SET007 Axioms: SET007+495.ax


%------------------------------------------------------------------------------
% File     : SET007+495 : TPTP v7.5.0. Released v3.4.0.
% Domain   : Set Theory
% Axioms   : Duality in Relation Structures
% 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_7 [Urb08]

% Status   : Satisfiable
% Syntax   : Number of formulae    :   70 (   0 unit)
%            Number of atoms       :  583 (  36 equality)
%            Maximal formula depth :   20 (   8 average)
%            Number of connectives :  557 (  44 ~  ;   2  |; 315  &)
%                                         (  25 <=>; 171 =>;   0 <=)
%                                         (   0 <~>;   0 ~|;   0 ~&)
%            Number of predicates  :   50 (   0 propositional; 1-4 arity)
%            Number of functors    :   33 (   0 constant; 1-6 arity)
%            Number of variables   :  149 (   0 singleton; 148 !;   1 ?)
%            Maximal term depth    :    5 (   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(fc1_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k7_lattice3(A))
        & v2_orders_2(k7_lattice3(A)) ) ) )).

fof(fc2_yellow_7,axiom,(
    ! [A] :
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k7_lattice3(A))
        & v3_orders_2(k7_lattice3(A)) ) ) )).

fof(fc3_yellow_7,axiom,(
    ! [A] :
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k7_lattice3(A))
        & v4_orders_2(k7_lattice3(A)) ) ) )).

fof(fc4_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v16_waybel_0(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k7_lattice3(A))
        & v1_orders_2(k7_lattice3(A))
        & v16_waybel_0(k7_lattice3(A)) ) ) )).

fof(fc5_yellow_7,axiom,(
    ! [A] :
      ( ( v2_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k7_lattice3(A))
        & v1_orders_2(k7_lattice3(A))
        & v1_lattice3(k7_lattice3(A)) ) ) )).

fof(fc6_yellow_7,axiom,(
    ! [A] :
      ( ( v1_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k7_lattice3(A))
        & v1_orders_2(k7_lattice3(A))
        & v2_lattice3(k7_lattice3(A)) ) ) )).

fof(fc7_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k7_lattice3(A))
        & v1_orders_2(k7_lattice3(A))
        & v1_lattice3(k7_lattice3(A))
        & v2_lattice3(k7_lattice3(A))
        & v3_lattice3(k7_lattice3(A))
        & v1_yellow_0(k7_lattice3(A))
        & v2_yellow_0(k7_lattice3(A))
        & v3_yellow_0(k7_lattice3(A)) ) ) )).

fof(fc8_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v2_waybel_1(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k7_lattice3(A))
        & v1_orders_2(k7_lattice3(A))
        & v2_orders_2(k7_lattice3(A))
        & v3_orders_2(k7_lattice3(A))
        & v4_orders_2(k7_lattice3(A))
        & v1_lattice3(k7_lattice3(A))
        & v2_lattice3(k7_lattice3(A))
        & v2_waybel_1(k7_lattice3(A)) ) ) )).

fof(fc9_yellow_7,axiom,(
    ! [A] :
      ( ( v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k7_lattice3(A))
        & v2_yellow_0(k7_lattice3(A)) ) ) )).

fof(fc10_yellow_7,axiom,(
    ! [A] :
      ( ( v2_yellow_0(A)
        & l1_orders_2(A) )
     => ( v1_orders_2(k7_lattice3(A))
        & v1_yellow_0(k7_lattice3(A)) ) ) )).

fof(fc11_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_yellow_0(A)
        & v10_waybel_1(A)
        & l1_orders_2(A) )
     => ( ~ v3_struct_0(k7_lattice3(A))
        & v1_orders_2(k7_lattice3(A))
        & v2_orders_2(k7_lattice3(A))
        & v3_orders_2(k7_lattice3(A))
        & v4_orders_2(k7_lattice3(A))
        & v1_lattice3(k7_lattice3(A))
        & v2_lattice3(k7_lattice3(A))
        & v1_yellow_0(k7_lattice3(A))
        & v2_yellow_0(k7_lattice3(A))
        & v3_yellow_0(k7_lattice3(A))
        & v10_waybel_1(k7_lattice3(A)) ) ) )).

fof(fc12_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_yellow_7(A))
        & v1_funct_1(k1_yellow_7(A))
        & v2_funct_1(k1_yellow_7(A))
        & v1_funct_2(k1_yellow_7(A),u1_struct_0(A),u1_struct_0(k7_lattice3(A))) ) ) )).

fof(fc13_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ( v1_relat_1(k1_yellow_7(A))
        & v1_funct_1(k1_yellow_7(A))
        & v2_funct_1(k1_yellow_7(A))
        & v1_funct_2(k1_yellow_7(A),u1_struct_0(A),u1_struct_0(k7_lattice3(A)))
        & v23_waybel_0(k1_yellow_7(A),A,k7_lattice3(A))
        & v5_orders_3(k1_yellow_7(A),A,k7_lattice3(A)) ) ) )).

fof(cc1_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( ( ~ v3_struct_0(A)
          & v1_waybel_5(A) )
       => ( ~ v3_struct_0(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & v3_lattice3(A)
          & v1_yellow_0(A)
          & v2_yellow_0(A)
          & v3_yellow_0(A) ) ) ) )).

fof(rc1_yellow_7,axiom,(
    ? [A] :
      ( l1_orders_2(A)
      & ~ v3_struct_0(A)
      & v1_orders_2(A)
      & v2_orders_2(A)
      & v3_orders_2(A)
      & v4_orders_2(A)
      & v1_lattice3(A)
      & v2_lattice3(A)
      & v3_lattice3(A)
      & v1_yellow_0(A)
      & v2_yellow_0(A)
      & v3_yellow_0(A)
      & v16_waybel_0(A)
      & v24_waybel_0(A)
      & v25_waybel_0(A)
      & v2_waybel_1(A)
      & v9_waybel_1(A)
      & v1_waybel_5(A)
      & v3_realset2(A) ) )).

fof(t1_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_lattice3(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
             => ( r1_orders_2(k7_lattice3(A),B,C)
              <=> r1_orders_2(A,k9_lattice3(A,C),k9_lattice3(A,B)) ) ) ) ) )).

fof(t2_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
             => ( ( r1_orders_2(A,B,k9_lattice3(A,C))
                 => r1_orders_2(k7_lattice3(A),C,k8_lattice3(A,B)) )
                & ( r1_orders_2(k7_lattice3(A),C,k8_lattice3(A,B))
                 => r1_orders_2(A,B,k9_lattice3(A,C)) )
                & ( r1_orders_2(A,k9_lattice3(A,C),B)
                 => r1_orders_2(k7_lattice3(A),k8_lattice3(A,B),C) )
                & ( r1_orders_2(k7_lattice3(A),k8_lattice3(A,B),C)
                 => r1_orders_2(A,k9_lattice3(A,C),B) ) ) ) ) ) )).

fof(t3_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_struct_0(A)
      <=> v3_struct_0(k7_lattice3(A)) ) ) )).

fof(t4_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v2_orders_2(A)
      <=> v2_orders_2(k7_lattice3(A)) ) ) )).

fof(t5_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v4_orders_2(A)
      <=> v4_orders_2(k7_lattice3(A)) ) ) )).

fof(t6_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_orders_2(A)
      <=> v3_orders_2(k7_lattice3(A)) ) ) )).

fof(t7_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v16_waybel_0(A)
      <=> v16_waybel_0(k7_lattice3(A)) ) ) )).

fof(t8_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] :
              ( ( r1_lattice3(A,C,B)
               => r2_lattice3(k7_lattice3(A),C,k8_lattice3(A,B)) )
              & ( r2_lattice3(k7_lattice3(A),C,k8_lattice3(A,B))
               => r1_lattice3(A,C,B) )
              & ( r2_lattice3(A,C,B)
               => r1_lattice3(k7_lattice3(A),C,k8_lattice3(A,B)) )
              & ( r1_lattice3(k7_lattice3(A),C,k8_lattice3(A,B))
               => r2_lattice3(A,C,B) ) ) ) ) )).

fof(t9_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(k7_lattice3(A)))
         => ! [C] :
              ( ( r1_lattice3(k7_lattice3(A),C,B)
               => r2_lattice3(A,C,k9_lattice3(A,B)) )
              & ( r2_lattice3(A,C,k9_lattice3(A,B))
               => r1_lattice3(k7_lattice3(A),C,B) )
              & ( r2_lattice3(k7_lattice3(A),C,B)
               => r1_lattice3(A,C,k9_lattice3(A,B)) )
              & ( r1_lattice3(A,C,k9_lattice3(A,B))
               => r2_lattice3(k7_lattice3(A),C,B) ) ) ) ) )).

fof(t10_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( r1_yellow_0(A,B)
        <=> r2_yellow_0(k7_lattice3(A),B) ) ) )).

fof(t11_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( r1_yellow_0(k7_lattice3(A),B)
        <=> r2_yellow_0(A,B) ) ) )).

fof(t12_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( r1_yellow_0(A,B)
            | r2_yellow_0(k7_lattice3(A),B) )
         => k1_yellow_0(A,B) = k2_yellow_0(k7_lattice3(A),B) ) ) )).

fof(t13_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( r2_yellow_0(A,B)
            | r1_yellow_0(k7_lattice3(A),B) )
         => k2_yellow_0(A,B) = k1_yellow_0(k7_lattice3(A),B) ) ) )).

fof(t14_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v2_lattice3(A) )
           => v2_lattice3(B) ) ) ) )).

fof(t15_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( l1_orders_2(B)
         => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
              & v1_lattice3(A) )
           => v1_lattice3(B) ) ) ) )).

fof(t16_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v2_lattice3(A)
      <=> v1_lattice3(k7_lattice3(A)) ) ) )).

fof(t17_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v3_lattice3(A)
      <=> v3_lattice3(k7_lattice3(A)) ) ) )).

fof(t18_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_lattice3(A))))
             => ( B = C
               => ( k13_waybel_0(A,B) = k12_waybel_0(k7_lattice3(A),C)
                  & k12_waybel_0(A,B) = k13_waybel_0(k7_lattice3(A),C) ) ) ) ) ) )).

fof(t19_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] :
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(k7_lattice3(A))))
             => ( B = C
               => ( k4_waybel_0(A,B) = k5_waybel_0(k7_lattice3(A),C)
                  & k5_waybel_0(A,B) = k4_waybel_0(k7_lattice3(A),C) ) ) ) ) ) )).

fof(t20_yellow_7,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(k7_lattice3(A)))
             => ( B = C
               => ( k6_waybel_0(A,B) = k7_waybel_0(k7_lattice3(A),C)
                  & k7_waybel_0(A,B) = k6_waybel_0(k7_lattice3(A),C) ) ) ) ) ) )).

fof(t21_yellow_7,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))
             => k12_lattice3(A,B,C) = k13_lattice3(k7_lattice3(A),k8_lattice3(A,B),k8_lattice3(A,C)) ) ) ) )).

fof(t22_yellow_7,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(k7_lattice3(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
             => k12_lattice3(A,k9_lattice3(A,B),k9_lattice3(A,C)) = k13_lattice3(k7_lattice3(A),B,C) ) ) ) )).

fof(t23_yellow_7,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))
             => k13_lattice3(A,B,C) = k12_lattice3(k7_lattice3(A),k8_lattice3(A,B),k8_lattice3(A,C)) ) ) ) )).

fof(t24_yellow_7,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(k7_lattice3(A)))
         => ! [C] :
              ( m1_subset_1(C,u1_struct_0(k7_lattice3(A)))
             => k13_lattice3(A,k9_lattice3(A,B),k9_lattice3(A,C)) = k12_lattice3(k7_lattice3(A),B,C) ) ) ) )).

fof(t25_yellow_7,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)
      <=> v2_waybel_1(k7_lattice3(A)) ) ) )).

fof(t26_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v1_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
        <=> ( v2_waybel_0(B,k7_lattice3(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) ) ) ) )).

fof(t27_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v1_waybel_0(B,k7_lattice3(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) )
        <=> ( v2_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t28_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
        <=> ( v13_waybel_0(B,k7_lattice3(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) ) ) ) )).

fof(t29_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ! [B] :
          ( ( v12_waybel_0(B,k7_lattice3(A))
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k7_lattice3(A)))) )
        <=> ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) ) ) ) )).

fof(t30_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_yellow_0(A)
      <=> v2_yellow_0(k7_lattice3(A)) ) ) )).

fof(t31_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v1_yellow_0(k7_lattice3(A))
      <=> v2_yellow_0(A) ) ) )).

fof(t32_yellow_7,axiom,(
    ! [A] :
      ( l1_orders_2(A)
     => ( v3_yellow_0(A)
      <=> v3_yellow_0(k7_lattice3(A)) ) ) )).

fof(t33_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( k8_lattice3(A,k3_yellow_0(A)) = k4_yellow_0(k7_lattice3(A))
        & k9_lattice3(A,k4_yellow_0(k7_lattice3(A))) = k3_yellow_0(A) ) ) )).

fof(t34_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ( k8_lattice3(A,k4_yellow_0(A)) = k3_yellow_0(k7_lattice3(A))
        & k9_lattice3(A,k3_yellow_0(k7_lattice3(A))) = k4_yellow_0(A) ) ) )).

fof(t35_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_yellow_0(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)
              <=> r6_waybel_1(k7_lattice3(A),k8_lattice3(A,B),k8_lattice3(A,C)) ) ) ) ) )).

fof(t36_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_yellow_0(A)
        & l1_orders_2(A) )
     => ( v10_waybel_1(A)
      <=> v10_waybel_1(k7_lattice3(A)) ) ) )).

fof(t37_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_waybel_1(k7_lattice3(A),k8_lattice3(A,B)) = k7_waybel_1(A,B) ) ) )).

fof(d1_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k7_lattice3(A)))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k7_lattice3(A))) )
         => ( B = k1_yellow_7(A)
          <=> ! [C] :
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_waybel_0(A,k7_lattice3(A),B,C) = k7_waybel_1(A,C) ) ) ) ) )).

fof(t38_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v11_waybel_1(A)
        & l1_orders_2(A) )
     => r5_waybel_1(A,k7_lattice3(A)) ) )).

fof(t39_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
               => ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(B)) ) )
              & ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(B)) )
               => ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) )
              & ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
               => ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B)))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B))) ) )
              & ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B)))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B))) )
               => ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) )
              & ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
               => ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
                  & m2_relset_1(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) ) )
              & ( ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
                  & m2_relset_1(C,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) )
               => ( v1_funct_1(C)
                  & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) ) ) ) ) ) )).

fof(t40_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k7_lattice3(B)))
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k7_lattice3(B))) )
                 => ( C = D
                   => ( ( v5_orders_3(C,A,B)
                       => v5_waybel_0(D,A,k7_lattice3(B)) )
                      & ( v5_waybel_0(D,A,k7_lattice3(B))
                       => v5_orders_3(C,A,B) )
                      & ( v5_waybel_0(C,A,B)
                       => v5_orders_3(D,A,k7_lattice3(B)) )
                      & ( v5_orders_3(D,A,k7_lattice3(B))
                       => v5_waybel_0(C,A,B) ) ) ) ) ) ) ) )).

fof(t41_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B)))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k7_lattice3(B))) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k7_lattice3(A)),u1_struct_0(B))
                    & m2_relset_1(D,u1_struct_0(k7_lattice3(A)),u1_struct_0(B)) )
                 => ( C = D
                   => ( ( v5_orders_3(C,A,k7_lattice3(B))
                       => v5_orders_3(D,k7_lattice3(A),B) )
                      & ( v5_orders_3(D,k7_lattice3(A),B)
                       => v5_orders_3(C,A,k7_lattice3(B)) )
                      & ( v5_waybel_0(C,A,k7_lattice3(B))
                       => v5_waybel_0(D,k7_lattice3(A),B) )
                      & ( v5_waybel_0(D,k7_lattice3(A),B)
                       => v5_waybel_0(C,A,k7_lattice3(B)) ) ) ) ) ) ) ) )).

fof(t42_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
                    & m2_relset_1(D,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) )
                 => ( C = D
                   => ( ( v5_orders_3(C,A,B)
                       => v5_orders_3(D,k7_lattice3(A),k7_lattice3(B)) )
                      & ( v5_orders_3(D,k7_lattice3(A),k7_lattice3(B))
                       => v5_orders_3(C,A,B) )
                      & ( v5_waybel_0(C,A,B)
                       => v5_waybel_0(D,k7_lattice3(A),k7_lattice3(B)) )
                      & ( v5_waybel_0(D,k7_lattice3(A),k7_lattice3(B))
                       => v5_waybel_0(C,A,B) ) ) ) ) ) ) ) )).

fof(t43_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( m1_waybel_1(C,A,B)
               => m1_waybel_1(C,k7_lattice3(A),B) )
              & ( m1_waybel_1(C,k7_lattice3(A),B)
               => m1_waybel_1(C,A,B) )
              & ( m1_waybel_1(C,A,B)
               => m1_waybel_1(C,A,k7_lattice3(B)) )
              & ( m1_waybel_1(C,A,k7_lattice3(B))
               => m1_waybel_1(C,A,B) )
              & ( m1_waybel_1(C,A,B)
               => m1_waybel_1(C,k7_lattice3(A),k7_lattice3(B)) )
              & ( m1_waybel_1(C,k7_lattice3(A),k7_lattice3(B))
               => m1_waybel_1(C,A,B) ) ) ) ) )).

fof(t44_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( ~ v3_struct_0(B)
            & v2_orders_2(B)
            & v3_orders_2(B)
            & v4_orders_2(B)
            & l1_orders_2(B) )
         => ! [C] :
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] :
                  ( ( v1_funct_1(D)
                    & v1_funct_2(D,u1_struct_0(B),u1_struct_0(A))
                    & m2_relset_1(D,u1_struct_0(B),u1_struct_0(A)) )
                 => ! [E] :
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B)))
                        & m2_relset_1(E,u1_struct_0(k7_lattice3(A)),u1_struct_0(k7_lattice3(B))) )
                     => ! [F] :
                          ( ( v1_funct_1(F)
                            & v1_funct_2(F,u1_struct_0(k7_lattice3(B)),u1_struct_0(k7_lattice3(A)))
                            & m2_relset_1(F,u1_struct_0(k7_lattice3(B)),u1_struct_0(k7_lattice3(A))) )
                         => ( ( C = E
                              & D = F )
                           => ( v3_waybel_1(k1_waybel_1(A,B,C,D),A,B)
                            <=> v3_waybel_1(k1_waybel_1(k7_lattice3(B),k7_lattice3(A),F,E),k7_lattice3(B),k7_lattice3(A)) ) ) ) ) ) ) ) ) )).

fof(t45_yellow_7,axiom,(
    ! [A,B] :
      ( ~ v1_xboole_0(B)
     => ! [C] :
          ( m1_pboole(C,A)
         => ! [D] :
              ( m3_pboole(D,A,C,k2_pre_circ(A,B))
             => k2_funct_6(D) = C ) ) ) )).

fof(t46_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] :
          ( m1_pboole(C,B)
         => ! [D] :
              ( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
            <=> m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(k7_lattice3(A)))) ) ) ) )).

fof(t47_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ~ v1_xboole_0(B)
         => ! [C] :
              ( ( v2_relat_1(C)
                & m1_pboole(C,B) )
             => ! [D] :
                  ( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
                 => r3_orders_2(A,k5_yellow_2(A,k5_waybel_5(A,D)),k6_yellow_2(A,k4_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D)))) ) ) ) ) )).

fof(t48_yellow_7,axiom,(
    ! [A] :
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_waybel_5(A)
      <=> ! [B] :
            ( ~ v1_xboole_0(B)
           => ! [C] :
                ( ( v2_relat_1(C)
                  & m1_pboole(C,B) )
               => ! [D] :
                    ( m3_pboole(D,B,C,k2_pre_circ(B,u1_struct_0(A)))
                   => k5_yellow_2(A,k5_waybel_5(A,D)) = k6_yellow_2(A,k4_waybel_5(A,k2_waybel_5(B,u1_struct_0(A),C,D))) ) ) ) ) ) )).

fof(t49_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( k5_yellow_2(A,B) = k6_yellow_2(k7_lattice3(A),B)
            & k6_yellow_2(A,B) = k5_yellow_2(k7_lattice3(A),B) ) ) ) )).

fof(t50_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] :
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_funcop_1(B) )
         => ( k4_waybel_5(A,B) = k5_waybel_5(k7_lattice3(A),B)
            & k5_waybel_5(A,B) = k4_waybel_5(k7_lattice3(A),B) ) ) ) )).

fof(t51_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_waybel_5(A)
      <=> v1_waybel_5(k7_lattice3(A)) ) ) )).

fof(dt_k1_yellow_7,axiom,(
    ! [A] :
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k1_yellow_7(A))
        & v1_funct_2(k1_yellow_7(A),u1_struct_0(A),u1_struct_0(k7_lattice3(A)))
        & m2_relset_1(k1_yellow_7(A),u1_struct_0(A),u1_struct_0(k7_lattice3(A))) ) ) )).

fof(dt_k2_yellow_7,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B))
        & m1_subset_1(E,A)
        & m1_subset_1(F,k1_funct_1(C,E)) )
     => m1_subset_1(k2_yellow_7(A,B,C,D,E,F),B) ) )).

fof(redefinition_k2_yellow_7,axiom,(
    ! [A,B,C,D,E,F] :
      ( ( ~ v1_xboole_0(A)
        & ~ v1_xboole_0(B)
        & v2_relat_1(C)
        & m1_pboole(C,A)
        & m3_pboole(D,A,C,k2_pre_circ(A,B))
        & m1_subset_1(E,A)
        & m1_subset_1(F,k1_funct_1(C,E)) )
     => k2_yellow_7(A,B,C,D,E,F) = k5_funct_6(D,E,F) ) )).
%------------------------------------------------------------------------------