TPTP Problem File: LAT375+1.p
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%------------------------------------------------------------------------------
% File : LAT375+1 : TPTP v8.2.0. Released v3.4.0.
% Domain : Lattice Theory
% Problem : Duality Based on Galois Connection - Part I T51
% 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 : t51_waybel34 [Urb08]
% Status : Theorem
% Rating : 1.00 v3.7.0, 0.95 v3.5.0, 1.00 v3.4.0
% Syntax : Number of formulae : 279 ( 34 unt; 0 def)
% Number of atoms : 1989 ( 48 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 1963 ( 253 ~; 2 |;1339 &)
% ( 24 <=>; 345 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 102 ( 100 usr; 1 prp; 0-4 aty)
% Number of functors : 31 ( 31 usr; 1 con; 0-3 aty)
% Number of variables : 470 ( 414 !; 56 ?)
% SPC : FOF_THM_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(t51_waybel34,conjecture,
! [A] :
( ~ v2_setfam_1(A)
=> k8_waybel34(A) = k2_yellow20(k4_waybel34(A),k6_yellow21(A)) ) ).
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_v6_altcat_1,axiom,
! [A] :
( l2_altcat_1(A)
=> ( v6_altcat_1(A)
=> A = g2_altcat_1(u1_struct_0(A),u1_altcat_1(A),u2_altcat_1(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_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v11_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v2_waybel_1(A)
& v9_waybel_1(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_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v2_yellow18(B)
& v3_yellow18(B)
& v4_yellow18(B)
& v1_yellow21(B)
& v2_yellow21(B)
& v3_yellow21(B) ) ) ) ) ).
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(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_relset_1,axiom,
! [A,B,C] :
( m1_subset_1(C,k1_zfmisc_1(k2_zfmisc_1(A,B)))
=> v1_relat_1(C) ) ).
fof(cc1_setfam_1,axiom,
! [A] :
( ( ~ v1_xboole_0(A)
& v1_setfam_1(A) )
=> ! [B] :
( m1_subset_1(B,A)
=> ~ v1_xboole_0(B) ) ) ).
fof(cc1_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A) )
=> ( v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v11_quantal1(B)
& v5_orders_3(B,A,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_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v16_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(cc1_waybel_3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v16_waybel_0(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(cc1_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_8(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A) ) ) ) ).
fof(cc1_yellow21,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow21(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(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_functor0,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v12_altcat_1(A) )
=> ( ~ v3_struct_0(A)
& v1_altcat_2(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_setfam_1,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ~ v1_xboole_0(A) ) ).
fof(cc2_waybel11,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> v13_waybel_0(B,A) ) ) ).
fof(cc2_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& ~ v1_yellow_3(A)
& v2_waybel_1(A)
& v10_waybel_1(A) ) ) ) ).
fof(cc2_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_yellow_0(A)
& v16_waybel_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)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ) ) ).
fof(cc2_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_waybel_8(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v1_waybel_8(A) ) ) ) ).
fof(cc2_yellow21,axiom,
! [A] :
( l2_altcat_1(A)
=> ( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A) )
=> ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A)
& v1_yellow21(A) ) ) ) ).
fof(cc2_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A) ) ) ) ).
fof(cc3_membered,axiom,
! [A] :
( v3_membered(A)
=> v2_membered(A) ) ).
fof(cc3_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A) )
=> ( v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A) ) ) ) ) ).
fof(cc3_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& ~ v1_yellow_3(A)
& v1_waybel_2(A) ) ) ) ).
fof(cc3_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v3_realset2(A)
& v2_orders_2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_waybel_3(A) ) ) ) ).
fof(cc3_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_8(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v1_waybel_8(A)
& v2_waybel_8(A) ) ) ) ).
fof(cc3_yellow21,axiom,
! [A] :
( ( v1_relat_1(A)
& v2_wellord1(A) )
=> ( v1_relat_1(A)
& v1_wellord1(A)
& v1_relat_2(A)
& v4_relat_2(A)
& v6_relat_2(A)
& v8_relat_2(A) ) ) ).
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(cc4_membered,axiom,
! [A] :
( v2_membered(A)
=> v1_membered(A) ) ).
fof(cc4_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
=> ( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v8_waybel_1(B,A) )
=> ( v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A) ) ) ) ) ).
fof(cc4_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v2_waybel_2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_waybel_2(A) ) ) ) ).
fof(cc4_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_waybel_3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v2_waybel_3(A) ) ) ) ).
fof(cc4_waybel_8,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_yellow_0(A)
& v24_waybel_0(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v1_waybel_8(A)
& v2_waybel_8(A)
& v3_waybel_8(A) ) ) ) ).
fof(cc4_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( v3_yellow_0(A)
=> ( v1_yellow_0(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc5_waybel_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v16_waybel_0(A) ) ) ) ).
fof(cc5_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v9_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(cc5_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v24_waybel_0(A)
& v1_waybel_2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& ~ v1_yellow_3(A)
& v2_waybel_2(A) ) ) ) ).
fof(cc5_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v24_waybel_0(A)
& v2_waybel_3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v1_yellow_0(A)
& v3_waybel_3(A) ) ) ) ).
fof(cc5_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v3_yellow18(B) ) ) ) ) ).
fof(cc5_yellow_0,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( v1_yellow_0(A)
& v2_yellow_0(A) )
=> v3_yellow_0(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_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v9_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_waybel_1(A) ) ) ) ).
fof(cc6_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& v9_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v24_waybel_0(A)
& ~ v1_yellow_3(A)
& v2_waybel_1(A)
& v1_waybel_2(A)
& v2_waybel_2(A) ) ) ) ).
fof(cc6_waybel_3,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& v16_waybel_0(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(A)
& v2_waybel_3(A) ) ) ) ).
fof(cc6_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v2_yellow18(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_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v9_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_yellow_0(A) ) ) ) ).
fof(cc7_waybel_2,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v2_waybel_2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v2_yellow_0(A)
& ~ v1_yellow_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v2_waybel_1(A)
& v9_waybel_1(A) ) ) ) ).
fof(cc7_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B) ) ) ) ) ).
fof(cc8_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))
& v23_waybel_0(C,A,B) )
=> ( v1_funct_1(C)
& v2_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B) ) ) ) ) ).
fof(cc8_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( ( ~ v3_struct_0(A)
& v11_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_1(A)
& v10_waybel_1(A) ) ) ) ).
fof(cc8_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v1_yellow21(B) ) ) ) ) ).
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_waybel_1,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_yellow_0(A)
& v2_waybel_1(A)
& v10_waybel_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A) ) ) ) ).
fof(cc9_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_altcat_2(B,A)
=> ( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v3_altcat_2(B,A) )
=> ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v1_altcat_2(B)
& v3_altcat_2(B,A)
& v2_yellow18(B)
& v3_yellow18(B)
& v4_yellow18(B)
& v1_yellow21(B)
& v2_yellow21(B) ) ) ) ) ).
fof(commutativity_k1_yellow20,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> k1_yellow20(A,B) = k1_yellow20(B,A) ) ).
fof(commutativity_k2_tarski,axiom,
! [A,B] : k2_tarski(A,B) = k2_tarski(B,A) ).
fof(commutativity_k3_xboole_0,axiom,
! [A,B] : k3_xboole_0(A,B) = k3_xboole_0(B,A) ).
fof(d10_xboole_0,axiom,
! [A,B] :
( A = B
<=> ( r1_tarski(A,B)
& r1_tarski(B,A) ) ) ).
fof(d10_yellow21,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ ! [B] :
( m1_subset_1(B,A)
=> v1_xboole_0(B) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v6_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow21(B)
& l2_altcat_1(B) )
=> ( B = k6_yellow21(A)
<=> ( ! [C] :
( ( v2_orders_2(C)
& v3_orders_2(C)
& v4_orders_2(C)
& v1_lattice3(C)
& v2_lattice3(C)
& l1_orders_2(C) )
=> ( m1_subset_1(C,u1_struct_0(B))
<=> ( v1_orders_2(C)
& v3_lattice3(C)
& r2_hidden(u1_struct_0(C),A) ) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D)))
& v5_orders_3(E,k3_yellow21(B,C),k3_yellow21(B,D))
& m2_relset_1(E,u1_struct_0(k3_yellow21(B,C)),u1_struct_0(k3_yellow21(B,D))) )
=> ( r2_hidden(E,k1_altcat_1(B,C,D))
<=> v22_waybel_0(E,k3_yellow21(B,C),k3_yellow21(B,D)) ) ) ) ) ) ) ) ) ) ).
fof(d11_setfam_1,axiom,
! [A] :
( v2_setfam_1(A)
<=> ! [B] :
( ~ v1_xboole_0(B)
=> ~ r2_hidden(B,A) ) ) ).
fof(d1_binop_1,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B,C] : k1_binop_1(A,B,C) = k1_funct_1(A,k4_tarski(B,C)) ) ).
fof(d1_struct_0,axiom,
! [A] :
( l1_struct_0(A)
=> ( v3_struct_0(A)
<=> v1_xboole_0(u1_struct_0(A)) ) ) ).
fof(d2_altcat_1,axiom,
! [A] :
( l1_altcat_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_altcat_1(A,B,C) = k1_binop_1(u1_altcat_1(A),B,C) ) ) ) ).
fof(d2_yellow20,axiom,
! [A] :
( ( v1_relat_1(A)
& v1_funct_1(A) )
=> ! [B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ! [C] :
( ( v1_relat_1(C)
& v1_funct_1(C) )
=> ( C = k1_yellow20(A,B)
<=> ( k1_relat_1(C) = k3_xboole_0(k1_relat_1(A),k1_relat_1(B))
& ! [D] :
( r2_hidden(D,k3_xboole_0(k1_relat_1(A),k1_relat_1(B)))
=> k1_funct_1(C,D) = k3_xboole_0(k1_funct_1(A,D),k1_funct_1(B,D)) ) ) ) ) ) ) ).
fof(d2_zfmisc_1,axiom,
! [A,B,C] :
( C = k2_zfmisc_1(A,B)
<=> ! [D] :
( r2_hidden(D,C)
<=> ? [E,F] :
( r2_hidden(E,A)
& r2_hidden(F,B)
& D = k4_tarski(E,F) ) ) ) ).
fof(d3_pboole,axiom,
! [A,B] :
( ( v1_relat_1(B)
& v1_funct_1(B) )
=> ( m1_pboole(B,A)
<=> k1_relat_1(B) = A ) ) ).
fof(d3_tarski,axiom,
! [A,B] :
( r1_tarski(A,B)
<=> ! [C] :
( r2_hidden(C,A)
=> r2_hidden(C,B) ) ) ).
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(d3_yellow20,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( l2_altcat_1(B)
=> ( r1_yellow20(A,B)
=> ! [C] :
( ( v6_altcat_1(C)
& l2_altcat_1(C) )
=> ( C = k2_yellow20(A,B)
<=> ( u1_struct_0(C) = k3_xboole_0(u1_struct_0(A),u1_struct_0(B))
& u1_altcat_1(C) = k1_yellow20(u1_altcat_1(A),u1_altcat_1(B))
& u2_altcat_1(C) = k1_yellow20(u2_altcat_1(A),u2_altcat_1(B)) ) ) ) ) ) ) ).
fof(d4_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ( v2_yellow21(A)
<=> ( v9_altcat_1(A)
& v3_yellow18(A)
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) ) )
& ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( ( v2_orders_2(D)
& v3_orders_2(D)
& v4_orders_2(D)
& v1_lattice3(D)
& v2_lattice3(D)
& l1_orders_2(D) )
=> ! [E] :
( ( v2_orders_2(E)
& v3_orders_2(E)
& v4_orders_2(E)
& v1_lattice3(E)
& v2_lattice3(E)
& l1_orders_2(E) )
=> ( ( D = B
& E = C )
=> r1_tarski(k1_altcat_1(A,B,C),k1_orders_3(D,E)) ) ) ) ) ) ) ) ) ).
fof(d5_tarski,axiom,
! [A,B] : k4_tarski(A,B) = k2_tarski(k2_tarski(A,B),k1_tarski(A)) ).
fof(d6_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_yellow21(A,B) = B ) ) ).
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_g2_altcat_1,axiom,
! [A,B,C] :
( ( m1_pboole(B,k2_zfmisc_1(A,A))
& m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B)) )
=> ( v6_altcat_1(g2_altcat_1(A,B,C))
& l2_altcat_1(g2_altcat_1(A,B,C)) ) ) ).
fof(dt_k1_altcat_1,axiom,
$true ).
fof(dt_k1_binop_1,axiom,
$true ).
fof(dt_k1_funct_1,axiom,
$true ).
fof(dt_k1_orders_3,axiom,
$true ).
fof(dt_k1_relat_1,axiom,
$true ).
fof(dt_k1_tarski,axiom,
$true ).
fof(dt_k1_xboole_0,axiom,
$true ).
fof(dt_k1_yellow20,axiom,
! [A,B] :
( ( v1_relat_1(A)
& v1_funct_1(A)
& v1_relat_1(B)
& v1_funct_1(B) )
=> ( v1_relat_1(k1_yellow20(A,B))
& v1_funct_1(k1_yellow20(A,B)) ) ) ).
fof(dt_k1_yellow21,axiom,
! [A] : l1_struct_0(k1_yellow21(A)) ).
fof(dt_k1_zfmisc_1,axiom,
$true ).
fof(dt_k2_altcat_1,axiom,
! [A,B] :
( m1_pboole(B,k2_zfmisc_1(A,A))
=> m1_pboole(k2_altcat_1(A,B),k3_zfmisc_1(A,A,A)) ) ).
fof(dt_k2_tarski,axiom,
$true ).
fof(dt_k2_yellow20,axiom,
! [A,B] :
( ( l2_altcat_1(A)
& l2_altcat_1(B) )
=> ( v6_altcat_1(k2_yellow20(A,B))
& l2_altcat_1(k2_yellow20(A,B)) ) ) ).
fof(dt_k2_zfmisc_1,axiom,
$true ).
fof(dt_k3_altcat_1,axiom,
! [A,B,C] :
( ( m1_pboole(B,k2_zfmisc_1(A,A))
& m1_pboole(C,k2_zfmisc_1(A,A)) )
=> m1_pboole(k3_altcat_1(A,B,C),k3_zfmisc_1(A,A,A)) ) ).
fof(dt_k3_xboole_0,axiom,
$true ).
fof(dt_k3_yellow21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v2_orders_2(k3_yellow21(A,B))
& v3_orders_2(k3_yellow21(A,B))
& v4_orders_2(k3_yellow21(A,B))
& v1_lattice3(k3_yellow21(A,B))
& v2_lattice3(k3_yellow21(A,B))
& l1_orders_2(k3_yellow21(A,B)) ) ) ).
fof(dt_k3_zfmisc_1,axiom,
$true ).
fof(dt_k4_tarski,axiom,
$true ).
fof(dt_k4_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k4_waybel34(A))
& v2_altcat_1(k4_waybel34(A))
& v6_altcat_1(k4_waybel34(A))
& v11_altcat_1(k4_waybel34(A))
& v12_altcat_1(k4_waybel34(A))
& v2_yellow21(k4_waybel34(A))
& l2_altcat_1(k4_waybel34(A)) ) ) ).
fof(dt_k4_yellow21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v2_orders_2(k4_yellow21(A,B))
& v3_orders_2(k4_yellow21(A,B))
& v4_orders_2(k4_yellow21(A,B))
& v1_lattice3(k4_yellow21(A,B))
& v2_lattice3(k4_yellow21(A,B))
& v3_lattice3(k4_yellow21(A,B))
& l1_orders_2(k4_yellow21(A,B)) ) ) ).
fof(dt_k6_yellow21,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k6_yellow21(A))
& v2_altcat_1(k6_yellow21(A))
& v6_altcat_1(k6_yellow21(A))
& v11_altcat_1(k6_yellow21(A))
& v12_altcat_1(k6_yellow21(A))
& v2_yellow21(k6_yellow21(A))
& l2_altcat_1(k6_yellow21(A)) ) ) ).
fof(dt_k7_grcat_1,axiom,
! [A] :
( l1_struct_0(A)
=> ( v1_funct_1(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k8_altcat_1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k8_altcat_1(A,B),k1_altcat_1(A,B,B)) ) ).
fof(dt_k8_waybel34,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v3_struct_0(k8_waybel34(A))
& v2_altcat_1(k8_waybel34(A))
& v6_altcat_1(k8_waybel34(A))
& v3_altcat_2(k8_waybel34(A),k4_waybel34(A))
& m1_altcat_2(k8_waybel34(A),k4_waybel34(A)) ) ) ).
fof(dt_l1_altcat_1,axiom,
! [A] :
( l1_altcat_1(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_orders_2,axiom,
! [A] :
( l1_orders_2(A)
=> l1_struct_0(A) ) ).
fof(dt_l1_struct_0,axiom,
$true ).
fof(dt_l2_altcat_1,axiom,
! [A] :
( l2_altcat_1(A)
=> l1_altcat_1(A) ) ).
fof(dt_m1_altcat_2,axiom,
! [A] :
( l2_altcat_1(A)
=> ! [B] :
( m1_altcat_2(B,A)
=> l2_altcat_1(B) ) ) ).
fof(dt_m1_pboole,axiom,
! [A,B] :
( m1_pboole(B,A)
=> ( v1_relat_1(B)
& v1_funct_1(B) ) ) ).
fof(dt_m1_relset_1,axiom,
$true ).
fof(dt_m1_subset_1,axiom,
$true ).
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_m3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ! [D] :
( m3_pboole(D,A,B,C)
=> m1_pboole(D,A) ) ) ).
fof(dt_u1_altcat_1,axiom,
! [A] :
( l1_altcat_1(A)
=> m1_pboole(u1_altcat_1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A))) ) ).
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_struct_0,axiom,
$true ).
fof(dt_u2_altcat_1,axiom,
! [A] :
( l2_altcat_1(A)
=> m3_pboole(u2_altcat_1(A),k3_zfmisc_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A)),k3_altcat_1(u1_struct_0(A),u1_altcat_1(A),u1_altcat_1(A)),k2_altcat_1(u1_struct_0(A),u1_altcat_1(A))) ) ).
fof(existence_l1_altcat_1,axiom,
? [A] : l1_altcat_1(A) ).
fof(existence_l1_orders_2,axiom,
? [A] : l1_orders_2(A) ).
fof(existence_l1_struct_0,axiom,
? [A] : l1_struct_0(A) ).
fof(existence_l2_altcat_1,axiom,
? [A] : l2_altcat_1(A) ).
fof(existence_m1_altcat_2,axiom,
! [A] :
( l2_altcat_1(A)
=> ? [B] : m1_altcat_2(B,A) ) ).
fof(existence_m1_pboole,axiom,
! [A] :
? [B] : m1_pboole(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_m2_relset_1,axiom,
! [A,B] :
? [C] : m2_relset_1(C,A,B) ).
fof(existence_m3_pboole,axiom,
! [A,B,C] :
( ( m1_pboole(B,A)
& m1_pboole(C,A) )
=> ? [D] : m3_pboole(D,A,B,C) ) ).
fof(fc10_finset_1,axiom,
! [A,B] :
( v1_finset_1(B)
=> v1_finset_1(k3_xboole_0(A,B)) ) ).
fof(fc10_membered,axiom,
! [A] :
( v1_int_1(A)
=> ( v1_membered(k1_tarski(A))
& v2_membered(k1_tarski(A))
& v3_membered(k1_tarski(A))
& v4_membered(k1_tarski(A)) ) ) ).
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(fc11_membered,axiom,
! [A] :
( v4_ordinal2(A)
=> ( v1_membered(k1_tarski(A))
& v2_membered(k1_tarski(A))
& v3_membered(k1_tarski(A))
& v4_membered(k1_tarski(A))
& v5_membered(k1_tarski(A)) ) ) ).
fof(fc11_waybel_8,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v4_orders_2(A)
& v2_waybel_8(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)))
& v4_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)))
& v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc12_membered,axiom,
! [A,B] :
( ( v1_xcmplx_0(A)
& v1_xcmplx_0(B) )
=> v1_membered(k2_tarski(A,B)) ) ).
fof(fc12_waybel_8,axiom,
! [A] :
( ( v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_waybel_8(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)))
& v3_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)))
& v1_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_lattice3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_yellow_0(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)))
& v2_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v3_waybel_3(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v1_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v2_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A)))
& v3_waybel_8(g1_orders_2(u1_struct_0(A),u1_orders_2(A))) ) ) ).
fof(fc13_membered,axiom,
! [A,B] :
( ( v1_xreal_0(A)
& v1_xreal_0(B) )
=> ( v1_membered(k2_tarski(A,B))
& v2_membered(k2_tarski(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(fc14_membered,axiom,
! [A,B] :
( ( v1_rat_1(A)
& v1_rat_1(B) )
=> ( v1_membered(k2_tarski(A,B))
& v2_membered(k2_tarski(A,B))
& v3_membered(k2_tarski(A,B)) ) ) ).
fof(fc15_finset_1,axiom,
! [A,B,C] :
( ( v1_finset_1(A)
& v1_finset_1(B)
& v1_finset_1(C) )
=> v1_finset_1(k3_zfmisc_1(A,B,C)) ) ).
fof(fc15_membered,axiom,
! [A,B] :
( ( v1_int_1(A)
& v1_int_1(B) )
=> ( v1_membered(k2_tarski(A,B))
& v2_membered(k2_tarski(A,B))
& v3_membered(k2_tarski(A,B))
& v4_membered(k2_tarski(A,B)) ) ) ).
fof(fc16_membered,axiom,
! [A,B] :
( ( v4_ordinal2(A)
& v4_ordinal2(B) )
=> ( v1_membered(k2_tarski(A,B))
& v2_membered(k2_tarski(A,B))
& v3_membered(k2_tarski(A,B))
& v4_membered(k2_tarski(A,B))
& v5_membered(k2_tarski(A,B)) ) ) ).
fof(fc1_altcat_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ~ v1_xboole_0(k1_altcat_1(A,B,B)) ) ).
fof(fc1_finset_1,axiom,
! [A] :
( ~ v1_xboole_0(k1_tarski(A))
& v1_finset_1(k1_tarski(A)) ) ).
fof(fc1_struct_0,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_struct_0(A) )
=> ~ v1_xboole_0(u1_struct_0(A)) ) ).
fof(fc1_yellow_0,axiom,
! [A,B] :
( m1_relset_1(B,k1_tarski(A),k1_tarski(A))
=> ( ~ v3_struct_0(g1_orders_2(k1_tarski(A),B))
& v1_orders_2(g1_orders_2(k1_tarski(A),B))
& v3_realset2(g1_orders_2(k1_tarski(A),B)) ) ) ).
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_altcat_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_altcat_3(k8_altcat_1(A,B),A,B,B)
& v2_altcat_3(k8_altcat_1(A,B),A,B,B)
& v4_altcat_3(k8_altcat_1(A,B),A,B,B)
& v5_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) ).
fof(fc2_finset_1,axiom,
! [A,B] :
( ~ v1_xboole_0(k2_tarski(A,B))
& v1_finset_1(k2_tarski(A,B)) ) ).
fof(fc2_setfam_1,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ( ~ v1_xboole_0(k1_tarski(A))
& v1_setfam_1(k1_tarski(A)) ) ) ).
fof(fc2_triang_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& m1_relset_1(B,A,A) )
=> ( ~ v3_struct_0(g1_orders_2(A,B))
& v1_orders_2(g1_orders_2(A,B))
& v2_orders_2(g1_orders_2(A,B))
& v3_orders_2(g1_orders_2(A,B))
& v4_orders_2(g1_orders_2(A,B)) ) ) ).
fof(fc2_waybel_1,axiom,
! [A] :
( l1_orders_2(A)
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v23_waybel_0(k7_grcat_1(A),A,A) ) ) ).
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_altcat_4,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> ( v1_altcat_3(k8_altcat_1(A,B),A,B,B)
& v2_altcat_3(k8_altcat_1(A,B),A,B,B)
& v3_altcat_3(k8_altcat_1(A,B),A,B,B)
& v4_altcat_3(k8_altcat_1(A,B),A,B,B)
& v5_altcat_3(k8_altcat_1(A,B),A,B,B) ) ) ).
fof(fc3_setfam_1,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& ~ v1_xboole_0(B) )
=> ( ~ v1_xboole_0(k2_tarski(A,B))
& v1_setfam_1(k2_tarski(A,B)) ) ) ).
fof(fc3_waybel10,axiom,
! [A] :
( l1_struct_0(A)
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v2_funct_1(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(fc3_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v2_funct_1(k7_grcat_1(A))
& ~ v1_xboole_0(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k7_grcat_1(A),A,A)
& v23_waybel_0(k7_grcat_1(A),A,A)
& v6_waybel_1(k7_grcat_1(A),A) ) ) ).
fof(fc4_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v2_funct_1(k7_grcat_1(A))
& ~ v1_xboole_0(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v11_quantal1(k7_grcat_1(A))
& v5_orders_3(k7_grcat_1(A),A,A)
& v17_waybel_0(k7_grcat_1(A),A,A)
& v18_waybel_0(k7_grcat_1(A),A,A)
& v19_waybel_0(k7_grcat_1(A),A,A)
& v20_waybel_0(k7_grcat_1(A),A,A)
& v21_waybel_0(k7_grcat_1(A),A,A)
& v22_waybel_0(k7_grcat_1(A),A,A)
& v23_waybel_0(k7_grcat_1(A),A,A)
& v6_waybel_1(k7_grcat_1(A),A)
& v7_waybel_1(k7_grcat_1(A),A)
& v8_waybel_1(k7_grcat_1(A),A) ) ) ).
fof(fc4_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v2_funct_1(k7_grcat_1(A))
& ~ v1_xboole_0(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k7_grcat_1(A),A,A)
& v23_waybel_0(k7_grcat_1(A),A,A)
& v6_waybel_1(k7_grcat_1(A),A)
& v7_waybel_1(k7_grcat_1(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_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k4_waybel34(A))
& v2_altcat_1(k4_waybel34(A))
& v6_altcat_1(k4_waybel34(A))
& v9_altcat_1(k4_waybel34(A))
& v11_altcat_1(k4_waybel34(A))
& v12_altcat_1(k4_waybel34(A))
& v1_altcat_2(k4_waybel34(A))
& v2_yellow18(k4_waybel34(A))
& v3_yellow18(k4_waybel34(A))
& v4_yellow18(k4_waybel34(A))
& v1_yellow21(k4_waybel34(A))
& v2_yellow21(k4_waybel34(A))
& v3_yellow21(k4_waybel34(A)) ) ) ).
fof(fc5_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( v1_relat_1(k7_grcat_1(A))
& v1_funct_1(k7_grcat_1(A))
& v2_funct_1(k7_grcat_1(A))
& ~ v1_xboole_0(k7_grcat_1(A))
& v1_funct_2(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_grcat_1(A),u1_struct_0(A),u1_struct_0(A))
& v5_orders_3(k7_grcat_1(A),A,A)
& v23_waybel_0(k7_grcat_1(A),A,A)
& v6_waybel_1(k7_grcat_1(A),A)
& v7_waybel_1(k7_grcat_1(A),A)
& v8_waybel_1(k7_grcat_1(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_yellow21,axiom,
! [A,B] :
( ( ~ v1_xboole_0(A)
& v2_wellord1(B)
& v1_relat_2(B)
& v4_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& v5_yellow21(B)
& m1_relset_1(B,A,A) )
=> ( ~ v3_struct_0(g1_orders_2(A,B))
& v1_orders_2(g1_orders_2(A,B))
& v2_orders_2(g1_orders_2(A,B))
& v3_orders_2(g1_orders_2(A,B))
& v4_orders_2(g1_orders_2(A,B))
& v1_yellow_0(g1_orders_2(A,B))
& v2_yellow_0(g1_orders_2(A,B))
& v3_yellow_0(g1_orders_2(A,B))
& v16_waybel_0(g1_orders_2(A,B))
& v24_waybel_0(g1_orders_2(A,B))
& v25_waybel_0(g1_orders_2(A,B))
& v1_waybel_8(g1_orders_2(A,B))
& v2_waybel_8(g1_orders_2(A,B))
& v1_lattice3(g1_orders_2(A,B))
& v2_lattice3(g1_orders_2(A,B))
& v3_lattice3(g1_orders_2(A,B))
& v2_waybel_3(g1_orders_2(A,B))
& v3_waybel_3(g1_orders_2(A,B)) ) ) ).
fof(fc7_membered,axiom,
! [A] :
( v1_xcmplx_0(A)
=> v1_membered(k1_tarski(A)) ) ).
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(fc7_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ( ~ v3_struct_0(k6_yellow21(A))
& v2_altcat_1(k6_yellow21(A))
& v6_altcat_1(k6_yellow21(A))
& v9_altcat_1(k6_yellow21(A))
& v11_altcat_1(k6_yellow21(A))
& v12_altcat_1(k6_yellow21(A))
& v1_altcat_2(k6_yellow21(A))
& v2_yellow18(k6_yellow21(A))
& v3_yellow18(k6_yellow21(A))
& v4_yellow18(k6_yellow21(A))
& v1_yellow21(k6_yellow21(A))
& v2_yellow21(k6_yellow21(A))
& v3_yellow21(k6_yellow21(A))
& v4_yellow21(k6_yellow21(A)) ) ) ).
fof(fc8_membered,axiom,
! [A] :
( v1_xreal_0(A)
=> ( v1_membered(k1_tarski(A))
& v2_membered(k1_tarski(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(fc8_yellow21,axiom,
! [A,B,C] :
( ( ~ v2_setfam_1(A)
& m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
& m1_subset_1(C,u1_struct_0(k6_yellow21(A))) )
=> ~ v1_xboole_0(k1_altcat_1(k6_yellow21(A),B,C)) ) ).
fof(fc9_membered,axiom,
! [A] :
( v1_rat_1(A)
=> ( v1_membered(k1_tarski(A))
& v2_membered(k1_tarski(A))
& v3_membered(k1_tarski(A)) ) ) ).
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_g2_altcat_1,axiom,
! [A,B,C] :
( ( m1_pboole(B,k2_zfmisc_1(A,A))
& m3_pboole(C,k3_zfmisc_1(A,A,A),k3_altcat_1(A,B,B),k2_altcat_1(A,B)) )
=> ! [D,E,F] :
( g2_altcat_1(A,B,C) = g2_altcat_1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(idempotence_k3_xboole_0,axiom,
! [A,B] : k3_xboole_0(A,A) = A ).
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(rc12_waybel_0,axiom,
? [A] :
( l1_orders_2(A)
& ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v16_waybel_0(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_setfam_1,axiom,
? [A] :
( ~ v1_xboole_0(A)
& v1_setfam_1(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_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(rc1_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A) ) ) ).
fof(rc1_waybel_2,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_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A)
& v3_realset2(A) ) ).
fof(rc1_waybel_3,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)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A) ) ).
fof(rc1_waybel_8,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)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A)
& v2_waybel_3(A)
& v3_waybel_3(A)
& v3_realset2(A)
& v1_waybel_8(A)
& v2_waybel_8(A)
& v3_waybel_8(A) ) ).
fof(rc1_yellow21,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A)
& v1_yellow21(A)
& v2_yellow21(A)
& v3_yellow21(A) ) ).
fof(rc1_yellow_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)
& v3_realset2(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_setfam_1,axiom,
? [A] : ~ v2_setfam_1(A) ).
fof(rc2_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& v2_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v11_quantal1(B)
& v5_orders_3(B,A,A)
& v17_waybel_0(B,A,A)
& v18_waybel_0(B,A,A)
& v19_waybel_0(B,A,A)
& v20_waybel_0(B,A,A)
& v21_waybel_0(B,A,A)
& v22_waybel_0(B,A,A)
& v6_waybel_1(B,A)
& v7_waybel_1(B,A)
& v8_waybel_1(B,A) ) ) ).
fof(rc2_waybel34,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_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)
& v22_waybel_0(C,A,B) ) ) ).
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_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A)
& v7_waybel_1(B,A) ) ) ).
fof(rc2_waybel_2,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_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v16_waybel_0(A)
& v24_waybel_0(A)
& v25_waybel_0(A)
& ~ v1_yellow_3(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A)
& v3_realset2(A)
& v1_waybel_2(A)
& v2_waybel_2(A) ) ).
fof(rc2_waybel_3,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)
& v2_waybel_3(A)
& v3_waybel_3(A) ) ).
fof(rc2_yellow21,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v2_altcat_1(A)
& v6_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v1_altcat_2(A)
& v2_yellow18(A)
& v3_yellow18(A)
& v4_yellow18(A)
& v1_yellow21(A)
& v2_yellow21(A)
& v4_yellow21(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_setfam_1,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ? [B] :
( m1_subset_1(B,A)
& ~ v1_xboole_0(B) ) ) ).
fof(rc3_struct_0,axiom,
? [A] :
( l1_struct_0(A)
& ~ v3_struct_0(A) ) ).
fof(rc3_waybel34,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_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v18_waybel_0(C,A,B)
& v20_waybel_0(C,A,B)
& v21_waybel_0(C,A,B)
& v22_waybel_0(C,A,B) ) ) ).
fof(rc3_waybel_1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ? [B] :
( m1_relset_1(B,u1_struct_0(A),u1_struct_0(A))
& v1_relat_1(B)
& v1_funct_1(B)
& ~ v1_xboole_0(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(B,u1_struct_0(A),u1_struct_0(A))
& v6_waybel_1(B,A)
& v8_waybel_1(B,A) ) ) ).
fof(rc3_yellow21,axiom,
? [A] :
( v1_relat_1(A)
& v1_wellord1(A)
& v2_wellord1(A)
& v1_relat_2(A)
& v4_relat_2(A)
& v6_relat_2(A)
& v8_relat_2(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_waybel_1,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)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v2_waybel_1(A)
& v9_waybel_1(A)
& v10_waybel_1(A)
& v11_waybel_1(A) ) ).
fof(rc4_yellow21,axiom,
! [A] :
( ~ v1_xboole_0(A)
=> ? [B] :
( m1_relset_1(B,A,A)
& v1_relat_1(B)
& v1_wellord1(B)
& v2_wellord1(B)
& v1_relat_2(B)
& v4_relat_2(B)
& v6_relat_2(B)
& v8_relat_2(B)
& v1_partfun1(B,A,A)
& v5_yellow21(B) ) ) ).
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_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_waybel_1,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)
& v2_yellow_0(A)
& v2_waybel_1(A)
& v9_waybel_1(A) ) ).
fof(rc7_functor0,axiom,
? [A] :
( l2_altcat_1(A)
& ~ v3_struct_0(A)
& v1_altcat_2(A) ) ).
fof(redefinition_k3_yellow21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k3_yellow21(A,B) = k1_yellow21(B) ) ).
fof(redefinition_k4_yellow21,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow21(A)
& l2_altcat_1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> k4_yellow21(A,B) = k1_yellow21(B) ) ).
fof(redefinition_m2_relset_1,axiom,
! [A,B,C] :
( m2_relset_1(C,A,B)
<=> m1_relset_1(C,A,B) ) ).
fof(reflexivity_r1_tarski,axiom,
! [A,B] : r1_tarski(A,A) ).
fof(s19_yellow18__e11_76__waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow18(B)
& l2_altcat_1(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& v2_altcat_1(C)
& v9_altcat_1(C)
& v11_altcat_1(C)
& v12_altcat_1(C)
& v2_yellow18(C)
& l2_altcat_1(C) )
=> ( ( u1_struct_0(B) = u1_struct_0(k8_waybel34(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> k1_altcat_1(B,D,E) = k1_binop_1(u1_altcat_1(k8_waybel34(A)),D,E) ) )
& u1_struct_0(C) = u1_struct_0(k8_waybel34(A))
& ! [D] :
( m1_subset_1(D,u1_struct_0(C))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(C))
=> k1_altcat_1(C,D,E) = k1_binop_1(u1_altcat_1(k8_waybel34(A)),D,E) ) ) )
=> g2_altcat_1(u1_struct_0(B),u1_altcat_1(B),u2_altcat_1(B)) = g2_altcat_1(u1_struct_0(C),u1_altcat_1(C),u2_altcat_1(C)) ) ) ) ) ).
fof(symmetry_r1_yellow20,axiom,
! [A,B] :
( ( l2_altcat_1(A)
& l2_altcat_1(B) )
=> ( r1_yellow20(A,B)
=> r1_yellow20(B,A) ) ) ).
fof(t123_zfmisc_1,axiom,
! [A,B,C,D] : k2_zfmisc_1(k3_xboole_0(A,B),k3_xboole_0(C,D)) = k3_xboole_0(k2_zfmisc_1(A,C),k2_zfmisc_1(B,D)) ).
fof(t12_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v9_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v2_yellow18(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v9_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& v2_yellow18(B)
& l2_altcat_1(B) )
=> r1_yellow20(A,B) ) ) ).
fof(t13_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( m1_subset_1(B,u1_struct_0(k4_waybel34(A)))
<=> ( v1_orders_2(B)
& v3_lattice3(B)
& r2_hidden(u1_struct_0(B),A) ) ) ) ) ).
fof(t14_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k4_waybel34(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k4_waybel34(A)))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(k4_waybel34(A),B,C))
<=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k4_yellow21(k4_waybel34(A),B)),u1_struct_0(k4_yellow21(k4_waybel34(A),C)))
& v17_waybel_0(D,k4_yellow21(k4_waybel34(A),B),k4_yellow21(k4_waybel34(A),C))
& m2_relset_1(D,u1_struct_0(k4_yellow21(k4_waybel34(A),B)),u1_struct_0(k4_yellow21(k4_waybel34(A),C))) ) ) ) ) ) ).
fof(t14_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( r2_hidden(u1_struct_0(B),A)
=> ( m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
<=> ( v1_orders_2(B)
& v3_lattice3(B) ) ) ) ) ) ).
fof(t15_yellow21,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k6_yellow21(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k6_yellow21(A)))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(k6_yellow21(A),B,C))
<=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k4_yellow21(k6_yellow21(A),B)),u1_struct_0(k4_yellow21(k6_yellow21(A),C)))
& v22_waybel_0(D,k4_yellow21(k6_yellow21(A),B),k4_yellow21(k6_yellow21(A),C))
& m2_relset_1(D,u1_struct_0(k4_yellow21(k6_yellow21(A),B)),u1_struct_0(k4_yellow21(k6_yellow21(A),C))) ) ) ) ) ) ).
fof(t1_subset,axiom,
! [A,B] :
( r2_hidden(A,B)
=> m1_subset_1(A,B) ) ).
fof(t26_yellow20,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& l2_altcat_1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_altcat_1(B)
& v11_altcat_1(B)
& v12_altcat_1(B)
& l2_altcat_1(B) )
=> ( ( r1_yellow20(A,B)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( C = D
=> k8_altcat_1(A,C) = k8_altcat_1(B,D) ) ) ) )
=> ( v3_struct_0(k2_yellow20(A,B))
| ( v2_altcat_1(k2_yellow20(A,B))
& v3_altcat_2(k2_yellow20(A,B),A)
& m1_altcat_2(k2_yellow20(A,B),A) ) ) ) ) ) ).
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(t2_tarski,axiom,
! [A,B] :
( ! [C] :
( r2_hidden(C,A)
<=> r2_hidden(C,B) )
=> A = B ) ).
fof(t2_yellow21,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_altcat_1(A)
& v11_altcat_1(A)
& v12_altcat_1(A)
& v3_yellow18(A)
& v1_yellow21(A)
& l2_altcat_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k8_altcat_1(A,B) = k7_grcat_1(k1_yellow21(B)) ) ) ).
fof(t3_subset,axiom,
! [A,B] :
( m1_subset_1(A,k1_zfmisc_1(B))
<=> r1_tarski(A,B) ) ).
fof(t47_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( ( v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& l1_orders_2(B) )
=> ( m1_subset_1(B,u1_struct_0(k8_waybel34(A)))
<=> ( v1_orders_2(B)
& v3_lattice3(B)
& r2_hidden(u1_struct_0(B),A) ) ) ) ) ).
fof(t48_waybel34,axiom,
! [A] :
( ~ v2_setfam_1(A)
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_waybel34(A)))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k8_waybel34(A)))
=> ! [D] :
( r2_hidden(D,k1_altcat_1(k8_waybel34(A),B,C))
<=> ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(k4_yellow21(k8_waybel34(A),B)),u1_struct_0(k4_yellow21(k8_waybel34(A),C)))
& v17_waybel_0(D,k4_yellow21(k8_waybel34(A),B),k4_yellow21(k8_waybel34(A),C))
& v22_waybel_0(D,k4_yellow21(k8_waybel34(A),B),k4_yellow21(k8_waybel34(A),C))
& m2_relset_1(D,u1_struct_0(k4_yellow21(k8_waybel34(A),B)),u1_struct_0(k4_yellow21(k8_waybel34(A),C))) ) ) ) ) ) ).
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(t5_subset,axiom,
! [A,B,C] :
~ ( r2_hidden(A,B)
& m1_subset_1(B,k1_zfmisc_1(C))
& v1_xboole_0(C) ) ).
fof(t6_boole,axiom,
! [A] :
( v1_xboole_0(A)
=> A = k1_xboole_0 ) ).
fof(t7_boole,axiom,
! [A,B] :
~ ( r2_hidden(A,B)
& v1_xboole_0(B) ) ).
fof(t8_boole,axiom,
! [A,B] :
~ ( v1_xboole_0(A)
& A != B
& v1_xboole_0(B) ) ).
%------------------------------------------------------------------------------