fof(t4_bvfunc_1,theorem,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => k3_valuat_1(k3_valuat_1(A)) = A ) ),
    inference(mizar_proof,[status(thm)],[d3_valuat_1,t40_margrel1,d3_valuat_1,d3_valuat_1]),
    [file(bvfunc_1,t4_bvfunc_1),interesting(1.00)]).

fof(t36_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => r1_bvfunc_1(A,B,k24_bvfunc_1(A,B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d20_bvfunc_1,d14_bvfunc_1,d5_valuat_1,d7_bvfunc_1,t13_bvfunc_1,d11_bvfunc_1,d1_t_1topsp,t43_margrel1,d16_margrel1,d14_bvfunc_1,d7_bvfunc_1,t13_bvfunc_1,d11_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,t19_bvfunc_1]),
    [file(bvfunc_1,t36_bvfunc_1),interesting(0.96)]).

fof(t10_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k8_bvfunc_1(A,B,B) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d7_bvfunc_1,t21_binarith,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t10_bvfunc_1),interesting(0.95)]).

fof(t35_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => r1_bvfunc_1(A,k23_bvfunc_1(A,B,C),B) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d1_t_1topsp,d5_valuat_1,d14_bvfunc_1,d7_bvfunc_1,t13_bvfunc_1,d11_bvfunc_1,d19_bvfunc_1,d16_margrel1,d14_bvfunc_1,d7_bvfunc_1,t13_bvfunc_1,d11_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,t19_bvfunc_1]),
    [file(bvfunc_1,t35_bvfunc_1),interesting(0.95)]).

fof(t12_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k8_bvfunc_1(A,B,k18_bvfunc_1(A)) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d7_bvfunc_1,d13_bvfunc_1,t7_binarith,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t12_bvfunc_1),interesting(0.86)]).

fof(t9_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k6_valuat_1(A,B,k19_bvfunc_1(A)) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d6_valuat_1,d14_bvfunc_1,t50_margrel1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t9_bvfunc_1),interesting(0.86)]).

fof(t6_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))
             => k6_valuat_1(A,B,B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_valuat_1,t16_binarith,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t6_bvfunc_1),interesting(0.85)]).

fof(t21_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( r1_bvfunc_1(A,k18_bvfunc_1(A),B)
            & r1_bvfunc_1(A,B,k19_bvfunc_1(A)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d13_bvfunc_1,d16_margrel1,t19_binarith,d14_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,d11_bvfunc_1,d14_bvfunc_1,t19_binarith,d14_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,t19_bvfunc_1]),
    [file(bvfunc_1,t21_bvfunc_1),interesting(0.84)]).

fof(t8_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k6_valuat_1(A,B,k18_bvfunc_1(A)) = k18_bvfunc_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t49_margrel1,d13_bvfunc_1,d6_valuat_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t8_bvfunc_1),interesting(0.83)]).

fof(t13_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k8_bvfunc_1(A,B,k19_bvfunc_1(A)) = k19_bvfunc_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_binarith,d14_bvfunc_1,d7_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t13_bvfunc_1),interesting(0.83)]).

fof(t33_bvfunc_1,theorem,(
    ! [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,k23_bvfunc_1(A,B,C),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_eqrel_1,d1_t_1topsp,d1_t_1topsp,t3_xboole_0,d6_eqrel_1,d19_bvfunc_1,d19_bvfunc_1,t3_xboole_0,d19_bvfunc_1,d19_bvfunc_1,t3_xboole_0,d18_bvfunc_1]),
    [file(bvfunc_1,t33_bvfunc_1),interesting(0.80)]).

fof(t34_bvfunc_1,theorem,(
    ! [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,k24_bvfunc_1(A,B,C),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_eqrel_1,d1_t_1topsp,d1_t_1topsp,t3_xboole_0,d20_bvfunc_1,d20_bvfunc_1,d20_bvfunc_1,d20_bvfunc_1,d18_bvfunc_1]),
    [file(bvfunc_1,t34_bvfunc_1),interesting(0.80)]).

fof(t44_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => r2_bvfunc_1(A,B,k25_bvfunc_1(A,B)) ) ) ),
    inference(mizar_proof,[status(thm)],[s7_domain_1,s7_domain_1,d4_xboole_0,d2_tarski,d18_bvfunc_1]),
    [file(bvfunc_1,t44_bvfunc_1),interesting(0.79)]).

fof(t25_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v5_seqm_3(B)
            & m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
         => ( k20_bvfunc_1(A,B) = B
            & k21_bvfunc_1(A,B) = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d13_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,t38_margrel1,d13_bvfunc_1,d14_bvfunc_1,t24_bvfunc_1]),
    [file(bvfunc_1,t25_bvfunc_1),interesting(0.78)]).

fof(t31_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => r2_bvfunc_1(A,B,k3_pua2mss1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[t35_partit1,d1_tarski,d18_bvfunc_1]),
    [file(bvfunc_1,t31_bvfunc_1),interesting(0.78)]).

fof(t22_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k5_valuat_1(A,k20_bvfunc_1(A,B)) = k21_bvfunc_1(A,k5_valuat_1(A,B))
            & k5_valuat_1(A,k21_bvfunc_1(A,B)) = k20_bvfunc_1(A,k5_valuat_1(A,B)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t41_margrel1,d5_valuat_1,d5_valuat_1,t41_margrel1,t41_margrel1,d5_valuat_1,d5_valuat_1,t41_margrel1,d16_bvfunc_1,t5_bvfunc_1,t41_margrel1,d5_valuat_1,d16_bvfunc_1,d17_bvfunc_1,d17_bvfunc_1,t5_bvfunc_1,d17_bvfunc_1,t5_bvfunc_1,t41_margrel1,d5_valuat_1,d17_bvfunc_1,d16_bvfunc_1,d16_bvfunc_1,t5_bvfunc_1,t38_margrel1,d16_bvfunc_1,t5_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,t5_bvfunc_1]),
    [file(bvfunc_1,t22_bvfunc_1),interesting(0.76)]).

fof(t40_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k23_bvfunc_1(A,B,k3_pua2mss1(A)) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d1_t_1topsp,d19_bvfunc_1,d1_t_1topsp,t35_partit1,d1_t_1topsp,d1_tarski,d1_tarski,t43_margrel1,d19_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t40_bvfunc_1),interesting(0.73)]).

fof(t41_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k24_bvfunc_1(A,B,k3_pua2mss1(A)) = B ) ) ),
    inference(mizar_proof,[status(thm)],[d1_t_1topsp,d1_t_1topsp,t35_partit1,d1_t_1topsp,d1_tarski,d1_tarski,t43_margrel1,d20_bvfunc_1,d20_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t41_bvfunc_1),interesting(0.73)]).

fof(t19_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))
             => ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
              <=> r1_bvfunc_1(A,B,C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d14_bvfunc_1,t39_margrel1,t7_binarith,t41_margrel1,d15_bvfunc_1,d15_bvfunc_1,t39_margrel1,t41_margrel1,t19_binarith,d11_bvfunc_1,d14_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t19_bvfunc_1),interesting(0.70)]).

fof(t32_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v5_seqm_3(B)
            & m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
         => r2_bvfunc_1(A,B,k6_partit1(A)) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_bvfunc_1,d13_bvfunc_1,d14_bvfunc_1,d14_bvfunc_1,t24_bvfunc_1,d18_bvfunc_1]),
    [file(bvfunc_1,t32_bvfunc_1),interesting(0.70)]).

fof(t20_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))
             => ( k15_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
              <=> B = C ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_bvfunc_1,d14_bvfunc_1,t41_margrel1,d2_binarith,t39_margrel1,t39_margrel1,t19_binarith,t39_margrel1,t45_margrel1,t39_margrel1,t45_margrel1,t41_margrel1,d2_funct_2,d2_funct_2,t9_funct_1,t41_margrel1,t39_margrel1,t45_margrel1,t7_binarith,d2_binarith,d16_margrel1,d12_bvfunc_1,d14_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t20_bvfunc_1),interesting(0.69)]).

fof(t24_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( ( v5_seqm_3(B)
            & m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
         => ( B = k18_bvfunc_1(A)
            | B = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_funct_2,t43_margrel1,d13_bvfunc_1,d14_bvfunc_1,d5_seqm_3]),
    [file(bvfunc_1,t24_bvfunc_1),interesting(0.69)]).

fof(t38_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k23_bvfunc_1(A,B,k6_partit1(A)) = k20_bvfunc_1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d16_bvfunc_1,d14_bvfunc_1,d19_bvfunc_1,d9_partit1,d1_tarski,d16_bvfunc_1,d13_bvfunc_1,d19_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t38_bvfunc_1),interesting(0.67)]).

fof(t39_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k24_bvfunc_1(A,B,k6_partit1(A)) = k21_bvfunc_1(A,B) ) ) ),
    inference(mizar_proof,[status(thm)],[d9_partit1,d1_tarski,t43_margrel1,d17_bvfunc_1,d14_bvfunc_1,d20_bvfunc_1,d17_bvfunc_1,d13_bvfunc_1,d20_bvfunc_1,t43_margrel1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t39_bvfunc_1),interesting(0.67)]).

fof(t5_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ( k5_valuat_1(A,k19_bvfunc_1(A)) = k18_bvfunc_1(A)
            & k5_valuat_1(A,k18_bvfunc_1(A)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_valuat_1,d14_bvfunc_1,d16_margrel1,d5_valuat_1,d13_bvfunc_1,d16_margrel1,d13_bvfunc_1,d14_bvfunc_1]),
    [file(bvfunc_1,t5_bvfunc_1),interesting(0.65)]).

fof(t30_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_subset_1(C,A)
             => r1_xreal_0(k1_funct_1(B,C),k1_funct_1(k21_bvfunc_1(A,B),C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d17_bvfunc_1,d13_bvfunc_1,d16_margrel1,t19_binarith,d3_bvfunc_1,d17_bvfunc_1,d14_bvfunc_1,t19_binarith,d3_bvfunc_1]),
    [file(bvfunc_1,t30_bvfunc_1),interesting(0.64)]).

fof(t27_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( ( v5_seqm_3(C)
                & m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
             => ( k20_bvfunc_1(A,k14_bvfunc_1(A,C,B)) = k14_bvfunc_1(A,C,k20_bvfunc_1(A,B))
                & k20_bvfunc_1(A,k14_bvfunc_1(A,B,C)) = k14_bvfunc_1(A,k21_bvfunc_1(A,B),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_bvfunc_1,t25_bvfunc_1,t25_bvfunc_1,t25_bvfunc_1,d14_bvfunc_1,d11_bvfunc_1,t19_binarith,d14_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,d11_bvfunc_1,d14_bvfunc_1,t19_binarith,d2_funct_2,d2_funct_2,t9_funct_1,d11_bvfunc_1,d13_bvfunc_1,d14_bvfunc_1,d16_margrel1,t7_binarith,d13_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,d13_bvfunc_1,d11_bvfunc_1,d16_margrel1,t19_binarith,d14_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,d11_bvfunc_1,t19_binarith,d11_bvfunc_1,t19_binarith,d17_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d16_bvfunc_1,d11_bvfunc_1,d16_margrel1,t7_binarith,t38_margrel1,d11_bvfunc_1,t19_binarith,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,t25_bvfunc_1,d16_bvfunc_1,d11_bvfunc_1,t19_binarith,d11_bvfunc_1,t19_binarith,d16_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d16_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d11_bvfunc_1,d5_valuat_1,d7_bvfunc_1,d16_bvfunc_1,t5_bvfunc_1,t12_bvfunc_1,d2_funct_2,d2_funct_2,d11_bvfunc_1,d5_valuat_1,d7_bvfunc_1,d16_bvfunc_1,t13_bvfunc_1,d14_bvfunc_1,t25_bvfunc_1,d16_bvfunc_1,t9_funct_1,d11_bvfunc_1,t19_binarith,d11_bvfunc_1,d16_margrel1,t7_binarith,t38_margrel1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,t25_bvfunc_1,d16_bvfunc_1,d11_bvfunc_1,d16_margrel1,t19_binarith,d11_bvfunc_1,d16_margrel1,t7_binarith,d16_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d11_bvfunc_1,t19_binarith,d11_bvfunc_1,d16_margrel1,t7_binarith,d16_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,t25_bvfunc_1,d16_bvfunc_1,d16_bvfunc_1,d5_valuat_1,d7_bvfunc_1,t5_bvfunc_1,t13_bvfunc_1,d14_bvfunc_1,d11_bvfunc_1,d5_valuat_1,d7_bvfunc_1,t12_bvfunc_1,d11_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,t22_bvfunc_1,d16_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,t5_bvfunc_1,t38_margrel1,d13_bvfunc_1,d14_bvfunc_1,t24_bvfunc_1]),
    [file(bvfunc_1,t27_bvfunc_1),interesting(0.62)]).

fof(t29_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_subset_1(C,A)
             => r1_xreal_0(k1_funct_1(k20_bvfunc_1(A,B),C),k1_funct_1(B,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t19_binarith,d3_bvfunc_1,d16_bvfunc_1,d13_bvfunc_1,d16_margrel1,t19_binarith,d3_bvfunc_1]),
    [file(bvfunc_1,t29_bvfunc_1),interesting(0.61)]).

fof(t45_bvfunc_1,theorem,(
    ! [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)
               => r1_setfam_1(C,k25_bvfunc_1(A,B)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[s7_domain_1,s7_domain_1,d6_eqrel_1,d15_margrel1,t37_margrel1,d2_tarski,d1_tarski,d2_tarski,d4_xboole_0,d3_tarski,t43_margrel1,d18_bvfunc_1,d1_tarski,d2_tarski,d4_xboole_0,d3_tarski,t43_margrel1,d18_bvfunc_1,d2_setfam_1]),
    [file(bvfunc_1,t45_bvfunc_1),interesting(0.58)]).

fof(t37_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( m1_eqrel_1(C,A)
             => k5_valuat_1(A,k23_bvfunc_1(A,B,C)) = k24_bvfunc_1(A,k5_valuat_1(A,B),C) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d5_valuat_1,t4_bvfunc_1,d16_margrel1,t43_margrel1,d19_bvfunc_1,d5_valuat_1,d20_bvfunc_1,d16_margrel1,d19_bvfunc_1,d5_valuat_1,d20_bvfunc_1,d16_margrel1,t43_margrel1,d5_valuat_1,d16_margrel1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t37_bvfunc_1),interesting(0.53)]).

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)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t45_margrel1,d6_valuat_1,d19_bvfunc_1,d19_bvfunc_1,t45_margrel1,d6_valuat_1,d19_bvfunc_1,t43_margrel1,t49_margrel1,d6_valuat_1,t43_margrel1,d19_bvfunc_1,t49_margrel1,d6_valuat_1,d19_bvfunc_1,t43_margrel1,t49_margrel1,d6_valuat_1,t43_margrel1,d19_bvfunc_1,d19_bvfunc_1,t49_margrel1,d6_valuat_1,d19_bvfunc_1,t43_margrel1,t49_margrel1,t43_margrel1,d6_valuat_1,d19_bvfunc_1,t49_margrel1,d6_valuat_1,d19_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t42_bvfunc_1),interesting(0.46)]).

fof(t16_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))
             => k5_valuat_1(A,k8_bvfunc_1(A,B,C)) = k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_bvfunc_1,d5_valuat_1,t10_binarith,d5_valuat_1,d5_valuat_1,d6_valuat_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t16_bvfunc_1),interesting(0.44)]).

fof(t17_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))
             => k5_valuat_1(A,k6_valuat_1(A,B,C)) = k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_valuat_1,d5_valuat_1,t9_binarith,d5_valuat_1,d5_valuat_1,d7_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t17_bvfunc_1),interesting(0.44)]).

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)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_bvfunc_1,t39_margrel1,d20_bvfunc_1,t19_binarith,d7_bvfunc_1,d20_bvfunc_1,d20_bvfunc_1,t19_binarith,d7_bvfunc_1,d20_bvfunc_1,d20_bvfunc_1,t19_binarith,d7_bvfunc_1,d20_bvfunc_1,t7_binarith,t19_binarith,d7_bvfunc_1,t19_binarith,d7_bvfunc_1,d20_bvfunc_1,d20_bvfunc_1,t7_binarith,d7_bvfunc_1,d20_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t43_bvfunc_1),interesting(0.43)]).

fof(t26_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))
             => ( k20_bvfunc_1(A,k6_valuat_1(A,B,C)) = k6_valuat_1(A,k20_bvfunc_1(A,B),k20_bvfunc_1(A,C))
                & k21_bvfunc_1(A,k8_bvfunc_1(A,B,C)) = k8_bvfunc_1(A,k21_bvfunc_1(A,B),k21_bvfunc_1(A,C)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_valuat_1,t39_margrel1,d17_margrel1,d6_valuat_1,t39_margrel1,d17_margrel1,d16_bvfunc_1,d16_bvfunc_1,d16_bvfunc_1,d7_bvfunc_1,t19_binarith,t38_margrel1,t38_margrel1,t38_margrel1,d17_bvfunc_1,d17_bvfunc_1,t10_bvfunc_1,d17_bvfunc_1,t6_bvfunc_1,d7_bvfunc_1,t39_margrel1,t19_binarith,d7_bvfunc_1,t39_margrel1,t19_binarith,d17_bvfunc_1,d17_bvfunc_1,d17_bvfunc_1,d6_valuat_1,t45_margrel1,t38_margrel1,t38_margrel1,t38_margrel1,d16_bvfunc_1,d16_bvfunc_1,t6_bvfunc_1,d16_bvfunc_1,t10_bvfunc_1,d6_valuat_1,t39_margrel1,d17_margrel1,d6_valuat_1,t39_margrel1,d17_margrel1,d17_margrel1,d6_valuat_1,d7_bvfunc_1,t39_margrel1,t19_binarith,d7_bvfunc_1,t39_margrel1,t19_binarith,t7_binarith,d7_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,t8_bvfunc_1,t13_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1]),
    [file(bvfunc_1,t26_bvfunc_1),interesting(0.35)]).

fof(t28_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => ! [C] : 
              ( ( v5_seqm_3(C)
                & m2_fraenkel(C,A,k6_margrel1,k1_fraenkel(A,k6_margrel1)) )
             => ( k20_bvfunc_1(A,k8_bvfunc_1(A,C,B)) = k8_bvfunc_1(A,C,k20_bvfunc_1(A,B))
                & k21_bvfunc_1(A,k6_valuat_1(A,C,B)) = k6_valuat_1(A,C,k21_bvfunc_1(A,B))
                & k21_bvfunc_1(A,k6_valuat_1(A,B,C)) = k6_valuat_1(A,k21_bvfunc_1(A,B),C) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t25_bvfunc_1,t25_bvfunc_1,t25_bvfunc_1,d7_bvfunc_1,t19_binarith,d6_valuat_1,t45_margrel1,t38_margrel1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,t10_bvfunc_1,t6_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d7_bvfunc_1,t19_binarith,d6_valuat_1,t50_margrel1,d16_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,t12_bvfunc_1,t8_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d7_bvfunc_1,t19_binarith,d6_valuat_1,t50_margrel1,d16_bvfunc_1,d17_bvfunc_1,t13_bvfunc_1,t8_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d16_bvfunc_1,t13_bvfunc_1,d14_bvfunc_1,d6_valuat_1,d14_bvfunc_1,t50_margrel1,d2_funct_2,d2_funct_2,t9_funct_1,t12_bvfunc_1,d16_bvfunc_1,t9_bvfunc_1,d7_bvfunc_1,t19_binarith,d6_valuat_1,t49_margrel1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,t12_bvfunc_1,t8_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d7_bvfunc_1,t7_binarith,t38_margrel1,d6_valuat_1,t45_margrel1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,t12_bvfunc_1,t8_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d7_bvfunc_1,t19_binarith,d6_valuat_1,t49_margrel1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,t12_bvfunc_1,t8_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d7_bvfunc_1,t7_binarith,d2_funct_2,d2_funct_2,t9_funct_1,d16_bvfunc_1,t8_bvfunc_1,d13_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,d17_bvfunc_1,d16_bvfunc_1,t8_bvfunc_1,t12_bvfunc_1,t38_margrel1,d13_bvfunc_1,d14_bvfunc_1,t24_bvfunc_1]),
    [file(bvfunc_1,t28_bvfunc_1),interesting(0.30)]).

fof(s2_bvfunc_1,theorem,(
    ! [A] : 
      ( m2_fraenkel(A,f1_s2_bvfunc_1,k6_margrel1,k1_fraenkel(f1_s2_bvfunc_1,k6_margrel1))
     => ! [B] : 
          ( m2_fraenkel(B,f1_s2_bvfunc_1,k6_margrel1,k1_fraenkel(f1_s2_bvfunc_1,k6_margrel1))
         => ( ( ! [C] : 
                  ( m1_subset_1(C,f1_s2_bvfunc_1)
                 => k1_funct_1(A,C) = f2_s2_bvfunc_1(C) )
              & ! [C] : 
                  ( m1_subset_1(C,f1_s2_bvfunc_1)
                 => k1_funct_1(B,C) = f2_s2_bvfunc_1(C) ) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,s2_bvfunc_1),interesting(0.28)]).

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(s1_bvfunc_1,theorem,(
    ! [A] : 
      ( m2_fraenkel(A,f1_s1_bvfunc_1,k6_margrel1,k1_fraenkel(f1_s1_bvfunc_1,k6_margrel1))
     => ! [B] : 
          ( m2_fraenkel(B,f1_s1_bvfunc_1,k6_margrel1,k1_fraenkel(f1_s1_bvfunc_1,k6_margrel1))
         => ( ( ! [C] : 
                  ( m1_subset_1(C,f1_s1_bvfunc_1)
                 => k1_funct_1(A,C) = f4_s1_bvfunc_1(C,f2_s1_bvfunc_1,f3_s1_bvfunc_1) )
              & ! [C] : 
                  ( m1_subset_1(C,f1_s1_bvfunc_1)
                 => k1_funct_1(B,C) = f4_s1_bvfunc_1(C,f2_s1_bvfunc_1,f3_s1_bvfunc_1) ) )
           => A = B ) ) ) ),
    inference(mizar_proof,[status(thm)],[d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,s1_bvfunc_1),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(t20_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k1_binarith(k1_binarith(A,B),C) = k1_binarith(A,k1_binarith(B,C)) ) ) ) ),
    file(binarith,t20_binarith),
    [interesting(0.00)]).

fof(t11_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))
                 => k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D) = k8_bvfunc_1(A,B,k8_bvfunc_1(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_bvfunc_1,d7_bvfunc_1,t20_binarith,d7_bvfunc_1,d7_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t11_bvfunc_1),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(t23_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k1_binarith(A,k10_margrel1(B,C)) = k10_margrel1(k1_binarith(A,B),k1_binarith(A,C)) ) ) ) ),
    file(binarith,t23_binarith),
    [interesting(0.00)]).

fof(t14_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))
                 => k8_bvfunc_1(A,k6_valuat_1(A,B,C),D) = k6_valuat_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d7_bvfunc_1,d6_valuat_1,t23_binarith,d7_bvfunc_1,d7_bvfunc_1,d6_valuat_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t14_bvfunc_1),interesting(0.00)]).

fof(t22_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k10_margrel1(A,k1_binarith(B,C)) = k1_binarith(k10_margrel1(A,B),k10_margrel1(A,C)) ) ) ) ),
    file(binarith,t22_binarith),
    [interesting(0.00)]).

fof(t15_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))
                 => k6_valuat_1(A,k8_bvfunc_1(A,B,C),D) = k8_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_valuat_1,d7_bvfunc_1,t22_binarith,d6_valuat_1,d6_valuat_1,d7_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t15_bvfunc_1),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(t10_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k9_margrel1(k1_binarith(A,B)) = k10_margrel1(k9_margrel1(A),k9_margrel1(B)) ) ) ),
    file(binarith,t10_binarith),
    [interesting(0.00)]).

fof(t9_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => k9_margrel1(k10_margrel1(A,B)) = k1_binarith(k9_margrel1(A),k9_margrel1(B)) ) ) ),
    file(binarith,t9_binarith),
    [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(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(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) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[t39_margrel1,d15_bvfunc_1,d2_funct_2,d2_funct_2,t9_funct_1,d15_bvfunc_1,d15_bvfunc_1,d15_bvfunc_1]),
    [file(bvfunc_1,t18_bvfunc_1),interesting(0.00)]).

fof(t1_bvfunc_1,theorem,(
    $true ),
    file(bvfunc_1,t1_bvfunc_1),
    [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(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)]).

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(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(t19_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k8_margrel1) = k8_margrel1 ) ),
    file(binarith,t19_binarith),
    [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(t7_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k7_margrel1) = A ) ),
    file(binarith,t7_binarith),
    [interesting(0.00)]).

fof(d16_margrel1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( ( A = k7_margrel1
         => k9_margrel1(A) = k8_margrel1 )
        & ( A != k7_margrel1
         => k9_margrel1(A) = k7_margrel1 ) ) ) ),
    file(margrel1,d16_margrel1),
    [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(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(t38_margrel1,theorem,(
    k7_margrel1 != k8_margrel1 ),
    file(margrel1,t38_margrel1),
    [interesting(0.00)]).

fof(d16_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] : 
                      ( m1_subset_1(D,A)
                     => k1_funct_1(B,D) = k8_margrel1 )
                 => ( C = k20_bvfunc_1(A,B)
                  <=> C = k19_bvfunc_1(A) ) )
                & ( ~ ! [D] : 
                        ( m1_subset_1(D,A)
                       => k1_funct_1(B,D) = k8_margrel1 )
                 => ( C = k20_bvfunc_1(A,B)
                  <=> C = k18_bvfunc_1(A) ) ) ) ) ) ) ),
    file(bvfunc_1,d16_bvfunc_1),
    [interesting(0.00)]).

fof(d17_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] : 
                      ( m1_subset_1(D,A)
                     => k1_funct_1(B,D) = k7_margrel1 )
                 => ( C = k21_bvfunc_1(A,B)
                  <=> C = k18_bvfunc_1(A) ) )
                & ( ~ ! [D] : 
                        ( m1_subset_1(D,A)
                       => k1_funct_1(B,D) = k7_margrel1 )
                 => ( C = k21_bvfunc_1(A,B)
                  <=> C = k19_bvfunc_1(A) ) ) ) ) ) ) ),
    file(bvfunc_1,d17_bvfunc_1),
    [interesting(0.00)]).

fof(t23_bvfunc_1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ( k20_bvfunc_1(A,k18_bvfunc_1(A)) = k18_bvfunc_1(A)
        & k20_bvfunc_1(A,k19_bvfunc_1(A)) = k19_bvfunc_1(A)
        & k21_bvfunc_1(A,k18_bvfunc_1(A)) = k18_bvfunc_1(A)
        & k21_bvfunc_1(A,k19_bvfunc_1(A)) = k19_bvfunc_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d13_bvfunc_1,d13_bvfunc_1,t38_margrel1,d14_bvfunc_1,d14_bvfunc_1,t38_margrel1,d16_bvfunc_1,d17_bvfunc_1]),
    [file(bvfunc_1,t23_bvfunc_1),interesting(0.00)]).

fof(d17_margrel1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ( ( ( A = k8_margrel1
                & B = k8_margrel1 )
             => k10_margrel1(A,B) = k8_margrel1 )
            & ( ~ ( A = k8_margrel1
                  & B = k8_margrel1 )
             => k10_margrel1(A,B) = k7_margrel1 ) ) ) ) ),
    file(margrel1,d17_margrel1),
    [interesting(0.00)]).

fof(t21_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,A) = A ) ),
    file(binarith,t21_binarith),
    [interesting(0.00)]).

fof(t16_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(A,A) = A ) ),
    file(binarith,t16_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(t43_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ( A != k8_margrel1
      <=> A = k7_margrel1 ) ) ),
    file(margrel1,t43_margrel1),
    [interesting(0.00)]).

fof(d5_seqm_3,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A) )
     => ( v5_seqm_3(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) ) ) ) ),
    file(seqm_3,d5_seqm_3),
    [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(d3_bvfunc_1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ( r1_xreal_0(A,B)
          <=> k1_bvfunc_1(A,B) = k8_margrel1 ) ) ) ),
    file(bvfunc_1,d3_bvfunc_1),
    [interesting(0.00)]).

fof(t2_bvfunc_1,theorem,(
    $true ),
    file(bvfunc_1,t2_bvfunc_1),
    [interesting(0.00)]).

fof(t35_partit1,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k3_pua2mss1(A) = a_1_0_partit1(A) ) ),
    file(partit1,t35_partit1),
    [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(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(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(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(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(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(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(d3_valuat_1,definition,(
    ! [A] : 
      ( ( v1_relat_1(A)
        & v1_funct_1(A)
        & v1_valuat_1(A) )
     => ! [B] : 
          ( ( v1_relat_1(B)
            & v1_funct_1(B) )
         => ( B = k3_valuat_1(A)
          <=> ( k1_relat_1(B) = k1_relat_1(A)
              & ! [C] : 
                  ( r2_hidden(C,k1_relat_1(A))
                 => k1_funct_1(B,C) = k9_margrel1(k1_funct_1(A,C)) ) ) ) ) ) ),
    file(valuat_1,d3_valuat_1),
    [interesting(0.00)]).

fof(t40_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,t40_margrel1),
    [interesting(0.00)]).

fof(d9_partit1,definition,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => k6_partit1(A) = k1_tarski(A) ) ),
    file(partit1,d9_partit1),
    [interesting(0.00)]).

fof(t3_bvfunc_1,theorem,(
    $true ),
    file(bvfunc_1,t3_bvfunc_1),
    [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(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(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(d15_margrel1,definition,(
    ! [A] : 
      ( v2_margrel1(A)
    <=> r2_hidden(A,k6_margrel1) ) ),
    file(margrel1,d15_margrel1),
    [interesting(0.00)]).

fof(t37_margrel1,theorem,(
    k6_margrel1 = k2_tarski(k7_margrel1,k8_margrel1) ),
    file(margrel1,t37_margrel1),
    [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(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(t52_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => ! [B] : 
          ( v2_margrel1(B)
         => ! [C] : 
              ( v2_margrel1(C)
             => k10_margrel1(A,k10_margrel1(B,C)) = k10_margrel1(k10_margrel1(A,B),C) ) ) ) ),
    file(margrel1,t52_margrel1),
    [interesting(0.00)]).

fof(t7_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))
                 => k6_valuat_1(A,k6_valuat_1(A,B,C),D) = k6_valuat_1(A,B,k6_valuat_1(A,C,D)) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d6_valuat_1,d6_valuat_1,t52_margrel1,d6_valuat_1,d6_valuat_1,d2_funct_2,d2_funct_2,t9_funct_1]),
    [file(bvfunc_1,t7_bvfunc_1),interesting(0.00)]).