SET007 Axioms: SET007+782.ax
%------------------------------------------------------------------------------
% File : SET007+782 : TPTP v8.2.0. Released v3.4.0.
% Domain : Set Theory
% Axioms : On the Two Short Axiomatizations of Ortholattices
% 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 : robbins2 [Urb08]
% Status : Satisfiable
% Syntax : Number of formulae : 77 ( 0 unt; 0 def)
% Number of atoms : 587 ( 61 equ)
% Maximal formula atoms : 23 ( 7 avg)
% Number of connectives : 597 ( 87 ~; 0 |; 264 &)
% ( 3 <=>; 243 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 9 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of predicates : 31 ( 30 usr; 0 prp; 1-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 234 ( 231 !; 3 ?)
% 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_robbins2,axiom,
( ~ v3_struct_0(k1_robbins1)
& v3_realset2(k1_robbins1)
& v4_lattices(k1_robbins1)
& v5_lattices(k1_robbins1)
& v14_lattices(k1_robbins1)
& v2_robbins1(k1_robbins1)
& v4_robbins1(k1_robbins1)
& v5_robbins1(k1_robbins1)
& v6_robbins1(k1_robbins1)
& v8_robbins1(k1_robbins1)
& v1_robbins2(k1_robbins1) ) ).
fof(fc2_robbins2,axiom,
( ~ v3_struct_0(k2_robbins1)
& v3_realset2(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)
& v1_robbins2(k2_robbins1) ) ).
fof(rc1_robbins2,axiom,
? [A] :
( l2_robbins1(A)
& ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v1_robbins2(A) ) ).
fof(cc1_robbins2,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v1_robbins2(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A) ) ) ) ).
fof(cc2_robbins2,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v1_robbins2(A) )
=> ( ~ v3_struct_0(A)
& v5_lattices(A) ) ) ) ).
fof(cc3_robbins2,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v1_robbins2(A) )
=> ( ~ v3_struct_0(A)
& v4_robbins1(A) ) ) ) ).
fof(cc4_robbins2,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)
& v4_robbins1(A)
& v5_robbins1(A)
& v6_robbins1(A)
& v1_robbins2(A) ) ) ) ).
fof(rc2_robbins2,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)
& v4_robbins1(A)
& v5_robbins1(A)
& v6_robbins1(A)
& v9_robbins1(A)
& v1_robbins2(A) ) ).
fof(cc5_robbins2,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v9_robbins1(A)
& v1_robbins2(A) )
=> ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A) ) ) ) ).
fof(cc6_robbins2,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)
& v10_lattices(A)
& v14_lattices(A)
& v4_robbins1(A)
& v5_robbins1(A)
& v6_robbins1(A)
& v7_robbins1(A)
& v1_robbins2(A) ) ) ) ).
fof(cc7_robbins2,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v2_robbins2(A)
& v3_robbins2(A) )
=> ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v14_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A) ) ) ) ).
fof(cc8_robbins2,axiom,
! [A] :
( l2_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A) )
=> ( ~ v3_struct_0(A)
& v2_robbins2(A)
& v3_robbins2(A) ) ) ) ).
fof(rc3_robbins2,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)
& v4_robbins1(A)
& v5_robbins1(A)
& v6_robbins1(A)
& v9_robbins1(A)
& v1_robbins2(A)
& v2_robbins2(A)
& v3_robbins2(A) ) ).
fof(cc9_robbins2,axiom,
! [A] :
( l3_robbins1(A)
=> ( ( ~ v3_struct_0(A)
& v10_lattices(A)
& v9_robbins1(A)
& v2_robbins2(A)
& v3_robbins2(A) )
=> ( ~ v3_struct_0(A)
& v10_lattices(A)
& v17_lattices(A) ) ) ) ).
fof(cc10_robbins2,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)
& v10_lattices(A)
& v14_lattices(A)
& v5_robbins1(A)
& v6_robbins1(A)
& v7_robbins1(A)
& v2_robbins2(A)
& v3_robbins2(A) ) ) ) ).
fof(d1_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( v1_robbins2(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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),D)),k3_robbins1(A,k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,D),k3_robbins1(A,k1_lattices(A,D,E)))))))) = D ) ) ) ) ) ) ).
fof(t1_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> ! [F] :
( m1_subset_1(F,u1_struct_0(A))
=> k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,D,E)),B)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,C),k3_robbins1(A,k1_lattices(A,C,F)))))))) = C ) ) ) ) ) ) ).
fof(t2_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,D,B)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,C),k3_robbins1(A,k1_lattices(A,C,E)))))))) = C ) ) ) ) ) ).
fof(t3_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,k3_robbins1(A,B))),B)) = k3_robbins1(A,B) ) ) ).
fof(t4_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,D,B)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,C,k3_robbins1(A,C))),C)),k3_robbins1(A,k1_lattices(A,C,E)))))))) = C ) ) ) ) ) ).
fof(t5_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,D,B)),C)))) = C ) ) ) ) ).
fof(t6_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),C)))) = C ) ) ) ).
fof(t7_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),B)),k3_robbins1(A,k1_lattices(A,B,C)))) = B ) ) ) ).
fof(t8_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),B)))) = k3_robbins1(A,k1_lattices(A,B,C)) ) ) ) ).
fof(t9_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),D)),k3_robbins1(A,k1_lattices(A,B,D)))) = D ) ) ) ) ).
fof(t10_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,C,D)),k3_robbins1(A,k1_lattices(A,C,B)))))) = k3_robbins1(A,k1_lattices(A,C,B)) ) ) ) ) ).
fof(t11_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),D)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),C)))),C)) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),C)) ) ) ) ) ).
fof(t12_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,C,D)),k3_robbins1(A,k1_lattices(A,D,B)))))) = k3_robbins1(A,k1_lattices(A,D,B)) ) ) ) ) ).
fof(t13_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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))
=> ! [E] :
( m1_subset_1(E,u1_struct_0(A))
=> k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,D,B)),k3_robbins1(A,k1_lattices(A,k3_robbins1(A,C),k3_robbins1(A,k1_lattices(A,E,C)))))))) = C ) ) ) ) ) ).
fof(t14_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,B,C)) = k3_robbins1(A,k1_lattices(A,C,B)) ) ) ) ).
fof(t15_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,k1_lattices(A,C,D)))),D)) = k3_robbins1(A,k1_lattices(A,C,D)) ) ) ) ) ).
fof(t16_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),D)))),D)) = k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),D)) ) ) ) ) ).
fof(t17_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),B)),C)) = k3_robbins1(A,k1_lattices(A,C,C)) ) ) ) ).
fof(t18_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,B),k3_robbins1(A,k1_lattices(A,C,B)))) = B ) ) ) ).
fof(t19_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),k3_robbins1(A,C))) = C ) ) ) ).
fof(t20_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,C,k3_robbins1(A,B))))) = k3_robbins1(A,B) ) ) ) ).
fof(t21_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,k1_lattices(A,B,B)) = k3_robbins1(A,B) ) ) ).
fof(t22_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k1_lattices(A,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,B,C)),B)),C)) = k3_robbins1(A,C) ) ) ) ).
fof(t23_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> k3_robbins1(A,k3_robbins1(A,B)) = B ) ) ).
fof(t24_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(A)
& l2_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,k1_lattices(A,B,C)),B)),C) = k3_robbins1(A,k3_robbins1(A,C)) ) ) ) ).
fof(t25_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k1_lattices(A,B,C))) = k1_lattices(A,C,B) ) ) ) ).
fof(t26_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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))
=> k1_lattices(A,B,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,k1_lattices(A,C,D)),k3_robbins1(A,k1_lattices(A,C,B))))) = k3_robbins1(A,k3_robbins1(A,k1_lattices(A,C,B))) ) ) ) ) ).
fof(t27_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(A)
& l2_robbins1(A) )
=> ! [B] :
( m1_subset_1(B,u1_struct_0(A))
=> ! [C] :
( m1_subset_1(C,u1_struct_0(A))
=> k1_lattices(A,B,C) = k1_lattices(A,C,B) ) ) ) ).
fof(t28_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,C)),B)),C) = C ) ) ) ).
fof(t29_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,C)),C)),B) = B ) ) ) ).
fof(t30_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,C,B)),C))) = B ) ) ) ).
fof(t31_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,B,k3_robbins1(A,C))),k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,C),C))) = k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C))) ) ) ) ).
fof(t32_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,B,C)),k3_robbins1(A,k5_robbins1(A,C,k3_robbins1(A,C)))) = k3_robbins1(A,k5_robbins1(A,B,C)) ) ) ) ).
fof(t33_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,B,C)),k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,C),C))) = k3_robbins1(A,k5_robbins1(A,B,C)) ) ) ) ).
fof(t34_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C)))),C)) = k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,C),C)) ) ) ) ).
fof(t35_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,B,k3_robbins1(A,C)),C)) = k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,C),C)) ) ) ) ).
fof(t36_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C)),D)),C)),k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,C),C)))) = C ) ) ) ) ).
fof(t37_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,C,D)),k3_robbins1(A,k5_robbins1(A,C,B))))) = k5_robbins1(A,C,B) ) ) ) ) ).
fof(t38_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,C,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,D,C)),B))))) = k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,D,C)),B) ) ) ) ) ).
fof(t39_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,C,B)),k3_robbins1(A,k5_robbins1(A,C,D))))) = k5_robbins1(A,C,B) ) ) ) ) ).
fof(t40_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,C)),k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,C)),k3_robbins1(A,k5_robbins1(A,B,D)))))),C) = C ) ) ) ) ).
fof(t41_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C)),D)),C))) = C ) ) ) ) ).
fof(t42_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k5_robbins1(A,C,k3_robbins1(A,B)),D))) = B ) ) ) ) ).
fof(t43_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,B),k3_robbins1(A,k5_robbins1(A,k5_robbins1(A,C,B),D))) = k3_robbins1(A,B) ) ) ) ) ).
fof(t44_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,B,C)),B) = k5_robbins1(A,B,k3_robbins1(A,C)) ) ) ) ).
fof(t45_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,B,k3_robbins1(A,C))))) = k3_robbins1(A,k5_robbins1(A,B,C)) ) ) ) ).
fof(t46_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,C)),k5_robbins1(A,B,D))),C) = C ) ) ) ) ).
fof(t47_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,C)),D)),k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,B),C)))),C) = k3_robbins1(A,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,B),C))) ) ) ) ) ).
fof(t48_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k5_robbins1(A,B,C)),D)),k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,B),C)))),C) = k5_robbins1(A,k3_robbins1(A,B),C) ) ) ) ) ).
fof(t49_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,k3_robbins1(A,k5_robbins1(A,C,B))),k5_robbins1(A,C,D))))),k5_robbins1(A,C,D)) = k5_robbins1(A,k3_robbins1(A,k3_robbins1(A,k5_robbins1(A,C,B))),k5_robbins1(A,C,D)) ) ) ) ) ).
fof(t50_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,k5_robbins1(A,k5_robbins1(A,C,B),k5_robbins1(A,C,D))))),k5_robbins1(A,C,D)) = k5_robbins1(A,k3_robbins1(A,k3_robbins1(A,k5_robbins1(A,C,B))),k5_robbins1(A,C,D)) ) ) ) ) ).
fof(t51_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k5_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,k5_robbins1(A,k5_robbins1(A,C,B),k5_robbins1(A,C,D))))),k5_robbins1(A,C,D)) = k5_robbins1(A,k5_robbins1(A,C,B),k5_robbins1(A,C,D)) ) ) ) ) ).
fof(t52_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k3_robbins1(A,k3_robbins1(A,B)),k5_robbins1(A,C,D)) = k5_robbins1(A,k5_robbins1(A,C,B),k5_robbins1(A,C,D)) ) ) ) ) ).
fof(t53_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,B,C),k5_robbins1(A,B,D)) = k5_robbins1(A,C,k5_robbins1(A,B,D)) ) ) ) ) ).
fof(t54_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,B,C),k5_robbins1(A,B,D)) = k5_robbins1(A,D,k5_robbins1(A,B,C)) ) ) ) ) ).
fof(t55_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,C,D)) = k5_robbins1(A,D,k5_robbins1(A,C,B)) ) ) ) ) ).
fof(t56_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,k5_robbins1(A,C,D)) = k5_robbins1(A,C,k5_robbins1(A,D,B)) ) ) ) ) ).
fof(t57_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& v1_robbins2(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,B,C),D) = k5_robbins1(A,B,k5_robbins1(A,C,D)) ) ) ) ) ).
fof(t58_robbins2,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))
=> ( ( v4_lattices(A)
& v5_lattices(A)
& v5_robbins1(A) )
=> k4_robbins1(A,k1_lattices(A,C,B),k1_lattices(A,C,k3_robbins1(A,B))) = C ) ) ) ) ).
fof(t59_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( ( v4_lattices(A)
& v5_lattices(A)
& v4_robbins1(A) )
=> v1_robbins2(A) ) ) ).
fof(d2_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( v2_robbins2(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),C)),B) = B ) ) ) ) ).
fof(d3_robbins2,axiom,
! [A] :
( ( ~ v3_struct_0(A)
& l2_robbins1(A) )
=> ( v3_robbins2(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,k3_robbins1(A,k1_lattices(A,k3_robbins1(A,B),C)),k1_lattices(A,D,C)) = k1_lattices(A,C,k1_lattices(A,D,B)) ) ) ) ) ) ).
%------------------------------------------------------------------------------