SET007 Axioms: SET007+494.ax
%------------------------------------------------------------------------------
% File : SET007+494 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : The Equational Characterization of Continuous Lattices
% 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 : waybel_5 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 62 ( 2 unt; 0 def)
% Number of atoms : 675 ( 47 equ)
% Maximal formula atoms : 26 ( 10 avg)
% Number of connectives : 691 ( 78 ~; 0 |; 414 &)
% ( 11 <=>; 188 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 11 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 47 ( 46 usr; 0 prp; 1-4 aty)
% Number of functors : 42 ( 42 usr; 0 con; 1-6 aty)
% Number of variables : 241 ( 228 !; 13 ?)
% 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_waybel_5,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v2_relat_1(C)
& m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B))
& m1_subset_1(E,A) )
=> ~ v1_xboole_0(k2_relat_1(k1_waybel_5(A,B,C,D,E))) ) ).
fof(cc1_waybel_5,axiom,
! [A,B,C] :
( ( ~ v1_xboole_0(B)
& v2_relat_1(C)
& m1_pboole(C,A) )
=> ! [D] :
( m3_pboole(D,A,C,k2_pre_circ(A,B))
=> ( v2_relat_1(D)
& v1_funcop_1(D) ) ) ) ).
fof(fc2_waybel_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_relat_1(A)
& v1_funct_1(A) )
=> ( v1_relat_1(k2_funct_6(A))
& v2_relat_1(k2_funct_6(A))
& v1_funct_1(k2_funct_6(A)) ) ) ).
fof(fc3_waybel_5,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& ~ v3_struct_0(C)
& l1_orders_2(C)
& m3_pboole(D,A,B,k2_pre_circ(A,u1_struct_0(C))) )
=> ~ v1_xboole_0(k2_relat_1(k4_waybel_5(C,D))) ) ).
fof(fc4_waybel_5,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& m1_pboole(B,A)
& ~ v3_struct_0(C)
& l1_orders_2(C)
& m3_pboole(D,A,B,k2_pre_circ(A,u1_struct_0(C))) )
=> ~ v1_xboole_0(k2_relat_1(k5_waybel_5(C,D))) ) ).
fof(cc2_waybel_5,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_waybel_5(A) ) ) ) ).
fof(rc1_waybel_5,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel_5(A) ) ).
fof(cc3_waybel_5,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel_5(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A) ) ) ) ).
fof(cc4_waybel_5,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel_5(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v9_waybel_1(A) ) ) ) ).
fof(t1_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( ~ v1_xboole_0(k1_waybel_3(A,B))
& v1_waybel_0(k1_waybel_3(A,B),A)
& v12_waybel_0(k1_waybel_3(A,B),A)
& m1_subset_1(k1_waybel_3(A,B),k1_zfmisc_1(u1_struct_0(A)))
& r3_orders_2(A,B,k1_yellow_0(A,k1_waybel_3(A,B)))
& ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_orders_2(A,B,k1_yellow_0(A,C))
=> r1_tarski(k1_waybel_3(A,B),C) ) ) ) ) ) ) ).
fof(t2_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ? [C] :
( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& v12_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
& r3_orders_2(A,B,k1_yellow_0(A,C))
& ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& v12_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( r3_orders_2(A,B,k1_yellow_0(A,D))
=> r1_tarski(C,D) ) ) ) ) ) ) ).
fof(t3_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A)
& l1_orders_2(A) )
=> v4_waybel_1(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ).
fof(t4_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( v4_waybel_1(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
=> v3_waybel_3(A) ) ) ).
fof(t5_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ( v17_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A)
& v18_waybel_0(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) )
=> v4_waybel_1(k3_yellow_2(A),k2_yellow_1(k8_waybel_0(A)),A) ) ) ).
fof(t6_waybel_5,axiom,
! [A,B,C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,C,k2_pre_circ(A,B))
=> ! [E] :
( r2_hidden(E,A)
=> ( v1_funct_1(k1_funct_1(D,E))
& v1_funct_2(k1_funct_1(D,E),k1_funct_1(C,E),B)
& m2_relset_1(k1_funct_1(D,E),k1_funct_1(C,E),B) ) ) ) ) ).
fof(t7_waybel_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ! [B] :
( r2_hidden(B,k1_relat_1(k3_pralg_2(A)))
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ) ).
fof(t8_waybel_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(B,k1_relat_1(k3_pralg_2(A)))
=> ( k1_relat_1(B) = k1_relat_1(A)
& k1_relat_1(A) = k1_relat_1(k1_funct_1(k3_pralg_2(A),B)) ) ) ) ) ).
fof(t9_waybel_5,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_funcop_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( r2_hidden(B,k1_relat_1(k3_pralg_2(A)))
=> ! [C] :
( r2_hidden(C,k1_relat_1(A))
=> ( r2_hidden(k1_funct_1(B,C),k1_relat_1(k1_funct_1(A,C)))
& k1_funct_1(k1_funct_1(k3_pralg_2(A),B),C) = k1_funct_1(k1_funct_1(A,C),k1_funct_1(B,C))
& r2_hidden(k1_funct_1(k1_funct_1(A,C),k1_funct_1(B,C)),k2_relat_1(k1_funct_1(k3_pralg_2(A),B))) ) ) ) ) ) ).
fof(t10_waybel_5,axiom,
! [A,B,C] :
( m1_pboole(C,A)
=> ! [D] :
( m3_pboole(D,A,C,k2_pre_circ(A,B))
=> ! [E] :
( ( v1_relat_1(E)
& v1_funct_1(E) )
=> ( r2_hidden(E,k1_relat_1(k3_pralg_2(D)))
=> ( v1_funct_1(k1_funct_1(k3_pralg_2(D),E))
& v1_funct_2(k1_funct_1(k3_pralg_2(D),E),A,B)
& m2_relset_1(k1_funct_1(k3_pralg_2(D),E),A,B) ) ) ) ) ) ).
fof(d1_waybel_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_relat_1(B),u1_struct_0(A))
& m2_relset_1(C,k1_relat_1(B),u1_struct_0(A)) )
=> ( C = k4_waybel_5(A,B)
<=> ! [D] :
( r2_hidden(D,k1_relat_1(B))
=> k1_funct_1(C,D) = k5_yellow_2(A,k1_funct_1(B,D)) ) ) ) ) ) ).
fof(d2_waybel_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,k1_relat_1(B),u1_struct_0(A))
& m2_relset_1(C,k1_relat_1(B),u1_struct_0(A)) )
=> ( C = k5_waybel_5(A,B)
<=> ! [D] :
( r2_hidden(D,k1_relat_1(B))
=> k1_funct_1(C,D) = k6_yellow_2(A,k1_funct_1(B,D)) ) ) ) ) ) ).
fof(t11_waybel_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_funcop_1(C) )
=> ( ( k1_relat_1(B) = k1_relat_1(C)
& ! [D] :
( r2_hidden(D,k1_relat_1(B))
=> k5_yellow_2(A,k1_funct_1(B,D)) = k5_yellow_2(A,k1_funct_1(C,D)) ) )
=> k4_waybel_5(A,B) = k4_waybel_5(A,C) ) ) ) ) ).
fof(t12_waybel_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_funcop_1(C) )
=> ( ( k1_relat_1(B) = k1_relat_1(C)
& ! [D] :
( r2_hidden(D,k1_relat_1(B))
=> k6_yellow_2(A,k1_funct_1(B,D)) = k6_yellow_2(A,k1_funct_1(C,D)) ) )
=> k5_waybel_5(A,B) = k5_waybel_5(A,C) ) ) ) ) ).
fof(t13_waybel_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_funcop_1(C) )
=> ( ~ ( r2_hidden(A,k8_yellow_2(k1_relat_1(C),B,k4_waybel_5(B,C)))
& ! [D] :
~ ( r2_hidden(D,k1_relat_1(C))
& A = k5_yellow_2(B,k1_funct_1(C,D)) ) )
& ( ? [D] :
( r2_hidden(D,k1_relat_1(C))
& A = k5_yellow_2(B,k1_funct_1(C,D)) )
=> r2_hidden(A,k8_yellow_2(k1_relat_1(C),B,k4_waybel_5(B,C))) )
& ~ ( r2_hidden(A,k8_yellow_2(k1_relat_1(C),B,k5_waybel_5(B,C)))
& ! [D] :
~ ( r2_hidden(D,k1_relat_1(C))
& A = k6_yellow_2(B,k1_funct_1(C,D)) ) )
& ( ? [D] :
( r2_hidden(D,k1_relat_1(C))
& A = k6_yellow_2(B,k1_funct_1(C,D)) )
=> r2_hidden(A,k8_yellow_2(k1_relat_1(C),B,k5_waybel_5(B,C))) ) ) ) ) ).
fof(t14_waybel_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_pboole(D,C)
=> ! [E] :
( m3_pboole(E,C,D,k2_pre_circ(C,u1_struct_0(B)))
=> ( ~ ( r2_hidden(A,k8_yellow_2(k1_relat_1(E),B,k4_waybel_5(B,E)))
& ! [F] :
( m1_subset_1(F,C)
=> A != k5_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) ) )
& ( ? [F] :
( m1_subset_1(F,C)
& A = k5_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) )
=> r2_hidden(A,k8_yellow_2(k1_relat_1(E),B,k4_waybel_5(B,E))) )
& ~ ( r2_hidden(A,k8_yellow_2(k1_relat_1(E),B,k5_waybel_5(B,E)))
& ! [F] :
( m1_subset_1(F,C)
=> A != k6_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) ) )
& ( ? [F] :
( m1_subset_1(F,C)
& A = k6_yellow_2(B,k1_waybel_5(C,u1_struct_0(B),D,E,F)) )
=> r2_hidden(A,k8_yellow_2(k1_relat_1(E),B,k5_waybel_5(B,E))) ) ) ) ) ) ) ).
fof(t15_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C)
& v1_funcop_1(C) )
=> ( ! [D] :
( ( v1_relat_1(D)
& v1_funct_1(D) )
=> ( r2_hidden(D,k1_relat_1(k3_pralg_2(C)))
=> r3_orders_2(A,k6_yellow_2(A,k1_funct_1(k3_pralg_2(C),D)),B) ) )
=> r3_orders_2(A,k5_yellow_2(A,k5_waybel_5(A,k3_pralg_2(C))),B) ) ) ) ) ).
fof(t16_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,B) )
=> ! [D] :
( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
=> r1_orders_2(A,k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))),k6_yellow_2(A,k4_waybel_5(A,D))) ) ) ) ) ).
fof(t17_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( v3_waybel_3(A)
& ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( r1_waybel_3(A,D,B)
=> r3_orders_2(A,D,C) ) ) )
=> r3_orders_2(A,B,C) ) ) ) ) ).
fof(t18_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( ! [B] :
( ~ v1_xboole_0(B)
=> ( r2_hidden(B,k2_yellow_6(u1_struct_0(A)))
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,B) )
=> ( ! [D] :
( m1_subset_1(D,B)
=> r2_hidden(k1_funct_1(C,D),k2_yellow_6(u1_struct_0(A))) )
=> ! [D] :
( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
=> ( ! [E] :
( m1_subset_1(E,B)
=> v1_waybel_0(k8_yellow_2(k1_funct_1(C,E),A,k1_waybel_5(B,u1_struct_0(A),C,D,E)),A) )
=> k6_yellow_2(A,k4_waybel_5(A,D)) = k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) )
=> v3_waybel_3(A) ) ) ).
fof(t19_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,B) )
=> ! [D] :
( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
=> ( ! [E] :
( m1_subset_1(E,B)
=> v1_waybel_0(k8_yellow_2(k1_funct_1(C,E),A,k1_waybel_5(B,u1_struct_0(A),C,D,E)),A) )
=> k6_yellow_2(A,k4_waybel_5(A,D)) = k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) ) ).
fof(t20_waybel_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_subset_1(D,A)
=> ! [E] :
( m1_subset_1(E,B)
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,k2_zfmisc_1(A,B),C)
& m2_relset_1(F,k2_zfmisc_1(A,B),C) )
=> ( k1_relat_1(k6_waybel_5(A,B,C,F)) = A
& k1_relat_1(k1_waybel_5(A,C,k2_pre_circ(A,B),k6_waybel_5(A,B,C,F),D)) = B
& k1_funct_1(F,k4_tarski(D,E)) = k1_funct_1(k1_waybel_5(A,C,k2_pre_circ(A,B),k6_waybel_5(A,B,C,F),D),E) ) ) ) ) ) ) ) ).
fof(t21_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,C),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(B,C),u1_struct_0(A)) )
=> ( ! [E] :
( m1_subset_1(E,B)
=> v1_waybel_0(k8_yellow_2(k1_funct_1(k2_pre_circ(B,C),E),A,k1_waybel_5(B,u1_struct_0(A),k2_pre_circ(B,C),k6_waybel_5(B,C,u1_struct_0(A),D),E)),A) )
=> k6_yellow_2(A,k4_waybel_5(A,k6_waybel_5(B,C,u1_struct_0(A),D))) = k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),k2_pre_circ(B,C),k6_waybel_5(B,C,u1_struct_0(A),D)))) ) ) ) ) ) ) ).
fof(d3_waybel_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v1_waybel_5(A)
<=> ( v3_lattice3(A)
& ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,B) )
=> ! [D] :
( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
=> k6_yellow_2(A,k4_waybel_5(A,D)) = k5_yellow_2(A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) ) ).
fof(t24_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel_5(A)
& l1_orders_2(A) )
=> v3_waybel_3(A) ) ).
fof(t27_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ( v2_relat_1(C)
& m1_pboole(C,B) )
=> ! [D] :
( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
=> ( ! [E] :
( m1_subset_1(E,B)
=> v1_waybel_0(k8_yellow_2(k1_funct_1(C,E),A,k1_waybel_5(B,u1_struct_0(A),C,D,E)),A) )
=> v1_waybel_0(k8_yellow_2(k1_relat_1(k2_waybel_5(B,u1_struct_0(A),C,D)),A,k5_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))),A) ) ) ) ) ) ).
fof(t28_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) ) ) ) ) ).
fof(t29_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) ) ) ) ) ).
fof(t30_waybel_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,B,C)
& m2_relset_1(D,B,C) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,C,B)
& m2_relset_1(E,C,B) )
=> ( k1_partfun1(B,C,C,B,D,E) = k6_partfun1(B)
=> k13_pboole(k8_waybel_5(B,C,A,D),k8_waybel_5(C,B,A,E)) = k2_msualg_3(A,k2_pre_circ(A,B)) ) ) ) ) ).
fof(t31_waybel_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C,D] :
( m1_pboole(D,A)
=> ! [E] :
( m3_pboole(E,A,D,k2_pre_circ(A,B))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,C)
& m2_relset_1(F,B,C) )
=> m3_pboole(k13_pboole(E,k8_waybel_5(B,C,A,F)),A,D,k2_pre_circ(A,C)) ) ) ) ) ) ).
fof(t32_waybel_5,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( m1_pboole(D,A)
=> ! [E] :
( m3_pboole(E,A,D,k2_pre_circ(A,B))
=> ! [F] :
( ( v1_funct_1(F)
& v1_funct_2(F,B,C)
& m2_relset_1(F,B,C) )
=> k2_funct_6(k3_msualg_3(A,D,k2_pre_circ(A,B),k2_pre_circ(A,C),E,k8_waybel_5(B,C,A,F))) = k2_funct_6(E) ) ) ) ) ) ) ).
fof(t33_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& l1_orders_2(B) )
=> ( ? [C] :
( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& v22_waybel_0(C,A,B)
& v2_funct_2(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_waybel_3(B)
& l1_orders_2(B) ) ) ) ) ) ).
fof(dt_k1_waybel_5,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B))
& m1_subset_1(E,A) )
=> ( v1_funct_1(k1_waybel_5(A,B,C,D,E))
& v1_funct_2(k1_waybel_5(A,B,C,D,E),k1_funct_1(C,E),B)
& m2_relset_1(k1_waybel_5(A,B,C,D,E),k1_funct_1(C,E),B) ) ) ).
fof(redefinition_k1_waybel_5,axiom,
! [A,B,C,D,E] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B))
& m1_subset_1(E,A) )
=> k1_waybel_5(A,B,C,D,E) = k1_funct_1(D,E) ) ).
fof(dt_k2_waybel_5,axiom,
! [A,B,C,D] :
( ( m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B)) )
=> m3_pboole(k2_waybel_5(A,B,C,D),k4_card_3(k2_funct_6(D)),k2_pre_circ(k4_card_3(k2_funct_6(D)),A),k2_pre_circ(k4_card_3(k2_funct_6(D)),B)) ) ).
fof(redefinition_k2_waybel_5,axiom,
! [A,B,C,D] :
( ( m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B)) )
=> k2_waybel_5(A,B,C,D) = k7_funct_6(D) ) ).
fof(dt_k3_waybel_5,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v2_relat_1(C)
& m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B))
& m3_pboole(E,k4_card_3(k2_funct_6(D)),k2_pre_circ(k4_card_3(k2_funct_6(D)),A),k2_pre_circ(k4_card_3(k2_funct_6(D)),B))
& m1_subset_1(F,k4_card_3(k2_funct_6(D))) )
=> ( v1_funct_1(k3_waybel_5(A,B,C,D,E,F))
& v1_funct_2(k3_waybel_5(A,B,C,D,E,F),A,B)
& m2_relset_1(k3_waybel_5(A,B,C,D,E,F),A,B) ) ) ).
fof(redefinition_k3_waybel_5,axiom,
! [A,B,C,D,E,F] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v2_relat_1(C)
& m1_pboole(C,A)
& m3_pboole(D,A,C,k2_pre_circ(A,B))
& m3_pboole(E,k4_card_3(k2_funct_6(D)),k2_pre_circ(k4_card_3(k2_funct_6(D)),A),k2_pre_circ(k4_card_3(k2_funct_6(D)),B))
& m1_subset_1(F,k4_card_3(k2_funct_6(D))) )
=> k3_waybel_5(A,B,C,D,E,F) = k1_funct_1(E,F) ) ).
fof(dt_k4_waybel_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ( v1_funct_1(k4_waybel_5(A,B))
& v1_funct_2(k4_waybel_5(A,B),k1_relat_1(B),u1_struct_0(A))
& m2_relset_1(k4_waybel_5(A,B),k1_relat_1(B),u1_struct_0(A)) ) ) ).
fof(dt_k5_waybel_5,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& v1_relat_1(B)
& v1_funct_1(B)
& v1_funcop_1(B) )
=> ( v1_funct_1(k5_waybel_5(A,B))
& v1_funct_2(k5_waybel_5(A,B),k1_relat_1(B),u1_struct_0(A))
& m2_relset_1(k5_waybel_5(A,B),k1_relat_1(B),u1_struct_0(A)) ) ) ).
fof(dt_k6_waybel_5,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C) )
=> m3_pboole(k6_waybel_5(A,B,C,D),A,k2_pre_circ(A,B),k2_pre_circ(A,C)) ) ).
fof(redefinition_k6_waybel_5,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& ~ v1_xboole_0(C)
& v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(A,B),C)
& m1_relset_1(D,k2_zfmisc_1(A,B),C) )
=> k6_waybel_5(A,B,C,D) = k3_funct_5(D) ) ).
fof(dt_k7_waybel_5,axiom,
! [A,B] : m1_pboole(k7_waybel_5(A,B),A) ).
fof(redefinition_k7_waybel_5,axiom,
! [A,B] : k7_waybel_5(A,B) = k2_funcop_1(A,B) ).
fof(dt_k8_waybel_5,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m1_relset_1(D,A,B) )
=> m3_pboole(k8_waybel_5(A,B,C,D),C,k2_pre_circ(C,A),k2_pre_circ(C,B)) ) ).
fof(redefinition_k8_waybel_5,axiom,
! [A,B,C,D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,B)
& m1_relset_1(D,A,B) )
=> k8_waybel_5(A,B,C,D) = k2_funcop_1(C,D) ) ).
fof(t22_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,C),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(B,C),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( E = a_4_0_waybel_5(A,B,C,D)
=> r1_orders_2(A,k1_yellow_0(A,E),k6_yellow_2(A,k4_waybel_5(A,k6_waybel_5(B,C,u1_struct_0(A),D)))) ) ) ) ) ) ) ).
fof(t23_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ( v3_waybel_3(A)
<=> ! [B] :
( ~ v1_xboole_0(B)
=> ! [C] :
( ~ v1_xboole_0(C)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,k2_zfmisc_1(B,C),u1_struct_0(A))
& m2_relset_1(D,k2_zfmisc_1(B,C),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
=> ( E = a_4_0_waybel_5(A,B,C,D)
=> k6_yellow_2(A,k4_waybel_5(A,k6_waybel_5(B,C,u1_struct_0(A),D))) = k1_yellow_0(A,E) ) ) ) ) ) ) ) ).
fof(t25_waybel_5,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( r1_yellow_0(A,C)
& r1_yellow_0(A,D)
& D = a_3_0_waybel_5(A,B,C) )
=> r1_orders_2(A,k1_yellow_0(A,D),k12_lattice3(A,B,k1_yellow_0(A,C))) ) ) ) ) ) ).
fof(t26_waybel_5,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_waybel_5(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k12_lattice3(A,C,k1_yellow_0(A,B)) = k1_yellow_0(A,a_3_1_waybel_5(A,B,C)) ) ) ) ).
fof(fraenkel_a_4_0_waybel_5,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& ~ v1_xboole_0(C)
& ~ v1_xboole_0(D)
& v1_funct_1(E)
& v1_funct_2(E,k2_zfmisc_1(C,D),u1_struct_0(B))
& m2_relset_1(E,k2_zfmisc_1(C,D),u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_0_waybel_5(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = F
& ? [G] :
( v2_relat_1(G)
& m1_pboole(G,C)
& r2_hidden(G,k1_funct_2(C,k5_finsub_1(D)))
& ? [H] :
( m3_pboole(H,C,G,k2_pre_circ(C,u1_struct_0(B)))
& ! [I] :
( m1_subset_1(I,C)
=> ! [J] :
( r2_hidden(J,k1_funct_1(G,I))
=> k1_funct_1(k1_waybel_5(C,u1_struct_0(B),G,H,I),J) = k1_funct_1(E,k4_tarski(I,J)) ) )
& F = k6_yellow_2(B,k4_waybel_5(B,H)) ) ) ) ) ) ).
fof(fraenkel_a_3_0_waybel_5,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B))
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_3_0_waybel_5(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k12_lattice3(B,C,E)
& r2_hidden(E,D) ) ) ) ).
fof(fraenkel_a_3_1_waybel_5,axiom,
! [A,B,C,D] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_waybel_5(B)
& l1_orders_2(B)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(D,u1_struct_0(B)) )
=> ( r2_hidden(A,a_3_1_waybel_5(B,C,D))
<=> ? [E] :
( m1_subset_1(E,u1_struct_0(B))
& A = k12_lattice3(B,D,E)
& r2_hidden(E,C) ) ) ) ).
%------------------------------------------------------------------------------