fof(t4_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( r2_hidden(C,B)
               => r1_setfam_1(C,k3_bvfunc_2(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_eqrel_1,d3_tarski,d6_eqrel_1,d4_tarski,d3_bvfunc_2,d2_bvfunc_2,d1_partit1,d4_tarski,d3_xboole_0,d7_xboole_0,d6_eqrel_1,t92_zfmisc_1,d2_setfam_1]),
    [file(bvfunc_2,t4_bvfunc_2),interesting(1.00)]).

fof(t2_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ~ ( B != k1_xboole_0
                  & ! [D] : 
                      ( m1_subset_1(D,k1_zfmisc_1(A))
                     => ~ ( r2_hidden(C,D)
                          & r1_bvfunc_2(A,B,D) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_xboole_0,d3_partit1,d6_eqrel_1,t9_partit1,s7_domain_1,d1_setfam_1,d10_setfam_1,t10_partit1,d1_partit1,t95_zfmisc_1,d3_tarski,d10_setfam_1,d1_setfam_1,d10_xboole_0,t95_zfmisc_1,d5_subset_1,d4_xboole_0,t44_subset_1,d7_xboole_0,t12_partit1,d3_tarski,d10_setfam_1,d1_setfam_1,t26_xboole_1,t3_xboole_1,t26_xboole_1,t3_xboole_1,d1_xboole_0,t92_zfmisc_1,d1_xboole_0,d2_bvfunc_2,d10_setfam_1]),
    [file(bvfunc_2,t2_bvfunc_2),interesting(0.94)]).

fof(t3_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( r2_hidden(C,B)
               => r1_setfam_1(k2_bvfunc_2(A,B),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_bvfunc_2,d5_funct_1,d10_setfam_1,t4_setfam_1,d2_setfam_1]),
    [file(bvfunc_2,t3_bvfunc_2),interesting(0.85)]).

fof(t11_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => r1_bvfunc_1(A,k6_bvfunc_2(A,C,B,D),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d1_t_1topsp]),
    [file(bvfunc_2,t11_bvfunc_2),interesting(0.67)]).

fof(t12_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => r1_bvfunc_1(A,C,k7_bvfunc_2(A,C,B,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d1_t_1topsp,d20_bvfunc_1]),
    [file(bvfunc_2,t12_bvfunc_2),interesting(0.66)]).

fof(t41_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k9_bvfunc_1(A,k7_bvfunc_2(A,D,B,E),C),k7_bvfunc_2(A,k9_bvfunc_1(A,D,C),B,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t40_bvfunc_2]),
    [file(bvfunc_2,t41_bvfunc_2),interesting(0.65)]).

fof(t28_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k6_bvfunc_2(A,k6_valuat_1(A,D,C),B,E) = k6_valuat_1(A,k6_bvfunc_2(A,D,B,E),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t27_bvfunc_2]),
    [file(bvfunc_2,t28_bvfunc_2),interesting(0.64)]).

fof(t37_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k7_bvfunc_2(A,k6_valuat_1(A,D,C),B,E) = k6_valuat_1(A,k7_bvfunc_2(A,D,B,E),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t36_bvfunc_2]),
    [file(bvfunc_2,t37_bvfunc_2),interesting(0.64)]).

fof(t31_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,D,C),B,E),k9_bvfunc_1(A,k6_bvfunc_2(A,D,B,E),C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t30_bvfunc_2]),
    [file(bvfunc_2,t31_bvfunc_2),interesting(0.63)]).

fof(t35_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k7_bvfunc_2(A,k8_bvfunc_1(A,D,C),B,E) = k8_bvfunc_1(A,k7_bvfunc_2(A,D,B,E),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t34_bvfunc_2]),
    [file(bvfunc_2,t35_bvfunc_2),interesting(0.61)]).

fof(t5_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => r2_bvfunc_1(A,k6_bvfunc_2(A,C,B,D),k5_bvfunc_2(A,D,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_bvfunc_1,d1_t_1topsp,d6_eqrel_1,d1_t_1topsp,t3_xboole_0,d19_bvfunc_1,d19_bvfunc_1,d19_bvfunc_1,d19_bvfunc_1]),
    [file(bvfunc_2,t5_bvfunc_2),interesting(0.60)]).

fof(t6_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => r2_bvfunc_1(A,k7_bvfunc_2(A,C,B,D),k5_bvfunc_2(A,D,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d18_bvfunc_1,d1_t_1topsp,d6_eqrel_1,d1_t_1topsp,t3_xboole_0,d20_bvfunc_1,d20_bvfunc_1,d20_bvfunc_1,d20_bvfunc_1]),
    [file(bvfunc_2,t6_bvfunc_2),interesting(0.59)]).

fof(t33_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k15_bvfunc_1(A,D,C),B,E),k15_bvfunc_1(A,k6_bvfunc_2(A,D,B,E),C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t32_bvfunc_2]),
    [file(bvfunc_2,t33_bvfunc_2),interesting(0.58)]).

fof(t40_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k9_bvfunc_1(A,C,k7_bvfunc_2(A,D,B,E)),k7_bvfunc_2(A,k9_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,d15_bvfunc_1,d8_bvfunc_1,d2_binarith,t39_margrel1,d1_t_1topsp,t41_margrel1,t49_margrel1,t45_margrel1,t41_margrel1,d20_bvfunc_1,t43_margrel1,d18_bvfunc_1,d8_bvfunc_1,d2_binarith,t50_margrel1,t19_binarith,d20_bvfunc_1,t45_margrel1,t41_margrel1,d20_bvfunc_1,t43_margrel1,t43_margrel1,d8_bvfunc_1,d2_binarith,t50_margrel1,t19_binarith,d20_bvfunc_1,t7_binarith]),
    [file(bvfunc_2,t40_bvfunc_2),interesting(0.54)]).

fof(t25_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k6_bvfunc_2(A,k8_bvfunc_1(A,D,C),B,E) = k8_bvfunc_1(A,k6_bvfunc_2(A,D,B,E),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t24_bvfunc_2]),
    [file(bvfunc_2,t25_bvfunc_2),interesting(0.53)]).

fof(t27_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k6_bvfunc_2(A,k6_valuat_1(A,C,D),B,E) = k6_valuat_1(A,C,k6_bvfunc_2(A,D,B,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d6_valuat_1,t45_margrel1,d6_valuat_1,t45_margrel1,d6_valuat_1,d19_bvfunc_1,d1_t_1topsp,t45_margrel1,d15_bvfunc_1,d6_valuat_1,t45_margrel1,d19_bvfunc_1,t43_margrel1,d1_t_1topsp,d18_bvfunc_1,d6_valuat_1,t45_margrel1,d19_bvfunc_1,t18_bvfunc_1]),
    [file(bvfunc_2,t27_bvfunc_2),interesting(0.53)]).

fof(t30_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k9_bvfunc_1(A,C,D),B,E),k9_bvfunc_1(A,C,k6_bvfunc_2(A,D,B,E))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t41_margrel1,d8_bvfunc_2,d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d1_t_1topsp,d8_bvfunc_1,t45_margrel1,d8_bvfunc_1,d2_binarith,t7_binarith,t43_margrel1,d19_bvfunc_1,d18_bvfunc_1,t49_margrel1,d2_binarith,t50_margrel1,t7_binarith,t45_margrel1,d19_bvfunc_1,d18_bvfunc_1,t43_margrel1,t49_margrel1,d2_binarith,t50_margrel1,t7_binarith,d18_bvfunc_1,t43_margrel1,t43_margrel1,d8_bvfunc_1,d2_binarith,t7_binarith,t43_margrel1]),
    [file(bvfunc_2,t30_bvfunc_2),interesting(0.53)]).

fof(t36_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k7_bvfunc_2(A,k6_valuat_1(A,C,D),B,E) = k6_valuat_1(A,C,k7_bvfunc_2(A,D,B,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,d15_bvfunc_1,d20_bvfunc_1,t43_margrel1,d6_valuat_1,t45_margrel1,d1_t_1topsp,d20_bvfunc_1,d18_bvfunc_1,d6_valuat_1,t45_margrel1,d15_bvfunc_1,d6_valuat_1,t45_margrel1,d1_t_1topsp,d20_bvfunc_1,t43_margrel1,d18_bvfunc_1,d6_valuat_1,t45_margrel1,d20_bvfunc_1,t18_bvfunc_1]),
    [file(bvfunc_2,t36_bvfunc_2),interesting(0.53)]).

fof(t34_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k7_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E) = k8_bvfunc_1(A,C,k7_bvfunc_2(A,D,B,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,d15_bvfunc_1,d20_bvfunc_1,t43_margrel1,d7_bvfunc_1,t39_margrel1,d1_t_1topsp,d7_bvfunc_1,d18_bvfunc_1,t19_binarith,d20_bvfunc_1,t19_binarith,t7_binarith,d15_bvfunc_1,d7_bvfunc_1,t39_margrel1,d1_t_1topsp,d7_bvfunc_1,t19_binarith,d20_bvfunc_1,d20_bvfunc_1,t43_margrel1,d7_bvfunc_1,t19_binarith,d20_bvfunc_1,t7_binarith,t18_bvfunc_1]),
    [file(bvfunc_2,t34_bvfunc_2),interesting(0.51)]).

fof(t18_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k9_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)),k7_bvfunc_2(A,k9_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d8_bvfunc_1,d2_binarith,t39_margrel1,t41_margrel1,t49_margrel1,t45_margrel1,t41_margrel1,t43_margrel1,d20_bvfunc_1,t43_margrel1,d20_bvfunc_1,t43_margrel1,d8_bvfunc_1,d2_binarith,t50_margrel1,t19_binarith,d20_bvfunc_1,t45_margrel1,t41_margrel1,t43_margrel1,d20_bvfunc_1,t43_margrel1,d20_bvfunc_1,t43_margrel1,d8_bvfunc_1,d2_binarith,t50_margrel1,t19_binarith,d20_bvfunc_1,t7_binarith]),
    [file(bvfunc_2,t18_bvfunc_2),interesting(0.50)]).

fof(t20_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k5_valuat_1(A,k6_bvfunc_2(A,C,B,D)) = k7_bvfunc_2(A,k5_valuat_1(A,C),B,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_valuat_1,t41_margrel1,t43_margrel1,d19_bvfunc_1,d20_bvfunc_1,d5_valuat_1,t41_margrel1,d19_bvfunc_1,d20_bvfunc_1,d5_valuat_1,t41_margrel1,d5_valuat_1,t43_margrel1,t41_margrel1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_2,t20_bvfunc_2),interesting(0.49)]).

fof(t21_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k5_valuat_1(A,k7_bvfunc_2(A,C,B,D)) = k6_bvfunc_2(A,k5_valuat_1(A,C),B,D) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_valuat_1,t41_margrel1,t43_margrel1,d20_bvfunc_1,t41_margrel1,d5_valuat_1,d19_bvfunc_1,d19_bvfunc_1,d20_bvfunc_1,d5_valuat_1,t41_margrel1,t43_margrel1,d5_valuat_1,t41_margrel1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_2,t21_bvfunc_2),interesting(0.49)]).

fof(t32_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k15_bvfunc_1(A,C,D),B,E),k15_bvfunc_1(A,C,k6_bvfunc_2(A,D,B,E))) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,t41_margrel1,d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d1_t_1topsp,d19_bvfunc_1,t49_margrel1,d12_bvfunc_1,d2_binarith,t7_binarith,t41_margrel1,t43_margrel1,t49_margrel1,d12_bvfunc_1,d2_binarith,t50_margrel1,t7_binarith,t41_margrel1,t43_margrel1,t43_margrel1,t49_margrel1,d12_bvfunc_1,d2_binarith,t50_margrel1,t7_binarith,t41_margrel1,t43_margrel1,d19_bvfunc_1,d18_bvfunc_1,t43_margrel1,t49_margrel1,d12_bvfunc_1,d2_binarith,t7_binarith,t41_margrel1]),
    [file(bvfunc_2,t32_bvfunc_2),interesting(0.49)]).

fof(t9_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k6_bvfunc_2(A,k18_bvfunc_1(A),B,D) = k18_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_t_1topsp,d13_bvfunc_1,t43_margrel1,d19_bvfunc_1,d13_bvfunc_1]),
    [file(bvfunc_2,t9_bvfunc_2),interesting(0.49)]).

fof(t10_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k7_bvfunc_2(A,k18_bvfunc_1(A),B,D) = k18_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_bvfunc_1,t43_margrel1,d20_bvfunc_1,d13_bvfunc_1]),
    [file(bvfunc_2,t10_bvfunc_2),interesting(0.48)]).

fof(t8_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k7_bvfunc_2(A,k19_bvfunc_1(A),B,D) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_t_1topsp,d14_bvfunc_1,d20_bvfunc_1,d14_bvfunc_1]),
    [file(bvfunc_2,t8_bvfunc_2),interesting(0.48)]).

fof(t7_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k6_bvfunc_2(A,k19_bvfunc_1(A),B,D) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d19_bvfunc_1,d14_bvfunc_1]),
    [file(bvfunc_2,t7_bvfunc_2),interesting(0.47)]).

fof(t39_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),D),k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d11_bvfunc_1,t39_margrel1,d1_t_1topsp,t41_margrel1,t43_margrel1,d20_bvfunc_1,d11_bvfunc_1,t43_margrel1,t41_margrel1,t19_binarith,d20_bvfunc_1,d11_bvfunc_1,t19_binarith,d20_bvfunc_1,t7_binarith]),
    [file(bvfunc_2,t39_bvfunc_2),interesting(0.45)]).

fof(t24_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k6_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E) = k8_bvfunc_1(A,C,k6_bvfunc_2(A,D,B,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,d7_bvfunc_1,d19_bvfunc_1,t19_binarith,d7_bvfunc_1,t19_binarith,d19_bvfunc_1,d1_t_1topsp,t19_binarith,d7_bvfunc_1,t19_binarith,d19_bvfunc_1,d19_bvfunc_1,d1_t_1topsp,d18_bvfunc_1,t43_margrel1,t43_margrel1,d7_bvfunc_1,t7_binarith,t43_margrel1,d19_bvfunc_1,d18_bvfunc_1,t7_binarith,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_2,t24_bvfunc_2),interesting(0.44)]).

fof(t17_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(k1_bvfunc_2(A)))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k7_bvfunc_2(A,k6_valuat_1(A,B,C),D,E),k6_valuat_1(A,k7_bvfunc_2(A,B,D,E),k7_bvfunc_2(A,C,D,E))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d20_bvfunc_1,t43_margrel1,d6_valuat_1,t45_margrel1,d20_bvfunc_1,d6_valuat_1,d20_bvfunc_1,t45_margrel1]),
    [file(bvfunc_2,t17_bvfunc_2),interesting(0.43)]).

fof(t29_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k6_valuat_1(A,C,D),B,E),k6_valuat_1(A,k7_bvfunc_2(A,C,B,E),D)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d6_valuat_1,t45_margrel1,d1_t_1topsp,d6_valuat_1,d20_bvfunc_1,t45_margrel1]),
    [file(bvfunc_2,t29_bvfunc_2),interesting(0.43)]).

fof(t15_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E),k14_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E))) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d11_bvfunc_1,d19_bvfunc_1,d11_bvfunc_1,t19_binarith,d11_bvfunc_1,t43_margrel1,t41_margrel1,t7_binarith,t43_margrel1,d19_bvfunc_1,t19_binarith,d19_bvfunc_1,t41_margrel1,t19_binarith]),
    [file(bvfunc_2,t15_bvfunc_2),interesting(0.42)]).

fof(t19_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)),k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d11_bvfunc_1,t39_margrel1,d1_t_1topsp,t41_margrel1,t43_margrel1,d20_bvfunc_1,d11_bvfunc_1,t43_margrel1,t41_margrel1,t19_binarith,d20_bvfunc_1,d20_bvfunc_1,t43_margrel1,d11_bvfunc_1,t19_binarith,d20_bvfunc_1,t7_binarith]),
    [file(bvfunc_2,t19_bvfunc_2),interesting(0.42)]).

fof(t38_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k14_bvfunc_1(A,C,k7_bvfunc_2(A,D,B,E)),k7_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d11_bvfunc_1,t39_margrel1,d1_t_1topsp,d11_bvfunc_1,t19_binarith,d20_bvfunc_1,d20_bvfunc_1,t43_margrel1,d11_bvfunc_1,t19_binarith,d20_bvfunc_1,t7_binarith]),
    [file(bvfunc_2,t38_bvfunc_2),interesting(0.41)]).

fof(t14_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => r1_bvfunc_1(A,k8_bvfunc_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)),k6_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d15_bvfunc_1,d7_bvfunc_1,t39_margrel1,d19_bvfunc_1,t43_margrel1,d7_bvfunc_1,t19_binarith,d19_bvfunc_1,d19_bvfunc_1,t43_margrel1,d7_bvfunc_1,t19_binarith,d19_bvfunc_1,t7_binarith]),
    [file(bvfunc_2,t14_bvfunc_2),interesting(0.39)]).

fof(t22_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k6_bvfunc_2(A,k14_bvfunc_1(A,C,D),B,E) = k14_bvfunc_1(A,C,k6_bvfunc_2(A,D,B,E)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d1_t_1topsp,d11_bvfunc_1,d19_bvfunc_1,t19_binarith,t19_binarith,d18_bvfunc_1,t43_margrel1,t41_margrel1,t43_margrel1,d11_bvfunc_1,t41_margrel1,t7_binarith,t43_margrel1,d15_bvfunc_1,d11_bvfunc_1,t39_margrel1,d19_bvfunc_1,t43_margrel1,d11_bvfunc_1,t19_binarith,d19_bvfunc_1,d1_t_1topsp,d11_bvfunc_1,d18_bvfunc_1,t19_binarith,d19_bvfunc_1,t7_binarith,t18_bvfunc_1]),
    [file(bvfunc_2,t22_bvfunc_2),interesting(0.38)]).

fof(t23_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => k6_bvfunc_2(A,k14_bvfunc_1(A,D,C),B,E) = k14_bvfunc_1(A,k7_bvfunc_2(A,D,B,E),C) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d1_t_1topsp,d11_bvfunc_1,t19_binarith,d18_bvfunc_1,d11_bvfunc_1,t43_margrel1,t41_margrel1,t7_binarith,t43_margrel1,d20_bvfunc_1,t41_margrel1,t19_binarith,d15_bvfunc_1,d11_bvfunc_1,t39_margrel1,d1_t_1topsp,d11_bvfunc_1,d18_bvfunc_1,t19_binarith,d19_bvfunc_1,t41_margrel1,d20_bvfunc_1,t43_margrel1,d11_bvfunc_1,t43_margrel1,t41_margrel1,t19_binarith,d19_bvfunc_1,t7_binarith,t39_margrel1,t18_bvfunc_1]),
    [file(bvfunc_2,t23_bvfunc_2),interesting(0.34)]).

fof(t26_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => ( r3_bvfunc_2(A,C,B,E)
                       => r1_bvfunc_1(A,k6_bvfunc_2(A,k8_bvfunc_1(A,D,C),B,E),k8_bvfunc_1(A,k7_bvfunc_2(A,D,B,E),C)) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d8_bvfunc_2,d15_bvfunc_1,d19_bvfunc_1,t43_margrel1,d7_bvfunc_1,t39_margrel1,t7_binarith,d1_t_1topsp,d7_bvfunc_1,t19_binarith,d20_bvfunc_1,t19_binarith,d1_t_1topsp,d18_bvfunc_1]),
    [file(bvfunc_2,t26_bvfunc_2),interesting(0.26)]).

fof(d13_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( B = k18_bvfunc_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => k1_funct_1(B,C) = k7_margrel1 ) ) ) ) ),
    file(bvfunc_1,d13_bvfunc_1),
    [interesting(0.00)]).

fof(t43_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A != k8_margrel1
      <=> A = k7_margrel1 ) ) ),
    file(margrel1,t43_margrel1),
    [interesting(0.00)]).

fof(d20_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k24_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => ( ( ? [F] : 
                                ( m1_subset_1(F,A)
                                & r2_hidden(F,k22_bvfunc_1(A,E,C))
                                & k1_funct_1(B,F) = k8_margrel1 )
                           => k1_funct_1(D,E) = k8_margrel1 )
                          & ( ! [F] : 
                                ( m1_subset_1(F,A)
                               => ~ ( r2_hidden(F,k22_bvfunc_1(A,E,C))
                                    & k1_funct_1(B,F) = k8_margrel1 ) )
                           => k1_funct_1(D,E) = k7_margrel1 ) ) ) ) ) ) ) ) ),
    file(bvfunc_1,d20_bvfunc_1),
    [interesting(0.00)]).

fof(d15_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( r1_bvfunc_1(A,B,C)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => ( k1_funct_1(B,D) = k8_margrel1
                     => k1_funct_1(C,D) = k8_margrel1 ) ) ) ) ) ) ),
    file(bvfunc_1,d15_bvfunc_1),
    [interesting(0.00)]).

fof(d19_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k23_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => ( ( ! [F] : 
                                ( m1_subset_1(F,A)
                               => ( r2_hidden(F,k22_bvfunc_1(A,E,C))
                                 => k1_funct_1(B,F) = k8_margrel1 ) )
                           => k1_funct_1(D,E) = k8_margrel1 )
                          & ( ? [F] : 
                                ( m1_subset_1(F,A)
                                & r2_hidden(F,k22_bvfunc_1(A,E,C))
                                & k1_funct_1(B,F) != k8_margrel1 )
                           => k1_funct_1(D,E) = k7_margrel1 ) ) ) ) ) ) ) ) ),
    file(bvfunc_1,d19_bvfunc_1),
    [interesting(0.00)]).

fof(d1_t_1topsp,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,A)
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ! [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                 => ( D = k1_t_1topsp(A,B,C)
                  <=> ( r2_hidden(B,D)
                      & r2_hidden(D,C) ) ) ) ) ) ) ),
    file(t_1topsp,d1_t_1topsp),
    [interesting(0.00)]).

fof(t42_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k23_bvfunc_1(A,k6_valuat_1(A,B,C),D) = k6_valuat_1(A,k23_bvfunc_1(A,B,D),k23_bvfunc_1(A,C,D)) ) ) ) ) ),
    file(bvfunc_1,t42_bvfunc_1),
    [interesting(0.00)]).

fof(t13_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => k6_bvfunc_2(A,k6_valuat_1(A,C,D),B,E) = k6_valuat_1(A,k6_bvfunc_2(A,C,B,E),k6_bvfunc_2(A,D,B,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t42_bvfunc_1]),
    [file(bvfunc_2,t13_bvfunc_2),interesting(0.00)]).

fof(d7_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k8_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k3_binarith(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) ),
    file(bvfunc_1,d7_bvfunc_1),
    [interesting(0.00)]).

fof(t39_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A = k7_margrel1
        | A = k8_margrel1 ) ) ),
    file(margrel1,t39_margrel1),
    [interesting(0.00)]).

fof(t19_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k8_margrel1) = k8_margrel1 ) ),
    file(binarith,t19_binarith),
    [interesting(0.00)]).

fof(t7_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k7_margrel1) = A ) ),
    file(binarith,t7_binarith),
    [interesting(0.00)]).

fof(d11_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k14_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k1_binarith(k9_margrel1(k1_funct_1(B,E)),k1_funct_1(C,E)) ) ) ) ) ) ) ),
    file(bvfunc_1,d11_bvfunc_1),
    [interesting(0.00)]).

fof(t41_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( ( A = k7_margrel1
         => k9_margrel1(A) = k8_margrel1 )
        & ( k9_margrel1(A) = k8_margrel1
         => A = k7_margrel1 )
        & ( A = k8_margrel1
         => k9_margrel1(A) = k7_margrel1 )
        & ( k9_margrel1(A) = k7_margrel1
         => A = k8_margrel1 ) ) ) ),
    file(margrel1,t41_margrel1),
    [interesting(0.00)]).

fof(t43_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => k24_bvfunc_1(A,k8_bvfunc_1(A,B,C),D) = k8_bvfunc_1(A,k24_bvfunc_1(A,B,D),k24_bvfunc_1(A,C,D)) ) ) ) ) ),
    file(bvfunc_1,t43_bvfunc_1),
    [interesting(0.00)]).

fof(t16_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ! [E] : 
                      ( m1_eqrel_1(E,A)
                     => k7_bvfunc_2(A,k8_bvfunc_1(A,C,D),B,E) = k8_bvfunc_1(A,k7_bvfunc_2(A,C,B,E),k7_bvfunc_2(A,D,B,E)) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t43_bvfunc_1]),
    [file(bvfunc_2,t16_bvfunc_2),interesting(0.00)]).

fof(d6_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k6_valuat_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k12_margrel1(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) ),
    file(valuat_1,d6_valuat_1),
    [interesting(0.00)]).

fof(t45_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ( ( k10_margrel1(A,B) = k8_margrel1
             => ( A = k8_margrel1
                & B = k8_margrel1 ) )
            & ( ( A = k8_margrel1
                & B = k8_margrel1 )
             => k10_margrel1(A,B) = k8_margrel1 )
            & ~ ( k10_margrel1(A,B) = k7_margrel1
                & A != k7_margrel1
                & B != k7_margrel1 )
            & ( ( A = k7_margrel1
                | B = k7_margrel1 )
             => k10_margrel1(A,B) = k7_margrel1 ) ) ) ) ),
    file(margrel1,t45_margrel1),
    [interesting(0.00)]).

fof(d8_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k9_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k4_binarith(k8_funct_2(A,k6_margrel1,B,E),k8_funct_2(A,k6_margrel1,C,E)) ) ) ) ) ) ) ),
    file(bvfunc_1,d8_bvfunc_1),
    [interesting(0.00)]).

fof(d2_binarith,definition,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k2_binarith(A,B) = k1_binarith(k10_margrel1(k9_margrel1(A),B),k10_margrel1(A,k9_margrel1(B))) ) ) ),
    file(binarith,d2_binarith),
    [interesting(0.00)]).

fof(t49_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(k7_margrel1,A) = k7_margrel1 ) ),
    file(margrel1,t49_margrel1),
    [interesting(0.00)]).

fof(t50_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(k8_margrel1,A) = A ) ),
    file(margrel1,t50_margrel1),
    [interesting(0.00)]).

fof(s2_partfun2,theorem,(
    ? [A] : 
      ( v1_funct_1(A)
      & m2_relset_1(A,f1_s2_partfun2,f2_s2_partfun2)
      & ! [B] : 
          ( m1_subset_1(B,f1_s2_partfun2)
         => ( r2_hidden(B,k4_relset_1(f1_s2_partfun2,f2_s2_partfun2,A))
          <=> p1_s2_partfun2(B) ) )
      & ! [B] : 
          ( m1_subset_1(B,f1_s2_partfun2)
         => ( r2_hidden(B,k4_relset_1(f1_s2_partfun2,f2_s2_partfun2,A))
           => k4_finseq_4(f1_s2_partfun2,f2_s2_partfun2,A,B) = f3_s2_partfun2(B) ) ) ) ),
    file(partfun2,s2_partfun2),
    [interesting(0.00)]).

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

fof(d10_xboole_0,definition,(
    ! [A,B] : 
      ( A = B
    <=> ( r1_tarski(A,B)
        & r1_tarski(B,A) ) ) ),
    file(xboole_0,d10_xboole_0),
    [interesting(0.00)]).

fof(d3_partit1,definition,(
    ! [A,B] : 
      ( B = k1_partit1(A)
    <=> ! [C] : 
          ( r2_hidden(C,B)
        <=> m1_eqrel_1(C,A) ) ) ),
    file(partit1,d3_partit1),
    [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(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(d10_setfam_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( B != k1_xboole_0
         => k8_setfam_1(A,B) = k6_setfam_1(A,B) )
        & ( B = k1_xboole_0
         => k8_setfam_1(A,B) = A ) ) ) ),
    file(setfam_1,d10_setfam_1),
    [interesting(0.00)]).

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

fof(t1_bvfunc_2,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_partit1(A)))
         => ! [C] : 
              ( m1_subset_1(C,A)
             => ? [D] : 
                  ( m1_subset_1(D,k1_zfmisc_1(A))
                  & r2_hidden(C,D)
                  & ? [E] : 
                      ( v1_relat_1(E)
                      & v1_funct_1(E)
                      & ? [F] : 
                          ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(A)))
                          & k1_relat_1(E) = B
                          & k2_relat_1(E) = F
                          & ! [G] : 
                              ( r2_hidden(G,B)
                             => r2_hidden(k1_funct_1(E,G),G) )
                          & D = k8_setfam_1(A,F)
                          & D != k1_xboole_0 ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s2_partfun2,d3_tarski,d3_tarski,d10_xboole_0,d3_partit1,d4_finseq_4,d4_finseq_4,d1_t_1topsp,d5_funct_1,d10_setfam_1,d1_setfam_1,d10_setfam_1]),
    [file(bvfunc_2,t1_bvfunc_2),interesting(0.00)]).

fof(d5_valuat_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ( C = k5_valuat_1(A,B)
              <=> ! [D] : 
                    ( m1_subset_1(D,A)
                   => k8_funct_2(A,k6_margrel1,C,D) = k11_margrel1(k8_funct_2(A,k6_margrel1,B,D)) ) ) ) ) ) ),
    file(valuat_1,d5_valuat_1),
    [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(t9_funct_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( ( k1_relat_1(A) = k1_relat_1(B)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(A,C) = k1_funct_1(B,C) ) )
           => A = B ) ) ) ),
    file(funct_1,t9_funct_1),
    [interesting(0.00)]).

fof(d8_bvfunc_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_bvfunc_2(A)))
             => ! [D] : 
                  ( m1_eqrel_1(D,A)
                 => ( r3_bvfunc_2(A,B,C,D)
                  <=> r2_bvfunc_1(A,B,k5_bvfunc_2(A,D,C)) ) ) ) ) ) ),
    file(bvfunc_2,d8_bvfunc_2),
    [interesting(0.00)]).

fof(d18_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( r2_bvfunc_1(A,B,C)
              <=> ! [D] : 
                    ( r2_hidden(D,C)
                   => ! [E,F] : 
                        ( ( r2_hidden(E,D)
                          & r2_hidden(F,D) )
                       => k1_funct_1(B,E) = k1_funct_1(B,F) ) ) ) ) ) ) ),
    file(bvfunc_1,d18_bvfunc_1),
    [interesting(0.00)]).

fof(t18_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( ( ( r1_bvfunc_1(A,B,C)
                        & r1_bvfunc_1(A,C,B) )
                     => B = C )
                    & ( ( r1_bvfunc_1(A,B,C)
                        & r1_bvfunc_1(A,C,D) )
                     => r1_bvfunc_1(A,B,D) ) ) ) ) ) ) ),
    file(bvfunc_1,t18_bvfunc_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(d6_eqrel_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(k1_zfmisc_1(A)))
     => ( ( A != k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> ( k5_setfam_1(A,B) = A
              & ! [C] : 
                  ( m1_subset_1(C,k1_zfmisc_1(A))
                 => ( r2_hidden(C,B)
                   => ( C != k1_xboole_0
                      & ! [D] : 
                          ( m1_subset_1(D,k1_zfmisc_1(A))
                         => ~ ( r2_hidden(D,B)
                              & C != D
                              & ~ r1_xboole_0(C,D) ) ) ) ) ) ) ) )
        & ( A = k1_xboole_0
         => ( m1_eqrel_1(B,A)
          <=> B = k1_xboole_0 ) ) ) ) ),
    file(eqrel_1,d6_eqrel_1),
    [interesting(0.00)]).

fof(t9_partit1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => r1_partit1(A,B,A) ) ) ),
    file(partit1,t9_partit1),
    [interesting(0.00)]).

fof(s7_domain_1,theorem,(
    m1_subset_1(a_0_0_domain_1,k1_zfmisc_1(f1_s7_domain_1)) ),
    file(domain_1,s7_domain_1),
    [interesting(0.00)]).

fof(t10_partit1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(k1_zfmisc_1(A)))
             => ( ! [D] : 
                    ( r2_hidden(D,C)
                   => r1_partit1(A,B,D) )
               => ( k8_setfam_1(A,C) = k1_xboole_0
                  | r1_partit1(A,B,k8_setfam_1(A,C)) ) ) ) ) ) ),
    file(partit1,t10_partit1),
    [interesting(0.00)]).

fof(d1_partit1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( r1_partit1(A,B,C)
            <=> ? [D] : 
                  ( r1_tarski(D,B)
                  & D != k1_xboole_0
                  & C = k3_tarski(D) ) ) ) ) ),
    file(partit1,d1_partit1),
    [interesting(0.00)]).

fof(t95_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_tarski(A),k3_tarski(B)) ) ),
    file(zfmisc_1,t95_zfmisc_1),
    [interesting(0.00)]).

fof(d5_subset_1,definition,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => k3_subset_1(A,B) = k4_xboole_0(A,B) ) ),
    file(subset_1,d5_subset_1),
    [interesting(0.00)]).

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

fof(t44_subset_1,theorem,(
    ! [A,B] : 
      ( m1_subset_1(B,k1_zfmisc_1(A))
     => ! [C] : 
          ( m1_subset_1(C,k1_zfmisc_1(A))
         => ( r1_xboole_0(B,k3_subset_1(A,C))
          <=> r1_tarski(B,C) ) ) ) ),
    file(subset_1,t44_subset_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(t12_partit1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_eqrel_1(B,A)
         => ! [C] : 
              ( m1_subset_1(C,k1_zfmisc_1(A))
             => ( r1_partit1(A,B,C)
               => ( C = A
                  | r1_partit1(A,B,k3_subset_1(A,C)) ) ) ) ) ) ),
    file(partit1,t12_partit1),
    [interesting(0.00)]).

fof(t26_xboole_1,theorem,(
    ! [A,B,C] : 
      ( r1_tarski(A,B)
     => r1_tarski(k3_xboole_0(A,C),k3_xboole_0(B,C)) ) ),
    file(xboole_1,t26_xboole_1),
    [interesting(0.00)]).

fof(t3_xboole_1,theorem,(
    ! [A] : 
      ( r1_tarski(A,k1_xboole_0)
     => A = k1_xboole_0 ) ),
    file(xboole_1,t3_xboole_1),
    [interesting(0.00)]).

fof(t92_zfmisc_1,theorem,(
    ! [A,B] : 
      ( r2_hidden(A,B)
     => r1_tarski(A,k3_tarski(B)) ) ),
    file(zfmisc_1,t92_zfmisc_1),
    [interesting(0.00)]).

fof(d2_bvfunc_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] : 
              ( r1_bvfunc_2(A,B,C)
            <=> ( ! [D] : 
                    ( m1_eqrel_1(D,A)
                   => ( r2_hidden(D,B)
                     => r1_partit1(A,D,C) ) )
                & ! [D] : 
                    ( ( r1_tarski(D,C)
                      & ! [E] : 
                          ( m1_eqrel_1(E,A)
                         => ( r2_hidden(E,B)
                           => r1_partit1(A,E,D) ) ) )
                   => D = C ) ) ) ) ) ),
    file(bvfunc_2,d2_bvfunc_2),
    [interesting(0.00)]).

fof(d12_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
             => ! [D] : 
                  ( m2_fraenkel(D,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                 => ( D = k15_bvfunc_1(A,B,C)
                  <=> ! [E] : 
                        ( m1_subset_1(E,A)
                       => k8_funct_2(A,k6_margrel1,D,E) = k9_margrel1(k2_binarith(k1_funct_1(B,E),k1_funct_1(C,E))) ) ) ) ) ) ) ),
    file(bvfunc_1,d12_bvfunc_1),
    [interesting(0.00)]).

fof(d1_bvfunc_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( C = k2_bvfunc_2(A,B)
              <=> ! [D] : 
                    ( r2_hidden(D,C)
                  <=> ? [E] : 
                        ( v1_relat_1(E)
                        & v1_funct_1(E)
                        & ? [F] : 
                            ( m1_subset_1(F,k1_zfmisc_1(k1_zfmisc_1(A)))
                            & k1_relat_1(E) = B
                            & k2_relat_1(E) = F
                            & ! [G] : 
                                ( r2_hidden(G,B)
                               => r2_hidden(k1_funct_1(E,G),G) )
                            & D = k8_setfam_1(A,F)
                            & D != k1_xboole_0 ) ) ) ) ) ) ) ),
    file(bvfunc_2,d1_bvfunc_2),
    [interesting(0.00)]).

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

fof(d2_setfam_1,definition,(
    ! [A,B] : 
      ( r1_setfam_1(A,B)
    <=> ! [C] : ~ ( r2_hidden(C,A)
          & ! [D] : ~ ( r2_hidden(D,B)
              & r1_tarski(C,D) ) ) ) ),
    file(setfam_1,d2_setfam_1),
    [interesting(0.00)]).

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

fof(d3_bvfunc_2,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m1_subset_1(B,k1_zfmisc_1(k1_bvfunc_2(A)))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => ( ( B != k1_xboole_0
                 => ( C = k3_bvfunc_2(A,B)
                  <=> ! [D] : 
                        ( r2_hidden(D,C)
                      <=> r1_bvfunc_2(A,B,D) ) ) )
                & ( B = k1_xboole_0
                 => ( C = k3_bvfunc_2(A,B)
                  <=> C = k3_pua2mss1(A) ) ) ) ) ) ) ),
    file(bvfunc_2,d3_bvfunc_2),
    [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(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(d14_bvfunc_1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( B = k19_bvfunc_1(A)
          <=> ! [C] : 
                ( m1_subset_1(C,A)
               => k1_funct_1(B,C) = k8_margrel1 ) ) ) ) ),
    file(bvfunc_1,d14_bvfunc_1),
    [interesting(0.00)]).