k13_glib_001(A,C) = k13_glib_001(B,D) ) ) ) ) ) ).
fof(t100_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( r2_hidden(C,k14_glib_001(A,B))
<=> ? [D] :
( v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers)
& r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,D) = C ) ) ) ) ).
fof(t101_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( r2_hidden(C,k14_glib_001(A,B))
<=> ? [D] :
( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers)
& ~ r1_xreal_0(k3_finseq_1(B),D)
& k1_funct_1(B,k1_nat_1(D,np__1)) = C ) ) ) ) ).
fof(t102_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k5_relset_1(k5_numbers,k2_xboole_0(k6_glib_000(A),k7_glib_000(A)),B) = k2_xboole_0(k13_glib_001(A,B),k14_glib_001(A,B)) ) ) ).
fof(t103_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( k4_glib_001(A,B) = k3_glib_001(A,C)
=> k14_glib_001(A,k7_glib_001(A,B,C)) = k4_subset_1(k7_glib_000(A),k14_glib_001(A,B),k14_glib_001(A,C)) ) ) ) ) ).
fof(t104_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
~ ( r2_hidden(C,k14_glib_001(A,B))
& ! [D] :
( m1_subset_1(D,k6_glib_000(A))
=> ! [E] :
( m1_subset_1(E,k6_glib_000(A))
=> ! [F] :
( ( ~ v1_abian(F)
& m2_subset_1(F,k1_numbers,k5_numbers) )
=> ~ ( r1_xreal_0(k1_nat_1(F,np__2),k3_finseq_1(B))
& D = k1_funct_1(B,F)
& C = k1_funct_1(B,k1_nat_1(F,np__1))
& E = k1_funct_1(B,k1_nat_1(F,np__2))
& r1_glib_000(A,D,E,C) ) ) ) ) ) ) ) ).
fof(t105_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( r2_hidden(C,k14_glib_001(A,B))
<=> ? [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
& r2_hidden(D,k4_relset_1(k5_numbers,k7_glib_000(A),k12_glib_001(A,B)))
& k1_funct_1(k12_glib_001(A,B),D) = C ) ) ) ) ).
fof(t106_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D,E] :
( ( r2_hidden(C,k14_glib_001(A,B))
& r1_glib_000(A,D,E,C) )
=> ( r2_hidden(D,k13_glib_001(A,B))
& r2_hidden(E,k13_glib_001(A,B)) ) ) ) ) ).
fof(t107_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> r1_tarski(k14_glib_001(A,k8_glib_001(A,B,C,D)),k14_glib_001(A,B)) ) ) ) ) ).
fof(t108_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k14_glib_001(A,B) = k14_glib_001(A,k6_glib_001(A,B)) ) ) ).
fof(t109_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C,D] :
( r1_glib_000(A,C,D,B)
<=> k14_glib_001(A,k2_glib_001(A,C,D,B)) = k1_tarski(B) ) ) ).
fof(t110_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> r1_tarski(k14_glib_001(A,B),k22_glib_000(A,k13_glib_001(A,B))) ) ) ).
fof(t111_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> k14_glib_001(A,C) = k14_glib_001(B,D) ) ) ) ) ) ).
fof(t112_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> k14_glib_001(A,k10_glib_001(A,B,C)) = k2_xboole_0(k14_glib_001(A,B),k1_tarski(C)) ) ) ) ).
fof(t113_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> k3_finseq_1(B) = k1_nat_1(k2_nat_1(np__2,k15_glib_001(A,B)),np__1) ) ) ).
fof(t114_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( k3_finseq_1(B) = k3_finseq_1(C)
<=> k15_glib_001(A,B) = k15_glib_001(A,C) ) ) ) ) ).
fof(t115_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> k15_glib_001(A,C) = k15_glib_001(B,D) ) ) ) ) ) ).
fof(t116_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> ( r1_xreal_0(k16_glib_001(A,B,k1_funct_1(B,C)),C)
& r1_xreal_0(C,k18_glib_001(A,B,k1_funct_1(B,C))) ) ) ) ) ) ).
fof(t117_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ! [E] :
( C = D
=> ( k16_glib_001(A,C,E) = k16_glib_001(B,D,E)
& k18_glib_001(A,C,E) = k18_glib_001(B,D,E) ) ) ) ) ) ) ).
fof(t118_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> ( r1_xreal_0(k17_glib_001(A,B,C),C)
& r1_xreal_0(C,k19_glib_001(A,B,C)) ) ) ) ) ) ).
fof(t119_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v1_glib_001(B,A)
<=> k1_funct_1(B,np__1) = k1_funct_1(B,k3_finseq_1(B)) ) ) ) ).
fof(t120_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v1_glib_001(B,A)
<=> ? [C] : r1_glib_001(A,C,C,B) ) ) ) ).
fof(t121_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v1_glib_001(B,A)
<=> v1_glib_001(k6_glib_001(A,B),A) ) ) ) ).
fof(t122_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( ( C = D
& v1_glib_001(C,A) )
=> v1_glib_001(D,B) ) ) ) ) ) ).
fof(t123_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v2_glib_001(B,A)
<=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( ~ r1_xreal_0(k3_finseq_1(B),C)
=> r2_glib_000(A,k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,np__2)),k1_funct_1(B,k1_nat_1(C,np__1))) ) ) ) ) ) ).
fof(t124_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D,E,F] :
( ( v2_glib_001(B,A)
& r1_glib_001(A,C,D,B)
& r2_glib_000(A,D,F,E) )
=> ( v2_glib_001(k10_glib_001(A,B,E),A)
& r1_glib_001(A,C,F,k10_glib_001(A,B,E)) ) ) ) ) ).
fof(t125_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v2_glib_001(B,A)
& m3_glib_001(B,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> v2_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) ).
fof(t126_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( ~ v3_glib_001(B,A)
<=> r1_xreal_0(np__3,k3_finseq_1(B)) ) ) ) ).
fof(t127_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( ~ ( ~ v3_glib_001(B,A)
& k3_finseq_1(B) = np__1 )
& ~ ( k3_finseq_1(B) != np__1
& v3_glib_001(B,A) ) ) ) ) ).
fof(t128_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ~ ( k3_glib_001(A,B) != k4_glib_001(A,B)
& v3_glib_001(B,A) ) ) ) ).
fof(t129_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v3_glib_001(B,A)
<=> ? [C] :
( m1_subset_1(C,k6_glib_000(A))
& B = k1_glib_001(A,C) ) ) ) ) ).
fof(t130_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v3_glib_001(B,A)
<=> v3_glib_001(k6_glib_001(A,B),A) ) ) ) ).
fof(t131_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( v3_glib_001(B,A)
=> k7_glib_001(A,C,B) = C ) ) ) ) ).
fof(t132_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,D)
& r1_xreal_0(D,k3_finseq_1(B)) )
=> ( v3_glib_001(k8_glib_001(A,B,C,D),A)
<=> C = D ) ) ) ) ) ) ).
fof(t133_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
~ ( r1_glib_000(A,k4_glib_001(A,B),D,C)
& v3_glib_001(k10_glib_001(A,B,C),A) ) ) ) ).
fof(t134_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ~ ( ~ v3_glib_001(B,A)
& ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ~ ( C = k6_xcmplx_0(k3_finseq_1(B),np__2)
& k10_glib_001(A,k8_glib_001(A,B,np__1,C),k1_funct_1(B,k1_nat_1(C,np__1))) = B ) ) ) ) ) ).
fof(t135_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( r1_tarski(k14_glib_001(A,B),k14_glib_001(A,C))
=> ( v3_glib_001(B,A)
| r1_tarski(k13_glib_001(A,B),k13_glib_001(A,C)) ) ) ) ) ) ).
fof(t136_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( ~ v3_glib_001(B,A)
=> ! [C] :
( m1_subset_1(C,k6_glib_000(A))
=> ~ ( r2_hidden(C,k13_glib_001(A,B))
& v10_glib_000(C,A) ) ) ) ) ) ).
fof(t137_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v3_glib_001(B,A)
<=> k14_glib_001(A,B) = k1_xboole_0 ) ) ) ).
fof(t138_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( ( C = D
& v3_glib_001(C,A) )
=> v3_glib_001(D,B) ) ) ) ) ) ).
fof(t139_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v4_glib_001(B,A)
<=> ! [C] :
( ( v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ~ ( r1_xreal_0(np__1,C)
& ~ r1_xreal_0(D,C)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) ) ) ) ) ) ) ).
fof(t140_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( r1_xreal_0(k3_finseq_1(B),np__3)
=> v4_glib_001(B,A) ) ) ) ).
fof(t141_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v4_glib_001(B,A)
<=> v4_glib_001(k6_glib_001(A,B),A) ) ) ) ).
fof(t142_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v4_glib_001(B,A)
& m3_glib_001(B,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> v4_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) ).
fof(t143_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v4_glib_001(B,A)
& m3_glib_001(B,A) )
=> ! [C] :
( r2_hidden(C,k29_glib_000(A,k4_glib_001(A,B)))
=> ( r2_hidden(C,k14_glib_001(A,B))
| v4_glib_001(k10_glib_001(A,B,C),A) ) ) ) ) ).
fof(t144_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v4_glib_001(B,A)
& m3_glib_001(B,A) )
=> ! [C] :
( m1_subset_1(C,k6_glib_000(A))
=> ~ ( r2_hidden(C,k13_glib_001(A,B))
& v11_glib_000(C,A)
& C != k3_glib_001(A,B)
& C != k4_glib_001(A,B) ) ) ) ) ).
fof(t145_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& v2_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v4_glib_001(B,A)
& m3_glib_001(B,A) )
=> r1_xreal_0(k3_finseq_1(k12_glib_001(A,B)),k18_glib_000(A)) ) ) ).
fof(t146_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( r1_xreal_0(k3_finseq_1(B),np__3)
=> v5_glib_001(B,A) ) ) ) ).
fof(t147_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ( ( r1_xreal_0(C,k3_finseq_1(B))
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) )
=> C = D ) ) )
=> v5_glib_001(B,A) ) ) ) ).
fof(t148_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v5_glib_001(B,A)
& m3_glib_001(B,A) )
=> ( ~ v1_glib_001(B,A)
=> ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ~ ( ~ r1_xreal_0(D,C)
& r1_xreal_0(D,k3_finseq_1(B))
& k1_funct_1(B,C) = k1_funct_1(B,D) ) ) ) ) ) ) ).
fof(t149_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( v5_glib_001(B,A)
<=> v5_glib_001(k6_glib_001(A,B),A) ) ) ) ).
fof(t150_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v5_glib_001(B,A)
& m3_glib_001(B,A) )
=> ! [C] :
( m2_subset_1(C,k1_numbers,k5_numbers)
=> ! [D] :
( m2_subset_1(D,k1_numbers,k5_numbers)
=> v5_glib_001(k8_glib_001(A,B,C,D),A) ) ) ) ) ).
fof(t151_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v5_glib_001(B,A)
& m3_glib_001(B,A) )
=> ! [C,D] :
( ( r1_glib_000(A,k4_glib_001(A,B),D,C)
& ! [E] :
( ( ~ v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ~ ( ~ r1_xreal_0(E,np__1)
& r1_xreal_0(E,k3_finseq_1(B))
& k1_funct_1(B,E) = D ) ) )
=> ( r2_hidden(C,k14_glib_001(A,B))
| ( ~ v3_glib_001(B,A)
& v1_glib_001(B,A) )
| v5_glib_001(k10_glib_001(A,B,C),A) ) ) ) ) ).
fof(t152_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v5_glib_001(B,A)
& m3_glib_001(B,A) )
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> ( r2_hidden(D,k13_glib_001(A,B))
| ( ~ v3_glib_001(B,A)
& v1_glib_001(B,A) )
| v5_glib_001(k10_glib_001(A,B,C),A) ) ) ) ) ).
fof(t153_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> k16_glib_001(A,B,k1_funct_1(B,C)) = k18_glib_001(A,B,k1_funct_1(B,C)) ) )
=> v5_glib_001(B,A) ) ) ) ).
fof(t154_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ( ! [C] :
( ( ~ v1_abian(C)
& m2_subset_1(C,k1_numbers,k5_numbers) )
=> ( r1_xreal_0(C,k3_finseq_1(B))
=> k19_glib_001(A,B,C) = C ) )
=> v5_glib_001(B,A) ) ) ) ).
fof(t155_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& v2_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v5_glib_001(B,A)
& m3_glib_001(B,A) )
=> r1_xreal_0(k3_finseq_1(k11_glib_001(A,B)),k1_nat_1(k16_glib_000(A),np__1)) ) ) ).
fof(t156_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v6_glib_001(B,A)
& m3_glib_001(B,A) )
=> ! [C,D] :
( r1_glib_000(A,k4_glib_001(A,B),D,C)
=> ( r2_hidden(D,k13_glib_001(A,B))
| v6_glib_001(k10_glib_001(A,B,C),A) ) ) ) ) ).
fof(t157_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B,C] :
( r1_glib_000(A,C,C,B)
=> v8_glib_001(k2_glib_001(A,C,C,B),A) ) ) ).
fof(t158_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D,E] :
~ ( r1_glib_000(A,D,E,C)
& r2_hidden(C,k14_glib_001(A,B))
& v8_glib_001(B,A)
& ! [F] :
( m3_glib_001(F,A)
=> ~ ( r1_glib_001(A,D,E,F)
& ~ r2_hidden(C,k14_glib_001(A,F)) ) ) ) ) ) ).
fof(t159_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> m4_glib_001(B,A,B) ) ) ).
fof(t160_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m4_glib_001(C,A,B)
=> ! [D] :
( m4_glib_001(D,A,C)
=> m4_glib_001(D,A,B) ) ) ) ) ).
fof(t161_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D,E] :
( m4_glib_001(B,A,C)
=> ( r1_glib_001(A,D,E,B)
<=> r1_glib_001(A,D,E,C) ) ) ) ) ) ).
fof(t162_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( m4_glib_001(B,A,C)
=> ( k3_glib_001(A,B) = k3_glib_001(A,C)
& k4_glib_001(A,B) = k4_glib_001(A,C) ) ) ) ) ) ).
fof(t163_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( m4_glib_001(B,A,C)
=> r1_xreal_0(k3_finseq_1(B),k3_finseq_1(C)) ) ) ) ) ).
fof(t164_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( m4_glib_001(B,A,C)
=> ( r1_tarski(k14_glib_001(A,B),k14_glib_001(A,C))
& r1_tarski(k13_glib_001(A,B),k13_glib_001(A,C)) ) ) ) ) ) ).
fof(t165_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( m4_glib_001(B,A,C)
=> ! [D] :
( ( ~ v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ~ ( r1_xreal_0(D,k3_finseq_1(B))
& ! [E] :
( ( ~ v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ~ ( r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(C))
& k1_funct_1(B,D) = k1_funct_1(C,E) ) ) ) ) ) ) ) ) ).
fof(t166_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( m4_glib_001(B,A,C)
=> ! [D] :
( ( v1_abian(D)
& m2_subset_1(D,k1_numbers,k5_numbers) )
=> ~ ( r1_xreal_0(np__1,D)
& r1_xreal_0(D,k3_finseq_1(B))
& ! [E] :
( ( v1_abian(E)
& m2_subset_1(E,k1_numbers,k5_numbers) )
=> ~ ( r1_xreal_0(D,E)
& r1_xreal_0(E,k3_finseq_1(C))
& k1_funct_1(B,D) = k1_funct_1(C,E) ) ) ) ) ) ) ) ) ).
fof(t167_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v4_glib_001(B,A)
& m3_glib_001(B,A) )
=> ~ ( ~ v3_glib_001(B,A)
& ! [C] :
( ( v5_glib_001(C,A)
& m4_glib_001(C,A,B) )
=> v3_glib_001(C,A) ) ) ) ) ).
fof(t168_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_000(B,A)
=> ! [C] :
( m3_glib_001(C,B)
=> m3_glib_001(C,A) ) ) ) ).
fof(t169_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_000(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( ( v3_glib_001(C,A)
& r2_hidden(k3_glib_001(A,C),k25_glib_000(A,B)) )
=> m3_glib_001(C,B) ) ) ) ) ).
fof(t170_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_000(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( r1_tarski(k14_glib_001(A,C),k26_glib_000(A,B))
=> ( v3_glib_001(C,A)
| m3_glib_001(C,B) ) ) ) ) ) ).
fof(t171_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_000(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ( ( r1_tarski(k13_glib_001(A,C),k25_glib_000(A,B))
& r1_tarski(k14_glib_001(A,C),k26_glib_000(A,B)) )
=> m3_glib_001(C,B) ) ) ) ) ).
fof(t172_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& ~ v4_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C] :
( m1_subset_1(C,k6_glib_000(A))
=> ! [D] :
( m3_glib_000(D,A,k1_card_fil(k6_glib_000(A),k1_tarski(C)),k22_glib_000(A,k1_card_fil(k6_glib_000(A),k1_tarski(C))))
=> ( ~ r2_hidden(C,k13_glib_001(A,B))
=> m3_glib_001(B,D) ) ) ) ) ) ).
fof(t173_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> ! [C,D] :
( m3_glib_000(D,A,k6_glib_000(A),k1_card_fil(k7_glib_000(A),k1_tarski(C)))
=> ( ~ r2_hidden(C,k14_glib_001(A,B))
=> m3_glib_001(B,D) ) ) ) ) ).
fof(t174_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_000(B,A)
=> ! [C,D,E] :
( r1_glib_000(B,C,D,E)
=> k2_glib_001(A,C,D,E) = k2_glib_001(B,C,D,E) ) ) ) ).
fof(t175_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_000(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ! [E] :
( ( C = D
& r2_hidden(E,k29_glib_000(B,k4_glib_001(B,D))) )
=> k10_glib_001(A,C,E) = k10_glib_001(B,D,E) ) ) ) ) ) ).
fof(t176_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_000(B,A)
=> ! [C] :
( m3_glib_001(C,B)
=> ( ( v1_glib_001(C,B)
=> ( v1_glib_001(C,A)
& m3_glib_001(C,A) ) )
& ( v2_glib_001(C,B)
=> ( v2_glib_001(C,A)
& m3_glib_001(C,A) ) )
& ( v3_glib_001(C,B)
=> ( v3_glib_001(C,A)
& m3_glib_001(C,A) ) )
& ( v4_glib_001(C,B)
=> ( v4_glib_001(C,A)
& m3_glib_001(C,A) ) )
& ( v5_glib_001(C,B)
=> ( v5_glib_001(C,A)
& m3_glib_001(C,A) ) )
& ( v6_glib_001(C,B)
=> ( v6_glib_001(C,A)
& m3_glib_001(C,A) ) ) ) ) ) ) ).
fof(t177_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_000(B,A)
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( C = D
=> ( ( v1_glib_001(C,A)
=> v1_glib_001(D,B) )
& ( v1_glib_001(D,B)
=> v1_glib_001(C,A) )
& ( v2_glib_001(C,A)
=> v2_glib_001(D,B) )
& ( v2_glib_001(D,B)
=> v2_glib_001(C,A) )
& ( v3_glib_001(C,A)
=> v3_glib_001(D,B) )
& ( v3_glib_001(D,B)
=> v3_glib_001(C,A) )
& ( v4_glib_001(C,A)
=> v4_glib_001(D,B) )
& ( v4_glib_001(D,B)
=> v4_glib_001(C,A) )
& ( v5_glib_001(C,A)
=> v5_glib_001(D,B) )
& ( v5_glib_001(D,B)
=> v5_glib_001(C,A) )
& ( v6_glib_001(C,A)
=> v6_glib_001(D,B) )
& ( v6_glib_001(D,B)
=> v6_glib_001(C,A) ) ) ) ) ) ) ) ).
fof(t178_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( ( r5_glib_000(A,B)
& m1_glib_001(C,A) )
=> m1_glib_001(C,B) ) ) ) ).
fof(t179_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( ( r5_glib_000(A,B)
& m2_glib_001(C,A) )
=> m2_glib_001(C,B) ) ) ) ).
fof(t180_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( ( r5_glib_000(A,B)
& m3_glib_001(C,A) )
=> m3_glib_001(C,B) ) ) ) ).
fof(t181_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C,D,E] :
( r5_glib_000(A,B)
=> k2_glib_001(A,C,E,D) = k2_glib_001(B,C,E,D) ) ) ) ).
fof(t182_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ! [C] :
( m3_glib_001(C,A)
=> ! [D] :
( m3_glib_001(D,B)
=> ( ( r5_glib_000(A,B)
& C = D )
=> ( ( v1_glib_001(C,A)
=> v1_glib_001(D,B) )
& ( v1_glib_001(D,B)
=> v1_glib_001(C,A) )
& ( v2_glib_001(C,A)
=> v2_glib_001(D,B) )
& ( v2_glib_001(D,B)
=> v2_glib_001(C,A) )
& ( v3_glib_001(C,A)
=> v3_glib_001(D,B) )
& ( v3_glib_001(D,B)
=> v3_glib_001(C,A) )
& ( v4_glib_001(C,A)
=> v4_glib_001(D,B) )
& ( v4_glib_001(D,B)
=> v4_glib_001(C,A) )
& ( v5_glib_001(C,A)
=> v5_glib_001(D,B) )
& ( v5_glib_001(D,B)
=> v5_glib_001(C,A) )
& ( v6_glib_001(C,A)
=> v6_glib_001(D,B) )
& ( v6_glib_001(D,B)
=> v6_glib_001(C,A) ) ) ) ) ) ) ) ).
fof(dt_m1_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m1_glib_001(B,A)
=> m2_finseq_1(B,k6_glib_000(A)) ) ) ).
fof(existence_m1_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ? [B] : m1_glib_001(B,A) ) ).
fof(dt_m2_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m2_glib_001(B,A)
=> m2_finseq_1(B,k7_glib_000(A)) ) ) ).
fof(existence_m2_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ? [B] : m2_glib_001(B,A) ) ).
fof(dt_m3_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ! [B] :
( m3_glib_001(B,A)
=> m2_finseq_1(B,k2_xboole_0(k6_glib_000(A),k7_glib_000(A))) ) ) ).
fof(existence_m3_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ? [B] : m3_glib_001(B,A) ) ).
fof(dt_m4_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> ! [C] :
( m4_glib_001(C,A,B)
=> m3_glib_001(C,A) ) ) ).
fof(existence_m4_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> ? [C] : m4_glib_001(C,A,B) ) ).
fof(dt_m5_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k21_glib_001(A))) )
=> ! [C] :
( m5_glib_001(C,A,B)
=> m3_glib_001(C,A) ) ) ).
fof(existence_m5_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k21_glib_001(A))) )
=> ? [C] : m5_glib_001(C,A,B) ) ).
fof(redefinition_m5_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k21_glib_001(A))) )
=> ! [C] :
( m5_glib_001(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m6_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k22_glib_001(A))) )
=> ! [C] :
( m6_glib_001(C,A,B)
=> ( v4_glib_001(C,A)
& m3_glib_001(C,A) ) ) ) ).
fof(existence_m6_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k22_glib_001(A))) )
=> ? [C] : m6_glib_001(C,A,B) ) ).
fof(redefinition_m6_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k22_glib_001(A))) )
=> ! [C] :
( m6_glib_001(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m7_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k23_glib_001(A))) )
=> ! [C] :
( m7_glib_001(C,A,B)
=> ( v5_glib_001(C,A)
& m3_glib_001(C,A) ) ) ) ).
fof(existence_m7_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k23_glib_001(A))) )
=> ? [C] : m7_glib_001(C,A,B) ) ).
fof(redefinition_m7_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k23_glib_001(A))) )
=> ! [C] :
( m7_glib_001(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m8_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k24_glib_001(A))) )
=> ! [C] :
( m8_glib_001(C,A,B)
=> ( v2_glib_001(C,A)
& m3_glib_001(C,A) ) ) ) ).
fof(existence_m8_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k24_glib_001(A))) )
=> ? [C] : m8_glib_001(C,A,B) ) ).
fof(redefinition_m8_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k24_glib_001(A))) )
=> ! [C] :
( m8_glib_001(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m9_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k25_glib_001(A))) )
=> ! [C] :
( m9_glib_001(C,A,B)
=> ( v2_glib_001(C,A)
& v4_glib_001(C,A)
& m3_glib_001(C,A) ) ) ) ).
fof(existence_m9_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k25_glib_001(A))) )
=> ? [C] : m9_glib_001(C,A,B) ) ).
fof(redefinition_m9_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k25_glib_001(A))) )
=> ! [C] :
( m9_glib_001(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_m10_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k26_glib_001(A))) )
=> ! [C] :
( m10_glib_001(C,A,B)
=> ( v2_glib_001(C,A)
& v5_glib_001(C,A)
& m3_glib_001(C,A) ) ) ) ).
fof(existence_m10_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k26_glib_001(A))) )
=> ? [C] : m10_glib_001(C,A,B) ) ).
fof(redefinition_m10_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(k26_glib_001(A))) )
=> ! [C] :
( m10_glib_001(C,A,B)
<=> m1_subset_1(C,B) ) ) ).
fof(dt_k1_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m1_subset_1(B,k6_glib_000(A)) )
=> m3_glib_001(k1_glib_001(A,B),A) ) ).
fof(dt_k2_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> m3_glib_001(k2_glib_001(A,B,C,D),A) ) ).
fof(dt_k3_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> m1_subset_1(k3_glib_001(A,B),k6_glib_000(A)) ) ).
fof(dt_k4_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> m1_subset_1(k4_glib_001(A,B),k6_glib_000(A)) ) ).
fof(dt_k5_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers) )
=> m1_subset_1(k5_glib_001(A,B,C),k6_glib_000(A)) ) ).
fof(dt_k6_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> m3_glib_001(k6_glib_001(A,B),A) ) ).
fof(dt_k7_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A)
& m3_glib_001(C,A) )
=> m3_glib_001(k7_glib_001(A,B,C),A) ) ).
fof(dt_k8_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> m3_glib_001(k8_glib_001(A,B,C,D),A) ) ).
fof(dt_k9_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> m3_glib_001(k9_glib_001(A,B,C,D),A) ) ).
fof(dt_k10_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> m3_glib_001(k10_glib_001(A,B,C),A) ) ).
fof(dt_k11_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> m1_glib_001(k11_glib_001(A,B),A) ) ).
fof(dt_k12_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> m2_glib_001(k12_glib_001(A,B),A) ) ).
fof(dt_k13_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> ( v1_finset_1(k13_glib_001(A,B))
& m1_subset_1(k13_glib_001(A,B),k1_zfmisc_1(k6_glib_000(A))) ) ) ).
fof(dt_k14_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> ( v1_finset_1(k14_glib_001(A,B))
& m1_subset_1(k14_glib_001(A,B),k1_zfmisc_1(k7_glib_000(A))) ) ) ).
fof(dt_k15_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> m2_subset_1(k15_glib_001(A,B),k1_numbers,k5_numbers) ) ).
fof(dt_k16_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> ( ~ v1_abian(k16_glib_001(A,B,C))
& m2_subset_1(k16_glib_001(A,B,C),k1_numbers,k5_numbers) ) ) ).
fof(dt_k17_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers) )
=> ( ~ v1_abian(k17_glib_001(A,B,C))
& m2_subset_1(k17_glib_001(A,B,C),k1_numbers,k5_numbers) ) ) ).
fof(dt_k18_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A) )
=> ( ~ v1_abian(k18_glib_001(A,B,C))
& m2_subset_1(k18_glib_001(A,B,C),k1_numbers,k5_numbers) ) ) ).
fof(dt_k19_glib_001,axiom,
! [A,B,C] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers) )
=> ( ~ v1_abian(k19_glib_001(A,B,C))
& m2_subset_1(k19_glib_001(A,B,C),k1_numbers,k5_numbers) ) ) ).
fof(dt_k20_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> m4_glib_001(k20_glib_001(A,B,C,D),A,B) ) ).
fof(redefinition_k20_glib_001,axiom,
! [A,B,C,D] :
( ( v1_glib_000(A)
& m1_glib_000(A)
& m3_glib_001(B,A)
& m1_subset_1(C,k5_numbers)
& m1_subset_1(D,k5_numbers) )
=> k20_glib_001(A,B,C,D) = k9_glib_001(A,B,C,D) ) ).
fof(dt_k21_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ( ~ v1_xboole_0(k21_glib_001(A))
& m1_subset_1(k21_glib_001(A),k1_zfmisc_1(k3_finseq_2(k2_xboole_0(k6_glib_000(A),k7_glib_000(A))))) ) ) ).
fof(dt_k22_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ( ~ v1_xboole_0(k22_glib_001(A))
& m1_subset_1(k22_glib_001(A),k1_zfmisc_1(k21_glib_001(A))) ) ) ).
fof(dt_k23_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ( ~ v1_xboole_0(k23_glib_001(A))
& m1_subset_1(k23_glib_001(A),k1_zfmisc_1(k22_glib_001(A))) ) ) ).
fof(dt_k24_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ( ~ v1_xboole_0(k24_glib_001(A))
& m1_subset_1(k24_glib_001(A),k1_zfmisc_1(k21_glib_001(A))) ) ) ).
fof(dt_k25_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ( ~ v1_xboole_0(k25_glib_001(A))
& m1_subset_1(k25_glib_001(A),k1_zfmisc_1(k22_glib_001(A))) ) ) ).
fof(dt_k26_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> ( ~ v1_xboole_0(k26_glib_001(A))
& m1_subset_1(k26_glib_001(A),k1_zfmisc_1(k25_glib_001(A))) ) ) ).
fof(d33_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> k21_glib_001(A) = a_1_0_glib_001(A) ) ).
fof(d34_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> k22_glib_001(A) = a_1_1_glib_001(A) ) ).
fof(d35_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> k23_glib_001(A) = a_1_2_glib_001(A) ) ).
fof(d36_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> k24_glib_001(A) = a_1_3_glib_001(A) ) ).
fof(d37_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> k25_glib_001(A) = a_1_4_glib_001(A) ) ).
fof(d38_glib_001,axiom,
! [A] :
( ( v1_glib_000(A)
& m1_glib_000(A) )
=> k26_glib_001(A) = a_1_5_glib_001(A) ) ).
fof(fraenkel_a_1_0_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ( r2_hidden(A,a_1_0_glib_001(B))
<=> ? [C] :
( m3_glib_001(C,B)
& A = C ) ) ) ).
fof(fraenkel_a_1_1_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ( r2_hidden(A,a_1_1_glib_001(B))
<=> ? [C] :
( v4_glib_001(C,B)
& m3_glib_001(C,B)
& A = C ) ) ) ).
fof(fraenkel_a_1_2_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ( r2_hidden(A,a_1_2_glib_001(B))
<=> ? [C] :
( v5_glib_001(C,B)
& m3_glib_001(C,B)
& A = C ) ) ) ).
fof(fraenkel_a_1_3_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ( r2_hidden(A,a_1_3_glib_001(B))
<=> ? [C] :
( v2_glib_001(C,B)
& m3_glib_001(C,B)
& A = C ) ) ) ).
fof(fraenkel_a_1_4_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ( r2_hidden(A,a_1_4_glib_001(B))
<=> ? [C] :
( v2_glib_001(C,B)
& v4_glib_001(C,B)
& m3_glib_001(C,B)
& A = C ) ) ) ).
fof(fraenkel_a_1_5_glib_001,axiom,
! [A,B] :
( ( v1_glib_000(B)
& m1_glib_000(B) )
=> ( r2_hidden(A,a_1_5_glib_001(B))
<=> ? [C] :
( v2_glib_001(C,B)
& v5_glib_001(C,B)
& m3_glib_001(C,B)
& A = C ) ) ) ).
%------------------------------------------------------------------------------