SET007 Axioms: SET007+690.ax
%------------------------------------------------------------------------------
% File : SET007+690 : TPTP v9.0.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : Robbins Algebras vs. Boolean Algebras
% 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 : robbins1 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 160 ( 5 unt; 0 def)
% Number of atoms : 1192 ( 127 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 1188 ( 156 ~; 0 |; 741 &)
% ( 10 <=>; 281 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 10 ( 1 avg)
% Number of predicates : 38 ( 37 usr; 0 prp; 1-3 aty)
% Number of functors : 37 ( 37 usr; 5 con; 0-4 aty)
% Number of variables : 328 ( 305 !; 23 ?)
% 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(rc1_robbins1,axiom,
? [A] :
( l1_robbins1(A)
& v1_robbins1(A) ) ).
fof(rc2_robbins1,axiom,
? [A] :
( l2_robbins1(A)
& v2_robbins1(A) ) ).
fof(rc3_robbins1,axiom,
? [A] :
( l3_robbins1(A)
& v3_robbins1(A) ) ).
fof(fc1_robbins1,axiom,
( ~ v3_struct_0(k1_robbins1)
& v3_realset2(k1_robbins1)
& v2_robbins1(k1_robbins1) ) ).
fof(fc2_robbins1,axiom,
( ~ v3_struct_0(k2_robbins1)
& v3_realset2(k2_robbins1)
& v3_robbins1(k2_robbins1) ) ).
fof(rc4_robbins1,axiom,
? [A] :
( l3_robbins1(A)
& ~ v3_struct_0(A)
& v3_realset2(A)
& v3_robbins1(A) ) ).
fof(rc5_robbins1,axiom,
? [A] :
( l2_robbins1(A)
& ~ v3_struct_0(A)
& v3_realset2(A)
& v2_robbins1(A) ) ).
fof(fc3_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v3_realset2(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(g1_robbins1(u1_struct_0(A),u1_robbins1(A)))
& v3_realset2(g1_robbins1(u1_struct_0(A),u1_robbins1(A)))
& v1_robbins1(g1_robbins1(u1_struct_0(A),u1_robbins1(A))) ) ) ).
fof(rc6_robbins1,axiom,
? [A] :
( l1_robbins1(A)
& ~ v3_struct_0(A)
& v3_realset2(A)
& v1_robbins1(A) ) ).
fof(fc4_robbins1,axiom,
( ~ v3_struct_0(k1_robbins1)
& v4_lattices(k1_robbins1)
& v5_lattices(k1_robbins1)
& v3_realset2(k1_robbins1)
& v2_robbins1(k1_robbins1)
& v4_robbins1(k1_robbins1)
& v5_robbins1(k1_robbins1)
& v6_robbins1(k1_robbins1) ) ).
fof(fc5_robbins1,axiom,
( ~ v3_struct_0(k2_robbins1)
& v4_lattices(k2_robbins1)
& v5_lattices(k2_robbins1)
& v3_realset2(k2_robbins1)
& v3_robbins1(k2_robbins1)
& v4_robbins1(k2_robbins1)
& v5_robbins1(k2_robbins1) ) ).
fof(fc6_robbins1,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)
& v3_realset2(k2_robbins1)
& v3_robbins1(k2_robbins1)
& v4_robbins1(k2_robbins1)
& v5_robbins1(k2_robbins1) ) ).
fof(rc7_robbins1,axiom,
? [A] :
( l2_robbins1(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v2_robbins1(A)
& v4_robbins1(A)
& v5_robbins1(A)
& v6_robbins1(A) ) ).
fof(rc8_robbins1,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)
& v3_robbins1(A)
& v4_robbins1(A)
& v5_robbins1(A) ) ).
fof(cc1_robbins1,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A) )
=> ( ~ v3_struct_0(A)
& v14_lattices(A) ) ) ) ).
fof(cc2_robbins1,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A) )
=> ( ~ v3_struct_0(A)
& v6_robbins1(A) ) ) ) ).
fof(fc7_robbins1,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_realset2(k2_robbins1)
& v3_robbins1(k2_robbins1)
& v4_robbins1(k2_robbins1)
& v5_robbins1(k2_robbins1)
& v6_robbins1(k2_robbins1)
& v7_robbins1(k2_robbins1) ) ).
fof(rc9_robbins1,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)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(A)
& v3_robbins1(A)
& v7_robbins1(A) ) ).
fof(fc8_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A)) ) ) ).
fof(fc9_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v4_lattices(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A)) ) ) ).
fof(fc10_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_lattices(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v5_lattices(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A)) ) ) ).
fof(fc11_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v4_lattices(k8_robbins1(A))
& v5_lattices(k8_robbins1(A))
& v6_lattices(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A)) ) ) ).
fof(fc12_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v4_lattices(k8_robbins1(A))
& v5_lattices(k8_robbins1(A))
& v6_lattices(k8_robbins1(A))
& v7_lattices(k8_robbins1(A))
& v8_lattices(k8_robbins1(A))
& v9_lattices(k8_robbins1(A))
& v10_lattices(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A)) ) ) ).
fof(fc13_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A))
& v5_robbins1(k8_robbins1(A)) ) ) ).
fof(fc14_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v4_lattices(k8_robbins1(A))
& v5_lattices(k8_robbins1(A))
& v6_lattices(k8_robbins1(A))
& v7_lattices(k8_robbins1(A))
& v8_lattices(k8_robbins1(A))
& v9_lattices(k8_robbins1(A))
& v10_lattices(k8_robbins1(A))
& v13_lattices(k8_robbins1(A))
& v14_lattices(k8_robbins1(A))
& v15_lattices(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A))
& v5_robbins1(k8_robbins1(A))
& v6_robbins1(k8_robbins1(A)) ) ) ).
fof(fc15_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v4_lattices(k8_robbins1(A))
& v5_lattices(k8_robbins1(A))
& v6_lattices(k8_robbins1(A))
& v7_lattices(k8_robbins1(A))
& v8_lattices(k8_robbins1(A))
& v9_lattices(k8_robbins1(A))
& v10_lattices(k8_robbins1(A))
& v11_lattices(k8_robbins1(A))
& v12_lattices(k8_robbins1(A))
& v13_lattices(k8_robbins1(A))
& v14_lattices(k8_robbins1(A))
& v15_lattices(k8_robbins1(A))
& v16_lattices(k8_robbins1(A))
& v17_lattices(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A))
& v5_robbins1(k8_robbins1(A))
& v6_robbins1(k8_robbins1(A)) ) ) ).
fof(fc16_robbins1,axiom,
( ~ v3_struct_0(k1_robbins1)
& v4_lattices(k1_robbins1)
& v5_lattices(k1_robbins1)
& v14_lattices(k1_robbins1)
& v3_realset2(k1_robbins1)
& v2_robbins1(k1_robbins1)
& v4_robbins1(k1_robbins1)
& v5_robbins1(k1_robbins1)
& v6_robbins1(k1_robbins1)
& v8_robbins1(k1_robbins1) ) ).
fof(cc3_robbins1,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& v8_robbins1(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v14_lattices(A)
& v4_robbins1(A)
& v5_robbins1(A)
& v6_robbins1(A) ) ) ) ).
fof(cc4_robbins1,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v14_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A) ) ) ) ).
fof(fc17_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( ~ v3_struct_0(k8_robbins1(A))
& v3_robbins1(k8_robbins1(A))
& v9_robbins1(k8_robbins1(A)) ) ) ).
fof(fc18_robbins1,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_realset2(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) ) ).
fof(rc10_robbins1,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)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(A)
& v3_robbins1(A)
& v4_robbins1(A)
& v5_robbins1(A)
& v6_robbins1(A)
& v9_robbins1(A) ) ).
fof(cc5_robbins1,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v9_robbins1(A) )
=> ( ~ v3_struct_0(A)
& v6_lattices(A) ) ) ) ).
fof(cc6_robbins1,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& v7_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)
& v14_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& v7_robbins1(A) ) ) ) ).
fof(cc7_robbins1,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v5_robbins1(A)
& v9_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)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(A)
& v9_robbins1(A) ) ) ) ).
fof(cc8_robbins1,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v4_robbins1(A)
& v9_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)
& v11_lattices(A)
& v12_lattices(A)
& v13_lattices(A)
& v14_lattices(A)
& v15_lattices(A)
& v16_lattices(A)
& v17_lattices(A) ) ) ) ).
fof(cc9_robbins1,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A)
& v7_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)
& v14_lattices(A)
& v4_robbins1(A)
& v5_robbins1(A)
& v6_robbins1(A)
& v7_robbins1(A) ) ) ) ).
fof(d1_robbins1,axiom,
k1_robbins1 = g2_robbins1(k1_tarski(k1_xboole_0),k2_midsp_1,k7_vectsp_2) ).
fof(d2_robbins1,axiom,
k2_robbins1 = g3_robbins1(k1_tarski(k1_xboole_0),k2_midsp_1,k2_midsp_1,k7_vectsp_2) ).
fof(d3_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l1_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,B) = k8_funct_2(u1_struct_0(A),u1_struct_0(A),u1_robbins1(A),B) ) ) ).
fof(d4_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_robbins1(A,B,C) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),k3_robbins1(A,C))) ) ) ) ).
fof(d5_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( v4_robbins1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,B,k3_robbins1(A,C))))) = B ) ) ) ) ).
fof(d6_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( v5_robbins1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),k3_robbins1(A,C))),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),C))) = B ) ) ) ) ).
fof(d7_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_lattices(A) )
=> ( v6_robbins1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k1_lattices(A,B,B) = B ) ) ) ).
fof(t1_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_robbins1(A,k4_robbins1(A,B,C),k4_robbins1(A,B,k3_robbins1(A,C))) = B ) ) ) ).
fof(t2_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_robbins1(A,B,k3_robbins1(A,B)) = k5_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,k3_robbins1(A,B))) ) ) ).
fof(t3_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,k3_robbins1(A,B)) = B ) ) ).
fof(t4_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_robbins1(A,B,k3_robbins1(A,B)) = k5_robbins1(A,C,k3_robbins1(A,C)) ) ) ) ).
fof(t5_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& l2_robbins1(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k5_robbins1(A,B,C) = B
& k5_robbins1(A,C,k3_robbins1(A,C)) = B ) ) ) ) ).
fof(t6_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& l2_robbins1(A) )
=> v14_lattices(A) ) ).
fof(d8_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B = k6_lattices(A)
<=> ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& B = k5_robbins1(A,C,k3_robbins1(A,C)) ) ) ) ) ).
fof(t7_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& l2_robbins1(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k4_robbins1(A,B,C) = B
& k3_robbins1(A,k5_robbins1(A,C,k3_robbins1(A,C))) = B ) ) ) ) ).
fof(t8_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_robbins1(A,B,C) = k4_robbins1(A,C,B) ) ) ) ).
fof(d9_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( B = k7_robbins1(A)
<=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_robbins1(A,B,C) = B ) ) ) ) ).
fof(t9_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k7_robbins1(A) = k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,B))) ) ) ).
fof(t10_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& l2_robbins1(A) )
=> ( k3_robbins1(A,k6_lattices(A)) = k7_robbins1(A)
& k6_lattices(A) = k3_robbins1(A,k7_robbins1(A)) ) ) ).
fof(t11_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( k3_robbins1(A,B) = k3_robbins1(A,C)
=> B = C ) ) ) ) ).
fof(t12_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_robbins1(A,B,k3_robbins1(A,k5_robbins1(A,C,k3_robbins1(A,C)))) = B ) ) ) ).
fof(t13_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_robbins1(A,B,B) = B ) ) ).
fof(t14_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_robbins1(A,B,k7_robbins1(A)) = B ) ) ).
fof(t15_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_robbins1(A,B,k6_lattices(A)) = B ) ) ).
fof(t16_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_robbins1(A,B,k3_robbins1(A,B)) = k7_robbins1(A) ) ) ).
fof(t17_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> k6_robbins1(A,B,k6_robbins1(A,C,D)) = k6_robbins1(A,k6_robbins1(A,B,C),D) ) ) ) ) ).
fof(t18_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_robbins1(A,B,C) = k3_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C))) ) ) ) ).
fof(t19_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k6_robbins1(A,B,B) = B ) ) ).
fof(t20_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_robbins1(A,B,k6_lattices(A)) = k6_lattices(A) ) ) ).
fof(t21_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_robbins1(A,B,k6_robbins1(A,B,C)) = B ) ) ) ).
fof(t22_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k6_robbins1(A,B,k5_robbins1(A,B,C)) = B ) ) ) ).
fof(t23_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( k5_robbins1(A,k3_robbins1(A,B),C) = k6_lattices(A)
& k5_robbins1(A,k3_robbins1(A,C),B) = k6_lattices(A) )
=> B = C ) ) ) ) ).
fof(t24_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ( ( k5_robbins1(A,B,C) = k6_lattices(A)
& k6_robbins1(A,B,C) = k7_robbins1(A) )
=> k3_robbins1(A,B) = C ) ) ) ) ).
fof(t25_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> k5_robbins1(A,k5_robbins1(A,k5_robbins1(A,k5_robbins1(A,k5_robbins1(A,k5_robbins1(A,k5_robbins1(A,k6_robbins1(A,k6_robbins1(A,B,C),D),k6_robbins1(A,k6_robbins1(A,B,C),k3_robbins1(A,D))),k6_robbins1(A,k6_robbins1(A,B,k3_robbins1(A,C)),D)),k6_robbins1(A,k6_robbins1(A,B,k3_robbins1(A,C)),k3_robbins1(A,D))),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),C),D)),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),C),k3_robbins1(A,D))),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C)),D)),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C)),k3_robbins1(A,D))) = k6_lattices(A) ) ) ) ) ).
fof(t26_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> ( k6_robbins1(A,k6_robbins1(A,B,D),k6_robbins1(A,C,k3_robbins1(A,D))) = k7_robbins1(A)
& k6_robbins1(A,k6_robbins1(A,k6_robbins1(A,B,C),D),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),C),D)) = k7_robbins1(A)
& k6_robbins1(A,k6_robbins1(A,k6_robbins1(A,B,k3_robbins1(A,C)),D),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),C),D)) = k7_robbins1(A)
& k6_robbins1(A,k6_robbins1(A,k6_robbins1(A,B,C),D),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C)),D)) = k7_robbins1(A)
& k6_robbins1(A,k6_robbins1(A,k6_robbins1(A,B,C),k3_robbins1(A,D)),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C)),k3_robbins1(A,D))) = k7_robbins1(A)
& k6_robbins1(A,k6_robbins1(A,k6_robbins1(A,B,k3_robbins1(A,C)),D),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),C),D)) = k7_robbins1(A) ) ) ) ) ) ).
fof(t27_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> k5_robbins1(A,k6_robbins1(A,B,C),k6_robbins1(A,B,D)) = k5_robbins1(A,k5_robbins1(A,k6_robbins1(A,k6_robbins1(A,B,C),D),k6_robbins1(A,k6_robbins1(A,B,C),k3_robbins1(A,D))),k6_robbins1(A,k6_robbins1(A,B,k3_robbins1(A,C)),D)) ) ) ) ) ).
fof(t28_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> k3_robbins1(A,k6_robbins1(A,B,k5_robbins1(A,C,D))) = k5_robbins1(A,k5_robbins1(A,k5_robbins1(A,k5_robbins1(A,k6_robbins1(A,k6_robbins1(A,B,k3_robbins1(A,C)),k3_robbins1(A,D)),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),C),D)),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),C),k3_robbins1(A,D))),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C)),D)),k6_robbins1(A,k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C)),k3_robbins1(A,D))) ) ) ) ) ).
fof(t29_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> k5_robbins1(A,k5_robbins1(A,k6_robbins1(A,B,C),k6_robbins1(A,B,D)),k3_robbins1(A,k6_robbins1(A,B,k5_robbins1(A,C,D)))) = k6_lattices(A) ) ) ) ) ).
fof(t30_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> k6_robbins1(A,k5_robbins1(A,k6_robbins1(A,B,C),k6_robbins1(A,B,D)),k3_robbins1(A,k6_robbins1(A,B,k5_robbins1(A,C,D)))) = k7_robbins1(A) ) ) ) ) ).
fof(t31_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> k6_robbins1(A,B,k5_robbins1(A,C,D)) = k5_robbins1(A,k6_robbins1(A,B,C),k6_robbins1(A,B,D)) ) ) ) ) ).
fof(t32_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(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))
=> k5_robbins1(A,B,k6_robbins1(A,C,D)) = k6_robbins1(A,k5_robbins1(A,B,C),k5_robbins1(A,B,D)) ) ) ) ) ).
fof(d10_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_robbins1(A) )
=> ( v7_robbins1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> r2_lattices(A,k3_robbins1(A,B),B) ) ) ) ).
fof(t33_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& v7_robbins1(A)
& l3_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,k3_robbins1(A,B)) = B ) ) ).
fof(t34_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& v15_lattices(A)
& v7_robbins1(A)
& l3_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k4_lattices(A,B,C) = k3_robbins1(A,k3_lattices(A,k3_robbins1(A,B),k3_robbins1(A,C))) ) ) ) ).
fof(d11_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( ( v3_robbins1(B)
& l3_robbins1(B) )
=> ( B = k8_robbins1(A)
<=> ( u1_struct_0(B) = u1_struct_0(A)
& u2_lattices(B) = u2_lattices(A)
& u1_robbins1(B) = u1_robbins1(A)
& ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> ! [D] :
( m1_subset_1(D,u1_struct_0(A))
=> k1_binop_1(u1_lattices(B),C,D) = k4_robbins1(A,C,D) ) ) ) ) ) ) ).
fof(t35_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(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(k8_robbins1(A)))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(k8_robbins1(A)))
=> ( ( B = D
& C = E )
=> ( k4_robbins1(A,B,C) = k2_lattices(k8_robbins1(A),D,E)
& k1_lattices(A,B,C) = k1_lattices(k8_robbins1(A),D,E)
& k3_robbins1(A,B) = k3_robbins1(k8_robbins1(A),D) ) ) ) ) ) ) ) ).
fof(t36_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& l2_robbins1(A) )
=> k7_robbins1(A) = k5_lattices(k8_robbins1(A)) ) ).
fof(d12_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_robbins1(A) )
=> ( v5_robbins1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C))),k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C)))) = C ) ) ) ) ).
fof(d13_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( v8_robbins1(A)
<=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& k1_lattices(A,B,B) = B ) ) ) ).
fof(d14_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_robbins1(A,B,C) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),C)) ) ) ) ).
fof(d15_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k10_robbins1(A,B,C) = k9_robbins1(A,k1_lattices(A,B,C),k9_robbins1(A,B,C)) ) ) ) ).
fof(d16_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k11_robbins1(A,B) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),B)) ) ) ).
fof(d17_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k12_robbins1(A,B) = k1_lattices(A,B,B) ) ) ).
fof(d18_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k13_robbins1(A,B) = k1_lattices(A,k11_robbins1(A,B),B) ) ) ).
fof(d19_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k14_robbins1(A,B) = k1_lattices(A,k11_robbins1(A,B),k12_robbins1(A,B)) ) ) ).
fof(d20_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k15_robbins1(A,B) = k1_lattices(A,k11_robbins1(A,B),k1_lattices(A,k12_robbins1(A,B),B)) ) ) ).
fof(d21_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k16_robbins1(A,B) = k1_lattices(A,k11_robbins1(A,B),k1_lattices(A,k12_robbins1(A,B),k12_robbins1(A,B))) ) ) ).
fof(t37_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_robbins1(A,k5_robbins1(A,B,C),k9_robbins1(A,B,C)) = C ) ) ) ).
fof(t38_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k10_robbins1(A,B,C) = C ) ) ) ).
fof(t39_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(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))
=> k9_robbins1(A,k5_robbins1(A,k3_robbins1(A,B),C),D) = k3_robbins1(A,k5_robbins1(A,k9_robbins1(A,B,C),D)) ) ) ) ) ).
fof(t40_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,B,B) = k11_robbins1(A,B) ) ) ).
fof(t41_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k12_robbins1(A,B),k11_robbins1(A,B)) = B ) ) ).
fof(t42_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k14_robbins1(A,B),B) = k11_robbins1(A,B) ) ) ).
fof(t43_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_robbins1(A,k14_robbins1(A,B),B) = k15_robbins1(A,B) ) ) ).
fof(t44_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_robbins1(A,k16_robbins1(A,B),k11_robbins1(A,B)) = k5_robbins1(A,k15_robbins1(A,B),k13_robbins1(A,B)) ) ) ).
fof(t45_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_robbins1(A,k15_robbins1(A,B),k11_robbins1(A,B)) = k5_robbins1(A,k14_robbins1(A,B),k13_robbins1(A,B)) ) ) ).
fof(t46_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k5_robbins1(A,k15_robbins1(A,B),B) = k16_robbins1(A,B) ) ) ).
fof(t47_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k15_robbins1(A,B),k11_robbins1(A,B)) = B ) ) ).
fof(t48_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(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))
=> ( k3_robbins1(A,B) = k3_robbins1(A,C)
=> k9_robbins1(A,B,D) = k9_robbins1(A,C,D) ) ) ) ) ) ).
fof(t49_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k9_robbins1(A,B,k3_robbins1(A,C)) = k9_robbins1(A,C,k3_robbins1(A,B)) ) ) ) ).
fof(t50_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k15_robbins1(A,B),B) = k11_robbins1(A,B) ) ) ).
fof(t51_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k5_robbins1(A,k13_robbins1(A,B),k15_robbins1(A,B)),B) = k11_robbins1(A,B) ) ) ).
fof(t52_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k5_robbins1(A,k13_robbins1(A,B),k14_robbins1(A,B)),B) = k11_robbins1(A,B) ) ) ).
fof(t53_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k5_robbins1(A,k13_robbins1(A,B),k15_robbins1(A,B)),k11_robbins1(A,B)) = B ) ) ).
fof(d22_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k17_robbins1(A,B) = k5_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,k13_robbins1(A,B),k15_robbins1(A,B))),B),k3_robbins1(A,k15_robbins1(A,B))) ) ) ).
fof(t54_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k17_robbins1(A,B),B) = k3_robbins1(A,k15_robbins1(A,B)) ) ) ).
fof(t55_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k9_robbins1(A,k17_robbins1(A,B),B) = k3_robbins1(A,k5_robbins1(A,k13_robbins1(A,B),k15_robbins1(A,B))) ) ) ).
fof(t56_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k3_robbins1(A,k5_robbins1(A,B,C)) = k3_robbins1(A,C) ) ) ) ).
fof(t57_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ( ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,k3_robbins1(A,B)) = B )
=> v5_robbins1(A) ) ) ).
fof(t58_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ( v8_robbins1(A)
=> v5_robbins1(A) ) ) ).
fof(t59_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ( ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k5_robbins1(A,B,C) = B ) )
=> v5_robbins1(A) ) ) ).
fof(t60_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A) )
=> ? [B] :
( m1_subset_1(B,u1_struct_0(A))
& ? [C] :
( m1_subset_1(C,u1_struct_0(A))
& k5_robbins1(A,B,C) = C ) ) ) ).
fof(d23_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l3_robbins1(A) )
=> ( v9_robbins1(A)
<=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k2_lattices(A,B,C) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),k3_robbins1(A,C))) ) ) ) ) ).
fof(t61_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v6_lattices(A)
& v7_robbins1(A)
& l3_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ( k5_robbins1(A,B,k3_robbins1(A,B)) = k6_lattices(A)
& k4_lattices(A,B,k3_robbins1(A,B)) = k5_lattices(A) ) ) ) ).
fof(t62_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v11_lattices(A)
& v15_lattices(A)
& v7_robbins1(A)
& l3_robbins1(A) )
=> k3_robbins1(A,k6_lattices(A)) = k5_lattices(A) ) ).
fof(t63_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v5_robbins1(A)
& v9_robbins1(A)
& l3_robbins1(A) )
=> k7_robbins1(A) = k5_lattices(A) ) ).
fof(dt_l1_robbins1,axiom,
! [A] :
( l1_robbins1(A)
=> l1_struct_0(A) ) ).
fof(existence_l1_robbins1,axiom,
? [A] : l1_robbins1(A) ).
fof(dt_l2_robbins1,axiom,
! [A] :
( l2_robbins1(A)
=> ( l2_lattices(A)
& l1_robbins1(A) ) ) ).
fof(existence_l2_robbins1,axiom,
? [A] : l2_robbins1(A) ).
fof(dt_l3_robbins1,axiom,
! [A] :
( l3_robbins1(A)
=> ( l2_robbins1(A)
& l3_lattices(A) ) ) ).
fof(existence_l3_robbins1,axiom,
? [A] : l3_robbins1(A) ).
fof(abstractness_v1_robbins1,axiom,
! [A] :
( l1_robbins1(A)
=> ( v1_robbins1(A)
=> A = g1_robbins1(u1_struct_0(A),u1_robbins1(A)) ) ) ).
fof(abstractness_v2_robbins1,axiom,
! [A] :
( l2_robbins1(A)
=> ( v2_robbins1(A)
=> A = g2_robbins1(u1_struct_0(A),u2_lattices(A),u1_robbins1(A)) ) ) ).
fof(abstractness_v3_robbins1,axiom,
! [A] :
( l3_robbins1(A)
=> ( v3_robbins1(A)
=> A = g3_robbins1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_robbins1(A)) ) ) ).
fof(dt_k1_robbins1,axiom,
( v2_robbins1(k1_robbins1)
& l2_robbins1(k1_robbins1) ) ).
fof(dt_k2_robbins1,axiom,
( v3_robbins1(k2_robbins1)
& l3_robbins1(k2_robbins1) ) ).
fof(dt_k3_robbins1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l1_robbins1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k3_robbins1(A,B),u1_struct_0(A)) ) ).
fof(dt_k4_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k4_robbins1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k5_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k5_robbins1(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k5_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k5_robbins1(A,B,C) = k5_robbins1(A,C,B) ) ).
fof(redefinition_k5_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k5_robbins1(A,B,C) = k1_lattices(A,B,C) ) ).
fof(dt_k6_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k6_robbins1(A,B,C),u1_struct_0(A)) ) ).
fof(commutativity_k6_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k6_robbins1(A,B,C) = k6_robbins1(A,C,B) ) ).
fof(redefinition_k6_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> k6_robbins1(A,B,C) = k4_robbins1(A,B,C) ) ).
fof(dt_k7_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& l2_robbins1(A) )
=> m1_subset_1(k7_robbins1(A),u1_struct_0(A)) ) ).
fof(dt_k8_robbins1,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( v3_robbins1(k8_robbins1(A))
& l3_robbins1(k8_robbins1(A)) ) ) ).
fof(dt_k9_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k9_robbins1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k10_robbins1,axiom,
! [A,B,C] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A))
& m1_subset_1(C,u1_struct_0(A)) )
=> m1_subset_1(k10_robbins1(A,B,C),u1_struct_0(A)) ) ).
fof(dt_k11_robbins1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k11_robbins1(A,B),u1_struct_0(A)) ) ).
fof(dt_k12_robbins1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k12_robbins1(A,B),u1_struct_0(A)) ) ).
fof(dt_k13_robbins1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k13_robbins1(A,B),u1_struct_0(A)) ) ).
fof(dt_k14_robbins1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k14_robbins1(A,B),u1_struct_0(A)) ) ).
fof(dt_k15_robbins1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k15_robbins1(A,B),u1_struct_0(A)) ) ).
fof(dt_k16_robbins1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k16_robbins1(A,B),u1_struct_0(A)) ) ).
fof(dt_k17_robbins1,axiom,
! [A,B] :
( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A)
& l2_robbins1(A)
& m1_subset_1(B,u1_struct_0(A)) )
=> m1_subset_1(k17_robbins1(A,B),u1_struct_0(A)) ) ).
fof(dt_u1_robbins1,axiom,
! [A] :
( l1_robbins1(A)
=> ( v1_funct_1(u1_robbins1(A))
& v1_funct_2(u1_robbins1(A),u1_struct_0(A),u1_struct_0(A))
& m2_relset_1(u1_robbins1(A),u1_struct_0(A),u1_struct_0(A)) ) ) ).
fof(dt_g1_robbins1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A) )
=> ( v1_robbins1(g1_robbins1(A,B))
& l1_robbins1(g1_robbins1(A,B)) ) ) ).
fof(free_g1_robbins1,axiom,
! [A,B] :
( ( v1_funct_1(B)
& v1_funct_2(B,A,A)
& m1_relset_1(B,A,A) )
=> ! [C,D] :
( g1_robbins1(A,B) = g1_robbins1(C,D)
=> ( A = C
& B = D ) ) ) ).
fof(dt_g2_robbins1,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)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ( v2_robbins1(g2_robbins1(A,B,C))
& l2_robbins1(g2_robbins1(A,B,C)) ) ) ).
fof(free_g2_robbins1,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)
& v1_funct_1(C)
& v1_funct_2(C,A,A)
& m1_relset_1(C,A,A) )
=> ! [D,E,F] :
( g2_robbins1(A,B,C) = g2_robbins1(D,E,F)
=> ( A = D
& B = E
& C = F ) ) ) ).
fof(dt_g3_robbins1,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)
& v1_funct_1(D)
& v1_funct_2(D,A,A)
& m1_relset_1(D,A,A) )
=> ( v3_robbins1(g3_robbins1(A,B,C,D))
& l3_robbins1(g3_robbins1(A,B,C,D)) ) ) ).
fof(free_g3_robbins1,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)
& v1_funct_1(D)
& v1_funct_2(D,A,A)
& m1_relset_1(D,A,A) )
=> ! [E,F,G,H] :
( g3_robbins1(A,B,C,D) = g3_robbins1(E,F,G,H)
=> ( A = E
& B = F
& C = G
& D = H ) ) ) ).
%------------------------------------------------------------------------------