fof(t42_bvfunc_6,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k14_bvfunc_1(A,B,k6_valuat_1(A,B,B)) = k19_bvfunc_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,t23_binarith,t18_binarith,t18_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t42_bvfunc_6),interesting(1.00)]).

fof(t32_bvfunc_6,theorem,(
    ! [A] : 
      ( ~ v1_xboole_0(A)
     => ! [B] : 
          ( m2_fraenkel(B,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
         => k14_bvfunc_1(A,k8_bvfunc_1(A,B,B),B) = k19_bvfunc_1(A) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d7_bvfunc_1,t10_binarith,t16_binarith,t18_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t32_bvfunc_6),interesting(0.87)]).

fof(t3_bvfunc_6,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,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,C,B)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d12_bvfunc_1,d2_binarith,t10_binarith,t9_binarith,t9_binarith,t40_margrel1,t18_binarith,t18_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t3_bvfunc_6),interesting(0.71)]).

fof(t39_bvfunc_6,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,k6_valuat_1(A,B,C),B) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,t9_binarith,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t39_bvfunc_6),interesting(0.70)]).

fof(t41_bvfunc_6,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,k6_valuat_1(A,B,C),C) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,t9_binarith,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t41_bvfunc_6),interesting(0.70)]).

fof(t43_bvfunc_6,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,k15_bvfunc_1(A,B,C),k14_bvfunc_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d12_bvfunc_1,t40_margrel1,d2_binarith,d11_bvfunc_1,t40_margrel1,t9_binarith,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t43_bvfunc_6),interesting(0.70)]).

fof(t44_bvfunc_6,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,k15_bvfunc_1(A,B,C),k14_bvfunc_1(A,C,B)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d12_bvfunc_1,t40_margrel1,d2_binarith,d11_bvfunc_1,t20_binarith,t40_margrel1,t9_binarith,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t44_bvfunc_6),interesting(0.70)]).

fof(t27_bvfunc_6,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,k8_bvfunc_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d7_bvfunc_1,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t27_bvfunc_6),interesting(0.68)]).

fof(t1_bvfunc_6,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,k14_bvfunc_1(A,C,k6_valuat_1(A,B,C))) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d6_valuat_1,t23_binarith,t18_binarith,t50_margrel1,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t1_bvfunc_6),interesting(0.67)]).

fof(t2_bvfunc_6,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,k14_bvfunc_1(A,B,C),k14_bvfunc_1(A,k14_bvfunc_1(A,C,B),k15_bvfunc_1(A,B,C))) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,t10_binarith,t10_binarith,t40_margrel1,t40_margrel1,d12_bvfunc_1,d2_binarith,t10_binarith,t23_binarith,t18_binarith,t50_margrel1,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t2_bvfunc_6),interesting(0.66)]).

fof(t15_bvfunc_6,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,C) = k19_bvfunc_1(A)
               => k8_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d6_valuat_1,t45_margrel1,d7_bvfunc_1,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t15_bvfunc_6),interesting(0.63)]).

fof(t20_bvfunc_6,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))
             => ( ( k8_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                  & k5_valuat_1(A,B) = k19_bvfunc_1(A) )
               => C = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d7_bvfunc_1,d14_bvfunc_1,d5_valuat_1,t41_margrel1,t7_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t20_bvfunc_6),interesting(0.51)]).

fof(t16_bvfunc_6,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))
                 => ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                   => k14_bvfunc_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,D)) = k19_bvfunc_1(A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,t10_binarith,t23_binarith,t20_binarith,t19_binarith,t20_binarith,t18_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t16_bvfunc_6),interesting(0.49)]).

fof(t17_bvfunc_6,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))
                 => ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                   => k14_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,C,D)) = k19_bvfunc_1(A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d6_valuat_1,d6_valuat_1,t9_binarith,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t17_bvfunc_6),interesting(0.49)]).

fof(t6_bvfunc_6,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))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,D,B),k14_bvfunc_1(A,k14_bvfunc_1(A,D,C),k14_bvfunc_1(A,D,k6_valuat_1(A,B,C)))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d6_valuat_1,t10_binarith,t10_binarith,t40_margrel1,t40_margrel1,t23_binarith,t23_binarith,t40_margrel1,t9_binarith,t18_binarith,t50_margrel1,t20_binarith,t40_margrel1,t9_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t6_bvfunc_6),interesting(0.47)]).

fof(t25_bvfunc_6,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,k5_valuat_1(A,C)) = k19_bvfunc_1(A)
               => k14_bvfunc_1(A,C,k5_valuat_1(A,B)) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d5_valuat_1,d11_bvfunc_1,d5_valuat_1,d14_bvfunc_1]),
    [file(bvfunc_6,t25_bvfunc_6),interesting(0.46)]).

fof(t26_bvfunc_6,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,k5_valuat_1(A,B),C) = k19_bvfunc_1(A)
               => k14_bvfunc_1(A,k5_valuat_1(A,C),B) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d5_valuat_1,t40_margrel1,d11_bvfunc_1,d5_valuat_1,t40_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t26_bvfunc_6),interesting(0.46)]).

fof(t7_bvfunc_6,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))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),k8_bvfunc_1(A,k14_bvfunc_1(A,B,D),k14_bvfunc_1(A,C,D))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,t10_binarith,t40_margrel1,t22_binarith,t40_margrel1,t9_binarith,t20_binarith,t20_binarith,t18_binarith,t19_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t7_bvfunc_6),interesting(0.46)]).

fof(t28_bvfunc_6,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,k8_bvfunc_1(A,B,C),k14_bvfunc_1(A,k5_valuat_1(A,B),C)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d7_bvfunc_1,d11_bvfunc_1,t10_binarith,d5_valuat_1,t40_margrel1,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t28_bvfunc_6),interesting(0.44)]).

fof(t34_bvfunc_6,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,k14_bvfunc_1(A,B,C),k8_bvfunc_1(A,k5_valuat_1(A,B),C)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d7_bvfunc_1,t10_binarith,t40_margrel1,d5_valuat_1,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t34_bvfunc_6),interesting(0.44)]).

fof(t8_bvfunc_6,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))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,B,D),k14_bvfunc_1(A,k14_bvfunc_1(A,C,D),k14_bvfunc_1(A,k8_bvfunc_1(A,B,C),D))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d7_bvfunc_1,t10_binarith,t23_binarith,t23_binarith,t18_binarith,t50_margrel1,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t8_bvfunc_6),interesting(0.44)]).

fof(t4_bvfunc_6,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))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,k6_valuat_1(A,B,C),D),k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d6_valuat_1,d11_bvfunc_1,d11_bvfunc_1,t9_binarith,t20_binarith,t18_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t4_bvfunc_6),interesting(0.43)]).

fof(t5_bvfunc_6,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))
                 => k14_bvfunc_1(A,k14_bvfunc_1(A,B,k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,k6_valuat_1(A,B,C),D)) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d6_valuat_1,t9_binarith,t20_binarith,t18_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t5_bvfunc_6),interesting(0.43)]).

fof(t45_bvfunc_6,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))
                 => k14_bvfunc_1(A,k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D),k8_bvfunc_1(A,B,k8_bvfunc_1(A,C,D))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,t20_binarith,t18_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t45_bvfunc_6),interesting(0.42)]).

fof(t47_bvfunc_6,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))
                 => k14_bvfunc_1(A,k8_bvfunc_1(A,B,k8_bvfunc_1(A,C,D)),k8_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,t20_binarith,t18_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t47_bvfunc_6),interesting(0.42)]).

fof(t35_bvfunc_6,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,k6_valuat_1(A,B,C),k5_valuat_1(A,k14_bvfunc_1(A,B,k5_valuat_1(A,C)))) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,d5_valuat_1,t9_binarith,d11_bvfunc_1,d5_valuat_1,t10_binarith,t40_margrel1,t40_margrel1,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t35_bvfunc_6),interesting(0.41)]).

fof(t46_bvfunc_6,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))
                 => k14_bvfunc_1(A,k6_valuat_1(A,k6_valuat_1(A,B,C),D),k6_valuat_1(A,B,k6_valuat_1(A,C,D))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,d6_valuat_1,d6_valuat_1,d6_valuat_1,t52_margrel1,t18_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t46_bvfunc_6),interesting(0.41)]).

fof(t19_bvfunc_6,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))
                 => ( ( k14_bvfunc_1(A,B,D) = k19_bvfunc_1(A)
                      & k14_bvfunc_1(A,C,D) = k19_bvfunc_1(A) )
                   => k14_bvfunc_1(A,k8_bvfunc_1(A,B,C),D) = k19_bvfunc_1(A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d14_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d7_bvfunc_1,t10_binarith,t23_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t19_bvfunc_6),interesting(0.39)]).

fof(t40_bvfunc_6,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,k6_valuat_1(A,B,C),k8_bvfunc_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,t9_binarith,d7_bvfunc_1,t20_binarith,t20_binarith,t18_binarith,t19_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t40_bvfunc_6),interesting(0.38)]).

fof(t18_bvfunc_6,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))
                 => ( ( k14_bvfunc_1(A,D,B) = k19_bvfunc_1(A)
                      & k14_bvfunc_1(A,D,C) = k19_bvfunc_1(A) )
                   => k14_bvfunc_1(A,D,k6_valuat_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d14_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d6_valuat_1,t23_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t18_bvfunc_6),interesting(0.37)]).

fof(t36_bvfunc_6,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,k5_valuat_1(A,k14_bvfunc_1(A,B,k5_valuat_1(A,C))),k6_valuat_1(A,B,C)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d5_valuat_1,d6_valuat_1,d11_bvfunc_1,t40_margrel1,d5_valuat_1,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t36_bvfunc_6),interesting(0.36)]).

fof(t33_bvfunc_6,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,k6_valuat_1(A,B,k5_valuat_1(A,B)),C) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,d5_valuat_1,t9_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t33_bvfunc_6),interesting(0.33)]).

fof(t31_bvfunc_6,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,k5_valuat_1(A,k8_bvfunc_1(A,B,C)),k5_valuat_1(A,B)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d5_valuat_1,d5_valuat_1,t40_margrel1,d7_bvfunc_1,t20_binarith,t18_binarith,t19_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t31_bvfunc_6),interesting(0.32)]).

fof(t10_bvfunc_6,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,k14_bvfunc_1(A,B,k6_valuat_1(A,C,k5_valuat_1(A,C))),k5_valuat_1(A,B)) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d11_bvfunc_1,d6_valuat_1,t10_binarith,t40_margrel1,t9_binarith,d5_valuat_1,t18_binarith,t50_margrel1,d5_valuat_1,t18_binarith,d14_bvfunc_1]),
    [file(bvfunc_6,t10_bvfunc_6),interesting(0.28)]).

fof(t21_bvfunc_6,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))
                 => ! [E] : 
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ( ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                          & k14_bvfunc_1(A,D,E) = k19_bvfunc_1(A) )
                       => k14_bvfunc_1(A,k6_valuat_1(A,B,D),k6_valuat_1(A,C,E)) = k19_bvfunc_1(A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d14_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d6_valuat_1,d6_valuat_1,t9_binarith,t23_binarith,t20_binarith,t20_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t21_bvfunc_6),interesting(0.27)]).

fof(t22_bvfunc_6,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))
                 => ! [E] : 
                      ( m2_fraenkel(E,A,k6_margrel1,k1_fraenkel(A,k6_margrel1))
                     => ( ( k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A)
                          & k14_bvfunc_1(A,D,E) = k19_bvfunc_1(A) )
                       => k14_bvfunc_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,E)) = k19_bvfunc_1(A) ) ) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d14_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,t10_binarith,t23_binarith,t20_binarith,t20_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t22_bvfunc_6),interesting(0.27)]).

fof(t12_bvfunc_6,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))
                 => k14_bvfunc_1(A,k6_valuat_1(A,B,k8_bvfunc_1(A,C,D)),k8_bvfunc_1(A,k6_valuat_1(A,B,C),k6_valuat_1(A,B,D))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,d7_bvfunc_1,d7_bvfunc_1,d6_valuat_1,d6_valuat_1,t22_binarith,t10_binarith,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t12_bvfunc_6),interesting(0.20)]).

fof(t14_bvfunc_6,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))
                 => k14_bvfunc_1(A,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))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,d7_bvfunc_1,d7_bvfunc_1,d6_valuat_1,d6_valuat_1,t22_binarith,t10_binarith,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t14_bvfunc_6),interesting(0.20)]).

fof(t9_bvfunc_6,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))
                 => k14_bvfunc_1(A,k6_valuat_1(A,k14_bvfunc_1(A,B,D),k14_bvfunc_1(A,C,D)),k14_bvfunc_1(A,k8_bvfunc_1(A,B,C),D)) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,d11_bvfunc_1,d11_bvfunc_1,d11_bvfunc_1,d7_bvfunc_1,t9_binarith,t10_binarith,t23_binarith,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t9_bvfunc_6),interesting(0.20)]).

fof(t11_bvfunc_6,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))
                 => k14_bvfunc_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,C),k8_bvfunc_1(A,B,D)),k8_bvfunc_1(A,B,k6_valuat_1(A,C,D))) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,d7_bvfunc_1,d7_bvfunc_1,d7_bvfunc_1,d6_valuat_1,t23_binarith,t9_binarith,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t11_bvfunc_6),interesting(0.18)]).

fof(t13_bvfunc_6,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))
                 => k14_bvfunc_1(A,k6_valuat_1(A,k8_bvfunc_1(A,B,D),k8_bvfunc_1(A,C,D)),k8_bvfunc_1(A,k6_valuat_1(A,B,C),D)) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d6_valuat_1,d7_bvfunc_1,d7_bvfunc_1,t9_binarith,d7_bvfunc_1,d6_valuat_1,t23_binarith,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t13_bvfunc_6),interesting(0.18)]).

fof(t23_bvfunc_6,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,k6_valuat_1(A,B,k5_valuat_1(A,C)),k5_valuat_1(A,B)) = k19_bvfunc_1(A)
               => k14_bvfunc_1(A,B,C) = k19_bvfunc_1(A) ) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d14_bvfunc_1,d11_bvfunc_1,d6_valuat_1,t9_binarith,d5_valuat_1,d5_valuat_1,t40_margrel1,t20_binarith,t21_binarith,d11_bvfunc_1,d14_bvfunc_1]),
    [file(bvfunc_6,t23_bvfunc_6),interesting(0.18)]).

fof(t30_bvfunc_6,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,k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k5_valuat_1(A,k8_bvfunc_1(A,B,C))) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d5_valuat_1,d6_valuat_1,d5_valuat_1,d5_valuat_1,t9_binarith,t40_margrel1,t40_margrel1,d7_bvfunc_1,t10_binarith,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t30_bvfunc_6),interesting(0.05)]).

fof(t38_bvfunc_6,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,k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C)),k5_valuat_1(A,k6_valuat_1(A,B,C))) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d5_valuat_1,d7_bvfunc_1,d5_valuat_1,d5_valuat_1,d6_valuat_1,t10_binarith,t9_binarith,t40_margrel1,t40_margrel1,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t38_bvfunc_6),interesting(0.05)]).

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(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(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(t40_margrel1,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k9_margrel1(k9_margrel1(A)) = A ) ),
    file(margrel1,t40_margrel1),
    [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(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(t18_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k9_margrel1(A)) = k8_margrel1 ) ),
    file(binarith,t18_binarith),
    [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(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(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(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(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(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(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(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(t7_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k1_binarith(A,k7_margrel1) = A ) ),
    file(binarith,t7_binarith),
    [interesting(0.00)]).

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

fof(t24_bvfunc_6,theorem,(
    $true ),
    file(bvfunc_6,t24_bvfunc_6),
    [interesting(0.00)]).

fof(t29_bvfunc_6,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,k5_valuat_1(A,k8_bvfunc_1(A,B,C)),k6_valuat_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C))) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d5_valuat_1,t40_margrel1,d7_bvfunc_1,d6_valuat_1,d5_valuat_1,d5_valuat_1,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t29_bvfunc_6),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(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(t16_binarith,theorem,(
    ! [A] : 
      ( v2_margrel1(A)
     => k10_margrel1(A,A) = A ) ),
    file(binarith,t16_binarith),
    [interesting(0.00)]).

fof(t37_bvfunc_6,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,k5_valuat_1(A,k6_valuat_1(A,B,C)),k8_bvfunc_1(A,k5_valuat_1(A,B),k5_valuat_1(A,C))) = k19_bvfunc_1(A) ) ) ) ),
    inference(mizar_proof,[status(thm)],[d11_bvfunc_1,d5_valuat_1,t40_margrel1,d6_valuat_1,d7_bvfunc_1,d5_valuat_1,d5_valuat_1,t23_binarith,t20_binarith,t20_binarith,t18_binarith,t18_binarith,t19_binarith,t19_binarith,t45_margrel1,d14_bvfunc_1]),
    [file(bvfunc_6,t37_bvfunc_6),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)]).