SET007 Axioms: SET007+848.ax


%------------------------------------------------------------------------------
% File     : SET007+848 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Axiomatization of Boolean Algebras Based on Sheffer Stroke
% 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    : sheffer1 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   93 (   7 unit)
%            Number of atoms       :  700 (  60 equality)
%            Maximal formula depth :   29 (   8 average)
%            Number of connectives :  685 (  78 ~  ;   0  |; 445  &)
%                                         (  15 <=>; 147 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   49 (   0 propositional; 1-3 arity)
%            Number of functors    :   29 (   4 constant; 0-6 arity)
%            Number of variables   :  177 (   0 singleton; 163 !;  14 ?)
%            Maximal term depth    :    4 (   1 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(rc1_sheffer1,axiom,(
    ? [A] :
      ( l3_lattices(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)
      & v6_robbins1(A)
      & v1_sheffer1(A)
      & v2_sheffer1(A)
      & v3_sheffer1(A)
      & v4_sheffer1(A) ) )).

fof(cc1_sheffer1,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v6_lattices(A)
          & v11_lattices(A)
          & v1_sheffer1(A)
          & v2_sheffer1(A)
          & v3_sheffer1(A)
          & v4_sheffer1(A) ) ) ) )).

fof(cc2_sheffer1,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v6_lattices(A)
          & v11_lattices(A)
          & v1_sheffer1(A)
          & v2_sheffer1(A)
          & v3_sheffer1(A)
          & v4_sheffer1(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(rc2_sheffer1,axiom,(
    ? [A] :
      ( l1_sheffer1(A)
      & v6_sheffer1(A) ) )).

fof(rc3_sheffer1,axiom,(
    ? [A] :
      ( l2_sheffer1(A)
      & v7_sheffer1(A) ) )).

fof(rc4_sheffer1,axiom,(
    ? [A] :
      ( l3_sheffer1(A)
      & v8_sheffer1(A) ) )).

fof(rc5_sheffer1,axiom,(
    ? [A] :
      ( l1_sheffer1(A)
      & ~ v3_struct_0(A) ) )).

fof(rc6_sheffer1,axiom,(
    ? [A] :
      ( l2_sheffer1(A)
      & ~ v3_struct_0(A) ) )).

fof(rc7_sheffer1,axiom,(
    ? [A] :
      ( l3_sheffer1(A)
      & ~ v3_struct_0(A) ) )).

fof(cc3_sheffer1,axiom,(
    ! [A] :
      ( l1_sheffer1(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v10_sheffer1(A)
          & v11_sheffer1(A)
          & v12_sheffer1(A) ) ) ) )).

fof(cc4_sheffer1,axiom,(
    ! [A] :
      ( l2_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v4_lattices(A)
          & v5_lattices(A) ) ) ) )).

fof(cc5_sheffer1,axiom,(
    ! [A] :
      ( l1_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v6_lattices(A)
          & v7_lattices(A) ) ) ) )).

fof(cc6_sheffer1,axiom,(
    ! [A] :
      ( l3_lattices(A)
     => ( ( ~ v3_struct_0(A)
          & v3_realset2(A) )
       => ( ~ v3_struct_0(A)
          & v8_lattices(A)
          & v9_lattices(A)
          & v11_lattices(A)
          & v13_lattices(A)
          & v14_lattices(A)
          & v15_lattices(A)
          & v16_lattices(A)
          & v17_lattices(A) ) ) ) )).

fof(fc1_sheffer1,axiom,(
    ~ v3_struct_0(k4_sheffer1) )).

fof(fc2_sheffer1,axiom,(
    v3_realset2(k4_sheffer1) )).

fof(fc3_sheffer1,axiom,
    ( v7_robbins1(k4_sheffer1)
    & v9_sheffer1(k4_sheffer1) )).

fof(rc8_sheffer1,axiom,(
    ? [A] :
      ( l3_sheffer1(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)
      & v7_robbins1(A)
      & v1_sheffer1(A)
      & v2_sheffer1(A)
      & v3_sheffer1(A)
      & v4_sheffer1(A)
      & v9_sheffer1(A)
      & v10_sheffer1(A)
      & v11_sheffer1(A)
      & v12_sheffer1(A) ) )).

fof(t1_sheffer1,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,k5_robbins1(A,B,C)) = k6_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C)) ) ) ) )).

fof(t2_sheffer1,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,k6_robbins1(A,B,C)) = k5_robbins1(A,k3_robbins1(A,B),k3_robbins1(A,C)) ) ) ) )).

fof(d1_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v1_sheffer1(A)
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( k2_lattices(A,B,C) = C
                  & k2_lattices(A,C,B) = C ) ) ) ) ) )).

fof(d2_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v1_sheffer1(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( B = k1_sheffer1(A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( k2_lattices(A,B,C) = C
                    & k2_lattices(A,C,B) = C ) ) ) ) ) ) )).

fof(d3_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v2_sheffer1(A)
      <=> ? [B] :
            ( m1_subset_1(B,u1_struct_0(A))
            & ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( k1_lattices(A,B,C) = C
                  & k1_lattices(A,C,B) = C ) ) ) ) ) )).

fof(d4_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v2_sheffer1(A)
       => ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ( B = k2_sheffer1(A)
            <=> ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => ( k1_lattices(A,B,C) = C
                    & k1_lattices(A,C,B) = C ) ) ) ) ) ) )).

fof(d5_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v3_sheffer1(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,k2_lattices(A,C,D)) = k2_lattices(A,k1_lattices(A,B,C),k1_lattices(A,B,D)) ) ) ) ) ) )).

fof(d6_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_sheffer1(A,B,C)
              <=> ( k1_lattices(A,C,B) = k1_sheffer1(A)
                  & k1_lattices(A,B,C) = k1_sheffer1(A)
                  & k2_lattices(A,C,B) = k2_sheffer1(A)
                  & k2_lattices(A,B,C) = k2_sheffer1(A) ) ) ) ) ) )).

fof(d7_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( v4_sheffer1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ? [C] :
                ( m1_subset_1(C,u1_struct_0(A))
                & r1_sheffer1(A,C,B) ) ) ) ) )).

fof(d8_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( ( v4_sheffer1(A)
              & v11_lattices(A)
              & v1_sheffer1(A)
              & v6_lattices(A) )
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => ( C = k3_sheffer1(A,B)
                <=> r1_sheffer1(A,C,B) ) ) ) ) ) )).

fof(t3_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v1_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_lattices(A,B,k3_sheffer1(A,B)) = k1_sheffer1(A) ) ) )).

fof(t4_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v1_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattices(A,B,k3_sheffer1(A,B)) = k2_sheffer1(A) ) ) )).

fof(t5_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k3_lattices(A,B,k1_sheffer1(A)) = k1_sheffer1(A) ) ) )).

fof(t6_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k4_lattices(A,B,k2_sheffer1(A)) = k2_sheffer1(A) ) ) )).

fof(t7_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & l3_lattices(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))
                 => k4_lattices(A,k3_lattices(A,k3_lattices(A,B,C),D),B) = B ) ) ) ) )).

fof(t8_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & v6_robbins1(A)
        & v3_sheffer1(A)
        & l3_lattices(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_lattices(A,k4_lattices(A,k4_lattices(A,B,C),D),B) = B ) ) ) ) )).

fof(d9_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_lattices(A) )
     => ( v5_sheffer1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => k2_lattices(A,B,B) = B ) ) ) )).

fof(t9_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => v5_sheffer1(A) ) )).

fof(t10_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => v6_robbins1(A) ) )).

fof(t11_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => v8_lattices(A) ) )).

fof(t12_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => v9_lattices(A) ) )).

fof(t13_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => v14_lattices(A) ) )).

fof(t14_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => v1_sheffer1(A) ) )).

fof(t15_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => v13_lattices(A) ) )).

fof(t16_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) )
     => v2_sheffer1(A) ) )).

fof(t17_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & l3_lattices(A) )
     => v5_lattices(A) ) )).

fof(t18_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v8_lattices(A)
        & v9_lattices(A)
        & v6_robbins1(A)
        & v3_sheffer1(A)
        & l3_lattices(A) )
     => v7_lattices(A) ) )).

fof(t19_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => k6_lattices(A) = k1_sheffer1(A) ) )).

fof(t20_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => k5_lattices(A) = k2_sheffer1(A) ) )).

fof(t21_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & v3_sheffer1(A)
        & l3_lattices(A) )
     => k6_lattices(A) = k1_sheffer1(A) ) )).

fof(t22_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v11_lattices(A)
        & v13_lattices(A)
        & v14_lattices(A)
        & v16_lattices(A)
        & v17_lattices(A)
        & v3_sheffer1(A)
        & l3_lattices(A) )
     => k5_lattices(A) = k2_sheffer1(A) ) )).

fof(t23_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_sheffer1(A,B,C)
              <=> r2_lattices(A,B,C) ) ) ) ) )).

fof(t24_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_lattices(A)
        & v6_lattices(A)
        & v11_lattices(A)
        & v6_robbins1(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & v4_sheffer1(A)
        & l3_lattices(A) )
     => v16_lattices(A) ) )).

fof(t25_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & v1_sheffer1(A)
        & v2_sheffer1(A)
        & v3_sheffer1(A)
        & l3_lattices(A) )
     => v4_sheffer1(A) ) )).

fof(t26_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v17_lattices(A)
          & l3_lattices(A) )
      <=> ( v2_sheffer1(A)
          & v1_sheffer1(A)
          & v4_lattices(A)
          & v6_lattices(A)
          & v11_lattices(A)
          & v3_sheffer1(A)
          & v4_sheffer1(A) ) ) ) )).

fof(d10_sheffer1,axiom,(
    k4_sheffer1 = g3_sheffer1(k1_tarski(k1_xboole_0),k2_midsp_1,k2_midsp_1,k7_vectsp_2,k2_midsp_1) )).

fof(d11_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_sheffer1(A,B,C) = k2_binop_1(u1_struct_0(A),u1_struct_0(A),u1_struct_0(A),u1_sheffer1(A),B,C) ) ) ) )).

fof(d12_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_sheffer1(A) )
     => ( v9_sheffer1(A)
      <=> ( ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => k5_sheffer1(A,B,B) = k3_robbins1(A,B) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k1_lattices(A,B,C) = k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,C,C)) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k2_lattices(A,B,C) = k5_sheffer1(A,k5_sheffer1(A,B,C),k5_sheffer1(A,B,C)) ) )
          & ! [B] :
              ( m1_subset_1(B,u1_struct_0(A))
             => ! [C] :
                  ( m1_subset_1(C,u1_struct_0(A))
                 => k5_sheffer1(A,B,C) = k1_lattices(A,k3_robbins1(A,B),k3_robbins1(A,C)) ) ) ) ) ) )).

fof(d13_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A) )
     => ( v10_sheffer1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => k5_sheffer1(A,k5_sheffer1(A,B,B),k5_sheffer1(A,B,B)) = B ) ) ) )).

fof(d14_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A) )
     => ( v11_sheffer1(A)
      <=> ! [B] :
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k5_sheffer1(A,B,k5_sheffer1(A,C,k5_sheffer1(A,C,C))) = k5_sheffer1(A,B,B) ) ) ) ) )).

fof(d15_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A) )
     => ( v12_sheffer1(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_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D)),k5_sheffer1(A,B,k5_sheffer1(A,C,D))) = k5_sheffer1(A,k5_sheffer1(A,k5_sheffer1(A,C,C),B),k5_sheffer1(A,k5_sheffer1(A,D,D),B)) ) ) ) ) ) )).

fof(t27_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & v7_robbins1(A)
        & v9_sheffer1(A)
        & l3_sheffer1(A) )
     => v10_sheffer1(A) ) )).

fof(t28_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & v7_robbins1(A)
        & v9_sheffer1(A)
        & l3_sheffer1(A) )
     => v11_sheffer1(A) ) )).

fof(t29_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & v7_robbins1(A)
        & v9_sheffer1(A)
        & l3_sheffer1(A) )
     => v12_sheffer1(A) ) )).

fof(d16_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_sheffer1(A,B) = k5_sheffer1(A,B,B) ) ) )).

fof(t30_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v12_sheffer1(A)
        & l3_sheffer1(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_sheffer1(A,k5_sheffer1(A,B,k5_sheffer1(A,C,D))) = k5_sheffer1(A,k5_sheffer1(A,k6_sheffer1(A,C),B),k5_sheffer1(A,k6_sheffer1(A,D),B)) ) ) ) ) )).

fof(t31_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v10_sheffer1(A)
        & l3_sheffer1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => B = k6_sheffer1(A,k6_sheffer1(A,B)) ) ) )).

fof(t32_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v9_sheffer1(A)
        & v10_sheffer1(A)
        & v11_sheffer1(A)
        & v12_sheffer1(A)
        & l3_sheffer1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_sheffer1(A,B,C) = k5_sheffer1(A,C,B) ) ) ) )).

fof(t33_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v9_sheffer1(A)
        & v10_sheffer1(A)
        & v11_sheffer1(A)
        & v12_sheffer1(A)
        & l3_sheffer1(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k5_sheffer1(A,B,k5_sheffer1(A,B,B)) = k5_sheffer1(A,C,k5_sheffer1(A,C,C)) ) ) ) )).

fof(t34_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v9_sheffer1(A)
        & v10_sheffer1(A)
        & v11_sheffer1(A)
        & v12_sheffer1(A)
        & l3_sheffer1(A) )
     => v4_lattices(A) ) )).

fof(t35_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v9_sheffer1(A)
        & v10_sheffer1(A)
        & v11_sheffer1(A)
        & v12_sheffer1(A)
        & l3_sheffer1(A) )
     => v6_lattices(A) ) )).

fof(t36_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v9_sheffer1(A)
        & v10_sheffer1(A)
        & v11_sheffer1(A)
        & v12_sheffer1(A)
        & l3_sheffer1(A) )
     => v11_lattices(A) ) )).

fof(t37_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v9_sheffer1(A)
        & v10_sheffer1(A)
        & v11_sheffer1(A)
        & v12_sheffer1(A)
        & l3_sheffer1(A) )
     => v3_sheffer1(A) ) )).

fof(t38_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v9_sheffer1(A)
        & v10_sheffer1(A)
        & v11_sheffer1(A)
        & v12_sheffer1(A)
        & l3_sheffer1(A) )
     => ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v17_lattices(A)
        & l3_lattices(A) ) ) )).

fof(dt_l1_sheffer1,axiom,(
    ! [A] :
      ( l1_sheffer1(A)
     => l1_struct_0(A) ) )).

fof(existence_l1_sheffer1,axiom,(
    ? [A] : l1_sheffer1(A) )).

fof(dt_l2_sheffer1,axiom,(
    ! [A] :
      ( l2_sheffer1(A)
     => ( l1_sheffer1(A)
        & l3_lattices(A) ) ) )).

fof(existence_l2_sheffer1,axiom,(
    ? [A] : l2_sheffer1(A) )).

fof(dt_l3_sheffer1,axiom,(
    ! [A] :
      ( l3_sheffer1(A)
     => ( l1_sheffer1(A)
        & l3_robbins1(A) ) ) )).

fof(existence_l3_sheffer1,axiom,(
    ? [A] : l3_sheffer1(A) )).

fof(abstractness_v6_sheffer1,axiom,(
    ! [A] :
      ( l1_sheffer1(A)
     => ( v6_sheffer1(A)
       => A = g1_sheffer1(u1_struct_0(A),u1_sheffer1(A)) ) ) )).

fof(abstractness_v7_sheffer1,axiom,(
    ! [A] :
      ( l2_sheffer1(A)
     => ( v7_sheffer1(A)
       => A = g2_sheffer1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_sheffer1(A)) ) ) )).

fof(abstractness_v8_sheffer1,axiom,(
    ! [A] :
      ( l3_sheffer1(A)
     => ( v8_sheffer1(A)
       => A = g3_sheffer1(u1_struct_0(A),u2_lattices(A),u1_lattices(A),u1_robbins1(A),u1_sheffer1(A)) ) ) )).

fof(dt_k1_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => m1_subset_1(k1_sheffer1(A),u1_struct_0(A)) ) )).

fof(dt_k2_sheffer1,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => m1_subset_1(k2_sheffer1(A),u1_struct_0(A)) ) )).

fof(dt_k3_sheffer1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k3_sheffer1(A,B),u1_struct_0(A)) ) )).

fof(dt_k4_sheffer1,axiom,(
    l3_sheffer1(k4_sheffer1) )).

fof(dt_k5_sheffer1,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k5_sheffer1(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k6_sheffer1,axiom,(
    ! [A,B] :
      ( ( ~ v3_struct_0(A)
        & l1_sheffer1(A)
        & m1_subset_1(B,u1_struct_0(A)) )
     => m1_subset_1(k6_sheffer1(A,B),u1_struct_0(A)) ) )).

fof(dt_u1_sheffer1,axiom,(
    ! [A] :
      ( l1_sheffer1(A)
     => ( v1_funct_1(u1_sheffer1(A))
        & v1_funct_2(u1_sheffer1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A))
        & m2_relset_1(u1_sheffer1(A),k2_zfmisc_1(u1_struct_0(A),u1_struct_0(A)),u1_struct_0(A)) ) ) )).

fof(dt_g1_sheffer1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ( v6_sheffer1(g1_sheffer1(A,B))
        & l1_sheffer1(g1_sheffer1(A,B)) ) ) )).

fof(free_g1_sheffer1,axiom,(
    ! [A,B] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A) )
     => ! [C,D] :
          ( g1_sheffer1(A,B) = g1_sheffer1(C,D)
         => ( A = C
            & B = D ) ) ) )).

fof(dt_g2_sheffer1,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,k2_zfmisc_1(A,A),A)
        & m1_relset_1(D,k2_zfmisc_1(A,A),A) )
     => ( v7_sheffer1(g2_sheffer1(A,B,C,D))
        & l2_sheffer1(g2_sheffer1(A,B,C,D)) ) ) )).

fof(free_g2_sheffer1,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,k2_zfmisc_1(A,A),A)
        & m1_relset_1(D,k2_zfmisc_1(A,A),A) )
     => ! [E,F,G,H] :
          ( g2_sheffer1(A,B,C,D) = g2_sheffer1(E,F,G,H)
         => ( A = E
            & B = F
            & C = G
            & D = H ) ) ) )).

fof(dt_g3_sheffer1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,A)
        & m1_relset_1(D,A,A)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
        & m1_relset_1(E,k2_zfmisc_1(A,A),A) )
     => ( v8_sheffer1(g3_sheffer1(A,B,C,D,E))
        & l3_sheffer1(g3_sheffer1(A,B,C,D,E)) ) ) )).

fof(free_g3_sheffer1,axiom,(
    ! [A,B,C,D,E] :
      ( ( v1_funct_1(B)
        & v1_funct_2(B,k2_zfmisc_1(A,A),A)
        & m1_relset_1(B,k2_zfmisc_1(A,A),A)
        & v1_funct_1(C)
        & v1_funct_2(C,k2_zfmisc_1(A,A),A)
        & m1_relset_1(C,k2_zfmisc_1(A,A),A)
        & v1_funct_1(D)
        & v1_funct_2(D,A,A)
        & m1_relset_1(D,A,A)
        & v1_funct_1(E)
        & v1_funct_2(E,k2_zfmisc_1(A,A),A)
        & m1_relset_1(E,k2_zfmisc_1(A,A),A) )
     => ! [F,G,H,I,J] :
          ( g3_sheffer1(A,B,C,D,E) = g3_sheffer1(F,G,H,I,J)
         => ( A = F
            & B = G
            & C = H
            & D = I
            & E = J ) ) ) )).
%------------------------------------------------------------------------------