author | wenzelm |
Tue, 27 Apr 1999 15:13:35 +0200 | |
changeset 6529 | 0f4c2ebc5018 |
parent 5723 | 81e1a83ee002 |
child 6645 | 6c62700fa48a |
permissions | -rw-r--r-- |
1462 | 1 |
(* Title: FOL/ex/cla.ML |
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ID: $Id$ |
1459 | 3 |
Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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FOL/ex/cla: proofs now use deepen_tac instead of best_tac FOL_dup_cs
lcp
parents:
644
diff
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Copyright 1994 University of Cambridge |
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|
6 |
Classical First-Order Logic |
|
7 |
*) |
|
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||
1462 | 9 |
writeln"File FOL/ex/cla.ML"; |
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|
5150 | 11 |
context FOL.thy; |
12 |
||
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b301958c465d
Renamed structure Int (intuitionistic prover) to IntPr to prevent clash
paulson
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13 |
open Cla; (*in case structure IntPr is open!*) |
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|
5150 | 15 |
Goal "(P --> Q | R) --> (P-->Q) | (P-->R)"; |
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Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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|
16 |
by (Blast_tac 1); |
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result(); |
18 |
||
19 |
(*If and only if*) |
|
20 |
||
5150 | 21 |
Goal "(P<->Q) <-> (Q<->P)"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
22 |
by (Blast_tac 1); |
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result(); |
24 |
||
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Goal "~ (P <-> ~P)"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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diff
changeset
|
26 |
by (Blast_tac 1); |
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result(); |
28 |
||
29 |
||
30 |
(*Sample problems from |
|
31 |
F. J. Pelletier, |
|
32 |
Seventy-Five Problems for Testing Automatic Theorem Provers, |
|
33 |
J. Automated Reasoning 2 (1986), 191-216. |
|
34 |
Errata, JAR 4 (1988), 236-236. |
|
35 |
||
36 |
The hardest problems -- judging by experience with several theorem provers, |
|
37 |
including matrix ones -- are 34 and 43. |
|
38 |
*) |
|
39 |
||
40 |
writeln"Pelletier's examples"; |
|
41 |
(*1*) |
|
5150 | 42 |
Goal "(P-->Q) <-> (~Q --> ~P)"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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diff
changeset
|
43 |
by (Blast_tac 1); |
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result(); |
45 |
||
46 |
(*2*) |
|
5150 | 47 |
Goal "~ ~ P <-> P"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
48 |
by (Blast_tac 1); |
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result(); |
50 |
||
51 |
(*3*) |
|
5150 | 52 |
Goal "~(P-->Q) --> (Q-->P)"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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diff
changeset
|
53 |
by (Blast_tac 1); |
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result(); |
55 |
||
56 |
(*4*) |
|
5150 | 57 |
Goal "(~P-->Q) <-> (~Q --> P)"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
58 |
by (Blast_tac 1); |
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result(); |
60 |
||
61 |
(*5*) |
|
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Goal "((P|Q)-->(P|R)) --> (P|(Q-->R))"; |
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Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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|
63 |
by (Blast_tac 1); |
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result(); |
65 |
||
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(*6*) |
|
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Goal "P | ~ P"; |
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Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
68 |
by (Blast_tac 1); |
0 | 69 |
result(); |
70 |
||
71 |
(*7*) |
|
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Goal "P | ~ ~ ~ P"; |
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Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
73 |
by (Blast_tac 1); |
0 | 74 |
result(); |
75 |
||
76 |
(*8. Peirce's law*) |
|
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Goal "((P-->Q) --> P) --> P"; |
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Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
78 |
by (Blast_tac 1); |
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result(); |
80 |
||
81 |
(*9*) |
|
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Goal "((P|Q) & (~P|Q) & (P| ~Q)) --> ~ (~P | ~Q)"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
83 |
by (Blast_tac 1); |
0 | 84 |
result(); |
85 |
||
86 |
(*10*) |
|
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Goal "(Q-->R) & (R-->P&Q) & (P-->Q|R) --> (P<->Q)"; |
2888
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Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
88 |
by (Blast_tac 1); |
0 | 89 |
result(); |
90 |
||
91 |
(*11. Proved in each direction (incorrectly, says Pelletier!!) *) |
|
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Goal "P<->P"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
93 |
by (Blast_tac 1); |
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result(); |
95 |
||
96 |
(*12. "Dijkstra's law"*) |
|
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Goal "((P <-> Q) <-> R) <-> (P <-> (Q <-> R))"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
98 |
by (Blast_tac 1); |
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result(); |
100 |
||
101 |
(*13. Distributive law*) |
|
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Goal "P | (Q & R) <-> (P | Q) & (P | R)"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
103 |
by (Blast_tac 1); |
0 | 104 |
result(); |
105 |
||
106 |
(*14*) |
|
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Goal "(P <-> Q) <-> ((Q | ~P) & (~Q|P))"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
108 |
by (Blast_tac 1); |
0 | 109 |
result(); |
110 |
||
111 |
(*15*) |
|
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Goal "(P --> Q) <-> (~P | Q)"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
113 |
by (Blast_tac 1); |
0 | 114 |
result(); |
115 |
||
116 |
(*16*) |
|
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Goal "(P-->Q) | (Q-->P)"; |
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e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
118 |
by (Blast_tac 1); |
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result(); |
120 |
||
121 |
(*17*) |
|
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Goal "((P & (Q-->R))-->S) <-> ((~P | Q | S) & (~P | ~R | S))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
123 |
by (Blast_tac 1); |
0 | 124 |
result(); |
125 |
||
126 |
writeln"Classical Logic: examples with quantifiers"; |
|
127 |
||
5150 | 128 |
Goal "(ALL x. P(x) & Q(x)) <-> (ALL x. P(x)) & (ALL x. Q(x))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
129 |
by (Blast_tac 1); |
0 | 130 |
result(); |
131 |
||
5150 | 132 |
Goal "(EX x. P-->Q(x)) <-> (P --> (EX x. Q(x)))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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diff
changeset
|
133 |
by (Blast_tac 1); |
0 | 134 |
result(); |
135 |
||
5150 | 136 |
Goal "(EX x. P(x)-->Q) <-> (ALL x. P(x)) --> Q"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
137 |
by (Blast_tac 1); |
0 | 138 |
result(); |
139 |
||
5150 | 140 |
Goal "(ALL x. P(x)) | Q <-> (ALL x. P(x) | Q)"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
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changeset
|
141 |
by (Blast_tac 1); |
0 | 142 |
result(); |
143 |
||
13
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Added example from Avron: Gentzen-Type Systems, Resolution and Tableaux, JAR 10
lcp
parents:
0
diff
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|
144 |
(*Discussed in Avron, Gentzen-Type Systems, Resolution and Tableaux, |
b73f7e42135e
Added example from Avron: Gentzen-Type Systems, Resolution and Tableaux, JAR 10
lcp
parents:
0
diff
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|
145 |
JAR 10 (265-281), 1993. Proof is trivial!*) |
5723 | 146 |
Goal "~ ((EX x.~P(x)) & ((EX x. P(x)) | (EX x. P(x) & Q(x))) & ~ (EX x. P(x)))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
147 |
by (Blast_tac 1); |
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Added example from Avron: Gentzen-Type Systems, Resolution and Tableaux, JAR 10
lcp
parents:
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diff
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|
148 |
result(); |
b73f7e42135e
Added example from Avron: Gentzen-Type Systems, Resolution and Tableaux, JAR 10
lcp
parents:
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|
149 |
|
0 | 150 |
writeln"Problems requiring quantifier duplication"; |
151 |
||
5150 | 152 |
(*Theorem B of Peter Andrews, Theorem Proving via General Matings, |
153 |
JACM 28 (1981).*) |
|
154 |
Goal "(EX x. ALL y. P(x) <-> P(y)) --> ((EX x. P(x)) <-> (ALL y. P(y)))"; |
|
155 |
by (Blast_tac 1); |
|
156 |
result(); |
|
157 |
||
0 | 158 |
(*Needs multiple instantiation of ALL.*) |
5150 | 159 |
Goal "(ALL x. P(x)-->P(f(x))) & P(d)-->P(f(f(f(d))))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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changeset
|
160 |
by (Blast_tac 1); |
0 | 161 |
result(); |
162 |
||
163 |
(*Needs double instantiation of the quantifier*) |
|
5150 | 164 |
Goal "EX x. P(x) --> P(a) & P(b)"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
165 |
by (Blast_tac 1); |
0 | 166 |
result(); |
167 |
||
5150 | 168 |
Goal "EX z. P(z) --> (ALL x. P(x))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
169 |
by (Blast_tac 1); |
0 | 170 |
result(); |
171 |
||
5150 | 172 |
Goal "EX x. (EX y. P(y)) --> P(x)"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
173 |
by (Blast_tac 1); |
492 | 174 |
result(); |
175 |
||
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FOL/ex/cla: proofs now use deepen_tac instead of best_tac FOL_dup_cs
lcp
parents:
644
diff
changeset
|
176 |
(*V. Lifschitz, What Is the Inverse Method?, JAR 5 (1989), 1--23. NOT PROVED*) |
5150 | 177 |
Goal "EX x x'. ALL y. EX z z'. \ |
0 | 178 |
\ (~P(y,y) | P(x,x) | ~S(z,x)) & \ |
179 |
\ (S(x,y) | ~S(y,z) | Q(z',z')) & \ |
|
180 |
\ (Q(x',y) | ~Q(y,z') | S(x',x'))"; |
|
181 |
||
5150 | 182 |
|
183 |
||
0 | 184 |
writeln"Hard examples with quantifiers"; |
185 |
||
186 |
writeln"Problem 18"; |
|
5150 | 187 |
Goal "EX y. ALL x. P(y)-->P(x)"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
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diff
changeset
|
188 |
by (Blast_tac 1); |
0 | 189 |
result(); |
190 |
||
191 |
writeln"Problem 19"; |
|
5150 | 192 |
Goal "EX x. ALL y z. (P(y)-->Q(z)) --> (P(x)-->Q(x))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
193 |
by (Blast_tac 1); |
0 | 194 |
result(); |
195 |
||
196 |
writeln"Problem 20"; |
|
5150 | 197 |
Goal "(ALL x y. EX z. ALL w. (P(x)&Q(y)-->R(z)&S(w))) \ |
0 | 198 |
\ --> (EX x y. P(x) & Q(y)) --> (EX z. R(z))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
199 |
by (Blast_tac 1); |
0 | 200 |
result(); |
201 |
||
202 |
writeln"Problem 21"; |
|
5150 | 203 |
Goal "(EX x. P-->Q(x)) & (EX x. Q(x)-->P) --> (EX x. P<->Q(x))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
204 |
by (Blast_tac 1); |
0 | 205 |
result(); |
206 |
||
207 |
writeln"Problem 22"; |
|
5150 | 208 |
Goal "(ALL x. P <-> Q(x)) --> (P <-> (ALL x. Q(x)))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
209 |
by (Blast_tac 1); |
0 | 210 |
result(); |
211 |
||
212 |
writeln"Problem 23"; |
|
5150 | 213 |
Goal "(ALL x. P | Q(x)) <-> (P | (ALL x. Q(x)))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
214 |
by (Blast_tac 1); |
0 | 215 |
result(); |
216 |
||
217 |
writeln"Problem 24"; |
|
5150 | 218 |
Goal "~(EX x. S(x)&Q(x)) & (ALL x. P(x) --> Q(x)|R(x)) & \ |
3835 | 219 |
\ (~(EX x. P(x)) --> (EX x. Q(x))) & (ALL x. Q(x)|R(x) --> S(x)) \ |
0 | 220 |
\ --> (EX x. P(x)&R(x))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
221 |
by (Blast_tac 1); |
0 | 222 |
result(); |
223 |
||
224 |
writeln"Problem 25"; |
|
5150 | 225 |
Goal "(EX x. P(x)) & \ |
0 | 226 |
\ (ALL x. L(x) --> ~ (M(x) & R(x))) & \ |
227 |
\ (ALL x. P(x) --> (M(x) & L(x))) & \ |
|
228 |
\ ((ALL x. P(x)-->Q(x)) | (EX x. P(x)&R(x))) \ |
|
229 |
\ --> (EX x. Q(x)&P(x))"; |
|
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
230 |
by (Blast_tac 1); |
0 | 231 |
result(); |
232 |
||
233 |
writeln"Problem 26"; |
|
5150 | 234 |
Goal "((EX x. p(x)) <-> (EX x. q(x))) & \ |
1459 | 235 |
\ (ALL x. ALL y. p(x) & q(y) --> (r(x) <-> s(y))) \ |
0 | 236 |
\ --> ((ALL x. p(x)-->r(x)) <-> (ALL x. q(x)-->s(x)))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
237 |
by (Blast_tac 1); |
0 | 238 |
result(); |
239 |
||
240 |
writeln"Problem 27"; |
|
5150 | 241 |
Goal "(EX x. P(x) & ~Q(x)) & \ |
0 | 242 |
\ (ALL x. P(x) --> R(x)) & \ |
243 |
\ (ALL x. M(x) & L(x) --> P(x)) & \ |
|
244 |
\ ((EX x. R(x) & ~ Q(x)) --> (ALL x. L(x) --> ~ R(x))) \ |
|
245 |
\ --> (ALL x. M(x) --> ~L(x))"; |
|
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
246 |
by (Blast_tac 1); |
0 | 247 |
result(); |
248 |
||
249 |
writeln"Problem 28. AMENDED"; |
|
5150 | 250 |
Goal "(ALL x. P(x) --> (ALL x. Q(x))) & \ |
0 | 251 |
\ ((ALL x. Q(x)|R(x)) --> (EX x. Q(x)&S(x))) & \ |
3835 | 252 |
\ ((EX x. S(x)) --> (ALL x. L(x) --> M(x))) \ |
0 | 253 |
\ --> (ALL x. P(x) & L(x) --> M(x))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
254 |
by (Blast_tac 1); |
0 | 255 |
result(); |
256 |
||
257 |
writeln"Problem 29. Essentially the same as Principia Mathematica *11.71"; |
|
5150 | 258 |
Goal "(EX x. P(x)) & (EX y. Q(y)) \ |
0 | 259 |
\ --> ((ALL x. P(x)-->R(x)) & (ALL y. Q(y)-->S(y)) <-> \ |
260 |
\ (ALL x y. P(x) & Q(y) --> R(x) & S(y)))"; |
|
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
261 |
by (Blast_tac 1); |
0 | 262 |
result(); |
263 |
||
264 |
writeln"Problem 30"; |
|
5150 | 265 |
Goal "(ALL x. P(x) | Q(x) --> ~ R(x)) & \ |
0 | 266 |
\ (ALL x. (Q(x) --> ~ S(x)) --> P(x) & R(x)) \ |
267 |
\ --> (ALL x. S(x))"; |
|
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
268 |
by (Blast_tac 1); |
0 | 269 |
result(); |
270 |
||
271 |
writeln"Problem 31"; |
|
5150 | 272 |
Goal "~(EX x. P(x) & (Q(x) | R(x))) & \ |
0 | 273 |
\ (EX x. L(x) & P(x)) & \ |
274 |
\ (ALL x. ~ R(x) --> M(x)) \ |
|
275 |
\ --> (EX x. L(x) & M(x))"; |
|
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
276 |
by (Blast_tac 1); |
0 | 277 |
result(); |
278 |
||
279 |
writeln"Problem 32"; |
|
5150 | 280 |
Goal "(ALL x. P(x) & (Q(x)|R(x))-->S(x)) & \ |
0 | 281 |
\ (ALL x. S(x) & R(x) --> L(x)) & \ |
282 |
\ (ALL x. M(x) --> R(x)) \ |
|
283 |
\ --> (ALL x. P(x) & M(x) --> L(x))"; |
|
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
284 |
by (Blast_tac 1); |
0 | 285 |
result(); |
286 |
||
287 |
writeln"Problem 33"; |
|
5150 | 288 |
Goal "(ALL x. P(a) & (P(x)-->P(b))-->P(c)) <-> \ |
0 | 289 |
\ (ALL x. (~P(a) | P(x) | P(c)) & (~P(a) | ~P(b) | P(c)))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
290 |
by (Blast_tac 1); |
0 | 291 |
result(); |
292 |
||
665
97e9ad6c1c4a
FOL/ex/cla: proofs now use deepen_tac instead of best_tac FOL_dup_cs
lcp
parents:
644
diff
changeset
|
293 |
writeln"Problem 34 AMENDED (TWICE!!)"; |
0 | 294 |
(*Andrews's challenge*) |
5150 | 295 |
Goal "((EX x. ALL y. p(x) <-> p(y)) <-> \ |
1459 | 296 |
\ ((EX x. q(x)) <-> (ALL y. p(y)))) <-> \ |
297 |
\ ((EX x. ALL y. q(x) <-> q(y)) <-> \ |
|
0 | 298 |
\ ((EX x. p(x)) <-> (ALL y. q(y))))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
299 |
by (Blast_tac 1); |
0 | 300 |
result(); |
301 |
||
302 |
writeln"Problem 35"; |
|
5150 | 303 |
Goal "EX x y. P(x,y) --> (ALL u v. P(u,v))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
304 |
by (Blast_tac 1); |
0 | 305 |
result(); |
306 |
||
307 |
writeln"Problem 36"; |
|
5723 | 308 |
Goal "(ALL x. EX y. J(x,y)) & \ |
0 | 309 |
\ (ALL x. EX y. G(x,y)) & \ |
310 |
\ (ALL x y. J(x,y) | G(x,y) --> (ALL z. J(y,z) | G(y,z) --> H(x,z))) \ |
|
311 |
\ --> (ALL x. EX y. H(x,y))"; |
|
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
312 |
by (Blast_tac 1); |
0 | 313 |
result(); |
314 |
||
315 |
writeln"Problem 37"; |
|
5150 | 316 |
Goal "(ALL z. EX w. ALL x. EX y. \ |
3835 | 317 |
\ (P(x,z)-->P(y,w)) & P(y,z) & (P(y,w) --> (EX u. Q(u,w)))) & \ |
0 | 318 |
\ (ALL x z. ~P(x,z) --> (EX y. Q(y,z))) & \ |
319 |
\ ((EX x y. Q(x,y)) --> (ALL x. R(x,x))) \ |
|
320 |
\ --> (ALL x. EX y. R(x,y))"; |
|
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
321 |
by (Blast_tac 1); |
0 | 322 |
result(); |
323 |
||
428 | 324 |
writeln"Problem 38"; |
5723 | 325 |
Goal "(ALL x. p(a) & (p(x) --> (EX y. p(y) & r(x,y))) --> \ |
1459 | 326 |
\ (EX z. EX w. p(z) & r(x,w) & r(w,z))) <-> \ |
327 |
\ (ALL x. (~p(a) | p(x) | (EX z. EX w. p(z) & r(x,w) & r(w,z))) & \ |
|
328 |
\ (~p(a) | ~(EX y. p(y) & r(x,y)) | \ |
|
0 | 329 |
\ (EX z. EX w. p(z) & r(x,w) & r(w,z))))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
330 |
by (Blast_tac 1); (*beats fast_tac!*) |
665
97e9ad6c1c4a
FOL/ex/cla: proofs now use deepen_tac instead of best_tac FOL_dup_cs
lcp
parents:
644
diff
changeset
|
331 |
result(); |
0 | 332 |
|
333 |
writeln"Problem 39"; |
|
5150 | 334 |
Goal "~ (EX x. ALL y. F(y,x) <-> ~F(y,y))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
335 |
by (Blast_tac 1); |
0 | 336 |
result(); |
337 |
||
338 |
writeln"Problem 40. AMENDED"; |
|
5150 | 339 |
Goal "(EX y. ALL x. F(x,y) <-> F(x,x)) --> \ |
0 | 340 |
\ ~(ALL x. EX y. ALL z. F(z,y) <-> ~ F(z,x))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
341 |
by (Blast_tac 1); |
0 | 342 |
result(); |
343 |
||
344 |
writeln"Problem 41"; |
|
5150 | 345 |
Goal "(ALL z. EX y. ALL x. f(x,y) <-> f(x,z) & ~ f(x,x)) \ |
0 | 346 |
\ --> ~ (EX z. ALL x. f(x,z))"; |
2888
e551e4bd262a
Now calls Blast_tac and has some hard examples (Halting Problem
paulson
parents:
2729
diff
changeset
|
347 |
by (Blast_tac 1); |
0 | 348 |
result(); |
349 |
||
428 |