fof(t32_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k2_funct_1(k9_waybel_4(A)) = k10_waybel_4(A) ) ),
    inference(mizar_proof,[status(thm)],[t24_funct_2,t30_waybel_4,t31_waybel_4,d1_funct_2,t63_funct_1]),
    [file(waybel_4,t32_waybel_4),interesting(1.00)]).

fof(t38_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v2_waybel_2(A) ) ),
    inference(mizar_proof,[status(thm)],[t17_yellow_0,d3_tarski,d3_waybel_3,t1_waybel_3,d1_waybel_3,d1_tarski,d4_yellow_4,t17_yellow_0,t19_yellow_0,t32_yellow_0,d9_lattice3,t26_orders_2,t17_waybel_0,t34_yellow_0,t34_waybel_0,d5_waybel_3,l68_waybel_4,t25_orders_2,t52_waybel_2]),
    [file(waybel_4,t38_waybel_4),interesting(0.98)]).

fof(t44_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_waybel_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_setfam_1(a_2_2_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d20_waybel_4,t34_waybel_4,t43_waybel_4,d3_tarski,t37_waybel_4,t35_waybel_4,d16_waybel_4,t42_waybel_4,d19_waybel_4,d3_tarski,t13_waybel_4,d10_xboole_0,d3_tarski,d20_waybel_4,t7_setfam_1,d10_xboole_0,d3_tarski,d20_waybel_4,d18_waybel_4,t7_setfam_1]),
    [file(waybel_4,t44_waybel_4),interesting(0.96)]).

fof(t45_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v3_waybel_3(A)
      <=> ! [B] : 
            ( ( v5_waybel_4(B,A)
              & v6_waybel_4(B,A)
              & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
           => ( r1_tarski(k1_waybel_4(A),B)
              & v6_waybel_4(k1_waybel_4(A),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_waybel_4,t106_zfmisc_1,d2_waybel_4,t7_waybel_3,t44_waybel_4,d20_waybel_4,t4_setfam_1,t13_waybel_4,d3_relat_1,l73_waybel_4,d18_waybel_4,t40_waybel_4,d5_waybel_3,d6_waybel_3]),
    [file(waybel_4,t45_waybel_4),interesting(0.94)]).

fof(t48_waybel_4,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v8_waybel_4(B,A)
           => v9_waybel_4(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d22_waybel_4,d21_waybel_4]),
    [file(waybel_4,t48_waybel_4),interesting(0.92)]).

fof(t52_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v8_waybel_4(k1_waybel_4(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d21_waybel_4,d2_waybel_4,t51_waybel_4]),
    [file(waybel_4,t52_waybel_4),interesting(0.92)]).

fof(t46_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ( v3_waybel_3(A)
      <=> ( v2_waybel_2(A)
          & ? [B] : 
              ( v5_waybel_4(B,A)
              & v6_waybel_4(B,A)
              & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
              & ! [C] : 
                  ( ( v5_waybel_4(C,A)
                    & v6_waybel_4(C,A)
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => r1_tarski(B,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t38_waybel_4,l73_waybel_4,t45_waybel_4,t44_waybel_4,d20_waybel_4,t4_setfam_1,d18_waybel_4,d20_waybel_4,d3_tarski,t29_waybel_4,t6_setfam_1,d10_xboole_0,d5_waybel_3,d6_waybel_3]),
    [file(waybel_4,t46_waybel_4),interesting(0.89)]).

fof(t19_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => r2_hidden(k4_yellow_2(A),u1_struct_0(k8_waybel_4(A))) ) ),
    inference(mizar_proof,[status(thm)],[d4_yellow_2,d14_waybel_4]),
    [file(waybel_4,t19_waybel_4),interesting(0.88)]).

fof(t55_waybel_4,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ( r1_waybel_4(A,B,u1_orders_2(A))
           => v1_waybel_0(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_waybel_0,d23_waybel_4,d9_orders_2]),
    [file(waybel_4,t55_waybel_4),interesting(0.87)]).

fof(t33_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => v23_waybel_0(k9_waybel_4(A),k2_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) ),
    inference(mizar_proof,[status(thm)],[t32_waybel_4,d38_waybel_0]),
    [file(waybel_4,t33_waybel_4),interesting(0.85)]).

fof(t43_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_setfam_1(a_2_1_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d17_waybel_4,d10_xboole_0,d3_tarski,d17_waybel_4,d3_tarski,d17_waybel_4,d10_xboole_0,d3_tarski,d17_waybel_4,d3_tarski,d2_xboole_0,d10_xboole_0,d3_tarski,d2_xboole_0,t44_yellow_0,t44_yellow_0,d3_tarski,t42_yellow_2,t44_yellow_0,t7_setfam_1,t44_yellow_0,t23_waybel_4,t4_setfam_1,d10_xboole_0,l43_waybel_4,t23_waybel_4,t19_xboole_1,t6_setfam_1,t44_yellow_0,l43_waybel_4,t6_setfam_1,d10_xboole_0,t34_waybel_4,t34_waybel_0,t44_yellow_0,t30_orders_2,d10_orders_2,t34_waybel_0,t4_setfam_1,d10_xboole_0,t6_setfam_1,t10_setfam_1,t4_setfam_1,t28_xboole_1,d3_tarski,t12_pre_topc,t17_yellow_0,d9_yellow_0,d9_lattice3,t17_xboole_1,d1_setfam_1,d1_setfam_1,d3_xboole_0,d3_tarski,d3_xboole_0,d1_setfam_1,d3_xboole_0,d1_setfam_1,d10_xboole_0,t34_waybel_4,t11_waybel_3,t28_xboole_1]),
    [file(waybel_4,t43_waybel_4),interesting(0.84)]).

fof(t26_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => r2_hidden(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(k8_waybel_4(A))) ) ),
    inference(mizar_proof,[status(thm)],[t25_waybel_4,t13_funcop_1,l43_waybel_4,l45_waybel_4,d14_waybel_4]),
    [file(waybel_4,t26_waybel_4),interesting(0.80)]).

fof(l73_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v6_waybel_4(k1_waybel_4(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d18_waybel_4,d5_waybel_3,t40_waybel_4]),
    [file(waybel_4,l73_waybel_4),interesting(0.79)]).

fof(t41_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => v6_waybel_4(k2_waybel_4(A),A) ) ),
    inference(mizar_proof,[status(thm)],[d18_waybel_4,d3_tarski,l4_waybel_4,d10_xboole_0,d3_tarski,l4_waybel_4,d3_tarski,d9_lattice3,d9_lattice3,t30_yellow_0]),
    [file(waybel_4,t41_waybel_4),interesting(0.78)]).

fof(l54_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => v5_orders_3(k10_waybel_4(A),k8_waybel_4(A),k2_yellow_1(k3_waybel_4(A))) ) ),
    inference(mizar_proof,[status(thm)],[d1_yellow_1,d5_orders_3,d9_orders_2,d14_waybel_4,t7_funct_2,t1_yellow_1,d9_waybel_4,t7_funct_2,t106_zfmisc_1,t106_zfmisc_1,d1_yellow_2,t3_yellow_1,d16_waybel_4,d16_waybel_4,d3_relat_1,d1_wellord2,d9_orders_2]),
    [file(waybel_4,l54_waybel_4),interesting(0.77)]).

fof(t23_waybel_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => k6_waybel_0(A,k3_yellow_0(A)) = k1_struct_0(A,k3_yellow_0(A)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t14_waybel_0,t44_yellow_0,d1_tarski,t25_orders_2,d10_xboole_0,d3_tarski,d1_tarski,t17_waybel_0]),
    [file(waybel_4,t23_waybel_4),interesting(0.77)]).

fof(l4_waybel_4,theorem,(
    ! [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(k4_tarski(B,C),k2_waybel_4(A))
              <=> r1_orders_2(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_orders_2]),
    [file(waybel_4,l4_waybel_4),interesting(0.76)]).

fof(t56_waybel_4,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r3_waybel_4(A,B,C)
          <=> ( r2_hidden(C,B)
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r2_hidden(D,B)
                      & r2_orders_2(A,C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d25_waybel_4,d24_waybel_4,d9_orders_2,d10_orders_2,d24_waybel_4,d25_waybel_4,d24_waybel_4,t106_zfmisc_1,d9_orders_2,d10_orders_2]),
    [file(waybel_4,t56_waybel_4),interesting(0.76)]).

fof(t57_waybel_4,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r5_waybel_4(A,B,C)
          <=> ( r2_hidden(C,B)
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ~ ( r2_hidden(D,B)
                      & r2_orders_2(A,D,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d27_waybel_4,d26_waybel_4,d9_orders_2,d10_orders_2,d26_waybel_4,d27_waybel_4,d26_waybel_4,t106_zfmisc_1,d9_orders_2,d10_orders_2]),
    [file(waybel_4,t57_waybel_4),interesting(0.76)]).

fof(l52_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => v5_orders_3(k9_waybel_4(A),k2_yellow_1(k3_waybel_4(A)),k8_waybel_4(A)) ) ),
    inference(mizar_proof,[status(thm)],[d5_orders_3,t1_yellow_1,d9_waybel_4,t3_yellow_1,d15_waybel_4,d14_waybel_4,d14_waybel_4,d1_yellow_2,d13_waybel_4,d13_waybel_4,t29_waybel_4,t3_yellow_1,d14_waybel_4,d9_orders_2]),
    [file(waybel_4,l52_waybel_4),interesting(0.75)]).

fof(t13_waybel_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C,D] : 
              ( m1_subset_1(D,u1_struct_0(A))
             => ( r2_hidden(C,k5_waybel_4(A,D,B))
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1]),
    [file(waybel_4,t13_waybel_4),interesting(0.74)]).

fof(t2_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r1_tarski(B,k2_waybel_4(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_relat_1,l13_waybel_4]),
    [file(waybel_4,t2_waybel_4),interesting(0.73)]).

fof(t18_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r2_hidden(k7_waybel_4(A,B),u1_struct_0(k8_waybel_4(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_waybel_4,t12_waybel_4,d14_waybel_4]),
    [file(waybel_4,t18_waybel_4),interesting(0.72)]).

fof(t4_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v4_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r1_tarski(k4_waybel_4(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_relat_1,t106_zfmisc_1,d10_waybel_4,d7_waybel_4]),
    [file(waybel_4,t4_waybel_4),interesting(0.71)]).

fof(t35_waybel_4,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)
            & v1_waybel_0(B,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => r2_hidden(k11_waybel_4(A,B),u1_struct_0(k8_waybel_4(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[l61_waybel_4,l62_waybel_4,d14_waybel_4]),
    [file(waybel_4,t35_waybel_4),interesting(0.69)]).

fof(l48_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ? [B] : 
          ( m1_subset_1(B,u1_struct_0(k8_waybel_4(A)))
          & r2_lattice3(k8_waybel_4(A),u1_struct_0(k8_waybel_4(A)),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_waybel_4,d9_lattice3,d14_waybel_4,d1_yellow_2,d4_yellow_2,t3_yellow_1,d14_waybel_4,d9_orders_2]),
    [file(waybel_4,l48_waybel_4),interesting(0.67)]).

fof(t34_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_setfam_1(a_2_0_waybel_4(A,B)) = k1_waybel_3(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t34_waybel_0,d3_tarski,d1_setfam_1,t21_waybel_3,t7_waybel_3,d10_xboole_0,d3_tarski,d3_waybel_3,t20_waybel_3,d1_setfam_1]),
    [file(waybel_4,t34_waybel_4),interesting(0.67)]).

fof(t37_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v2_waybel_2(A)
        & v2_lattice3(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))) )
         => v7_waybel_4(k11_waybel_4(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_yellow_1,d17_waybel_4,t36_waybel_4,d6_waybel_2,t25_yellow_0,d17_waybel_4,t34_waybel_0,d19_waybel_4]),
    [file(waybel_4,t37_waybel_4),interesting(0.63)]).

fof(t3_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k4_yellow_0(k2_yellow_1(k3_waybel_4(A))) = k2_waybel_4(A) ) ),
    inference(mizar_proof,[status(thm)],[d9_waybel_4,t1_yellow_1,t6_yellow_0,t1_yellow_1,d9_waybel_4,t2_waybel_4,t3_yellow_1,t31_yellow_0]),
    [file(waybel_4,t3_waybel_4),interesting(0.61)]).

fof(t24_waybel_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => k7_waybel_0(A,k4_yellow_0(A)) = k1_struct_0(A,k4_yellow_0(A)) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t18_waybel_0,t45_yellow_0,t25_orders_2,d1_tarski,d10_xboole_0,d3_tarski,d1_tarski,t18_waybel_0]),
    [file(waybel_4,t24_waybel_4),interesting(0.60)]).

fof(t40_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k5_waybel_4(A,B,k1_waybel_4(A)) = k1_waybel_3(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d2_waybel_4,d10_xboole_0,d3_tarski,d2_waybel_4,d3_waybel_3]),
    [file(waybel_4,t40_waybel_4),interesting(0.60)]).

fof(t5_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k3_yellow_0(k2_yellow_1(k3_waybel_4(A))) = k4_waybel_4(A) ) ),
    inference(mizar_proof,[status(thm)],[d9_waybel_4,t1_yellow_1,t6_yellow_0,t1_yellow_1,d9_waybel_4,t4_waybel_4,t3_yellow_1,t30_yellow_0]),
    [file(waybel_4,t5_waybel_4),interesting(0.59)]).

fof(l11_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => v8_relat_2(B) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_relset_1,d4_waybel_4,d5_waybel_4,d8_relat_2,d16_relat_2]),
    [file(waybel_4,l11_waybel_4),interesting(0.56)]).

fof(t31_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k7_funct_2(u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),k10_waybel_4(A),k9_waybel_4(A)) = k6_partfun1(u1_struct_0(k8_waybel_4(A))) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t34_funct_1,d14_waybel_4,t7_funct_2,d14_waybel_4,t7_funct_2,t1_yellow_1,d9_waybel_4,d1_funct_2,t23_funct_1,d15_waybel_4,d1_funct_2,d1_funct_2,d3_tarski,d13_waybel_4,t13_waybel_4,d16_waybel_4,d10_xboole_0,d3_tarski,t7_funct_2,t1_yellow_1,d16_waybel_4,d13_waybel_4,t9_funct_1,t35_funct_1,t9_funct_1]),
    [file(waybel_4,t31_waybel_4),interesting(0.56)]).

fof(t21_waybel_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(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))) )
         => r2_hidden(k3_yellow_0(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_yellow_0,d19_waybel_0]),
    [file(waybel_4,t21_waybel_4),interesting(0.55)]).

fof(l43_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(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))) )
         => r1_tarski(k1_struct_0(A,k3_yellow_0(A)),B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d1_tarski,t21_waybel_4]),
    [file(waybel_4,l43_waybel_4),interesting(0.49)]).

fof(t14_waybel_4,theorem,(
    ! [A,B] : 
      ( ( v2_orders_2(B)
        & v3_orders_2(B)
        & v4_orders_2(B)
        & v1_lattice3(B)
        & l1_orders_2(B) )
     => ! [C] : 
          ( m2_relset_1(C,u1_struct_0(B),u1_struct_0(B))
         => ! [D] : 
              ( m1_subset_1(D,u1_struct_0(B))
             => ( r2_hidden(A,k6_waybel_4(B,D,C))
              <=> r2_hidden(k4_tarski(D,A),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1]),
    [file(waybel_4,t14_waybel_4),interesting(0.45)]).

fof(t51_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( ( v5_waybel_4(D,A)
                    & v6_waybel_4(D,A)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ~ ( r1_waybel_3(A,B,C)
                      & B != C
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(k4_tarski(B,E),D)
                              & r2_hidden(k4_tarski(E,C),D)
                              & B != E ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_waybel_4,d7_waybel_4,d3_tarski,d19_waybel_0,d5_waybel_4,d1_waybel_0,t1_waybel_4,d6_waybel_4,t22_yellow_0,d3_tarski,d4_waybel_4,d5_waybel_4,t17_yellow_0,t34_yellow_0,d18_waybel_4,d10_orders_2,t30_orders_2,t49_waybel_4,t49_waybel_4,t30_yellow_0,d9_lattice3,t17_yellow_0,t20_waybel_3,d4_waybel_4,d5_waybel_4,t50_waybel_4,d10_orders_2,t22_yellow_0,t32_orders_2,d5_waybel_4,d6_waybel_4]),
    [file(waybel_4,t51_waybel_4),interesting(0.45)]).

fof(t62_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_waybel_4(B,A)
            & v2_waybel_4(B,A)
            & v3_waybel_4(B,A)
            & v6_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v9_waybel_4(B,A)
           => v8_waybel_4(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_waybel_4,d22_waybel_4,t50_waybel_4,d10_orders_2,d4_waybel_4,t22_yellow_0,t32_orders_2,d5_waybel_4,d6_waybel_4,t32_orders_2,t24_yellow_0,d10_orders_2,d5_waybel_4,d6_waybel_4,t32_orders_2]),
    [file(waybel_4,t62_waybel_4),interesting(0.45)]).

fof(t30_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => k7_funct_2(u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))),k9_waybel_4(A),k10_waybel_4(A)) = k6_partfun1(k4_relset_1(u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)),k9_waybel_4(A))) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,t1_yellow_1,t34_funct_1,d1_funct_2,t1_yellow_1,d9_waybel_4,t1_yellow_1,d1_funct_2,t23_funct_1,d15_waybel_4,t7_funct_2,t1_yellow_1,d9_waybel_4,t18_waybel_4,d16_waybel_4,d13_waybel_4,t13_waybel_4,t106_zfmisc_1,d13_waybel_4,d16_waybel_4,d2_relat_1,t35_funct_1,t9_funct_1]),
    [file(waybel_4,t30_waybel_4),interesting(0.40)]).

fof(t39_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(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))) )
         => v7_waybel_4(k11_waybel_4(A,B),A) ) ) ),
    inference(mizar_proof,[status(thm)],[t37_waybel_4]),
    [file(waybel_4,t39_waybel_4),interesting(0.37)]).

fof(t60_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v2_waybel_4(B,A)
            & v3_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ( v9_waybel_4(B,A)
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_waybel_4(A,k5_waybel_4(A,C,B),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d23_waybel_4,t13_waybel_4,d22_waybel_4,d22_waybel_4,d6_waybel_4,t22_yellow_0,d5_waybel_4,t22_yellow_0,d5_waybel_4]),
    [file(waybel_4,t60_waybel_4),interesting(0.36)]).

fof(t22_waybel_4,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v2_yellow_0(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))) )
         => r2_hidden(k4_yellow_0(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_yellow_0,d20_waybel_0]),
    [file(waybel_4,t22_waybel_4),interesting(0.34)]).

fof(t27_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r2_hidden(k4_tarski(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),k7_waybel_4(A,B)),u1_orders_2(k8_waybel_4(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_waybel_4,d1_yellow_2,d13_waybel_4,t13_funcop_1,l43_waybel_4,t3_yellow_1,t18_waybel_4,t26_waybel_4,d14_waybel_4]),
    [file(waybel_4,t27_waybel_4),interesting(0.34)]).

fof(t50_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( ( v1_waybel_4(D,A)
                    & v3_waybel_4(D,A)
                    & v6_waybel_4(D,A)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ~ ( r2_hidden(k4_tarski(B,C),D)
                      & B != C
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r3_orders_2(A,B,E)
                              & r2_hidden(k4_tarski(E,C),D)
                              & B != E ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_waybel_4,d10_orders_2,t28_orders_2,d10_orders_2,t49_waybel_4,t22_yellow_0,d6_waybel_4,t24_yellow_0]),
    [file(waybel_4,t50_waybel_4),interesting(0.29)]).

fof(t25_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v1_funct_1(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))))
        & v1_funct_2(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
        & m2_relset_1(k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A))),u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) ) ) ),
    inference(mizar_proof,[status(thm)],[t23_waybel_4,t1_yellow_1,t57_funcop_1]),
    [file(waybel_4,t25_waybel_4),interesting(0.27)]).

fof(t58_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v8_waybel_4(B,A)
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( ? [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                      & r2_waybel_4(k5_waybel_4(A,C,B),D,B) )
                 => r2_hidden(k4_tarski(C,C),B) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_waybel_4,t13_waybel_4,t13_waybel_4,d21_waybel_4,d24_waybel_4]),
    [file(waybel_4,t58_waybel_4),interesting(0.22)]).

fof(t59_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( ? [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                      & r2_waybel_4(k5_waybel_4(A,C,B),D,B) )
                 => r2_hidden(k4_tarski(C,C),B) ) )
           => v8_waybel_4(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_waybel_4,t13_waybel_4,d21_waybel_4]),
    [file(waybel_4,t59_waybel_4),interesting(0.21)]).

fof(t54_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_waybel_3(A,B,C)
              <=> ! [D] : 
                    ( ( ~ v1_xboole_0(D)
                      & v1_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => ~ ( r3_orders_2(A,C,k1_yellow_0(A,D))
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,D)
                                & r1_waybel_3(A,B,E) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t53_waybel_4,d1_waybel_3,t2_waybel_3,t1_waybel_3,d1_waybel_3]),
    [file(waybel_4,t54_waybel_4),interesting(0.06)]).

fof(t19_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => r1_tarski(k3_relat_1(C),k2_xboole_0(A,B)) ) ),
    file(relset_1,t19_relset_1),
    [interesting(0.00)]).

fof(d4_waybel_4,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v1_waybel_4(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                     => r1_orders_2(A,C,D) ) ) ) ) ) ) ),
    file(waybel_4,d4_waybel_4),
    [interesting(0.00)]).

fof(d5_waybel_4,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v2_waybel_4(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r1_orders_2(A,F,C)
                                & r2_hidden(k4_tarski(C,D),B)
                                & r1_orders_2(A,D,E) )
                             => r2_hidden(k4_tarski(F,E),B) ) ) ) ) ) ) ) ) ),
    file(waybel_4,d5_waybel_4),
    [interesting(0.00)]).

fof(d8_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r8_relat_2(A,B)
        <=> ! [C,D,E] : 
              ( ( r2_hidden(C,B)
                & r2_hidden(D,B)
                & r2_hidden(E,B)
                & r2_hidden(k4_tarski(C,D),A)
                & r2_hidden(k4_tarski(D,E),A) )
             => r2_hidden(k4_tarski(C,E),A) ) ) ) ),
    file(relat_2,d8_relat_2),
    [interesting(0.00)]).

fof(d16_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v8_relat_2(A)
      <=> r8_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d16_relat_2),
    [interesting(0.00)]).

fof(d4_yellow_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
         => ( B = k4_yellow_2(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),B,C) = k6_waybel_0(A,C) ) ) ) ) ),
    file(yellow_2,d4_yellow_2),
    [interesting(0.00)]).

fof(d14_waybel_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_orders_2(B)
            & l1_orders_2(B) )
         => ( B = k8_waybel_4(A)
          <=> ! [C] : 
                ( ~ ( r2_hidden(C,u1_struct_0(B))
                    & ! [D] : 
                        ( ( v1_funct_1(D)
                          & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                          & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
                       => ~ ( C = D
                            & v5_orders_3(D,A,k2_yellow_1(k8_waybel_0(A)))
                            & ! [E] : 
                                ( m1_subset_1(E,u1_struct_0(A))
                               => r1_tarski(k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),D,E),k6_waybel_0(A,E)) ) ) ) )
                & ( ? [D] : 
                      ( v1_funct_1(D)
                      & v1_funct_2(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                      & C = D
                      & v5_orders_3(D,A,k2_yellow_1(k8_waybel_0(A)))
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => r1_tarski(k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),D,E),k6_waybel_0(A,E)) ) )
                 => r2_hidden(C,u1_struct_0(B)) )
                & ! [D,E] : 
                    ( r2_hidden(k4_tarski(D,E),u1_orders_2(B))
                  <=> ? [F] : 
                        ( v1_funct_1(F)
                        & v1_funct_2(F,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                        & m2_relset_1(F,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                        & ? [G] : 
                            ( v1_funct_1(G)
                            & v1_funct_2(G,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                            & m2_relset_1(G,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                            & D = F
                            & E = G
                            & r2_hidden(D,u1_struct_0(B))
                            & r2_hidden(E,u1_struct_0(B))
                            & r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),F,G) ) ) ) ) ) ) ) ),
    file(waybel_4,d14_waybel_4),
    [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(d1_yellow_2,definition,(
    ! [A,B] : 
      ( l1_orders_2(B)
     => ! [C] : 
          ( ( v1_funct_1(C)
            & v1_funct_2(C,A,u1_struct_0(B))
            & m2_relset_1(C,A,u1_struct_0(B)) )
         => ! [D] : 
              ( ( v1_funct_1(D)
                & v1_funct_2(D,A,u1_struct_0(B))
                & m2_relset_1(D,A,u1_struct_0(B)) )
             => ( r1_yellow_2(A,B,C,D)
              <=> ! [E] : ~ ( r2_hidden(E,A)
                    & ! [F] : 
                        ( m1_subset_1(F,u1_struct_0(B))
                       => ! [G] : 
                            ( m1_subset_1(G,u1_struct_0(B))
                           => ~ ( F = k1_funct_1(C,E)
                                & G = k1_funct_1(D,E)
                                & r1_orders_2(B,F,G) ) ) ) ) ) ) ) ) ),
    file(yellow_2,d1_yellow_2),
    [interesting(0.00)]).

fof(t3_yellow_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(k2_yellow_1(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(k2_yellow_1(A)))
             => ( r3_orders_2(k2_yellow_1(A),B,C)
              <=> r1_tarski(B,C) ) ) ) ) ),
    file(yellow_1,t3_yellow_1),
    [interesting(0.00)]).

fof(d9_orders_2,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_orders_2(A,B,C)
              <=> r2_hidden(k4_tarski(B,C),u1_orders_2(A)) ) ) ) ) ),
    file(orders_2,d9_orders_2),
    [interesting(0.00)]).

fof(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(t1_yellow_1,theorem,(
    ! [A] : 
      ( u1_struct_0(k2_yellow_1(A)) = A
      & u1_orders_2(k2_yellow_1(A)) = k1_yellow_1(A) ) ),
    file(yellow_1,t1_yellow_1),
    [interesting(0.00)]).

fof(d9_waybel_4,definition,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( B = k3_waybel_4(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ( v5_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ),
    file(waybel_4,d9_waybel_4),
    [interesting(0.00)]).

fof(d15_waybel_4,definition,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A)))
            & m2_relset_1(B,u1_struct_0(k2_yellow_1(k3_waybel_4(A))),u1_struct_0(k8_waybel_4(A))) )
         => ( B = k9_waybel_4(A)
          <=> ! [C] : 
                ( ( v5_waybel_4(C,A)
                  & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
               => k1_funct_1(B,C) = k7_waybel_4(A,C) ) ) ) ) ),
    file(waybel_4,d15_waybel_4),
    [interesting(0.00)]).

fof(d13_waybel_4,definition,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v2_waybel_4(B,A)
            & v3_waybel_4(B,A)
            & v4_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
             => ( C = k7_waybel_4(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k5_waybel_4(A,D,B) ) ) ) ) ) ),
    file(waybel_4,d13_waybel_4),
    [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(t29_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => ! [D] : 
                  ( m2_relset_1(D,u1_struct_0(A),u1_struct_0(A))
                 => ( r1_tarski(C,D)
                   => r1_tarski(k5_waybel_4(A,B,C),k5_waybel_4(A,B,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski]),
    [file(waybel_4,t29_waybel_4),interesting(0.00)]).

fof(d1_yellow_1,definition,(
    ! [A] : k2_yellow_1(A) = g1_orders_2(A,k1_yellow_1(A)) ),
    file(yellow_1,d1_yellow_1),
    [interesting(0.00)]).

fof(t7_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( r2_hidden(C,A)
       => ( B = k1_xboole_0
          | r2_hidden(k1_funct_1(D,C),B) ) ) ) ),
    file(funct_2,t7_funct_2),
    [interesting(0.00)]).

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

fof(d16_waybel_4,definition,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A))))
            & m2_relset_1(B,u1_struct_0(k8_waybel_4(A)),u1_struct_0(k2_yellow_1(k3_waybel_4(A)))) )
         => ( B = k10_waybel_4(A)
          <=> ! [C] : ~ ( r2_hidden(C,u1_struct_0(k8_waybel_4(A)))
                & ! [D] : 
                    ( ( v5_waybel_4(D,A)
                      & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                   => ~ ( D = k1_funct_1(B,C)
                        & ! [E,F] : 
                            ( r2_hidden(k4_tarski(E,F),D)
                          <=> ? [G] : 
                                ( m1_subset_1(G,u1_struct_0(A))
                                & ? [H] : 
                                    ( m1_subset_1(H,u1_struct_0(A))
                                    & ? [I] : 
                                        ( v1_funct_1(I)
                                        & v1_funct_2(I,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                                        & m2_relset_1(I,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                                        & G = E
                                        & H = F
                                        & I = C
                                        & r2_hidden(G,k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),I,H)) ) ) ) ) ) ) ) ) ) ) ),
    file(waybel_4,d16_waybel_4),
    [interesting(0.00)]).

fof(d3_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
               => r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d3_relat_1),
    [interesting(0.00)]).

fof(d1_wellord2,definition,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => ( B = k1_wellord2(A)
      <=> ( k3_relat_1(B) = A
          & ! [C,D] : 
              ( ( r2_hidden(C,A)
                & r2_hidden(D,A) )
             => ( r2_hidden(k4_tarski(C,D),B)
              <=> r1_tarski(C,D) ) ) ) ) ) ),
    file(wellord2,d1_wellord2),
    [interesting(0.00)]).

fof(s1_partfun1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_partfun1
      & ! [B] : 
          ( r2_hidden(B,f1_s1_partfun1)
         => ( ( p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f2_s1_partfun1(B) )
            & ( ~ p1_s1_partfun1(B)
             => k1_funct_1(A,B) = f3_s1_partfun1(B) ) ) ) ) ),
    file(partfun1,s1_partfun1),
    [interesting(0.00)]).

fof(s1_waybel_4,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s1_waybel_4
      & ! [B] : 
          ( m1_subset_1(B,f1_s1_waybel_4)
         => ( ( p1_s1_waybel_4(B)
             => k1_funct_1(A,B) = f2_s1_waybel_4(B) )
            & ( ~ p1_s1_waybel_4(B)
             => k1_funct_1(A,B) = f3_s1_waybel_4(B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s1_partfun1]),
    [file(waybel_4,s1_waybel_4),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(t6_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( ( v1_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v1_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,d4_waybel_4,d4_waybel_4]),
    [file(waybel_4,t6_waybel_4),interesting(0.00)]).

fof(t7_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( ( v2_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v2_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,d5_waybel_4,d3_xboole_0,d5_waybel_4]),
    [file(waybel_4,t7_waybel_4),interesting(0.00)]).

fof(d6_waybel_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v3_waybel_4(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( ( r2_hidden(k4_tarski(C,E),B)
                            & r2_hidden(k4_tarski(D,E),B) )
                         => r2_hidden(k4_tarski(k10_lattice3(A,C,D),E),B) ) ) ) ) ) ) ) ),
    file(waybel_4,d6_waybel_4),
    [interesting(0.00)]).

fof(t8_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v3_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( ( v3_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v3_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_xboole_0,d6_waybel_4,d3_xboole_0,d6_waybel_4]),
    [file(waybel_4,t8_waybel_4),interesting(0.00)]).

fof(d7_waybel_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v4_waybel_4(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r2_hidden(k4_tarski(k3_yellow_0(A),C),B) ) ) ) ) ),
    file(waybel_4,d7_waybel_4),
    [interesting(0.00)]).

fof(t9_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v4_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( ( v4_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v4_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_waybel_4,d3_xboole_0,d7_waybel_4]),
    [file(waybel_4,t9_waybel_4),interesting(0.00)]).

fof(d8_waybel_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v5_waybel_4(B,A)
          <=> ( v1_waybel_4(B,A)
              & v2_waybel_4(B,A)
              & v3_waybel_4(B,A)
              & v4_waybel_4(B,A) ) ) ) ) ),
    file(waybel_4,d8_waybel_4),
    [interesting(0.00)]).

fof(t10_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( ( v5_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( v5_waybel_4(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),A)
                & m2_relset_1(k2_relset_1(u1_struct_0(A),u1_struct_0(A),B,C),u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t6_waybel_4,t7_waybel_4,t8_waybel_4,t9_waybel_4,d8_waybel_4]),
    [file(waybel_4,t10_waybel_4),interesting(0.00)]).

fof(t8_setfam_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_hidden(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(k1_setfam_1(B),C) ) ),
    file(setfam_1,t8_setfam_1),
    [interesting(0.00)]).

fof(d1_relset_1,definition,(
    ! [A,B,C] : 
      ( m1_relset_1(C,A,B)
    <=> r1_tarski(C,k2_zfmisc_1(A,B)) ) ),
    file(relset_1,d1_relset_1),
    [interesting(0.00)]).

fof(d1_setfam_1,definition,(
    ! [A,B] : 
      ( ( A != k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ! [D] : 
                  ( r2_hidden(D,A)
                 => r2_hidden(C,D) ) ) ) )
      & ( A = k1_xboole_0
       => ( B = k1_setfam_1(A)
        <=> B = k1_xboole_0 ) ) ) ),
    file(setfam_1,d1_setfam_1),
    [interesting(0.00)]).

fof(t11_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(k2_yellow_1(k3_waybel_4(A))))) )
         => ( v5_waybel_4(k1_setfam_1(B),A)
            & m2_relset_1(k1_setfam_1(B),u1_struct_0(A),u1_struct_0(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t1_yellow_1,d9_waybel_4,t8_setfam_1,d1_relset_1,d4_waybel_4,d1_setfam_1,d9_waybel_4,d4_waybel_4,d5_waybel_4,d9_waybel_4,d1_setfam_1,d5_waybel_4,d1_setfam_1,d6_waybel_4,d9_waybel_4,d1_setfam_1,d6_waybel_4,d1_setfam_1,d7_waybel_4,d9_waybel_4,d7_waybel_4,d1_setfam_1,d8_waybel_4]),
    [file(waybel_4,t11_waybel_4),interesting(0.00)]).

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) ) ) ) ) ),
    file(waybel_0,t17_waybel_0),
    [interesting(0.00)]).

fof(t12_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => r1_tarski(k5_waybel_4(A,B,C),k6_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_waybel_4,t17_waybel_0]),
    [file(waybel_4,t12_waybel_4),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(l31_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ! [C,D] : 
              ( m1_subset_1(D,u1_struct_0(A))
             => ( r2_hidden(C,k6_waybel_0(A,D))
              <=> r2_hidden(k4_tarski(C,D),u1_orders_2(A)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t17_waybel_0,d9_orders_2,t106_zfmisc_1,d9_orders_2,t17_waybel_0]),
    [file(waybel_4,l31_waybel_4),interesting(0.00)]).

fof(t15_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B = u1_orders_2(A)
               => k5_waybel_4(A,C,B) = k6_waybel_0(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t12_waybel_4,d10_xboole_0,d3_tarski,l31_waybel_4,t13_waybel_4]),
    [file(waybel_4,t15_waybel_4),interesting(0.00)]).

fof(t11_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ( ( B = k1_xboole_0
         => A = k1_xboole_0 )
       => r2_hidden(C,k1_funct_2(A,B)) ) ) ),
    file(funct_2,t11_funct_2),
    [interesting(0.00)]).

fof(t28_yellow_1,theorem,(
    ! [A,B] : 
      ( l1_orders_2(B)
     => k1_funct_2(A,u1_struct_0(B)) = u1_struct_0(k6_yellow_1(A,B)) ) ),
    file(yellow_1,t28_yellow_1),
    [interesting(0.00)]).

fof(d5_yellow_1,definition,(
    ! [A,B] : 
      ( l1_orders_2(B)
     => k6_yellow_1(A,B) = k5_yellow_1(A,k2_pre_circ(A,B)) ) ),
    file(yellow_1,d5_yellow_1),
    [interesting(0.00)]).

fof(d4_yellow_1,definition,(
    ! [A,B] : 
      ( ( v1_yellow_1(B)
        & m1_pboole(B,A) )
     => ! [C] : 
          ( ( v1_orders_2(C)
            & l1_orders_2(C) )
         => ( C = k5_yellow_1(A,B)
          <=> ( u1_struct_0(C) = k4_card_3(k12_pralg_1(A,B))
              & ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(C))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(C))
                     => ( r2_hidden(D,k4_card_3(k12_pralg_1(A,B)))
                       => ( r1_orders_2(C,D,E)
                        <=> ? [F] : 
                              ( v1_relat_1(F)
                              & v1_funct_1(F)
                              & ? [G] : 
                                  ( v1_relat_1(G)
                                  & v1_funct_1(G)
                                  & F = D
                                  & G = E
                                  & ! [H] : ~ ( r2_hidden(H,A)
                                      & ! [I] : 
                                          ( l1_orders_2(I)
                                         => ! [J] : 
                                              ( m1_subset_1(J,u1_struct_0(I))
                                             => ! [K] : 
                                                  ( m1_subset_1(K,u1_struct_0(I))
                                                 => ~ ( I = k1_funct_1(B,H)
                                                      & J = k1_funct_1(F,H)
                                                      & K = k1_funct_1(G,H)
                                                      & r1_orders_2(I,J,K) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
    file(yellow_1,d4_yellow_1),
    [interesting(0.00)]).

fof(t13_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k2_funcop_1(A,C),B) = C ) ),
    file(funcop_1,t13_funcop_1),
    [interesting(0.00)]).

fof(d2_relat_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( A = B
          <=> ! [C,D] : 
                ( r2_hidden(k4_tarski(C,D),A)
              <=> r2_hidden(k4_tarski(C,D),B) ) ) ) ) ),
    file(relat_1,d2_relat_1),
    [interesting(0.00)]).

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

fof(t121_funct_2,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,k1_funct_2(A,B))
     => ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) ) ) ),
    file(funct_2,t121_funct_2),
    [interesting(0.00)]).

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

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

fof(t16_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ( v4_yellow_0(k8_waybel_4(A),k6_yellow_1(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A))))
        & m1_yellow_0(k8_waybel_4(A),k6_yellow_1(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)))) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d14_waybel_4,t11_funct_2,t28_yellow_1,d3_relat_1,d14_waybel_4,d5_yellow_1,t11_funct_2,t28_yellow_1,t28_yellow_1,d4_yellow_1,t13_funcop_1,d1_yellow_2,d4_yellow_1,d9_orders_2,d5_yellow_1,d2_relat_1,t16_wellord1,t16_wellord1,t106_zfmisc_1,d5_yellow_1,d5_yellow_1,d5_yellow_1,d9_orders_2,d4_yellow_1,d4_yellow_1,t28_yellow_1,t121_funct_2,d1_yellow_2,t13_funcop_1,t106_zfmisc_1,d14_waybel_4,d13_yellow_0,d14_yellow_0]),
    [file(waybel_4,t16_waybel_4),interesting(0.00)]).

fof(t17_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v2_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( r3_orders_2(A,C,D)
                   => r1_tarski(k5_waybel_4(A,C,B),k5_waybel_4(A,D,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_waybel_4]),
    [file(waybel_4,t17_waybel_4),interesting(0.00)]).

fof(t20_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),k7_waybel_4(A,B),k4_yellow_2(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_yellow_2,d13_waybel_4,d4_yellow_2,t12_waybel_4,t3_yellow_1]),
    [file(waybel_4,t20_waybel_4),interesting(0.00)]).

fof(t45_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v2_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_orders_2(A,B,k4_yellow_0(A)) ) ) ),
    file(yellow_0,t45_yellow_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(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) ) ) ) ) ),
    file(waybel_0,t18_waybel_0),
    [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(d1_tarski,definition,(
    ! [A,B] : 
      ( B = k1_tarski(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> C = A ) ) ),
    file(tarski,d1_tarski),
    [interesting(0.00)]).

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) ) ) ),
    file(waybel_0,t14_waybel_0),
    [interesting(0.00)]).

fof(t44_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_orders_2(A,k3_yellow_0(A),B) ) ) ),
    file(yellow_0,t44_yellow_0),
    [interesting(0.00)]).

fof(t57_funcop_1,theorem,(
    ! [A,B,C] : 
      ( r2_hidden(C,B)
     => ( v1_funct_1(k2_funcop_1(A,C))
        & v1_funct_2(k2_funcop_1(A,C),A,B)
        & m2_relset_1(k2_funcop_1(A,C),A,B) ) ) ),
    file(funcop_1,t57_funcop_1),
    [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(l45_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
         => ( B = k2_pre_circ(u1_struct_0(A),k1_struct_0(A,k3_yellow_0(A)))
           => v5_orders_3(B,A,k2_yellow_1(k8_waybel_0(A))) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_orders_3,t13_funcop_1,t3_yellow_1]),
    [file(waybel_4,l45_waybel_4),interesting(0.00)]).

fof(t28_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v5_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( ( v5_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
             => ( r1_tarski(B,C)
               => r1_yellow_2(u1_struct_0(A),k2_yellow_1(k8_waybel_0(A)),k7_waybel_4(A,B),k7_waybel_4(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_yellow_2,d3_tarski,d13_waybel_4,t3_yellow_1]),
    [file(waybel_4,t28_waybel_4),interesting(0.00)]).

fof(t24_funct_2,theorem,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & v1_funct_2(C,A,B)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( ( v1_funct_1(D)
            & v1_funct_2(D,B,A)
            & m2_relset_1(D,B,A) )
         => ( k1_partfun1(B,A,A,B,D,C) = k6_partfun1(B)
           => k2_relat_1(C) = B ) ) ) ),
    file(funct_2,t24_funct_2),
    [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(t34_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( B = k6_relat_1(A)
      <=> ( k1_relat_1(B) = A
          & ! [C] : 
              ( r2_hidden(C,A)
             => k1_funct_1(B,C) = C ) ) ) ) ),
    file(funct_1,t34_funct_1),
    [interesting(0.00)]).

fof(t23_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k5_relat_1(B,C),A) = k1_funct_1(C,k1_funct_1(B,A)) ) ) ) ),
    file(funct_1,t23_funct_1),
    [interesting(0.00)]).

fof(t35_funct_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(B,A)
     => k1_funct_1(k6_relat_1(A),B) = B ) ),
    file(funct_1,t35_funct_1),
    [interesting(0.00)]).

fof(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(t63_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( v2_funct_1(A)
              & k2_relat_1(A) = k1_relat_1(B)
              & k5_relat_1(A,B) = k6_relat_1(k1_relat_1(A)) )
           => B = k2_funct_1(A) ) ) ) ),
    file(funct_1,t63_funct_1),
    [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(d17_waybel_4,definition,(
    ! [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)
            & v1_waybel_0(B,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
             => ( C = k11_waybel_4(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r3_orders_2(A,D,k1_yellow_0(A,B))
                       => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k5_subset_1(u1_struct_0(A),k6_waybel_0(A,D),B) )
                      & ( ~ r3_orders_2(A,D,k1_yellow_0(A,B))
                       => k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),C,D) = k6_waybel_0(A,D) ) ) ) ) ) ) ) ),
    file(waybel_4,d17_waybel_4),
    [interesting(0.00)]).

fof(d4_yellow_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => k3_yellow_4(A,B,C) = a_3_2_yellow_4(A,B,C) ) ) ) ),
    file(yellow_4,d4_yellow_4),
    [interesting(0.00)]).

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

fof(d14_lattice3,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v4_orders_2(A)
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( ? [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                      & r1_orders_2(A,D,B)
                      & r1_orders_2(A,D,C)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ( ( r1_orders_2(A,E,B)
                              & r1_orders_2(A,E,C) )
                           => r1_orders_2(A,E,D) ) ) )
                 => ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ( D = k11_lattice3(A,B,C)
                      <=> ( r1_orders_2(A,D,B)
                          & r1_orders_2(A,D,C)
                          & ! [E] : 
                              ( m1_subset_1(E,u1_struct_0(A))
                             => ( ( r1_orders_2(A,E,B)
                                  & r1_orders_2(A,E,C) )
                               => r1_orders_2(A,E,D) ) ) ) ) ) ) ) ) ) ) ),
    file(lattice3,d14_lattice3),
    [interesting(0.00)]).

fof(t25_yellow_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B = k12_lattice3(A,B,C)
              <=> r3_orders_2(A,B,C) ) ) ) ) ),
    file(yellow_0,t25_yellow_0),
    [interesting(0.00)]).

fof(t36_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( ~ v1_xboole_0(C)
                & v12_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => k4_yellow_4(A,k1_struct_0(A,B),C) = k5_subset_1(u1_struct_0(A),k6_waybel_0(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_yellow_4,d3_tarski,d4_yellow_4,d1_tarski,d11_lattice3,d14_lattice3,t17_waybel_0,d19_waybel_0,d3_xboole_0,d10_xboole_0,d3_tarski,d3_xboole_0,d3_xboole_0,d1_tarski,t17_waybel_0,t25_yellow_0]),
    [file(waybel_4,t36_waybel_4),interesting(0.00)]).

fof(d6_waybel_2,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v1_waybel_2(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => k11_lattice3(A,B,k1_yellow_0(A,C)) = k1_yellow_0(A,k3_yellow_4(A,k1_struct_0(A,B),C)) ) ) ) ) ),
    file(waybel_2,d6_waybel_2),
    [interesting(0.00)]).

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 ) ) ) ),
    file(waybel_0,t34_waybel_0),
    [interesting(0.00)]).

fof(d19_waybel_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
         => ( v7_waybel_4(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ? [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                    & D = k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),B,C)
                    & C = k1_yellow_0(A,D) ) ) ) ) ) ),
    file(waybel_4,d19_waybel_4),
    [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(l13_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C,D] : 
              ( r2_hidden(k4_tarski(C,D),B)
             => r2_hidden(k4_tarski(C,D),k2_waybel_4(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t106_zfmisc_1,d4_waybel_4,l4_waybel_4]),
    [file(waybel_4,l13_waybel_4),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(d18_waybel_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v6_waybel_4(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => C = k1_yellow_0(A,k5_waybel_4(A,C,B)) ) ) ) ) ),
    file(waybel_4,d18_waybel_4),
    [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(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(d3_waybel_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k1_waybel_3(A,B) = a_2_0_waybel_3(A,B) ) ) ),
    file(waybel_3,d3_waybel_3),
    [interesting(0.00)]).

fof(t1_waybel_3,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))
             => ( r1_waybel_3(A,B,C)
               => r3_orders_2(A,B,C) ) ) ) ) ),
    file(waybel_3,t1_waybel_3),
    [interesting(0.00)]).

fof(d1_waybel_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_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_waybel_3(A,B,C)
              <=> ! [D] : 
                    ( ( ~ v1_xboole_0(D)
                      & v1_waybel_0(D,A)
                      & m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A))) )
                   => ~ ( r3_orders_2(A,C,k1_yellow_0(A,D))
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(E,D)
                                & r3_orders_2(A,B,E) ) ) ) ) ) ) ) ) ),
    file(waybel_3,d1_waybel_3),
    [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(t32_yellow_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( B = k1_yellow_0(A,C)
            <=> ( r2_lattice3(A,C,B)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_lattice3(A,C,D)
                     => r1_orders_2(A,B,D) ) ) ) ) ) ) ),
    file(yellow_0,t32_yellow_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(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(d5_waybel_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v2_waybel_3(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => B = k1_yellow_0(A,k1_waybel_3(A,B)) ) ) ) ),
    file(waybel_3,d5_waybel_3),
    [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(l68_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_waybel_0(C,A)
                & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
             => r3_orders_2(A,k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C)),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_yellow_4,t17_yellow_0,d1_tarski,t23_yellow_0,d9_lattice3,t30_yellow_0]),
    [file(waybel_4,l68_waybel_4),interesting(0.00)]).

fof(t52_waybel_2,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ( v2_waybel_2(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( ( ~ v1_xboole_0(C)
                  & v1_waybel_0(C,A)
                  & m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A))) )
               => ( r3_orders_2(A,B,k1_yellow_0(A,C))
                 => B = k1_yellow_0(A,k4_yellow_4(A,k1_struct_0(A,B),C)) ) ) ) ) ) ),
    file(waybel_2,t52_waybel_2),
    [interesting(0.00)]).

fof(d2_waybel_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k1_waybel_4(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> r1_waybel_3(A,C,D) ) ) ) ) ) ) ),
    file(waybel_4,d2_waybel_4),
    [interesting(0.00)]).

fof(t7_waybel_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_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))
             => ( r2_hidden(B,k1_waybel_3(A,C))
              <=> r1_waybel_3(A,B,C) ) ) ) ) ),
    file(waybel_3,t7_waybel_3),
    [interesting(0.00)]).

fof(d20_waybel_4,definition,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( B = k12_waybel_4(A)
        <=> ! [C] : 
              ( r2_hidden(C,B)
            <=> ( v5_waybel_4(C,A)
                & v6_waybel_4(C,A)
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) ) ) ) ) ),
    file(waybel_4,d20_waybel_4),
    [interesting(0.00)]).

fof(t21_waybel_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v24_waybel_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( ! [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))) )
                   => ( r3_orders_2(A,C,k1_yellow_0(A,D))
                     => r2_hidden(B,D) ) )
               => r1_waybel_3(A,B,C) ) ) ) ) ),
    file(waybel_3,t21_waybel_3),
    [interesting(0.00)]).

fof(t20_waybel_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(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_waybel_3(A,B,C)
               => ! [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))) )
                   => ( r3_orders_2(A,C,k1_yellow_0(A,D))
                     => r2_hidden(B,D) ) ) ) ) ) ) ),
    file(waybel_3,t20_waybel_3),
    [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(t42_yellow_2,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)
            & v1_waybel_0(B,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ! [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))) )
             => ( ~ v1_xboole_0(k5_subset_1(u1_struct_0(A),B,C))
                & v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
                & v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
                & m1_subset_1(k5_subset_1(u1_struct_0(A),B,C),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ),
    file(yellow_2,t42_yellow_2),
    [interesting(0.00)]).

fof(t7_setfam_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => ( A = k1_xboole_0
        | r1_tarski(k1_setfam_1(B),k1_setfam_1(A)) ) ) ),
    file(setfam_1,t7_setfam_1),
    [interesting(0.00)]).

fof(t4_setfam_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(k1_setfam_1(B),A) ) ),
    file(setfam_1,t4_setfam_1),
    [interesting(0.00)]).

fof(t19_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(A,C) )
     => r1_tarski(A,k3_xboole_0(B,C)) ) ),
    file(xboole_1,t19_xboole_1),
    [interesting(0.00)]).

fof(t6_setfam_1,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
         => r1_tarski(B,C) )
     => ( A = k1_xboole_0
        | r1_tarski(B,k1_setfam_1(A)) ) ) ),
    file(setfam_1,t6_setfam_1),
    [interesting(0.00)]).

fof(t30_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)
                  & r2_orders_2(A,C,B) ) ) ) ) ),
    file(orders_2,t30_orders_2),
    [interesting(0.00)]).

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

fof(t10_setfam_1,theorem,(
    ! [A,B] : ~ ( A != k1_xboole_0
      & B != k1_xboole_0
      & k1_setfam_1(k2_xboole_0(A,B)) != k3_xboole_0(k1_setfam_1(A),k1_setfam_1(B)) ) ),
    file(setfam_1,t10_setfam_1),
    [interesting(0.00)]).

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

fof(t12_pre_topc,theorem,(
    ! [A] : 
      ( l1_struct_0(A)
     => k2_pre_topc(A) = u1_struct_0(A) ) ),
    file(pre_topc,t12_pre_topc),
    [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(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(t11_waybel_3,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_tarski(k1_waybel_3(A,B),k6_waybel_0(A,B))
            & r1_tarski(k2_waybel_3(A,B),k7_waybel_0(A,B)) ) ) ) ),
    file(waybel_3,t11_waybel_3),
    [interesting(0.00)]).

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)) ) ) ) ) ),
    file(waybel_0,t21_waybel_0),
    [interesting(0.00)]).

fof(t26_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ),
    file(xboole_1,t26_xboole_1),
    [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(l61_waybel_4,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)
            & v1_waybel_0(B,A)
            & v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => v5_orders_3(k11_waybel_4(A,B),A,k2_yellow_1(k8_waybel_0(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_orders_3,d17_waybel_4,t21_waybel_0,t26_xboole_1,t3_yellow_1,d17_waybel_4,t21_waybel_0,t17_xboole_1,t1_xboole_1,t3_yellow_1,t26_orders_2,d17_waybel_4,t21_waybel_0,t3_yellow_1]),
    [file(waybel_4,l61_waybel_4),interesting(0.00)]).

fof(l62_waybel_4,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] : 
              ( ( ~ 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(k1_waybel_0(A,k2_yellow_1(k8_waybel_0(A)),k11_waybel_4(A,C),B),k6_waybel_0(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_waybel_4,t17_xboole_1,d17_waybel_4]),
    [file(waybel_4,l62_waybel_4),interesting(0.00)]).

fof(t42_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v1_funct_1(B)
            & v1_funct_2(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A))))
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(k2_yellow_1(k8_waybel_0(A)))) )
         => ~ ( v7_waybel_4(B,A)
              & r2_hidden(B,u1_struct_0(k8_waybel_4(A)))
              & ! [C] : 
                  ( ( v5_waybel_4(C,A)
                    & v6_waybel_4(C,A)
                    & m2_relset_1(C,u1_struct_0(A),u1_struct_0(A)) )
                 => C != k1_funct_1(k10_waybel_4(A),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_waybel_4,d19_waybel_4,d3_tarski,t13_waybel_4,d10_xboole_0,d3_tarski,d18_waybel_4]),
    [file(waybel_4,t42_waybel_4),interesting(0.00)]).

fof(d6_waybel_3,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & l1_orders_2(A) )
     => ( v3_waybel_3(A)
      <=> ( ! [B] : 
              ( m1_subset_1(B,u1_struct_0(A))
             => ( ~ v1_xboole_0(k1_waybel_3(A,B))
                & v1_waybel_0(k1_waybel_3(A,B),A) ) )
          & v24_waybel_0(A)
          & v2_waybel_3(A) ) ) ) ),
    file(waybel_3,d6_waybel_3),
    [interesting(0.00)]).

fof(t47_waybel_4,theorem,(
    $true ),
    file(waybel_4,t47_waybel_4),
    [interesting(0.00)]).

fof(d22_waybel_4,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v9_waybel_4(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(k4_tarski(C,D),B)
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(k4_tarski(C,E),B)
                                & r2_hidden(k4_tarski(E,D),B) ) ) ) ) ) ) ) ) ),
    file(waybel_4,d22_waybel_4),
    [interesting(0.00)]).

fof(d21_waybel_4,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( v8_waybel_4(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(k4_tarski(C,D),B)
                        & C != D
                        & ! [E] : 
                            ( m1_subset_1(E,u1_struct_0(A))
                           => ~ ( r2_hidden(k4_tarski(C,E),B)
                                & r2_hidden(k4_tarski(E,D),B)
                                & C != E ) ) ) ) ) ) ) ) ),
    file(waybel_4,d21_waybel_4),
    [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(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(t1_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v2_waybel_4(B,A)
            & v3_waybel_4(B,A)
            & m2_relset_1(B,u1_struct_0(A),u1_struct_0(A)) )
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ! [F] : 
                          ( m1_subset_1(F,u1_struct_0(A))
                         => ( ( r2_hidden(k4_tarski(C,E),B)
                              & r2_hidden(k4_tarski(D,F),B) )
                           => r2_hidden(k4_tarski(k13_lattice3(A,C,D),k13_lattice3(A,E,F)),B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t22_yellow_0,d5_waybel_4,d6_waybel_4]),
    [file(waybel_4,t1_waybel_4),interesting(0.00)]).

fof(t49_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ! [D] : 
                  ( ( v6_waybel_4(D,A)
                    & m2_relset_1(D,u1_struct_0(A),u1_struct_0(A)) )
                 => ~ ( ~ r3_orders_2(A,B,C)
                      & ! [E] : 
                          ( m1_subset_1(E,u1_struct_0(A))
                         => ~ ( r2_hidden(k4_tarski(E,B),D)
                              & ~ r3_orders_2(A,E,C) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_waybel_4,t17_yellow_0,d9_yellow_0,d9_lattice3,t13_waybel_4]),
    [file(waybel_4,t49_waybel_4),interesting(0.00)]).

fof(t28_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))
             => ~ ( r2_orders_2(A,B,C)
                  & r2_orders_2(A,C,B) ) ) ) ) ),
    file(orders_2,t28_orders_2),
    [interesting(0.00)]).

fof(t24_yellow_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( B = k13_lattice3(A,B,C)
              <=> r1_orders_2(A,C,B) ) ) ) ) ),
    file(yellow_0,t24_yellow_0),
    [interesting(0.00)]).

fof(t32_orders_2,theorem,(
    ! [A] : 
      ( ( v3_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))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( ( r2_orders_2(A,B,C)
                        & r1_orders_2(A,C,D) )
                      | ( r1_orders_2(A,B,C)
                        & r2_orders_2(A,C,D) ) )
                   => r2_orders_2(A,B,D) ) ) ) ) ) ),
    file(orders_2,t32_orders_2),
    [interesting(0.00)]).

fof(t53_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_yellow_0(A)
        & v3_waybel_3(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( r1_waybel_3(A,B,C)
                  & ! [D] : 
                      ( m1_subset_1(D,u1_struct_0(A))
                     => ~ ( r1_waybel_3(A,B,D)
                          & r1_waybel_3(A,D,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_waybel_4,d22_waybel_4,d2_waybel_4]),
    [file(waybel_4,t53_waybel_4),interesting(0.00)]).

fof(t2_waybel_3,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(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))
                 => ! [E] : 
                      ( m1_subset_1(E,u1_struct_0(A))
                     => ( ( r3_orders_2(A,B,C)
                          & r1_waybel_3(A,C,D)
                          & r3_orders_2(A,D,E) )
                       => r1_waybel_3(A,B,E) ) ) ) ) ) ) ),
    file(waybel_3,t2_waybel_3),
    [interesting(0.00)]).

fof(d23_waybel_4,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m2_relset_1(C,u1_struct_0(A),u1_struct_0(A))
             => ( r1_waybel_4(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ~ ( r2_hidden(D,B)
                            & r2_hidden(E,B)
                            & ! [F] : 
                                ( m1_subset_1(F,u1_struct_0(A))
                               => ~ ( r2_hidden(F,B)
                                    & r2_hidden(k4_tarski(D,F),C)
                                    & r2_hidden(k4_tarski(E,F),C) ) ) ) ) ) ) ) ) ) ),
    file(waybel_4,d23_waybel_4),
    [interesting(0.00)]).

fof(d25_waybel_4,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r3_waybel_4(A,B,C)
          <=> r2_waybel_4(B,C,u1_orders_2(A)) ) ) ) ),
    file(waybel_4,d25_waybel_4),
    [interesting(0.00)]).

fof(d24_waybel_4,definition,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r2_waybel_4(A,B,C)
      <=> ( r2_hidden(B,A)
          & ! [D] : ~ ( r2_hidden(D,A)
              & D != B
              & r2_hidden(k4_tarski(B,D),C) ) ) ) ) ),
    file(waybel_4,d24_waybel_4),
    [interesting(0.00)]).

fof(d27_waybel_4,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( r5_waybel_4(A,B,C)
          <=> r4_waybel_4(B,C,u1_orders_2(A)) ) ) ) ),
    file(waybel_4,d27_waybel_4),
    [interesting(0.00)]).

fof(d26_waybel_4,definition,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( r4_waybel_4(A,B,C)
      <=> ( r2_hidden(B,A)
          & ! [D] : ~ ( r2_hidden(D,A)
              & D != B
              & r2_hidden(k4_tarski(D,B),C) ) ) ) ) ),
    file(waybel_4,d26_waybel_4),
    [interesting(0.00)]).

fof(d10_waybel_4,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k4_waybel_4(A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(k4_tarski(C,D),B)
                    <=> C = k3_yellow_0(A) ) ) ) ) ) ) ),
    file(waybel_4,d10_waybel_4),
    [interesting(0.00)]).

fof(t61_waybel_4,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v2_lattice3(A)
        & v3_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => r1_waybel_4(A,k5_waybel_4(A,C,B),B) )
           => v9_waybel_4(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d22_waybel_4,d23_waybel_4,t13_waybel_4]),
    [file(waybel_4,t61_waybel_4),interesting(0.00)]).