SET007 Axioms: SET007+503.ax
%------------------------------------------------------------------------------
% File : SET007+503 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Closure Operators and Subalgebras
% Version : [Urb08] axioms.
% English :
% Refs : [Mat90] Matuszewski (1990), Formalized Mathematics
% : [Urb07] Urban (2007), MPTP 0.2: Design, Implementation, and In
% : [Urb08] Urban (2006), Email to G. Sutcliffe
% Source : [Urb08]
% Names : waybel10 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 73 ( 1 unt; 0 def)
% Number of atoms : 799 ( 30 equ)
% Maximal formula atoms : 23 ( 10 avg)
% Number of connectives : 789 ( 63 ~; 0 |; 521 &)
% ( 34 <=>; 171 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 10 avg)
% Maximal term depth : 6 ( 1 avg)
% Number of predicates : 64 ( 62 usr; 1 prp; 0-4 aty)
% Number of functors : 40 ( 40 usr; 9 con; 0-4 aty)
% Number of variables : 174 ( 170 !; 4 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(fc1_waybel10,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ( v1_relat_1(k2_funcop_1(A,B))
& v1_funct_1(k2_funcop_1(A,B))
& v1_yellow_1(k2_funcop_1(A,B))
& v4_waybel_3(k2_funcop_1(A,B))
& v2_pralg_1(k2_funcop_1(A,B)) ) ) ).
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(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(fc2_waybel10,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ( v1_relat_1(k2_waybel_1(A,B,C))
& v1_funct_1(k2_waybel_1(A,B,C))
& ~ v1_xboole_0(k2_waybel_1(A,B,C))
& v1_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
& v2_funct_2(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
& v1_partfun1(k2_waybel_1(A,B,C),u1_struct_0(A),u1_struct_0(k2_yellow_2(A,B,C)))
& v5_orders_3(k2_waybel_1(A,B,C),A,k2_yellow_2(A,B,C)) ) ) ).
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(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(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(fc5_waybel10,axiom,
! [A,B,C,D] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B)
& v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m1_relset_1(C,u1_struct_0(A),u1_struct_0(B))
& m1_yellow_0(D,A) )
=> ( v1_relat_1(k2_waybel10(A,B,C,D))
& v1_funct_1(k2_waybel10(A,B,C,D))
& v1_funct_2(k2_waybel10(A,B,C,D),u1_struct_0(D),u1_struct_0(B))
& v1_partfun1(k2_waybel10(A,B,C,D),u1_struct_0(D),u1_struct_0(B))
& v5_orders_3(k2_waybel10(A,B,C,D),D,B) ) ) ).
fof(fc6_waybel10,axiom,
! [A,B] :
( ( l1_orders_2(A)
& ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ( ~ v3_struct_0(k7_yellow_1(A,B))
& v1_orders_2(k7_yellow_1(A,B))
& v2_orders_2(k7_yellow_1(A,B))
& v4_yellow_0(k7_yellow_1(A,B),k6_yellow_1(u1_struct_0(A),B)) ) ) ).
fof(fc7_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ( ~ v3_struct_0(k4_waybel10(A))
& v1_orders_2(k4_waybel10(A))
& v2_orders_2(k4_waybel10(A))
& v3_orders_2(k4_waybel10(A))
& v4_orders_2(k4_waybel10(A)) ) ) ).
fof(fc8_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ( ~ v3_struct_0(k4_waybel10(A))
& v1_orders_2(k4_waybel10(A))
& v2_orders_2(k4_waybel10(A))
& v3_orders_2(k4_waybel10(A))
& v4_orders_2(k4_waybel10(A))
& v1_lattice3(k4_waybel10(A))
& v2_lattice3(k4_waybel10(A))
& v3_lattice3(k4_waybel10(A))
& v1_yellow_0(k4_waybel10(A))
& v2_yellow_0(k4_waybel10(A))
& v3_yellow_0(k4_waybel10(A))
& v24_waybel_0(k4_waybel10(A))
& v25_waybel_0(k4_waybel10(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(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(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(fc10_waybel10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ~ v3_struct_0(k2_yellow_2(A,A,B))
& v1_orders_2(k2_yellow_2(A,A,B))
& v2_orders_2(k2_yellow_2(A,A,B))
& v3_orders_2(k2_yellow_2(A,A,B))
& v4_orders_2(k2_yellow_2(A,A,B))
& v4_yellow_0(k2_yellow_2(A,A,B),A)
& v5_yellow_0(k2_yellow_2(A,A,B),A)
& v7_yellow_0(k2_yellow_2(A,A,B),A)
& v3_waybel_0(k2_yellow_2(A,A,B),A) ) ) ).
fof(fc11_waybel10,axiom,
! [A,B] :
( ( 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)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v1_relat_1(k7_waybel10(A,B))
& v1_funct_1(k7_waybel10(A,B))
& ~ v1_xboole_0(k7_waybel10(A,B))
& v1_funct_2(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
& v11_quantal1(k7_waybel10(A,B))
& v5_orders_3(k7_waybel10(A,B),A,A)
& v6_waybel_1(k7_waybel10(A,B),A)
& v7_waybel_1(k7_waybel10(A,B),A) ) ) ).
fof(fc12_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) )
=> ( v1_relat_1(k6_waybel10(A))
& v1_funct_1(k6_waybel10(A))
& v2_funct_1(k6_waybel10(A))
& ~ v1_xboole_0(k6_waybel10(A))
& v1_funct_2(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
& v1_partfun1(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A)))) ) ) ).
fof(fc13_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) )
=> ( v1_relat_1(k6_waybel10(A))
& v1_funct_1(k6_waybel10(A))
& v2_funct_1(k6_waybel10(A))
& ~ v1_xboole_0(k6_waybel10(A))
& v1_funct_2(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
& v1_partfun1(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
& v5_orders_3(k6_waybel10(A),k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)))
& v23_waybel_0(k6_waybel10(A),k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A))) ) ) ).
fof(fc14_waybel10,axiom,
! [A,B] :
( ( 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)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) )
=> ( v1_relat_1(k7_waybel10(A,B))
& v1_funct_1(k7_waybel10(A,B))
& ~ v1_xboole_0(k7_waybel10(A,B))
& v1_funct_2(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
& v1_partfun1(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
& v11_quantal1(k7_waybel10(A,B))
& v5_orders_3(k7_waybel10(A,B),A,A)
& v22_waybel_0(k7_waybel10(A,B),A,A)
& v6_waybel_1(k7_waybel10(A,B),A)
& v7_waybel_1(k7_waybel10(A,B),A) ) ) ).
fof(fc15_waybel10,axiom,
! [A,B] :
( ( 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)
& v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v22_waybel_0(B,A,A)
& v7_waybel_1(B,A)
& m1_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( ~ v3_struct_0(k2_yellow_2(A,A,B))
& v1_orders_2(k2_yellow_2(A,A,B))
& v2_orders_2(k2_yellow_2(A,A,B))
& v3_orders_2(k2_yellow_2(A,A,B))
& v4_orders_2(k2_yellow_2(A,A,B))
& v2_lattice3(k2_yellow_2(A,A,B))
& v4_yellow_0(k2_yellow_2(A,A,B),A)
& v5_yellow_0(k2_yellow_2(A,A,B),A)
& v7_yellow_0(k2_yellow_2(A,A,B),A)
& v3_waybel_0(k2_yellow_2(A,A,B),A)
& v4_waybel_0(k2_yellow_2(A,A,B),A) ) ) ).
fof(fc16_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) )
=> ( v1_relat_1(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
& v1_funct_1(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
& v2_funct_1(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
& ~ v1_xboole_0(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
& v1_funct_2(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),u1_struct_0(k8_waybel10(A)),u1_struct_0(k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))))
& v2_funct_2(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),u1_struct_0(k8_waybel10(A)),u1_struct_0(k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))))
& v3_funct_2(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),u1_struct_0(k8_waybel10(A)),u1_struct_0(k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))))
& v1_partfun1(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),u1_struct_0(k8_waybel10(A)),u1_struct_0(k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))))
& v5_orders_3(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),k8_waybel10(A),k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))))
& v23_waybel_0(k2_waybel_1(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))),k8_waybel10(A),k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A)))) ) ) ).
fof(t1_waybel10,axiom,
! [A] :
( v1_relat_1(A)
=> ! [B] :
( v1_relat_1(B)
=> ( ( r1_tarski(A,B)
=> r1_tarski(k4_relat_1(A),k4_relat_1(B)) )
& ( r1_tarski(k4_relat_1(A),k4_relat_1(B))
=> r1_tarski(A,B) )
& ( r1_tarski(k4_relat_1(A),B)
=> r1_tarski(A,k4_relat_1(B)) )
& ( r1_tarski(A,k4_relat_1(B))
=> r1_tarski(k4_relat_1(A),B) ) ) ) ) ).
fof(t2_waybel10,axiom,
$true ).
fof(t3_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( ( m1_yellow_0(B,A)
=> m1_yellow_0(k7_lattice3(B),k7_lattice3(A)) )
& ( m1_yellow_0(k7_lattice3(B),k7_lattice3(A))
=> m1_yellow_0(B,A) )
& ( m1_yellow_0(k7_lattice3(B),A)
=> m1_yellow_0(B,k7_lattice3(A)) )
& ( m1_yellow_0(B,k7_lattice3(A))
=> m1_yellow_0(k7_lattice3(B),A) ) ) ) ) ).
fof(t4_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ( ( ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v4_yellow_0(k7_lattice3(B),k7_lattice3(A))
& m1_yellow_0(k7_lattice3(B),k7_lattice3(A)) ) )
& ( ( v4_yellow_0(k7_lattice3(B),k7_lattice3(A))
& m1_yellow_0(k7_lattice3(B),k7_lattice3(A)) )
=> ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) ) )
& ( ( v4_yellow_0(k7_lattice3(B),A)
& m1_yellow_0(k7_lattice3(B),A) )
=> ( v4_yellow_0(B,k7_lattice3(A))
& m1_yellow_0(B,k7_lattice3(A)) ) )
& ( ( v4_yellow_0(B,k7_lattice3(A))
& m1_yellow_0(B,k7_lattice3(A)) )
=> ( v4_yellow_0(k7_lattice3(B),A)
& m1_yellow_0(k7_lattice3(B),A) ) ) ) ) ) ).
fof(t5_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
=> ( v1_funct_1(k6_partfun1(B))
& v1_funct_2(k6_partfun1(B),u1_struct_0(k5_yellow_0(A,B)),u1_struct_0(A))
& m2_relset_1(k6_partfun1(B),u1_struct_0(k5_yellow_0(A,B)),u1_struct_0(A))
& ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(k5_yellow_0(A,B)),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(k5_yellow_0(A,B)),u1_struct_0(A)) )
=> ( C = k6_partfun1(B)
=> v5_orders_3(C,k5_yellow_0(A,B),A) ) ) ) ) ) ).
fof(t6_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> r1_orders_2(A,C,k7_yellow_2(u1_struct_0(A),A,B,C)) ) ) ) ).
fof(d1_waybel10,axiom,
! [A] :
( l1_struct_0(A)
=> ! [B] :
( l1_struct_0(B)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
=> ! [D] :
( l1_struct_0(D)
=> ( r1_tarski(u1_struct_0(D),u1_struct_0(A))
=> k2_waybel10(A,B,C,D) = k2_partfun1(u1_struct_0(A),u1_struct_0(B),C,u1_struct_0(D)) ) ) ) ) ) ).
fof(t7_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_yellow_0(C,A)
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ( k2_waybel10(A,B,D,C) = k2_partfun1(u1_struct_0(A),u1_struct_0(B),D,u1_struct_0(C))
& ! [E] :
( r2_hidden(E,u1_struct_0(C))
=> k1_funct_1(k2_waybel10(A,B,D,C),E) = k1_funct_1(D,E) ) ) ) ) ) ) ).
fof(t8_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [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)) )
=> ( v2_funct_1(C)
=> ! [D] :
( m1_yellow_0(D,A)
=> v2_funct_1(k2_waybel10(A,B,C,D)) ) ) ) ) ) ).
fof(t9_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( ~ v3_struct_0(C)
& m1_yellow_0(C,A) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,u1_struct_0(A),u1_struct_0(B))
& m2_relset_1(D,u1_struct_0(A),u1_struct_0(B)) )
=> ! [E] :
( ( v1_funct_1(E)
& v1_funct_2(E,u1_struct_0(B),u1_struct_0(A))
& m2_relset_1(E,u1_struct_0(B),u1_struct_0(A)) )
=> ( ( v2_funct_1(D)
& E = k2_funct_1(D) )
=> ( v1_funct_1(k2_waybel10(B,A,E,k2_yellow_2(C,B,k2_waybel10(A,B,D,C))))
& v1_funct_2(k2_waybel10(B,A,E,k2_yellow_2(C,B,k2_waybel10(A,B,D,C))),u1_struct_0(k2_yellow_2(C,B,k2_waybel10(A,B,D,C))),u1_struct_0(C))
& m2_relset_1(k2_waybel10(B,A,E,k2_yellow_2(C,B,k2_waybel10(A,B,D,C))),u1_struct_0(k2_yellow_2(C,B,k2_waybel10(A,B,D,C))),u1_struct_0(C))
& k2_waybel10(B,A,E,k2_yellow_2(C,B,k2_waybel10(A,B,D,C))) = k2_funct_1(k2_waybel10(A,B,D,C)) ) ) ) ) ) ) ) ).
fof(t10_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v2_orders_2(B)
& l1_orders_2(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k7_yellow_1(A,B)))
<=> ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
& v5_orders_3(C,A,B)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ).
fof(d2_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,k7_yellow_1(A,A))
& m1_yellow_0(B,k7_yellow_1(A,A)) )
=> ( B = k3_waybel10(A)
<=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( m1_subset_1(C,u1_struct_0(B))
<=> v7_waybel_1(C,A) ) ) ) ) ) ).
fof(t11_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k3_waybel10(A)))
<=> ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ) ).
fof(t12_waybel10,axiom,
! [A,B] :
( ( ~ v3_struct_0(B)
& l1_orders_2(B) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,A,u1_struct_0(B))
& m2_relset_1(C,A,u1_struct_0(B)) )
=> ! [D] :
( ( v1_funct_1(D)
& v1_funct_2(D,A,u1_struct_0(B))
& m2_relset_1(D,A,u1_struct_0(B)) )
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k6_yellow_1(A,B)))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(k6_yellow_1(A,B)))
=> ( ( E = C
& F = D )
=> ( r1_orders_2(k6_yellow_1(A,B),E,F)
<=> r1_yellow_2(A,B,C,D) ) ) ) ) ) ) ) ).
fof(t13_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] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k3_waybel10(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k3_waybel10(A)))
=> ( ( D = B
& E = C )
=> ( r3_orders_2(k3_waybel10(A),D,E)
<=> r1_yellow_2(u1_struct_0(A),A,B,C) ) ) ) ) ) ) ) ).
fof(t14_waybel10,axiom,
! [A] :
( ( v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( ( v4_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ( r1_tarski(u1_struct_0(B),u1_struct_0(C))
=> m1_yellow_0(B,C) ) ) ) ) ).
fof(t15_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] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( r1_yellow_2(u1_struct_0(A),A,B,C)
<=> m1_yellow_0(k2_yellow_2(A,A,C),k2_yellow_2(A,A,B)) ) ) ) ) ).
fof(d3_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_orders_2(B)
& l1_orders_2(B) )
=> ( B = k4_waybel10(A)
<=> ( ! [C] :
( m1_subset_1(C,u1_struct_0(B))
<=> ( v1_orders_2(C)
& m1_yellow_0(C,A) ) )
& ! [C] :
( m1_subset_1(C,u1_struct_0(B))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( r1_orders_2(B,C,D)
<=> ? [E] :
( l1_orders_2(E)
& D = E
& m1_yellow_0(C,E) ) ) ) ) ) ) ) ) ).
fof(t16_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k4_waybel10(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k4_waybel10(A)))
=> ( D = B
=> ( r1_orders_2(k4_waybel10(A),C,D)
<=> m1_yellow_0(C,B) ) ) ) ) ) ) ).
fof(d4_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,k4_waybel10(A))
& m1_yellow_0(B,k4_waybel10(A)) )
=> ( B = k5_waybel10(A)
<=> ! [C] :
( ( v1_orders_2(C)
& m1_yellow_0(C,A) )
=> ( m1_subset_1(C,u1_struct_0(B))
<=> ( v7_yellow_0(C,A)
& v4_yellow_0(C,A) ) ) ) ) ) ) ).
fof(t17_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k5_waybel10(A)))
<=> ( v1_orders_2(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& m1_yellow_0(B,A) ) ) ) ).
fof(t18_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( l1_orders_2(B)
=> ! [C] :
( m1_subset_1(C,u1_struct_0(k5_waybel10(A)))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(k5_waybel10(A)))
=> ( D = B
=> ( r3_orders_2(k5_waybel10(A),C,D)
<=> m1_yellow_0(C,B) ) ) ) ) ) ) ).
fof(d5_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
& m2_relset_1(B,u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A)))) )
=> ( B = k6_waybel10(A)
<=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> k1_funct_1(B,C) = k2_yellow_2(A,A,C) ) ) ) ) ).
fof(d6_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_yellow_0(B,A)
=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( C = k7_waybel10(A,B)
<=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k7_yellow_2(u1_struct_0(A),A,C,D) = k2_yellow_0(A,k3_xboole_0(k7_waybel_0(A,D),u1_struct_0(B))) ) ) ) ) ) ).
fof(t19_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] :
( ( v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> k2_yellow_2(A,A,k7_waybel10(A,B)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B)) ) ) ).
fof(t20_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] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> k7_waybel10(A,k2_yellow_2(A,A,B)) = B ) ) ).
fof(t21_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) )
=> ( v1_funct_1(k2_funct_1(k6_waybel10(A)))
& v1_funct_2(k2_funct_1(k6_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))),u1_struct_0(k3_waybel10(A)))
& m2_relset_1(k2_funct_1(k6_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))),u1_struct_0(k3_waybel10(A))) ) ) ).
fof(t22_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] :
( ( v1_orders_2(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> k1_funct_1(k2_funct_1(k6_waybel10(A)),B) = k7_waybel10(A,B) ) ) ).
fof(t23_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) )
=> r5_waybel_1(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A))) ) ).
fof(t24_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( ( v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ! [C] :
( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
=> ( ( ( v1_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v1_waybel_0(C,B) )
& ( ( v2_waybel_0(C,A)
& m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
=> v2_waybel_0(C,B) ) ) ) ) ) ).
fof(t25_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] :
( ( v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v22_waybel_0(k7_waybel10(A,B),A,A)
<=> v4_waybel_0(B,A) ) ) ) ).
fof(t26_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] :
( ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
=> ( v22_waybel_0(B,A,A)
<=> v4_waybel_0(k2_yellow_2(A,A,B),A) ) ) ) ).
fof(d7_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,k3_waybel10(A))
& m1_yellow_0(B,k3_waybel10(A)) )
=> ( B = k8_waybel10(A)
<=> ! [C] :
( ( v1_funct_1(C)
& v1_funct_2(C,u1_struct_0(A),u1_struct_0(A))
& v7_waybel_1(C,A)
& m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
=> ( m1_subset_1(C,u1_struct_0(B))
<=> v22_waybel_0(C,A,A) ) ) ) ) ) ).
fof(t27_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k8_waybel10(A)))
<=> ( v1_funct_1(B)
& v1_funct_2(B,u1_struct_0(A),u1_struct_0(A))
& v22_waybel_0(B,A,A)
& v7_waybel_1(B,A)
& m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) ) ) ) ).
fof(d8_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& v1_orders_2(B)
& v4_yellow_0(B,k5_waybel10(A))
& m1_yellow_0(B,k5_waybel10(A)) )
=> ( B = k9_waybel10(A)
<=> ! [C] :
( ( v1_orders_2(C)
& v4_yellow_0(C,A)
& v7_yellow_0(C,A)
& m1_yellow_0(C,A) )
=> ( m1_subset_1(C,u1_struct_0(B))
<=> v4_waybel_0(C,A) ) ) ) ) ) ).
fof(t28_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(k9_waybel10(A)))
<=> ( v1_orders_2(B)
& v4_yellow_0(B,A)
& v7_yellow_0(B,A)
& v4_waybel_0(B,A)
& m1_yellow_0(B,A) ) ) ) ).
fof(t29_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) )
=> k2_yellow_2(k8_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k2_waybel10(k3_waybel10(A),k1_waybel10(k4_waybel10(A),k5_waybel10(A)),k6_waybel10(A),k8_waybel10(A))) = k1_waybel10(k5_waybel10(A),k9_waybel10(A)) ) ).
fof(t30_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) )
=> r5_waybel_1(k8_waybel10(A),k1_waybel10(k5_waybel10(A),k9_waybel10(A))) ) ).
fof(s1_waybel10,axiom,
( ( p1_s1_waybel10(f2_s1_waybel10)
& r2_hidden(f2_s1_waybel10,u1_struct_0(f1_s1_waybel10)) )
=> ? [A] :
( ~ v3_struct_0(A)
& v1_orders_2(A)
& v4_yellow_0(A,f1_s1_waybel10)
& m1_yellow_0(A,f1_s1_waybel10)
& ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s1_waybel10))
=> ( m1_subset_1(B,u1_struct_0(A))
<=> p1_s1_waybel10(B) ) ) ) ) ).
fof(s2_waybel10,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s2_waybel10))
<=> p1_s2_waybel10(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s2_waybel10))
<=> p1_s2_waybel10(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s2_waybel10))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f1_s2_waybel10))
=> ( r1_orders_2(f1_s2_waybel10,A,B)
<=> p2_s2_waybel10(A,B) ) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s2_waybel10))
=> ! [B] :
( m1_subset_1(B,u1_struct_0(f2_s2_waybel10))
=> ( r1_orders_2(f2_s2_waybel10,A,B)
<=> p2_s2_waybel10(A,B) ) ) ) )
=> g1_orders_2(u1_struct_0(f1_s2_waybel10),u1_orders_2(f1_s2_waybel10)) = g1_orders_2(u1_struct_0(f2_s2_waybel10),u1_orders_2(f2_s2_waybel10)) ) ).
fof(s3_waybel10,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f2_s3_waybel10))
<=> p1_s3_waybel10(A) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f3_s3_waybel10))
<=> p1_s3_waybel10(A) ) )
=> g1_orders_2(u1_struct_0(f2_s3_waybel10),u1_orders_2(f2_s3_waybel10)) = g1_orders_2(u1_struct_0(f3_s3_waybel10),u1_orders_2(f3_s3_waybel10)) ) ).
fof(s4_waybel10,axiom,
( ( ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s4_waybel10))
=> ( m1_subset_1(A,u1_struct_0(f2_s4_waybel10))
<=> p1_s4_waybel10(A) ) )
& ! [A] :
( m1_subset_1(A,u1_struct_0(f1_s4_waybel10))
=> ( m1_subset_1(A,u1_struct_0(f3_s4_waybel10))
<=> p1_s4_waybel10(A) ) ) )
=> g1_orders_2(u1_struct_0(f2_s4_waybel10),u1_orders_2(f2_s4_waybel10)) = g1_orders_2(u1_struct_0(f3_s4_waybel10),u1_orders_2(f3_s4_waybel10)) ) ).
fof(dt_k1_waybel10,axiom,
! [A,B] :
( ( l1_orders_2(A)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> ( v1_orders_2(k1_waybel10(A,B))
& v4_yellow_0(k1_waybel10(A,B),k7_lattice3(A))
& m1_yellow_0(k1_waybel10(A,B),k7_lattice3(A)) ) ) ).
fof(redefinition_k1_waybel10,axiom,
! [A,B] :
( ( l1_orders_2(A)
& v4_yellow_0(B,A)
& m1_yellow_0(B,A) )
=> k1_waybel10(A,B) = k7_lattice3(B) ) ).
fof(dt_k2_waybel10,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))
& l1_struct_0(D) )
=> ( v1_funct_1(k2_waybel10(A,B,C,D))
& v1_funct_2(k2_waybel10(A,B,C,D),u1_struct_0(D),u1_struct_0(B))
& m2_relset_1(k2_waybel10(A,B,C,D),u1_struct_0(D),u1_struct_0(B)) ) ) ).
fof(dt_k3_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k3_waybel10(A))
& v1_orders_2(k3_waybel10(A))
& v4_yellow_0(k3_waybel10(A),k7_yellow_1(A,A))
& m1_yellow_0(k3_waybel10(A),k7_yellow_1(A,A)) ) ) ).
fof(dt_k4_waybel10,axiom,
! [A] :
( l1_orders_2(A)
=> ( ~ v3_struct_0(k4_waybel10(A))
& v1_orders_2(k4_waybel10(A))
& l1_orders_2(k4_waybel10(A)) ) ) ).
fof(dt_k5_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k5_waybel10(A))
& v1_orders_2(k5_waybel10(A))
& v4_yellow_0(k5_waybel10(A),k4_waybel10(A))
& m1_yellow_0(k5_waybel10(A),k4_waybel10(A)) ) ) ).
fof(dt_k6_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& l1_orders_2(A) )
=> ( v1_funct_1(k6_waybel10(A))
& v1_funct_2(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A))))
& m2_relset_1(k6_waybel10(A),u1_struct_0(k3_waybel10(A)),u1_struct_0(k1_waybel10(k4_waybel10(A),k5_waybel10(A)))) ) ) ).
fof(dt_k7_waybel10,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A)
& m1_yellow_0(B,A) )
=> ( v1_funct_1(k7_waybel10(A,B))
& v1_funct_2(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k7_waybel10(A,B),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_k8_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k8_waybel10(A))
& v1_orders_2(k8_waybel10(A))
& v4_yellow_0(k8_waybel10(A),k3_waybel10(A))
& m1_yellow_0(k8_waybel10(A),k3_waybel10(A)) ) ) ).
fof(dt_k9_waybel10,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ~ v3_struct_0(k9_waybel10(A))
& v1_orders_2(k9_waybel10(A))
& v4_yellow_0(k9_waybel10(A),k5_waybel10(A))
& m1_yellow_0(k9_waybel10(A),k5_waybel10(A)) ) ) ).
%------------------------------------------------------------------------------