fof(t83_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r3_orders_2(A,B,C)
               => r3_orders_2(A,k12_abcmiz_0(A,B),k12_abcmiz_0(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t80_abcmiz_0,t79_abcmiz_0,d2_yellow_0,d31_abcmiz_0,t82_abcmiz_0,s2_abcmiz_0]),
    [file(abcmiz_0,t83_abcmiz_0),interesting(1.00)]).

fof(t78_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ( v8_rewrite1(k11_abcmiz_0(A))
        & v4_rewrite1(k11_abcmiz_0(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d24_rewrite1,t106_zfmisc_1,d31_abcmiz_0,d31_abcmiz_0,d27_abcmiz_0,t21_abcmiz_0,d30_abcmiz_0,d30_abcmiz_0,d7_rewrite1,t73_abcmiz_0,t70_abcmiz_0]),
    [file(abcmiz_0,t78_abcmiz_0),interesting(0.90)]).

fof(t82_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(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_abcmiz_0(A))
                 => ( ( r4_abcmiz_0(A,B,D)
                      & r3_orders_2(A,k5_abcmiz_0(A,B,D),k12_abcmiz_0(A,C)) )
                   => r3_orders_2(A,B,k12_abcmiz_0(A,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t70_abcmiz_0,t78_abcmiz_0,d30_abcmiz_0,t55_rewrite1,d6_rewrite1,t77_abcmiz_0,d29_abcmiz_0,d29_abcmiz_0,t44_finseq_1,t58_abcmiz_0,t57_abcmiz_0,t62_abcmiz_0,d29_abcmiz_0,t58_abcmiz_0,t57_abcmiz_0,t38_abcmiz_0,t57_abcmiz_0,t81_abcmiz_0,t1_yellow_4,t81_abcmiz_0,t22_yellow_0,d2_yellow_0]),
    [file(abcmiz_0,t82_abcmiz_0),interesting(0.90)]).

fof(t75_abcmiz_0,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_relset_1(B,A,A)
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ! [D] : 
                  ( r1_rewrite1(B,C,D)
                 => r2_hidden(D,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,d2_rewrite1,t38_nat_1,t74_abcmiz_0,t27_finseq_3,d4_finseq_1,t12_funct_1]),
    [file(abcmiz_0,t75_abcmiz_0),interesting(0.87)]).

fof(t80_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r3_orders_2(A,B,k12_abcmiz_0(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t79_abcmiz_0,t68_abcmiz_0]),
    [file(abcmiz_0,t80_abcmiz_0),interesting(0.87)]).

fof(t79_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r1_rewrite1(k11_abcmiz_0(A),B,k12_abcmiz_0(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[t70_abcmiz_0,t78_abcmiz_0,t55_rewrite1,d6_rewrite1]),
    [file(abcmiz_0,t79_abcmiz_0),interesting(0.84)]).

fof(t81_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( C = a_2_2_abcmiz_0(A,B)
             => ( r1_yellow_0(A,C)
                & k12_abcmiz_0(A,B) = k1_yellow_0(A,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t70_abcmiz_0,t78_abcmiz_0,d9_lattice3,t73_abcmiz_0,t26_rewrite1,t56_rewrite1,t55_rewrite1,d6_rewrite1,t68_abcmiz_0,t79_abcmiz_0,t77_abcmiz_0,d9_lattice3,t30_yellow_0]),
    [file(abcmiz_0,t81_abcmiz_0),interesting(0.83)]).

fof(t74_abcmiz_0,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_relset_1(B,A,A)
         => ! [C] : 
              ( m1_rewrite1(C,B)
             => ( r2_hidden(k1_funct_1(C,1),A)
               => m2_finseq_1(C,A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d4_finseq_1,d5_funct_1,t27_finseq_3,t38_nat_1,t28_nat_1,t27_finseq_3,t29_nat_1,t38_nat_1,t27_finseq_3,d2_rewrite1,t106_zfmisc_1,t1_xreal_1]),
    [file(abcmiz_0,t74_abcmiz_0),interesting(0.80)]).

fof(t70_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => v3_rewrite1(k11_abcmiz_0(A)) ) ),
    inference(mizar_proof,[status(thm)],[t67_abcmiz_0,t31_relat_1,d16_rewrite1,t1_xboole_1,d16_rewrite1,t69_abcmiz_0]),
    [file(abcmiz_0,t70_abcmiz_0),interesting(0.78)]).

fof(t69_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => v2_relat_2(k11_abcmiz_0(A)) ) ),
    inference(mizar_proof,[status(thm)],[d2_relat_2,d10_relat_2,t106_zfmisc_1,d31_abcmiz_0,d27_abcmiz_0,t22_abcmiz_0]),
    [file(abcmiz_0,t69_abcmiz_0),interesting(0.77)]).

fof(t73_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
             => ( r6_abcmiz_0(A,B,C)
               => r1_rewrite1(k11_abcmiz_0(A),k6_abcmiz_0(A,B,C),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t65_abcmiz_0,t66_abcmiz_0,t58_abcmiz_0,t72_abcmiz_0,d3_rewrite1,t65_finseq_5,d19_abcmiz_0,t57_abcmiz_0,d3_finseq_5,t65_finseq_5,d19_abcmiz_0]),
    [file(abcmiz_0,t73_abcmiz_0),interesting(0.77)]).

fof(t16_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => k4_abcmiz_0(A,k1_subset_1(u1_abcmiz_0(A))) = u1_struct_0(A) ) ),
    inference(mizar_proof,[status(thm)],[d10_xboole_0,d3_tarski,d13_abcmiz_0]),
    [file(abcmiz_0,t16_abcmiz_0),interesting(0.76)]).

fof(t76_abcmiz_0,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_relset_1(B,A,A)
         => ( ( v4_rewrite1(B)
              & v2_rewrite1(B) )
           => ! [C] : 
                ( m1_subset_1(C,A)
               => r2_hidden(k2_rewrite1(B,C),A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t55_rewrite1,d6_rewrite1,t75_abcmiz_0]),
    [file(abcmiz_0,t76_abcmiz_0),interesting(0.68)]).

fof(t58_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r5_abcmiz_0(A,B,C)
               => r3_abcmiz_0(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d28_abcmiz_0,d21_abcmiz_0,d27_abcmiz_0]),
    [file(abcmiz_0,t58_abcmiz_0),interesting(0.67)]).

fof(t55_abcmiz_0,theorem,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                 => ( ( r2_abcmiz_0(A,B,C)
                      & r1_tarski(D,C) )
                   => r2_abcmiz_0(A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_abcmiz_0,d16_abcmiz_0,t1_xboole_1]),
    [file(abcmiz_0,t55_abcmiz_0),interesting(0.67)]).

fof(t67_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => r1_tarski(k11_abcmiz_0(A),u1_orders_2(A)) ) ),
    inference(mizar_proof,[status(thm)],[d1_lattice8,d31_abcmiz_0,d27_abcmiz_0,t21_abcmiz_0,d9_orders_2]),
    [file(abcmiz_0,t67_abcmiz_0),interesting(0.66)]).

fof(t40_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
              <=> r3_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_abcmiz_0,t55_finseq_1,t4_finseq_1,d1_tarski,d19_abcmiz_0,t57_finseq_1,d21_abcmiz_0,t57_finseq_1,d19_abcmiz_0,t57_finseq_1,t27_finseq_3]),
    [file(abcmiz_0,t40_abcmiz_0),interesting(0.66)]).

fof(s1_abcmiz_0,theorem,
    ( ? [A] : 
        ( v1_finset_1(A)
        & p1_s1_abcmiz_0(A) )
   => ? [A] : 
        ( v1_finset_1(A)
        & p1_s1_abcmiz_0(A)
        & ! [B] : 
            ( ( r1_tarski(B,A)
              & p1_s1_abcmiz_0(B) )
           => B = A ) ) ),
    inference(mizar_proof,[status(thm)],[s1_xboole_0,t24_finset_1,d3_tarski,t13_finset_1,d10_xboole_0,t1_xboole_1,s3_funct_1,d3_tarski,t13_finset_1,t78_card_1,d3_tarski,t13_finset_1,d3_tarski,t13_finset_1,d3_tarski,t56_xboole_1,t27_card_1,t56_card_1,t3_triang_1,d5_real_1,s7_nat_1,d8_xboole_0,t59_card_2,s2_orders_1,t13_finset_1,t1_xboole_1]),
    [file(abcmiz_0,s1_abcmiz_0),interesting(0.65)]).

fof(t66_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ~ ( r6_abcmiz_0(A,B,C)
                  & ! [D] : 
                      ( ( v2_funct_1(D)
                        & m2_finseq_1(D,u1_abcmiz_0(A)) )
                     => ~ ( k2_relat_1(D) = C
                          & r5_abcmiz_0(A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d29_abcmiz_0,s5_nat_1,d8_funct_1,d5_real_1,t27_finseq_3,t28_nat_1,t23_finseq_1,d1_trees_1,t8_trees_1,t50_finseq_1,t23_finseq_1,t27_finseq_3,t38_nat_1,t2_xreal_1,t21_finseq_1,t35_finseq_1,t8_xreal_1,t21_finseq_1,t57_finseq_1,t56_finseq_1,d4_finseq_1,t37_zfmisc_1,d1_trees_1,t8_trees_1,t50_finseq_1,t27_finseq_3,t58_finseq_1,d7_finseq_1,t27_finseq_3,t38_nat_1,t61_abcmiz_0,t27_finseq_3,t58_abcmiz_0,d7_finseq_1,t45_abcmiz_0,t12_funct_1,t25_abcmiz_0,t32_abcmiz_0,t61_abcmiz_0,t61_abcmiz_0,t62_abcmiz_0,t37_zfmisc_1,t12_xboole_1,t44_finseq_1,t4_xboole_1,t35_finseq_1,t8_xreal_1,t8_xreal_1]),
    [file(abcmiz_0,t66_abcmiz_0),interesting(0.65)]).

fof(t28_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k6_abcmiz_0(A,B,k1_subset_1(u1_abcmiz_0(A))) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t16_abcmiz_0,t28_xboole_1,t34_waybel_0]),
    [file(abcmiz_0,t28_abcmiz_0),interesting(0.65)]).

fof(t77_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ~ ( r1_rewrite1(k11_abcmiz_0(A),B,C)
                  & ! [D] : 
                      ( ( v1_finset_1(D)
                        & m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A))) )
                     => ~ ( r6_abcmiz_0(A,C,D)
                          & B = k6_abcmiz_0(A,C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,d2_rewrite1,t38_nat_1,t28_nat_1,t3_finseq_1,t8_xreal_1,t38_nat_1,t27_finseq_3,d2_rewrite1,t106_zfmisc_1,d31_abcmiz_0,s1_wellord2,d2_finseq_1,d4_finseq_1,d19_abcmiz_0,d3_finseq_1,d3_finseq_5,t27_finseq_3,d3_finseq_5,d19_abcmiz_0,t8_xreal_1,t28_nat_1,t29_nat_1,t29_nat_1,t8_xreal_1,t29_nat_1,t27_finseq_3,t29_nat_1,t38_nat_1,t27_finseq_3,d3_finseq_5,d3_finseq_5,d19_abcmiz_0,t38_nat_1,s1_nat_1,t28_nat_1,t18_finseq_1,t29_finseq_6,d28_abcmiz_0,t27_finseq_3,t60_finseq_5,t28_nat_1,d3_finseq_5,t27_finseq_3,t8_xreal_1,t29_nat_1,t8_xreal_1,t29_nat_1,t27_finseq_3,d3_finseq_5,d3_finseq_5,t60_finseq_5,d29_abcmiz_0,t60_finseq_5,t58_abcmiz_0,t57_abcmiz_0,t65_finseq_5]),
    [file(abcmiz_0,t77_abcmiz_0),interesting(0.64)]).

fof(t13_abcmiz_0,theorem,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r2_hidden(C,k2_abcmiz_0(A,B))
              <=> r2_hidden(B,k3_abcmiz_0(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_abcmiz_0,d12_abcmiz_0]),
    [file(abcmiz_0,t13_abcmiz_0),interesting(0.62)]).

fof(t15_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k2_abcmiz_0(A,B) = a_2_1_abcmiz_0(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,t13_abcmiz_0,d10_xboole_0,d3_tarski,t13_abcmiz_0]),
    [file(abcmiz_0,t15_abcmiz_0),interesting(0.62)]).

fof(t18_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v8_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => r1_xboole_0(k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B))) ) ) ),
    inference(mizar_proof,[status(thm)],[t3_xboole_0,d12_abcmiz_0,d12_abcmiz_0,d9_abcmiz_0]),
    [file(abcmiz_0,t18_abcmiz_0),interesting(0.62)]).

fof(t21_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
               => r3_orders_2(A,k5_abcmiz_0(A,B,C),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_abcmiz_0,t1_abcmiz_0,d3_xboole_0,t17_waybel_0]),
    [file(abcmiz_0,t21_abcmiz_0),interesting(0.61)]).

fof(t2_abcmiz_0,theorem,(
    ! [A] : 
      ( l1_abcmiz_0(A)
     => ! [B] : 
          ( l1_abcmiz_0(B)
         => ( ( u1_abcmiz_0(A) = u1_abcmiz_0(B)
              & v4_abcmiz_0(A) )
           => v4_abcmiz_0(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_abcmiz_0,d4_abcmiz_0]),
    [file(abcmiz_0,t2_abcmiz_0),interesting(0.61)]).

fof(t14_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r1_tarski(C,k2_abcmiz_0(A,B))
              <=> r2_hidden(B,k4_abcmiz_0(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_abcmiz_0,d13_abcmiz_0,d3_tarski,d13_abcmiz_0,t13_abcmiz_0]),
    [file(abcmiz_0,t14_abcmiz_0),interesting(0.61)]).

fof(t32_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => k8_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) = k5_abcmiz_0(A,B,C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_abcmiz_0,t57_finseq_1,t61_finseq_1]),
    [file(abcmiz_0,t32_abcmiz_0),interesting(0.61)]).

fof(t57_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                   => ( D = k2_relat_1(C)
                     => k8_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,t31_abcmiz_0,t28_abcmiz_0,t22_finseq_2,d4_finseq_1,t57_finseq_1,t35_finseq_1,t41_abcmiz_0,t40_abcmiz_0,t44_finseq_1,t55_finseq_1,t46_abcmiz_0,t38_abcmiz_0,t32_abcmiz_0,t56_abcmiz_0,s1_nat_1]),
    [file(abcmiz_0,t57_abcmiz_0),interesting(0.61)]).

fof(t12_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => k3_abcmiz_0(A,B) = a_2_0_abcmiz_0(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d12_abcmiz_0]),
    [file(abcmiz_0,t12_abcmiz_0),interesting(0.60)]).

fof(t10_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l2_abcmiz_0(A) )
     => ( v9_abcmiz_0(A)
       => ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ( r3_orders_2(A,B,C)
                 => r1_tarski(k2_abcmiz_0(A,C),k2_abcmiz_0(A,B)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_abcmiz_0,t24_yellow_0,t17_xboole_1]),
    [file(abcmiz_0,t10_abcmiz_0),interesting(0.59)]).

fof(t84_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & v14_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r4_abcmiz_0(A,B,C)
               => k12_abcmiz_0(A,k5_abcmiz_0(A,B,C)) = k12_abcmiz_0(A,B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t70_abcmiz_0,t78_abcmiz_0,d31_abcmiz_0,t25_abcmiz_0,t13_rewrite1,t16_rewrite1,t26_rewrite1,t56_rewrite1]),
    [file(abcmiz_0,t84_abcmiz_0),interesting(0.58)]).

fof(t31_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k8_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) = B ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,d19_abcmiz_0]),
    [file(abcmiz_0,t31_abcmiz_0),interesting(0.56)]).

fof(t46_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                   => ( D = k2_relat_1(C)
                     => r2_abcmiz_0(A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t44_abcmiz_0,t45_abcmiz_0,d16_abcmiz_0]),
    [file(abcmiz_0,t46_abcmiz_0),interesting(0.56)]).

fof(t45_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => r1_tarski(k2_relat_1(C),k2_abcmiz_0(A,k8_abcmiz_0(A,B,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_tarski,d5_funct_1,d4_finseq_1,t27_finseq_3,d19_abcmiz_0,t8_xreal_1,t38_nat_1,t27_finseq_3,d4_finseq_1,t12_funct_1,d21_abcmiz_0,t22_abcmiz_0,d19_abcmiz_0,t43_abcmiz_0,t10_abcmiz_0]),
    [file(abcmiz_0,t45_abcmiz_0),interesting(0.55)]).

fof(t5_abcmiz_0,theorem,(
    ! [A] : 
      ( l1_abcmiz_0(A)
     => ! [B] : 
          ( l1_abcmiz_0(B)
         => ( ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
              & v5_abcmiz_0(A) )
           => v5_abcmiz_0(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_abcmiz_0,d6_abcmiz_0]),
    [file(abcmiz_0,t5_abcmiz_0),interesting(0.53)]).

fof(t6_abcmiz_0,theorem,(
    ! [A] : 
      ( l1_abcmiz_0(A)
     => ! [B] : 
          ( l1_abcmiz_0(B)
         => ( ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
              & v6_abcmiz_0(A) )
           => v6_abcmiz_0(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_abcmiz_0,d7_abcmiz_0]),
    [file(abcmiz_0,t6_abcmiz_0),interesting(0.53)]).

fof(t64_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r6_abcmiz_0(A,B,k1_subset_1(u1_abcmiz_0(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[d29_abcmiz_0,d28_abcmiz_0]),
    [file(abcmiz_0,t64_abcmiz_0),interesting(0.52)]).

fof(t60_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r4_abcmiz_0(A,B,C)
              <=> r5_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d28_abcmiz_0,t55_finseq_1,t4_finseq_1,d1_tarski,d19_abcmiz_0,t57_finseq_1,d28_abcmiz_0,t57_finseq_1,d19_abcmiz_0,t57_finseq_1,t27_finseq_3]),
    [file(abcmiz_0,t60_abcmiz_0),interesting(0.50)]).

fof(t39_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r3_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_abcmiz_0]),
    [file(abcmiz_0,t39_abcmiz_0),interesting(0.49)]).

fof(t59_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => r5_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) ) ) ),
    inference(mizar_proof,[status(thm)],[d28_abcmiz_0]),
    [file(abcmiz_0,t59_abcmiz_0),interesting(0.49)]).

fof(t4_abcmiz_0,theorem,(
    ! [A,B] : 
      ( A != B
     => ! [C] : 
          ( l1_abcmiz_0(C)
         => ( ( u1_abcmiz_0(C) = k2_tarski(A,B)
              & k1_funct_1(u2_abcmiz_0(C),A) = B
              & k1_funct_1(u2_abcmiz_0(C),B) = A )
           => ( ~ v4_abcmiz_0(C)
              & v5_abcmiz_0(C)
              & v6_abcmiz_0(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_abcmiz_0,d2_tarski,d6_abcmiz_0,d7_abcmiz_0,d2_tarski]),
    [file(abcmiz_0,t4_abcmiz_0),interesting(0.46)]).

fof(t54_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r1_tarski(C,k2_abcmiz_0(A,B))
               => ( r2_abcmiz_0(A,B,C)
                  & k6_abcmiz_0(A,B,C) = B ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t53_abcmiz_0,t50_abcmiz_0,t53_abcmiz_0,d3_yellow_0]),
    [file(abcmiz_0,t54_abcmiz_0),interesting(0.45)]).

fof(t29_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => k7_abcmiz_0(A,B,k6_finseq_1(u1_abcmiz_0(A))) = k12_finseq_1(u1_struct_0(A),B) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,d19_abcmiz_0,t57_finseq_1]),
    [file(abcmiz_0,t29_abcmiz_0),interesting(0.44)]).

fof(t56_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                 => ! [E] : 
                      ( m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A)))
                     => ( ( E = k2_xboole_0(D,k1_tarski(C))
                          & r2_abcmiz_0(A,B,E) )
                       => k5_abcmiz_0(A,k6_abcmiz_0(A,B,D),C) = k6_abcmiz_0(A,B,E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t7_xboole_1,t55_abcmiz_0,d3_tarski,d3_xboole_0,t50_abcmiz_0,t51_abcmiz_0,t17_waybel_0,d2_yellow_0,t17_waybel_0,t10_abcmiz_0,t13_abcmiz_0,t1_xboole_1,t37_zfmisc_1,t8_xboole_1,t14_abcmiz_0,d3_xboole_0,d10_xboole_0,d3_tarski,d3_xboole_0,t14_abcmiz_0,t17_waybel_0,t37_zfmisc_1,t1_xboole_1,t53_abcmiz_0,t13_abcmiz_0,t17_waybel_0,d3_xboole_0]),
    [file(abcmiz_0,t56_abcmiz_0),interesting(0.44)]).

fof(t63_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r6_abcmiz_0(A,B,C)
               => v1_finset_1(C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d29_abcmiz_0]),
    [file(abcmiz_0,t63_abcmiz_0),interesting(0.43)]).

fof(t43_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,k2_relat_1(k7_abcmiz_0(A,B,C)))
                     => ( r3_orders_2(A,k8_abcmiz_0(A,B,C),D)
                        & r3_orders_2(A,D,B) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1,t27_finseq_3,d19_abcmiz_0,t42_abcmiz_0]),
    [file(abcmiz_0,t43_abcmiz_0),interesting(0.40)]).

fof(t72_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
             => ( ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                   => ( ( r1_tarski(D,C)
                        & r6_abcmiz_0(A,B,D)
                        & k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) )
                     => D = C ) )
               => ! [D] : 
                    ( ( v2_funct_1(D)
                      & m2_finseq_1(D,u1_abcmiz_0(A)) )
                   => ( ( k2_relat_1(D) = C
                        & r5_abcmiz_0(A,B,D) )
                     => m1_rewrite1(k4_finseq_5(u1_struct_0(A),k7_abcmiz_0(A,B,D)),k11_abcmiz_0(A)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_abcmiz_0,t60_finseq_5,d3_finseq_5,d2_rewrite1,t27_finseq_3,d3_finseq_5,t28_nat_1,t8_xreal_1,t29_nat_1,t71_abcmiz_0]),
    [file(abcmiz_0,t72_abcmiz_0),interesting(0.30)]).

fof(t47_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( ( r3_abcmiz_0(A,B,C)
                      & r1_tarski(k2_relat_1(D),k2_relat_1(C)) )
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => ( r2_hidden(E,k2_relat_1(k7_abcmiz_0(A,B,D)))
                         => r3_orders_2(A,k8_abcmiz_0(A,B,C),E) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_funct_1,d3_finseq_1,t5_binarith,t27_finseq_3,d19_abcmiz_0,t44_abcmiz_0,d19_abcmiz_0,t38_nat_1,t8_xreal_1,t27_finseq_3,d4_finseq_1,t12_funct_1,t38_nat_1,t27_finseq_3,d4_finseq_1,t12_funct_1,d19_abcmiz_0,t45_abcmiz_0,t38_nat_1,t24_abcmiz_0,s1_binarith]),
    [file(abcmiz_0,t47_abcmiz_0),interesting(0.26)]).

fof(t42_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => ! [D] : 
                    ( v4_ordinal2(D)
                   => ! [E] : 
                        ( v4_ordinal2(E)
                       => ( ( r1_xreal_0(1,D)
                            & r1_xreal_0(D,E)
                            & r1_xreal_0(E,k1_nat_1(k3_finseq_1(C),1)) )
                         => ! [F] : 
                              ( m1_subset_1(F,u1_struct_0(A))
                             => ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( F = k1_funct_1(k7_abcmiz_0(A,B,C),D)
                                      & G = k1_funct_1(k7_abcmiz_0(A,B,C),E) )
                                   => r3_orders_2(A,G,F) ) ) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_abcmiz_0,t28_nat_1,d19_abcmiz_0,t29_nat_1,t2_xreal_1,d21_ordinal2,t8_xreal_1,t27_finseq_3,d4_finseq_1,t12_funct_1,t38_nat_1,t27_finseq_3,d4_finseq_1,t12_funct_1,d19_abcmiz_0,t21_abcmiz_0,t38_nat_1,d2_yellow_0,s1_nat_1]),
    [file(abcmiz_0,t42_abcmiz_0),interesting(0.23)]).

fof(t20_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_abcmiz_0(A,C,B)
               => ( ~ v1_xboole_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)))
                  & v1_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
                  & v12_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
                  & m1_subset_1(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k6_waybel_0(A,C)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_abcmiz_0,t17_waybel_0,t27_waybel_0,t44_waybel_0,d3_xboole_0]),
    [file(abcmiz_0,t20_abcmiz_0),interesting(0.12)]).

fof(t27_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r2_abcmiz_0(A,C,B)
               => ( ~ v1_xboole_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)))
                  & v1_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
                  & v12_waybel_0(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),A)
                  & m1_subset_1(k3_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k4_abcmiz_0(A,B),k6_waybel_0(A,C)),k1_zfmisc_1(u1_struct_0(A))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_abcmiz_0,t14_abcmiz_0,t17_waybel_0,t27_waybel_0,t44_waybel_0,d3_xboole_0]),
    [file(abcmiz_0,t27_abcmiz_0),interesting(0.08)]).

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(d12_abcmiz_0,definition,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_abcmiz_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = k3_abcmiz_0(A,B)
              <=> ! [D] : 
                    ( r2_hidden(D,C)
                  <=> ? [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                        & D = E
                        & r2_hidden(B,k2_abcmiz_0(A,E)) ) ) ) ) ) ) ),
    file(abcmiz_0,d12_abcmiz_0),
    [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(d14_abcmiz_0,definition,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ( v10_abcmiz_0(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_abcmiz_0(A))
           => ~ v1_xboole_0(k1_finsub_1(k1_zfmisc_1(u1_struct_0(A)),k3_abcmiz_0(A,B),k3_abcmiz_0(A,k1_abcmiz_0(A,B)))) ) ) ) ),
    file(abcmiz_0,d14_abcmiz_0),
    [interesting(0.00)]).

fof(t11_abcmiz_0,theorem,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( l2_abcmiz_0(B)
         => ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
           => ! [C] : 
                ( m1_subset_1(C,u1_abcmiz_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_abcmiz_0(B))
                   => ( C = D
                     => k3_abcmiz_0(A,C) = k3_abcmiz_0(B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_abcmiz_0,d12_abcmiz_0,d12_abcmiz_0]),
    [file(abcmiz_0,t11_abcmiz_0),interesting(0.00)]).

fof(t17_abcmiz_0,theorem,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( l2_abcmiz_0(B)
         => ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
              & v10_abcmiz_0(A) )
           => v10_abcmiz_0(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_abcmiz_0,d14_abcmiz_0,t11_abcmiz_0]),
    [file(abcmiz_0,t17_abcmiz_0),interesting(0.00)]).

fof(t3_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ ( r2_hidden(C,A)
              & r2_hidden(C,B) ) )
      & ~ ( ? [C] : 
              ( r2_hidden(C,A)
              & r2_hidden(C,B) )
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t3_xboole_0),
    [interesting(0.00)]).

fof(d9_abcmiz_0,definition,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ( v8_abcmiz_0(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_abcmiz_0(A))
               => ~ ( r2_hidden(C,k2_abcmiz_0(A,B))
                    & r2_hidden(k1_abcmiz_0(A,C),k2_abcmiz_0(A,B)) ) ) ) ) ) ),
    file(abcmiz_0,d9_abcmiz_0),
    [interesting(0.00)]).

fof(t19_abcmiz_0,theorem,(
    $true ),
    file(abcmiz_0,t19_abcmiz_0),
    [interesting(0.00)]).

fof(d15_abcmiz_0,definition,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
              <=> ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r2_hidden(D,k3_abcmiz_0(A,C))
                    & r1_orders_2(A,D,B) ) ) ) ) ) ),
    file(abcmiz_0,d15_abcmiz_0),
    [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(t27_waybel_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( ( v12_waybel_0(B,A)
                  & v12_waybel_0(C,A) )
               => ( v12_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A)
                  & v12_waybel_0(k4_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ),
    file(waybel_0,t27_waybel_0),
    [interesting(0.00)]).

fof(t44_waybel_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v4_orders_2(A)
        & l1_orders_2(A) )
     => ( ( v1_lattice3(A)
          | v2_lattice3(A) )
       => ! [B] : 
            ( m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A)))
           => ! [C] : 
                ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
               => ( ( v12_waybel_0(B,A)
                    & v1_waybel_0(B,A)
                    & v12_waybel_0(C,A)
                    & v1_waybel_0(C,A) )
                 => v1_waybel_0(k5_subset_1(u1_struct_0(A),B,C),A) ) ) ) ) ) ),
    file(waybel_0,t44_waybel_0),
    [interesting(0.00)]).

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

fof(d2_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ( v1_abcmiz_0(A)
      <=> ! [B] : 
            ( ( ~ v1_xboole_0(B)
              & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
           => ? [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
                & r2_hidden(C,B)
                & ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ~ ( r2_hidden(D,B)
                        & r2_orders_2(A,C,D) ) ) ) ) ) ) ),
    file(abcmiz_0,d2_abcmiz_0),
    [interesting(0.00)]).

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

fof(t40_waybel_0,theorem,(
    ! [A] : 
      ( ( v4_orders_2(A)
        & v1_lattice3(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( v12_waybel_0(B,A)
            & m1_subset_1(B,k1_zfmisc_1(u1_struct_0(A))) )
         => ( v1_waybel_0(B,A)
          <=> ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( ( r2_hidden(C,B)
                        & r2_hidden(D,B) )
                     => r2_hidden(k13_lattice3(A,C,D),B) ) ) ) ) ) ) ),
    file(waybel_0,t40_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(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(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(t1_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_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))) )
         => ( r1_yellow_0(A,B)
            & r2_hidden(k1_yellow_0(A,B),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_abcmiz_0,d9_lattice3,t40_waybel_0,t22_yellow_0,d10_orders_2,t22_yellow_0,d9_lattice3,t30_yellow_0]),
    [file(abcmiz_0,t1_abcmiz_0),interesting(0.00)]).

fof(t23_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
               => r2_hidden(k5_abcmiz_0(A,B,C),k3_abcmiz_0(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_abcmiz_0,t1_abcmiz_0,d3_xboole_0]),
    [file(abcmiz_0,t23_abcmiz_0),interesting(0.00)]).

fof(d2_yellow_0,definition,(
    ! [A] : 
      ( l1_orders_2(A)
     => ( v3_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(yellow_0,d2_yellow_0),
    [interesting(0.00)]).

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

fof(t24_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_orders_2(A,D,B)
                      & r2_hidden(C,k2_abcmiz_0(A,D)) )
                   => ( r1_abcmiz_0(A,B,C)
                      & r3_orders_2(A,D,k5_abcmiz_0(A,B,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t13_abcmiz_0,t17_waybel_0,d15_abcmiz_0,t13_abcmiz_0,t20_abcmiz_0,t1_abcmiz_0,d3_xboole_0,t30_yellow_0,d9_lattice3]),
    [file(abcmiz_0,t24_abcmiz_0),interesting(0.00)]).

fof(t22_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r1_abcmiz_0(A,B,C)
               => r2_hidden(C,k2_abcmiz_0(A,k5_abcmiz_0(A,B,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t20_abcmiz_0,t1_abcmiz_0,d3_xboole_0,t13_abcmiz_0]),
    [file(abcmiz_0,t22_abcmiz_0),interesting(0.00)]).

fof(t26_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_abcmiz_0(A))
                 => ( ( r1_abcmiz_0(A,B,C)
                      & r1_abcmiz_0(A,k5_abcmiz_0(A,B,C),D) )
                   => ( r1_abcmiz_0(A,B,D)
                      & r1_abcmiz_0(A,k5_abcmiz_0(A,B,D),C)
                      & k5_abcmiz_0(A,k5_abcmiz_0(A,B,D),C) = k5_abcmiz_0(A,k5_abcmiz_0(A,B,C),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t21_abcmiz_0,t23_abcmiz_0,d15_abcmiz_0,t13_abcmiz_0,d2_yellow_0,d15_abcmiz_0,d2_yellow_0,t21_abcmiz_0,t23_abcmiz_0,d15_abcmiz_0,t23_abcmiz_0,d19_waybel_0,t24_abcmiz_0,d9_lattice3,d3_xboole_0,t13_abcmiz_0,t17_waybel_0,d19_waybel_0,d2_yellow_0,t13_abcmiz_0,t24_abcmiz_0,t24_abcmiz_0,t21_abcmiz_0,t22_abcmiz_0,d2_yellow_0,t21_abcmiz_0,t24_abcmiz_0,t17_waybel_0,d19_waybel_0,d3_xboole_0,d9_lattice3,t30_yellow_0]),
    [file(abcmiz_0,t26_abcmiz_0),interesting(0.00)]).

fof(t25_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k3_finseq_1(A) = 0
      <=> A = k1_xboole_0 ) ) ),
    file(finseq_1,t25_finseq_1),
    [interesting(0.00)]).

fof(d19_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_struct_0(A))
                 => ( D = k7_abcmiz_0(A,B,C)
                  <=> ( k3_finseq_1(D) = k1_nat_1(k3_finseq_1(C),1)
                      & k1_funct_1(D,1) = B
                      & ! [E] : 
                          ( m2_subset_1(E,k1_numbers,k5_numbers)
                         => ! [F] : 
                              ( m1_subset_1(F,u1_abcmiz_0(A))
                             => ! [G] : 
                                  ( m1_subset_1(G,u1_struct_0(A))
                                 => ( ( r2_hidden(E,k4_finseq_1(C))
                                      & F = k1_funct_1(C,E)
                                      & G = k1_funct_1(D,E) )
                                   => k1_funct_1(D,k1_nat_1(E,1)) = k5_abcmiz_0(A,G,F) ) ) ) ) ) ) ) ) ) ) ),
    file(abcmiz_0,d19_abcmiz_0),
    [interesting(0.00)]).

fof(t57_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k1_funct_1(B,1) = A ) ) ) ),
    file(finseq_1,t57_finseq_1),
    [interesting(0.00)]).

fof(d4_abcmiz_0,definition,(
    ! [A] : 
      ( l1_abcmiz_0(A)
     => ( v4_abcmiz_0(A)
      <=> v1_xboole_0(u1_abcmiz_0(A)) ) ) ),
    file(abcmiz_0,d4_abcmiz_0),
    [interesting(0.00)]).

fof(t1_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k1_rewrite1(k1_xboole_0,A) = A
        & k1_rewrite1(A,k1_xboole_0) = A ) ) ),
    file(rewrite1,t1_rewrite1),
    [interesting(0.00)]).

fof(d1_rewrite1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( ( A = k1_xboole_0
                    | B = k1_xboole_0 )
                 => ( C = k1_rewrite1(A,B)
                  <=> C = k7_finseq_1(A,B) ) )
                & ~ ( A != k1_xboole_0
                    & B != k1_xboole_0
                    & ~ ( C = k1_rewrite1(A,B)
                      <=> ? [D] : 
                            ( m2_subset_1(D,k1_numbers,k5_numbers)
                            & ? [E] : 
                                ( v1_relat_1(E)
                                & v1_funct_1(E)
                                & v1_finseq_1(E)
                                & k3_finseq_1(A) = k1_nat_1(D,1)
                                & E = k7_relat_1(A,k2_finseq_1(D))
                                & C = k7_finseq_1(E,B) ) ) ) ) ) ) ) ) ),
    file(rewrite1,d1_rewrite1),
    [interesting(0.00)]).

fof(t38_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(k2_xcmplx_0(B,1),A)
          <=> r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,t38_nat_1),
    [interesting(0.00)]).

fof(t21_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( ( r1_xreal_0(A,k3_finseq_1(B))
                  & C = k7_relat_1(B,k2_finseq_1(A)) )
               => ( k3_finseq_1(C) = A
                  & k4_finseq_1(C) = k2_finseq_1(A) ) ) ) ) ) ),
    file(finseq_1,t21_finseq_1),
    [interesting(0.00)]).

fof(d21_ordinal2,definition,(
    ! [A] : 
      ( v4_ordinal2(A)
    <=> r2_hidden(A,k5_ordinal2) ) ),
    file(ordinal2,d21_ordinal2),
    [interesting(0.00)]).

fof(t27_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(B,k4_finseq_1(A))
          <=> ( r1_xreal_0(1,B)
              & r1_xreal_0(B,k3_finseq_1(A)) ) ) ) ) ),
    file(finseq_3,t27_finseq_3),
    [interesting(0.00)]).

fof(d7_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( C = k7_finseq_1(A,B)
              <=> ( k4_finseq_1(C) = k2_finseq_1(k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)))
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(A))
                       => k1_funct_1(C,D) = k1_funct_1(A,D) ) )
                  & ! [D] : 
                      ( m2_subset_1(D,k1_numbers,k5_numbers)
                     => ( r2_hidden(D,k4_finseq_1(B))
                       => k1_funct_1(C,k1_nat_1(k3_finseq_1(A),D)) = k1_funct_1(B,D) ) ) ) ) ) ) ) ),
    file(finseq_1,d7_finseq_1),
    [interesting(0.00)]).

fof(t61_finseq_3,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( ( k3_finseq_1(A) = k2_xcmplx_0(C,1)
                  & B = k7_relat_1(A,k2_finseq_1(C)) )
               => A = k7_finseq_1(B,k9_finseq_1(k1_funct_1(A,k2_xcmplx_0(C,1)))) ) ) ) ) ),
    file(finseq_3,t61_finseq_3),
    [interesting(0.00)]).

fof(t33_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( r1_xreal_0(1,C)
               => ( r1_xreal_0(k3_finseq_1(A),C)
                  | k1_funct_1(k1_rewrite1(A,B),C) = k1_funct_1(A,C) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,t1_rewrite1,d1_rewrite1,t38_nat_1,t21_finseq_1,t38_nat_1,d21_ordinal2,t27_finseq_3,d7_finseq_1,t61_finseq_3,d7_finseq_1]),
    [file(abcmiz_0,t33_abcmiz_0),interesting(0.00)]).

fof(d21_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
              <=> ! [D] : 
                    ( v4_ordinal2(D)
                   => ! [E] : 
                        ( m1_subset_1(E,u1_abcmiz_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r2_hidden(D,k4_finseq_1(C))
                                & E = k1_funct_1(C,D)
                                & F = k1_funct_1(k7_abcmiz_0(A,B,C),D) )
                             => r1_abcmiz_0(A,F,E) ) ) ) ) ) ) ) ) ),
    file(abcmiz_0,d21_abcmiz_0),
    [interesting(0.00)]).

fof(t3_abcmiz_0,theorem,(
    ! [A] : 
      ( l1_abcmiz_0(A)
     => ! [B] : 
          ( l1_abcmiz_0(B)
         => ( g1_abcmiz_0(u1_abcmiz_0(A),u2_abcmiz_0(A)) = g1_abcmiz_0(u1_abcmiz_0(B),u2_abcmiz_0(B))
           => ! [C] : 
                ( m1_subset_1(C,u1_abcmiz_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_abcmiz_0(B))
                   => ( C = D
                     => k1_abcmiz_0(A,C) = k1_abcmiz_0(B,D) ) ) ) ) ) ) ),
    file(abcmiz_0,t3_abcmiz_0),
    [interesting(0.00)]).

fof(t44_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k2_relat_1(k7_finseq_1(A,B)) = k2_xboole_0(k2_relat_1(A),k2_relat_1(B)) ) ) ),
    file(finseq_1,t44_finseq_1),
    [interesting(0.00)]).

fof(t12_funct_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ( r2_hidden(A,k1_relat_1(B))
       => r2_hidden(k1_funct_1(B,A),k2_relat_1(B)) ) ) ),
    file(funct_1,t12_funct_1),
    [interesting(0.00)]).

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

fof(d3_finseq_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( B = k3_finseq_1(A)
          <=> k2_finseq_1(B) = k1_relat_1(A) ) ) ) ),
    file(finseq_1,d3_finseq_1),
    [interesting(0.00)]).

fof(t5_binarith,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ~ ( r2_hidden(A,k2_finseq_1(B))
              & v1_xboole_0(A) ) ) ) ),
    file(binarith,t5_binarith),
    [interesting(0.00)]).

fof(t29_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => r1_xreal_0(A,k2_xcmplx_0(A,B)) ) ) ),
    file(nat_1,t29_nat_1),
    [interesting(0.00)]).

fof(t28_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ~ ( r1_xreal_0(A,B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => B != k2_xcmplx_0(A,C) ) ) ) ) ),
    file(nat_1,t28_nat_1),
    [interesting(0.00)]).

fof(t2_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( ( r1_xreal_0(A,B)
                  & r1_xreal_0(B,C) )
               => r1_xreal_0(A,C) ) ) ) ) ),
    file(xreal_1,t2_xreal_1),
    [interesting(0.00)]).

fof(t8_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ( r1_xreal_0(A,B)
              <=> r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,C)) ) ) ) ) ),
    file(xreal_1,t8_xreal_1),
    [interesting(0.00)]).

fof(d4_finseq_1,definition,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( m1_finseq_1(B,A)
      <=> r1_tarski(k2_relat_1(B),A) ) ) ),
    file(finseq_1,d4_finseq_1),
    [interesting(0.00)]).

fof(s1_nat_1,theorem,
    ( ( p1_s1_nat_1(0)
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ( p1_s1_nat_1(A)
           => p1_s1_nat_1(k1_nat_1(A,1)) ) ) )
   => ! [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
       => p1_s1_nat_1(A) ) ),
    file(nat_1,s1_nat_1),
    [interesting(0.00)]).

fof(t44_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r3_abcmiz_0(A,B,C)
               => r3_orders_2(A,k8_abcmiz_0(A,B,C),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_abcmiz_0,t29_nat_1,t27_finseq_3,t12_funct_1,t43_abcmiz_0]),
    [file(abcmiz_0,t44_abcmiz_0),interesting(0.00)]).

fof(d11_abcmiz_0,definition,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & l2_abcmiz_0(A) )
     => ( v9_abcmiz_0(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_struct_0(A))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => k2_abcmiz_0(A,k13_lattice3(A,B,C)) = k3_finsub_1(k1_zfmisc_1(u1_abcmiz_0(A)),k2_abcmiz_0(A,B),k2_abcmiz_0(A,C)) ) ) ) ) ),
    file(abcmiz_0,d11_abcmiz_0),
    [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(t17_xboole_1,theorem,(
    ! [A,B] : r1_tarski(k3_xboole_0(A,B),A) ),
    file(xboole_1,t17_xboole_1),
    [interesting(0.00)]).

fof(s1_binarith,theorem,
    ( ( p1_s1_binarith(1)
      & ! [A] : 
          ( ( ~ v1_xboole_0(A)
            & m2_subset_1(A,k1_numbers,k5_numbers) )
         => ( p1_s1_binarith(A)
           => p1_s1_binarith(k23_binop_2(A,1)) ) ) )
   => ! [A] : 
        ( ( ~ v1_xboole_0(A)
          & m2_subset_1(A,k1_numbers,k5_numbers) )
       => p1_s1_binarith(A) ) ),
    file(binarith,s1_binarith),
    [interesting(0.00)]).

fof(t48_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
                   => r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),D,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_abcmiz_0,t27_finseq_3,t44_finseq_1,d19_abcmiz_0,t38_nat_1,t27_finseq_3,t12_funct_1,t47_abcmiz_0,t45_abcmiz_0,t12_funct_1,t24_abcmiz_0]),
    [file(abcmiz_0,t48_abcmiz_0),interesting(0.00)]).

fof(t35_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => k3_finseq_1(k7_finseq_1(A,B)) = k1_nat_1(k3_finseq_1(A),k3_finseq_1(B)) ) ) ),
    file(finseq_1,t35_finseq_1),
    [interesting(0.00)]).

fof(d3_yellow_0,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))
               => ( ( r1_orders_2(A,B,C)
                    & r1_orders_2(A,C,B) )
                 => B = C ) ) ) ) ) ),
    file(yellow_0,d3_yellow_0),
    [interesting(0.00)]).

fof(t49_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
                   => k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) = k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),D,C)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t48_abcmiz_0,d19_abcmiz_0,t35_finseq_1,t44_finseq_1,t29_nat_1,t27_finseq_3,t12_funct_1,t47_abcmiz_0,d3_yellow_0]),
    [file(abcmiz_0,t49_abcmiz_0),interesting(0.00)]).

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

fof(d6_abcmiz_0,definition,(
    ! [A] : 
      ( l1_abcmiz_0(A)
     => ( v5_abcmiz_0(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_abcmiz_0(A))
           => k1_abcmiz_0(A,k1_abcmiz_0(A,B)) = B ) ) ) ),
    file(abcmiz_0,d6_abcmiz_0),
    [interesting(0.00)]).

fof(d7_abcmiz_0,definition,(
    ! [A] : 
      ( l1_abcmiz_0(A)
     => ( v6_abcmiz_0(A)
      <=> ! [B] : 
            ( m1_subset_1(B,u1_abcmiz_0(A))
           => k1_abcmiz_0(A,B) != B ) ) ) ),
    file(abcmiz_0,d7_abcmiz_0),
    [interesting(0.00)]).

fof(d16_abcmiz_0,definition,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r2_abcmiz_0(A,B,C)
              <=> ? [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                    & r1_tarski(C,k2_abcmiz_0(A,D))
                    & r1_orders_2(A,D,B) ) ) ) ) ) ),
    file(abcmiz_0,d16_abcmiz_0),
    [interesting(0.00)]).

fof(d13_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_abcmiz_0(A)))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_struct_0(A)))
             => ( C = k4_abcmiz_0(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ( r2_hidden(D,C)
                    <=> ! [E] : 
                          ( m1_subset_1(E,u1_abcmiz_0(A))
                         => ( r2_hidden(E,B)
                           => r2_hidden(D,k3_abcmiz_0(A,E)) ) ) ) ) ) ) ) ) ),
    file(abcmiz_0,d13_abcmiz_0),
    [interesting(0.00)]).

fof(t52_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r2_abcmiz_0(A,B,C)
               => r2_hidden(k6_abcmiz_0(A,B,C),k4_abcmiz_0(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_abcmiz_0,t1_abcmiz_0,d3_xboole_0]),
    [file(abcmiz_0,t52_abcmiz_0),interesting(0.00)]).

fof(t53_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ! [D] : 
                  ( m1_subset_1(D,u1_struct_0(A))
                 => ( ( r3_orders_2(A,D,B)
                      & r1_tarski(C,k2_abcmiz_0(A,D)) )
                   => ( r2_abcmiz_0(A,B,C)
                      & r3_orders_2(A,D,k6_abcmiz_0(A,B,C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t14_abcmiz_0,t17_waybel_0,d16_abcmiz_0,t27_abcmiz_0,t1_abcmiz_0,d3_xboole_0,t30_yellow_0,d9_lattice3]),
    [file(abcmiz_0,t53_abcmiz_0),interesting(0.00)]).

fof(t50_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r2_abcmiz_0(A,B,C)
               => r3_orders_2(A,k6_abcmiz_0(A,B,C),B) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_abcmiz_0,t1_abcmiz_0,d3_xboole_0,t17_waybel_0]),
    [file(abcmiz_0,t50_abcmiz_0),interesting(0.00)]).

fof(d28_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ( r5_abcmiz_0(A,B,C)
              <=> ! [D] : 
                    ( v4_ordinal2(D)
                   => ! [E] : 
                        ( m1_subset_1(E,u1_abcmiz_0(A))
                       => ! [F] : 
                            ( m1_subset_1(F,u1_struct_0(A))
                           => ( ( r2_hidden(D,k4_finseq_1(C))
                                & E = k1_funct_1(C,D)
                                & F = k1_funct_1(k7_abcmiz_0(A,B,C),D) )
                             => r4_abcmiz_0(A,F,E) ) ) ) ) ) ) ) ) ),
    file(abcmiz_0,d28_abcmiz_0),
    [interesting(0.00)]).

fof(t55_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k4_finseq_1(B) = k2_finseq_1(1)
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t55_finseq_1),
    [interesting(0.00)]).

fof(t4_finseq_1,theorem,
    ( k2_finseq_1(0) = k1_xboole_0
    & k2_finseq_1(1) = k1_tarski(1)
    & k2_finseq_1(2) = k2_tarski(1,2) ),
    file(finseq_1,t4_finseq_1),
    [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(d29_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r6_abcmiz_0(A,B,C)
              <=> ? [D] : 
                    ( m2_finseq_1(D,u1_abcmiz_0(A))
                    & k2_relat_1(D) = C
                    & r5_abcmiz_0(A,B,D) ) ) ) ) ) ),
    file(abcmiz_0,d29_abcmiz_0),
    [interesting(0.00)]).

fof(t55_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_rewrite1(A)
        & v4_rewrite1(A) )
     => ! [B] : r4_rewrite1(A,B,k2_rewrite1(A,B)) ) ),
    file(rewrite1,t55_rewrite1),
    [interesting(0.00)]).

fof(d6_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r4_rewrite1(A,B,C)
        <=> ( r3_rewrite1(A,C)
            & r1_rewrite1(A,B,C) ) ) ) ),
    file(rewrite1,d6_rewrite1),
    [interesting(0.00)]).

fof(d3_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
        <=> ? [D] : 
              ( m1_rewrite1(D,A)
              & k1_funct_1(D,1) = B
              & k1_funct_1(D,k3_finseq_1(D)) = C ) ) ) ),
    file(rewrite1,d3_rewrite1),
    [interesting(0.00)]).

fof(d2_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( m1_rewrite1(B,A)
          <=> ( ~ r1_xreal_0(k3_finseq_1(B),0)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r2_hidden(C,k4_finseq_1(B))
                      & r2_hidden(k1_nat_1(C,1),k4_finseq_1(B)) )
                   => r2_hidden(k4_tarski(k1_funct_1(B,C),k1_funct_1(B,k1_nat_1(C,1))),A) ) ) ) ) ) ) ),
    file(rewrite1,d2_rewrite1),
    [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(t1_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( ( r1_xreal_0(A,B)
              & r1_xreal_0(B,A) )
           => A = B ) ) ) ),
    file(xreal_1,t1_xreal_1),
    [interesting(0.00)]).

fof(t7_abcmiz_0,theorem,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( l2_abcmiz_0(B)
         => ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
           => ! [C] : 
                ( m1_subset_1(C,u1_struct_0(A))
               => ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(B))
                   => ( C = D
                     => k2_abcmiz_0(A,C) = k2_abcmiz_0(B,D) ) ) ) ) ) ) ),
    file(abcmiz_0,t7_abcmiz_0),
    [interesting(0.00)]).

fof(d1_lattice8,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_relset_1(B,A,A)
         => ! [C] : 
              ( m2_relset_1(C,A,A)
             => ( r1_lattice8(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ! [E] : 
                        ( m1_subset_1(E,A)
                       => ( r2_hidden(k1_domain_1(A,A,D,E),B)
                         => r2_hidden(k1_domain_1(A,A,D,E),C) ) ) ) ) ) ) ) ),
    file(lattice8,d1_lattice8),
    [interesting(0.00)]).

fof(d31_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m2_relset_1(B,u1_struct_0(A),u1_struct_0(A))
         => ( B = k11_abcmiz_0(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_abcmiz_0(A))
                          & ~ r2_hidden(E,k2_abcmiz_0(A,D))
                          & r4_abcmiz_0(A,D,E)
                          & k5_abcmiz_0(A,D,E) = C ) ) ) ) ) ) ) ),
    file(abcmiz_0,d31_abcmiz_0),
    [interesting(0.00)]).

fof(d27_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r4_abcmiz_0(A,B,C)
              <=> ( r1_orders_2(A,B,k10_abcmiz_0(A,C))
                  & r1_abcmiz_0(A,B,C) ) ) ) ) ) ),
    file(abcmiz_0,d27_abcmiz_0),
    [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(t31_relat_1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( v1_relat_1(B)
         => ( r1_tarski(A,B)
           => r1_tarski(k3_relat_1(A),k3_relat_1(B)) ) ) ) ),
    file(relat_1,t31_relat_1),
    [interesting(0.00)]).

fof(d16_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_rewrite1(A)
      <=> ! [B] : ~ ( r1_tarski(B,k3_relat_1(A))
            & B != k1_xboole_0
            & ! [C] : ~ ( r2_hidden(C,B)
                & ! [D] : ~ ( r2_hidden(D,B)
                    & C != D
                    & r2_hidden(k4_tarski(C,D),A) ) ) ) ) ) ),
    file(rewrite1,d16_rewrite1),
    [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(d2_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : 
          ( r2_relat_2(A,B)
        <=> ! [C] : ~ ( r2_hidden(C,B)
              & r2_hidden(k4_tarski(C,C),A) ) ) ) ),
    file(relat_2,d2_relat_2),
    [interesting(0.00)]).

fof(d10_relat_2,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v2_relat_2(A)
      <=> r2_relat_2(A,k3_relat_1(A)) ) ) ),
    file(relat_2,d10_relat_2),
    [interesting(0.00)]).

fof(d24_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v9_rewrite1(A)
      <=> ! [B,C,D] : 
            ( ( r2_hidden(k4_tarski(B,C),A)
              & r2_hidden(k4_tarski(B,D),A) )
           => r5_rewrite1(A,C,D) ) ) ) ),
    file(rewrite1,d24_rewrite1),
    [interesting(0.00)]).

fof(d30_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ( v14_abcmiz_0(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_abcmiz_0(A))
                   => ~ ( r4_abcmiz_0(A,B,D)
                        & r3_orders_2(A,k5_abcmiz_0(A,B,D),C)
                        & ! [E] : 
                            ( ( v1_finset_1(E)
                              & m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A))) )
                           => ~ ( r6_abcmiz_0(A,k10_lattice3(A,B,C),E)
                                & k6_abcmiz_0(A,k10_lattice3(A,B,C),E) = C ) ) ) ) ) ) ) ) ),
    file(abcmiz_0,d30_abcmiz_0),
    [interesting(0.00)]).

fof(d7_rewrite1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r5_rewrite1(A,B,C)
        <=> ? [D] : 
              ( r1_rewrite1(A,B,D)
              & r1_rewrite1(A,C,D) ) ) ) ),
    file(rewrite1,d7_rewrite1),
    [interesting(0.00)]).

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

fof(t24_finset_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
    <=> v1_finset_1(k1_zfmisc_1(A)) ) ),
    file(finset_1,t24_finset_1),
    [interesting(0.00)]).

fof(t13_finset_1,theorem,(
    ! [A,B] : 
      ( ( r1_tarski(A,B)
        & v1_finset_1(B) )
     => v1_finset_1(A) ) ),
    file(finset_1,t13_finset_1),
    [interesting(0.00)]).

fof(s3_funct_1,theorem,(
    ? [A] : 
      ( v1_relat_1(A)
      & v1_funct_1(A)
      & k1_relat_1(A) = f1_s3_funct_1
      & ! [B] : 
          ( r2_hidden(B,f1_s3_funct_1)
         => k1_funct_1(A,B) = f2_s3_funct_1(B) ) ) ),
    file(funct_1,s3_funct_1),
    [interesting(0.00)]).

fof(t78_card_1,theorem,(
    k4_card_1(k1_xboole_0) = 0 ),
    file(card_1,t78_card_1),
    [interesting(0.00)]).

fof(t56_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r2_xboole_0(A,B)
        & r2_xboole_0(B,C) )
     => r2_xboole_0(A,C) ) ),
    file(xboole_1,t56_xboole_1),
    [interesting(0.00)]).

fof(t27_card_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k1_card_1(A),k1_card_1(B)) ) ),
    file(card_1,t27_card_1),
    [interesting(0.00)]).

fof(t56_card_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( m2_subset_1(B,k1_numbers,k5_numbers)
         => ( r1_xreal_0(A,B)
          <=> r1_ordinal1(A,B) ) ) ) ),
    file(card_1,t56_card_1),
    [interesting(0.00)]).

fof(t3_triang_1,theorem,(
    ! [A] : 
      ( v1_finset_1(A)
     => ! [B] : 
          ( v1_finset_1(B)
         => ( ( r1_tarski(A,B)
              & k4_card_1(A) = k4_card_1(B) )
           => A = B ) ) ) ),
    file(triang_1,t3_triang_1),
    [interesting(0.00)]).

fof(d5_real_1,definition,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ( r1_xreal_0(A,B)
          <=> ~ ( r1_xreal_0(B,A)
                & B != A ) ) ) ) ),
    file(real_1,d5_real_1),
    [interesting(0.00)]).

fof(s7_nat_1,theorem,
    ( ( ? [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
          & p1_s7_nat_1(A) )
      & ! [A] : 
          ( m2_subset_1(A,k1_numbers,k5_numbers)
         => ~ ( A != 0
              & p1_s7_nat_1(A)
              & ! [B] : 
                  ( m2_subset_1(B,k1_numbers,k5_numbers)
                 => ~ ( ~ r1_xreal_0(A,B)
                      & p1_s7_nat_1(B) ) ) ) ) )
   => p1_s7_nat_1(0) ),
    file(nat_1,s7_nat_1),
    [interesting(0.00)]).

fof(d8_xboole_0,definition,(
    ! [A,B] : 
      ( r2_xboole_0(A,B)
    <=> ( r1_tarski(A,B)
        & A != B ) ) ),
    file(xboole_0,d8_xboole_0),
    [interesting(0.00)]).

fof(t59_card_2,theorem,(
    ! [A] : 
      ( k1_card_1(A) = 0
     => A = k1_xboole_0 ) ),
    file(card_2,t59_card_2),
    [interesting(0.00)]).

fof(s2_orders_1,theorem,
    ( ( ! [A] : 
          ( m1_subset_1(A,f1_s2_orders_1)
         => p1_s2_orders_1(A,A) )
      & ! [A] : 
          ( m1_subset_1(A,f1_s2_orders_1)
         => ! [B] : 
              ( m1_subset_1(B,f1_s2_orders_1)
             => ( ( p1_s2_orders_1(A,B)
                  & p1_s2_orders_1(B,A) )
               => A = B ) ) )
      & ! [A] : 
          ( m1_subset_1(A,f1_s2_orders_1)
         => ! [B] : 
              ( m1_subset_1(B,f1_s2_orders_1)
             => ! [C] : 
                  ( m1_subset_1(C,f1_s2_orders_1)
                 => ( ( p1_s2_orders_1(A,B)
                      & p1_s2_orders_1(B,C) )
                   => p1_s2_orders_1(A,C) ) ) ) )
      & ! [A] : ~ ( r1_tarski(A,f1_s2_orders_1)
          & ! [B] : 
              ( m1_subset_1(B,f1_s2_orders_1)
             => ! [C] : 
                  ( m1_subset_1(C,f1_s2_orders_1)
                 => ~ ( r2_hidden(B,A)
                      & r2_hidden(C,A)
                      & ~ p1_s2_orders_1(B,C)
                      & ~ p1_s2_orders_1(C,B) ) ) )
          & ! [B] : 
              ( m1_subset_1(B,f1_s2_orders_1)
             => ? [C] : 
                  ( m1_subset_1(C,f1_s2_orders_1)
                  & r2_hidden(C,A)
                  & ~ p1_s2_orders_1(B,C) ) ) ) )
   => ? [A] : 
        ( m1_subset_1(A,f1_s2_orders_1)
        & ! [B] : 
            ( m1_subset_1(B,f1_s2_orders_1)
           => ~ ( A != B
                & p1_s2_orders_1(B,A) ) ) ) ),
    file(orders_1,s2_orders_1),
    [interesting(0.00)]).

fof(t65_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ~ ( r6_abcmiz_0(A,B,C)
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                     => ~ ( r1_tarski(D,C)
                          & r6_abcmiz_0(A,B,D)
                          & k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D)
                          & ! [E] : 
                              ( m1_subset_1(E,k1_zfmisc_1(u1_abcmiz_0(A)))
                             => ( ( r1_tarski(E,D)
                                  & r6_abcmiz_0(A,B,E)
                                  & k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,E) )
                               => E = D ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t63_abcmiz_0,s1_abcmiz_0,t1_xboole_1]),
    [file(abcmiz_0,t65_abcmiz_0),interesting(0.00)]).

fof(s5_nat_1,theorem,
    ( ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & p1_s5_nat_1(A) )
   => ? [A] : 
        ( m2_subset_1(A,k1_numbers,k5_numbers)
        & p1_s5_nat_1(A)
        & ! [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
           => ( p1_s5_nat_1(B)
             => r1_xreal_0(A,B) ) ) ) ),
    file(nat_1,s5_nat_1),
    [interesting(0.00)]).

fof(d8_funct_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v2_funct_1(A)
      <=> ! [B,C] : 
            ( ( r2_hidden(B,k1_relat_1(A))
              & r2_hidden(C,k1_relat_1(A))
              & k1_funct_1(A,B) = k1_funct_1(A,C) )
           => B = C ) ) ) ),
    file(funct_1,d8_funct_1),
    [interesting(0.00)]).

fof(t23_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B,C] : 
          ( m2_finseq_1(C,B)
         => m2_finseq_1(k7_relat_1(C,k2_finseq_1(A)),B) ) ) ),
    file(finseq_1,t23_finseq_1),
    [interesting(0.00)]).

fof(d1_trees_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_tarski(A,B)
          <=> ? [C] : 
                ( m2_subset_1(C,k1_numbers,k5_numbers)
                & A = k7_relat_1(B,k2_finseq_1(C)) ) ) ) ) ),
    file(trees_1,d1_trees_1),
    [interesting(0.00)]).

fof(t8_trees_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( r1_tarski(A,B)
          <=> ? [C] : 
                ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C)
                & B = k7_finseq_1(A,C) ) ) ) ) ),
    file(trees_1,t8_trees_1),
    [interesting(0.00)]).

fof(t50_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( m2_finseq_1(k7_finseq_1(A,B),C)
             => ( m2_finseq_1(A,C)
                & m2_finseq_1(B,C) ) ) ) ) ),
    file(finseq_1,t50_finseq_1),
    [interesting(0.00)]).

fof(t56_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => ( B = k9_finseq_1(A)
      <=> ( k3_finseq_1(B) = 1
          & k2_relat_1(B) = k1_tarski(A) ) ) ) ),
    file(finseq_1,t56_finseq_1),
    [interesting(0.00)]).

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

fof(t58_finseq_1,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B)
        & v1_finseq_1(B) )
     => k1_funct_1(k7_finseq_1(k9_finseq_1(A),B),1) = A ) ),
    file(finseq_1,t58_finseq_1),
    [interesting(0.00)]).

fof(t39_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => r1_tarski(k4_finseq_1(A),k4_finseq_1(k7_finseq_1(A,B))) ) ) ),
    file(finseq_1,t39_finseq_1),
    [interesting(0.00)]).

fof(t4_hilbert2,theorem,(
    ! [A,B] : 
      ( m2_finseq_1(B,A)
     => ~ ( B != k1_xboole_0
          & ! [C] : 
              ( m2_finseq_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,A)
                 => B != k7_finseq_1(C,k9_finseq_1(D)) ) ) ) ) ),
    file(hilbert2,t4_hilbert2),
    [interesting(0.00)]).

fof(t2_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( A != k1_xboole_0
             => k1_rewrite1(k7_finseq_1(B,k9_finseq_1(C)),A) = k7_finseq_1(B,A) ) ) ) ),
    file(rewrite1,t2_rewrite1),
    [interesting(0.00)]).

fof(t47_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k7_finseq_1(A,k1_xboole_0) = A
        & k7_finseq_1(k1_xboole_0,A) = A ) ) ),
    file(finseq_1,t47_finseq_1),
    [interesting(0.00)]).

fof(t9_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ! [C] : 
              ( v1_xreal_0(C)
             => ! [D] : 
                  ( v1_xreal_0(D)
                 => ( ( r1_xreal_0(A,B)
                      & r1_xreal_0(C,D) )
                   => r1_xreal_0(k2_xcmplx_0(A,C),k2_xcmplx_0(B,D)) ) ) ) ) ) ),
    file(xreal_1,t9_xreal_1),
    [interesting(0.00)]).

fof(t35_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) = k1_rewrite1(k7_abcmiz_0(A,B,C),k7_abcmiz_0(A,k8_abcmiz_0(A,B,C),D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_abcmiz_0,t4_hilbert2,t2_rewrite1,t56_finseq_1,t35_finseq_1,t35_finseq_1,t35_finseq_1,t25_finseq_1,t31_abcmiz_0,t47_finseq_1,d19_abcmiz_0,t38_nat_1,t27_finseq_3,d7_finseq_1,d19_abcmiz_0,t35_finseq_1,t27_finseq_3,d19_abcmiz_0,t29_nat_1,t38_nat_1,t27_finseq_3,d7_finseq_1,d19_abcmiz_0,t29_nat_1,t27_finseq_3,d7_finseq_1,d19_abcmiz_0,d19_abcmiz_0,t38_nat_1,t28_nat_1,t29_nat_1,t8_xreal_1,t29_nat_1,t9_xreal_1,t27_finseq_3,d7_finseq_1,d19_abcmiz_0,t1_xreal_1,d19_abcmiz_0]),
    [file(abcmiz_0,t35_abcmiz_0),interesting(0.00)]).

fof(t36_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ! [E] : 
                      ( v4_ordinal2(E)
                     => ( r2_hidden(E,k4_finseq_1(C))
                       => k1_funct_1(k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)),E) = k1_funct_1(k7_abcmiz_0(A,B,C),E) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_abcmiz_0,t4_hilbert2,t35_abcmiz_0,t2_rewrite1,t56_finseq_1,t35_finseq_1,t27_finseq_3,t27_finseq_3,d7_finseq_1]),
    [file(abcmiz_0,t36_abcmiz_0),interesting(0.00)]).

fof(t34_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v1_xboole_0(A)
        & v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( v4_ordinal2(C)
             => ( ~ r1_xreal_0(k3_finseq_1(B),C)
               => k1_funct_1(k1_rewrite1(A,B),k2_xcmplx_0(k3_finseq_1(A),C)) = k1_funct_1(B,k2_xcmplx_0(C,1)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,d1_rewrite1,t38_nat_1,t21_finseq_1,t29_nat_1,t38_nat_1,d21_ordinal2,t27_finseq_3,d7_finseq_1]),
    [file(abcmiz_0,t34_abcmiz_0),interesting(0.00)]).

fof(t41_finseq_1,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C)
                & v1_finseq_1(C) )
             => ( r2_hidden(A,k4_finseq_1(B))
               => r2_hidden(k1_nat_1(k3_finseq_1(C),A),k4_finseq_1(k7_finseq_1(C,B))) ) ) ) ) ),
    file(finseq_1,t41_finseq_1),
    [interesting(0.00)]).

fof(t61_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( r5_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
                   => ( r5_abcmiz_0(A,B,C)
                      & r5_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d28_abcmiz_0,t39_finseq_1,t36_abcmiz_0,d7_finseq_1,d28_abcmiz_0,d28_abcmiz_0,t35_abcmiz_0,t27_finseq_3,t28_nat_1,t27_finseq_3,d19_abcmiz_0,t38_nat_1,t38_nat_1,t34_abcmiz_0,t41_finseq_1,d7_finseq_1]),
    [file(abcmiz_0,t61_abcmiz_0),interesting(0.00)]).

fof(t25_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => ( r2_hidden(C,k2_abcmiz_0(A,B))
               => ( r1_abcmiz_0(A,B,C)
                  & k5_abcmiz_0(A,B,C) = B ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_abcmiz_0,t21_abcmiz_0,t24_abcmiz_0,d3_yellow_0]),
    [file(abcmiz_0,t25_abcmiz_0),interesting(0.00)]).

fof(t61_finseq_1,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C)
        & v1_finseq_1(C) )
     => ( C = k10_finseq_1(A,B)
      <=> ( k3_finseq_1(C) = 2
          & k1_funct_1(C,1) = A
          & k1_funct_1(C,2) = B ) ) ) ),
    file(finseq_1,t61_finseq_1),
    [interesting(0.00)]).

fof(t30_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_abcmiz_0(A))
             => k7_abcmiz_0(A,B,k12_finseq_1(u1_abcmiz_0(A),C)) = k10_finseq_1(B,k5_abcmiz_0(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t57_finseq_1,d19_abcmiz_0,t57_finseq_1,t27_finseq_3,d19_abcmiz_0,t61_finseq_1]),
    [file(abcmiz_0,t30_abcmiz_0),interesting(0.00)]).

fof(t62_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( ( r5_abcmiz_0(A,B,C)
                      & r5_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) )
                   => r5_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d28_abcmiz_0,d28_abcmiz_0,d28_abcmiz_0,t35_abcmiz_0,t27_finseq_3,t27_finseq_3,t36_abcmiz_0,d7_finseq_1,t38_nat_1,t28_nat_1,t35_finseq_1,t29_nat_1,t8_xreal_1,d19_abcmiz_0,t27_finseq_3,t38_nat_1,t38_nat_1,t34_abcmiz_0,d7_finseq_1]),
    [file(abcmiz_0,t62_abcmiz_0),interesting(0.00)]).

fof(t12_xboole_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => k2_xboole_0(A,B) = B ) ),
    file(xboole_1,t12_xboole_1),
    [interesting(0.00)]).

fof(t4_xboole_1,theorem,(
    ! [A,B,C] : k2_xboole_0(k2_xboole_0(A,B),C) = k2_xboole_0(A,k2_xboole_0(B,C)) ),
    file(xboole_1,t4_xboole_1),
    [interesting(0.00)]).

fof(t60_finseq_5,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k4_finseq_1(A) = k4_finseq_1(k3_finseq_5(A))
        & k2_relat_1(A) = k2_relat_1(k3_finseq_5(A)) ) ) ),
    file(finseq_5,t60_finseq_5),
    [interesting(0.00)]).

fof(d3_finseq_5,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( B = k3_finseq_5(A)
          <=> ( k3_finseq_1(B) = k3_finseq_1(A)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( r2_hidden(C,k4_finseq_1(B))
                   => k1_funct_1(B,C) = k1_funct_1(A,k2_xcmplx_0(k6_xcmplx_0(k3_finseq_1(A),C),1)) ) ) ) ) ) ) ),
    file(finseq_5,d3_finseq_5),
    [interesting(0.00)]).

fof(t37_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => k1_funct_1(k7_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)),k1_nat_1(k3_finseq_1(C),1)) = k8_abcmiz_0(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_abcmiz_0,t35_abcmiz_0,t34_abcmiz_0,d19_abcmiz_0]),
    [file(abcmiz_0,t37_abcmiz_0),interesting(0.00)]).

fof(t38_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => k8_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) = k8_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_abcmiz_0,t4_hilbert2,t35_abcmiz_0,t2_rewrite1,d19_abcmiz_0,t29_nat_1,t27_finseq_3,t56_finseq_1,t35_finseq_1,d7_finseq_1,t35_finseq_1]),
    [file(abcmiz_0,t38_abcmiz_0),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(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(t22_finseq_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ~ ( k3_finseq_1(B) != 0
              & ! [C] : 
                  ( m2_finseq_1(C,A)
                 => ! [D] : 
                      ( m1_subset_1(D,A)
                     => B != k8_finseq_1(A,C,k12_finseq_1(A,D)) ) ) ) ) ) ),
    file(finseq_2,t22_finseq_2),
    [interesting(0.00)]).

fof(t41_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & v2_orders_2(A)
        & v3_orders_2(A)
        & ~ v4_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m2_finseq_1(C,u1_abcmiz_0(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u1_abcmiz_0(A))
                 => ( r3_abcmiz_0(A,B,k8_finseq_1(u1_abcmiz_0(A),C,D))
                   => ( r3_abcmiz_0(A,B,C)
                      & r3_abcmiz_0(A,k8_abcmiz_0(A,B,C),D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d21_abcmiz_0,t39_finseq_1,t36_abcmiz_0,d7_finseq_1,d21_abcmiz_0,d21_abcmiz_0,t35_abcmiz_0,t27_finseq_3,t28_nat_1,t27_finseq_3,d19_abcmiz_0,t38_nat_1,t38_nat_1,t34_abcmiz_0,t41_finseq_1,d7_finseq_1]),
    [file(abcmiz_0,t41_abcmiz_0),interesting(0.00)]).

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

fof(t51_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A)))
             => ( r2_abcmiz_0(A,B,C)
               => r1_tarski(C,k2_abcmiz_0(A,k6_abcmiz_0(A,B,C))) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_abcmiz_0,t1_abcmiz_0,d3_xboole_0,t14_abcmiz_0]),
    [file(abcmiz_0,t51_abcmiz_0),interesting(0.00)]).

fof(t8_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,B) )
     => r1_tarski(k2_xboole_0(A,C),B) ) ),
    file(xboole_1,t8_xboole_1),
    [interesting(0.00)]).

fof(t9_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,C)) ) ),
    file(xboole_1,t9_xboole_1),
    [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(t71_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( ( v1_finset_1(C)
                & m1_subset_1(C,k1_zfmisc_1(u1_abcmiz_0(A))) )
             => ( ! [D] : 
                    ( m1_subset_1(D,k1_zfmisc_1(u1_abcmiz_0(A)))
                   => ( ( r1_tarski(D,C)
                        & r6_abcmiz_0(A,B,D)
                        & k6_abcmiz_0(A,B,C) = k6_abcmiz_0(A,B,D) )
                     => D = C ) )
               => ! [D] : 
                    ( ( v2_funct_1(D)
                      & m2_finseq_1(D,u1_abcmiz_0(A)) )
                   => ( ( k2_relat_1(D) = C
                        & r5_abcmiz_0(A,B,D) )
                     => ! [E] : 
                          ( v4_ordinal2(E)
                         => ( ( r1_xreal_0(1,E)
                              & r1_xreal_0(E,k3_finseq_1(D)) )
                           => r2_hidden(k4_tarski(k1_funct_1(k7_abcmiz_0(A,B,D),k2_xcmplx_0(E,1)),k1_funct_1(k7_abcmiz_0(A,B,D),E)),k11_abcmiz_0(A)) ) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d19_abcmiz_0,t38_nat_1,d21_ordinal2,t27_finseq_3,d4_finseq_1,t12_funct_1,d4_finseq_1,t12_funct_1,d19_abcmiz_0,d28_abcmiz_0,t28_nat_1,t23_finseq_1,d1_trees_1,t8_trees_1,t50_finseq_1,t23_finseq_1,t38_nat_1,t21_finseq_1,t35_finseq_1,t8_xreal_1,t21_finseq_1,t57_finseq_1,t56_finseq_1,d4_finseq_1,t37_zfmisc_1,d1_trees_1,t8_trees_1,t50_finseq_1,t27_finseq_3,t58_finseq_1,d7_finseq_1,t61_abcmiz_0,t37_abcmiz_0,t25_abcmiz_0,t32_abcmiz_0,t61_abcmiz_0,t61_abcmiz_0,t62_abcmiz_0,t58_abcmiz_0,d4_finseq_1,t38_abcmiz_0,t38_abcmiz_0,t38_abcmiz_0,t57_abcmiz_0,t57_abcmiz_0,d29_abcmiz_0,t44_finseq_1,t7_xboole_1,t9_xboole_1,d1_tarski,d2_xboole_0,d2_xboole_0,d5_funct_1,t39_finseq_1,t27_finseq_3,d7_finseq_1,t38_nat_1,d8_funct_1,d5_funct_1,t27_finseq_3,t8_xreal_1,t41_finseq_1,d7_finseq_1,t41_finseq_1,d7_finseq_1,d8_funct_1,d2_xboole_0,d31_abcmiz_0]),
    [file(abcmiz_0,t71_abcmiz_0),interesting(0.00)]).

fof(t65_finseq_5,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ( k1_funct_1(A,1) = k1_funct_1(k3_finseq_5(A),k3_finseq_1(A))
        & k1_funct_1(A,k3_finseq_1(A)) = k1_funct_1(k3_finseq_5(A),1) ) ) ),
    file(finseq_5,t65_finseq_5),
    [interesting(0.00)]).

fof(s2_abcmiz_0,theorem,
    ( ( ! [A] : 
          ( m1_subset_1(A,f1_s2_abcmiz_0)
         => ! [B] : 
              ( m1_subset_1(B,f1_s2_abcmiz_0)
             => ( r2_hidden(k4_tarski(A,B),f2_s2_abcmiz_0)
               => p1_s2_abcmiz_0(A,B) ) ) )
      & ! [A] : 
          ( m1_subset_1(A,f1_s2_abcmiz_0)
         => p1_s2_abcmiz_0(A,A) )
      & ! [A] : 
          ( m1_subset_1(A,f1_s2_abcmiz_0)
         => ! [B] : 
              ( m1_subset_1(B,f1_s2_abcmiz_0)
             => ! [C] : 
                  ( m1_subset_1(C,f1_s2_abcmiz_0)
                 => ( ( p1_s2_abcmiz_0(A,B)
                      & p1_s2_abcmiz_0(B,C) )
                   => p1_s2_abcmiz_0(A,C) ) ) ) ) )
   => ! [A] : 
        ( m1_subset_1(A,f1_s2_abcmiz_0)
       => ! [B] : 
            ( m1_subset_1(B,f1_s2_abcmiz_0)
           => ( r1_rewrite1(f2_s2_abcmiz_0,A,B)
             => p1_s2_abcmiz_0(A,B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d3_rewrite1,t29_nat_1,t38_nat_1,t27_finseq_3,d2_rewrite1,t106_zfmisc_1,t38_nat_1,d2_rewrite1,t38_nat_1,t28_nat_1,s1_nat_1]),
    [file(abcmiz_0,s2_abcmiz_0),interesting(0.00)]).

fof(t68_abcmiz_0,theorem,(
    ! [A] : 
      ( ( v2_orders_2(A)
        & v3_orders_2(A)
        & v4_orders_2(A)
        & v1_lattice3(A)
        & v1_abcmiz_0(A)
        & ~ v4_abcmiz_0(A)
        & v9_abcmiz_0(A)
        & l3_abcmiz_0(A) )
     => ! [B] : 
          ( m1_subset_1(B,u1_struct_0(A))
         => ! [C] : 
              ( m1_subset_1(C,u1_struct_0(A))
             => ( r1_rewrite1(k11_abcmiz_0(A),B,C)
               => r3_orders_2(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t67_abcmiz_0,d9_orders_2,d2_yellow_0,s2_abcmiz_0]),
    [file(abcmiz_0,t68_abcmiz_0),interesting(0.00)]).

fof(t3_finseq_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( r2_hidden(A,k2_finseq_1(B))
          <=> ( r1_xreal_0(1,A)
              & r1_xreal_0(A,B) ) ) ) ) ),
    file(finseq_1,t3_finseq_1),
    [interesting(0.00)]).

fof(s1_wellord2,theorem,
    ( ! [A] : ~ ( r2_hidden(A,f1_s1_wellord2)
        & ! [B] : ~ ( r2_hidden(B,f2_s1_wellord2)
            & p1_s1_wellord2(A,B) ) )
   => ? [A] : 
        ( v1_relat_1(A)
        & v1_funct_1(A)
        & k1_relat_1(A) = f1_s1_wellord2
        & r1_tarski(k2_relat_1(A),f2_s1_wellord2)
        & ! [B] : 
            ( r2_hidden(B,f1_s1_wellord2)
           => p1_s1_wellord2(B,k1_funct_1(A,B)) ) ) ),
    file(wellord2,s1_wellord2),
    [interesting(0.00)]).

fof(d2_finseq_1,definition,(
    ! [A] : 
      ( v1_relat_1(A)
     => ( v1_finseq_1(A)
      <=> ? [B] : 
            ( m2_subset_1(B,k1_numbers,k5_numbers)
            & k1_relat_1(A) = k2_finseq_1(B) ) ) ) ),
    file(finseq_1,d2_finseq_1),
    [interesting(0.00)]).

fof(t18_finseq_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B)
            & v1_finseq_1(B) )
         => ( ( k3_finseq_1(A) = k3_finseq_1(B)
              & ! [C] : 
                  ( m2_subset_1(C,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(1,C)
                      & r1_xreal_0(C,k3_finseq_1(A)) )
                   => k1_funct_1(A,C) = k1_funct_1(B,C) ) ) )
           => A = B ) ) ) ),
    file(finseq_1,t18_finseq_1),
    [interesting(0.00)]).

fof(t29_finseq_6,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_finseq_1(A) )
     => k3_finseq_5(k3_finseq_5(A)) = A ) ),
    file(finseq_6,t29_finseq_6),
    [interesting(0.00)]).

fof(t26_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r1_rewrite1(A,B,C)
         => ( r2_rewrite1(A,B,C)
            & r2_rewrite1(A,C,B) ) ) ) ),
    file(rewrite1,t26_rewrite1),
    [interesting(0.00)]).

fof(t56_rewrite1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v2_rewrite1(A)
        & v4_rewrite1(A) )
     => ! [B,C] : 
          ( r2_rewrite1(A,B,C)
         => k2_rewrite1(A,B) = k2_rewrite1(A,C) ) ) ),
    file(rewrite1,t56_rewrite1),
    [interesting(0.00)]).

fof(t1_yellow_4,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B,C] : 
          ( m1_subset_1(C,u1_struct_0(A))
         => ( ( r2_hidden(C,B)
              & r1_yellow_0(A,B) )
           => r1_orders_2(A,C,k1_yellow_0(A,B)) ) ) ) ),
    file(yellow_4,t1_yellow_4),
    [interesting(0.00)]).

fof(t13_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B] : r1_rewrite1(A,B,B) ) ),
    file(rewrite1,t13_rewrite1),
    [interesting(0.00)]).

fof(t16_rewrite1,theorem,(
    ! [A] : 
      ( v1_relat_1(A)
     => ! [B,C] : 
          ( r2_hidden(k4_tarski(B,C),A)
         => r1_rewrite1(A,B,C) ) ) ),
    file(rewrite1,t16_rewrite1),
    [interesting(0.00)]).

fof(t8_abcmiz_0,theorem,(
    ! [A] : 
      ( l2_abcmiz_0(A)
     => ! [B] : 
          ( l2_abcmiz_0(B)
         => ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
              & v8_abcmiz_0(A) )
           => v8_abcmiz_0(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_abcmiz_0,d9_abcmiz_0]),
    [file(abcmiz_0,t8_abcmiz_0),interesting(0.00)]).

fof(d10_abcmiz_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ( v9_abcmiz_0(A)
      <=> ( v1_funct_1(u3_abcmiz_0(A))
          & v1_funct_2(u3_abcmiz_0(A),u1_struct_0(A),u1_struct_0(k7_lattice3(k3_yellow_1(u1_abcmiz_0(A)))))
          & v20_waybel_0(u3_abcmiz_0(A),A,k7_lattice3(k3_yellow_1(u1_abcmiz_0(A))))
          & m2_relset_1(u3_abcmiz_0(A),u1_struct_0(A),u1_struct_0(k7_lattice3(k3_yellow_1(u1_abcmiz_0(A))))) ) ) ) ),
    file(abcmiz_0,d10_abcmiz_0),
    [interesting(0.00)]).

fof(d35_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ( v20_waybel_0(C,A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,u1_struct_0(A))
                   => ! [E] : 
                        ( m1_subset_1(E,u1_struct_0(A))
                       => r4_waybel_0(A,B,C,k2_struct_0(A,D,E)) ) ) ) ) ) ) ),
    file(waybel_0,d35_waybel_0),
    [interesting(0.00)]).

fof(d31_waybel_0,definition,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l1_orders_2(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l1_orders_2(B) )
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,u1_struct_0(A),u1_struct_0(B))
                & m2_relset_1(C,u1_struct_0(A),u1_struct_0(B)) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(u1_struct_0(A)))
                 => ( r4_waybel_0(A,B,C,D)
                  <=> ( r1_yellow_0(A,D)
                     => ( r1_yellow_0(B,k4_pre_topc(A,B,C,D))
                        & k1_yellow_0(B,k4_pre_topc(A,B,C,D)) = k1_waybel_0(A,B,C,k1_yellow_0(A,D)) ) ) ) ) ) ) ) ),
    file(waybel_0,d31_waybel_0),
    [interesting(0.00)]).

fof(t14_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( l1_orders_2(B)
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ! [C] : 
                ( ( r1_yellow_0(A,C)
                 => r1_yellow_0(B,C) )
                & ( r2_yellow_0(A,C)
                 => r2_yellow_0(B,C) ) ) ) ) ) ),
    file(yellow_0,t14_yellow_0),
    [interesting(0.00)]).

fof(t26_yellow_0,theorem,(
    ! [A] : 
      ( l1_orders_2(A)
     => ! [B] : 
          ( l1_orders_2(B)
         => ( g1_orders_2(u1_struct_0(A),u1_orders_2(A)) = g1_orders_2(u1_struct_0(B),u1_orders_2(B))
           => ! [C] : 
                ( r1_yellow_0(A,C)
               => k1_yellow_0(A,C) = k1_yellow_0(B,C) ) ) ) ) ),
    file(yellow_0,t26_yellow_0),
    [interesting(0.00)]).

fof(t9_abcmiz_0,theorem,(
    ! [A] : 
      ( ( ~ v3_struct_0(A)
        & l2_abcmiz_0(A) )
     => ! [B] : 
          ( ( ~ v3_struct_0(B)
            & l2_abcmiz_0(B) )
         => ( ( g2_abcmiz_0(u1_struct_0(A),u1_abcmiz_0(A),u1_orders_2(A),u2_abcmiz_0(A),u3_abcmiz_0(A)) = g2_abcmiz_0(u1_struct_0(B),u1_abcmiz_0(B),u1_orders_2(B),u2_abcmiz_0(B),u3_abcmiz_0(B))
              & v9_abcmiz_0(A) )
           => v9_abcmiz_0(B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d10_abcmiz_0,d35_waybel_0,d31_waybel_0,d35_waybel_0,t14_yellow_0,d31_waybel_0,d31_waybel_0,t26_yellow_0,d10_abcmiz_0]),
    [file(abcmiz_0,t9_abcmiz_0),interesting(0.00)]).