fof(t16_waybel_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_tarski(B,k4_waybel_0(A,B))
            & r1_tarski(B,k5_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_orders_2,d1_relat_2,d9_orders_2,d15_waybel_0,d3_tarski,d3_tarski,d1_relat_2,d9_orders_2,d16_waybel_0]),
    [file(waybel_0,t16_waybel_0),interesting(1.00)]).

fof(t32_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_yellow_0(A,B)
          <=> r1_yellow_0(A,k4_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_waybel_0,t46_yellow_0]),
    [file(waybel_0,t32_waybel_0),interesting(0.97)]).

fof(t37_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_yellow_0(A,B)
          <=> r2_yellow_0(A,k5_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_waybel_0,t48_yellow_0]),
    [file(waybel_0,t37_waybel_0),interesting(0.97)]).

fof(t22_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(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)
               => r1_tarski(k7_waybel_0(A,C),k7_waybel_0(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t18_waybel_0,t26_orders_2,t18_waybel_0]),
    [file(waybel_0,t22_waybel_0),interesting(0.97)]).

fof(t21_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(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)
               => r1_tarski(k6_waybel_0(A,B),k6_waybel_0(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t17_waybel_0,t26_orders_2,t17_waybel_0]),
    [file(waybel_0,t21_waybel_0),interesting(0.97)]).

fof(t14_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k4_waybel_0(A,B) = a_2_0_waybel_0(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_waybel_0,d3_tarski,d10_xboole_0,d3_tarski,d15_waybel_0]),
    [file(waybel_0,t14_waybel_0),interesting(0.93)]).

fof(t15_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => k5_waybel_0(A,B) = a_2_1_waybel_0(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_waybel_0,d3_tarski,d10_xboole_0,d3_tarski,d16_waybel_0]),
    [file(waybel_0,t15_waybel_0),interesting(0.93)]).

fof(t30_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_waybel_0(B,A)
          <=> v1_waybel_0(k4_waybel_0(A,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_waybel_0,d1_waybel_0,d15_waybel_0,d15_waybel_0,d15_waybel_0,t26_orders_2,d1_waybel_0,d1_waybel_0,d15_waybel_0,d15_waybel_0,t26_orders_2]),
    [file(waybel_0,t30_waybel_0),interesting(0.92)]).

fof(t23_waybel_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v12_waybel_0(B,A)
          <=> r1_tarski(k4_waybel_0(A,B),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d15_waybel_0,d19_waybel_0,d19_waybel_0,d15_waybel_0]),
    [file(waybel_0,t23_waybel_0),interesting(0.90)]).

fof(t24_waybel_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v13_waybel_0(B,A)
          <=> r1_tarski(k5_waybel_0(A,B),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d16_waybel_0,d20_waybel_0,d20_waybel_0,d16_waybel_0]),
    [file(waybel_0,t24_waybel_0),interesting(0.90)]).

fof(t35_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_waybel_0(B,A)
          <=> v2_waybel_0(k5_waybel_0(A,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_waybel_0,d2_waybel_0,d16_waybel_0,d16_waybel_0,t24_orders_2,d16_waybel_0,t26_orders_2,d2_waybel_0,d2_waybel_0,t24_orders_2,d16_waybel_0,d16_waybel_0,t26_orders_2]),
    [file(waybel_0,t35_waybel_0),interesting(0.89)]).

fof(t5_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( v1_waybel_0(k1_struct_0(A,B),A)
            & v2_waybel_0(k1_struct_0(A,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_tarski,d1_waybel_0,d1_tarski,d2_waybel_0]),
    [file(waybel_0,t5_waybel_0),interesting(0.89)]).

fof(t17_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k6_waybel_0(A,B))
              <=> r1_orders_2(A,C,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_waybel_0,d1_tarski,d1_tarski]),
    [file(waybel_0,t17_waybel_0),interesting(0.88)]).

fof(t18_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_hidden(C,k7_waybel_0(A,B))
              <=> r1_orders_2(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t15_waybel_0,d1_tarski,d1_tarski]),
    [file(waybel_0,t18_waybel_0),interesting(0.88)]).

fof(t31_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_lattice3(A,B,C)
              <=> r2_lattice3(A,k4_waybel_0(A,B),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_lattice3,d9_lattice3,d15_waybel_0,t26_orders_2,d9_lattice3,d9_lattice3,d15_waybel_0]),
    [file(waybel_0,t31_waybel_0),interesting(0.85)]).

fof(t34_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r1_yellow_0(A,k6_waybel_0(A,B))
            & k1_yellow_0(A,k6_waybel_0(A,B)) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_yellow_0,t32_waybel_0,t33_waybel_0,t39_yellow_0]),
    [file(waybel_0,t34_waybel_0),interesting(0.85)]).

fof(t36_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_lattice3(A,B,C)
              <=> r1_lattice3(A,k5_waybel_0(A,B),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,d8_lattice3,d16_waybel_0,t26_orders_2,d8_lattice3,d8_lattice3,d16_waybel_0]),
    [file(waybel_0,t36_waybel_0),interesting(0.85)]).

fof(t39_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ( r2_yellow_0(A,k7_waybel_0(A,B))
            & k2_yellow_0(A,k7_waybel_0(A,B)) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_yellow_0,t37_waybel_0,t38_waybel_0,t39_yellow_0]),
    [file(waybel_0,t39_waybel_0),interesting(0.85)]).

fof(t33_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_yellow_0(A,B)
           => k1_yellow_0(A,B) = k1_yellow_0(A,k4_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t31_waybel_0,t47_yellow_0]),
    [file(waybel_0,t33_waybel_0),interesting(0.83)]).

fof(t38_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r2_yellow_0(A,B)
           => k2_yellow_0(A,B) = k2_yellow_0(A,k5_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_waybel_0,t49_yellow_0]),
    [file(waybel_0,t38_waybel_0),interesting(0.83)]).

fof(t10_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] : 
              ( r2_waybel_0(A,B,C)
            <=> ~ r1_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_waybel_0,d11_waybel_0,d4_xboole_0,d11_waybel_0,d12_waybel_0,d4_xboole_0]),
    [file(waybel_0,t10_waybel_0),interesting(0.79)]).

fof(t19_waybel_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))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k6_waybel_0(A,B) = k6_waybel_0(A,C)
               => B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_waybel_0,t17_waybel_0,t25_orders_2]),
    [file(waybel_0,t19_waybel_0),interesting(0.79)]).

fof(t20_waybel_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))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( k7_waybel_0(A,B) = k7_waybel_0(A,C)
               => B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t18_waybel_0,t18_waybel_0,t25_orders_2]),
    [file(waybel_0,t20_waybel_0),interesting(0.79)]).

fof(t9_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] : 
              ( r1_waybel_0(A,B,C)
            <=> ~ r2_waybel_0(A,B,k4_xboole_0(u1_struct_0(A),C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_waybel_0,d12_waybel_0,d4_xboole_0,d12_waybel_0,d11_waybel_0,d4_xboole_0]),
    [file(waybel_0,t9_waybel_0),interesting(0.79)]).

fof(t8_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C,D] : 
              ( r1_tarski(C,D)
             => ( ( r1_waybel_0(A,B,C)
                 => r1_waybel_0(A,B,D) )
                & ( r2_waybel_0(A,B,C)
                 => r2_waybel_0(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_waybel_0,d11_waybel_0,d12_waybel_0,d12_waybel_0]),
    [file(waybel_0,t8_waybel_0),interesting(0.76)]).

fof(t76_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v25_waybel_0(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => r2_yellow_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d40_waybel_0,d8_yellow_0,t25_orders_2,d40_waybel_0,d8_yellow_0]),
    [file(waybel_0,t76_waybel_0),interesting(0.75)]).

fof(t50_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_tarski(B,k12_waybel_0(A,B))
            & r1_tarski(B,k13_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_zfmisc_1,t38_yellow_0,t39_yellow_0,d3_tarski,t37_zfmisc_1,t38_yellow_0,t39_yellow_0,d3_tarski]),
    [file(waybel_0,t50_waybel_0),interesting(0.69)]).

fof(t70_waybel_0,theorem,(
    ! [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_xboole_0(D)
                      & v2_waybel_0(D,A)
                      & v13_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => r3_waybel_0(A,B,C,D) )
               => v21_waybel_0(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d36_waybel_0,d30_waybel_0,t37_waybel_0,d30_waybel_0,t38_waybel_0,t16_waybel_0,t156_relat_1,t31_yellow_0,d8_lattice3,d8_lattice3,d8_lattice3,d12_funct_1,t15_waybel_0,t69_waybel_0,t43_funct_2,d8_lattice3,d5_orders_3,t26_orders_2,t31_yellow_0,t16_yellow_0,d10_yellow_0]),
    [file(waybel_0,t70_waybel_0),interesting(0.63)]).

fof(t73_waybel_0,theorem,(
    ! [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_xboole_0(D)
                      & v1_waybel_0(D,A)
                      & v12_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => r4_waybel_0(A,B,C,D) )
               => v22_waybel_0(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d37_waybel_0,d31_waybel_0,t32_waybel_0,d31_waybel_0,t33_waybel_0,t16_waybel_0,t156_relat_1,t30_yellow_0,d9_lattice3,d9_lattice3,d9_lattice3,d12_funct_1,t14_waybel_0,t72_waybel_0,t43_funct_2,d9_lattice3,d5_orders_3,t26_orders_2,t30_yellow_0,t15_yellow_0,d9_yellow_0]),
    [file(waybel_0,t73_waybel_0),interesting(0.63)]).

fof(t55_waybel_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,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( r1_yellow_0(A,B)
              | v3_lattice3(A) )
           => k1_yellow_0(A,B) = k1_yellow_0(A,k12_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_yellow_0,t1_xboole_1,t54_yellow_0,t1_xboole_1,t54_yellow_0,t54_waybel_0]),
    [file(waybel_0,t55_waybel_0),interesting(0.61)]).

fof(t60_waybel_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,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( r2_yellow_0(A,B)
              | v3_lattice3(A) )
           => k2_yellow_0(A,B) = k2_yellow_0(A,k13_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_yellow_0,t1_xboole_1,t55_yellow_0,t1_xboole_1,t55_yellow_0,t59_waybel_0]),
    [file(waybel_0,t60_waybel_0),interesting(0.61)]).

fof(t75_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( v24_waybel_0(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => r1_yellow_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d39_waybel_0,d7_yellow_0,t25_orders_2,d39_waybel_0,d7_yellow_0]),
    [file(waybel_0,t75_waybel_0),interesting(0.61)]).

fof(t42_waybel_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v1_waybel_0(B,A)
          <=> ! [C] : 
                ( ( v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(B)) )
               => ( C != k1_xboole_0
                 => r2_hidden(k1_yellow_0(A,C),B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_waybel_0,t1_xboole_1,t54_yellow_0,t30_yellow_0,d19_waybel_0,t6_yellow_0,t1_xboole_1,t54_yellow_0,t30_yellow_0,t1_waybel_0]),
    [file(waybel_0,t42_waybel_0),interesting(0.55)]).

fof(t43_waybel_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v2_waybel_0(B,A)
          <=> ! [C] : 
                ( ( v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(B)) )
               => ( C != k1_xboole_0
                 => r2_hidden(k2_yellow_0(A,C),B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t2_waybel_0,t1_xboole_1,t55_yellow_0,t31_yellow_0,d20_waybel_0,t6_yellow_0,t1_xboole_1,t55_yellow_0,t31_yellow_0,t2_waybel_0]),
    [file(waybel_0,t43_waybel_0),interesting(0.55)]).

fof(t61_waybel_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,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_tarski(B,k4_waybel_0(A,k12_waybel_0(A,B)))
            & ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & v12_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( r1_tarski(B,C)
                 => r1_tarski(k4_waybel_0(A,k12_waybel_0(A,B)),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_waybel_0,t50_waybel_0,t1_xboole_1,d3_tarski,d15_waybel_0,t2_xboole_1,t38_yellow_0,t39_yellow_0,t34_yellow_0,d19_waybel_0,t1_xboole_1,t42_waybel_0,d19_waybel_0]),
    [file(waybel_0,t61_waybel_0),interesting(0.51)]).

fof(t62_waybel_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,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_tarski(B,k5_waybel_0(A,k13_waybel_0(A,B)))
            & ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v2_waybel_0(C,A)
                  & v13_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( r1_tarski(B,C)
                 => r1_tarski(k5_waybel_0(A,k13_waybel_0(A,B)),C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t16_waybel_0,t50_waybel_0,t1_xboole_1,d3_tarski,d16_waybel_0,t2_xboole_1,t38_yellow_0,t39_yellow_0,t35_yellow_0,d20_waybel_0,t1_xboole_1,t43_waybel_0,d20_waybel_0]),
    [file(waybel_0,t62_waybel_0),interesting(0.51)]).

fof(t63_waybel_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ( ~ v1_xboole_0(B)
              & v2_waybel_0(B,A)
              & v13_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
          <=> v5_yellow_0(k5_yellow_0(A,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_yellow_0,d16_yellow_0,d2_waybel_0,t8_yellow_0,d10_yellow_0,d20_waybel_0,d16_yellow_0,d2_waybel_0,t21_yellow_0,t40_yellow_0,t19_yellow_0]),
    [file(waybel_0,t63_waybel_0),interesting(0.51)]).

fof(t64_waybel_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & v12_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
          <=> v6_yellow_0(k5_yellow_0(A,B),A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_yellow_0,d17_yellow_0,d1_waybel_0,t8_yellow_0,d9_yellow_0,d19_waybel_0,d17_yellow_0,d1_waybel_0,t20_yellow_0,t41_yellow_0,t18_yellow_0]),
    [file(waybel_0,t64_waybel_0),interesting(0.51)]).

fof(t69_waybel_0,theorem,(
    ! [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_xboole_0(D)
                      & v2_waybel_0(D,A)
                      & v13_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => r3_waybel_0(A,B,C,D) )
               => v5_orders_3(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_orders_3,t38_yellow_0,t37_waybel_0,d30_waybel_0,t22_waybel_0,t156_relat_1,t38_waybel_0,t39_yellow_0,t35_yellow_0]),
    [file(waybel_0,t69_waybel_0),interesting(0.50)]).

fof(t72_waybel_0,theorem,(
    ! [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_xboole_0(D)
                      & v1_waybel_0(D,A)
                      & v12_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => r4_waybel_0(A,B,C,D) )
               => v5_orders_3(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_orders_3,t38_yellow_0,t32_waybel_0,d31_waybel_0,t21_waybel_0,t156_relat_1,t33_waybel_0,t39_yellow_0,t34_yellow_0]),
    [file(waybel_0,t72_waybel_0),interesting(0.50)]).

fof(t6_waybel_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)
            & v3_waybel_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( ( v2_waybel_0(C,B)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
             => ( r2_yellow_0(A,C)
               => ( C = k1_xboole_0
                  | ( r2_yellow_0(B,C)
                    & k2_yellow_0(B,C) = k2_yellow_0(A,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_waybel_0,t64_yellow_0]),
    [file(waybel_0,t6_waybel_0),interesting(0.10)]).

fof(t7_waybel_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)
            & v4_waybel_0(B,A)
            & m1_yellow_0(B,A) )
         => ! [C] : 
              ( ( v1_waybel_0(C,B)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
             => ( r1_yellow_0(A,C)
               => ( C = k1_xboole_0
                  | ( r1_yellow_0(B,C)
                    & k1_yellow_0(B,C) = k1_yellow_0(A,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_waybel_0,t65_yellow_0]),
    [file(waybel_0,t7_waybel_0),interesting(0.10)]).

fof(t71_waybel_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)
            & 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_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => r3_waybel_0(A,B,C,D) )
                  & ! [D] : 
                      ( ( ~ v1_xboole_0(D)
                        & v2_waybel_0(D,A)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => r3_waybel_0(A,B,C,D) ) )
               => v17_waybel_0(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d32_waybel_0,d30_waybel_0,s1_xboole_0,d3_tarski,t1_xboole_1,t55_yellow_0,t1_xboole_1,t55_yellow_0,t56_waybel_0,t58_waybel_0,t59_waybel_0,d30_waybel_0,d3_tarski,t37_zfmisc_1,t1_xboole_1,t39_yellow_0,t55_yellow_0,t156_relat_1,t31_yellow_0,d8_lattice3,d8_lattice3,d8_lattice3,d12_funct_1,t1_xboole_1,t156_relat_1,d30_waybel_0,t9_yellow_0,d10_yellow_0,t31_yellow_0,t16_yellow_0,d10_yellow_0]),
    [file(waybel_0,t71_waybel_0),interesting(0.09)]).

fof(t74_waybel_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)
            & 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_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => r4_waybel_0(A,B,C,D) )
                  & ! [D] : 
                      ( ( ~ v1_xboole_0(D)
                        & v1_waybel_0(D,A)
                        & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                     => r4_waybel_0(A,B,C,D) ) )
               => v18_waybel_0(C,A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d33_waybel_0,d31_waybel_0,s1_xboole_0,d3_tarski,t1_xboole_1,t54_yellow_0,t1_xboole_1,t54_yellow_0,t51_waybel_0,t53_waybel_0,t54_waybel_0,d31_waybel_0,d3_tarski,t37_zfmisc_1,t1_xboole_1,t39_yellow_0,t54_yellow_0,t156_relat_1,t30_yellow_0,d9_lattice3,d9_lattice3,d9_lattice3,d12_funct_1,t1_xboole_1,t156_relat_1,d31_waybel_0,t9_yellow_0,d9_yellow_0,t30_yellow_0,t15_yellow_0,d9_yellow_0]),
    [file(waybel_0,t74_waybel_0),interesting(0.09)]).

fof(d12_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] : 
              ( r2_waybel_0(A,B,C)
            <=> ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                 => ? [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                      & r1_orders_2(B,D,E)
                      & r2_hidden(k3_waybel_0(A,B,E),C) ) ) ) ) ) ),
    file(waybel_0,d12_waybel_0),
    [interesting(0.00)]).

fof(d11_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_struct_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ! [C] : 
              ( r1_waybel_0(A,B,C)
            <=> ? [D] : 
                  ( m1_subset_1(D,u1_struct_0(B))
                  & ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(B))
                     => ( r1_orders_2(B,D,E)
                       => r2_hidden(k3_waybel_0(A,B,E),C) ) ) ) ) ) ) ),
    file(waybel_0,d11_waybel_0),
    [interesting(0.00)]).

fof(d4_xboole_0,definition,(
    ! [A,B,C] : 
      ( C = k4_xboole_0(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ( r2_hidden(D,A)
            & ~ r2_hidden(D,B) ) ) ) ),
    file(xboole_0,d4_xboole_0),
    [interesting(0.00)]).

fof(s1_waybel_0,theorem,
    ( r1_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,a_0_0_waybel_0)
  <=> ? [A] : 
        ( m1_subset_1(A,u1_struct_0(f2_s1_waybel_0))
        & ! [B] : 
            ( m1_subset_1(B,u1_struct_0(f2_s1_waybel_0))
           => ( r1_orders_2(f2_s1_waybel_0,A,B)
             => p1_s1_waybel_0(k3_waybel_0(f1_s1_waybel_0,f2_s1_waybel_0,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_waybel_0,d11_waybel_0]),
    [file(waybel_0,s1_waybel_0),interesting(0.00)]).

fof(d13_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ( v10_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(B))
               => r1_waybel_0(A,B,a_3_0_waybel_0(A,B,C)) ) ) ) ) ),
    file(waybel_0,d13_waybel_0),
    [interesting(0.00)]).

fof(t11_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ( v10_waybel_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(B))
                       => ( r1_orders_2(B,D,E)
                         => r1_orders_2(A,k3_waybel_0(A,B,C),k3_waybel_0(A,B,E)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_waybel_0,d13_waybel_0,d13_waybel_0]),
    [file(waybel_0,t11_waybel_0),interesting(0.00)]).

fof(d14_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ( v11_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(B))
               => r1_waybel_0(A,B,a_3_1_waybel_0(A,B,C)) ) ) ) ) ),
    file(waybel_0,d14_waybel_0),
    [interesting(0.00)]).

fof(t12_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_waybel_0(B,A) )
         => ( v11_waybel_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(B))
                       => ( r1_orders_2(B,D,E)
                         => r1_orders_2(A,k3_waybel_0(A,B,E),k3_waybel_0(A,B,C)) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_waybel_0,d14_waybel_0,d14_waybel_0]),
    [file(waybel_0,t12_waybel_0),interesting(0.00)]).

fof(d15_waybel_0,definition,(
    ! [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(A)))
             => ( C = k4_waybel_0(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> ? [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r1_orders_2(A,D,E)
                          & r2_hidden(E,B) ) ) ) ) ) ) ) ),
    file(waybel_0,d15_waybel_0),
    [interesting(0.00)]).

fof(d3_tarski,definition,(
    ! [A,B] : 
      ( r1_tarski(A,B)
    <=> ! [C] : 
          ( r2_hidden(C,A)
         => r2_hidden(C,B) ) ) ),
    file(tarski,d3_tarski),
    [interesting(0.00)]).

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_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(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(d16_waybel_0,definition,(
    ! [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(A)))
             => ( C = k5_waybel_0(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> ? [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                          & r1_orders_2(A,E,D)
                          & r2_hidden(E,B) ) ) ) ) ) ) ) ),
    file(waybel_0,d16_waybel_0),
    [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) ) ) ) ) ) ) ) ) ) ) ),
    file(yellow_0,t1_yellow_0),
    [interesting(0.00)]).

fof(t13_waybel_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,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( C = D
                     => ( k4_waybel_0(A,C) = k4_waybel_0(B,D)
                        & k5_waybel_0(A,C) = k5_waybel_0(B,D) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d15_waybel_0,t1_yellow_0,d15_waybel_0,d10_xboole_0,d3_tarski,d15_waybel_0,t1_yellow_0,d15_waybel_0,d3_tarski,d16_waybel_0,t1_yellow_0,d16_waybel_0,d10_xboole_0,d3_tarski,d16_waybel_0,t1_yellow_0,d16_waybel_0]),
    [file(waybel_0,t13_waybel_0),interesting(0.00)]).

fof(d19_waybel_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v12_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r1_orders_2(A,D,C) )
                     => r2_hidden(D,B) ) ) ) ) ) ) ),
    file(waybel_0,d19_waybel_0),
    [interesting(0.00)]).

fof(d20_waybel_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v13_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r1_orders_2(A,C,D) )
                     => r2_hidden(D,B) ) ) ) ) ) ) ),
    file(waybel_0,d20_waybel_0),
    [interesting(0.00)]).

fof(t25_waybel_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,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( C = D
                     => ( ( v12_waybel_0(C,A)
                         => v12_waybel_0(D,B) )
                        & ( v13_waybel_0(C,A)
                         => v13_waybel_0(D,B) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_waybel_0,t23_waybel_0,t23_waybel_0,t13_waybel_0,t24_waybel_0,t24_waybel_0]),
    [file(waybel_0,t25_waybel_0),interesting(0.00)]).

fof(d4_tarski,definition,(
    ! [A,B] : 
      ( B = k3_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> ? [D] : 
              ( r2_hidden(C,D)
              & r2_hidden(D,A) ) ) ) ),
    file(tarski,d4_tarski),
    [interesting(0.00)]).

fof(t26_waybel_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v12_waybel_0(C,A) ) )
           => ( v12_waybel_0(k5_setfam_1(u1_struct_0(A),B),A)
              & m1_subset_1(k5_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_waybel_0,d4_tarski,d19_waybel_0,d4_tarski]),
    [file(waybel_0,t26_waybel_0),interesting(0.00)]).

fof(t28_waybel_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( r2_hidden(C,B)
                 => v13_waybel_0(C,A) ) )
           => ( v13_waybel_0(k5_setfam_1(u1_struct_0(A),B),A)
              & m1_subset_1(k5_setfam_1(u1_struct_0(A),B),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d20_waybel_0,d4_tarski,d20_waybel_0,d4_tarski]),
    [file(waybel_0,t28_waybel_0),interesting(0.00)]).

fof(d1_waybel_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v1_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(C,B)
                        & r2_hidden(D,B)
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,B)
                                & r1_orders_2(A,C,E)
                                & r1_orders_2(A,D,E) ) ) ) ) ) ) ) ) ),
    file(waybel_0,d1_waybel_0),
    [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(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)) ) ) ) ),
    file(yellow_0,t38_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(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) ) ) ),
    file(yellow_0,t46_yellow_0),
    [interesting(0.00)]).

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) ) ) ),
    file(yellow_0,t47_yellow_0),
    [interesting(0.00)]).

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 ) ) ) ),
    file(yellow_0,t39_yellow_0),
    [interesting(0.00)]).

fof(d2_waybel_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( v2_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(C,B)
                        & r2_hidden(D,B)
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,B)
                                & r1_orders_2(A,E,C)
                                & r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ),
    file(waybel_0,d2_waybel_0),
    [interesting(0.00)]).

fof(t24_orders_2,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_orders_2(A,B,B) ) ) ),
    file(orders_2,t24_orders_2),
    [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(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) ) ) ),
    file(yellow_0,t48_yellow_0),
    [interesting(0.00)]).

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) ) ) ),
    file(yellow_0,t49_yellow_0),
    [interesting(0.00)]).

fof(t3_waybel_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,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( ( C = D
                        & v1_waybel_0(C,A) )
                     => v1_waybel_0(D,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_waybel_0,d1_waybel_0,t1_yellow_0]),
    [file(waybel_0,t3_waybel_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(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(t27_waybel_0,theorem,(
    ! [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(A)))
             => ( ( v12_waybel_0(B,A)
                  & v12_waybel_0(C,A) )
               => ( v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
                  & v12_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_waybel_0,d3_xboole_0,d3_xboole_0,d19_waybel_0,d19_waybel_0,d2_xboole_0,d2_xboole_0]),
    [file(waybel_0,t27_waybel_0),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) ) ) ) ) ) ) ) ) ),
    file(yellow_0,t22_yellow_0),
    [interesting(0.00)]).

fof(t40_waybel_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v1_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r2_hidden(k13_lattice3(A,C,D),B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_waybel_0,t22_yellow_0,d19_waybel_0,d1_waybel_0,t22_yellow_0]),
    [file(waybel_0,t40_waybel_0),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) ) ) ) ) ) ) ) ) ),
    file(yellow_0,t23_yellow_0),
    [interesting(0.00)]).

fof(t44_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( ( v1_lattice3(A)
          | v2_lattice3(A) )
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( ( v12_waybel_0(B,A)
                    & v1_waybel_0(B,A)
                    & v12_waybel_0(C,A)
                    & v1_waybel_0(C,A) )
                 => v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_waybel_0,d3_xboole_0,t40_waybel_0,d3_xboole_0,t40_waybel_0,d1_waybel_0,d3_xboole_0,d1_waybel_0,d1_waybel_0,t23_yellow_0,d19_waybel_0,d3_xboole_0,t23_yellow_0]),
    [file(waybel_0,t44_waybel_0),interesting(0.00)]).

fof(t29_waybel_0,theorem,(
    ! [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(A)))
             => ( ( v13_waybel_0(B,A)
                  & v13_waybel_0(C,A) )
               => ( v13_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
                  & v13_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d20_waybel_0,d3_xboole_0,d3_xboole_0,d20_waybel_0,d20_waybel_0,d2_xboole_0,d2_xboole_0]),
    [file(waybel_0,t29_waybel_0),interesting(0.00)]).

fof(t41_waybel_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v2_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r2_hidden(k12_lattice3(A,C,D),B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_waybel_0,t23_yellow_0,d20_waybel_0,d2_waybel_0,t23_yellow_0]),
    [file(waybel_0,t41_waybel_0),interesting(0.00)]).

fof(t45_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( ( v1_lattice3(A)
          | v2_lattice3(A) )
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( ( v13_waybel_0(B,A)
                    & v2_waybel_0(B,A)
                    & v13_waybel_0(C,A)
                    & v2_waybel_0(C,A) )
                 => v2_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_waybel_0,d3_xboole_0,t41_waybel_0,d3_xboole_0,t41_waybel_0,d2_waybel_0,d3_xboole_0,d2_waybel_0,d2_waybel_0,t22_yellow_0,d20_waybel_0,d3_xboole_0,t22_yellow_0]),
    [file(waybel_0,t45_waybel_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(t46_waybel_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ( ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_hidden(C,B)
                   => v1_waybel_0(C,A) ) )
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(C,B)
                          & r2_hidden(D,B)
                          & ! [E] : 
                              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                             => ~ ( r2_hidden(E,B)
                                  & r1_tarski(k4_subset_1(u1_struct_0(A),C,D),E) ) ) ) ) ) )
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( C = k5_setfam_1(u1_struct_0(A),B)
                 => v1_waybel_0(C,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_waybel_0,d4_tarski,d4_tarski,t7_xboole_1,d1_waybel_0,d4_tarski]),
    [file(waybel_0,t46_waybel_0),interesting(0.00)]).

fof(t47_waybel_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(u1_struct_0(A))))
         => ( ( ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r2_hidden(C,B)
                   => v2_waybel_0(C,A) ) )
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
                 => ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                     => ~ ( r2_hidden(C,B)
                          & r2_hidden(D,B)
                          & ! [E] : 
                              ( m1_subset_1(E,k1_zfmisc_1(u1_struct_0(A)))
                             => ~ ( r2_hidden(E,B)
                                  & r1_tarski(k4_subset_1(u1_struct_0(A),C,D),E) ) ) ) ) ) )
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( C = k5_setfam_1(u1_struct_0(A),B)
                 => v2_waybel_0(C,A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_waybel_0,d4_tarski,d4_tarski,t7_xboole_1,d2_waybel_0,d4_tarski]),
    [file(waybel_0,t47_waybel_0),interesting(0.00)]).

fof(d21_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v14_waybel_0(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & r2_hidden(C,B)
                & r2_lattice3(A,B,C) ) ) ) ) ),
    file(waybel_0,d21_waybel_0),
    [interesting(0.00)]).

fof(t48_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v1_waybel_0(B,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v14_waybel_0(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & B = k6_waybel_0(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_waybel_0,d3_tarski,d9_lattice3,t17_waybel_0,d10_xboole_0,d3_tarski,t17_waybel_0,d19_waybel_0,d21_waybel_0,t17_waybel_0,d9_lattice3,t17_waybel_0]),
    [file(waybel_0,t48_waybel_0),interesting(0.00)]).

fof(d22_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,A)
            & v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v15_waybel_0(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & r2_hidden(C,B)
                & r1_lattice3(A,B,C) ) ) ) ) ),
    file(waybel_0,d22_waybel_0),
    [interesting(0.00)]).

fof(t49_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & v2_waybel_0(B,A)
            & v13_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v15_waybel_0(B,A)
          <=> ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & B = k7_waybel_0(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d22_waybel_0,d3_tarski,d8_lattice3,t18_waybel_0,d10_xboole_0,d3_tarski,t18_waybel_0,d20_waybel_0,d22_waybel_0,t18_waybel_0,d8_lattice3,t18_waybel_0]),
    [file(waybel_0,t49_waybel_0),interesting(0.00)]).

fof(t4_waybel_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,k1_zfmisc_1(u1_struct_0(A)))
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(B)))
                   => ( ( C = D
                        & v2_waybel_0(C,A) )
                     => v2_waybel_0(D,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_waybel_0,d2_waybel_0,t1_yellow_0]),
    [file(waybel_0,t4_waybel_0),interesting(0.00)]).

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) ) ) ),
    file(yellow_0,t17_yellow_0),
    [interesting(0.00)]).

fof(t1_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(B,C) )
     => r1_tarski(A,C) ) ),
    file(xboole_1,t1_xboole_1),
    [interesting(0.00)]).

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) ) ) ) ),
    file(yellow_0,t54_yellow_0),
    [interesting(0.00)]).

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) ) ) ) ) ) ),
    file(yellow_0,t9_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(t37_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(k1_tarski(A),B)
    <=> r2_hidden(A,B) ) ),
    file(zfmisc_1,t37_zfmisc_1),
    [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) ) ) ) ) ) ),
    file(yellow_0,t7_yellow_0),
    [interesting(0.00)]).

fof(t52_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(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(A)))
             => ( ( ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r1_yellow_0(A,D) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( ( v1_finset_1(E)
                                & m1_subset_1(E,k1_zfmisc_1(B)) )
                             => ~ ( r1_yellow_0(A,E)
                                  & D = k1_yellow_0(A,E) ) ) ) )
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_hidden(k1_yellow_0(A,D),C) ) ) )
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_lattice3(A,B,D)
                    <=> r2_lattice3(A,C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_lattice3,t9_yellow_0,d9_yellow_0,d9_lattice3,t37_zfmisc_1,d9_lattice3,d9_yellow_0,t7_yellow_0,t26_orders_2]),
    [file(waybel_0,t52_waybel_0),interesting(0.00)]).

fof(t54_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(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(A)))
             => ( ( ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r1_yellow_0(A,D) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( ( v1_finset_1(E)
                                & m1_subset_1(E,k1_zfmisc_1(B)) )
                             => ~ ( r1_yellow_0(A,E)
                                  & D = k1_yellow_0(A,E) ) ) ) )
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_hidden(k1_yellow_0(A,D),C) ) )
                  & r1_yellow_0(A,B) )
               => k1_yellow_0(A,C) = k1_yellow_0(A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t52_waybel_0,t47_yellow_0]),
    [file(waybel_0,t54_waybel_0),interesting(0.00)]).

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) ) ) ) ),
    file(yellow_0,t55_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(t57_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(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(A)))
             => ( ( ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_yellow_0(A,D) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( ( v1_finset_1(E)
                                & m1_subset_1(E,k1_zfmisc_1(B)) )
                             => ~ ( r2_yellow_0(A,E)
                                  & D = k2_yellow_0(A,E) ) ) ) )
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_hidden(k2_yellow_0(A,D),C) ) ) )
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r1_lattice3(A,B,D)
                    <=> r1_lattice3(A,C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_lattice3,t9_yellow_0,d10_yellow_0,d8_lattice3,t37_zfmisc_1,d8_lattice3,d10_yellow_0,t7_yellow_0,t26_orders_2]),
    [file(waybel_0,t57_waybel_0),interesting(0.00)]).

fof(t59_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(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(A)))
             => ( ( ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_yellow_0(A,D) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( ( v1_finset_1(E)
                                & m1_subset_1(E,k1_zfmisc_1(B)) )
                             => ~ ( r2_yellow_0(A,E)
                                  & D = k2_yellow_0(A,E) ) ) ) )
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_hidden(k2_yellow_0(A,D),C) ) )
                  & r2_yellow_0(A,B) )
               => k2_yellow_0(A,C) = k2_yellow_0(A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t57_waybel_0,t49_yellow_0]),
    [file(waybel_0,t59_waybel_0),interesting(0.00)]).

fof(d4_orders_2,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v2_orders_2(A)
      <=> r1_relat_2(u1_orders_2(A),u1_struct_0(A)) ) ) ),
    file(orders_2,d4_orders_2),
    [interesting(0.00)]).

fof(d1_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r1_relat_2(A,B)
        <=> ! [C] : 
              ( r2_hidden(C,B)
             => r2_hidden(k4_tarski(C,C),A) ) ) ) ),
    file(relat_2,d1_relat_2),
    [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(t2_xboole_1,theorem,(
    ! [A] : r1_tarski(k1_xboole_0,A) ),
    file(xboole_1,t2_xboole_1),
    [interesting(0.00)]).

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)) ) ) ),
    file(yellow_0,t34_yellow_0),
    [interesting(0.00)]).

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) ) ) ) ),
    file(yellow_0,t6_yellow_0),
    [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(t38_zfmisc_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(k2_tarski(A,B),C)
    <=> ( r2_hidden(A,C)
        & r2_hidden(B,C) ) ) ),
    file(zfmisc_1,t38_zfmisc_1),
    [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(t1_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A) )
          <=> ! [C] : 
                ( ( v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(B)) )
               => ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r2_hidden(D,B)
                    & r2_lattice3(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_yellow_0,d1_waybel_0,d9_lattice3,d2_xboole_0,d9_lattice3,d1_tarski,t26_orders_2,s2_finset_1,t2_xboole_1,d1_waybel_0,t38_zfmisc_1,d2_tarski,d9_lattice3]),
    [file(waybel_0,t1_waybel_0),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) ) ) ) ) ) ),
    file(yellow_0,t30_yellow_0),
    [interesting(0.00)]).

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)) ) ) ),
    file(yellow_0,t35_yellow_0),
    [interesting(0.00)]).

fof(t2_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( ( ~ v1_xboole_0(B)
              & v2_waybel_0(B,A) )
          <=> ! [C] : 
                ( ( v1_finset_1(C)
                  & m1_subset_1(C,k1_zfmisc_1(B)) )
               => ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r2_hidden(D,B)
                    & r1_lattice3(A,C,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_yellow_0,d2_waybel_0,d8_lattice3,d2_xboole_0,d8_lattice3,d1_tarski,t26_orders_2,s2_finset_1,t2_xboole_1,d2_waybel_0,t38_zfmisc_1,d2_tarski,d8_lattice3]),
    [file(waybel_0,t2_waybel_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) ) ) ) ) ) ),
    file(yellow_0,t31_yellow_0),
    [interesting(0.00)]).

fof(d15_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( ( v1_orders_2(C)
                & v4_yellow_0(C,A)
                & m1_yellow_0(C,A) )
             => ( C = k5_yellow_0(A,B)
              <=> u1_struct_0(C) = B ) ) ) ) ),
    file(yellow_0,d15_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(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) ) ) ) ) ) ) ),
    file(yellow_0,t8_yellow_0),
    [interesting(0.00)]).

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)) ) ) ) ) ),
    file(yellow_0,t21_yellow_0),
    [interesting(0.00)]).

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) ) ) ) ),
    file(yellow_0,t40_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)) ) ) ) ) ) ) ) ),
    file(yellow_0,t19_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)]).

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)) ) ) ) ) ),
    file(yellow_0,t20_yellow_0),
    [interesting(0.00)]).

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) ) ) ) ),
    file(yellow_0,t41_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)) ) ) ) ) ) ) ) ),
    file(yellow_0,t18_yellow_0),
    [interesting(0.00)]).

fof(d31_waybel_0,definition,(
    ! [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] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r4_waybel_0(A,B,C,D)
                  <=> ( r1_yellow_0(A,D)
                     => ( r1_yellow_0(B,k4_pre_topc(A,B,C,D))
                        & k1_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k1_yellow_0(A,D)) ) ) ) ) ) ) ) ),
    file(waybel_0,d31_waybel_0),
    [interesting(0.00)]).

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) ) ) ) ) ) ),
    file(yellow_0,t14_yellow_0),
    [interesting(0.00)]).

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) ) ) ) ) ),
    file(yellow_0,t26_yellow_0),
    [interesting(0.00)]).

fof(d30_waybel_0,definition,(
    ! [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] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r3_waybel_0(A,B,C,D)
                  <=> ( r2_yellow_0(A,D)
                     => ( r2_yellow_0(B,k4_pre_topc(A,B,C,D))
                        & k2_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k2_yellow_0(A,D)) ) ) ) ) ) ) ) ),
    file(waybel_0,d30_waybel_0),
    [interesting(0.00)]).

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) ) ) ) ) ),
    file(yellow_0,t27_yellow_0),
    [interesting(0.00)]).

fof(t65_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( ~ v3_struct_0(C)
                & l1_orders_2(C) )
             => ! [D] : 
                  ( ( ~ v3_struct_0(D)
                    & l1_orders_2(D) )
                 => ( ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(C),u1_orders_2(C))
                      & g1_orders_2(u1_struct_0(B),u1_orders_2(B)) = g1_orders_2(u1_struct_0(D),u1_orders_2(D)) )
                   => ! [E] : 
                        ( ( v1_funct_1(E)
                          & v1_funct_2(E,u1_struct_0(A),u1_struct_0(B))
                          & m2_relset_1(E,u1_struct_0(A),u1_struct_0(B)) )
                       => ! [F] : 
                            ( ( v1_funct_1(F)
                              & v1_funct_2(F,u1_struct_0(C),u1_struct_0(D))
                              & m2_relset_1(F,u1_struct_0(C),u1_struct_0(D)) )
                           => ( E = F
                             => ! [G] : 
                                  ( m1_subset_1(G,k1_zfmisc_1(u1_struct_0(A)))
                                 => ! [H] : 
                                      ( m1_subset_1(H,k1_zfmisc_1(u1_struct_0(C)))
                                     => ( G = H
                                       => ( ( r4_waybel_0(A,B,E,G)
                                           => r4_waybel_0(C,D,F,H) )
                                          & ( r3_waybel_0(A,B,E,G)
                                           => r3_waybel_0(C,D,F,H) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d31_waybel_0,d31_waybel_0,t14_yellow_0,t14_yellow_0,t26_yellow_0,t14_yellow_0,d30_waybel_0,d30_waybel_0,t14_yellow_0,t14_yellow_0,t27_yellow_0,t14_yellow_0]),
    [file(waybel_0,t65_waybel_0),interesting(0.00)]).

fof(d38_waybel_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [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)) )
             => ( ~ ( ~ v3_struct_0(A)
                    & ~ v3_struct_0(B)
                    & ~ ( v23_waybel_0(C,A,B)
                      <=> ( v2_funct_1(C)
                          & v5_orders_3(C,A,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))
                              & D = k2_funct_1(C)
                              & v5_orders_3(D,B,A) ) ) ) )
                & ( ~ ( ~ v3_struct_0(A)
                      & ~ v3_struct_0(B) )
                 => ( v23_waybel_0(C,A,B)
                  <=> ( v3_struct_0(A)
                      & v3_struct_0(B) ) ) ) ) ) ) ) ),
    file(waybel_0,d38_waybel_0),
    [interesting(0.00)]).

fof(t55_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => ( k2_relat_1(A) = k1_relat_1(k2_funct_1(A))
          & k1_relat_1(A) = k2_relat_1(k2_funct_1(A)) ) ) ) ),
    file(funct_1,t55_funct_1),
    [interesting(0.00)]).

fof(d1_funct_2,definition,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( ( ( B = k1_xboole_0
           => A = k1_xboole_0 )
         => ( v1_funct_2(C,A,B)
          <=> A = k4_relset_1(A,B,C) ) )
        & ( B = k1_xboole_0
         => ( A = k1_xboole_0
            | ( v1_funct_2(C,A,B)
            <=> C = k1_xboole_0 ) ) ) ) ) ),
    file(funct_2,d1_funct_2),
    [interesting(0.00)]).

fof(d5_orders_3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [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)) )
             => ( v5_orders_3(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r1_orders_2(A,D,E)
                         => ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(B))
                             => ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(B))
                                 => ( ( F = k1_funct_1(C,D)
                                      & G = k1_funct_1(C,E) )
                                   => r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ) ) ),
    file(orders_3,d5_orders_3),
    [interesting(0.00)]).

fof(t32_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( ( v2_funct_1(D)
          & r2_hidden(C,A) )
       => ( B = k1_xboole_0
          | k1_funct_1(k2_funct_1(D),k1_funct_1(D,C)) = C ) ) ) ),
    file(funct_2,t32_funct_2),
    [interesting(0.00)]).

fof(t31_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( v2_funct_1(C)
          & k2_relat_1(C) = B )
       => ( v1_funct_1(k2_funct_1(C))
          & v1_funct_2(k2_funct_1(C),B,A)
          & m2_relset_1(k2_funct_1(C),B,A) ) ) ) ),
    file(funct_2,t31_funct_2),
    [interesting(0.00)]).

fof(d5_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( B = k2_relat_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ? [D] : 
                  ( r2_hidden(D,k1_relat_1(A))
                  & C = k1_funct_1(A,D) ) ) ) ) ),
    file(funct_1,d5_funct_1),
    [interesting(0.00)]).

fof(t66_waybel_0,theorem,(
    ! [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)) )
             => ( v23_waybel_0(C,A,B)
              <=> ( v2_funct_1(C)
                  & k2_relat_1(C) = u1_struct_0(B)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( r1_orders_2(A,D,E)
                          <=> r1_orders_2(B,k1_waybel_0(A,B,C,D),k1_waybel_0(A,B,C,E)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d38_waybel_0,d38_waybel_0,d38_waybel_0,t55_funct_1,d1_funct_2,d5_orders_3,t32_funct_2,d5_orders_3,d5_orders_3,t31_funct_2,d5_orders_3,d5_funct_1,d5_funct_1,t32_funct_2,d38_waybel_0]),
    [file(waybel_0,t66_waybel_0),interesting(0.00)]).

fof(t3_funct_2,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v1_funct_1(A)
        & v1_funct_2(A,k1_relat_1(A),k2_relat_1(A))
        & m2_relset_1(A,k1_relat_1(A),k2_relat_1(A)) ) ) ),
    file(funct_2,t3_funct_2),
    [interesting(0.00)]).

fof(t67_waybel_0,theorem,(
    ! [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)) )
             => ( v23_waybel_0(C,A,B)
               => ( v1_funct_1(k2_funct_1(C))
                  & v1_funct_2(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A))
                  & m2_relset_1(k2_funct_1(C),u1_struct_0(B),u1_struct_0(A))
                  & k2_relat_1(k2_funct_1(C)) = u1_struct_0(A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t66_waybel_0,d1_funct_2,t55_funct_1,t3_funct_2]),
    [file(waybel_0,t67_waybel_0),interesting(0.00)]).

fof(t62_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => v2_funct_1(k2_funct_1(A)) ) ) ),
    file(funct_1,t62_funct_1),
    [interesting(0.00)]).

fof(t65_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
       => k2_funct_1(k2_funct_1(A)) = A ) ) ),
    file(funct_1,t65_funct_1),
    [interesting(0.00)]).

fof(t68_waybel_0,theorem,(
    ! [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)) )
             => ( v23_waybel_0(C,A,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)) )
                   => ( D = k2_funct_1(C)
                     => v23_waybel_0(D,B,A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d38_waybel_0,d38_waybel_0,t62_funct_1,t65_funct_1,d38_waybel_0]),
    [file(waybel_0,t68_waybel_0),interesting(0.00)]).

fof(d3_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v3_waybel_0(B,A)
          <=> ! [C] : 
                ( ( v2_waybel_0(C,B)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
               => ( r2_yellow_0(A,C)
                 => ( C = k1_xboole_0
                    | r2_hidden(k2_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) ) ),
    file(waybel_0,d3_waybel_0),
    [interesting(0.00)]).

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) ) ) ) ) ) ),
    file(yellow_0,t64_yellow_0),
    [interesting(0.00)]).

fof(d36_waybel_0,definition,(
    ! [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)) )
             => ( v21_waybel_0(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( v2_waybel_0(D,A)
                     => ( v1_xboole_0(D)
                        | r3_waybel_0(A,B,C,D) ) ) ) ) ) ) ) ),
    file(waybel_0,d36_waybel_0),
    [interesting(0.00)]).

fof(t156_relat_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r1_tarski(A,B)
       => r1_tarski(k9_relat_1(C,A),k9_relat_1(C,B)) ) ) ),
    file(relat_1,t156_relat_1),
    [interesting(0.00)]).

fof(d12_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B,C] : 
          ( C = k9_relat_1(A,B)
        <=> ! [D] : 
              ( r2_hidden(D,C)
            <=> ? [E] : 
                  ( r2_hidden(E,k1_relat_1(A))
                  & r2_hidden(E,B)
                  & D = k1_funct_1(A,E) ) ) ) ) ),
    file(funct_1,d12_funct_1),
    [interesting(0.00)]).

fof(t43_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( ? [F] : 
                ( r2_hidden(F,A)
                & r2_hidden(F,C)
                & E = k1_funct_1(D,F) )
           => r2_hidden(E,k9_relat_1(D,C)) ) ) ) ),
    file(funct_2,t43_funct_2),
    [interesting(0.00)]).

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) ) ) ) ) ) ),
    file(yellow_0,t16_yellow_0),
    [interesting(0.00)]).

fof(d32_waybel_0,definition,(
    ! [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)) )
             => ( v17_waybel_0(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => r3_waybel_0(A,B,C,D) ) ) ) ) ) ),
    file(waybel_0,d32_waybel_0),
    [interesting(0.00)]).

fof(s1_xboole_0,theorem,(
    ? [A] : 
    ! [B] : 
      ( r2_hidden(B,A)
    <=> ( r2_hidden(B,f1_s1_xboole_0)
        & p1_s1_xboole_0(B) ) ) ),
    file(xboole_0,s1_xboole_0),
    [interesting(0.00)]).

fof(t15_xboole_1,theorem,(
    ! [A,B] : 
      ( k2_xboole_0(A,B) = k1_xboole_0
     => A = k1_xboole_0 ) ),
    file(xboole_1,t15_xboole_1),
    [interesting(0.00)]).

fof(t56_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(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(A)))
             => ( ( ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_yellow_0(A,D) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( ( v1_finset_1(E)
                                & m1_subset_1(E,k1_zfmisc_1(B)) )
                             => ~ ( r2_yellow_0(A,E)
                                  & D = k2_yellow_0(A,E) ) ) ) )
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_hidden(k2_yellow_0(A,D),C) ) ) )
               => v2_waybel_0(C,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_waybel_0,t15_xboole_1,t7_xboole_1,t35_yellow_0]),
    [file(waybel_0,t56_waybel_0),interesting(0.00)]).

fof(t58_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(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(A)))
             => ( ( ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_yellow_0(A,D) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( ( v1_finset_1(E)
                                & m1_subset_1(E,k1_zfmisc_1(B)) )
                             => ~ ( r2_yellow_0(A,E)
                                  & D = k2_yellow_0(A,E) ) ) ) )
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_hidden(k2_yellow_0(A,D),C) ) ) )
               => ( r2_yellow_0(A,B)
                <=> r2_yellow_0(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t57_waybel_0,t48_yellow_0]),
    [file(waybel_0,t58_waybel_0),interesting(0.00)]).

fof(d37_waybel_0,definition,(
    ! [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)) )
             => ( v22_waybel_0(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => ( v1_waybel_0(D,A)
                     => ( v1_xboole_0(D)
                        | r4_waybel_0(A,B,C,D) ) ) ) ) ) ) ) ),
    file(waybel_0,d37_waybel_0),
    [interesting(0.00)]).

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) ) ) ) ) ) ),
    file(yellow_0,t15_yellow_0),
    [interesting(0.00)]).

fof(d33_waybel_0,definition,(
    ! [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)) )
             => ( v18_waybel_0(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                   => r4_waybel_0(A,B,C,D) ) ) ) ) ) ),
    file(waybel_0,d33_waybel_0),
    [interesting(0.00)]).

fof(t51_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v3_orders_2(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(A)))
             => ( ( ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r1_yellow_0(A,D) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( ( v1_finset_1(E)
                                & m1_subset_1(E,k1_zfmisc_1(B)) )
                             => ~ ( r1_yellow_0(A,E)
                                  & D = k1_yellow_0(A,E) ) ) ) )
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_hidden(k1_yellow_0(A,D),C) ) ) )
               => v1_waybel_0(C,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_waybel_0,t15_xboole_1,t7_xboole_1,t34_yellow_0]),
    [file(waybel_0,t51_waybel_0),interesting(0.00)]).

fof(t53_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(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(A)))
             => ( ( ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r1_yellow_0(A,D) ) )
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r2_hidden(D,C)
                          & ! [E] : 
                              ( ( v1_finset_1(E)
                                & m1_subset_1(E,k1_zfmisc_1(B)) )
                             => ~ ( r1_yellow_0(A,E)
                                  & D = k1_yellow_0(A,E) ) ) ) )
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(B)) )
                     => ( D != k1_xboole_0
                       => r2_hidden(k1_yellow_0(A,D),C) ) ) )
               => ( r1_yellow_0(A,B)
                <=> r1_yellow_0(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t52_waybel_0,t46_yellow_0]),
    [file(waybel_0,t53_waybel_0),interesting(0.00)]).

fof(d39_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v24_waybel_0(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & v1_waybel_0(B,A)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ? [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)
                     => r3_orders_2(A,C,D) ) ) ) ) ) ) ),
    file(waybel_0,d39_waybel_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(d40_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v25_waybel_0(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ? [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) ) ) ) ) ) ) ),
    file(waybel_0,d40_waybel_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(d4_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_yellow_0(B,A)
         => ( v4_waybel_0(B,A)
          <=> ! [C] : 
                ( ( v1_waybel_0(C,B)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(B))) )
               => ( r1_yellow_0(A,C)
                 => ( C = k1_xboole_0
                    | r2_hidden(k1_yellow_0(A,C),u1_struct_0(B)) ) ) ) ) ) ) ),
    file(waybel_0,d4_waybel_0),
    [interesting(0.00)]).

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) ) ) ) ) ) ),
    file(yellow_0,t65_yellow_0),
    [interesting(0.00)]).