fof(t17_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( r1_yellow_0(A,B)
          & r2_yellow_0(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_lattice3,t15_yellow_0,d12_lattice3,d8_lattice3,d9_lattice3,d8_lattice3,d9_lattice3,t16_yellow_0]),
    [file(yellow_0,t17_yellow_0),interesting(1.00)]).

fof(t20_yellow_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_lattice3(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_lattice3,t18_yellow_0,d10_lattice3,t18_yellow_0]),
    [file(yellow_0,t20_yellow_0),interesting(0.95)]).

fof(t21_yellow_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_lattice3(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_lattice3,t19_yellow_0,d11_lattice3,t19_yellow_0]),
    [file(yellow_0,t21_yellow_0),interesting(0.95)]).

fof(t42_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ( r1_yellow_0(A,k1_xboole_0)
        & r2_yellow_0(A,u1_struct_0(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_yellow_0,t6_yellow_0,d8_lattice3,t15_yellow_0,d8_lattice3,t16_yellow_0]),
    [file(yellow_0,t42_yellow_0),interesting(0.85)]).

fof(t43_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ( r2_yellow_0(A,k1_xboole_0)
        & r1_yellow_0(A,u1_struct_0(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_yellow_0,t6_yellow_0,d9_lattice3,t16_yellow_0,d9_lattice3,t15_yellow_0]),
    [file(yellow_0,t43_yellow_0),interesting(0.85)]).

fof(t53_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => r1_yellow_0(A,B) )
       => v3_lattice3(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_lattice3,t17_xboole_1,t50_yellow_0,d9_yellow_0]),
    [file(yellow_0,t53_yellow_0),interesting(0.82)]).

fof(t14_yellow_0,theorem,(
    ! [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))
           => ! [C] : 
                ( ( r1_yellow_0(A,C)
                 => r1_yellow_0(B,C) )
                & ( r2_yellow_0(A,C)
                 => r2_yellow_0(B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_yellow_0,d7_yellow_0,t2_yellow_0,t2_yellow_0,t1_yellow_0,t2_yellow_0,t2_yellow_0,t1_yellow_0,d8_yellow_0,d8_yellow_0,t2_yellow_0,t2_yellow_0,t1_yellow_0,t2_yellow_0,t2_yellow_0,t1_yellow_0]),
    [file(yellow_0,t14_yellow_0),interesting(0.81)]).

fof(t54_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_lattice3(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_finset_1(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => r1_yellow_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_yellow_0,d7_yellow_0,t20_yellow_0,d9_yellow_0,t18_yellow_0,t7_yellow_0,t11_yellow_0,t10_yellow_0,d1_tarski,t7_xboole_1,t9_yellow_0,d2_xboole_0,d9_yellow_0,d9_lattice3,t18_yellow_0,d1_tarski,t7_xboole_1,t9_yellow_0,d2_xboole_0,d9_yellow_0,d9_lattice3,t18_yellow_0,t25_orders_2,s2_finset_1,t20_yellow_0]),
    [file(yellow_0,t54_yellow_0),interesting(0.81)]).

fof(t55_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_lattice3(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_finset_1(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => r2_yellow_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_yellow_0,d8_yellow_0,t21_yellow_0,d10_yellow_0,t19_yellow_0,t7_yellow_0,t12_yellow_0,t10_yellow_0,d1_tarski,t7_xboole_1,t9_yellow_0,d2_xboole_0,d10_yellow_0,d8_lattice3,t19_yellow_0,d1_tarski,t7_xboole_1,t9_yellow_0,d2_xboole_0,d10_yellow_0,d8_lattice3,t19_yellow_0,t25_orders_2,s2_finset_1,t21_yellow_0]),
    [file(yellow_0,t55_yellow_0),interesting(0.81)]).

fof(t56_yellow_0,theorem,(
    ! [A,B] : 
      ( m2_relset_1(B,A,A)
     => B = k1_toler_1(B,A) ) ),
    inference(mizar_proof,[status(thm)],[t28_xboole_1,d6_wellord1]),
    [file(yellow_0,t56_yellow_0),interesting(0.80)]).

fof(t34_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( ( r1_tarski(B,C)
            & r1_yellow_0(A,B)
            & r1_yellow_0(A,C) )
         => r1_orders_2(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_lattice3,d9_yellow_0,d9_lattice3,d9_yellow_0]),
    [file(yellow_0,t34_yellow_0),interesting(0.79)]).

fof(t35_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( ( r1_tarski(B,C)
            & r2_yellow_0(A,B)
            & r2_yellow_0(A,C) )
         => r1_orders_2(A,k2_yellow_0(A,C),k2_yellow_0(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,d10_yellow_0,d8_lattice3,d10_yellow_0]),
    [file(yellow_0,t35_yellow_0),interesting(0.79)]).

fof(t44_yellow_0,theorem,(
    ! [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,k3_yellow_0(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_yellow_0,t42_yellow_0,t30_yellow_0]),
    [file(yellow_0,t44_yellow_0),interesting(0.79)]).

fof(t45_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_orders_2(A,B,k4_yellow_0(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_yellow_0,t43_yellow_0,t31_yellow_0]),
    [file(yellow_0,t45_yellow_0),interesting(0.78)]).

fof(t6_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r2_lattice3(A,k1_xboole_0,B)
            & r1_lattice3(A,k1_xboole_0,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_lattice3,d8_lattice3]),
    [file(yellow_0,t6_yellow_0),interesting(0.77)]).

fof(t59_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => m1_subset_1(C,u1_struct_0(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_yellow_0]),
    [file(yellow_0,t59_yellow_0),interesting(0.76)]).

fof(t38_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r1_yellow_0(A,k1_struct_0(A,B))
            & r2_yellow_0(A,k1_struct_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_yellow_0,t7_yellow_0,t15_yellow_0,t7_yellow_0,t16_yellow_0]),
    [file(yellow_0,t38_yellow_0),interesting(0.74)]).

fof(t11_yellow_0,theorem,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(A))
             => ( ( r2_lattice3(A,B,C)
                  & r1_orders_2(A,C,D) )
               => r2_lattice3(A,B,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_lattice3,d9_lattice3,t26_orders_2]),
    [file(yellow_0,t11_yellow_0),interesting(0.74)]).

fof(t9_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( r1_tarski(B,C)
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(A))
             => ( ( r1_lattice3(A,C,D)
                 => r1_lattice3(A,B,D) )
                & ( r2_lattice3(A,C,D)
                 => r2_lattice3(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,d8_lattice3,d9_lattice3,d9_lattice3]),
    [file(yellow_0,t9_yellow_0),interesting(0.74)]).

fof(t12_yellow_0,theorem,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(A))
             => ( ( r1_lattice3(A,B,C)
                  & r1_orders_2(A,D,C) )
               => r1_lattice3(A,B,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,d8_lattice3,t26_orders_2]),
    [file(yellow_0,t12_yellow_0),interesting(0.74)]).

fof(t26_yellow_0,theorem,(
    ! [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))
           => ! [C] : 
                ( r1_yellow_0(A,C)
               => k1_yellow_0(A,C) = k1_yellow_0(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_yellow_0,d9_yellow_0,t2_yellow_0,t2_yellow_0,d9_yellow_0,t1_yellow_0,d9_yellow_0]),
    [file(yellow_0,t26_yellow_0),interesting(0.73)]).

fof(t27_yellow_0,theorem,(
    ! [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))
           => ! [C] : 
                ( r2_yellow_0(A,C)
               => k2_yellow_0(A,C) = k2_yellow_0(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_yellow_0,d10_yellow_0,t2_yellow_0,t2_yellow_0,d10_yellow_0,t1_yellow_0,d10_yellow_0]),
    [file(yellow_0,t27_yellow_0),interesting(0.73)]).

fof(t4_yellow_0,theorem,(
    ! [A] : 
      ( ( v3_orders_2(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,B,C)
               => ! [D] : 
                    ( ( r1_lattice3(A,D,C)
                     => r1_lattice3(A,D,B) )
                    & ( r2_lattice3(A,D,B)
                     => r2_lattice3(A,D,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,d8_lattice3,t26_orders_2,d9_lattice3,d9_lattice3,t26_orders_2]),
    [file(yellow_0,t4_yellow_0),interesting(0.68)]).

fof(t47_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( ( r1_yellow_0(A,B)
            & ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_lattice3(A,B,D)
                <=> r2_lattice3(A,C,D) ) ) )
         => k1_yellow_0(A,B) = k1_yellow_0(A,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t46_yellow_0,d9_yellow_0,d9_yellow_0,d9_yellow_0]),
    [file(yellow_0,t47_yellow_0),interesting(0.68)]).

fof(t49_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( ( r2_yellow_0(A,B)
            & ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r1_lattice3(A,B,D)
                <=> r1_lattice3(A,C,D) ) ) )
         => k2_yellow_0(A,B) = k2_yellow_0(A,C) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_yellow_0,d10_yellow_0,d10_yellow_0,d10_yellow_0]),
    [file(yellow_0,t49_yellow_0),interesting(0.68)]).

fof(t10_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C,D] : 
          ( m1_subset_1(D,u1_struct_0(A))
         => ( ( ( r1_lattice3(A,B,D)
                & r1_lattice3(A,C,D) )
             => r1_lattice3(A,k2_xboole_0(B,C),D) )
            & ( ( r2_lattice3(A,B,D)
                & r2_lattice3(A,C,D) )
             => r2_lattice3(A,k2_xboole_0(B,C),D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,d8_lattice3,d2_xboole_0,d9_lattice3,d9_lattice3,d2_xboole_0]),
    [file(yellow_0,t10_yellow_0),interesting(0.67)]).

fof(t46_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( ( ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_lattice3(A,B,D)
                <=> r2_lattice3(A,C,D) ) )
            & r1_yellow_0(A,B) )
         => r1_yellow_0(A,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_yellow_0,d7_yellow_0]),
    [file(yellow_0,t46_yellow_0),interesting(0.67)]).

fof(t48_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( ( ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r1_lattice3(A,B,D)
                <=> r1_lattice3(A,C,D) ) )
            & r2_yellow_0(A,B) )
         => r2_yellow_0(A,C) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_yellow_0,d8_yellow_0]),
    [file(yellow_0,t48_yellow_0),interesting(0.67)]).

fof(t15_yellow_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( r1_yellow_0(A,B)
        <=> ? [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
              & r2_lattice3(A,B,C)
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_lattice3(A,B,D)
                   => r1_orders_2(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_yellow_0,d7_yellow_0,t25_orders_2]),
    [file(yellow_0,t15_yellow_0),interesting(0.66)]).

fof(t16_yellow_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( r2_yellow_0(A,B)
        <=> ? [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
              & r1_lattice3(A,B,C)
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_lattice3(A,B,D)
                   => r1_orders_2(A,D,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_yellow_0,d8_yellow_0,t25_orders_2]),
    [file(yellow_0,t16_yellow_0),interesting(0.66)]).

fof(t40_yellow_0,theorem,(
    ! [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))
             => k2_yellow_0(A,k2_struct_0(A,B,C)) = k12_lattice3(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_yellow_0,t8_yellow_0,t8_yellow_0,t23_yellow_0,t16_yellow_0,d10_yellow_0]),
    [file(yellow_0,t40_yellow_0),interesting(0.64)]).

fof(t41_yellow_0,theorem,(
    ! [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))
             => k1_yellow_0(A,k2_struct_0(A,B,C)) = k13_lattice3(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_yellow_0,t8_yellow_0,t8_yellow_0,t22_yellow_0,t15_yellow_0,d9_yellow_0]),
    [file(yellow_0,t41_yellow_0),interesting(0.64)]).

fof(t51_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( r1_yellow_0(A,B)
            | r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
         => k1_yellow_0(A,B) = k1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_yellow_0,t50_yellow_0,t47_yellow_0]),
    [file(yellow_0,t51_yellow_0),interesting(0.62)]).

fof(t52_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( r2_yellow_0(A,B)
            | r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
         => k2_yellow_0(A,B) = k2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_yellow_0,t50_yellow_0,t49_yellow_0]),
    [file(yellow_0,t52_yellow_0),interesting(0.62)]).

fof(t36_yellow_0,theorem,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( ( r1_yellow_0(A,B)
            & r1_yellow_0(A,C)
            & r1_yellow_0(A,k2_xboole_0(B,C)) )
         => k1_yellow_0(A,k2_xboole_0(B,C)) = k10_lattice3(A,k1_yellow_0(A,B),k1_yellow_0(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t34_yellow_0,t30_yellow_0,t4_yellow_0,t10_yellow_0,t30_yellow_0,t18_yellow_0]),
    [file(yellow_0,t36_yellow_0),interesting(0.58)]).

fof(t37_yellow_0,theorem,(
    ! [A] : 
      ( ( v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( ( r2_yellow_0(A,B)
            & r2_yellow_0(A,C)
            & r2_yellow_0(A,k2_xboole_0(B,C)) )
         => k2_yellow_0(A,k2_xboole_0(B,C)) = k11_lattice3(A,k2_yellow_0(A,B),k2_yellow_0(A,C)) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t35_yellow_0,t31_yellow_0,t4_yellow_0,t10_yellow_0,t31_yellow_0,t19_yellow_0]),
    [file(yellow_0,t37_yellow_0),interesting(0.58)]).

fof(t3_yellow_0,theorem,(
    ! [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))
              & v3_lattice3(A) )
           => v3_lattice3(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_lattice3,d12_lattice3,t2_yellow_0,t2_yellow_0,t1_yellow_0]),
    [file(yellow_0,t3_yellow_0),interesting(0.57)]).

fof(t60_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_yellow_0(B,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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( E = C
                              & F = D
                              & r1_orders_2(B,E,F) )
                           => r1_orders_2(A,C,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_yellow_0,d9_orders_2,d9_orders_2]),
    [file(yellow_0,t60_yellow_0),interesting(0.55)]).

fof(t62_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C,D] : 
              ( m1_subset_1(D,u1_struct_0(A))
             => ! [E] : 
                  ( m1_subset_1(E,u1_struct_0(B))
                 => ( E = D
                   => ( ( r1_lattice3(A,C,D)
                       => r1_lattice3(B,C,E) )
                      & ( r2_lattice3(A,C,D)
                       => r2_lattice3(B,C,E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,t59_yellow_0,d8_lattice3,t61_yellow_0,d9_lattice3,t59_yellow_0,d9_lattice3,t61_yellow_0]),
    [file(yellow_0,t62_yellow_0),interesting(0.52)]).

fof(t24_yellow_0,theorem,(
    ! [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))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B = k13_lattice3(A,B,C)
              <=> r1_orders_2(A,C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_yellow_0]),
    [file(yellow_0,t24_yellow_0),interesting(0.51)]).

fof(t39_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( k1_yellow_0(A,k1_struct_0(A,B)) = B
            & k2_yellow_0(A,k1_struct_0(A,B)) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_yellow_0,t7_yellow_0,t30_yellow_0,t7_yellow_0,t31_yellow_0]),
    [file(yellow_0,t39_yellow_0),interesting(0.51)]).

fof(t25_yellow_0,theorem,(
    ! [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))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B = k12_lattice3(A,B,C)
              <=> r3_orders_2(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_yellow_0]),
    [file(yellow_0,t25_yellow_0),interesting(0.50)]).

fof(t13_yellow_0,theorem,(
    ! [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_yellow_0(A)
               => v1_yellow_0(B) )
              & ( v2_yellow_0(A)
               => v2_yellow_0(B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_yellow_0,d4_yellow_0,t2_yellow_0,d5_yellow_0,d5_yellow_0,t2_yellow_0]),
    [file(yellow_0,t13_yellow_0),interesting(0.46)]).

fof(t32_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( B = k1_yellow_0(A,C)
            <=> ( r2_lattice3(A,C,B)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_lattice3(A,C,D)
                     => r1_orders_2(A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_yellow_0,t30_yellow_0]),
    [file(yellow_0,t32_yellow_0),interesting(0.45)]).

fof(t33_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( B = k2_yellow_0(A,C)
            <=> ( r1_lattice3(A,C,B)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_lattice3(A,C,D)
                     => r1_orders_2(A,D,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_yellow_0,t31_yellow_0]),
    [file(yellow_0,t33_yellow_0),interesting(0.45)]).

fof(t29_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( k15_lattice3(A,B) = k1_yellow_0(k3_lattice3(A),B)
          & k16_lattice3(A,B) = k2_yellow_0(k3_lattice3(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_lattice3,t30_lattice3,t31_lattice3,d21_lattice3,t7_lattice3,t15_yellow_0,d9_yellow_0,t34_lattice3,t28_lattice3,t29_lattice3,t34_lattice3,t7_lattice3,t16_yellow_0,d10_yellow_0]),
    [file(yellow_0,t29_yellow_0),interesting(0.44)]).

fof(t64_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( ( r2_yellow_0(A,C)
                  & r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) )
               => ( r2_yellow_0(B,C)
                  & k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_yellow_0,d10_yellow_0,d10_yellow_0,t62_yellow_0,t59_yellow_0,t63_yellow_0,d10_yellow_0,t61_yellow_0,d8_yellow_0,t59_yellow_0,t63_yellow_0,t60_yellow_0,t26_orders_2,d10_yellow_0,d10_yellow_0]),
    [file(yellow_0,t64_yellow_0),interesting(0.40)]).

fof(t65_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( ( r1_yellow_0(A,C)
                  & r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) )
               => ( r1_yellow_0(B,C)
                  & k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_yellow_0,d9_yellow_0,d9_yellow_0,t62_yellow_0,t59_yellow_0,t63_yellow_0,d9_yellow_0,t61_yellow_0,d7_yellow_0,t59_yellow_0,t63_yellow_0,t60_yellow_0,t26_orders_2,d9_yellow_0,d9_yellow_0]),
    [file(yellow_0,t65_yellow_0),interesting(0.40)]).

fof(s1_yellow_0,theorem,(
    ? [A] : 
      ( ~ v3_struct_0(A)
      & v1_orders_2(A)
      & l1_orders_2(A)
      & u1_struct_0(A) = f1_s1_yellow_0
      & ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_orders_2(A,B,C)
              <=> p1_s1_yellow_0(B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s2_relset_1,d9_orders_2]),
    [file(yellow_0,s1_yellow_0),interesting(0.32)]).

fof(t28_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( k1_yellow_0(A,B) = k15_lattice3(k14_lattice3(A),B)
          & k2_yellow_0(A,B) = k16_lattice3(k14_lattice3(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_lattice3,d12_lattice3,t15_yellow_0,d9_yellow_0,t2_yellow_0,t31_lattice3,t30_lattice3,t2_yellow_0,d9_yellow_0,t1_yellow_0,t7_lattice3,d21_lattice3,t34_lattice3,t28_lattice3,t2_yellow_0,t2_yellow_0,t29_lattice3,t34_lattice3,t7_lattice3,t1_yellow_0,t16_yellow_0,d10_yellow_0]),
    [file(yellow_0,t28_yellow_0),interesting(0.30)]).

fof(t57_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v4_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A)
            & m1_yellow_0(g1_orders_2(B,k1_toler_1(u1_orders_2(A),B)),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_yellow_0,t15_wellord1,d14_yellow_0]),
    [file(yellow_0,t57_yellow_0),interesting(0.30)]).

fof(t70_yellow_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v5_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( E = C
                              & F = D )
                           => k12_lattice3(B,C,D) = k12_lattice3(A,E,F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_yellow_0,d16_yellow_0,t40_yellow_0,t64_yellow_0,t40_yellow_0]),
    [file(yellow_0,t70_yellow_0),interesting(0.18)]).

fof(t71_yellow_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & v6_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( E = C
                              & F = D )
                           => k13_lattice3(B,C,D) = k13_lattice3(A,E,F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_yellow_0,d17_yellow_0,t41_yellow_0,t65_yellow_0,t41_yellow_0]),
    [file(yellow_0,t71_yellow_0),interesting(0.18)]).

fof(t68_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( r2_hidden(k2_yellow_0(A,C),u1_struct_0(B))
               => k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_yellow_0,t64_yellow_0]),
    [file(yellow_0,t68_yellow_0),interesting(0.05)]).

fof(t69_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ( r2_hidden(k1_yellow_0(A,C),u1_struct_0(B))
               => k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_yellow_0,t65_yellow_0]),
    [file(yellow_0,t69_yellow_0),interesting(0.05)]).

fof(s2_relset_1,theorem,(
    ? [A] : 
      ( m2_relset_1(A,f1_s2_relset_1,f2_s2_relset_1)
      & ! [B] : 
          ( m1_subset_1(B,f1_s2_relset_1)
         => ! [C] : 
              ( m1_subset_1(C,f2_s2_relset_1)
             => ( r2_hidden(k4_tarski(B,C),A)
              <=> p1_s2_relset_1(B,C) ) ) ) ) ),
    file(relset_1,s2_relset_1),
    [interesting(0.00)]).

fof(d9_orders_2,definition,(
    ! [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,B,C)
              <=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) ),
    file(orders_2,d9_orders_2),
    [interesting(0.00)]).

fof(d4_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_yellow_0(A)
      <=> ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & r1_lattice3(A,u1_struct_0(A),B) ) ) ) ),
    file(yellow_0,d4_yellow_0),
    [interesting(0.00)]).

fof(d9_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r2_lattice3(A,B,C)
          <=> ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_hidden(D,B)
                 => r1_orders_2(A,D,C) ) ) ) ) ) ),
    file(lattice3,d9_lattice3),
    [interesting(0.00)]).

fof(d10_orders_2,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_orders_2(A,B,C)
              <=> ( r1_orders_2(A,B,C)
                  & B != C ) ) ) ) ) ),
    file(orders_2,d10_orders_2),
    [interesting(0.00)]).

fof(t1_yellow_0,theorem,(
    ! [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))
           => ! [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(B))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(B))
                           => ( ( C = E
                                & D = F )
                             => ( ( r1_orders_2(A,C,D)
                                 => r1_orders_2(B,E,F) )
                                & ( r2_orders_2(A,C,D)
                                 => r2_orders_2(B,E,F) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_orders_2,d10_orders_2]),
    [file(yellow_0,t1_yellow_0),interesting(0.00)]).

fof(d8_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r1_lattice3(A,B,C)
          <=> ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_hidden(D,B)
                 => r1_orders_2(A,C,D) ) ) ) ) ) ),
    file(lattice3,d8_lattice3),
    [interesting(0.00)]).

fof(t2_yellow_0,theorem,(
    ! [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))
           => ! [C,D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ! [E] : 
                    ( m1_subset_1(E,u1_struct_0(B))
                   => ( D = E
                     => ( ( r2_lattice3(A,C,D)
                         => r2_lattice3(B,C,E) )
                        & ( r1_lattice3(A,C,D)
                         => r1_lattice3(B,C,E) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_lattice3,d9_lattice3,t1_yellow_0,d8_lattice3,d8_lattice3,t1_yellow_0]),
    [file(yellow_0,t2_yellow_0),interesting(0.00)]).

fof(d5_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_yellow_0(A)
      <=> ? [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
            & r2_lattice3(A,u1_struct_0(A),B) ) ) ) ),
    file(yellow_0,d5_yellow_0),
    [interesting(0.00)]).

fof(d10_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v1_lattice3(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,C,D)
                    & ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r1_orders_2(A,B,E)
                            & r1_orders_2(A,C,E) )
                         => r1_orders_2(A,D,E) ) ) ) ) ) ) ) ),
    file(lattice3,d10_lattice3),
    [interesting(0.00)]).

fof(d13_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v4_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,C,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,B,E)
                              & r1_orders_2(A,C,E) )
                           => r1_orders_2(A,D,E) ) ) )
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( D = k10_lattice3(A,B,C)
                      <=> ( r1_orders_2(A,B,D)
                          & r1_orders_2(A,C,D)
                          & ! [E] : 
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ( ( r1_orders_2(A,B,E)
                                  & r1_orders_2(A,C,E) )
                               => r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ) ) ),
    file(lattice3,d13_lattice3),
    [interesting(0.00)]).

fof(t22_yellow_0,theorem,(
    ! [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))
                 => ( D = k13_lattice3(A,B,C)
                  <=> ( r1_orders_2(A,B,D)
                      & r1_orders_2(A,C,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,B,E)
                              & r1_orders_2(A,C,E) )
                           => r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_lattice3,d13_lattice3]),
    [file(yellow_0,t22_yellow_0),interesting(0.00)]).

fof(d11_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_lattice3(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,B)
                    & r1_orders_2(A,D,C)
                    & ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r1_orders_2(A,E,B)
                            & r1_orders_2(A,E,C) )
                         => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ),
    file(lattice3,d11_lattice3),
    [interesting(0.00)]).

fof(d14_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v4_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,B)
                      & r1_orders_2(A,D,C)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,E,B)
                              & r1_orders_2(A,E,C) )
                           => r1_orders_2(A,E,D) ) ) )
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( D = k11_lattice3(A,B,C)
                      <=> ( r1_orders_2(A,D,B)
                          & r1_orders_2(A,D,C)
                          & ! [E] : 
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ( ( r1_orders_2(A,E,B)
                                  & r1_orders_2(A,E,C) )
                               => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) ) ),
    file(lattice3,d14_lattice3),
    [interesting(0.00)]).

fof(t23_yellow_0,theorem,(
    ! [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))
                 => ( D = k12_lattice3(A,B,C)
                  <=> ( r1_orders_2(A,D,B)
                      & r1_orders_2(A,D,C)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,E,B)
                              & r1_orders_2(A,E,C) )
                           => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_lattice3,d14_lattice3]),
    [file(yellow_0,t23_yellow_0),interesting(0.00)]).

fof(d7_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( r1_yellow_0(A,B)
        <=> ? [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
              & r2_lattice3(A,B,C)
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r2_lattice3(A,B,D)
                   => r1_orders_2(A,C,D) ) )
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r2_lattice3(A,B,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r2_lattice3(A,B,E)
                           => r1_orders_2(A,D,E) ) ) )
                   => D = C ) ) ) ) ) ),
    file(yellow_0,d7_yellow_0),
    [interesting(0.00)]).

fof(d8_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( r2_yellow_0(A,B)
        <=> ? [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
              & r1_lattice3(A,B,C)
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r1_lattice3(A,B,D)
                   => r1_orders_2(A,D,C) ) )
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r1_lattice3(A,B,D)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r1_lattice3(A,B,E)
                           => r1_orders_2(A,E,D) ) ) )
                   => D = C ) ) ) ) ) ),
    file(yellow_0,d8_yellow_0),
    [interesting(0.00)]).

fof(d9_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r1_yellow_0(A,B)
           => ( C = k1_yellow_0(A,B)
            <=> ( r2_lattice3(A,B,C)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_lattice3(A,B,D)
                     => r1_orders_2(A,C,D) ) ) ) ) ) ) ) ),
    file(yellow_0,d9_yellow_0),
    [interesting(0.00)]).

fof(d10_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r2_yellow_0(A,B)
           => ( C = k2_yellow_0(A,B)
            <=> ( r1_lattice3(A,B,C)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_lattice3(A,B,D)
                     => r1_orders_2(A,D,C) ) ) ) ) ) ) ) ),
    file(yellow_0,d10_yellow_0),
    [interesting(0.00)]).

fof(d15_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( ( v2_orders_2(A)
          & v3_orders_2(A)
          & v4_orders_2(A)
          & v1_lattice3(A)
          & v2_lattice3(A)
          & l1_orders_2(A) )
       => ! [B] : 
            ( ( ~ v3_struct_0(B)
              & v3_lattices(B)
              & v10_lattices(B)
              & l3_lattices(B) )
           => ( B = k14_lattice3(A)
            <=> g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = k3_lattice3(B) ) ) ) ) ),
    file(lattice3,d15_lattice3),
    [interesting(0.00)]).

fof(d12_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_lattice3(A)
      <=> ! [B] : 
          ? [C] : 
            ( m1_subset_1(C,u1_struct_0(A))
            & r2_lattice3(A,B,C)
            & ! [D] : 
                ( m1_subset_1(D,u1_struct_0(A))
               => ( r2_lattice3(A,B,D)
                 => r1_orders_2(A,C,D) ) ) ) ) ) ),
    file(lattice3,d12_lattice3),
    [interesting(0.00)]).

fof(t25_orders_2,theorem,(
    ! [A] : 
      ( ( v4_orders_2(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,B,C)
                  & r1_orders_2(A,C,B) )
               => B = C ) ) ) ) ),
    file(orders_2,t25_orders_2),
    [interesting(0.00)]).

fof(t31_lattice3,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(k3_lattice3(B)))
         => ( r2_lattice3(k3_lattice3(B),A,C)
          <=> r4_lattice3(B,k5_lattice3(B,C),A) ) ) ) ),
    file(lattice3,t31_lattice3),
    [interesting(0.00)]).

fof(t30_lattice3,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r4_lattice3(B,C,A)
          <=> r2_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) ) ) ) ),
    file(lattice3,t30_lattice3),
    [interesting(0.00)]).

fof(t7_lattice3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_lattices(A,B,C)
              <=> r3_orders_2(k3_lattice3(A),k4_lattice3(A,B),k4_lattice3(A,C)) ) ) ) ) ),
    file(lattice3,t7_lattice3),
    [interesting(0.00)]).

fof(d21_lattice3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l3_lattices(A) )
     => ( ( ~ v3_struct_0(A)
          & v10_lattices(A)
          & v4_lattice3(A)
          & l3_lattices(A) )
       => ! [B,C] : 
            ( m1_subset_1(C,u1_struct_0(A))
           => ( C = k15_lattice3(A,B)
            <=> ( r4_lattice3(A,C,B)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r4_lattice3(A,D,B)
                     => r1_lattices(A,C,D) ) ) ) ) ) ) ) ),
    file(lattice3,d21_lattice3),
    [interesting(0.00)]).

fof(t34_lattice3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v10_lattices(A)
        & v4_lattice3(A)
        & l3_lattices(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( B = k16_lattice3(A,C)
            <=> ( r3_lattice3(A,B,C)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r3_lattice3(A,D,C)
                     => r3_lattices(A,D,B) ) ) ) ) ) ) ),
    file(lattice3,t34_lattice3),
    [interesting(0.00)]).

fof(t28_lattice3,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(B))
         => ( r3_lattice3(B,C,A)
          <=> r1_lattice3(k3_lattice3(B),A,k4_lattice3(B,C)) ) ) ) ),
    file(lattice3,t28_lattice3),
    [interesting(0.00)]).

fof(t29_lattice3,theorem,(
    ! [A,B] : 
      ( ( ~ v3_struct_0(B)
        & v10_lattices(B)
        & l3_lattices(B) )
     => ! [C] : 
          ( m1_subset_1(C,u1_struct_0(k3_lattice3(B)))
         => ( r1_lattice3(k3_lattice3(B),A,C)
          <=> r3_lattice3(B,k5_lattice3(B,C),A) ) ) ) ),
    file(lattice3,t29_lattice3),
    [interesting(0.00)]).

fof(t30_yellow_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( ( B = k1_yellow_0(A,C)
                  & r1_yellow_0(A,C) )
               => ( r2_lattice3(A,C,B)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_lattice3(A,C,D)
                       => r1_orders_2(A,B,D) ) ) ) )
              & ( ( r2_lattice3(A,C,B)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r2_lattice3(A,C,D)
                       => r1_orders_2(A,B,D) ) ) )
               => ( B = k1_yellow_0(A,C)
                  & r1_yellow_0(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_yellow_0,d9_yellow_0]),
    [file(yellow_0,t30_yellow_0),interesting(0.00)]).

fof(t31_yellow_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( ( B = k2_yellow_0(A,C)
                  & r2_yellow_0(A,C) )
               => ( r1_lattice3(A,C,B)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r1_lattice3(A,C,D)
                       => r1_orders_2(A,D,B) ) ) ) )
              & ( ( r1_lattice3(A,C,B)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( r1_lattice3(A,C,D)
                       => r1_orders_2(A,D,B) ) ) )
               => ( B = k2_yellow_0(A,C)
                  & r2_yellow_0(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_yellow_0,d10_yellow_0]),
    [file(yellow_0,t31_yellow_0),interesting(0.00)]).

fof(t7_xboole_1,theorem,(
    ! [A,B] : r1_tarski(A,k2_xboole_0(A,B)) ),
    file(xboole_1,t7_xboole_1),
    [interesting(0.00)]).

fof(t26_orders_2,theorem,(
    ! [A] : 
      ( ( v3_orders_2(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,C,D) )
                   => r1_orders_2(A,B,D) ) ) ) ) ) ),
    file(orders_2,t26_orders_2),
    [interesting(0.00)]).

fof(d2_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k2_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            | r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d2_xboole_0),
    [interesting(0.00)]).

fof(d2_tarski,definition,(
    ! [A,B,C] : 
      ( C = k2_tarski(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( D = A
            | D = B ) ) ) ),
    file(tarski,d2_tarski),
    [interesting(0.00)]).

fof(t8_yellow_0,theorem,(
    ! [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_lattice3(A,k2_tarski(C,D),B)
                     => ( r1_orders_2(A,B,C)
                        & r1_orders_2(A,B,D) ) )
                    & ( ( r1_orders_2(A,B,C)
                        & r1_orders_2(A,B,D) )
                     => r1_lattice3(A,k2_tarski(C,D),B) )
                    & ( r2_lattice3(A,k2_tarski(C,D),B)
                     => ( r1_orders_2(A,C,B)
                        & r1_orders_2(A,D,B) ) )
                    & ( ( r1_orders_2(A,C,B)
                        & r1_orders_2(A,D,B) )
                     => r2_lattice3(A,k2_tarski(C,D),B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_tarski,d8_lattice3,d8_lattice3,d2_tarski,d9_lattice3,d9_lattice3,d2_tarski]),
    [file(yellow_0,t8_yellow_0),interesting(0.00)]).

fof(t18_yellow_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(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))
                 => ( ( ( D = k10_lattice3(A,B,C)
                        & r1_yellow_0(A,k2_tarski(B,C)) )
                     => ( r1_orders_2(A,B,D)
                        & r1_orders_2(A,C,D)
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( ( r1_orders_2(A,B,E)
                                & r1_orders_2(A,C,E) )
                             => r1_orders_2(A,D,E) ) ) ) )
                    & ( ( r1_orders_2(A,B,D)
                        & r1_orders_2(A,C,D)
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( ( r1_orders_2(A,B,E)
                                & r1_orders_2(A,C,E) )
                             => r1_orders_2(A,D,E) ) ) )
                     => ( D = k10_lattice3(A,B,C)
                        & r1_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_yellow_0,t8_yellow_0,t8_yellow_0,d13_lattice3,d13_lattice3,t8_yellow_0,t8_yellow_0,t15_yellow_0]),
    [file(yellow_0,t18_yellow_0),interesting(0.00)]).

fof(t19_yellow_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(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))
                 => ( ( ( D = k11_lattice3(A,B,C)
                        & r2_yellow_0(A,k2_tarski(B,C)) )
                     => ( r1_orders_2(A,D,B)
                        & r1_orders_2(A,D,C)
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( ( r1_orders_2(A,E,B)
                                & r1_orders_2(A,E,C) )
                             => r1_orders_2(A,E,D) ) ) ) )
                    & ( ( r1_orders_2(A,D,B)
                        & r1_orders_2(A,D,C)
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ( ( r1_orders_2(A,E,B)
                                & r1_orders_2(A,E,C) )
                             => r1_orders_2(A,E,D) ) ) )
                     => ( D = k11_lattice3(A,B,C)
                        & r2_yellow_0(A,k2_tarski(B,C)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_yellow_0,t8_yellow_0,t8_yellow_0,d14_lattice3,d14_lattice3,t8_yellow_0,t8_yellow_0,t16_yellow_0]),
    [file(yellow_0,t19_yellow_0),interesting(0.00)]).

fof(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

fof(t7_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ( r1_lattice3(A,k1_tarski(C),B)
                 => r1_orders_2(A,B,C) )
                & ( r1_orders_2(A,B,C)
                 => r1_lattice3(A,k1_tarski(C),B) )
                & ( r2_lattice3(A,k1_tarski(C),B)
                 => r1_orders_2(A,C,B) )
                & ( r1_orders_2(A,C,B)
                 => r2_lattice3(A,k1_tarski(C),B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d8_lattice3,d8_lattice3,d1_tarski,d9_lattice3,d9_lattice3,d1_tarski]),
    [file(yellow_0,t7_yellow_0),interesting(0.00)]).

fof(d3_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k3_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d3_xboole_0),
    [interesting(0.00)]).

fof(t5_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( ( r2_lattice3(A,B,C)
             => r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) )
            & ( r2_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)
             => r2_lattice3(A,B,C) )
            & ( r1_lattice3(A,B,C)
             => r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C) )
            & ( r1_lattice3(A,k3_xboole_0(B,u1_struct_0(A)),C)
             => r1_lattice3(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_lattice3,d9_lattice3,d3_xboole_0,d9_lattice3,d9_lattice3,d3_xboole_0,d8_lattice3,d8_lattice3,d3_xboole_0,d8_lattice3,d8_lattice3,d3_xboole_0]),
    [file(yellow_0,t5_yellow_0),interesting(0.00)]).

fof(t50_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( r1_yellow_0(A,B)
           => r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
          & ( r1_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))
           => r1_yellow_0(A,B) )
          & ( r2_yellow_0(A,B)
           => r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A))) )
          & ( r2_yellow_0(A,k3_xboole_0(B,u1_struct_0(A)))
           => r2_yellow_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_yellow_0,t46_yellow_0,t48_yellow_0]),
    [file(yellow_0,t50_yellow_0),interesting(0.00)]).

fof(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(s2_finset_1,theorem,
    ( ( v1_finset_1(f1_s2_finset_1)
      & p1_s2_finset_1(k1_xboole_0)
      & ! [A,B] : 
          ( ( r2_hidden(A,f1_s2_finset_1)
            & r1_tarski(B,f1_s2_finset_1)
            & p1_s2_finset_1(B) )
         => p1_s2_finset_1(k2_xboole_0(B,k1_tarski(A))) ) )
   => p1_s2_finset_1(f1_s2_finset_1) ),
    file(finset_1,s2_finset_1),
    [interesting(0.00)]).

fof(t28_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k3_xboole_0(A,B) = A ) ),
    file(xboole_1,t28_xboole_1),
    [interesting(0.00)]).

fof(d6_wellord1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : k2_wellord1(A,B) = k3_xboole_0(A,k2_zfmisc_1(B,B)) ) ),
    file(wellord1,d6_wellord1),
    [interesting(0.00)]).

fof(d13_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( l1_orders_2(B)
         => ( m1_yellow_0(B,A)
          <=> ( r1_tarski(u1_struct_0(B),u1_struct_0(A))
              & r1_tarski(u1_orders_2(B),u1_orders_2(A)) ) ) ) ) ),
    file(yellow_0,d13_yellow_0),
    [interesting(0.00)]).

fof(t15_wellord1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( r1_tarski(k2_wellord1(B,A),B)
        & r1_tarski(k2_wellord1(B,A),k2_zfmisc_1(A,A)) ) ) ),
    file(wellord1,t15_wellord1),
    [interesting(0.00)]).

fof(d14_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v4_yellow_0(B,A)
          <=> u1_orders_2(B) = k1_toler_1(u1_orders_2(A),u1_struct_0(B)) ) ) ) ),
    file(yellow_0,d14_yellow_0),
    [interesting(0.00)]).

fof(t58_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( ( v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( ( v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ( u1_struct_0(B) = u1_struct_0(C)
               => g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_yellow_0]),
    [file(yellow_0,t58_yellow_0),interesting(0.00)]).

fof(t106_zfmisc_1,theorem,(
    ! [A,B,C,D] : 
      ( r2_hidden(k4_tarski(A,B),k2_zfmisc_1(C,D))
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,D) ) ) ),
    file(zfmisc_1,t106_zfmisc_1),
    [interesting(0.00)]).

fof(t16_wellord1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_hidden(A,k2_wellord1(C,B))
      <=> ( r2_hidden(A,C)
          & r2_hidden(A,k2_zfmisc_1(B,B)) ) ) ) ),
    file(wellord1,t16_wellord1),
    [interesting(0.00)]).

fof(t61_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( ( v4_yellow_0(B,A)
            & m1_yellow_0(B,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(B))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(B))
                         => ( ( E = C
                              & F = D
                              & r1_orders_2(A,C,D)
                              & r2_hidden(E,u1_struct_0(B))
                              & r2_hidden(F,u1_struct_0(B)) )
                           => r1_orders_2(B,E,F) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_yellow_0,d9_orders_2,t106_zfmisc_1,t16_wellord1,d9_orders_2]),
    [file(yellow_0,t61_yellow_0),interesting(0.00)]).

fof(t63_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( E = D
                       => ( ( r1_lattice3(B,C,E)
                           => r1_lattice3(A,C,D) )
                          & ( r2_lattice3(B,C,E)
                           => r2_lattice3(A,C,D) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,d8_lattice3,t60_yellow_0,d9_lattice3,d9_lattice3,t60_yellow_0]),
    [file(yellow_0,t63_yellow_0),interesting(0.00)]).

fof(t66_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r2_yellow_0(A,k2_struct_0(B,C,D))
                      & r2_hidden(k2_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) )
                   => ( r2_yellow_0(B,k2_struct_0(B,C,D))
                      & k2_yellow_0(B,k2_struct_0(B,C,D)) = k2_yellow_0(A,k2_struct_0(B,C,D)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t64_yellow_0]),
    [file(yellow_0,t66_yellow_0),interesting(0.00)]).

fof(t67_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & v4_yellow_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(B))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ( ( r1_yellow_0(A,k2_struct_0(B,C,D))
                      & r2_hidden(k1_yellow_0(A,k2_struct_0(B,C,D)),u1_struct_0(B)) )
                   => ( r1_yellow_0(B,k2_struct_0(B,C,D))
                      & k1_yellow_0(B,k2_struct_0(B,C,D)) = k1_yellow_0(A,k2_struct_0(B,C,D)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t65_yellow_0]),
    [file(yellow_0,t67_yellow_0),interesting(0.00)]).

fof(d16_yellow_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v5_yellow_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,u1_struct_0(B))
                        & r2_hidden(D,u1_struct_0(B))
                        & r2_yellow_0(A,k2_struct_0(A,C,D)) )
                     => r2_hidden(k2_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ),
    file(yellow_0,d16_yellow_0),
    [interesting(0.00)]).

fof(d17_yellow_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v6_yellow_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,u1_struct_0(B))
                        & r2_hidden(D,u1_struct_0(B))
                        & r1_yellow_0(A,k2_struct_0(A,C,D)) )
                     => r2_hidden(k1_yellow_0(A,k2_struct_0(A,C,D)),u1_struct_0(B)) ) ) ) ) ) ) ),
    file(yellow_0,d17_yellow_0),
    [interesting(0.00)]).