TPTP Problem File: LAT364+1.p
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%------------------------------------------------------------------------------
% File : LAT364+1 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Duality Based on Galois Connection - Part I T29
% Version : [Urb08] axioms : Especial.
% English :
% Refs : [Ban01] Bancerek (2001), Duality Based on the Galois Connectio
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : t29_waybel34 [Urb08]
% Status : Unknown
% Rating : 1.00 v3.4.0
% Syntax : Number of formulae : 249 ( 21 unt; 0 def)
% Number of atoms : 1558 ( 40 equ)
% Maximal formula atoms : 34 ( 6 avg)
% Number of connectives : 1474 ( 165 ~; 1 |; 922 &)
% ( 18 <=>; 368 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 84 ( 82 usr; 1 prp; 0-3 aty)
% Number of functors : 21 ( 21 usr; 1 con; 0-4 aty)
% Number of variables : 491 ( 435 !; 56 ?)
% SPC : FOF_UNK_RFO_SEQ
% Comments : Normal version: includes the axioms (which may be theorems from
% other articles) and background that are possibly necessary.
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : The problem encoding is based on set theory.
%------------------------------------------------------------------------------
fof(t29_waybel34,conjecture,
! [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))
& v17_waybel_0(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( ( v4_waybel11(D)
& m1_yellow_9(D,B) )
=> ! [E] :
( ( v4_waybel11(E)
& m1_yellow_9(E,A) )
=> ! [F] :
( ( v4_waybel11(F)
& m1_yellow_9(F,k2_yellow_2(B,A,k1_waybel34(A,B,C))) )
=> ! [G] :
( ( v1_funct_1(G)
& v1_funct_2(G,u1_struct_0(D),u1_struct_0(E))
& m2_relset_1(G,u1_struct_0(D),u1_struct_0(E)) )
=> ! [H] :
( ( v1_funct_1(H)
& v1_funct_2(H,u1_struct_0(D),u1_struct_0(F))
& m2_relset_1(H,u1_struct_0(D),u1_struct_0(F)) )
=> ( ( G = k1_waybel34(A,B,C)
& H = G
& v2_waybel34(G,D,E) )
=> v1_t_0topsp(H,D,F) ) ) ) ) ) ) ) ) ) ).
fof(abstractness_v1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_orders_2(A)
=> A = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ).
fof(abstractness_v1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ( v1_pre_topc(A)
=> A = g1_pre_topc(u1_struct_0(A),u1_pre_topc(A)) ) ) ).
fof(antisymmetry_r2_hidden,axiom,
! [A,B] :
( r2_hidden(A,B)
=> ~ r2_hidden(B,A) ) ).
fof(cc10_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> v1_xcmplx_0(B) ) ) ).
fof(cc10_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ) ) ).
fof(cc10_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v8_yellow_0(B,A)
=> v6_yellow_0(B,A) ) ) ) ).
fof(cc11_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B) ) ) ) ).
fof(cc11_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v1_yellow_0(A) ) ) ) ).
fof(cc11_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A) )
=> ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A) ) ) ) ) ).
fof(cc12_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B)
& v1_rat_1(B) ) ) ) ).
fof(cc12_waybel_0,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)
& v1_yellow_0(A)
& v24_waybel_0(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) ) ) ) ).
fof(cc12_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& v6_yellow_0(B,A) )
=> ( ~ v3_struct_0(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v4_yellow_0(B,A)
& v6_yellow_0(B,A) ) ) ) ) ).
fof(cc13_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v1_xreal_0(B)
& v1_int_1(B)
& v1_rat_1(B) ) ) ) ).
fof(cc13_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A) ) ) ) ).
fof(cc14_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( m1_subset_1(B,A)
=> ( v1_xcmplx_0(B)
& v4_ordinal2(B)
& v1_xreal_0(B)
& v1_int_1(B)
& v1_rat_1(B) ) ) ) ).
fof(cc14_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc15_membered,axiom,
! [A] :
( v1_xboole_0(A)
=> ( v1_membered(A)
& v2_membered(A)
& v3_membered(A)
& v4_membered(A)
& v5_membered(A) ) ) ).
fof(cc16_membered,axiom,
! [A] :
( v1_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_membered(B) ) ) ).
fof(cc17_membered,axiom,
! [A] :
( v2_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_membered(B)
& v2_membered(B) ) ) ) ).
fof(cc18_membered,axiom,
! [A] :
( v3_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_membered(B)
& v2_membered(B)
& v3_membered(B) ) ) ) ).
fof(cc19_membered,axiom,
! [A] :
( v4_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B) ) ) ) ).
fof(cc1_finset_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_finset_1(A) ) ).
fof(cc1_funct_1,axiom,
! [A] :
( v1_xboole_0(A)
=> v1_funct_1(A) ) ).
fof(cc1_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_lattice3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc1_membered,axiom,
! [A] :
( v5_membered(A)
=> v4_membered(A) ) ).
fof(cc1_pre_topc,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_pre_topc(B,A)
=> v2_pre_topc(B) ) ) ).
fof(cc1_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ) ).
fof(cc1_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> ( v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ) ) ).
fof(cc1_waybel17,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_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))
& v22_waybel_0(C,A,B) )
=> ( ~ 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(cc1_waybel21,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v2_lattice3(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))
& v19_waybel_0(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B) ) ) ) ) ).
fof(cc1_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v7_yellow_0(B,A)
=> v3_waybel_0(B,A) ) ) ) ).
fof(cc1_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(cc1_yellow_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A) ) ) ) ).
fof(cc1_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ~ v3_struct_0(B) ) ) ).
fof(cc20_membered,axiom,
! [A] :
( v5_membered(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> ( v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B) ) ) ) ).
fof(cc2_finset_1,axiom,
! [A] :
( v1_finset_1(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
=> v1_finset_1(B) ) ) ).
fof(cc2_funct_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) )
=> ( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ) ).
fof(cc2_lattice3,axiom,
! [A] :
( l1_orders_2(A)
=> ( v2_lattice3(A)
=> ~ v3_struct_0(A) ) ) ).
fof(cc2_membered,axiom,
! [A] :
( v4_membered(A)
=> v3_membered(A) ) ).
fof(cc2_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> v2_tops_1(B,A) ) ) ) ).
fof(cc2_waybel10,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_yellow_0(B,A)
=> ( v7_yellow_0(B,A)
=> ~ v3_struct_0(B) ) ) ) ).
fof(cc2_waybel17,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_waybel_9(A)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v24_waybel_0(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_waybel_9(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_pre_topc(C,A,B) )
=> ( ~ 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(cc2_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v8_yellow_0(B,A)
=> v4_waybel_0(B,A) ) ) ) ).
fof(cc2_waybel_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_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_waybel_1(C,B,A) )
=> ( v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B))
& v18_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& v22_waybel_0(C,A,B) ) ) ) ) ).
fof(cc2_yellow_9,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v2_orders_2(B) ) ) ).
fof(cc3_membered,axiom,
! [A] :
( v3_membered(A)
=> v2_membered(A) ) ).
fof(cc3_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_xboole_0(B)
=> v3_tops_1(B,A) ) ) ) ).
fof(cc3_waybel10,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_yellow_0(B,A)
=> ( v8_yellow_0(B,A)
=> ~ v3_struct_0(B) ) ) ) ).
fof(cc3_waybel17,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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_pre_topc(C,A,B) )
=> ( ~ 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))
& v22_waybel_0(C,A,B) ) ) ) ) ).
fof(cc3_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_lattice3(A) )
=> ( ~ v3_struct_0(A)
& v3_yellow_0(A) ) ) ) ).
fof(cc3_yellow_9,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v3_orders_2(B) ) ) ).
fof(cc4_membered,axiom,
! [A] :
( v2_membered(A)
=> v1_membered(A) ) ).
fof(cc4_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_tops_1(B,A)
=> v2_tops_1(B,A) ) ) ) ).
fof(cc4_waybel11,axiom,
! [A] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v12_waybel_0(B,A)
=> v3_waybel11(B,A) ) ) ) ).
fof(cc4_waybel17,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v4_waybel11(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& l1_waybel_9(A)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v4_waybel11(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B)
& l1_waybel_9(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))
& v22_waybel_0(C,A,B) )
=> ( ~ v1_xboole_0(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_pre_topc(C,A,B)
& v5_orders_3(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(cc4_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_yellow_0(A)
=> ( v1_yellow_0(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc4_yellow_9,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> v4_orders_2(B) ) ) ).
fof(cc5_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v4_pre_topc(B,A)
& v2_tops_1(B,A) )
=> ( v2_tops_1(B,A)
& v3_tops_1(B,A) ) ) ) ) ).
fof(cc5_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v1_yellow_0(A)
& v2_yellow_0(A) )
=> v3_yellow_0(A) ) ) ).
fof(cc5_yellow_9,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_9(B,A)
=> ( ~ v3_struct_0(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B) ) ) ) ).
fof(cc6_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( ( v3_pre_topc(B,A)
& v3_tops_1(B,A) )
=> ( v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A)
& v3_tops_1(B,A) ) ) ) ) ).
fof(cc6_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(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))
& v17_waybel_0(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B)
& v21_waybel_0(C,A,B) ) ) ) ) ).
fof(cc6_yellow_0,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
=> ( v2_orders_2(B)
& v4_yellow_0(B,A) ) ) ) ) ).
fof(cc6_yellow_9,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_yellow_9(B,A)
=> ( v4_waybel11(B)
=> ( ~ v3_struct_0(B)
& v2_pre_topc(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B) ) ) ) ) ).
fof(cc7_waybel_0,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(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))
& v18_waybel_0(C,A,B) )
=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v20_waybel_0(C,A,B)
& v22_waybel_0(C,A,B) ) ) ) ) ).
fof(cc7_yellow_0,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
=> ( v3_orders_2(B)
& v4_yellow_0(B,A) ) ) ) ) ).
fof(cc8_yellow_0,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v4_yellow_0(B,A)
=> ( v4_orders_2(B)
& v4_yellow_0(B,A) ) ) ) ) ).
fof(cc9_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v1_lattice3(A)
& v24_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v1_lattice3(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc9_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v7_yellow_0(B,A)
=> v5_yellow_0(B,A) ) ) ) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ).
fof(commutativity_k5_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> k5_subset_1(A,B,C) = k5_subset_1(A,C,B) ) ).
fof(d10_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v1_pre_topc(C)
& m1_pre_topc(C,A) )
=> ( C = k3_pre_topc(A,B)
<=> k2_pre_topc(C) = B ) ) ) ) ).
fof(d15_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ! [C] :
( ( v1_orders_2(C)
& v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ( C = k5_yellow_0(A,B)
<=> u1_struct_0(C) = B ) ) ) ) ).
fof(d19_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ( v8_yellow_0(B,A)
<=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r1_yellow_0(A,C)
=> r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) ).
fof(d1_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_waybel11(B,A)
<=> ! [C] :
( ( ~ v1_xboole_0(C)
& v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> ~ ( r2_hidden(k1_yellow_0(A,C),B)
& r1_xboole_0(C,B) ) ) ) ) ) ).
fof(d20_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v13_waybel_0(B,A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ( ( r2_hidden(C,B)
& r1_orders_2(A,C,D) )
=> r2_hidden(D,B) ) ) ) ) ) ) ).
fof(d2_t_0topsp,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(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)) )
=> ( v1_t_0topsp(C,A,B)
<=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(D,A)
=> v3_pre_topc(k4_pre_topc(A,B,C,D),B) ) ) ) ) ) ) ).
fof(d2_yellow_2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(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)) )
=> k2_yellow_2(A,B,C) = k5_yellow_0(B,k1_yellow_2(A,B,C)) ) ) ) ).
fof(d3_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> k2_pre_topc(A) = u1_struct_0(A) ) ).
fof(d3_xboole_0,axiom,
! [A,B,C] :
( C = k3_xboole_0(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ( r2_hidden(D,A)
& r2_hidden(D,B) ) ) ) ).
fof(d4_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_waybel_9(A) )
=> ( v4_waybel11(A)
<=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> ( v1_waybel11(B,A)
& v13_waybel_0(B,A) ) ) ) ) ) ).
fof(d4_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_waybel_9(B)
=> ( m1_yellow_9(B,A)
<=> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ) ).
fof(d5_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v3_pre_topc(B,A)
<=> r2_hidden(B,u1_pre_topc(A)) ) ) ) ).
fof(d9_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( l1_pre_topc(B)
=> ( m1_pre_topc(B,A)
<=> ( r1_tarski(k2_pre_topc(B),k2_pre_topc(A))
& ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(C,u1_pre_topc(B))
<=> ? [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
& r2_hidden(D,u1_pre_topc(A))
& C = k3_xboole_0(D,k2_pre_topc(B)) ) ) ) ) ) ) ) ).
fof(d9_waybel34,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ! [B] :
( ( v2_pre_topc(B)
& l1_pre_topc(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)) )
=> ( v2_waybel34(C,A,B)
<=> ! [D] :
( ( v3_pre_topc(D,A)
& m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v3_pre_topc(k4_pre_topc(A,B,C,D),k3_pre_topc(B,k1_yellow_2(A,B,C)))
& m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(k3_pre_topc(B,k1_yellow_2(A,B,C))))) ) ) ) ) ) ) ).
fof(dt_g1_orders_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ( v1_orders_2(g1_orders_2(A,B))
& l1_orders_2(g1_orders_2(A,B)) ) ) ).
fof(dt_g1_pre_topc,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ( v1_pre_topc(g1_pre_topc(A,B))
& l1_pre_topc(g1_pre_topc(A,B)) ) ) ).
fof(dt_k1_waybel34,axiom,
! [A,B,C] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_funct_1(k1_waybel34(A,B,C))
& v1_funct_2(k1_waybel34(A,B,C),u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(k1_waybel34(A,B,C),u1_struct_0(B),u1_struct_0(A)) ) ) ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_k1_yellow_0,axiom,
! [A,B] :
( l1_orders_2(A)
=> m1_subset_1(k1_yellow_0(A,B),u1_struct_0(A)) ) ).
fof(dt_k1_yellow_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> m1_subset_1(k1_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k2_pre_topc,axiom,
! [A] :
( l1_struct_0(A)
=> m1_subset_1(k2_pre_topc(A),k1_zfmisc_1(u1_struct_0(A))) ) ).
fof(dt_k2_relat_1,axiom,
$true ).
fof(dt_k2_yellow_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_orders_2(k2_yellow_2(A,B,C))
& v4_yellow_0(k2_yellow_2(A,B,C),B)
& m1_yellow_0(k2_yellow_2(A,B,C),B) ) ) ).
fof(dt_k2_zfmisc_1,axiom,
$true ).
fof(dt_k3_pre_topc,axiom,
! [A,B] :
( ( l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_pre_topc(k3_pre_topc(A,B))
& m1_pre_topc(k3_pre_topc(A,B),A) ) ) ).
fof(dt_k3_xboole_0,axiom,
$true ).
fof(dt_k4_pre_topc,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> m1_subset_1(k4_pre_topc(A,B,C,D),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k5_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> m1_subset_1(k5_subset_1(A,B,C),k1_zfmisc_1(A)) ) ).
fof(dt_k5_yellow_0,axiom,
! [A,B] :
( ( l1_orders_2(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A)
& m1_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(dt_k8_yellow_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> m1_subset_1(k8_yellow_2(A,B,C),k1_zfmisc_1(u1_struct_0(B))) ) ).
fof(dt_k9_relat_1,axiom,
$true ).
fof(dt_l1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_l1_waybel_9,axiom,
! [A] :
( l1_waybel_9(A)
=> ( l1_pre_topc(A)
& l1_orders_2(A) ) ) ).
fof(dt_m1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ! [B] :
( m1_pre_topc(B,A)
=> l1_pre_topc(B) ) ) ).
fof(dt_m1_relset_1,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
fof(dt_m1_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_0(B,A)
=> l1_orders_2(B) ) ) ).
fof(dt_m1_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_9(B,A)
=> l1_waybel_9(B) ) ) ).
fof(dt_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
=> m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B))) ) ).
fof(dt_u1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> m2_relset_1(u1_orders_2(A),u1_struct_0(A),u1_struct_0(A)) ) ).
fof(dt_u1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> m1_subset_1(u1_pre_topc(A),k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A)))) ) ).
fof(dt_u1_struct_0,axiom,
$true ).
fof(existence_l1_orders_2,axiom,
? [A] : l1_orders_2(A) ).
fof(existence_l1_pre_topc,axiom,
? [A] : l1_pre_topc(A) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A) ).
fof(existence_l1_waybel_9,axiom,
? [A] : l1_waybel_9(A) ).
fof(existence_m1_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] : m1_pre_topc(B,A) ) ).
fof(existence_m1_relset_1,axiom,
! [A,B] :
? [C] : m1_relset_1(C,A,B) ).
fof(existence_m1_subset_1,axiom,
! [A] :
? [B] : m1_subset_1(B,A) ).
fof(existence_m1_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] : m1_yellow_0(B,A) ) ).
fof(existence_m1_yellow_9,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] : m1_yellow_9(B,A) ) ).
fof(existence_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B) ).
fof(fc10_finset_1,axiom,
! [A,B] :
( v1_finset_1(B)
=> v1_finset_1(k3_xboole_0(A,B)) ) ).
fof(fc10_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v24_waybel_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc11_finset_1,axiom,
! [A,B] :
( v1_finset_1(A)
=> v1_finset_1(k3_xboole_0(A,B)) ) ).
fof(fc13_finset_1,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_finset_1(B) )
=> v1_finset_1(k9_relat_1(A,B)) ) ).
fof(fc14_finset_1,axiom,
! [A,B] :
( ( v1_finset_1(A)
& v1_finset_1(B) )
=> v1_finset_1(k2_zfmisc_1(A,B)) ) ).
fof(fc15_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v12_waybel_0(k2_pre_topc(A),A)
& v13_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ) ).
fof(fc1_waybel34,axiom,
! [A,B,C] :
( ( 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)
& 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_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_relat_1(k1_waybel34(A,B,C))
& v1_funct_1(k1_waybel34(A,B,C))
& ~ v1_xboole_0(k1_waybel34(A,B,C))
& v1_funct_2(k1_waybel34(A,B,C),u1_struct_0(B),u1_struct_0(A))
& v1_partfun1(k1_waybel34(A,B,C),u1_struct_0(B),u1_struct_0(A))
& v18_waybel_0(k1_waybel34(A,B,C),B,A)
& v20_waybel_0(k1_waybel34(A,B,C),B,A)
& v22_waybel_0(k1_waybel34(A,B,C),B,A)
& v5_waybel_1(k1_waybel34(A,B,C),A,B)
& v5_orders_3(k1_waybel34(A,B,C),B,A) ) ) ).
fof(fc1_waybel_2,axiom,
! [A,B,C,D] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,B)
& m1_relset_1(C,A,B)
& ~ v1_xboole_0(D)
& m1_subset_1(D,k1_zfmisc_1(A)) )
=> ~ v1_xboole_0(k9_relat_1(C,D)) ) ).
fof(fc1_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k5_yellow_0(A,B))
& v1_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A) ) ) ).
fof(fc27_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(k3_xboole_0(A,B)) ) ).
fof(fc28_membered,axiom,
! [A,B] :
( v1_membered(A)
=> v1_membered(k3_xboole_0(B,A)) ) ).
fof(fc29_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v1_membered(k3_xboole_0(A,B))
& v2_membered(k3_xboole_0(A,B)) ) ) ).
fof(fc2_pre_topc,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(k2_pre_topc(A)) ) ).
fof(fc2_waybel_0,axiom,
! [A] :
( ( v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v1_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc2_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ~ v1_xboole_0(k2_pre_topc(A)) ) ).
fof(fc2_yellow_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ~ v3_struct_0(k2_yellow_2(A,B,C))
& v1_orders_2(k2_yellow_2(A,B,C))
& v4_yellow_0(k2_yellow_2(A,B,C),B) ) ) ).
fof(fc30_membered,axiom,
! [A,B] :
( v2_membered(A)
=> ( v1_membered(k3_xboole_0(B,A))
& v2_membered(k3_xboole_0(B,A)) ) ) ).
fof(fc31_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v1_membered(k3_xboole_0(A,B))
& v2_membered(k3_xboole_0(A,B))
& v3_membered(k3_xboole_0(A,B)) ) ) ).
fof(fc32_membered,axiom,
! [A,B] :
( v3_membered(A)
=> ( v1_membered(k3_xboole_0(B,A))
& v2_membered(k3_xboole_0(B,A))
& v3_membered(k3_xboole_0(B,A)) ) ) ).
fof(fc33_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v1_membered(k3_xboole_0(A,B))
& v2_membered(k3_xboole_0(A,B))
& v3_membered(k3_xboole_0(A,B))
& v4_membered(k3_xboole_0(A,B)) ) ) ).
fof(fc34_membered,axiom,
! [A,B] :
( v4_membered(A)
=> ( v1_membered(k3_xboole_0(B,A))
& v2_membered(k3_xboole_0(B,A))
& v3_membered(k3_xboole_0(B,A))
& v4_membered(k3_xboole_0(B,A)) ) ) ).
fof(fc35_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v1_membered(k3_xboole_0(A,B))
& v2_membered(k3_xboole_0(A,B))
& v3_membered(k3_xboole_0(A,B))
& v4_membered(k3_xboole_0(A,B))
& v5_membered(k3_xboole_0(A,B)) ) ) ).
fof(fc36_membered,axiom,
! [A,B] :
( v5_membered(A)
=> ( v1_membered(k3_xboole_0(B,A))
& v2_membered(k3_xboole_0(B,A))
& v3_membered(k3_xboole_0(B,A))
& v4_membered(k3_xboole_0(B,A))
& v5_membered(k3_xboole_0(B,A)) ) ) ).
fof(fc3_pre_topc,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A)
& ~ v1_xboole_0(B)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( ~ v3_struct_0(k3_pre_topc(A,B))
& v1_pre_topc(k3_pre_topc(A,B)) ) ) ).
fof(fc3_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v1_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc4_pre_topc,axiom,
! [A,B] :
( ( v2_pre_topc(A)
& l1_pre_topc(A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_pre_topc(k3_pre_topc(A,B))
& v2_pre_topc(k3_pre_topc(A,B)) ) ) ).
fof(fc4_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v12_waybel_0(k2_pre_topc(A),A)
& v13_waybel_0(k2_pre_topc(A),A)
& v1_waybel11(k2_pre_topc(A),A)
& v2_waybel11(k2_pre_topc(A),A) ) ) ).
fof(fc4_waybel_0,axiom,
! [A] :
( ( v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v2_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc4_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc5_pre_topc,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> v4_pre_topc(k2_pre_topc(A),A) ) ).
fof(fc5_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_yellow_0(A)
& l1_orders_2(A) )
=> ( ~ v1_xboole_0(k2_pre_topc(A))
& v2_waybel_0(k2_pre_topc(A),A) ) ) ).
fof(fc5_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc6_membered,axiom,
( v1_xboole_0(k1_xboole_0)
& v1_membered(k1_xboole_0)
& v2_membered(k1_xboole_0)
& v3_membered(k1_xboole_0)
& v4_membered(k1_xboole_0)
& v5_membered(k1_xboole_0) ) ).
fof(fc6_waybel_8,axiom,
! [A] :
( ( v3_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v3_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc6_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& v1_waybel_0(B,A)
& m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
=> ( v1_orders_2(k5_yellow_0(A,B))
& v2_orders_2(k5_yellow_0(A,B))
& v4_yellow_0(k5_yellow_0(A,B),A)
& v7_waybel_0(k5_yellow_0(A,B)) ) ) ).
fof(fc7_waybel_8,axiom,
! [A] :
( ( v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v4_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc8_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ( v3_pre_topc(k2_pre_topc(A),A)
& v4_pre_topc(k2_pre_topc(A),A) ) ) ).
fof(fc8_waybel_8,axiom,
! [A] :
( ( v2_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc9_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> v1_tops_1(k2_pre_topc(A),A) ) ).
fof(fc9_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k5_yellow_0(A,k2_pre_topc(A)))
& v1_orders_2(k5_yellow_0(A,k2_pre_topc(A)))
& v4_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
& v5_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
& v6_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
& v7_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
& v8_yellow_0(k5_yellow_0(A,k2_pre_topc(A)),A)
& v3_waybel_0(k5_yellow_0(A,k2_pre_topc(A)),A)
& v4_waybel_0(k5_yellow_0(A,k2_pre_topc(A)),A) ) ) ).
fof(fc9_waybel34,axiom,
! [A,B,C] :
( ( 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)
& 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_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v18_waybel_0(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( ~ v3_struct_0(k2_yellow_2(A,B,C))
& v1_orders_2(k2_yellow_2(A,B,C))
& v2_orders_2(k2_yellow_2(A,B,C))
& v3_orders_2(k2_yellow_2(A,B,C))
& v4_orders_2(k2_yellow_2(A,B,C))
& v1_yellow_0(k2_yellow_2(A,B,C))
& v2_yellow_0(k2_yellow_2(A,B,C))
& v3_yellow_0(k2_yellow_2(A,B,C))
& v4_yellow_0(k2_yellow_2(A,B,C),B)
& v24_waybel_0(k2_yellow_2(A,B,C))
& v25_waybel_0(k2_yellow_2(A,B,C))
& v1_lattice3(k2_yellow_2(A,B,C))
& v2_lattice3(k2_yellow_2(A,B,C))
& v3_lattice3(k2_yellow_2(A,B,C)) ) ) ).
fof(fc9_waybel_8,axiom,
! [A] :
( ( v1_lattice3(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_orders_2(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(free_g1_orders_2,axiom,
! [A,B] :
( m1_relset_1(B,A,A)
=> ! [C,D] :
( g1_orders_2(A,B) = g1_orders_2(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(free_g1_pre_topc,axiom,
! [A,B] :
( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
=> ! [C,D] :
( g1_pre_topc(A,B) = g1_pre_topc(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : k3_xboole_0(A,A) = A ).
fof(idempotence_k5_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> k5_subset_1(A,B,B) = B ) ).
fof(irreflexivity_r2_orders_2,axiom,
! [A,B,C] :
( ( l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ~ r2_orders_2(A,B,B) ) ).
fof(rc10_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v2_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc11_waybel_0,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] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v2_waybel_0(B,A)
& v12_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc13_waybel_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(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) ) ).
fof(rc1_finset_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_finset_1(A) ) ).
fof(rc1_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A) ) ).
fof(rc1_lattice3,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A) ) ).
fof(rc1_lattice5,axiom,
! [A,B] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& l1_orders_2(A)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v19_waybel_0(C,A,B)
& v20_waybel_0(C,A,B) ) ) ).
fof(rc1_membered,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_membered(A)
& v2_membered(A)
& v3_membered(A)
& v4_membered(A)
& v5_membered(A) ) ).
fof(rc1_pre_topc,axiom,
? [A] :
( l1_pre_topc(A)
& v1_pre_topc(A) ) ).
fof(rc1_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_pre_topc(B,A) ) ) ).
fof(rc1_waybel10,axiom,
! [A,B] :
( ( 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_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_orders_3(C,A,B) ) ) ).
fof(rc1_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_waybel_0(B,A) ) ) ).
fof(rc1_waybel21,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_yellow_0(B,A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& v2_yellow_0(B)
& v3_yellow_0(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& v7_yellow_0(B,A)
& v3_waybel_0(B,A)
& v4_waybel_0(B,A)
& v24_waybel_0(B)
& v25_waybel_0(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v3_lattice3(B) ) ) ).
fof(rc1_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_waybel_0(B,A)
& v2_waybel_0(B,A) ) ) ).
fof(rc2_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_xboole_0(A)
& v1_funct_1(A) ) ).
fof(rc2_lattice3,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v1_orders_2(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A) ) ).
fof(rc2_lattice5,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] :
( m1_yellow_0(B,A)
& v1_orders_2(B)
& v5_yellow_0(B,A)
& v6_yellow_0(B,A) ) ) ).
fof(rc2_pre_topc,axiom,
? [A] :
( l1_pre_topc(A)
& ~ v3_struct_0(A)
& v1_pre_topc(A)
& v2_pre_topc(A) ) ).
fof(rc2_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ).
fof(rc2_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_finset_1(B)
& v1_waybel_0(B,A)
& v2_waybel_0(B,A) ) ) ).
fof(rc2_yellow_0,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)
& v3_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ).
fof(rc3_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc3_funct_1,axiom,
? [A] :
( v1_relat_1(A)
& v1_funct_1(A)
& v2_funct_1(A) ) ).
fof(rc3_pre_topc,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m1_pre_topc(B,A)
& v1_pre_topc(B) ) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A) ) ).
fof(rc3_tops_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A) ) ) ).
fof(rc3_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_0(B,A)
& ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& v6_yellow_0(B,A)
& v7_yellow_0(B,A)
& v8_yellow_0(B,A)
& v3_waybel_0(B,A)
& v4_waybel_0(B,A) ) ) ).
fof(rc3_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_yellow_0(B,A)
& v1_orders_2(B)
& v4_yellow_0(B,A) ) ) ).
fof(rc3_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v2_yellow_0(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v17_waybel_0(C,A,B)
& v19_waybel_0(C,A,B)
& v21_waybel_0(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(rc4_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(A))
& ~ v1_xboole_0(B)
& v1_finset_1(B) ) ) ).
fof(rc4_pre_topc,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& ~ v3_struct_0(B)
& v1_pre_topc(B) ) ) ).
fof(rc4_tops_1,axiom,
! [A] :
( l1_pre_topc(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_xboole_0(B)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A) ) ) ).
fof(rc4_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v2_waybel11(B,A)
& v3_waybel11(B,A) ) ) ).
fof(rc4_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_0(B,A)
& ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,A) ) ) ).
fof(rc4_yellow_9,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& v4_orders_2(B)
& v1_yellow_0(B)
& l1_orders_2(B) )
=> ? [C] :
( m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& v1_relat_1(C)
& v1_funct_1(C)
& ~ v1_xboole_0(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v18_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& v22_waybel_0(C,A,B)
& v1_partfun1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ).
fof(rc5_pre_topc,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_pre_topc(B,A)
& v1_pre_topc(B)
& v2_pre_topc(B) ) ) ).
fof(rc5_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B) ) ) ).
fof(rc5_tops_1,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v1_xboole_0(B)
& v3_pre_topc(B,A)
& v4_pre_topc(B,A)
& v1_membered(B)
& v2_membered(B)
& v3_membered(B)
& v4_membered(B)
& v5_membered(B)
& v2_tops_1(B,A)
& v3_tops_1(B,A) ) ) ).
fof(rc5_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_yellow_0(B,A)
& ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,A)
& v5_yellow_0(B,A)
& v6_yellow_0(B,A)
& v7_yellow_0(B,A)
& v8_yellow_0(B,A) ) ) ).
fof(rc6_pre_topc,axiom,
! [A] :
( ( v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v4_pre_topc(B,A) ) ) ).
fof(rc6_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v12_waybel_0(B,A)
& v13_waybel_0(B,A)
& v1_waybel11(B,A)
& v2_waybel11(B,A) ) ) ).
fof(rc7_pre_topc,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_pre_topc(A)
& l1_pre_topc(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v4_pre_topc(B,A) ) ) ).
fof(rc7_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& v12_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc8_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v12_waybel_0(B,A)
& v13_waybel_0(B,A) ) ) ).
fof(rc9_waybel_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
& ~ v1_xboole_0(B)
& v1_waybel_0(B,A)
& v12_waybel_0(B,A) ) ) ).
fof(redefinition_k1_yellow_2,axiom,
! [A,B,C] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k1_yellow_2(A,B,C) = k2_relat_1(C) ) ).
fof(redefinition_k4_pre_topc,axiom,
! [A,B,C,D] :
( ( l1_struct_0(A)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> k4_pre_topc(A,B,C,D) = k9_relat_1(C,D) ) ).
fof(redefinition_k5_subset_1,axiom,
! [A,B,C] :
( ( m1_subset_1(B,k1_zfmisc_1(A))
& m1_subset_1(C,k1_zfmisc_1(A)) )
=> k5_subset_1(A,B,C) = k3_xboole_0(B,C) ) ).
fof(redefinition_k8_yellow_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(B)
& l1_struct_0(B)
& v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m1_relset_1(C,A,u1_struct_0(B)) )
=> k8_yellow_2(A,B,C) = k2_relat_1(C) ) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ) ).
fof(redefinition_r3_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> ( r3_orders_2(A,B,C)
<=> r1_orders_2(A,B,C) ) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A) ).
fof(reflexivity_r3_orders_2,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> r3_orders_2(A,B,B) ) ).
fof(symmetry_r1_xboole_0,axiom,
! [A,B] :
( r1_xboole_0(A,B)
=> r1_xboole_0(B,A) ) ).
fof(t17_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( r1_yellow_0(A,B)
& r2_yellow_0(A,B) ) ) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ) ).
fof(t1_xboole_1,axiom,
! [A,B,C] :
( ( r1_tarski(A,B)
& r1_tarski(B,C) )
=> r1_tarski(A,C) ) ).
fof(t1_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( C = E
& D = F )
=> ( ( r1_orders_2(A,C,D)
=> r1_orders_2(B,E,F) )
& ( r2_orders_2(A,C,D)
=> r2_orders_2(B,E,F) ) ) ) ) ) ) ) ) ) ) ).
fof(t26_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> ! [C] :
( r1_yellow_0(A,C)
=> k1_yellow_0(A,C) = k1_yellow_0(B,C) ) ) ) ) ).
fof(t2_boole,axiom,
! [A] : k3_xboole_0(A,k1_xboole_0) = k1_xboole_0 ).
fof(t2_subset,axiom,
! [A,B] :
( m1_subset_1(A,B)
=> ( v1_xboole_0(B)
| r2_hidden(A,B) ) ) ).
fof(t34_yellow_2,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)
& 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)) )
=> ( v18_waybel_0(C,A,B)
=> v8_yellow_0(k2_yellow_2(A,B,C),B) ) ) ) ) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ) ).
fof(t3_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
=> ! [D] :
( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( C = D
& v1_waybel_0(C,A) )
=> v1_waybel_0(D,B) ) ) ) ) ) ) ).
fof(t4_subset,axiom,
! [A,B,C] :
( ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C)) )
=> m1_subset_1(A,C) ) ).
fof(t59_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> m1_subset_1(C,u1_struct_0(A)) ) ) ) ).
fof(t5_subset,axiom,
! [A,B,C] :
~ ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C))
& v1_xboole_0(C) ) ).
fof(t60_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_yellow_0(B,A)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( E = C
& F = D
& r1_orders_2(B,E,F) )
=> r1_orders_2(A,C,D) ) ) ) ) ) ) ) ).
fof(t69_yellow_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( r2_hidden(k1_yellow_0(A,C),u1_struct_0(B))
=> k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ) ).
fof(t77_xboole_1,axiom,
! [A,B,C] :
~ ( ~ r1_xboole_0(A,B)
& r1_tarski(A,C)
& r1_xboole_0(A,k3_xboole_0(B,C)) ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( r2_hidden(A,B)
& v1_xboole_0(B) ) ).
fof(t7_yellow_2,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_yellow_0(C,B) )
=> ( ( ( v1_waybel_0(A,C)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) )
=> ( v1_waybel_0(A,B)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) )
& ( ( v2_waybel_0(A,C)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(C))) )
=> ( v2_waybel_0(A,B)
& m1_subset_1(A,k1_zfmisc_1(u1_struct_0(B))) ) ) ) ) ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(A)
& A != B
& v1_xboole_0(B) ) ).
%------------------------------------------------------------------------------