SET007 Axioms: SET007+885.ax
%------------------------------------------------------------------------------
% File : SET007+885 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Formalization of Ortholattices via~Orthoposets
% 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 : robbins3 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 133 ( 8 unt; 0 def)
% Number of atoms : 1181 ( 67 equ)
% Maximal formula atoms : 37 ( 8 avg)
% Number of connectives : 1188 ( 140 ~; 0 |; 815 &)
% ( 14 <=>; 219 =>; 0 <=; 0 <~>)
% Maximal formula depth : 37 ( 10 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 85 ( 84 usr; 0 prp; 1-3 aty)
% Number of functors : 34 ( 34 usr; 6 con; 0-5 aty)
% Number of variables : 250 ( 224 !; 26 ?)
% SPC :
% Comments : The individual reference can be found in [Mat90] by looking for
% the name provided by [Urb08].
% : Translated by MPTP from the Mizar Mathematical Library 4.48.930.
% : These set theory axioms are used in encodings of problems in
% various domains, including ALG, CAT, GRP, LAT, SET, and TOP.
%------------------------------------------------------------------------------
fof(cc1_robbins3,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A) )
=> ( ~ v3_struct_0(A)
& v8_lattices(A)
& v9_lattices(A)
& v1_robbins3(A)
& v2_robbins3(A) ) ) ) ).
fof(cc2_robbins3,axiom,
! [A] :
( l3_lattices(A)
=> ( ( ~ v3_struct_0(A)
& v9_lattices(A)
& v1_robbins3(A)
& v2_robbins3(A)
& v3_robbins3(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A) ) ) ) ).
fof(cc3_robbins3,axiom,
! [A] :
( l1_oposet_1(A)
=> ( ( ~ v3_struct_0(A)
& v14_oposet_1(A)
& v19_oposet_1(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v3_oposet_1(A)
& v7_oposet_1(A)
& v9_oposet_1(A)
& v13_oposet_1(A)
& v14_oposet_1(A) ) ) ) ).
fof(rc1_robbins3,axiom,
? [A] :
( l1_oposet_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_oposet_1(A)
& v3_oposet_1(A)
& v7_oposet_1(A)
& v9_oposet_1(A)
& v13_oposet_1(A)
& v14_oposet_1(A)
& v15_oposet_1(A)
& v19_oposet_1(A) ) ).
fof(rc2_robbins3,axiom,
? [A] :
( l1_robbins3(A)
& v4_robbins3(A) ) ).
fof(rc3_robbins3,axiom,
? [A] :
( l2_robbins3(A)
& v5_robbins3(A) ) ).
fof(rc4_robbins3,axiom,
? [A] :
( l3_robbins3(A)
& v6_robbins3(A) ) ).
fof(fc1_robbins3,axiom,
( ~ v3_struct_0(k1_robbins3)
& v4_lattices(k1_robbins3)
& v5_lattices(k1_robbins3)
& v6_lattices(k1_robbins3)
& v7_lattices(k1_robbins3)
& v8_lattices(k1_robbins3)
& v9_lattices(k1_robbins3)
& v10_lattices(k1_robbins3)
& v11_lattices(k1_robbins3)
& v12_lattices(k1_robbins3)
& v13_lattices(k1_robbins3)
& v14_lattices(k1_robbins3)
& v15_lattices(k1_robbins3)
& v16_lattices(k1_robbins3)
& v17_lattices(k1_robbins3)
& v3_realset2(k1_robbins3)
& v1_sheffer1(k1_robbins3)
& v2_sheffer1(k1_robbins3)
& v3_sheffer1(k1_robbins3)
& v4_sheffer1(k1_robbins3)
& v1_robbins3(k1_robbins3)
& v2_robbins3(k1_robbins3) ) ).
fof(rc5_robbins3,axiom,
? [A] :
( l1_robbins3(A)
& ~ v3_struct_0(A) ) ).
fof(rc6_robbins3,axiom,
? [A] :
( l2_robbins3(A)
& ~ v3_struct_0(A) ) ).
fof(rc7_robbins3,axiom,
? [A] :
( l3_robbins3(A)
& ~ v3_struct_0(A) ) ).
fof(fc2_robbins3,axiom,
( ~ v3_struct_0(k1_robbins3)
& v4_lattices(k1_robbins3)
& v5_lattices(k1_robbins3)
& v6_lattices(k1_robbins3)
& v7_lattices(k1_robbins3)
& v8_lattices(k1_robbins3)
& v9_lattices(k1_robbins3)
& v10_lattices(k1_robbins3)
& v11_lattices(k1_robbins3)
& v12_lattices(k1_robbins3)
& v13_lattices(k1_robbins3)
& v14_lattices(k1_robbins3)
& v15_lattices(k1_robbins3)
& v16_lattices(k1_robbins3)
& v17_lattices(k1_robbins3)
& v2_orders_2(k1_robbins3)
& v3_orders_2(k1_robbins3)
& v4_orders_2(k1_robbins3)
& v1_lattice3(k1_robbins3)
& v2_lattice3(k1_robbins3)
& v3_lattice3(k1_robbins3)
& v3_realset2(k1_robbins3)
& v1_yellow_0(k1_robbins3)
& v2_yellow_0(k1_robbins3)
& v3_yellow_0(k1_robbins3)
& v1_sheffer1(k1_robbins3)
& v2_sheffer1(k1_robbins3)
& v3_sheffer1(k1_robbins3)
& v4_sheffer1(k1_robbins3)
& v1_robbins3(k1_robbins3)
& v2_robbins3(k1_robbins3) ) ).
fof(rc8_robbins3,axiom,
? [A] :
( l3_robbins3(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ).
fof(fc3_robbins3,axiom,
( ~ v3_struct_0(k1_robbins3)
& v4_lattices(k1_robbins3)
& v5_lattices(k1_robbins3)
& v6_lattices(k1_robbins3)
& v7_lattices(k1_robbins3)
& v8_lattices(k1_robbins3)
& v9_lattices(k1_robbins3)
& v10_lattices(k1_robbins3)
& v11_lattices(k1_robbins3)
& v12_lattices(k1_robbins3)
& v13_lattices(k1_robbins3)
& v14_lattices(k1_robbins3)
& v15_lattices(k1_robbins3)
& v16_lattices(k1_robbins3)
& v17_lattices(k1_robbins3)
& v2_orders_2(k1_robbins3)
& v3_orders_2(k1_robbins3)
& v4_orders_2(k1_robbins3)
& v1_lattice3(k1_robbins3)
& v2_lattice3(k1_robbins3)
& v3_lattice3(k1_robbins3)
& v3_realset2(k1_robbins3)
& v1_yellow_0(k1_robbins3)
& v2_yellow_0(k1_robbins3)
& v3_yellow_0(k1_robbins3)
& v1_sheffer1(k1_robbins3)
& v2_sheffer1(k1_robbins3)
& v3_sheffer1(k1_robbins3)
& v4_sheffer1(k1_robbins3)
& v1_robbins3(k1_robbins3)
& v2_robbins3(k1_robbins3)
& v3_robbins3(k1_robbins3) ) ).
fof(rc9_robbins3,axiom,
? [A] :
( l3_robbins3(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v1_robbins3(A)
& v2_robbins3(A) ) ).
fof(rc10_robbins3,axiom,
? [A] :
( l4_robbins3(A)
& v7_robbins3(A) ) ).
fof(fc4_robbins3,axiom,
( ~ v3_struct_0(k2_robbins1)
& v4_lattices(k2_robbins1)
& v5_lattices(k2_robbins1)
& v6_lattices(k2_robbins1)
& v7_lattices(k2_robbins1)
& v8_lattices(k2_robbins1)
& v9_lattices(k2_robbins1)
& v10_lattices(k2_robbins1)
& v11_lattices(k2_robbins1)
& v12_lattices(k2_robbins1)
& v13_lattices(k2_robbins1)
& v14_lattices(k2_robbins1)
& v15_lattices(k2_robbins1)
& v16_lattices(k2_robbins1)
& v17_lattices(k2_robbins1)
& v3_robbins1(k2_robbins1)
& v4_robbins1(k2_robbins1)
& v5_robbins1(k2_robbins1)
& v6_robbins1(k2_robbins1)
& v7_robbins1(k2_robbins1)
& v9_robbins1(k2_robbins1)
& v3_realset2(k2_robbins1)
& v1_sheffer1(k2_robbins1)
& v2_sheffer1(k2_robbins1)
& v3_sheffer1(k2_robbins1)
& v4_sheffer1(k2_robbins1)
& v1_robbins3(k2_robbins1)
& v2_robbins3(k2_robbins1)
& v8_robbins3(k2_robbins1)
& v9_robbins3(k2_robbins1) ) ).
fof(fc5_robbins3,axiom,
( ~ v3_struct_0(k3_robbins3)
& v4_lattices(k3_robbins3)
& v5_lattices(k3_robbins3)
& v6_lattices(k3_robbins3)
& v7_lattices(k3_robbins3)
& v8_lattices(k3_robbins3)
& v9_lattices(k3_robbins3)
& v10_lattices(k3_robbins3)
& v11_lattices(k3_robbins3)
& v12_lattices(k3_robbins3)
& v13_lattices(k3_robbins3)
& v14_lattices(k3_robbins3)
& v15_lattices(k3_robbins3)
& v16_lattices(k3_robbins3)
& v17_lattices(k3_robbins3)
& v3_realset2(k3_robbins3)
& v1_sheffer1(k3_robbins3)
& v2_sheffer1(k3_robbins3)
& v3_sheffer1(k3_robbins3)
& v4_sheffer1(k3_robbins3)
& v1_robbins3(k3_robbins3)
& v2_robbins3(k3_robbins3) ) ).
fof(fc6_robbins3,axiom,
( ~ v3_struct_0(k3_robbins3)
& v4_lattices(k3_robbins3)
& v5_lattices(k3_robbins3)
& v6_lattices(k3_robbins3)
& v7_lattices(k3_robbins3)
& v8_lattices(k3_robbins3)
& v9_lattices(k3_robbins3)
& v10_lattices(k3_robbins3)
& v11_lattices(k3_robbins3)
& v12_lattices(k3_robbins3)
& v13_lattices(k3_robbins3)
& v14_lattices(k3_robbins3)
& v15_lattices(k3_robbins3)
& v16_lattices(k3_robbins3)
& v17_lattices(k3_robbins3)
& v2_orders_2(k3_robbins3)
& v3_orders_2(k3_robbins3)
& v4_orders_2(k3_robbins3)
& v1_lattice3(k3_robbins3)
& v2_lattice3(k3_robbins3)
& v3_lattice3(k3_robbins3)
& v7_oposet_1(k3_robbins3)
& v9_oposet_1(k3_robbins3)
& v13_oposet_1(k3_robbins3)
& v14_oposet_1(k3_robbins3)
& v3_realset2(k3_robbins3)
& v1_yellow_0(k3_robbins3)
& v2_yellow_0(k3_robbins3)
& v3_yellow_0(k3_robbins3)
& v1_sheffer1(k3_robbins3)
& v2_sheffer1(k3_robbins3)
& v3_sheffer1(k3_robbins3)
& v4_sheffer1(k3_robbins3)
& v1_robbins3(k3_robbins3)
& v2_robbins3(k3_robbins3) ) ).
fof(fc7_robbins3,axiom,
( ~ v3_struct_0(k3_robbins3)
& v4_lattices(k3_robbins3)
& v5_lattices(k3_robbins3)
& v6_lattices(k3_robbins3)
& v7_lattices(k3_robbins3)
& v8_lattices(k3_robbins3)
& v9_lattices(k3_robbins3)
& v10_lattices(k3_robbins3)
& v11_lattices(k3_robbins3)
& v12_lattices(k3_robbins3)
& v13_lattices(k3_robbins3)
& v14_lattices(k3_robbins3)
& v15_lattices(k3_robbins3)
& v16_lattices(k3_robbins3)
& v17_lattices(k3_robbins3)
& v2_orders_2(k3_robbins3)
& v3_orders_2(k3_robbins3)
& v4_orders_2(k3_robbins3)
& v1_lattice3(k3_robbins3)
& v2_lattice3(k3_robbins3)
& v3_lattice3(k3_robbins3)
& v7_oposet_1(k3_robbins3)
& v9_oposet_1(k3_robbins3)
& v13_oposet_1(k3_robbins3)
& v14_oposet_1(k3_robbins3)
& v3_realset2(k3_robbins3)
& v1_yellow_0(k3_robbins3)
& v2_yellow_0(k3_robbins3)
& v3_yellow_0(k3_robbins3)
& v1_sheffer1(k3_robbins3)
& v2_sheffer1(k3_robbins3)
& v3_sheffer1(k3_robbins3)
& v4_sheffer1(k3_robbins3)
& v1_robbins3(k3_robbins3)
& v2_robbins3(k3_robbins3)
& v8_robbins3(k3_robbins3)
& v9_robbins3(k3_robbins3) ) ).
fof(rc11_robbins3,axiom,
? [A] :
( l3_robbins1(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v9_robbins1(A)
& v1_robbins3(A)
& v2_robbins3(A)
& v8_robbins3(A)
& v9_robbins3(A) ) ).
fof(cc4_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( m2_robbins3(B,A)
=> ~ v3_struct_0(B) ) ) ).
fof(cc5_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v7_lattices(B) ) ) ) ).
fof(cc6_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v5_lattices(B) ) ) ) ).
fof(cc7_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v6_lattices(B) ) ) ) ).
fof(cc8_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v4_lattices(B) ) ) ) ).
fof(cc9_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v9_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v9_lattices(B) ) ) ) ).
fof(cc10_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v8_lattices(A)
& l3_lattices(A) )
=> ! [B] :
( m2_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v8_lattices(B) ) ) ) ).
fof(rc12_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ? [B] :
( m2_robbins3(B,A)
& ~ v3_struct_0(B)
& v4_lattices(B)
& v5_lattices(B)
& v6_lattices(B)
& v7_lattices(B)
& v8_lattices(B)
& v9_lattices(B)
& v10_lattices(B)
& v1_robbins3(B)
& v2_robbins3(B)
& v10_robbins3(B)
& v11_robbins3(B) ) ) ).
fof(rc13_robbins3,axiom,
? [A] :
( l3_robbins3(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(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)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v1_sheffer1(A)
& v2_sheffer1(A)
& v3_sheffer1(A)
& v4_sheffer1(A)
& v1_robbins3(A)
& v2_robbins3(A) ) ).
fof(rc14_robbins3,axiom,
? [A] :
( l4_robbins3(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v3_lattice3(A)
& v7_oposet_1(A)
& v9_oposet_1(A)
& v13_oposet_1(A)
& v14_oposet_1(A)
& v3_realset2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A)
& v1_sheffer1(A)
& v2_sheffer1(A)
& v3_sheffer1(A)
& v4_sheffer1(A)
& v1_robbins3(A)
& v2_robbins3(A) ) ).
fof(rc15_robbins3,axiom,
? [A] :
( l1_oposet_1(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)
& v7_oposet_1(A)
& v9_oposet_1(A)
& v13_oposet_1(A)
& v14_oposet_1(A)
& v3_realset2(A)
& v1_yellow_0(A)
& v2_yellow_0(A)
& v3_yellow_0(A) ) ).
fof(cc11_robbins3,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v7_robbins1(A)
& v9_robbins1(A)
& v8_robbins3(A)
& v9_robbins3(A) ) ) ) ).
fof(cc12_robbins3,axiom,
! [A] :
( l1_oposet_1(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_oposet_1(A)
& v7_oposet_1(A)
& v9_oposet_1(A)
& v13_oposet_1(A)
& v14_oposet_1(A)
& v15_oposet_1(A)
& v19_oposet_1(A) ) ) ) ).
fof(cc13_robbins3,axiom,
! [A] :
( l3_robbins3(A)
=> ( ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v3_realset2(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A)
& v10_robbins3(A)
& v11_robbins3(A) ) ) ) ).
fof(rc16_robbins3,axiom,
? [A] :
( l4_robbins3(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v2_orders_2(A)
& v3_orders_2(A)
& v4_orders_2(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v9_robbins1(A)
& v3_oposet_1(A)
& v7_oposet_1(A)
& v9_oposet_1(A)
& v13_oposet_1(A)
& v14_oposet_1(A)
& v15_oposet_1(A)
& v19_oposet_1(A)
& v1_robbins3(A)
& v2_robbins3(A)
& v10_robbins3(A)
& v11_robbins3(A) ) ).
fof(rc17_robbins3,axiom,
? [A] :
( l3_robbins3(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v1_robbins3(A)
& v2_robbins3(A)
& v10_robbins3(A)
& v11_robbins3(A) ) ).
fof(cc14_robbins3,axiom,
! [A] :
( l3_robbins3(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v10_robbins3(A) )
=> ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A) ) ) ) ).
fof(cc15_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ~ v3_struct_0(B) ) ) ).
fof(cc16_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v7_lattices(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v7_lattices(B) ) ) ) ).
fof(cc17_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_lattices(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v5_lattices(B) ) ) ) ).
fof(cc18_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v6_lattices(B) ) ) ) ).
fof(cc19_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v4_lattices(B) ) ) ) ).
fof(cc20_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v8_lattices(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v8_lattices(B) ) ) ) ).
fof(cc21_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v9_lattices(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v9_lattices(B) ) ) ) ).
fof(cc22_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v9_robbins3(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v9_robbins3(B) ) ) ) ).
fof(rc18_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v9_robbins1(A)
& v8_robbins3(A)
& v9_robbins3(A)
& l3_robbins1(A) )
=> ? [B] :
( m3_robbins3(B,A)
& ~ v3_struct_0(B)
& v4_lattices(B)
& v5_lattices(B)
& v6_lattices(B)
& v7_lattices(B)
& v8_lattices(B)
& v9_lattices(B)
& v10_lattices(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v1_robbins3(B)
& v2_robbins3(B)
& v9_robbins3(B)
& v10_robbins3(B)
& v11_robbins3(B) ) ) ).
fof(rc19_robbins3,axiom,
? [A] :
( l4_robbins3(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v6_lattices(A)
& v7_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_lattices(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v7_robbins1(A)
& v9_robbins1(A)
& v1_robbins3(A)
& v2_robbins3(A)
& v8_robbins3(A)
& v9_robbins3(A)
& v10_robbins3(A) ) ).
fof(cc23_robbins3,axiom,
! [A] :
( l3_robbins3(A)
=> ( ( ~ v3_struct_0(A)
& v6_lattices(A)
& v8_lattices(A)
& v9_lattices(A)
& v10_robbins3(A) )
=> ( ~ v3_struct_0(A)
& v2_orders_2(A) ) ) ) ).
fof(cc24_robbins3,axiom,
! [A] :
( l3_robbins3(A)
=> ( ( ~ v3_struct_0(A)
& v5_lattices(A)
& v10_robbins3(A) )
=> ( ~ v3_struct_0(A)
& v3_orders_2(A) ) ) ) ).
fof(cc25_robbins3,axiom,
! [A] :
( l3_robbins3(A)
=> ( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v10_robbins3(A) )
=> ( ~ v3_struct_0(A)
& v4_orders_2(A) ) ) ) ).
fof(cc26_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v9_robbins1(A)
& v8_robbins3(A)
& v9_robbins3(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v4_lattices(B)
& v5_lattices(B)
& v6_lattices(B)
& v7_lattices(B)
& v8_lattices(B)
& v9_lattices(B)
& v10_lattices(B)
& v1_robbins3(B)
& v2_robbins3(B)
& v8_robbins3(B)
& v9_robbins3(B) ) ) ) ).
fof(cc27_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v9_robbins1(A)
& v8_robbins3(A)
& v9_robbins3(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( ~ v3_struct_0(B)
& v4_lattices(B)
& v5_lattices(B)
& v6_lattices(B)
& v7_lattices(B)
& v8_lattices(B)
& v9_lattices(B)
& v10_lattices(B)
& v9_robbins1(B)
& v1_robbins3(B)
& v2_robbins3(B)
& v8_robbins3(B)
& v9_robbins3(B) ) ) ) ).
fof(cc28_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v9_robbins1(A)
& v8_robbins3(A)
& v9_robbins3(A)
& l3_robbins1(A) )
=> ! [B] :
( m3_robbins3(B,A)
=> ( v10_robbins3(B)
=> ( ~ v3_struct_0(B)
& v4_lattices(B)
& v5_lattices(B)
& v6_lattices(B)
& v7_lattices(B)
& v8_lattices(B)
& v9_lattices(B)
& v10_lattices(B)
& v2_orders_2(B)
& v3_orders_2(B)
& v4_orders_2(B)
& v1_lattice3(B)
& v2_lattice3(B)
& v9_robbins1(B)
& v7_oposet_1(B)
& v9_oposet_1(B)
& v13_oposet_1(B)
& v14_oposet_1(B)
& v21_oposet_1(B)
& v1_robbins3(B)
& v2_robbins3(B)
& v8_robbins3(B)
& v9_robbins3(B)
& v10_robbins3(B) ) ) ) ) ).
fof(cc29_robbins3,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& v7_robbins1(A) )
=> ( ~ v3_struct_0(A)
& v9_robbins1(A)
& v8_robbins3(A)
& v9_robbins3(A) ) ) ) ).
fof(d1_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_lattices(A) )
=> ( v1_robbins3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_lattices(A,B,k1_lattices(A,C,D)) = k1_lattices(A,C,k1_lattices(A,B,D)) ) ) ) ) ) ).
fof(d2_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lattices(A) )
=> ( v2_robbins3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k2_lattices(A,B,k2_lattices(A,C,D)) = k2_lattices(A,C,k2_lattices(A,B,D)) ) ) ) ) ) ).
fof(d3_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( v3_robbins3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_lattices(A,B,k2_lattices(A,B,C)) = B ) ) ) ) ).
fof(t1_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( ( v2_robbins3(A)
& v1_robbins3(A)
& v3_robbins3(A)
& v9_lattices(A) )
=> ( v5_sheffer1(A)
& v6_robbins1(A) ) ) ) ).
fof(t2_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( ( v2_robbins3(A)
& v1_robbins3(A)
& v3_robbins3(A)
& v9_lattices(A) )
=> ( v6_lattices(A)
& v4_lattices(A) ) ) ) ).
fof(t3_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( ( v2_robbins3(A)
& v1_robbins3(A)
& v3_robbins3(A)
& v9_lattices(A) )
=> v8_lattices(A) ) ) ).
fof(t4_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( ( v2_robbins3(A)
& v1_robbins3(A)
& v3_robbins3(A)
& v9_lattices(A) )
=> ( v7_lattices(A)
& v5_lattices(A) ) ) ) ).
fof(t5_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ( v10_lattices(A)
<=> ( v2_robbins3(A)
& v1_robbins3(A)
& v3_robbins3(A)
& v9_lattices(A) ) ) ) ).
fof(t6_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_oposet_1(A)
& l1_oposet_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,k3_robbins1(A,B)) = B ) ) ).
fof(t7_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v14_oposet_1(A)
& v19_oposet_1(A)
& l1_oposet_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> r3_orders_2(A,k3_robbins1(A,C),k3_robbins1(A,B)) ) ) ) ) ).
fof(d4_robbins3,axiom,
k1_robbins3 = g3_robbins3(k1_tarski(k1_xboole_0),k2_midsp_1,k2_midsp_1,k6_partfun1(k1_tarski(k1_xboole_0))) ).
fof(t8_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_orders_2(A) )
=> ( ( r1_relat_2(u1_orders_2(A),u1_struct_0(A))
& v4_relat_2(u1_orders_2(A))
& v8_relat_2(u1_orders_2(A)) )
=> ( v2_orders_2(A)
& v4_orders_2(A)
& v3_orders_2(A) ) ) ) ).
fof(d5_robbins3,axiom,
k3_robbins3 = g4_robbins3(k1_tarski(k1_xboole_0),k2_midsp_1,k2_midsp_1,k6_partfun1(k1_tarski(k1_xboole_0)),k7_vectsp_2) ).
fof(d6_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_robbins1(A) )
=> ( v8_robbins3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,k3_robbins1(A,B)) = B ) ) ) ).
fof(d7_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( v9_robbins3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_lattices(A,B,k3_robbins1(A,B)) = k1_lattices(A,C,k3_robbins1(A,C)) ) ) ) ) ).
fof(t9_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
& v4_lattices(A) )
=> v4_lattices(B) ) ) ) ).
fof(t10_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
& v6_lattices(A) )
=> v6_lattices(B) ) ) ) ).
fof(t11_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
& v5_lattices(A) )
=> v5_lattices(B) ) ) ) ).
fof(t12_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
& v7_lattices(A) )
=> v7_lattices(B) ) ) ) ).
fof(t13_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
& v9_lattices(A) )
=> v9_lattices(B) ) ) ) ).
fof(t14_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
& v8_lattices(A) )
=> v8_lattices(B) ) ) ) ).
fof(t15_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_lattices(B) )
=> ( ( g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) = g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B))
& v10_lattices(A) )
=> v10_lattices(B) ) ) ) ).
fof(t16_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_lattices(B) )
=> ( g2_lattices(u1_struct_0(A),u2_lattices(A)) = g2_lattices(u1_struct_0(B),u2_lattices(B))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( C = E
& D = F )
=> k1_lattices(A,C,D) = k1_lattices(B,E,F) ) ) ) ) ) ) ) ) ).
fof(t17_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_lattices(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_lattices(B) )
=> ( g1_lattices(u1_struct_0(A),u1_lattices(A)) = g1_lattices(u1_struct_0(B),u1_lattices(B))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(B))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(B))
=> ( ( C = E
& D = F )
=> k2_lattices(A,C,D) = k2_lattices(B,E,F) ) ) ) ) ) ) ) ) ).
fof(t18_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_robbins1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l1_robbins1(B) )
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(B))
=> ( ( u1_robbins1(A) = u1_robbins1(B)
& C = D )
=> k3_robbins1(A,C) = k3_robbins1(B,D) ) ) ) ) ) ).
fof(t19_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l2_robbins1(B) )
=> ( ( g2_robbins1(u1_struct_0(A),u2_lattices(A),u1_robbins1(A)) = g2_robbins1(u1_struct_0(B),u2_lattices(B),u1_robbins1(B))
& v9_robbins3(A) )
=> v9_robbins3(B) ) ) ) ).
fof(t20_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_robbins1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_robbins1(B) )
=> ( ( g3_robbins1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_robbins1(A)) = g3_robbins1(u1_struct_0(B),u2_lattices(B),u1_lattices(B),u1_robbins1(B))
& v9_robbins1(A) )
=> v9_robbins1(B) ) ) ) ).
fof(t21_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_robbins1(A) )
=> ! [B] :
( ( ~ v3_struct_0(B)
& l3_robbins1(B) )
=> ( ( g3_robbins1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_robbins1(A)) = g3_robbins1(u1_struct_0(B),u2_lattices(B),u1_lattices(B),u1_robbins1(B))
& v8_robbins3(A) )
=> v8_robbins3(B) ) ) ) ).
fof(d8_robbins3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( l3_robbins3(B)
=> ( m1_robbins3(B,A)
<=> g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(A),u1_orders_2(A)) ) ) ) ).
fof(d9_robbins3,axiom,
! [A] :
( l3_lattices(A)
=> ! [B] :
( l3_robbins3(B)
=> ( m2_robbins3(B,A)
<=> g3_lattices(u1_struct_0(B),u2_lattices(B),u1_lattices(B)) = g3_lattices(u1_struct_0(A),u2_lattices(A),u1_lattices(A)) ) ) ) ).
fof(d10_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_robbins3(A) )
=> ( v10_robbins3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> k1_lattices(A,B,C) = C ) ) ) ) ) ).
fof(d11_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins3(A) )
=> ( v11_robbins3(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> k2_lattices(A,B,C) = B ) ) ) ) ) ).
fof(t22_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_robbins3(A)
& l3_robbins3(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r1_orders_2(A,B,C)
<=> r1_lattices(A,B,C) ) ) ) ) ).
fof(t23_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v10_robbins3(A)
& l3_robbins3(A) )
=> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(A) ) ).
fof(d12_robbins3,axiom,
! [A] :
( l3_robbins1(A)
=> ! [B] :
( l4_robbins3(B)
=> ( m3_robbins3(B,A)
<=> g3_robbins1(u1_struct_0(B),u2_lattices(B),u1_lattices(B),u1_robbins1(B)) = g3_robbins1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_robbins1(A)) ) ) ) ).
fof(t24_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v14_oposet_1(A)
& l1_oposet_1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( r3_orders_2(A,B,C)
=> ( C = k10_lattice3(A,B,C)
& B = k11_lattice3(A,B,C) ) ) ) ) ) ).
fof(t25_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v10_robbins3(A)
& l4_robbins3(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k10_lattice3(A,B,C) = k5_robbins3(A,B,C) ) ) ) ).
fof(t26_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v10_robbins3(A)
& l4_robbins3(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k11_lattice3(A,B,C) = k4_robbins3(A,B,C) ) ) ) ).
fof(t27_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v1_lattice3(A)
& v2_lattice3(A)
& v14_oposet_1(A)
& v19_oposet_1(A)
& v10_robbins3(A)
& v11_robbins3(A)
& l4_robbins3(A) )
=> v9_robbins1(A) ) ).
fof(t28_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l4_robbins3(A) )
=> ( ( v8_robbins3(A)
& v9_robbins3(A)
& v9_robbins1(A)
& v10_lattices(A)
& v10_robbins3(A) )
=> ( v21_oposet_1(A)
& v14_oposet_1(A) ) ) ) ).
fof(t29_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v9_robbins1(A)
& v8_robbins3(A)
& v9_robbins3(A)
& l3_robbins1(A) )
=> ! [B] :
( ( v10_robbins3(B)
& m3_robbins3(B,A) )
=> v21_oposet_1(B) ) ) ).
fof(t30_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_robbins1(A) )
=> ( ( v17_lattices(A)
& v7_robbins1(A)
& v10_lattices(A) )
=> ( ~ v3_struct_0(A)
& v10_lattices(A)
& v9_robbins1(A)
& v8_robbins3(A)
& v9_robbins3(A)
& l3_robbins1(A) ) ) ) ).
fof(dt_m1_robbins3,axiom,
! [A] :
( l1_orders_2(A)
=> ! [B] :
( m1_robbins3(B,A)
=> l3_robbins3(B) ) ) ).
fof(existence_m1_robbins3,axiom,
! [A] :
( l1_orders_2(A)
=> ? [B] : m1_robbins3(B,A) ) ).
fof(dt_m2_robbins3,axiom,
! [A] :
( l3_lattices(A)
=> ! [B] :
( m2_robbins3(B,A)
=> l3_robbins3(B) ) ) ).
fof(existence_m2_robbins3,axiom,
! [A] :
( l3_lattices(A)
=> ? [B] : m2_robbins3(B,A) ) ).
fof(dt_m3_robbins3,axiom,
! [A] :
( l3_robbins1(A)
=> ! [B] :
( m3_robbins3(B,A)
=> l4_robbins3(B) ) ) ).
fof(existence_m3_robbins3,axiom,
! [A] :
( l3_robbins1(A)
=> ? [B] : m3_robbins3(B,A) ) ).
fof(dt_l1_robbins3,axiom,
! [A] :
( l1_robbins3(A)
=> ( l2_lattices(A)
& l1_orders_2(A) ) ) ).
fof(existence_l1_robbins3,axiom,
? [A] : l1_robbins3(A) ).
fof(dt_l2_robbins3,axiom,
! [A] :
( l2_robbins3(A)
=> ( l1_lattices(A)
& l1_orders_2(A) ) ) ).
fof(existence_l2_robbins3,axiom,
? [A] : l2_robbins3(A) ).
fof(dt_l3_robbins3,axiom,
! [A] :
( l3_robbins3(A)
=> ( l2_robbins3(A)
& l1_robbins3(A)
& l3_lattices(A) ) ) ).
fof(existence_l3_robbins3,axiom,
? [A] : l3_robbins3(A) ).
fof(dt_l4_robbins3,axiom,
! [A] :
( l4_robbins3(A)
=> ( l3_robbins3(A)
& l3_robbins1(A)
& l1_oposet_1(A) ) ) ).
fof(existence_l4_robbins3,axiom,
? [A] : l4_robbins3(A) ).
fof(abstractness_v4_robbins3,axiom,
! [A] :
( l1_robbins3(A)
=> ( v4_robbins3(A)
=> A = g1_robbins3(u1_struct_0(A),u2_lattices(A),u1_orders_2(A)) ) ) ).
fof(abstractness_v5_robbins3,axiom,
! [A] :
( l2_robbins3(A)
=> ( v5_robbins3(A)
=> A = g2_robbins3(u1_struct_0(A),u1_lattices(A),u1_orders_2(A)) ) ) ).
fof(abstractness_v6_robbins3,axiom,
! [A] :
( l3_robbins3(A)
=> ( v6_robbins3(A)
=> A = g3_robbins3(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_orders_2(A)) ) ) ).
fof(abstractness_v7_robbins3,axiom,
! [A] :
( l4_robbins3(A)
=> ( v7_robbins3(A)
=> A = g4_robbins3(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_orders_2(A),u1_robbins1(A)) ) ) ).
fof(dt_k1_robbins3,axiom,
l3_robbins3(k1_robbins3) ).
fof(dt_k2_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> ( v1_relat_2(k2_robbins3(A))
& v4_relat_2(k2_robbins3(A))
& v8_relat_2(k2_robbins3(A))
& v1_partfun1(k2_robbins3(A),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(k2_robbins3(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(redefinition_k2_robbins3,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& l3_lattices(A) )
=> k2_robbins3(A) = k9_filter_1(A) ) ).
fof(dt_k3_robbins3,axiom,
l4_robbins3(k3_robbins3) ).
fof(dt_k4_robbins3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l1_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_robbins3(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k4_robbins3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l1_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k4_robbins3(A,B,C) = k4_robbins3(A,C,B) ) ).
fof(redefinition_k4_robbins3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v6_lattices(A)
& l1_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k4_robbins3(A,B,C) = k2_lattices(A,B,C) ) ).
fof(dt_k5_robbins3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k5_robbins3(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k5_robbins3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k5_robbins3(A,B,C) = k5_robbins3(A,C,B) ) ).
fof(redefinition_k5_robbins3,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_lattices(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k5_robbins3(A,B,C) = k1_lattices(A,B,C) ) ).
fof(dt_g1_robbins3,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,A,A) )
=> ( v4_robbins3(g1_robbins3(A,B,C))
& l1_robbins3(g1_robbins3(A,B,C)) ) ) ).
fof(free_g1_robbins3,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,A,A) )
=> ! [D,E,F] :
( g1_robbins3(A,B,C) = g1_robbins3(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(dt_g2_robbins3,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,A,A) )
=> ( v5_robbins3(g2_robbins3(A,B,C))
& l2_robbins3(g2_robbins3(A,B,C)) ) ) ).
fof(free_g2_robbins3,axiom,
! [A,B,C] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,A,A) )
=> ! [D,E,F] :
( g2_robbins3(A,B,C) = g2_robbins3(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(dt_g3_robbins3,axiom,
! [A,B,C,D] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(D,A,A) )
=> ( v6_robbins3(g3_robbins3(A,B,C,D))
& l3_robbins3(g3_robbins3(A,B,C,D)) ) ) ).
fof(free_g3_robbins3,axiom,
! [A,B,C,D] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(D,A,A) )
=> ! [E,F,G,H] :
( g3_robbins3(A,B,C,D) = g3_robbins3(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
fof(dt_g4_robbins3,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(D,A,A)
& v1_funct_1(E)
& v1_funct_2(E,A,A)
& m1_relset_1(E,A,A) )
=> ( v7_robbins3(g4_robbins3(A,B,C,D,E))
& l4_robbins3(g4_robbins3(A,B,C,D,E)) ) ) ).
fof(free_g4_robbins3,axiom,
! [A,B,C,D,E] :
( ( v1_funct_1(B)
& v1_funct_2(B,k2_zfmisc_1(A,A),A)
& m1_relset_1(B,k2_zfmisc_1(A,A),A)
& v1_funct_1(C)
& v1_funct_2(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(C,k2_zfmisc_1(A,A),A)
& m1_relset_1(D,A,A)
& v1_funct_1(E)
& v1_funct_2(E,A,A)
& m1_relset_1(E,A,A) )
=> ! [F,G,H,I,J] :
( g4_robbins3(A,B,C,D,E) = g4_robbins3(F,G,H,I,J)
=> ( A = F
& B = G
& C = H
& D = I
& E = J ) ) ) ).
%------------------------------------------------------------------------------