SET007 Axioms: SET007+782.ax


%------------------------------------------------------------------------------
% File     : SET007+782 : TPTP v7.5.0. 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 unit)
%            Number of atoms       :  587 (  61 equality)
%            Maximal formula depth :   24 (   9 average)
%            Number of connectives :  597 (  87 ~  ;   0  |; 264  &)
%                                         (   3 <=>; 243 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   31 (   0 propositional; 1-2 arity)
%            Number of functors    :    7 (   2 constant; 0-3 arity)
%            Number of variables   :  234 (   0 singleton; 231 !;   3 ?)
%            Maximal term depth    :   12 (   2 average)
% 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)) ) ) ) ) ) )).
%------------------------------------------------------------------------------