/
binarysans-examples.mod
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binarysans-examples.mod
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%% Binary resolution with subsitution terms
module binarysans-examples.
accumulate lib.
accumulate classical.
accumulate test-constants.
accumulate lkf-formulas.
accumulate polarize.
accumulate lkf-kernel.
accumulate binarysans-fpc.
test_all :- example N _ _ _,
term_to_string N Str, print Str, print " ",
test_resol' N, print "\n", fail.
test_resol' N :- (test_resol N, print "#", fail); true.
test_resol N :-
example N Clauses Lemmas Resol, false- False,
foldr (C\A\R\ sigma D\sigma D'\
nnf conj+ disj- (ng C) D, ensure+ D D', disj- D' A R)
Clauses False B,
length Clauses C, C' is C + 1,
assume_lemmas C' Lemmas (lkf_entry (start' 1 Resol) B).
test_reveal N :-
example N Clauses Lemmas Resol, false- False,
foldr (C\A\R\ sigma D\sigma D'\
nnf conj+ disj- (ng C) D, ensure+ D D', disj- D' A R)
Clauses False B,
length Clauses C, C' is C + 1,
assume_lemmas C' Lemmas (lkf_entry (start' 1 Resol) B),
term_to_string (start' 1 Resol) String,
print "Certificate = \n", print String, print "\n".
assume_lemmas C nil G :- G.
assume_lemmas C [L|Ls] G :-
C' is C + 1, nnf conj+ disj- L L', ensure- L' L'',
(lemma C L'' => assume_lemmas C' Ls G).
% The following are example certificates from the client's point-of-view.
% There are three lists:
% 1. The list of clauses, which when taken as hypothesis, yields
% a contradiction.
% 2. A list of "lemma". These are new clauses that are resolvants
% of previous clauses.
% 3. The certificate
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Propositional examples
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% A single propositional letter
example 10
[a,
(ng a)]
[ff]
[resolve' 3 (res' 1 (rex' 2 done'))].
example 20
[(ng a),
a]
[ff]
[resolve' 3 (res' 2 (rex' 1 done'))].
example 30
[(or a ff),
(or (ng a) ff)]
[ff]
[resolve' 3 (res' 1 (rex' 2 done'))].
example 40 % This one fails. One must factor explicitly to proceed.
[(or a a),
(or (ng a) (ng a))]
[ff]
[resolve' 3 (res' 1 (rex' 2 done'))].
example 41 % This variant works but leaves lots of backtrack points.
[(or a a), % 1
(or (ng a) (ng a))] % 2
[a, % 3
(ng a), % 4
ff] % 5
[factor' 1 3,
resolve' 4 (res' 3 (rex' 2 done')),
resolve' 5 (res' 3 (rex' 4 done'))].
example 42 % This variant is a "permutation" of above but with fewer backtrack points.
[(or a a), % 1
(or (ng a) (ng a))] % 2
[a, % 3
(ng a), % 4
ff] % 5
[factor' 1 3,
factor' 2 4,
resolve' 5 (res' 3 (rex' 4 done'))].
example 43
[(or a a), % 1
(ng a)] % 2
[a, % 3
ff] % 4
[factor' 1 3,
resolve' 4 (res' 3 (rex' 2 done'))].
example 44 % dual of 40
[(or (ng a) (ng a)), % 1
a] % 2
[(ng a), % 3
ff] % 4
[factor' 1 3,
resolve' 4 (res' 2 (rex' 3 done'))].
example 45 % not checkable
[a, % 1
(ng a)] % 2
[(or a a), % 3
ff] % 4
[factor' 1 3,
resolve' 4 (res' 3 (rex' 2 done'))].
%%%% Multiple propositional letters
example 70
[(or a b), % 1
(or (ng a) e), % 2
(ng b), % 3
(ng e)] % 4
[(or b e), % 5
e, % 6
ff] % 7
[resolve' 5 (res' 1 (rex' 2 done')),
resolve' 6 (res' 5 (rex' 3 done')),
resolve' 7 (res' 6 (rex' 4 done'))].
example 71
[(or a b), % 1
(or a (ng b)), % 2
(or (ng a) b), % 3
(or (ng a) (ng b))] % 4
[(or a a), % 5
a, % 6
(or (ng a) (ng a)), % 7
(ng a), % 8
ff] % 9
[resolve' 5 (res' 1 (rex' 2 done')),
factor' 5 6,
resolve' 7 (res' 3 (rex' 4 done')),
factor' 7 8,
resolve' 9 (res' 6 (rex' 8 done'))].
example 72 % Just like 71 but factoring is moved into the resol method
[(or a b), % 1
(or a (ng b)), % 2
(or (ng a) b), % 3
(or (ng a) (ng b))] % 4
[a, % 5
(ng a), % 6
ff] % 7
[resolve' 5 (res' 1 (rex' 2 done')),
resolve' 6 (res' 3 (rex' 4 done')),
resolve' 7 (res' 5 (rex' 6 done'))].
example 80
[(or a b), % 1
(or a (ng b)), % 2
(ng a)] % 3
[(or a a), % 4
a, % 5
ff] % 6
[resolve' 4 (res' 1 (rex' 2 done')),
factor' 4 5,
resolve' 6 (res' 5 (rex' 3 done'))].
example 81 % A variation on 80. Permute the rules to eliminate "a"
% first so it is not appearring twice in the combined side formulas.
[(or a b), % 1
(or a (ng b)), % 2
(ng a)] % 3
[b, % 4
(ng b), % 5
ff] % 6
[resolve' 4 (res' 1 (rex' 3 done')),
resolve' 5 (res' 2 (rex' 3 done')),
resolve' 6 (res' 4 (rex' 5 done'))].
example 82 % Another variation but the factoring is done internally.
[(or a b), % 1
(or a (ng b)), % 2
(ng a)] % 3
[a, % 4
ff] % 5
[resolve' 4 (res' 1 (rex' 2 done')),
resolve' 5 (res' 4 (rex' 3 done'))].
example 90
[(or a b), % 1
(or a (ng b)), % 2
(ng a)] % 3
[a, % 4
ff] % 5
[resolve' 4 (res' 1 (rex' 2 done')),
resolve' 5 (res' 4 (rex' 3 done'))].
example 91
[(or a b), % 1
(or a (ng b)), % 2
(ng a)] % 3
[(or (or a a) (or a a)), % 4 It is repetition here that causes backtracking
a, % 5
ff] % 6
[resolve' 4 (res' 1 (rex' 2 done')),
factor' 4 5,
resolve' 6 (res' 5 (rex' 3 done'))].
% Conjectures: The following are for the propositional case.
% (1) If there repeated literals in the resolvant, then there are
% backtrack points that are not useful to have.
% (2) If there are repeated literals in the combined side formulas,
% then there are also backtrack points.
% The use of implicit factoring (write down the resolvant without
% repeats) can eliminate (1) backtracking. Use of explicit factoring
% (as defined in this FPC) is too late to get rid of backtrack
% points.
% Eliminating (2) seems hard in this framework.
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Simple quantificational examples
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
example 100
[(r z), % 1
(forall x\ or (ng (r x)) (t x)), % 2
(ng (t z))] % 3
[(t z), % 4
ff] % 5
[resolve' 4 (res' 1 (rex' 2 done')),
resolve' 5 (res' 4 (rex' 3 done'))].
example 110
[(r z), % 1
(forall x\ or (ng (r x)) (r (k x))), % 2
(ng (r (k (k (k (k z))))))] % 3
[(forall x\ or (ng (r x)) (r (k (k x)))), % 4
(forall x\ or (ng (r x)) (r (k (k (k (k x)))))), % 5
(r (k (k (k (k z))))), % 6
ff] % 7
[ resolve' 4 (res' 2 (rex' 2 done')),
resolve' 5 (res' 4 (rex' 4 done')),
resolve' 6 (res' 1 (rex' 5 done')),
resolve' 7 (res' 6 (rex' 3 done'))].
example 111 % same a 110 but without explicit subterm
[(r z), % 1
(forall x\ or (ng (r x)) (r (k x))), % 2
(ng (r (k (k (k (k z))))))] % 3
[(forall x\ or (ng (r x)) (r (k (k x)))), % 4
(forall x\ or (ng (r x)) (r (k (k (k (k x)))))), % 5
(r (k (k (k (k z))))), % 6
ff] % 7
[ resolve' 4 (res' 2 (rex' 2 done')),
resolve' 5 (res' 4 (rex' 4 done')),
resolve' 6 (res' 1 (rex' 5 done')),
resolve' 7 (res' 6 (rex' 3 done'))].
example 120
[(r z), % 1
(forall x\ or (ng (r x)) (r (k x))), % 2
(ng (r (k (k (k (k z))))))] % 3
[(r (k z)), % 4
(r (k (k z))), % 5
(r (k (k (k z)))), % 6
(r (k (k (k (k z))))), % 7
ff] % 8
[ resolve' 4 (res' 1 (rex' 2 done')),
resolve' 5 (res' 4 (rex' 2 done')),
resolve' 6 (res' 5 (rex' 2 done')),
resolve' 7 (res' 6 (rex' 2 done')),
resolve' 8 (res' 7 (rex' 3 done'))].
example 130
[ (is_wolf wi), % 1
(forall x\ forall y\ or (ng (is_wolf x)) (or (ng (is_fox y)) (ng (eats x y)))), % 2
(is_fox fi), % 3
(eats wi fi)] % 4
[ (or (ng (is_fox fi)) (ng (eats wi fi))), % 5
(ng (eats wi fi)), % 6
ff] % 7
[ resolve' 5 (res' 1 (rex' 2 done')),
resolve' 6 (res' 3 (rex' 5 done')),
resolve' 7 (res' 4 (rex' 6 done'))].
example 131
[ (is_wolf wi), % 1
(forall x\ forall y\ (or (ng (is_wolf x)) (or (ng (is_fox y)) (ng (eats x y))))), % 2
(is_fox fi), % 3
(eats wi fi)] % 4
[ (or (ng (is_fox fi)) (ng (eats wi fi))), % 5
(ng (eats wi fi)), % 6
ff] % 7
[ resolve' 5 (res' 1 (rex' 2 done')),
resolve' 6 (res' 3 (rex' 5 done')),
resolve' 7 (res' 4 (rex' 6 done'))].
example 132
[ (is_wolf wi), % 1
(or (ng (is_wolf wi)) (or (ng (is_fox fi)) (ng (eats wi fi)))), % 2
(is_fox fi), % 3
(eats wi fi)] % 4
[ (or (ng (is_fox fi)) (ng (eats wi fi))), % 5
(ng (eats wi fi)), % 6
ff] % 7
[ resolve' 5 (res' 1 (rex' 2 done')),
resolve' 6 (res' 3 (rex' 5 done')),
resolve' 7 (res' 4 (rex' 6 done'))].
example 133
[ a, % 1
(or (ng a) (or (ng b) (ng c))), % 2
b, % 3
c] % 4
[ (or (ng b) (ng c)), % 5
(ng c), % 6
ff] % 7
[ resolve' 5 (res' 1 (rex' 2 done')),
resolve' 6 (res' 3 (rex' 5 done')),
resolve' 7 (res' 4 (rex' 6 done'))].
example 134
[ a, % 1
(or (ng a) (ng b)), % 2
b] % 3
[ (ng b), % 4
ff] % 5
[ resolve' 4 (res' 1 (rex' 2 done')),
resolve' 5 (res' 3 (rex' 4 done'))].
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
%%%% Steam roller example
%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
fun_pname bi "bi" [].
fun_pname ci "ci" [].
fun_pname gi "gi" [].
fun_pname si "si" [].
pred_pname (is_animal X) "is_animal" [X].
pred_pname (is_bird X) "is_bird" [X].
pred_pname (is_cater X) "is_cater" [X].
pred_pname (is_grain X) "is_grain" [X].
pred_pname (is_plant X) "is_plant" [X].
pred_pname (is_snail X) "is_snail" [X].
pred_pname (much_smaller X Y) "much_smaller" [X,Y].
pred_pname dummy "dummy" [].
example 200 % steamroller
[
(forall (x\ or (ng(is_wolf x)) (is_animal x))), % 1
(forall (x\ or (ng(is_fox x)) (is_animal x))), % 2
(forall (x\ or (ng(is_bird x)) (is_animal x))), % 3
(forall (x\ or (ng(is_cater x)) (is_animal x))), % 4
(forall (x\ or (ng(is_snail x)) (is_animal x))), % 5
(is_wolf wi), % 6
(is_fox fi), % 7
(is_bird bi), % 8
(is_cater ci), % 9
(is_snail si), % 10
(is_grain gi), % 11
(forall (x\ or (ng(is_grain x)) (is_plant x))), % 12
(forall (x\ forall (y\ forall (z\ forall (v\ or (ng(is_animal x)) (or (ng(is_plant y)) (or (ng(is_animal z)) (or (ng(is_plant v)) (or (ng(eats x y)) (or (ng(much_smaller z x)) (or (ng(eats z v)) (eats x z)))))))))))), % 13
(forall (x\ forall (y\ or (ng(is_cater x)) (or (ng(is_bird y)) (much_smaller x y))))), % 14
(forall (x\ forall (y\ or (ng(is_snail x)) (or (ng(is_bird y)) (much_smaller x y))))), % 15
(forall (x\ forall (y\ or (ng(is_bird x)) (or (ng(is_fox y)) (much_smaller x y))))), % 16
(forall (x\ forall (y\ or (ng(is_fox x)) (or (ng(is_wolf y)) (much_smaller x y))))), % 17
(forall (x\ forall (y\ or (ng(is_wolf x)) (or (ng(is_fox y)) (ng(eats x y)))))), % 18
(forall (x\ forall (y\ or (ng(is_wolf x)) (or (ng(is_grain y)) (ng(eats x y)))))), % 19
(forall (x\ forall (y\ or (ng(is_bird x)) (or (ng(is_cater y)) (ng(eats x y)))))), % 20
(forall (x\ forall (y\ or (ng(is_bird x)) (or (ng(is_snail y)) (ng(eats x y)))))), % 21
dummy, % 22
(forall (x\ forall (y\ or (ng(is_cater x)) (or (ng(is_grain y)) (eats x y))))), % 23
dummy, % 24
(forall (x\ forall (y\ or (ng(is_snail x)) (or (ng(is_grain y)) (eats x y))))), % 25
(forall (x\ forall (y\ forall (z\ or (ng(is_animal x)) (or (ng(is_animal y)) (or (ng(is_grain z)) (or (ng(eats x y)) (eats y z)))))))) % 26
]
[
dummy, % 27
dummy, % 28
dummy, % 29
dummy, % 30
dummy, % 31
dummy, % 32
dummy, % 33
dummy, % 34
dummy, % 35
dummy, % 36
dummy, % 37
dummy, % 38
dummy, % 39
dummy, % 40
dummy, % 41
dummy, % 42
dummy, % 43
dummy, % 44
dummy, % 45
dummy, % 46
dummy, % 47
dummy, % 48
dummy, % 49
dummy, % 50
dummy, % 51
dummy, % 52
dummy, % 53
dummy, % 54
dummy, % 55
dummy, % 56
dummy, % 57
dummy, % 58
dummy, % 59
dummy, % 60
dummy, % 61
dummy, % 62
dummy, % 63
dummy, % 64
dummy, % 65
dummy, % 66
dummy, % 67
dummy, % 68
dummy, % 69
dummy, % 70
dummy, % 71
dummy, % 72
dummy, % 73
dummy, % 74
dummy, % 75
dummy, % 76
dummy, % 77
dummy, % 78
dummy, % 79
dummy, % 80
dummy, % 81
dummy, % 82
dummy, % 83
dummy, % 84
dummy, % 85
dummy, % 86
dummy, % 87
dummy, % 88
dummy, % 89
dummy, % 90
dummy, % 91
dummy, % 92
dummy, % 93
dummy, % 94
dummy, % 95
dummy, % 96
dummy, % 97
dummy, % 98
dummy, % 99
dummy, % 100
(ng(eats bi gi)), % 101
(or (ng(eats fi bi)) (ng(eats bi gi))), % 102
(or (ng(is_grain gi)) (or (ng(eats fi bi)) (ng(eats bi gi)))), % 103
(or (ng (is_animal bi)) (or (ng(is_grain gi)) (or (ng(eats fi bi)) (eats bi gi)))), % 104
dummy, % 105
dummy, % 106
dummy, % 107
dummy, % 108
dummy, % 109
(is_animal fi), % 110
dummy, % 111
dummy, % 112
dummy, % 113
dummy, % 114
dummy, % 115
dummy, % 116
dummy, % 117
dummy, % 118
dummy, % 119
(is_animal bi), % 120
dummy, % 121
dummy, % 122
dummy, % 123
dummy, % 124
dummy, % 125
dummy, % 126
dummy, % 127
dummy, % 128
dummy, % 129
dummy, % 130
dummy, % 131
dummy, % 132
dummy, % 133
dummy, % 134
dummy, % 135
dummy, % 136
dummy, % 137
dummy, % 138
dummy, % 139
(ng(eats fi bi)), % 140
(or (ng(eats bi gi)) (eats fi bi)), % 141
(or (ng(much_smaller bi fi)) (or (ng(eats bi gi)) (eats fi bi))), % 142
(or (eats fi gi) (or (ng(much_smaller bi fi)) (or (ng(eats bi gi)) (eats fi bi)))), % 143
(or (ng(is_plant gi)) (or (eats fi gi) (or (ng(much_smaller bi fi)) (or (ng(eats bi gi)) (eats fi bi))))), % 144
(or (ng(is_animal bi)) (or (ng(is_plant gi)) (or (eats fi gi) (or (ng(much_smaller bi fi)) (or (ng(eats bi gi)) (eats fi bi)))))), % 145
(or (ng(is_plant gi)) (or (ng(is_animal bi)) (or (ng(is_plant gi)) (or (eats fi gi) (or (ng(much_smaller bi fi)) (or (ng(eats bi gi)) (eats fi bi))))))), % 146
dummy, % 147
dummy, % 148
dummy, % 149
(eats bi gi), % 150
(or (eats bi gi) (eats bi si)), % 151
(or (eats bi gi) (or (ng(eats si gi)) (eats bi si))), % 152
(or (eats bi gi) (or (ng(much_smaller si bi)) (or (ng(eats si gi)) (eats bi si)))), % 153
(or (ng(is_plant gi)) (or (eats bi gi) (or (ng(much_smaller si bi)) (or (ng(eats si gi)) (eats bi si))))), % 154
(or (ng(is_animal si)) (or (ng(is_plant gi)) (or (eats bi gi) (or (ng(much_smaller si bi)) (or (ng(eats si gi)) (eats bi si)))))), % 155
(or (ng(is_plant gi)) (or (ng(is_animal si)) (or (ng(is_plant gi)) (or (eats bi gi) (or (ng(much_smaller si bi)) (or (ng(eats si gi)) (eats bi si))))))), % 156
dummy, % 157
dummy, % 158
dummy, % 159
(is_plant gi), % 160
dummy, % 161
dummy, % 162
dummy, % 163
dummy, % 164
dummy, % 165
dummy, % 166
dummy, % 167
dummy, % 168
dummy, % 169
(ng(eats fi gi)), % 170
(or (ng(eats fi gi)) (eats wi fi)), % 171
(or (ng(much_smaller fi wi)) (or (ng(eats fi gi)) (eats wi fi))), % 172
(or (eats wi gi) (or (ng(much_smaller fi wi)) (or (ng(eats fi gi)) (eats wi fi)))), % 173
(or (ng(is_plant gi)) (or (eats wi gi) (or (ng(much_smaller fi wi)) (or (ng(eats fi gi)) (eats wi fi))))), % 174
(or (ng(is_animal fi)) (or (ng(is_plant gi)) (or (eats wi gi) (or (ng(much_smaller fi wi)) (or (ng(eats fi gi)) (eats wi fi)))))), % 175
(or (ng(is_plant gi)) (or (ng(is_animal fi)) (or (ng(is_plant gi)) (or (eats wi gi) (or (ng(much_smaller fi wi)) (or (ng(eats fi gi)) (eats wi fi))))))), % 176
dummy, % 177
dummy, % 178
dummy, % 179
(much_smaller bi fi), % 180
(or (ng(is_fox fi)) (much_smaller bi fi)), % 181
dummy, % 182
dummy, % 183
dummy, % 184
dummy, % 185
dummy, % 186
dummy, % 187
dummy, % 188
dummy, % 189
(is_animal si), % 190
dummy, % 191
dummy, % 192
dummy, % 193
dummy, % 194
dummy, % 195
dummy, % 196
dummy, % 197
dummy, % 198
dummy, % 199
(much_smaller si bi), % 200
(or (ng(is_bird bi)) (much_smaller si bi)), % 201
dummy, % 202
dummy, % 203
dummy, % 204
dummy, % 205
dummy, % 206
dummy, % 207
dummy, % 208
dummy, % 209
(eats si gi), % 210
(or (ng(is_grain gi)) (eats si gi)), % 211
dummy, % 212
dummy, % 213
dummy, % 214
dummy, % 215
dummy, % 216
dummy, % 217
dummy, % 218
dummy, % 219
(ng(eats bi si)), % 220
(or (ng(is_snail si)) (ng(eats bi si))), % 221
dummy, % 222
dummy, % 223
dummy, % 224
dummy, % 225
dummy, % 226
dummy, % 227
dummy, % 228
dummy, % 229
(is_animal wi), % 230
dummy, % 231
dummy, % 232
dummy, % 233
dummy, % 234
dummy, % 235
dummy, % 236
dummy, % 237
dummy, % 238
dummy, % 239
(ng(eats wi gi)), % 240
(or (ng(is_grain gi)) (ng(eats wi gi))), % 241
dummy, % 242
dummy, % 243
dummy, % 244
dummy, % 245
dummy, % 246
dummy, % 247
dummy, % 248
dummy, % 249
(much_smaller fi wi), % 250
(or (ng(is_wolf wi)) (much_smaller fi wi)), % 251
dummy, % 252
dummy, % 253
dummy, % 254
dummy, % 255
dummy, % 256
dummy, % 257
dummy, % 258
dummy, % 259
(ng(eats wi fi)), % 260
(or (ng(is_fox fi)) (ng(eats wi fi))), % 261
dummy, % 262
dummy, % 263
dummy, % 264
dummy, % 265
dummy, % 266
dummy, % 267
dummy, % 268
dummy, % 269
ff % 270 (previously 0)
]
% :%s/^\tresolv.*(idx\([^)]\+\).*(idx\([^)]\+\).* \([0-9]\+\),$/\tresol\1\2 \3,/gc
[
resolveX 110 (res' 2 (rex' 7 done')),
resolveX 120 (res' 3 (rex' 8 done')),
resolveX 160 (res' 12 (rex' 11 done')),
resolveX 190 (res' 5 (rex' 10 done')),
resolveX 230 (res' 1 (rex' 6 done')),
resolveX 261 (res' 18 (rex' 6 done')),
resolveX 260 (res' 261 (rex' 7 done')),
resolveX 251 (res' 17 (rex' 7 done')),
resolveX 250 (res' 251 (rex' 6 done')),
resolveX 241 (res' 19 (rex' 6 done')),
resolveX 240 (res' 241 (rex' 11 done')),
resolveX 221 (res' 21 (rex' 8 done')),
resolveX 220 (res' 221 (rex' 10 done')),
resolveX 211 (res' 25 (rex' 10 done')),
resolveX 210 (res' 211 (rex' 11 done')),
resolveX 201 (res' 15 (rex' 10 done')),
resolveX 200 (res' 201 (rex' 8 done')),
resolveX 181 (res' 16 (rex' 8 done')),
resolveX 180 (res' 181 (rex' 7 done')),
resolveX 176 (res' 13 (rex' 230 done')), %
resolveX 175 (res' 176 (rex' 160 done')),
resolveX 174 (res' 175 (rex' 110 done')),
resolveX 173 (res' 174 (rex' 160 done')),
resolveX 172 (res' 173 (rex' 240 done')),
resolveX 171 (res' 172 (rex' 250 done')),
resolveX 170 (res' 171 (rex' 260 done')),
resolveX 156 (res' 13 (rex' 120 done')),
resolveX 155 (res' 156 (rex' 160 done')),
resolveX 154 (res' 155 (rex' 190 done')),
resolveX 153 (res' 154 (rex' 160 done')),
resolveX 152 (res' 153 (rex' 200 done')),
resolveX 151 (res' 152 (rex' 210 done')),
resolveX 150 (res' 151 (rex' 220 done')),
resolveX 146 (res' 13 (rex' 110 done')),
resolveX 145 (res' 146 (rex' 160 done')),
resolveX 144 (res' 145 (rex' 120 done')),
resolveX 143 (res' 144 (rex' 160 done')),
resolveX 142 (res' 143 (rex' 170 done')),
resolveX 141 (res' 142 (rex' 180 done')),
resolveX 140 (res' 141 (rex' 150 done')),
resolveX 104 (res' 26 (rex' 110 done')),
resolveX 103 (res' 104 (rex' 120 done')),
resolveX 102 (res' 103 (rex' 7 done')),
resolveX 101 (res' 102 (rex' 140 done')),
resolveX 270 (res' 101 (rex' 150 done'))
].
example 201
[
(forall (x\ forall (y\ forall (z\ forall (v\
or (ng(is_animal x)) (or (ng(is_plant y))
(or (ng(is_animal z)) (or (ng(is_plant v))
(or (ng(eats x y)) (or (ng(much_smaller z x))
(or (ng(eats z v)) (eats x z)))))))))))), % 13 -> 1
(is_animal wi), % 230 -> 2
ff % 3
]
[
(or (ng(is_plant gi)) (or (ng(is_animal fi)) (or (ng(is_plant gi)) (or (eats wi gi) (or (ng(much_smaller fi wi)) (or (ng(eats fi gi)) (eats wi fi))))))) % 176 -> 4
]
[
% resolve' 4 (res' 2 (rex' 1 done'))
].
% A Prover9 translation example: SYN405+1
/*
1 -((all A f(A)) & (exists B g(B)) -> (exists C (f(C) & g(C)))). [assumption].
2 -f(A) | -g(A). [clausify(1)].
3 f(A). [clausify(1)].
4 -g(A). [resolve(2,a,3,a)].
5 g(c1). [clausify(1)].
6 $F. [resolve(4,a,5,a)].
*/
example 300
[(forall A\ or (ng (r A)) (ng (t A))), % 2 -> 1
(forall A\ (r A)), % 3 -> 2
(t m)] % 5 -> 3
[(forall A\ (ng (t A))), % 4 -> 4
ff] % 6 -> 5
[resolve' 4 (res' 2 (rex' 1 done')),
resolve' 5 (res' 3 (rex' 4 done'))].
% Another example, with factoring: SYN980+1
/*
1 -(all A ((all B ((r(A) -> r(B)) -> p(f(B),B))) -> (exists C exists B (p(C,B) & (q(f(A),A) -> q(C,B)))))). [assumption].
2 -r(A) | p(f(A),A). [clausify(1)].
3 r(c1) | p(f(A),A). [clausify(1)].
4 -p(A,B) | q(f(c1),c1). [clausify(1)].
5 -p(A,B) | -q(A,B). [clausify(1)].
6 p(f(c1),c1) | p(f(A),A). [resolve(2,a,3,a)].
7 -p(A,B) | -p(f(c1),c1). [resolve(4,b,5,b)].
8 p(f(c1),c1). [factor(6,a,b)].
9 -p(f(c1),c1). [factor(7,a,b)].
10 $F. [resolve(8,a,9,a)].
*/
% All clauses offset by one; r, p -> w, q, f -> s, c1 -> m
example 310
[(forall A\ or (ng (r A)) (w (s A) A)), % 1
(forall A\ or (r m) (w (s A) A)), % 2
(forall A\ forall B\ or (ng (w A B)) (q (s m) m)), % 3
(forall A\ forall B\ or (ng (w A B)) (ng (q A B)))] % 4
[(forall A\ or (w (s m) m) (w (s A) A)), % 5
(forall A\ forall B\ or (ng (w A B)) (ng (w (s m) m))), % 6
(w (s m) m), % 7
(ng (w (s m) m)), % 8
ff] % 9
[resolve' 5 (res' 2 (rex' 1 done')),
resolve' 6 (res' 3 (rex' 4 done')),
/* Reversing the positive - negative pair does not work.
[resolve' 5 (res' 1 (rex' 2 done')),
resolve' 6 (res' 4 (rex' 3 done')),
*/
factor' 5 7,
factor' 6 8,
resolve' 9 (res' 7 (rex' 8 done'))].