a0 a1 a2 a3 a4 a5 a3 a6 2003{2004 a7 a8 a9 a10 a7 a11 a12 a13 a14 a11 a15 a16 a17 a17 a18 a19a21a20a21a22 a23a25a24a27a26a21a28a30a29a30a31 a19a21a20a21a32a34a33a21a24 2004 a35 1 a36 a37a21a38 a39 a40 a41a21a42 a43a21a44 a45 a44 a46 a47 a48 a49 a50 a51 a52 a53 a54 a55 a56a21a57 a58 a57 a59a61a60 (9 a62 ) a63a65a64a67a66a61a68a61a69a61a70a61a71 f:, _, ^, !, $ga72a61a73a61a74a61a75a61a76a61a77a61a78a25a79a25a80a61a70 a81a83a82 a84 a63a86a85a88a87 ) a89 a90a86a91 f:, _, ^, !, $g a92a67a93a61a94a61a95a61a96a65a97a61a98a67a99a25a100a25a101a25a102a25a94 3 a103a61a104a106a105a61a107a65a108 a91 f:, _g, f:, ^g, f:, !g. a109 a105a86a110a88a111 a91a113a112 a103 3 a105 a75 a60 (19 a62 ) a114 p; q a115 r a116a86a117a86a118a86a119a86a76a61a104a120a117a25a118a61a121a61a122 a123 p ! (:(q ! r) ^ r) (1) a63a88a64 a72a86a124a86a125a86a126a86a127 (2) a128a86a129 a59a86a130a86a131a61a132 a66a25a68a61a69 :;!a72a86a117a86a118a86a121a86a122 a133a86a134 , ; (3) a129 a72 a59a86a130a86a135a86a136a61a137 a122a61a138 a59a61a130 a71 a136a61a137 a122a61a139 a90a86a91 (1) a93a88a140a142a141a86a143a86a144a65a108 a91 p q r p q r 0 0 0 1 1 0 0 0 0 1 0 1 0 0 1 1 0 1 1 1 1 0 1 0 1 1 0 0 1 1 1 0 1 (2) a145a86a146 a108 :p. (3) a147a86a146a88a148a86a149a86a150a67a151a61a146a152a148a61a149a106a153a61a145a61a146a152a108 :p. a109 a105a86a110a88a111 a91 (1) a112a86a154 1 a105a86a139 (2) a155a86a156a88a157a142a158a86a159a61a104 5 a105a86a139 (3) a155a86a156a88a157a142a158a86a159a61a104 a112 a103a152a148a61a149 3 a105a86a139 a160 a60 (10 a62 ) a114 a160 a76a86a124a86a125a61a161a25a162 f : f0; 1g3 ! f0; 1ga163a86a164 a91 f(0; 0; 0) = 1; f(1; 0; 0) = 0; f(0; 1; 0) = 0; f(0; 0; 1) = 1 f(0; 1; 1) = 1; f(1; 0; 1) = 1; f(1; 1; 0) = 0; f(1; 1; 1) = 1 a128a86a129 a59a86a130a86a165a86a132 a66a86a68a61a69 :a60 _a115 ^a72a86a117a86a118a86a121a86a122 a133a86a134 a166a86a167a86a72a86a124a86a125a86a161a86a162a86a168 a116 f. a90a86a169 a159 (a148a86a149 a169 1): 0 = (:p _ q _ r) ^ (p _:q _ r) ^ (:p _:q _ r) , (:p _ q) ^ (p _:q) ^ (:p _:q) _ r , (:p _ q) ^ ((:p ^ p) _:q) _ r , (:p _ q) ^:q _ r , (:p ^:q) _ (q ^:q) _ r , (:p ^:q) _ r , :(p _ q) _ r a170 = :(p _ q) _ r a171a86a108a142a93a88a140a142a89 a90a86a169 a95 (a148a86a149 a169 2): 0 = (:p ^:q ^:r) _ (:p ^:q ^ r) _ (:p ^ q ^ r) _ (p ^:q ^ r) _ (p ^ q ^ r) , (:p ^:q ^:r) _ ((:p ^:q) _ (:p ^ q)) ^ r _ ((p ^:q) _ (p ^ q)) ^ r , (:p ^:q ^:r) _ :p ^ r _ p ^ r , (:p ^:q ^:r) _ r , (:p ^:q) _ r , :(p _ q) _ r a170 = :(p _ q) _ r a171a86a108a142a93a88a140a142a89 a90a86a169a86a172 ( a173a86a174 a169 ): 2 a175 f 1(q; r) = f(0; q; r), f2(q; r) = f(1; q; r), a171 f1 a60 f 2 a108a67a176a61a177a65a92a61a178a67a103a61a95a61a96 a141a86a143a88a179a142a180 a91 f1(0; 0) = 1; f1(0; 1) = 1; f1(1; 0) = 0; f1(1; 1) = 1 f2(0; 0) = 0; f2(0; 1) = 1; f2(1; 0) = 0; f2(1; 1) = 1 a181a142a182 a91 f 1 a145a88a183a142a184a86a185a88a186a86a149 1 = q ! r a144a86a187a86a104 f2 a145a88a183a142a184a86a185a88a186a86a149 2 = r a144 a187a86a104a106a188a88a189 f a145a88a183a142a176a86a177a86a184a61a185a152a186a61a149 0 a144a86a187 a91 0 = (:p ! (q ! r)) ^ (p ! r) , ((:p ^ q) ! r) ^ (p ! r) , ((:p ^ q) _ p) ! r , (p _ q) ! r , :(p _ q) _ r a170 = :(p _ q) _ r a171a86a108a142a93a88a140a142a89 a109 a105a86a110a88a111 a91 (1) a190a67a191a65a192a65a193a195a194a25a196a152a92a120a151a25a146a152a148a27a149a106a104 a170a106a197 6 a105a61a104a106a198a65a192 a60a25a199 a192a106a200a152a201a27a192a106a159a25a103 a151a86a146a86a202a86a203 2 a105a86a104a25a204a142a205a86a203a61a206 8 a105a88a108a142a207a86a89a106a194a86a196a25a208a210a209a195a211 2 a105a86a89 (2) a212a214a213a86a89 (3) a194a61a196a65a192a65a193 f1 a215 f2 a211 2 a105a61a104a106a194a61a196a65a192a65a193 f1 a215 f2 a92a67a144a61a187a61a211 2 a105a61a89a106a194 a196a86a151a88a216a88a193 f a92a142a144a86a187a86a211 2 a105a86a89a106a194a86a196a86a208a210a209 f a92a142a144a86a187a86a211 2 a105a86a89 a217 a60 (10 a62 ) a63a88a64a142a218a86a122 : ! ( ! ) a219 P a220a142a72 a59a86a130a86a221a65a222a67a223a25a224 a139 a225 a91 (1) (: ! : ) ! ( ! ) (A3) (2) ((: ! : ) ! ( ! )) ! (: ! ((: ! : ) ! ( ! ))) (A1) (3) : ! ((: ! : ) ! ( ! )) (M) (4) (: ! ((: ! : ) ! ( ! ))) ! ((: ! (: ! : )) ! (: ! ( ! ))) (A2) (5) (: ! (: ! : )) ! (: ! ( ! )) (M) (6) : ! (: ! : ) (A1) (7) : ! ( ! ) (M) a109 a105a86a110a88a111 a91 a155a86a156a88a157a142a158a86a159a61a104a120a226a61a191a25a227a65a228a61a229a106a177a61a110a152a111 a91 a230a210a231a195a232a61a233a65a150a67a234 a170a106a235 a153a152a157a106a236a25a237a152a238a106a104a240a239a242a241a152a157a106a243a152a238a106a244a25a245a25a246a25a104a120a247a25a185a152a248a106a89 a112a86a249a86a250 a159a86a251a61a203 2 a105a86a104a25a204a106a252a142a203a86a206 10 a105a88a108a142a207a86a89 a157a86a192a253a233a254a183a253a104a255a200a1a0a3a2a5a4a142a104 a112a86a249a86a250 a159a86a251a86a203 5a105 a89 a204 a252a253a203a86a206 10a105a254a108a253a207 a89 3 a238a88a231a7a6a7a8a86a141a65a149 a81a9a6a11a10a13a12a61a233a15a14a104 a170 a211 0 a105a86a89 a16 a60 (10 a62 ) a63a88a64a142a164 a224 a218a61a122 : $ ‘ :( $ ) a219 N a220a142a72 a59a86a130a86a221a65a222a67a223a61a224 a139 a225 a91 (1) : $ ; ::( $ ); : ;:( $ ) ‘ :( $ ) (2) (2) : $ ; ::( $ ); : ;:( $ ) ‘ ::( $ ) (2) (3) : $ ; ::( $ ); : ‘ $ (: (1)(2)) (4) : $ ; ::( $ ); : ‘ : (2) (5) : $ ; ::( $ ); : ‘ : $ (2) (6) : $ ; ::( $ ); : ‘ ($ (4)(5)) (7) : $ ; ::( $ ); : ‘ ($ (3)(6)) (8) : $ ; ::( $ ) ‘ ($ (4)(7)) (9) : $ ; ::( $ );:( $ ) ‘ :( $ ) (2) (10) : $ ; ::( $ );:( $ ) ‘ ::( $ ) (2) (11) : $ ; ::( $ ) ‘ $ (: (9)(10)) (12) : $ ; ::( $ ) ‘ ($ (8)(11)) (13) : $ ; ::( $ ) ‘ : $ (2) (14) : $ ; ::( $ ) ‘ : ($ (12)(13)) (15) : $ ; ::( $ ) ‘ :( $ ) (: (8)(14)) a109 a105a86a110a88a111 a91 a155a86a156a88a157a142a158a86a159a61a104a120a226a61a191a25a227a65a228a61a229a106a177a61a110a152a111 a91 a230a210a231a195a234 a170a67a235 a153a152a157a120a236a25a237a240a238a106a104a240a239a242a241a240a157a106a243a240a238a106a244a25a245a27a246a25a104a120a247a25a185a152a248a120a89 a112a25a249a25a250 a159a86a251a86a203 2 a105a86a104a25a204a86a252a142a203a61a206 10 a105a25a108a142a207a86a89 a192a86a157a88a193a214a233a88a183a67a104a142a200a65a238a106a198a61a233a65a183a67a104 a112a61a249a61a250 a159a25a251a61a203 5 a105a86a89 a204a86a252a142a203a86a206 10 a105 a108a142a207a86a89 a238a88a231a7a6a142a94a1a17a19a18a25a233a65a186a25a149 a81a20a6a67a145 a225 a149a21a14a104 a170 a211 0 a105a86a89 a22 a60 (12 a62 ) a114 NL a220a142a218a86a122 a123 a91 9x 2F21 (x1; f32 (x1; x2; x3)) ! 8x3F22 (x1; x2), a23 t a123 f21 (x1; x2). (1) a63a88a64 a72a3a24a142a87a142a119a86a76a61a115a19a25a27a26a61a119a25a76a61a139 (2) a129 (x1=t), (x2=t) a115 (x3=t). (3) a28 t a62a1a29a1a30 x1; x2; x3 a219 a220a142a116a1a31a3a24a142a87a11a32 a90a86a91 (1) a92a3a33a214a183a1a34a142a96 a91 x 1; x2; x3, a35a7a36a37a34a142a96 a91a39a38 (2) (x1=t) = 9x2F21 (t; f32 (t; x2; x3)) ! 8x3F22 (t; x2) (x2=t) = 9x2F21 (x1; f32 (x1; x2; x3)) ! 8x3F22 (x1; t) (x3=t) = 9x2F21 (x1; f32 (x1; x2; t)) ! 8x3F22 (x1; x2) 4 (3) t a40 x1 a60 x3 a41 a42a86a157a3a33a214a183a142a139 t a40 x2 a41 a42a3a33a214a183a142a139 a109 a105a86a110a88a111 a91 (1) a112 a103a37a34a142a96 1 a105a86a139 (2) a112 a103a88a149a142a100 2 a105a86a139 (3) t a40 a112 a103a37a34a142a96 1 a105a86a139 a43 a60 (10 a62 ) a63a88a64 NL a220a142a164 a224 a218a86a122a61a72a27a44a19a26 a137 a122 a91 (9x1F(x1; x2) _8x2F(x1; x2)) ! 8x1x2F(x1; x2): a90a86a91 (9x1F(x1; x2) _8x2F(x1; x2)) ! 8x1x2F(x1; x2) j j (9x3F(x3; x2) _8x4F(x1; x4)) ! 8x5x6F(x5; x6) j j 9x38x4(F(x3; x2) _ F(x1; x4)) ! 8x5x6F(x5; x6) j j 8x39x4 (F(x3; x2) _ F(x1; x4)) ! 8x5x6F(x5; x6) j j 8x39x48x5x6 (F(x3; x2) _ F(x1; x4)) ! F(x5; x6) a109 a105a86a110a88a111 a91 (1) a45a142a95a37a46a1a42a142a104a27a157a5a40a47a35a5a36a11a34a106a96a19a48a27a49a65a92a67a104 a112 a159a19a50a25a203 1 a105a86a89 a51 a33a214a183a1a34a142a96a19a48a27a49a65a92a106a104 a112 a159a19a50a25a203 1 a105a86a89 (2) a45 a172 a60a53a52 a150a5a54a11a46a27a42a67a104a120a176 a51a19a55a19a56 a48a61a198a27a49a65a92a67a104 a112 a50a61a203 2 a105a86a89 (3) a45 a52 a150a7a54a37a46a27a42a67a104 a55a19a56a27a57a19a58 a94a25a198a19a59a152a92a67a104 a112 a159a27a50a61a203 1 a105a86a139 a60 a60 (10 a62 ) a114 x a82a86a219a86a218a86a122 a220a37a24a142a87a86a64a7a61a61a89a120a219 NL a220 a221a88a222 a91 ( ! 9x ) ! 8x ‘ 8x( ! 8x ): a225 a91 (1) ( ! 9x ) ! 8x ; ; ‘ (2) (2) ( ! 9x ) ! 8x ; ; ‘ 9x (9+) (3) ( ! 9x ) ! 8x ; ‘ ! 9x (! +) (4) ( ! 9x ) ! 8x ; ‘ ( ! 9x ) ! 8x (2) (5) ( ! 9x ) ! 8x ; ‘ 8x (! ) (6) ( ! 9x ) ! 8x ‘ ! 8x (! +) (7) ( ! 9x ) ! 8x ‘ 8x( ! 8x ) (8+) (x a157 a41a1a62a1a63 a42a64a33a195a183a152a193a66a65 5 a109 a105a86a110a88a111 a91 a155a86a156a88a157a142a158a86a159a61a89 a192a86a157a88a193a214a233a88a183a67a104a142a200a65a238a106a198a61a233a65a183a67a104 a112a61a249a61a250 a159a25a251a61a203 5 a105a86a89 a204a86a252a142a203a86a206 10 a105 a108a142a207a86a89 a238a88a231a7a6a142a94a1a17a19a18a25a233a65a186a25a149 a81a20a6a67a145 a225 a149a21a14a104 a170 a211 0 a105a86a89 a67 a60 (10 a62 ) a219 KL a220 a221a88a222 a91 ‘ 9x8y ! 8y9x . a225 a91 (1) ‘ ! 9x ( a68 a225 ) (2) ‘ 8y( ! 9x ) (a68 a225 ) (3) ‘ 8y ! 8y9x (a68 a225 ) (4) ‘ 8x(8y ! 8y9x ) (a68 a225 ) (5) ‘ 8x(8y ! 8y9x ) ! (9x8y ! 8y9x ) (a68 a225 ) (6) ‘ 9x8y ! 8y9x (M) a109 a105a86a110a88a111 a91 a155a86a156a88a157a142a158a86a159a61a89 a192a86a157a88a193a214a233a88a183a67a104a142a200a65a238a106a198a61a233a65a183a67a104 a112a61a249a61a250 a159a25a251a61a203 5 a105a86a89 a204a86a252a142a203a86a206 10 a105 a108a142a207a86a89 a238a88a231a7a6a7a8a86a141a65a149 a81a9a6a11a10a13a12a61a233a15a14a104 a170 a211 0 a105a86a89 6