5461 lines
122 KiB
Plaintext
5461 lines
122 KiB
Plaintext
1 : U*v1 = v1
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2 : I(v1)*v1 = U
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3 : (v3*v2)*v1 = v3*(v2*v1)
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4 : A*B = B*A
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5 : C*C = U
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6 : I(A) = C*(A*I(C))
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7 : C*(B*I(C)) = B
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8 : I(v2)*(v2*v1) = v1
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9 : A*(B*v1) = B*(A*v1)
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10 : C*(C*v1) = v1
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11 : C*(A*(I(C)*A)) = U
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12 : C*(B*(I(C)*v1)) = B*v1
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13 : I(U)*v1 = v1
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14 : I(I(v1))*U = v1
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15 : I(v3*v2)*(v3*(v2*v1)) = v1
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16 : C*(A*(I(C)*(B*A))) = B
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17 : I(C)*U = C
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18 : C*(A*(I(C)*(A*v1))) = v1
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19 : I(C)*B = B*I(C)
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20 : I(I(v2))*v1 = v2*v1
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Rule 14 deleted
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21 : v1*U = v1
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Rule 17 deleted
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22 : I(C) = C
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Rule 19 deleted
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Rule 18 deleted
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Rule 16 deleted
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Rule 12 deleted
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Rule 11 deleted
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Rule 7 deleted
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23 : C*B = B*C
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24 : C*(A*(C*(A*v1))) = v1
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25 : C*(A*(C*(B*A))) = B
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26 : C*(B*(C*v1)) = B*v1
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27 : C*(A*(C*A)) = U
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28 : C*(B*C) = B
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29 : C*(A*(C*(B*(A*v1)))) = B*v1
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30 : I(I(v2*v1)*v2) = v1
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31 : I(v2*I(v1))*v2 = v1
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32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
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33 : I(v1*A)*(v1*(B*A)) = B
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34 : I(v1*C)*v1 = C
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35 : I(v3*I(v2))*(v3*v1) = v2*v1
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36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
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37 : I(v2*C)*(v2*v1) = C*v1
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38 : v1*I(v1) = U
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39 : I(C*(A*C))*v1 = A*v1
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40 : v2*(I(v2)*v1) = v1
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41 : I(U) = U
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Rule 13 deleted
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42 : I(I(v1)) = v1
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Rule 20 deleted
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43 : C*(B*v1) = B*(C*v1)
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Rule 29 deleted
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Rule 28 deleted
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Rule 26 deleted
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Rule 25 deleted
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44 : A*(C*(A*v1)) = C*v1
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Rule 24 deleted
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45 : A*(C*A) = C
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Rule 27 deleted
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46 : v2*(I(v1*v2)*v1) = U
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47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
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48 : I(I(B*A)*A) = B
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49 : v3*(I(v2*v3)*(v2*v1)) = v1
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50 : I(I(v1)*I(v2)) = v2*v1
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51 : I(I(B*(A*v1))*A) = B*v1
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52 : I(I(v1)*C) = C*v1
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53 : I(v2*I(v1*v2)) = v1
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54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
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55 : I(v1*(C*(A*C)))*v1 = A
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56 : v2*I(I(v1)*v2) = v1
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57 : I(v2*(I(v3*v1)*v3))*v2 = v1
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58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
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59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
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60 : I(v2*(v1*C))*(v2*v1) = C
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61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
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62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
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63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
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64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
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65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
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66 : I(I(B)*A)*A = B
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67 : I(A*A)*(B*(A*A)) = B
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68 : v1*(I(A*v1)*(B*A)) = B
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69 : I(I(v1*A)*(v1*B))*B = A
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70 : v1*I(C*v1) = C
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71 : I(A*I(v1))*(B*A) = v1*B
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72 : I(C*I(v1)) = v1*C
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73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
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74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
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75 : v3*(I(I(v2)*v3)*v1) = v2*v1
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76 : I(I(B*I(v1))*A)*(v1*A) = B
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77 : I(v1*A)*(v1*(B*(B*A))) = B*B
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78 : I(I(B)*A)*(A*v1) = B*v1
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79 : I(A*A)*(B*(A*(A*v1))) = B*v1
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80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
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81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
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82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
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83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
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84 : I(A*C)*(B*A) = B*C
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85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
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86 : v2*(I(C*v2)*v1) = C*v1
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87 : I(I(B*C)*A)*(C*A) = B
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88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
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89 : v2*(v1*I(v2*v1)) = U
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90 : B*(A*I(B)) = A
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91 : I(v2*v1)*v2 = I(v1)
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Rule 64 deleted
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Rule 57 deleted
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Rule 55 deleted
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Rule 46 deleted
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Rule 34 deleted
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Rule 31 deleted
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Rule 30 deleted
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92 : I(C*(A*C)) = A
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Rule 39 deleted
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93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
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Rule 60 deleted
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Rule 54 deleted
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Rule 47 deleted
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94 : I(v1*I(v2)) = v2*I(v1)
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Rule 83 deleted
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Rule 76 deleted
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Rule 74 deleted
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Rule 72 deleted
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Rule 71 deleted
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Rule 53 deleted
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Rule 50 deleted
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Rule 35 deleted
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95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
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96 : I(v1*(I(B)*A))*(v1*A) = B
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97 : I(v1*A)*(v1*B) = B*(C*(A*C))
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Rule 82 deleted
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Rule 69 deleted
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98 : I(v1*C) = C*I(v1)
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Rule 88 deleted
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Rule 87 deleted
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Rule 85 deleted
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Rule 84 deleted
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Rule 52 deleted
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Rule 37 deleted
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99 : v3*(v2*(I(v3*v2)*v1)) = v1
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100 : B*(A*(I(B)*v1)) = A*v1
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101 : I(v3*v2)*(v3*v1) = I(v2)*v1
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Rule 97 deleted
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Rule 96 deleted
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Rule 95 deleted
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Rule 93 deleted
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Rule 80 deleted
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Rule 77 deleted
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Rule 73 deleted
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Rule 65 deleted
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Rule 63 deleted
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Rule 62 deleted
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Rule 61 deleted
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Rule 59 deleted
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Rule 58 deleted
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Rule 49 deleted
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Rule 36 deleted
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Rule 33 deleted
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Rule 32 deleted
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Rule 15 deleted
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102 : B*(C*I(B)) = C
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103 : B*(C*(I(B)*v1)) = C*v1
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104 : B*(I(B*A)*A) = U
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105 : B*(I(B*A)*(A*v1)) = v1
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106 : I(B*A)*A = I(B)
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Rule 104 deleted
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Rule 48 deleted
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107 : B*(v1*(I(B*(A*v1))*A)) = U
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108 : I(I(B*(B*A))*A) = B*B
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109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
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110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
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111 : I(I(B)*A) = B*(C*(A*C))
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Rule 78 deleted
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Rule 66 deleted
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112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
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Rule 110 deleted
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Rule 108 deleted
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Rule 51 deleted
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113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
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114 : v1*I(C*(A*(C*v1))) = A
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115 : I(I(v1)*v2) = I(v2)*v1
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Rule 113 deleted
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Rule 112 deleted
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Rule 111 deleted
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Rule 75 deleted
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Rule 56 deleted
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116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
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117 : I(A*v1)*(B*A) = I(v1)*B
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Rule 116 deleted
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Rule 68 deleted
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118 : v2*(v1*I(C*(v2*v1))) = C
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119 : I(C*v1) = I(v1)*C
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Rule 118 deleted
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Rule 114 deleted
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Rule 92 deleted
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Rule 86 deleted
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Rule 70 deleted
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120 : v1*(I(A*(C*v1))*C) = A
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121 : I(A*A)*(B*(B*(A*A))) = B*B
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122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
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123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
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Rule 79 deleted
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Rule 67 deleted
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124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
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125 : v1*(I(A*v1)*(B*(B*A))) = B*B
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126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
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Rule 124 deleted
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Rule 123 deleted
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Rule 81 deleted
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127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
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128 : v2*I(v1*v2) = I(v1)
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Rule 89 deleted
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129 : A*I(B) = I(B)*A
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Rule 90 deleted
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130 : I(v1*v2) = I(v2)*I(v1)
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Rule 128 deleted
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Rule 127 deleted
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Rule 126 deleted
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Rule 125 deleted
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Rule 122 deleted
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Rule 121 deleted
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Rule 120 deleted
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Rule 119 deleted
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Rule 117 deleted
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Rule 115 deleted
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Rule 109 deleted
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Rule 107 deleted
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Rule 106 deleted
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Rule 105 deleted
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Rule 101 deleted
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Rule 99 deleted
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Rule 98 deleted
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Rule 94 deleted
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Rule 91 deleted
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131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
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132 : B*(C*(A*(C*(I(B)*A)))) = U
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133 : C*(A*(C*(I(B)*A))) = I(B)
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Rule 132 deleted
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134 : A*(I(B)*v1) = I(B)*(A*v1)
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Rule 100 deleted
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135 : C*I(B) = I(B)*C
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Rule 102 deleted
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136 : C*(I(B)*v1) = I(B)*(C*v1)
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Rule 133 deleted
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Rule 131 deleted
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Rule 103 deleted
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Canonical set found :
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1 : U*v1 = v1
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2 : I(v1)*v1 = U
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3 : (v3*v2)*v1 = v3*(v2*v1)
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4 : A*B = B*A
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5 : C*C = U
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6 : I(A) = C*(A*C)
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8 : I(v2)*(v2*v1) = v1
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9 : A*(B*v1) = B*(A*v1)
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10 : C*(C*v1) = v1
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21 : v1*U = v1
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22 : I(C) = C
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23 : C*B = B*C
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38 : v1*I(v1) = U
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40 : v2*(I(v2)*v1) = v1
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41 : I(U) = U
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42 : I(I(v1)) = v1
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43 : C*(B*v1) = B*(C*v1)
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44 : A*(C*(A*v1)) = C*v1
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45 : A*(C*A) = C
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129 : A*I(B) = I(B)*A
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130 : I(v1*v2) = I(v2)*I(v1)
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134 : A*(I(B)*v1) = I(B)*(A*v1)
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135 : C*I(B) = I(B)*C
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136 : C*(I(B)*v1) = I(B)*(C*v1)
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1 : U*v1 = v1
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2 : I(v1)*v1 = U
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3 : (v3*v2)*v1 = v3*(v2*v1)
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4 : A*B = B*A
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5 : C*C = U
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6 : I(A) = C*(A*I(C))
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7 : C*(B*I(C)) = B
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8 : I(v2)*(v2*v1) = v1
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9 : A*(B*v1) = B*(A*v1)
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10 : C*(C*v1) = v1
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11 : C*(A*(I(C)*A)) = U
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12 : C*(B*(I(C)*v1)) = B*v1
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13 : I(U)*v1 = v1
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14 : I(I(v1))*U = v1
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15 : I(v3*v2)*(v3*(v2*v1)) = v1
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16 : C*(A*(I(C)*(B*A))) = B
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17 : I(C)*U = C
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18 : C*(A*(I(C)*(A*v1))) = v1
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19 : I(C)*B = B*I(C)
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20 : I(I(v2))*v1 = v2*v1
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Rule 14 deleted
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21 : v1*U = v1
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Rule 17 deleted
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22 : I(C) = C
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Rule 19 deleted
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Rule 18 deleted
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Rule 16 deleted
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Rule 12 deleted
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Rule 11 deleted
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Rule 7 deleted
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23 : C*B = B*C
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24 : C*(A*(C*(A*v1))) = v1
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25 : C*(A*(C*(B*A))) = B
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26 : C*(B*(C*v1)) = B*v1
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27 : C*(A*(C*A)) = U
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28 : C*(B*C) = B
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29 : C*(A*(C*(B*(A*v1)))) = B*v1
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30 : I(I(v2*v1)*v2) = v1
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31 : I(v2*I(v1))*v2 = v1
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32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
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33 : I(v1*A)*(v1*(B*A)) = B
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34 : I(v1*C)*v1 = C
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35 : I(v3*I(v2))*(v3*v1) = v2*v1
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36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
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37 : I(v2*C)*(v2*v1) = C*v1
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38 : v1*I(v1) = U
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39 : I(C*(A*C))*v1 = A*v1
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40 : v2*(I(v2)*v1) = v1
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41 : I(U) = U
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Rule 13 deleted
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42 : I(I(v1)) = v1
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Rule 20 deleted
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43 : C*(B*v1) = B*(C*v1)
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Rule 29 deleted
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Rule 28 deleted
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Rule 26 deleted
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Rule 25 deleted
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44 : A*(C*(A*v1)) = C*v1
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Rule 24 deleted
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45 : A*(C*A) = C
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Rule 27 deleted
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46 : v2*(I(v1*v2)*v1) = U
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47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
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48 : I(I(B*A)*A) = B
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49 : v3*(I(v2*v3)*(v2*v1)) = v1
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50 : I(I(v1)*I(v2)) = v2*v1
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51 : I(I(B*(A*v1))*A) = B*v1
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52 : I(I(v1)*C) = C*v1
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53 : I(v2*I(v1*v2)) = v1
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54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
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55 : I(v1*(C*(A*C)))*v1 = A
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56 : v2*I(I(v1)*v2) = v1
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57 : I(v2*(I(v3*v1)*v3))*v2 = v1
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58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
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59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
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60 : I(v2*(v1*C))*(v2*v1) = C
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61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
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62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
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63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
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64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
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65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
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66 : I(I(B)*A)*A = B
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67 : I(A*A)*(B*(A*A)) = B
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68 : v1*(I(A*v1)*(B*A)) = B
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69 : I(I(v1*A)*(v1*B))*B = A
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70 : v1*I(C*v1) = C
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71 : I(A*I(v1))*(B*A) = v1*B
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72 : I(C*I(v1)) = v1*C
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73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
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74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
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75 : v3*(I(I(v2)*v3)*v1) = v2*v1
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76 : I(I(B*I(v1))*A)*(v1*A) = B
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77 : I(v1*A)*(v1*(B*(B*A))) = B*B
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78 : I(I(B)*A)*(A*v1) = B*v1
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79 : I(A*A)*(B*(A*(A*v1))) = B*v1
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80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
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81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
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82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
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83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
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84 : I(A*C)*(B*A) = B*C
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85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
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86 : v2*(I(C*v2)*v1) = C*v1
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87 : I(I(B*C)*A)*(C*A) = B
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88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
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89 : v2*(v1*I(v2*v1)) = U
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90 : B*(A*I(B)) = A
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91 : I(v2*v1)*v2 = I(v1)
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Rule 64 deleted
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Rule 57 deleted
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Rule 55 deleted
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Rule 46 deleted
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Rule 34 deleted
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Rule 31 deleted
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Rule 30 deleted
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92 : I(C*(A*C)) = A
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Rule 39 deleted
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93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
|
|
Rule 60 deleted
|
|
Rule 54 deleted
|
|
Rule 47 deleted
|
|
94 : I(v1*I(v2)) = v2*I(v1)
|
|
Rule 83 deleted
|
|
Rule 76 deleted
|
|
Rule 74 deleted
|
|
Rule 72 deleted
|
|
Rule 71 deleted
|
|
Rule 53 deleted
|
|
Rule 50 deleted
|
|
Rule 35 deleted
|
|
95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
|
|
96 : I(v1*(I(B)*A))*(v1*A) = B
|
|
97 : I(v1*A)*(v1*B) = B*(C*(A*C))
|
|
Rule 82 deleted
|
|
Rule 69 deleted
|
|
98 : I(v1*C) = C*I(v1)
|
|
Rule 88 deleted
|
|
Rule 87 deleted
|
|
Rule 85 deleted
|
|
Rule 84 deleted
|
|
Rule 52 deleted
|
|
Rule 37 deleted
|
|
99 : v3*(v2*(I(v3*v2)*v1)) = v1
|
|
100 : B*(A*(I(B)*v1)) = A*v1
|
|
101 : I(v3*v2)*(v3*v1) = I(v2)*v1
|
|
Rule 97 deleted
|
|
Rule 96 deleted
|
|
Rule 95 deleted
|
|
Rule 93 deleted
|
|
Rule 80 deleted
|
|
Rule 77 deleted
|
|
Rule 73 deleted
|
|
Rule 65 deleted
|
|
Rule 63 deleted
|
|
Rule 62 deleted
|
|
Rule 61 deleted
|
|
Rule 59 deleted
|
|
Rule 58 deleted
|
|
Rule 49 deleted
|
|
Rule 36 deleted
|
|
Rule 33 deleted
|
|
Rule 32 deleted
|
|
Rule 15 deleted
|
|
102 : B*(C*I(B)) = C
|
|
103 : B*(C*(I(B)*v1)) = C*v1
|
|
104 : B*(I(B*A)*A) = U
|
|
105 : B*(I(B*A)*(A*v1)) = v1
|
|
106 : I(B*A)*A = I(B)
|
|
Rule 104 deleted
|
|
Rule 48 deleted
|
|
107 : B*(v1*(I(B*(A*v1))*A)) = U
|
|
108 : I(I(B*(B*A))*A) = B*B
|
|
109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
|
|
110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
|
|
111 : I(I(B)*A) = B*(C*(A*C))
|
|
Rule 78 deleted
|
|
Rule 66 deleted
|
|
112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
|
|
Rule 110 deleted
|
|
Rule 108 deleted
|
|
Rule 51 deleted
|
|
113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
|
|
114 : v1*I(C*(A*(C*v1))) = A
|
|
115 : I(I(v1)*v2) = I(v2)*v1
|
|
Rule 113 deleted
|
|
Rule 112 deleted
|
|
Rule 111 deleted
|
|
Rule 75 deleted
|
|
Rule 56 deleted
|
|
116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
|
|
117 : I(A*v1)*(B*A) = I(v1)*B
|
|
Rule 116 deleted
|
|
Rule 68 deleted
|
|
118 : v2*(v1*I(C*(v2*v1))) = C
|
|
119 : I(C*v1) = I(v1)*C
|
|
Rule 118 deleted
|
|
Rule 114 deleted
|
|
Rule 92 deleted
|
|
Rule 86 deleted
|
|
Rule 70 deleted
|
|
120 : v1*(I(A*(C*v1))*C) = A
|
|
121 : I(A*A)*(B*(B*(A*A))) = B*B
|
|
122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
|
|
123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
|
|
Rule 79 deleted
|
|
Rule 67 deleted
|
|
124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
|
|
125 : v1*(I(A*v1)*(B*(B*A))) = B*B
|
|
126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
|
|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
|
127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
|
|
128 : v2*I(v1*v2) = I(v1)
|
|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*I(C))
|
|
7 : C*(B*I(C)) = B
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
11 : C*(A*(I(C)*A)) = U
|
|
12 : C*(B*(I(C)*v1)) = B*v1
|
|
13 : I(U)*v1 = v1
|
|
14 : I(I(v1))*U = v1
|
|
15 : I(v3*v2)*(v3*(v2*v1)) = v1
|
|
16 : C*(A*(I(C)*(B*A))) = B
|
|
17 : I(C)*U = C
|
|
18 : C*(A*(I(C)*(A*v1))) = v1
|
|
19 : I(C)*B = B*I(C)
|
|
20 : I(I(v2))*v1 = v2*v1
|
|
Rule 14 deleted
|
|
21 : v1*U = v1
|
|
Rule 17 deleted
|
|
22 : I(C) = C
|
|
Rule 19 deleted
|
|
Rule 18 deleted
|
|
Rule 16 deleted
|
|
Rule 12 deleted
|
|
Rule 11 deleted
|
|
Rule 7 deleted
|
|
23 : C*B = B*C
|
|
24 : C*(A*(C*(A*v1))) = v1
|
|
25 : C*(A*(C*(B*A))) = B
|
|
26 : C*(B*(C*v1)) = B*v1
|
|
27 : C*(A*(C*A)) = U
|
|
28 : C*(B*C) = B
|
|
29 : C*(A*(C*(B*(A*v1)))) = B*v1
|
|
30 : I(I(v2*v1)*v2) = v1
|
|
31 : I(v2*I(v1))*v2 = v1
|
|
32 : I(v4*(v3*v2))*(v4*(v3*(v2*v1))) = v1
|
|
33 : I(v1*A)*(v1*(B*A)) = B
|
|
34 : I(v1*C)*v1 = C
|
|
35 : I(v3*I(v2))*(v3*v1) = v2*v1
|
|
36 : I(v2*A)*(v2*(B*(A*v1))) = B*v1
|
|
37 : I(v2*C)*(v2*v1) = C*v1
|
|
38 : v1*I(v1) = U
|
|
39 : I(C*(A*C))*v1 = A*v1
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
Rule 13 deleted
|
|
42 : I(I(v1)) = v1
|
|
Rule 20 deleted
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
Rule 29 deleted
|
|
Rule 28 deleted
|
|
Rule 26 deleted
|
|
Rule 25 deleted
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
Rule 24 deleted
|
|
45 : A*(C*A) = C
|
|
Rule 27 deleted
|
|
46 : v2*(I(v1*v2)*v1) = U
|
|
47 : I(I(v3*(v2*v1))*(v3*v2)) = v1
|
|
48 : I(I(B*A)*A) = B
|
|
49 : v3*(I(v2*v3)*(v2*v1)) = v1
|
|
50 : I(I(v1)*I(v2)) = v2*v1
|
|
51 : I(I(B*(A*v1))*A) = B*v1
|
|
52 : I(I(v1)*C) = C*v1
|
|
53 : I(v2*I(v1*v2)) = v1
|
|
54 : I(v3*(v2*I(v1)))*(v3*v2) = v1
|
|
55 : I(v1*(C*(A*C)))*v1 = A
|
|
56 : v2*I(I(v1)*v2) = v1
|
|
57 : I(v2*(I(v3*v1)*v3))*v2 = v1
|
|
58 : I(v5*(v4*(v3*v2)))*(v5*(v4*(v3*(v2*v1)))) = v1
|
|
59 : I(v2*(v1*A))*(v2*(v1*(B*A))) = B
|
|
60 : I(v2*(v1*C))*(v2*v1) = C
|
|
61 : I(v4*(v3*I(v2)))*(v4*(v3*v1)) = v2*v1
|
|
62 : I(v3*(v2*A))*(v3*(v2*(B*(A*v1)))) = B*v1
|
|
63 : I(v3*(v2*C))*(v3*(v2*v1)) = C*v1
|
|
64 : I(v3*(I(v4*v2)*v4))*(v3*v1) = v2*v1
|
|
65 : v4*(I(v3*(v2*v4))*(v3*(v2*v1))) = v1
|
|
66 : I(I(B)*A)*A = B
|
|
67 : I(A*A)*(B*(A*A)) = B
|
|
68 : v1*(I(A*v1)*(B*A)) = B
|
|
69 : I(I(v1*A)*(v1*B))*B = A
|
|
70 : v1*I(C*v1) = C
|
|
71 : I(A*I(v1))*(B*A) = v1*B
|
|
72 : I(C*I(v1)) = v1*C
|
|
73 : I(v2*(C*(A*C)))*(v2*v1) = A*v1
|
|
74 : I(A*I(v2))*(B*(A*v1)) = v2*(B*v1)
|
|
75 : v3*(I(I(v2)*v3)*v1) = v2*v1
|
|
76 : I(I(B*I(v1))*A)*(v1*A) = B
|
|
77 : I(v1*A)*(v1*(B*(B*A))) = B*B
|
|
78 : I(I(B)*A)*(A*v1) = B*v1
|
|
79 : I(A*A)*(B*(A*(A*v1))) = B*v1
|
|
80 : I(v2*A)*(v2*(B*(B*(A*v1)))) = B*(B*v1)
|
|
81 : v2*(I(A*v2)*(B*(A*v1))) = B*v1
|
|
82 : I(I(v2*A)*(v2*B))*(B*v1) = A*v1
|
|
83 : I(I(B*I(v2))*A)*(v2*(A*v1)) = B*v1
|
|
84 : I(A*C)*(B*A) = B*C
|
|
85 : I(A*C)*(B*(A*v1)) = B*(C*v1)
|
|
86 : v2*(I(C*v2)*v1) = C*v1
|
|
87 : I(I(B*C)*A)*(C*A) = B
|
|
88 : I(I(B*C)*A)*(C*(A*v1)) = B*v1
|
|
89 : v2*(v1*I(v2*v1)) = U
|
|
90 : B*(A*I(B)) = A
|
|
91 : I(v2*v1)*v2 = I(v1)
|
|
Rule 64 deleted
|
|
Rule 57 deleted
|
|
Rule 55 deleted
|
|
Rule 46 deleted
|
|
Rule 34 deleted
|
|
Rule 31 deleted
|
|
Rule 30 deleted
|
|
92 : I(C*(A*C)) = A
|
|
Rule 39 deleted
|
|
93 : I(v3*(v2*v1))*(v3*v2) = I(v1)
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Rule 60 deleted
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Rule 54 deleted
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Rule 47 deleted
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94 : I(v1*I(v2)) = v2*I(v1)
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Rule 83 deleted
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Rule 76 deleted
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Rule 74 deleted
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Rule 72 deleted
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Rule 71 deleted
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Rule 53 deleted
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Rule 50 deleted
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Rule 35 deleted
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95 : I(v2*(I(B)*A))*(v2*(A*v1)) = B*v1
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96 : I(v1*(I(B)*A))*(v1*A) = B
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97 : I(v1*A)*(v1*B) = B*(C*(A*C))
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Rule 82 deleted
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Rule 69 deleted
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98 : I(v1*C) = C*I(v1)
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Rule 88 deleted
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Rule 87 deleted
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Rule 85 deleted
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Rule 84 deleted
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Rule 52 deleted
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Rule 37 deleted
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99 : v3*(v2*(I(v3*v2)*v1)) = v1
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100 : B*(A*(I(B)*v1)) = A*v1
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101 : I(v3*v2)*(v3*v1) = I(v2)*v1
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Rule 97 deleted
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Rule 96 deleted
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Rule 95 deleted
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Rule 93 deleted
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Rule 80 deleted
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Rule 77 deleted
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Rule 73 deleted
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Rule 65 deleted
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Rule 63 deleted
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Rule 62 deleted
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Rule 61 deleted
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Rule 59 deleted
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Rule 58 deleted
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Rule 49 deleted
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Rule 36 deleted
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Rule 33 deleted
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Rule 32 deleted
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Rule 15 deleted
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102 : B*(C*I(B)) = C
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103 : B*(C*(I(B)*v1)) = C*v1
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104 : B*(I(B*A)*A) = U
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105 : B*(I(B*A)*(A*v1)) = v1
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106 : I(B*A)*A = I(B)
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Rule 104 deleted
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Rule 48 deleted
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107 : B*(v1*(I(B*(A*v1))*A)) = U
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108 : I(I(B*(B*A))*A) = B*B
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109 : B*(v2*(I(B*(A*v2))*(A*v1))) = v1
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110 : I(I(B*(B*(A*v1)))*A) = B*(B*v1)
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111 : I(I(B)*A) = B*(C*(A*C))
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Rule 78 deleted
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Rule 66 deleted
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112 : I(I(B*v1)*A) = B*(C*(A*(C*v1)))
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Rule 110 deleted
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Rule 108 deleted
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Rule 51 deleted
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113 : v3*(v2*I(I(v1)*(v3*v2))) = v1
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114 : v1*I(C*(A*(C*v1))) = A
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115 : I(I(v1)*v2) = I(v2)*v1
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Rule 113 deleted
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Rule 112 deleted
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Rule 111 deleted
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Rule 75 deleted
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Rule 56 deleted
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116 : v2*(v1*(I(A*(v2*v1))*(B*A))) = B
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117 : I(A*v1)*(B*A) = I(v1)*B
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Rule 116 deleted
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Rule 68 deleted
|
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118 : v2*(v1*I(C*(v2*v1))) = C
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119 : I(C*v1) = I(v1)*C
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Rule 118 deleted
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Rule 114 deleted
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Rule 92 deleted
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Rule 86 deleted
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Rule 70 deleted
|
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120 : v1*(I(A*(C*v1))*C) = A
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121 : I(A*A)*(B*(B*(A*A))) = B*B
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122 : I(A*A)*(B*(B*(A*(A*v1)))) = B*(B*v1)
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123 : I(A*A)*(B*(A*v1)) = B*(C*(A*(C*v1)))
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|
Rule 79 deleted
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Rule 67 deleted
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124 : v3*(v2*(I(A*(v3*v2))*(B*(A*v1)))) = B*v1
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125 : v1*(I(A*v1)*(B*(B*A))) = B*B
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126 : I(A*v2)*(B*(A*v1)) = I(v2)*(B*v1)
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|
Rule 124 deleted
|
|
Rule 123 deleted
|
|
Rule 81 deleted
|
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127 : v3*(v2*(v1*I(v3*(v2*v1)))) = U
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128 : v2*I(v1*v2) = I(v1)
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|
Rule 89 deleted
|
|
129 : A*I(B) = I(B)*A
|
|
Rule 90 deleted
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
Rule 128 deleted
|
|
Rule 127 deleted
|
|
Rule 126 deleted
|
|
Rule 125 deleted
|
|
Rule 122 deleted
|
|
Rule 121 deleted
|
|
Rule 120 deleted
|
|
Rule 119 deleted
|
|
Rule 117 deleted
|
|
Rule 115 deleted
|
|
Rule 109 deleted
|
|
Rule 107 deleted
|
|
Rule 106 deleted
|
|
Rule 105 deleted
|
|
Rule 101 deleted
|
|
Rule 99 deleted
|
|
Rule 98 deleted
|
|
Rule 94 deleted
|
|
Rule 91 deleted
|
|
131 : B*(C*(A*(C*(I(B)*(A*v1))))) = v1
|
|
132 : B*(C*(A*(C*(I(B)*A)))) = U
|
|
133 : C*(A*(C*(I(B)*A))) = I(B)
|
|
Rule 132 deleted
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
Rule 100 deleted
|
|
135 : C*I(B) = I(B)*C
|
|
Rule 102 deleted
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|
|
Rule 133 deleted
|
|
Rule 131 deleted
|
|
Rule 103 deleted
|
|
Canonical set found :
|
|
1 : U*v1 = v1
|
|
2 : I(v1)*v1 = U
|
|
3 : (v3*v2)*v1 = v3*(v2*v1)
|
|
4 : A*B = B*A
|
|
5 : C*C = U
|
|
6 : I(A) = C*(A*C)
|
|
8 : I(v2)*(v2*v1) = v1
|
|
9 : A*(B*v1) = B*(A*v1)
|
|
10 : C*(C*v1) = v1
|
|
21 : v1*U = v1
|
|
22 : I(C) = C
|
|
23 : C*B = B*C
|
|
38 : v1*I(v1) = U
|
|
40 : v2*(I(v2)*v1) = v1
|
|
41 : I(U) = U
|
|
42 : I(I(v1)) = v1
|
|
43 : C*(B*v1) = B*(C*v1)
|
|
44 : A*(C*(A*v1)) = C*v1
|
|
45 : A*(C*A) = C
|
|
129 : A*I(B) = I(B)*A
|
|
130 : I(v1*v2) = I(v2)*I(v1)
|
|
134 : A*(I(B)*v1) = I(B)*(A*v1)
|
|
135 : C*I(B) = I(B)*C
|
|
136 : C*(I(B)*v1) = I(B)*(C*v1)
|