SET007 Axioms: SET007+492.ax


%------------------------------------------------------------------------------
% File     : SET007+492 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Miscellaneous Facts about Relation Structure
% 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    : yellow_5 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   82 (   0 unit)
%            Number of atoms       :  641 (  57 equality)
%            Maximal formula depth :   13 (   9 average)
%            Number of connectives :  614 (  55 ~  ;   1  |; 268  &)
%                                         (   6 <=>; 284 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   17 (   0 propositional; 1-3 arity)
%            Number of functors    :   11 (   0 constant; 1-3 arity)
%            Number of variables   :  266 (   0 singleton; 266 !;   0 ?)
%            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(t1_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k13_lattice3(A,B,B) = B ) ) )).

fof(t2_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k12_lattice3(A,B,B) = B ) ) )).

fof(t3_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(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))
                 => ( r1_orders_2(A,k13_lattice3(A,B,C),D)
                   => r1_orders_2(A,B,D) ) ) ) ) ) )).

fof(t4_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( r1_orders_2(A,D,k12_lattice3(A,B,C))
                   => r1_orders_2(A,D,B) ) ) ) ) ) )).

fof(t5_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => r1_orders_2(A,k12_lattice3(A,B,C),k13_lattice3(A,B,D)) ) ) ) ) )).

fof(t6_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( r1_orders_2(A,B,C)
                   => r1_orders_2(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D)) ) ) ) ) ) )).

fof(t7_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(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))
                 => ( r1_orders_2(A,B,C)
                   => r1_orders_2(A,k13_lattice3(A,B,D),k13_lattice3(A,C,D)) ) ) ) ) ) )).

fof(t8_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => k13_lattice3(A,B,C) = C ) ) ) ) )).

fof(t9_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(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))
                 => ( ( r3_orders_2(A,B,D)
                      & r3_orders_2(A,C,D) )
                   => r3_orders_2(A,k13_lattice3(A,B,C),D) ) ) ) ) ) )).

fof(t10_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,C,B)
               => k12_lattice3(A,B,C) = C ) ) ) ) )).

fof(t11_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v11_waybel_1(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r6_waybel_1(A,B,C)
              <=> C = k7_waybel_1(A,B) ) ) ) ) )).

fof(d1_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_5(A,B,C) = k11_lattice3(A,B,k7_waybel_1(A,C)) ) ) ) )).

fof(d2_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k2_yellow_5(A,B,C) = k10_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,C,B)) ) ) ) )).

fof(d3_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_yellow_5(A,B,C)
              <=> k11_lattice3(A,B,C) != k3_yellow_0(A) ) ) ) ) )).

fof(t12_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( r1_orders_2(A,B,D)
                   => r1_orders_2(A,k1_yellow_5(A,B,C),D) ) ) ) ) ) )).

fof(t13_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( r1_orders_2(A,B,C)
                   => r1_orders_2(A,k1_yellow_5(A,B,D),k1_yellow_5(A,C,D)) ) ) ) ) ) )).

fof(t14_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_orders_2(A,k1_yellow_5(A,B,C),B) ) ) ) )).

fof(t15_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => r1_orders_2(A,k1_yellow_5(A,B,C),k3_yellow_5(A,B,C)) ) ) ) )).

fof(t16_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( ( r3_orders_2(A,k1_yellow_5(A,B,C),D)
                      & r3_orders_2(A,k1_yellow_5(A,C,B),D) )
                   => r3_orders_2(A,k3_yellow_5(A,B,C),D) ) ) ) ) ) )).

fof(t17_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r2_yellow_5(A,B,B)
          <=> B != k3_yellow_0(A) ) ) ) )).

fof(t18_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => k12_lattice3(A,B,k1_yellow_5(A,C,D)) = k1_yellow_5(A,k12_lattice3(A,B,C),D) ) ) ) ) )).

fof(t19_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_1(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))
                   => ( k10_lattice3(A,k12_lattice3(A,B,C),k12_lattice3(A,B,D)) = B
                     => r1_orders_2(A,B,k10_lattice3(A,C,D)) ) ) ) ) ) ) )).

fof(t20_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_1(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))
                   => k13_lattice3(A,B,k12_lattice3(A,C,D)) = k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,B,D)) ) ) ) ) ) )).

fof(t21_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_1(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_yellow_5(A,k13_lattice3(A,B,C),D) = k13_lattice3(A,k1_yellow_5(A,B,D),k1_yellow_5(A,C,D)) ) ) ) ) ) )).

fof(t22_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r1_orders_2(A,B,k3_yellow_0(A))
           => B = k3_yellow_0(A) ) ) ) )).

fof(t23_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( ( r3_orders_2(A,B,C)
                      & r3_orders_2(A,B,D)
                      & k12_lattice3(A,C,D) = k3_yellow_0(A) )
                   => B = k3_yellow_0(A) ) ) ) ) ) )).

fof(t24_yellow_5,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k13_lattice3(A,B,C) = k3_yellow_0(A)
               => ( B = k3_yellow_0(A)
                  & C = k3_yellow_0(A) ) ) ) ) ) )).

fof(t25_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( ( r1_orders_2(A,B,C)
                      & k12_lattice3(A,C,D) = k3_yellow_0(A) )
                   => k12_lattice3(A,B,D) = k3_yellow_0(A) ) ) ) ) ) )).

fof(t26_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_yellow_5(A,k3_yellow_0(A),B) = k3_yellow_0(A) ) ) )).

fof(t27_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( ( r2_yellow_5(A,B,C)
                      & r1_orders_2(A,C,D) )
                   => r2_yellow_5(A,B,D) ) ) ) ) ) )).

fof(t28_yellow_5,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k12_lattice3(A,B,k3_yellow_0(A)) = k3_yellow_0(A) ) ) )).

fof(t29_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( r2_yellow_5(A,B,k12_lattice3(A,C,D))
                   => r2_yellow_5(A,B,C) ) ) ) ) ) )).

fof(t30_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( r2_yellow_5(A,B,k1_yellow_5(A,C,D))
                   => r2_yellow_5(A,B,C) ) ) ) ) ) )).

fof(t31_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ~ r1_yellow_5(A,B,k3_yellow_0(A)) ) ) )).

fof(t32_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ~ ( ~ r1_yellow_5(A,B,D)
                      & r1_orders_2(A,C,D)
                      & r1_yellow_5(A,B,C) ) ) ) ) ) )).

fof(t33_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ~ ( ~ ( r1_yellow_5(A,B,C)
                          & r1_yellow_5(A,B,D) )
                      & r1_yellow_5(A,B,k12_lattice3(A,C,D)) ) ) ) ) ) )).

fof(t34_yellow_5,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ( ( r3_orders_2(A,B,C)
                      & r3_orders_2(A,B,D) )
                   => ( r1_yellow_5(A,C,D)
                      | B = k3_yellow_0(A) ) ) ) ) ) ) )).

fof(t35_yellow_5,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_lattice3(A)
        & l1_orders_2(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))
                 => ~ ( ~ r1_yellow_5(A,B,C)
                      & r1_yellow_5(A,k12_lattice3(A,B,D),k12_lattice3(A,C,D)) ) ) ) ) ) )).

fof(t36_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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))
                 => k13_lattice3(A,k13_lattice3(A,k12_lattice3(A,B,C),k12_lattice3(A,C,D)),k12_lattice3(A,D,B)) = k12_lattice3(A,k12_lattice3(A,k13_lattice3(A,B,C),k13_lattice3(A,C,D)),k13_lattice3(A,D,B)) ) ) ) ) )).

fof(t37_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k12_lattice3(A,B,k7_waybel_1(A,B)) = k3_yellow_0(A)
            & k13_lattice3(A,B,k7_waybel_1(A,B)) = k4_yellow_0(A) ) ) ) )).

fof(t38_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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))
                 => ( r3_orders_2(A,k1_yellow_5(A,B,C),D)
                   => r3_orders_2(A,B,k13_lattice3(A,C,D)) ) ) ) ) ) )).

fof(t39_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k7_waybel_1(A,k13_lattice3(A,B,C)) = k12_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C))
                & k7_waybel_1(A,k12_lattice3(A,B,C)) = k13_lattice3(A,k7_waybel_1(A,B),k7_waybel_1(A,C)) ) ) ) ) )).

fof(t40_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => r3_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,B)) ) ) ) ) )).

fof(t41_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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))
                 => ( r3_orders_2(A,B,C)
                   => r3_orders_2(A,k1_yellow_5(A,D,C),k1_yellow_5(A,D,B)) ) ) ) ) ) )).

fof(t42_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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))
                     => ( ( r3_orders_2(A,B,C)
                          & r3_orders_2(A,D,E) )
                       => r3_orders_2(A,k1_yellow_5(A,B,E),k1_yellow_5(A,C,D)) ) ) ) ) ) ) )).

fof(t43_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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))
                 => ( r3_orders_2(A,B,k13_lattice3(A,C,D))
                   => ( r3_orders_2(A,k1_yellow_5(A,B,C),D)
                      & r3_orders_2(A,k1_yellow_5(A,B,D),C) ) ) ) ) ) ) )).

fof(t44_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,k7_waybel_1(A,B),k7_waybel_1(A,k12_lattice3(A,B,C)))
                & r3_orders_2(A,k7_waybel_1(A,C),k7_waybel_1(A,k12_lattice3(A,B,C))) ) ) ) ) )).

fof(t45_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,k7_waybel_1(A,k13_lattice3(A,B,C)),k7_waybel_1(A,B))
                & r3_orders_2(A,k7_waybel_1(A,k13_lattice3(A,B,C)),k7_waybel_1(A,C)) ) ) ) ) )).

fof(t46_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,k1_yellow_5(A,C,B))
               => B = k3_yellow_0(A) ) ) ) ) )).

fof(t47_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => C = k13_lattice3(A,B,k1_yellow_5(A,C,B)) ) ) ) ) )).

fof(t48_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k1_yellow_5(A,B,C) = k3_yellow_0(A)
              <=> r3_orders_2(A,B,C) ) ) ) ) )).

fof(t49_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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))
                 => ( ( r3_orders_2(A,B,k13_lattice3(A,C,D))
                      & k12_lattice3(A,B,D) = k3_yellow_0(A) )
                   => r3_orders_2(A,B,C) ) ) ) ) ) )).

fof(t50_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k13_lattice3(A,B,C) = k13_lattice3(A,k1_yellow_5(A,B,C),C) ) ) ) )).

fof(t51_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_5(A,B,k13_lattice3(A,B,C)) = k3_yellow_0(A) ) ) ) )).

fof(t52_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_5(A,B,k12_lattice3(A,B,C)) = k1_yellow_5(A,B,C) ) ) ) )).

fof(t53_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k12_lattice3(A,k1_yellow_5(A,B,C),C) = k3_yellow_0(A) ) ) ) )).

fof(t54_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k13_lattice3(A,B,k1_yellow_5(A,C,B)) = k13_lattice3(A,B,C) ) ) ) )).

fof(t55_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k13_lattice3(A,k12_lattice3(A,B,C),k1_yellow_5(A,B,C)) = B ) ) ) )).

fof(t56_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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_yellow_5(A,B,k1_yellow_5(A,C,D)) = k13_lattice3(A,k1_yellow_5(A,B,C),k12_lattice3(A,B,D)) ) ) ) ) )).

fof(t57_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_5(A,B,k1_yellow_5(A,B,C)) = k12_lattice3(A,B,C) ) ) ) )).

fof(t58_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_5(A,k13_lattice3(A,B,C),C) = k1_yellow_5(A,B,C) ) ) ) )).

fof(t59_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k12_lattice3(A,B,C) = k3_yellow_0(A)
              <=> k1_yellow_5(A,B,C) = B ) ) ) ) )).

fof(t60_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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_yellow_5(A,B,k13_lattice3(A,C,D)) = k12_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,B,D)) ) ) ) ) )).

fof(t61_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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_yellow_5(A,B,k12_lattice3(A,C,D)) = k13_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,B,D)) ) ) ) ) )).

fof(t62_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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))
                 => k12_lattice3(A,B,k1_yellow_5(A,C,D)) = k1_yellow_5(A,k12_lattice3(A,B,C),k12_lattice3(A,B,D)) ) ) ) ) )).

fof(t63_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k1_yellow_5(A,k13_lattice3(A,B,C),k12_lattice3(A,B,C)) = k13_lattice3(A,k1_yellow_5(A,B,C),k1_yellow_5(A,C,B)) ) ) ) )).

fof(t64_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(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_yellow_5(A,k1_yellow_5(A,B,C),D) = k1_yellow_5(A,B,k13_lattice3(A,C,D)) ) ) ) ) )).

fof(t65_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => k7_waybel_1(A,k3_yellow_0(A)) = k4_yellow_0(A) ) )).

fof(t66_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => k7_waybel_1(A,k4_yellow_0(A)) = k3_yellow_0(A) ) )).

fof(t67_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_yellow_5(A,B,B) = k3_yellow_0(A) ) ) )).

fof(t68_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_yellow_5(A,B,k3_yellow_0(A)) = B ) ) )).

fof(t69_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => k7_waybel_1(A,k1_yellow_5(A,B,C)) = k13_lattice3(A,k7_waybel_1(A,B),C) ) ) ) )).

fof(t70_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ r1_yellow_5(A,k12_lattice3(A,B,C),k1_yellow_5(A,B,C)) ) ) ) )).

fof(t71_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ r1_yellow_5(A,k1_yellow_5(A,B,C),C) ) ) ) )).

fof(t72_yellow_5,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ~ r1_yellow_5(A,B,C)
               => k1_yellow_5(A,k13_lattice3(A,B,C),C) = B ) ) ) ) )).

fof(symmetry_r2_yellow_5,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r2_yellow_5(A,B,C)
       => r2_yellow_5(A,C,B) ) ) )).

fof(redefinition_r2_yellow_5,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => ( r2_yellow_5(A,B,C)
      <=> r1_yellow_5(A,B,C) ) ) )).

fof(dt_k1_yellow_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k1_yellow_5(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k2_yellow_5,axiom,(
    ! [A,B,C] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k2_yellow_5(A,B,C),u1_struct_0(A)) ) )).

fof(dt_k3_yellow_5,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => m1_subset_1(k3_yellow_5(A,B,C),u1_struct_0(A)) ) )).

fof(commutativity_k3_yellow_5,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_yellow_5(A,B,C) = k3_yellow_5(A,C,B) ) )).

fof(redefinition_k3_yellow_5,axiom,(
    ! [A,B,C] :
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A)
        & m1_subset_1(B,u1_struct_0(A))
        & m1_subset_1(C,u1_struct_0(A)) )
     => k3_yellow_5(A,B,C) = k2_yellow_5(A,B,C) ) )).
%------------------------------------------------------------------------------