fof(t3_boolmark,theorem,(
    ! [A,B,C] : 
      ( ( v1_relat_1(C)
        & v1_funct_1(C) )
     => ! [D] : 
          ( r1_xboole_0(A,B)
         => k9_relat_1(k1_funct_4(C,k2_funcop_1(A,D)),B) = k9_relat_1(C,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d1_funct_4,t19_funcop_1,t2_tarski,d12_funct_1,d3_xboole_0,d2_xboole_0,t12_funct_4,d12_funct_1,d12_funct_1,d3_xboole_0,d2_xboole_0,t12_funct_4,d12_funct_1]),
    [file(boolmark,t3_boolmark),interesting(1.00)]).

fof(t11_boolmark,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m2_fraenkel(B,u1_petri(A),k6_margrel1,k1_boolmark(A))
         => ! [C] : 
              ( m2_finseq_1(C,u2_petri(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u2_petri(A))
                 => ( r2_boolmark(A,B,k8_finseq_1(u2_petri(A),C,D))
                   => ( r2_boolmark(A,k3_boolmark(A,B,C),D)
                      & r2_boolmark(A,B,C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d4_boolmark,d4_boolmark,d5_boolmark,t47_finseq_1,d4_boolmark,t47_finseq_1,t25_finseq_1,t25_finseq_1,t23_nat_1,t35_finseq_1,t25_finseq_1,d4_boolmark,d5_boolmark,d5_boolmark,t19_nat_1,t19_nat_1,t38_nat_1,t8_boolmark,t19_nat_1,t8_xreal_1,t35_finseq_1,t18_nat_1,t38_nat_1,t29_nat_1,t8_boolmark,t38_nat_1,t2_xreal_1,t38_nat_1,t38_nat_1,s1_nat_1,t38_nat_1,t60_nat_1,t5_goboard2,t18_nat_1,t38_nat_1,t18_nat_1,t38_nat_1,t29_nat_1,t5_goboard2,t38_nat_1,t8_xreal_1,t35_finseq_1,t38_nat_1,s1_nat_1,t22_nat_1,t5_goboard2,t35_finseq_1,t8_xreal_1,t31_xreal_1,t29_nat_1,t38_nat_1,t27_finseq_3,t84_finseq_4,t22_nat_1,t38_nat_1,d4_boolmark,t8_boolmark,t2_xreal_1,t29_nat_1,t38_nat_1,t27_finseq_3,t83_finseq_4,t22_nat_1,t38_nat_1,d4_boolmark]),
    [file(boolmark,t11_boolmark),interesting(0.94)]).

fof(t5_boolmark,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B,C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => k9_relat_1(k1_funct_4(C,k2_funcop_1(A,B)),A) = k1_tarski(B) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_funct_1,t19_funcop_1,t14_funct_4,t13_funcop_1,d1_xboole_0,t13_funcop_1,t19_funcop_1,t13_funct_4,t14_funct_4,d12_funct_1,d1_tarski]),
    [file(boolmark,t5_boolmark),interesting(0.94)]).

fof(t10_boolmark,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m2_fraenkel(B,u1_petri(A),k6_margrel1,k1_boolmark(A))
         => ! [C] : 
              ( m2_finseq_1(C,u2_petri(A))
             => ! [D] : 
                  ( m2_finseq_1(D,u2_petri(A))
                 => k3_boolmark(A,B,k8_finseq_1(u2_petri(A),C,D)) = k3_boolmark(A,k3_boolmark(A,B,C),D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t47_finseq_1,d5_boolmark,d5_boolmark,d5_boolmark,t47_finseq_1,d5_boolmark,t47_finseq_1,d5_boolmark,t25_finseq_1,t25_finseq_1,t23_nat_1,t35_finseq_1,t25_finseq_1,d5_boolmark,d5_boolmark,d5_boolmark,t19_nat_1,t19_nat_1,t8_boolmark,t19_nat_1,t8_xreal_1,t35_finseq_1,t18_nat_1,t38_nat_1,t29_nat_1,t8_boolmark,t38_nat_1,t2_xreal_1,t38_nat_1,t38_nat_1,s1_nat_1,t38_nat_1,t60_nat_1,t5_goboard2,t18_nat_1,t38_nat_1,t18_nat_1,t38_nat_1,t29_nat_1,t5_goboard2,t38_nat_1,t8_xreal_1,t35_finseq_1,t38_nat_1,s1_nat_1,t22_nat_1,t35_finseq_1]),
    [file(boolmark,t10_boolmark),interesting(0.83)]).

fof(t12_boolmark,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m2_fraenkel(B,u1_petri(A),k6_margrel1,k1_boolmark(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_petri(A))
             => ( r1_boolmark(A,B,C)
              <=> r2_boolmark(A,B,k12_finseq_1(u2_petri(A),C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t56_finseq_1,t56_finseq_1,t25_finseq_4,t25_finseq_4,t56_finseq_1,t38_nat_1,d4_boolmark,d4_boolmark,t25_finseq_4]),
    [file(boolmark,t12_boolmark),interesting(0.73)]).

fof(t2_boolmark,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ! [E] : 
                      ( ( v1_funct_1(E)
                        & v1_funct_2(E,A,B)
                        & m2_relset_1(E,A,B) )
                     => ( r1_xboole_0(k2_funct_2(A,B,E,C),k2_funct_2(A,B,E,D))
                       => r1_xboole_0(C,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_xboole_0,d7_xboole_0,t10_subset_1,d3_xboole_0,t43_funct_2,d3_xboole_0]),
    [file(boolmark,t2_boolmark),interesting(0.69)]).

fof(t13_boolmark,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m2_fraenkel(B,u1_petri(A),k6_margrel1,k1_boolmark(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_petri(A))
             => k2_boolmark(A,B,C) = k3_boolmark(A,B,k12_finseq_1(u2_petri(A),C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_finseq_1,t56_finseq_1,t56_finseq_1,t56_finseq_1,t25_finseq_4,t25_finseq_4,t56_finseq_1,t38_nat_1,d5_boolmark]),
    [file(boolmark,t13_boolmark),interesting(0.68)]).

fof(t8_boolmark,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ! [C] : 
              ( m2_finseq_1(C,A)
             => ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(1,D)
                      & r1_xreal_0(D,k3_finseq_1(B)) )
                   => k4_finseq_4(k5_numbers,A,k8_finseq_1(A,B,C),D) = k4_finseq_4(k5_numbers,A,B,D) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t29_nat_1,t2_xreal_1,d3_finseq_1,t3_finseq_1,t35_finseq_1,t27_finseq_3,d4_finseq_4,d7_finseq_1,d3_finseq_1,t3_finseq_1,d4_finseq_4]),
    [file(boolmark,t8_boolmark),interesting(0.62)]).

fof(t1_boolmark,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( ( v1_funct_1(C)
                & v1_funct_2(C,A,B)
                & m2_relset_1(C,A,B) )
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ! [E] : 
                      ( m1_subset_1(E,B)
                     => ( v1_funct_1(k1_funct_4(C,k2_funcop_1(D,E)))
                        & v1_funct_2(k1_funct_4(C,k2_funcop_1(D,E)),A,B)
                        & m2_relset_1(k1_funct_4(C,k2_funcop_1(D,E)),A,B) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_funct_2,d1_funct_4,t19_funcop_1,d4_subset_1,t28_subset_1,d4_subset_1,t12_relset_1,t19_funcop_1,t13_xboole_1,t18_funct_4,t1_xboole_1,t46_zfmisc_1,d1_funct_2,t11_relset_1]),
    [file(boolmark,t1_boolmark),interesting(0.53)]).

fof(t6_boolmark,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m2_fraenkel(B,u1_petri(A),k6_margrel1,k1_boolmark(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_petri(A))
             => ! [D] : 
                  ( m1_subset_1(D,u1_petri(A))
                 => ( r2_hidden(D,k8_petri(A,k6_domain_1(u2_petri(A),C)))
                   => k8_funct_2(u1_petri(A),k6_margrel1,k2_boolmark(A,B,C),D) = k8_margrel1 ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t5_boolmark,d4_subset_1,t19_funcop_1,d1_funct_2,d1_funct_4,d1_funct_4,t4_xboole_1,t28_subset_1,d12_funct_1,d1_tarski]),
    [file(boolmark,t6_boolmark),interesting(0.45)]).

fof(t14_boolmark,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
         => ( v2_petri(B,A)
          <=> ! [C] : 
                ( m2_fraenkel(C,u1_petri(A),k6_margrel1,k1_boolmark(A))
               => ( k2_funct_2(u1_petri(A),k6_margrel1,C,B) = k6_domain_1(k6_margrel1,k7_margrel1)
                 => ! [D] : 
                      ( m2_finseq_1(D,u2_petri(A))
                     => ( r2_boolmark(A,C,D)
                       => k2_funct_2(u1_petri(A),k6_margrel1,k3_boolmark(A,C,D),B) = k6_domain_1(k6_margrel1,k7_margrel1) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_petri,d5_boolmark,t11_boolmark,t10_boolmark,d5_boolmark,t25_finseq_4,t56_finseq_1,t12_boolmark,d2_boolmark,t38_margrel1,t17_zfmisc_1,t63_xboole_1,t2_boolmark,t11_boolmark,t19_petri,t20_petri,t3_boolmark,t3_boolmark,t11_boolmark,s2_finseq_2,d5_petri,t7_subset_1,d4_subset_1,t19_funcop_1,d1_funct_4,t28_subset_1,t19_funcop_1,t1_xboole_1,t8_xboole_1,t18_funct_4,t1_xboole_1,d2_funct_2,t5_boolmark,t19_petri,t3_boolmark,t19_funcop_1,t144_relat_1,t1_xboole_1,d2_boolmark,t12_boolmark,t20_petri,t4_xboole_0,d3_xboole_0,t6_boolmark,t43_funct_2,t38_margrel1,d1_tarski,t13_boolmark]),
    [file(boolmark,t14_boolmark),interesting(0.30)]).

fof(l12_boolmark,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
         => ( ! [C] : 
                ( m2_fraenkel(C,u1_petri(A),k6_margrel1,k1_boolmark(A))
               => ( k2_funct_2(u1_petri(A),k6_margrel1,C,B) = k6_domain_1(k6_margrel1,k7_margrel1)
                 => ! [D] : 
                      ( m1_subset_1(D,u2_petri(A))
                     => ( r1_boolmark(A,C,D)
                       => k2_funct_2(u1_petri(A),k6_margrel1,k2_boolmark(A,C,D),B) = k6_domain_1(k6_margrel1,k7_margrel1) ) ) ) )
           => v2_petri(B,A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_petri,t7_subset_1,d4_subset_1,t19_funcop_1,d1_funct_4,t28_subset_1,t19_funcop_1,t1_xboole_1,t8_xboole_1,t18_funct_4,t1_xboole_1,d2_funct_2,t5_boolmark,t19_petri,t3_boolmark,t19_funcop_1,t144_relat_1,t1_xboole_1,d2_boolmark,t20_petri,t4_xboole_0,d3_xboole_0,t6_boolmark,t43_funct_2,t38_margrel1,d1_tarski]),
    [file(boolmark,l12_boolmark),interesting(0.18)]).

fof(d5_petri,definition,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(u1_petri(A)))
         => ( v2_petri(B,A)
          <=> m1_subset_1(k5_petri(A,B),k1_zfmisc_1(k6_petri(A,B))) ) ) ) ),
    file(petri,d5_petri),
    [interesting(0.00)]).

fof(d5_boolmark,definition,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m2_fraenkel(B,u1_petri(A),k6_margrel1,k1_boolmark(A))
         => ! [C] : 
              ( m2_finseq_1(C,u2_petri(A))
             => ! [D] : 
                  ( m2_fraenkel(D,u1_petri(A),k6_margrel1,k1_boolmark(A))
                 => ( ( C = k1_xboole_0
                     => ( D = k3_boolmark(A,B,C)
                      <=> D = B ) )
                    & ( C != k1_xboole_0
                     => ( D = k3_boolmark(A,B,C)
                      <=> ? [E] : 
                            ( m2_finseq_1(E,k1_boolmark(A))
                            & k3_finseq_1(C) = k3_finseq_1(E)
                            & D = k4_finseq_4(k5_numbers,k1_boolmark(A),E,k3_finseq_1(E))
                            & k4_finseq_4(k5_numbers,k1_boolmark(A),E,1) = k2_boolmark(A,B,k4_finseq_4(k5_numbers,u2_petri(A),C,1))
                            & ! [F] : 
                                ( m2_subset_1(F,k1_numbers,k5_numbers)
                               => ~ ( ~ r1_xreal_0(k3_finseq_1(C),F)
                                    & ~ r1_xreal_0(F,0)
                                    & k4_finseq_4(k5_numbers,k1_boolmark(A),E,k1_nat_1(F,1)) != k2_boolmark(A,k4_finseq_4(k5_numbers,k1_boolmark(A),E,F),k4_finseq_4(k5_numbers,u2_petri(A),C,k1_nat_1(F,1))) ) ) ) ) ) ) ) ) ) ) ),
    file(boolmark,d5_boolmark),
    [interesting(0.00)]).

fof(d4_boolmark,definition,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m2_fraenkel(B,u1_petri(A),k6_margrel1,k1_boolmark(A))
         => ! [C] : 
              ( m2_finseq_1(C,u2_petri(A))
             => ( r2_boolmark(A,B,C)
              <=> ~ ( C != k1_xboole_0
                    & ! [D] : 
                        ( m2_finseq_1(D,k1_boolmark(A))
                       => ~ ( k3_finseq_1(C) = k3_finseq_1(D)
                            & r1_boolmark(A,B,k4_finseq_4(k5_numbers,u2_petri(A),C,1))
                            & k4_finseq_4(k5_numbers,k1_boolmark(A),D,1) = k2_boolmark(A,B,k4_finseq_4(k5_numbers,u2_petri(A),C,1))
                            & ! [E] : 
                                ( m2_subset_1(E,k1_numbers,k5_numbers)
                               => ~ ( ~ r1_xreal_0(k3_finseq_1(C),E)
                                    & ~ r1_xreal_0(E,0)
                                    & ~ ( r1_boolmark(A,k4_finseq_4(k5_numbers,k1_boolmark(A),D,E),k4_finseq_4(k5_numbers,u2_petri(A),C,k1_nat_1(E,1)))
                                        & k4_finseq_4(k5_numbers,k1_boolmark(A),D,k1_nat_1(E,1)) = k2_boolmark(A,k4_finseq_4(k5_numbers,k1_boolmark(A),D,E),k4_finseq_4(k5_numbers,u2_petri(A),C,k1_nat_1(E,1))) ) ) ) ) ) ) ) ) ) ) ),
    file(boolmark,d4_boolmark),
    [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(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(t23_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( k2_xcmplx_0(A,B) = 0
           => ( A = 0
              & B = 0 ) ) ) ) ),
    file(nat_1,t23_nat_1),
    [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(t19_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( 0 != A
          & r1_xreal_0(A,0) ) ) ),
    file(nat_1,t19_nat_1),
    [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(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(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(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(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(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(d4_finseq_4,definition,(
    ! [A,B,C] : 
      ( ( v1_funct_1(C)
        & m2_relset_1(C,A,B) )
     => ! [D] : 
          ( r2_hidden(D,k1_relat_1(C))
         => k4_finseq_4(A,B,C,D) = k1_funct_1(C,D) ) ) ),
    file(finseq_4,d4_finseq_4),
    [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(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(t18_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => r1_xreal_0(0,A) ) ),
    file(nat_1,t18_nat_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(t60_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ! [B] : 
          ( v4_ordinal2(B)
         => ( ~ r1_xreal_0(B,A)
           => m2_subset_1(k6_xcmplx_0(B,1),k1_numbers,k5_numbers) ) ) ) ),
    file(nat_1,t60_nat_1),
    [interesting(0.00)]).

fof(t5_goboard2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_finseq_1(B,A)
         => ! [C] : 
              ( m2_finseq_1(C,A)
             => ! [D] : 
                  ( m2_subset_1(D,k1_numbers,k5_numbers)
                 => ( ( r1_xreal_0(1,D)
                      & r1_xreal_0(D,k3_finseq_1(C)) )
                   => k4_finseq_4(k5_numbers,A,k8_finseq_1(A,B,C),k1_nat_1(D,k3_finseq_1(B))) = k4_finseq_4(k5_numbers,A,C,D) ) ) ) ) ) ),
    file(goboard2,t5_goboard2),
    [interesting(0.00)]).

fof(t22_nat_1,theorem,(
    ! [A] : 
      ( v4_ordinal2(A)
     => ~ ( A != 0
          & ! [B] : 
              ( m2_subset_1(B,k1_numbers,k5_numbers)
             => A != k1_nat_1(B,1) ) ) ) ),
    file(nat_1,t22_nat_1),
    [interesting(0.00)]).

fof(t31_xreal_1,theorem,(
    ! [A] : 
      ( v1_xreal_0(A)
     => ! [B] : 
          ( v1_xreal_0(B)
         => ~ ( ~ r1_xreal_0(A,0)
              & r1_xreal_0(k2_xcmplx_0(B,A),B) ) ) ) ),
    file(xreal_1,t31_xreal_1),
    [interesting(0.00)]).

fof(t84_finseq_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_1(C,B)
             => ! [D] : 
                  ( m2_finseq_1(D,B)
                 => ( r2_hidden(A,k4_finseq_1(D))
                   => k4_finseq_4(k5_numbers,B,k8_finseq_1(B,C,D),k1_nat_1(k3_finseq_1(C),A)) = k4_finseq_4(k5_numbers,B,D,A) ) ) ) ) ) ),
    file(finseq_4,t84_finseq_4),
    [interesting(0.00)]).

fof(t83_finseq_4,theorem,(
    ! [A] : 
      ( m2_subset_1(A,k1_numbers,k5_numbers)
     => ! [B] : 
          ( ~ v1_xboole_0(B)
         => ! [C] : 
              ( m2_finseq_1(C,B)
             => ! [D] : 
                  ( m2_finseq_1(D,B)
                 => ( r2_hidden(A,k4_finseq_1(C))
                   => k4_finseq_4(k5_numbers,B,k8_finseq_1(B,C,D),A) = k4_finseq_4(k5_numbers,B,C,A) ) ) ) ) ) ),
    file(finseq_4,t83_finseq_4),
    [interesting(0.00)]).

fof(t25_finseq_4,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => k4_finseq_4(k5_numbers,A,k12_finseq_1(A,B),1) = B ) ) ),
    file(finseq_4,t25_finseq_4),
    [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(d2_boolmark,definition,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m2_fraenkel(B,u1_petri(A),k6_margrel1,k1_boolmark(A))
         => ! [C] : 
              ( m1_subset_1(C,u2_petri(A))
             => ( r1_boolmark(A,B,C)
              <=> r1_tarski(k2_funct_2(u1_petri(A),k6_margrel1,B,k7_petri(A,k6_domain_1(u2_petri(A),C))),k6_domain_1(k6_margrel1,k8_margrel1)) ) ) ) ) ),
    file(boolmark,d2_boolmark),
    [interesting(0.00)]).

fof(t38_margrel1,theorem,(
    k7_margrel1 != k8_margrel1 ),
    file(margrel1,t38_margrel1),
    [interesting(0.00)]).

fof(t17_zfmisc_1,theorem,(
    ! [A,B] : 
      ( A != B
     => r1_xboole_0(k1_tarski(A),k1_tarski(B)) ) ),
    file(zfmisc_1,t17_zfmisc_1),
    [interesting(0.00)]).

fof(t63_xboole_1,theorem,(
    ! [A,B,C] : 
      ( ( r1_tarski(A,B)
        & r1_xboole_0(B,C) )
     => r1_xboole_0(A,C) ) ),
    file(xboole_1,t63_xboole_1),
    [interesting(0.00)]).

fof(d7_xboole_0,definition,(
    ! [A,B] : 
      ( r1_xboole_0(A,B)
    <=> k3_xboole_0(A,B) = k1_xboole_0 ) ),
    file(xboole_0,d7_xboole_0),
    [interesting(0.00)]).

fof(t10_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ~ ( B != k1_xboole_0
          & ! [C] : 
              ( m1_subset_1(C,A)
             => ~ r2_hidden(C,B) ) ) ) ),
    file(subset_1,t10_subset_1),
    [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(t43_funct_2,theorem,(
    ! [A,B,C,D] : 
      ( ( v1_funct_1(D)
        & v1_funct_2(D,A,B)
        & m2_relset_1(D,A,B) )
     => ( B != k1_xboole_0
       => ! [E] : 
            ( ? [F] : 
                ( r2_hidden(F,A)
                & r2_hidden(F,C)
                & E = k1_funct_1(D,F) )
           => r2_hidden(E,k9_relat_1(D,C)) ) ) ) ),
    file(funct_2,t43_funct_2),
    [interesting(0.00)]).

fof(t19_petri,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_petri(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_petri(A)))
             => ( r2_hidden(B,k6_petri(A,C))
              <=> ~ r1_xboole_0(k7_petri(A,k6_domain_1(u2_petri(A),B)),C) ) ) ) ) ),
    file(petri,t19_petri),
    [interesting(0.00)]).

fof(t20_petri,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( m1_subset_1(B,u2_petri(A))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(u1_petri(A)))
             => ( r2_hidden(B,k5_petri(A,C))
              <=> ~ r1_xboole_0(k8_petri(A,k6_domain_1(u2_petri(A),B)),C) ) ) ) ) ),
    file(petri,t20_petri),
    [interesting(0.00)]).

fof(d1_funct_4,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ! [C] : 
              ( ( v1_relat_1(C)
                & v1_funct_1(C) )
             => ( C = k1_funct_4(A,B)
              <=> ( k1_relat_1(C) = k2_xboole_0(k1_relat_1(A),k1_relat_1(B))
                  & ! [D] : 
                      ( r2_hidden(D,k2_xboole_0(k1_relat_1(A),k1_relat_1(B)))
                     => ( ( r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(B,D) )
                        & ( ~ r2_hidden(D,k1_relat_1(B))
                         => k1_funct_1(C,D) = k1_funct_1(A,D) ) ) ) ) ) ) ) ) ),
    file(funct_4,d1_funct_4),
    [interesting(0.00)]).

fof(t19_funcop_1,theorem,(
    ! [A,B] : 
      ( k1_relat_1(k2_funcop_1(A,B)) = A
      & r1_tarski(k2_relat_1(k2_funcop_1(A,B)),k1_tarski(B)) ) ),
    file(funcop_1,t19_funcop_1),
    [interesting(0.00)]).

fof(t2_tarski,theorem,(
    ! [A,B] : 
      ( ! [C] : 
          ( r2_hidden(C,A)
        <=> r2_hidden(C,B) )
     => A = B ) ),
    file(tarski,t2_tarski),
    [interesting(0.00)]).

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

fof(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(t12_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( ~ r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(C,A) ) ) ) ),
    file(funct_4,t12_funct_4),
    [interesting(0.00)]).

fof(s2_finseq_2,theorem,
    ( ( p1_s2_finseq_2(k6_finseq_1(f1_s2_finseq_2))
      & ! [A] : 
          ( m2_finseq_1(A,f1_s2_finseq_2)
         => ! [B] : 
              ( m1_subset_1(B,f1_s2_finseq_2)
             => ( p1_s2_finseq_2(A)
               => p1_s2_finseq_2(k8_finseq_1(f1_s2_finseq_2,A,k12_finseq_1(f1_s2_finseq_2,B))) ) ) ) )
   => ! [A] : 
        ( m2_finseq_1(A,f1_s2_finseq_2)
       => p1_s2_finseq_2(A) ) ),
    file(finseq_2,s2_finseq_2),
    [interesting(0.00)]).

fof(t7_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( ! [D] : 
                ( m1_subset_1(D,A)
               => ( r2_hidden(D,B)
                 => r2_hidden(D,C) ) )
           => r1_tarski(B,C) ) ) ) ),
    file(subset_1,t7_subset_1),
    [interesting(0.00)]).

fof(d4_subset_1,definition,(
    ! [A] : k2_subset_1(A) = A ),
    file(subset_1,d4_subset_1),
    [interesting(0.00)]).

fof(t28_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k4_subset_1(A,B,k2_subset_1(A)) = k2_subset_1(A) ) ),
    file(subset_1,t28_subset_1),
    [interesting(0.00)]).

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

fof(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(t18_funct_4,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => r1_tarski(k2_relat_1(k1_funct_4(A,B)),k2_xboole_0(k2_relat_1(A),k2_relat_1(B))) ) ) ),
    file(funct_4,t18_funct_4),
    [interesting(0.00)]).

fof(d2_funct_2,definition,(
    ! [A,B,C] : 
      ( C = k1_funct_2(A,B)
    <=> ! [D] : 
          ( r2_hidden(D,C)
        <=> ? [E] : 
              ( v1_relat_1(E)
              & v1_funct_1(E)
              & D = E
              & k1_relat_1(E) = A
              & r1_tarski(k2_relat_1(E),B) ) ) ) ),
    file(funct_2,d2_funct_2),
    [interesting(0.00)]).

fof(t14_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(B))
           => k1_funct_1(k1_funct_4(C,B),A) = k1_funct_1(B,A) ) ) ) ),
    file(funct_4,t14_funct_4),
    [interesting(0.00)]).

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

fof(d1_xboole_0,definition,(
    ! [A] : 
      ( A = k1_xboole_0
    <=> ! [B] : ~ r2_hidden(B,A) ) ),
    file(xboole_0,d1_xboole_0),
    [interesting(0.00)]).

fof(t13_funct_4,theorem,(
    ! [A,B] : 
      ( ( v1_relat_1(B)
        & v1_funct_1(B) )
     => ! [C] : 
          ( ( v1_relat_1(C)
            & v1_funct_1(C) )
         => ( r2_hidden(A,k1_relat_1(k1_funct_4(B,C)))
          <=> ( r2_hidden(A,k1_relat_1(B))
              | r2_hidden(A,k1_relat_1(C)) ) ) ) ) ),
    file(funct_4,t13_funct_4),
    [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(t144_relat_1,theorem,(
    ! [A,B] : 
      ( v1_relat_1(B)
     => r1_tarski(k9_relat_1(B,A),k2_relat_1(B)) ) ),
    file(relat_1,t144_relat_1),
    [interesting(0.00)]).

fof(t4_xboole_0,theorem,(
    ! [A,B] : 
      ( ~ ( ~ r1_xboole_0(A,B)
          & ! [C] : ~ r2_hidden(C,k3_xboole_0(A,B)) )
      & ~ ( ? [C] : r2_hidden(C,k3_xboole_0(A,B))
          & r1_xboole_0(A,B) ) ) ),
    file(xboole_0,t4_xboole_0),
    [interesting(0.00)]).

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

fof(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(t12_relset_1,theorem,(
    ! [A,B,C] : 
      ( m2_relset_1(C,A,B)
     => ( r1_tarski(k1_relat_1(C),A)
        & r1_tarski(k2_relat_1(C),B) ) ) ),
    file(relset_1,t12_relset_1),
    [interesting(0.00)]).

fof(t13_xboole_1,theorem,(
    ! [A,B,C,D] : 
      ( ( r1_tarski(A,B)
        & r1_tarski(C,D) )
     => r1_tarski(k2_xboole_0(A,C),k2_xboole_0(B,D)) ) ),
    file(xboole_1,t13_xboole_1),
    [interesting(0.00)]).

fof(t46_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => k2_xboole_0(k1_tarski(A),B) = B ) ),
    file(zfmisc_1,t46_zfmisc_1),
    [interesting(0.00)]).

fof(t11_relset_1,theorem,(
    ! [A,B,C] : 
      ( v1_relat_1(C)
     => ( ( r1_tarski(k1_relat_1(C),A)
          & r1_tarski(k2_relat_1(C),B) )
       => m2_relset_1(C,A,B) ) ) ),
    file(relset_1,t11_relset_1),
    [interesting(0.00)]).

fof(t4_boolmark,theorem,(
    $true ),
    file(boolmark,t4_boolmark),
    [interesting(0.00)]).

fof(t7_boolmark,theorem,(
    ! [A] : 
      ( l1_petri(A)
     => ! [B] : 
          ( ( ~ v1_xboole_0(B)
            & m1_subset_1(B,k1_zfmisc_1(u1_petri(A))) )
         => ( v2_petri(B,A)
          <=> ! [C] : 
                ( m2_fraenkel(C,u1_petri(A),k6_margrel1,k1_boolmark(A))
               => ( k2_funct_2(u1_petri(A),k6_margrel1,C,B) = k6_domain_1(k6_margrel1,k7_margrel1)
                 => ! [D] : 
                      ( m1_subset_1(D,u2_petri(A))
                     => ( r1_boolmark(A,C,D)
                       => k2_funct_2(u1_petri(A),k6_margrel1,k2_boolmark(A,C,D),B) = k6_domain_1(k6_margrel1,k7_margrel1) ) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_petri,d2_boolmark,t38_margrel1,t17_zfmisc_1,t63_xboole_1,t2_boolmark,t19_petri,t20_petri,t3_boolmark,t3_boolmark,l12_boolmark]),
    [file(boolmark,t7_boolmark),interesting(0.00)]).

fof(t9_boolmark,theorem,(
    $true ),
    file(boolmark,t9_boolmark),
    [interesting(0.00)]).