SET007 Axioms: SET007+611.ax
%------------------------------------------------------------------------------
% File : SET007+611 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Scott-Continuous Functions. Part II
% 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 : waybel24 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 83 ( 0 unt; 0 def)
% Number of atoms : 1249 ( 55 equ)
% Maximal formula atoms : 33 ( 15 avg)
% Number of connectives : 1291 ( 125 ~; 0 |; 921 &)
% ( 25 <=>; 220 =>; 0 <=; 0 <~>)
% Maximal formula depth : 29 ( 13 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 54 ( 53 usr; 0 prp; 1-3 aty)
% Number of functors : 71 ( 71 usr; 19 con; 0-5 aty)
% Number of variables : 311 ( 290 !; 21 ?)
% 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(cc1_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
=> ( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_seqm_3(C) )
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(fc1_waybel24,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k3_borsuk_1(A,B,C))
& v1_relat_1(k3_borsuk_1(A,B,C))
& v1_funct_1(k3_borsuk_1(A,B,C))
& v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(k3_borsuk_1(A,B,C),A,B)
& v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(rc1_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& ~ v1_xboole_0(C)
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& v5_waybel_0(C,A,B) ) ) ).
fof(fc2_waybel24,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v2_orders_2(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& v5_orders_3(D,k3_yellow_3(A,B),C)
& m1_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k1_waybel24(A,B,C,D,E))
& v1_relat_1(k1_waybel24(A,B,C,D,E))
& v1_funct_1(k1_waybel24(A,B,C,D,E))
& v1_funct_2(k1_waybel24(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C))
& v5_orders_3(k1_waybel24(A,B,C,D,E),B,C)
& v1_partfun1(k1_waybel24(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C)) ) ) ).
fof(fc3_waybel24,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v2_orders_2(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& v5_orders_3(D,k3_yellow_3(A,B),C)
& m1_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k2_waybel24(A,B,C,D,E))
& v1_relat_1(k2_waybel24(A,B,C,D,E))
& v1_funct_1(k2_waybel24(A,B,C,D,E))
& v1_funct_2(k2_waybel24(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C))
& v5_orders_3(k2_waybel24(A,B,C,D,E),A,C)
& v1_partfun1(k2_waybel24(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ).
fof(fc4_waybel24,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v2_orders_2(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& v5_waybel_0(D,k3_yellow_3(A,B),C)
& m1_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( ~ v1_xboole_0(k1_waybel24(A,B,C,D,E))
& v1_relat_1(k1_waybel24(A,B,C,D,E))
& v1_funct_1(k1_waybel24(A,B,C,D,E))
& v1_funct_2(k1_waybel24(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C))
& v1_partfun1(k1_waybel24(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C))
& v5_waybel_0(k1_waybel24(A,B,C,D,E),B,C) ) ) ).
fof(fc5_waybel24,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& v2_orders_2(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& v5_waybel_0(D,k3_yellow_3(A,B),C)
& m1_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k2_waybel24(A,B,C,D,E))
& v1_relat_1(k2_waybel24(A,B,C,D,E))
& v1_funct_1(k2_waybel24(A,B,C,D,E))
& v1_funct_2(k2_waybel24(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C))
& v1_partfun1(k2_waybel24(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C))
& v5_waybel_0(k2_waybel24(A,B,C,D,E),A,C) ) ) ).
fof(fc6_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k3_waybel24(A,B))
& v1_orders_2(k3_waybel24(A,B)) ) ) ).
fof(fc7_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k3_waybel24(A,B))
& v1_orders_2(k3_waybel24(A,B))
& v1_monoid_0(k3_waybel24(A,B)) ) ) ).
fof(fc8_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k3_waybel24(A,B))
& v1_orders_2(k3_waybel24(A,B))
& v2_orders_2(k3_waybel24(A,B))
& ~ v1_yellow_3(k3_waybel24(A,B))
& v1_monoid_0(k3_waybel24(A,B)) ) ) ).
fof(fc9_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v3_orders_2(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k3_waybel24(A,B))
& v1_orders_2(k3_waybel24(A,B))
& v3_orders_2(k3_waybel24(A,B))
& v1_monoid_0(k3_waybel24(A,B)) ) ) ).
fof(fc10_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A)
& ~ v3_struct_0(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k3_waybel24(A,B))
& v1_orders_2(k3_waybel24(A,B))
& v4_orders_2(k3_waybel24(A,B))
& v1_monoid_0(k3_waybel24(A,B)) ) ) ).
fof(fc11_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k6_yellow_1(A,B))
& v1_orders_2(k6_yellow_1(A,B))
& v1_monoid_0(k6_yellow_1(A,B)) ) ) ).
fof(fc12_waybel24,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& 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)
& m1_subset_1(C,u1_struct_0(B)) )
=> ( ~ v1_xboole_0(k3_borsuk_1(A,B,C))
& v1_relat_1(k3_borsuk_1(A,B,C))
& v1_funct_1(k3_borsuk_1(A,B,C))
& v1_funct_2(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(k3_borsuk_1(A,B,C),A,B)
& v1_partfun1(k3_borsuk_1(A,B,C),u1_struct_0(A),u1_struct_0(B))
& v22_waybel_0(k3_borsuk_1(A,B,C),A,B) ) ) ).
fof(fc13_waybel24,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ( ~ v3_struct_0(k3_waybel24(A,B))
& v1_orders_2(k3_waybel24(A,B))
& v2_orders_2(k3_waybel24(A,B))
& v3_orders_2(k3_waybel24(A,B))
& v4_orders_2(k3_waybel24(A,B))
& v1_yellow_0(k3_waybel24(A,B))
& v2_yellow_0(k3_waybel24(A,B))
& v3_yellow_0(k3_waybel24(A,B))
& v24_waybel_0(k3_waybel24(A,B))
& v25_waybel_0(k3_waybel24(A,B))
& ~ v1_yellow_3(k3_waybel24(A,B))
& v1_lattice3(k3_waybel24(A,B))
& v2_lattice3(k3_waybel24(A,B))
& v3_lattice3(k3_waybel24(A,B))
& v1_monoid_0(k3_waybel24(A,B)) ) ) ).
fof(t1_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v24_waybel_0(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k2_waybel17(A,B))))
=> ( v1_funct_1(k1_yellow_0(k2_waybel17(A,B),C))
& v1_funct_2(k1_yellow_0(k2_waybel17(A,B),C),u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(k1_yellow_0(k2_waybel17(A,B),C),A,B)
& m2_relset_1(k1_yellow_0(k2_waybel17(A,B),C),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(t2_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> k3_yellow_0(k7_yellow_1(A,B)) = k3_borsuk_1(A,B,k3_yellow_0(B)) ) ) ).
fof(t3_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& l1_orders_2(B) )
=> k4_yellow_0(k7_yellow_1(A,B)) = k3_borsuk_1(A,B,k4_yellow_0(B)) ) ) ).
fof(t4_waybel24,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] :
( ( 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) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,k4_pre_topc(A,B,C,k6_waybel_0(A,D))) ) ) ) ) ).
fof(t6_waybel24,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_yellow_1(u1_struct_0(A),B))))
=> ( v1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C))
& v1_funct_2(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(d1_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k1_waybel24(A,B,C,D,E) = k1_funct_1(k3_funct_5(D),E) ) ) ) ) ) ).
fof(t7_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(B,C)),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(B,C)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k7_yellow_2(u1_struct_0(C),A,k1_waybel24(B,C,A,D,E),F) = k7_yellow_2(u1_struct_0(k3_yellow_3(B,C)),A,D,k7_yellow_3(B,C,E,F)) ) ) ) ) ) ) ).
fof(d2_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k2_waybel24(A,B,C,D,E) = k1_funct_1(k5_funct_5(D),E) ) ) ) ) ) ).
fof(t8_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(C,B)),u1_struct_0(A))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(C,B)),u1_struct_0(A)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(C))
=> k7_yellow_2(u1_struct_0(C),A,k2_waybel24(C,B,A,D,E),F) = k7_yellow_2(u1_struct_0(k3_yellow_3(C,B)),A,D,k7_yellow_3(C,B,F,E)) ) ) ) ) ) ) ).
fof(t9_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> k7_yellow_2(u1_struct_0(B),C,k1_waybel24(A,B,C,D,E),F) = k7_yellow_2(u1_struct_0(A),C,k2_waybel24(A,B,C,D,F),E) ) ) ) ) ) ) ).
fof(t10_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( v5_orders_3(D,k3_yellow_3(A,B),C)
=> ( v5_orders_3(k1_waybel24(A,B,C,D,E),B,C)
& v5_orders_3(k2_waybel24(A,B,C,D,F),A,C) ) ) ) ) ) ) ) ) ).
fof(t11_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_orders_2(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( v5_waybel_0(D,k3_yellow_3(A,B),C)
=> ( v5_waybel_0(k1_waybel24(A,B,C,D,E),B,C)
& v5_waybel_0(k2_waybel24(A,B,C,D,F),A,C) ) ) ) ) ) ) ) ) ).
fof(t12_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( v5_orders_3(k1_waybel24(A,B,C,D,E),B,C)
& v5_orders_3(k2_waybel24(A,B,C,D,F),A,C) ) ) )
=> v5_orders_3(D,k3_yellow_3(A,B),C) ) ) ) ) ) ).
fof(t13_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( v5_waybel_0(k1_waybel24(A,B,C,D,E),B,C)
& v5_waybel_0(k2_waybel24(A,B,C,D,F),A,C) ) ) )
=> v5_waybel_0(D,k3_yellow_3(A,B),C) ) ) ) ) ) ).
fof(t14_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(A)))
=> k4_pre_topc(A,C,k2_waybel24(A,B,C,D,E),F) = k4_pre_topc(k3_yellow_3(A,B),C,D,k6_yellow_3(A,B,F,k1_struct_0(B,E))) ) ) ) ) ) ) ).
fof(t15_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,k1_zfmisc_1(u1_struct_0(B)))
=> k4_pre_topc(B,C,k1_waybel24(A,B,C,D,E),F) = k4_pre_topc(k3_yellow_3(A,B),C,D,k6_yellow_3(A,B,k1_struct_0(A,E),F)) ) ) ) ) ) ) ).
fof(t16_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( v22_waybel_0(D,k3_yellow_3(A,B),C)
=> ( v22_waybel_0(k1_waybel24(A,B,C,D,E),B,C)
& v22_waybel_0(k2_waybel24(A,B,C,D,F),A,C) ) ) ) ) ) ) ) ) ).
fof(t17_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& v5_orders_3(D,k3_yellow_3(A,B),C)
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ! [G] :
( ( v1_waybel_0(G,k3_yellow_3(A,B))
& m1_subset_1(G,k1_zfmisc_1(u1_struct_0(k3_yellow_3(A,B)))) )
=> ( ( r1_yellow_0(C,k4_pre_topc(k3_yellow_3(A,B),C,D,G))
& r2_hidden(E,k4_yellow_3(A,B,G))
& r2_hidden(F,k5_yellow_3(A,B,G)) )
=> r3_orders_2(C,k7_yellow_2(u1_struct_0(k3_yellow_3(A,B)),C,D,k7_yellow_3(A,B,E,F)),k1_yellow_0(C,k4_pre_topc(k3_yellow_3(A,B),C,D,G))) ) ) ) ) ) ) ) ) ).
fof(t18_waybel24,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] :
( ( 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) )
=> ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m2_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C)) )
=> ( ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( v22_waybel_0(k1_waybel24(A,B,C,D,E),B,C)
& v22_waybel_0(k2_waybel24(A,B,C,D,F),A,C) ) ) )
=> v22_waybel_0(D,k3_yellow_3(A,B),C) ) ) ) ) ) ).
fof(t19_waybel24,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_yellow_1(A,B)))
<=> ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) ) ) ) ).
fof(d3_waybel24,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( v1_orders_2(C)
& l1_orders_2(C) )
=> ( C = k3_waybel24(A,B)
<=> ( v4_yellow_0(C,k6_yellow_1(u1_struct_0(A),B))
& m1_yellow_0(C,k6_yellow_1(u1_struct_0(A),B))
& ! [D] :
( r2_hidden(D,u1_struct_0(C))
<=> ? [E] :
( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B))
& D = E
& v5_pre_topc(E,A,B) ) ) ) ) ) ) ) ).
fof(t20_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k3_waybel24(A,B)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel24(A,B)))
=> ( r1_orders_2(k3_waybel24(A,B),C,D)
<=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> r2_hidden(k4_tarski(k1_funct_1(C,E),k1_funct_1(D,E)),u1_orders_2(B)) ) ) ) ) ) ) ).
fof(t21_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v2_pre_topc(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
<=> m1_subset_1(C,u1_struct_0(k3_waybel24(A,B))) ) ) ) ).
fof(t22_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [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) )
=> ! [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)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( E = k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),k2_tarski(C,D))
=> k7_yellow_2(u1_struct_0(A),B,E,F) = k1_yellow_0(B,k2_struct_0(B,k7_yellow_2(u1_struct_0(A),B,C,F),k7_yellow_2(u1_struct_0(A),B,D,F))) ) ) ) ) ) ) ) ).
fof(t23_waybel24,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ! [B] :
( ( v1_yellow_1(B)
& v4_waybel_3(B)
& v5_waybel_3(B)
& m1_pboole(B,A) )
=> ( ! [C] :
( m1_subset_1(C,A)
=> ( v2_orders_2(k6_waybel_3(A,B,C))
& v3_orders_2(k6_waybel_3(A,B,C))
& v4_orders_2(k6_waybel_3(A,B,C))
& v1_lattice3(k6_waybel_3(A,B,C))
& v2_lattice3(k6_waybel_3(A,B,C))
& v3_lattice3(k6_waybel_3(A,B,C))
& l1_orders_2(k6_waybel_3(A,B,C)) ) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k5_yellow_1(A,B))))
=> ! [D] :
( m1_subset_1(D,A)
=> k7_waybel_3(A,B,k2_yellow_0(k5_yellow_1(A,B),C),D) = k2_yellow_0(k3_waybel_3(A,B,D),k5_waybel_3(A,B,D,C)) ) ) ) ) ) ).
fof(t24_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ! [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) )
=> ! [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)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> ( E = k2_yellow_0(k6_yellow_1(u1_struct_0(A),B),k2_tarski(C,D))
=> k7_yellow_2(u1_struct_0(A),B,E,F) = k2_yellow_0(B,k2_struct_0(B,k7_yellow_2(u1_struct_0(A),B,C,F),k7_yellow_2(u1_struct_0(A),B,D,F))) ) ) ) ) ) ) ) ).
fof(t29_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) )
=> ( v1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C))
& v1_funct_2(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),A,B)
& m2_relset_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(t31_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_yellow_0(B,k9_relat_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),D)) = k1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),k1_yellow_0(A,D)) ) ) ) ) ).
fof(t32_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) )
=> r2_hidden(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),u1_struct_0(k3_waybel24(A,B))) ) ) ) ).
fof(t33_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> k3_yellow_0(k6_yellow_1(u1_struct_0(A),B)) = k3_borsuk_1(A,B,k3_yellow_0(B)) ) ) ).
fof(t34_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& l1_orders_2(B) )
=> k4_yellow_0(k6_yellow_1(u1_struct_0(A),B)) = k3_borsuk_1(A,B,k4_yellow_0(B)) ) ) ).
fof(t35_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ( v8_yellow_0(k3_waybel24(A,B),k6_yellow_1(u1_struct_0(A),B))
& m1_yellow_0(k3_waybel24(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) ) ).
fof(t36_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> k3_yellow_0(k3_waybel24(A,B)) = k3_borsuk_1(A,B,k3_yellow_0(B)) ) ) ).
fof(t37_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> k4_yellow_0(k3_waybel24(A,B)) = k3_borsuk_1(A,B,k4_yellow_0(B)) ) ) ).
fof(t38_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> k2_waybel17(A,B) = k3_waybel24(A,B) ) ) ).
fof(dt_k1_waybel24,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m1_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(A)) )
=> ( v1_funct_1(k1_waybel24(A,B,C,D,E))
& v1_funct_2(k1_waybel24(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C))
& m2_relset_1(k1_waybel24(A,B,C,D,E),u1_struct_0(B),u1_struct_0(C)) ) ) ).
fof(dt_k2_waybel24,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& ~ v3_struct_0(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m1_relset_1(D,u1_struct_0(k3_yellow_3(A,B)),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( v1_funct_1(k2_waybel24(A,B,C,D,E))
& v1_funct_2(k2_waybel24(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C))
& m2_relset_1(k2_waybel24(A,B,C,D,E),u1_struct_0(A),u1_struct_0(C)) ) ) ).
fof(dt_k3_waybel24,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& ~ v3_struct_0(B)
& l1_waybel_9(B) )
=> ( v1_orders_2(k3_waybel24(A,B))
& l1_orders_2(k3_waybel24(A,B)) ) ) ).
fof(t5_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),B,C,D) = k1_yellow_0(B,a_4_0_waybel24(A,B,C,D)) ) ) ) ) ).
fof(t25_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_yellow_1(u1_struct_0(A),B)))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),D) = k1_yellow_0(B,a_4_1_waybel24(A,B,C,D)) ) ) ) ) ).
fof(t26_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_funct_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),D) = k1_yellow_0(B,a_4_2_waybel24(A,B,C,D)) ) ) ) ) ).
fof(t27_waybel24,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [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) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k6_yellow_1(u1_struct_0(A),B)))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> k9_relat_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),D) = a_4_3_waybel24(A,B,C,D) ) ) ) ) ).
fof(t28_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> k9_relat_1(k1_yellow_0(k6_yellow_1(u1_struct_0(A),B),C),D) = a_4_4_waybel24(A,B,C,D) ) ) ) ) ).
fof(t30_waybel24,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_pre_topc(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B) )
=> ! [C] :
( ( ~ v1_xboole_0(C)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k3_waybel24(A,B)))) )
=> ! [D] :
( ( ~ v1_xboole_0(D)
& v1_waybel_0(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> k1_yellow_0(B,a_4_6_waybel24(A,B,C,D)) = k1_yellow_0(B,a_4_8_waybel24(A,B,C,D)) ) ) ) ) ).
fof(s1_waybel24,axiom,
( r1_tarski(u1_struct_0(f2_s1_waybel24),k1_relat_1(f4_s1_waybel24))
=> k9_relat_1(f4_s1_waybel24,a_0_0_waybel24) = a_0_1_waybel24 ) ).
fof(s2_waybel24,axiom,
( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s2_waybel24))
=> ( p1_s2_waybel24(A)
<=> p2_s2_waybel24(A) ) )
=> a_0_2_waybel24 = a_0_3_waybel24 ) ).
fof(s3_waybel24,axiom,
( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s3_waybel24))
=> ( p1_s3_waybel24(A)
=> f2_s3_waybel24(A) = f3_s3_waybel24(A) ) )
=> a_0_4_waybel24 = a_0_5_waybel24 ) ).
fof(s4_waybel24,axiom,
( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s4_waybel24))
=> ( p1_s4_waybel24(A)
=> f2_s4_waybel24(A) = f3_s4_waybel24(A) ) )
=> a_0_6_waybel24 = a_0_7_waybel24 ) ).
fof(s5_waybel24,axiom,
( r1_tarski(u1_struct_0(f2_s5_waybel24),k1_relat_1(f4_s5_waybel24))
=> k9_relat_1(f4_s5_waybel24,a_0_8_waybel24) = a_0_9_waybel24 ) ).
fof(fraenkel_a_4_0_waybel24,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_orders_2(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_yellow_0(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C)
& v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(B),u1_struct_0(C))
& v5_orders_3(D,B,C)
& m2_relset_1(D,u1_struct_0(B),u1_struct_0(C))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_0_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k7_yellow_2(u1_struct_0(B),C,D,F)
& r3_orders_2(B,F,E) ) ) ) ).
fof(fraenkel_a_4_1_waybel24,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_yellow_1(u1_struct_0(B),C))))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_1_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k6_yellow_1(u1_struct_0(B),C)))
& A = k1_funct_1(F,E)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_4_2_waybel24,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v2_pre_topc(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_waybel24(B,C))))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_2_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k6_yellow_1(u1_struct_0(B),C)))
& A = k1_funct_1(F,E)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_4_3_waybel24,axiom,
! [A,B,C,D,E] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_orders_2(C)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k6_yellow_1(u1_struct_0(B),C))))
& ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_4_3_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k1_yellow_0(C,a_4_1_waybel24(B,C,D,F))
& r2_hidden(F,E) ) ) ) ).
fof(fraenkel_a_4_4_waybel24,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v2_pre_topc(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_waybel24(B,C))))
& ~ v1_xboole_0(E)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_4_4_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k1_yellow_0(C,a_4_5_waybel24(B,C,D,F))
& r2_hidden(F,E) ) ) ) ).
fof(fraenkel_a_4_5_waybel24,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v2_pre_topc(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_waybel24(B,C))))
& m1_subset_1(E,u1_struct_0(B)) )
=> ( r2_hidden(A,a_4_5_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k6_yellow_1(u1_struct_0(B),C)))
& A = k1_funct_1(F,E)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_4_6_waybel24,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v2_pre_topc(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_waybel24(B,C))))
& ~ v1_xboole_0(E)
& v1_waybel_0(E,B)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_4_6_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(k6_yellow_1(u1_struct_0(B),C)))
& A = k1_yellow_0(C,a_4_7_waybel24(B,C,E,F))
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_4_7_waybel24,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v2_pre_topc(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& ~ v1_xboole_0(D)
& v1_waybel_0(D,B)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
& m1_subset_1(E,u1_struct_0(k6_yellow_1(u1_struct_0(B),C))) )
=> ( r2_hidden(A,a_4_7_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k1_funct_1(E,F)
& r2_hidden(F,D) ) ) ) ).
fof(fraenkel_a_4_8_waybel24,axiom,
! [A,B,C,D,E] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_pre_topc(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(B)
& v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v2_pre_topc(C)
& v4_waybel11(C)
& v1_lattice3(C)
& v2_lattice3(C)
& v3_lattice3(C)
& l1_waybel_9(C)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(k3_waybel24(B,C))))
& ~ v1_xboole_0(E)
& v1_waybel_0(E,B)
& m1_subset_1(E,k1_zfmisc_1(u1_struct_0(B))) )
=> ( r2_hidden(A,a_4_8_waybel24(B,C,D,E))
<=> ? [F] :
( m1_subset_1(F,u1_struct_0(B))
& A = k1_yellow_0(C,a_4_5_waybel24(B,C,D,F))
& r2_hidden(F,E) ) ) ) ).
fof(fraenkel_a_0_0_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_0_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_waybel24))
& A = f3_s1_waybel24(B)
& p1_s1_waybel24(B) ) ) ).
fof(fraenkel_a_0_1_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_1_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_waybel24))
& A = k1_funct_1(f4_s1_waybel24,f3_s1_waybel24(B))
& p1_s1_waybel24(B) ) ) ).
fof(fraenkel_a_0_2_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_2_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_waybel24))
& A = f2_s2_waybel24(B)
& p1_s2_waybel24(B) ) ) ).
fof(fraenkel_a_0_3_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_3_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_waybel24))
& A = f2_s2_waybel24(B)
& p2_s2_waybel24(B) ) ) ).
fof(fraenkel_a_0_4_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_4_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s3_waybel24))
& A = f2_s3_waybel24(B)
& p1_s3_waybel24(B) ) ) ).
fof(fraenkel_a_0_5_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_5_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s3_waybel24))
& A = f3_s3_waybel24(B)
& p1_s3_waybel24(B) ) ) ).
fof(fraenkel_a_0_6_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_6_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s4_waybel24))
& A = f2_s4_waybel24(B)
& p1_s4_waybel24(B) ) ) ).
fof(fraenkel_a_0_7_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_7_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s4_waybel24))
& A = f3_s4_waybel24(B)
& p1_s4_waybel24(B) ) ) ).
fof(fraenkel_a_0_8_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_8_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s5_waybel24))
& A = f3_s5_waybel24(B)
& p1_s5_waybel24(B) ) ) ).
fof(fraenkel_a_0_9_waybel24,axiom,
! [A] :
( r2_hidden(A,a_0_9_waybel24)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(f1_s5_waybel24))
& A = k1_funct_1(f4_s5_waybel24,f3_s5_waybel24(B))
& p1_s5_waybel24(B) ) ) ).
%------------------------------------------------------------------------------