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ex14.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 6418 was started by qwang on grid01,
Wed Jun 26 22:33:07 2019
The command was "prover9 -f ex14.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file ex14.in
formulas(sos).
(all x (child(x) & (exists y ((egg(y) | bunny(y)) & find(x,y))) -> happy(x))).
(all x (child(x) & helped(x) -> (exists y (egg(y) & find(x,y))))).
(all x (child(x) & (-young(x) | tryhard(x)) -> (exists y (bunny(y) & find(x,y))))).
end_of_list.
formulas(goals).
(all x (child(x) & young(x) -> tryhard(x) | helped(x))) -> (all y (child(y) -> happy(y))).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x (child(x) & (exists y ((egg(y) | bunny(y)) & find(x,y))) -> happy(x))) # label(non_clause). [assumption].
2 (all x (child(x) & helped(x) -> (exists y (egg(y) & find(x,y))))) # label(non_clause). [assumption].
3 (all x (child(x) & (-young(x) | tryhard(x)) -> (exists y (bunny(y) & find(x,y))))) # label(non_clause). [assumption].
4 (all x (child(x) & young(x) -> tryhard(x) | helped(x))) -> (all y (child(y) -> happy(y))) # label(non_clause) # label(goal). [goal].
============================== end of process non-clausal formulas ===
============================== PROCESS INITIAL CLAUSES ===============
% Clauses before input processing:
formulas(usable).
end_of_list.
formulas(sos).
-child(x) | -egg(y) | -find(x,y) | happy(x). [clausify(1)].
-child(x) | -bunny(y) | -find(x,y) | happy(x). [clausify(1)].
-child(x) | -helped(x) | egg(f1(x)). [clausify(2)].
-child(x) | -helped(x) | find(x,f1(x)). [clausify(2)].
-child(x) | young(x) | bunny(f2(x)). [clausify(3)].
-child(x) | young(x) | find(x,f2(x)). [clausify(3)].
-child(x) | -tryhard(x) | bunny(f2(x)). [clausify(3)].
-child(x) | -tryhard(x) | find(x,f2(x)). [clausify(3)].
-child(x) | -young(x) | tryhard(x) | helped(x). [deny(4)].
child(c1). [deny(4)].
-happy(c1). [deny(4)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating child/1
5 child(c1). [deny(4)].
6 -child(x) | -egg(y) | -find(x,y) | happy(x). [clausify(1)].
7 -child(x) | -bunny(y) | -find(x,y) | happy(x). [clausify(1)].
8 -child(x) | -helped(x) | egg(f1(x)). [clausify(2)].
9 -child(x) | -helped(x) | find(x,f1(x)). [clausify(2)].
10 -child(x) | young(x) | bunny(f2(x)). [clausify(3)].
11 -child(x) | young(x) | find(x,f2(x)). [clausify(3)].
12 -child(x) | -tryhard(x) | bunny(f2(x)). [clausify(3)].
13 -child(x) | -tryhard(x) | find(x,f2(x)). [clausify(3)].
14 -child(x) | -young(x) | tryhard(x) | helped(x). [deny(4)].
Derived: -egg(x) | -find(c1,x) | happy(c1). [resolve(5,a,6,a)].
Derived: -bunny(x) | -find(c1,x) | happy(c1). [resolve(5,a,7,a)].
Derived: -helped(c1) | egg(f1(c1)). [resolve(5,a,8,a)].
Derived: -helped(c1) | find(c1,f1(c1)). [resolve(5,a,9,a)].
Derived: young(c1) | bunny(f2(c1)). [resolve(5,a,10,a)].
Derived: young(c1) | find(c1,f2(c1)). [resolve(5,a,11,a)].
Derived: -tryhard(c1) | bunny(f2(c1)). [resolve(5,a,12,a)].
Derived: -tryhard(c1) | find(c1,f2(c1)). [resolve(5,a,13,a)].
Derived: -young(c1) | tryhard(c1) | helped(c1). [resolve(5,a,14,a)].
Eliminating happy/1
15 -egg(x) | -find(c1,x) | happy(c1). [resolve(5,a,6,a)].
16 -happy(c1). [deny(4)].
Derived: -egg(x) | -find(c1,x). [resolve(15,c,16,a)].
17 -bunny(x) | -find(c1,x) | happy(c1). [resolve(5,a,7,a)].
Derived: -bunny(x) | -find(c1,x). [resolve(17,c,16,a)].
Eliminating helped/1
18 -young(c1) | tryhard(c1) | helped(c1). [resolve(5,a,14,a)].
19 -helped(c1) | egg(f1(c1)). [resolve(5,a,8,a)].
20 -helped(c1) | find(c1,f1(c1)). [resolve(5,a,9,a)].
Derived: -young(c1) | tryhard(c1) | egg(f1(c1)). [resolve(18,c,19,a)].
Derived: -young(c1) | tryhard(c1) | find(c1,f1(c1)). [resolve(18,c,20,a)].
Eliminating young/1
21 -young(c1) | tryhard(c1) | egg(f1(c1)). [resolve(18,c,19,a)].
22 young(c1) | bunny(f2(c1)). [resolve(5,a,10,a)].
23 young(c1) | find(c1,f2(c1)). [resolve(5,a,11,a)].
Derived: tryhard(c1) | egg(f1(c1)) | bunny(f2(c1)). [resolve(21,a,22,a)].
Derived: tryhard(c1) | egg(f1(c1)) | find(c1,f2(c1)). [resolve(21,a,23,a)].
24 -young(c1) | tryhard(c1) | find(c1,f1(c1)). [resolve(18,c,20,a)].
Derived: tryhard(c1) | find(c1,f1(c1)) | bunny(f2(c1)). [resolve(24,a,22,a)].
Derived: tryhard(c1) | find(c1,f1(c1)) | find(c1,f2(c1)). [resolve(24,a,23,a)].
Eliminating tryhard/1
25 tryhard(c1) | egg(f1(c1)) | bunny(f2(c1)). [resolve(21,a,22,a)].
26 -tryhard(c1) | bunny(f2(c1)). [resolve(5,a,12,a)].
27 -tryhard(c1) | find(c1,f2(c1)). [resolve(5,a,13,a)].
Derived: egg(f1(c1)) | bunny(f2(c1)) | bunny(f2(c1)). [resolve(25,a,26,a)].
28 tryhard(c1) | egg(f1(c1)) | find(c1,f2(c1)). [resolve(21,a,23,a)].
Derived: egg(f1(c1)) | find(c1,f2(c1)) | find(c1,f2(c1)). [resolve(28,a,27,a)].
29 tryhard(c1) | find(c1,f1(c1)) | bunny(f2(c1)). [resolve(24,a,22,a)].
Derived: find(c1,f1(c1)) | bunny(f2(c1)) | bunny(f2(c1)). [resolve(29,a,26,a)].
30 tryhard(c1) | find(c1,f1(c1)) | find(c1,f2(c1)). [resolve(24,a,23,a)].
Derived: find(c1,f1(c1)) | find(c1,f2(c1)) | find(c1,f2(c1)). [resolve(30,a,27,a)].
Eliminating egg/1
31 egg(f1(c1)) | bunny(f2(c1)) | bunny(f2(c1)). [resolve(25,a,26,a)].
32 -egg(x) | -find(c1,x). [resolve(15,c,16,a)].
Derived: bunny(f2(c1)) | bunny(f2(c1)) | -find(c1,f1(c1)). [resolve(31,a,32,a)].
33 egg(f1(c1)) | find(c1,f2(c1)) | find(c1,f2(c1)). [resolve(28,a,27,a)].
Derived: find(c1,f2(c1)) | find(c1,f2(c1)) | -find(c1,f1(c1)). [resolve(33,a,32,a)].
============================== end predicate elimination =============
Auto_denials: (non-Horn, no changes).
Term ordering decisions:
Predicate symbol precedence: predicate_order([ bunny, find ]).
Function symbol precedence: function_order([ c1, f1, f2 ]).
After inverse_order: (no changes).
Unfolding symbols: (none).
Auto_inference settings:
% set(binary_resolution). % (non-Horn)
% set(neg_ur_resolution). % (non-Horn, less than 100 clauses)
Auto_process settings:
% set(factor). % (non-Horn)
% set(unit_deletion). % (non-Horn)
kept: 34 -bunny(x) | -find(c1,x). [resolve(17,c,16,a)].
35 find(c1,f1(c1)) | bunny(f2(c1)) | bunny(f2(c1)). [resolve(29,a,26,a)].
kept: 36 find(c1,f1(c1)) | bunny(f2(c1)). [copy(35),merge(c)].
37 find(c1,f1(c1)) | find(c1,f2(c1)) | find(c1,f2(c1)). [resolve(30,a,27,a)].
kept: 38 find(c1,f1(c1)) | find(c1,f2(c1)). [copy(37),merge(c)].
39 bunny(f2(c1)) | bunny(f2(c1)) | -find(c1,f1(c1)). [resolve(31,a,32,a)].
kept: 40 bunny(f2(c1)) | -find(c1,f1(c1)). [copy(39),merge(b)].
41 find(c1,f2(c1)) | find(c1,f2(c1)) | -find(c1,f1(c1)). [resolve(33,a,32,a)].
kept: 42 find(c1,f2(c1)) | -find(c1,f1(c1)). [copy(41),merge(b)].
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
% Clauses after input processing:
formulas(usable).
end_of_list.
formulas(sos).
34 -bunny(x) | -find(c1,x). [resolve(17,c,16,a)].
36 find(c1,f1(c1)) | bunny(f2(c1)). [copy(35),merge(c)].
38 find(c1,f1(c1)) | find(c1,f2(c1)). [copy(37),merge(c)].
40 bunny(f2(c1)) | -find(c1,f1(c1)). [copy(39),merge(b)].
42 find(c1,f2(c1)) | -find(c1,f1(c1)). [copy(41),merge(b)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.00 seconds.
given #1 (I,wt=5): 34 -bunny(x) | -find(c1,x). [resolve(17,c,16,a)].
given #2 (I,wt=7): 36 find(c1,f1(c1)) | bunny(f2(c1)). [copy(35),merge(c)].
given #3 (I,wt=8): 38 find(c1,f1(c1)) | find(c1,f2(c1)). [copy(37),merge(c)].
given #4 (I,wt=7): 40 bunny(f2(c1)) | -find(c1,f1(c1)). [copy(39),merge(b)].
given #5 (A,wt=3): 45 bunny(f2(c1)). [resolve(40,b,36,a),merge(b)].
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 47.
% Level of proof is 11.
% Maximum clause weight is 8.000.
% Given clauses 5.
1 (all x (child(x) & (exists y ((egg(y) | bunny(y)) & find(x,y))) -> happy(x))) # label(non_clause). [assumption].
2 (all x (child(x) & helped(x) -> (exists y (egg(y) & find(x,y))))) # label(non_clause). [assumption].
3 (all x (child(x) & (-young(x) | tryhard(x)) -> (exists y (bunny(y) & find(x,y))))) # label(non_clause). [assumption].
4 (all x (child(x) & young(x) -> tryhard(x) | helped(x))) -> (all y (child(y) -> happy(y))) # label(non_clause) # label(goal). [goal].
5 child(c1). [deny(4)].
6 -child(x) | -egg(y) | -find(x,y) | happy(x). [clausify(1)].
7 -child(x) | -bunny(y) | -find(x,y) | happy(x). [clausify(1)].
8 -child(x) | -helped(x) | egg(f1(x)). [clausify(2)].
9 -child(x) | -helped(x) | find(x,f1(x)). [clausify(2)].
10 -child(x) | young(x) | bunny(f2(x)). [clausify(3)].
11 -child(x) | young(x) | find(x,f2(x)). [clausify(3)].
12 -child(x) | -tryhard(x) | bunny(f2(x)). [clausify(3)].
13 -child(x) | -tryhard(x) | find(x,f2(x)). [clausify(3)].
14 -child(x) | -young(x) | tryhard(x) | helped(x). [deny(4)].
15 -egg(x) | -find(c1,x) | happy(c1). [resolve(5,a,6,a)].
16 -happy(c1). [deny(4)].
17 -bunny(x) | -find(c1,x) | happy(c1). [resolve(5,a,7,a)].
18 -young(c1) | tryhard(c1) | helped(c1). [resolve(5,a,14,a)].
19 -helped(c1) | egg(f1(c1)). [resolve(5,a,8,a)].
20 -helped(c1) | find(c1,f1(c1)). [resolve(5,a,9,a)].
21 -young(c1) | tryhard(c1) | egg(f1(c1)). [resolve(18,c,19,a)].
22 young(c1) | bunny(f2(c1)). [resolve(5,a,10,a)].
23 young(c1) | find(c1,f2(c1)). [resolve(5,a,11,a)].
24 -young(c1) | tryhard(c1) | find(c1,f1(c1)). [resolve(18,c,20,a)].
25 tryhard(c1) | egg(f1(c1)) | bunny(f2(c1)). [resolve(21,a,22,a)].
26 -tryhard(c1) | bunny(f2(c1)). [resolve(5,a,12,a)].
27 -tryhard(c1) | find(c1,f2(c1)). [resolve(5,a,13,a)].
28 tryhard(c1) | egg(f1(c1)) | find(c1,f2(c1)). [resolve(21,a,23,a)].
29 tryhard(c1) | find(c1,f1(c1)) | bunny(f2(c1)). [resolve(24,a,22,a)].
30 tryhard(c1) | find(c1,f1(c1)) | find(c1,f2(c1)). [resolve(24,a,23,a)].
31 egg(f1(c1)) | bunny(f2(c1)) | bunny(f2(c1)). [resolve(25,a,26,a)].
32 -egg(x) | -find(c1,x). [resolve(15,c,16,a)].
33 egg(f1(c1)) | find(c1,f2(c1)) | find(c1,f2(c1)). [resolve(28,a,27,a)].
34 -bunny(x) | -find(c1,x). [resolve(17,c,16,a)].
35 find(c1,f1(c1)) | bunny(f2(c1)) | bunny(f2(c1)). [resolve(29,a,26,a)].
36 find(c1,f1(c1)) | bunny(f2(c1)). [copy(35),merge(c)].
37 find(c1,f1(c1)) | find(c1,f2(c1)) | find(c1,f2(c1)). [resolve(30,a,27,a)].
38 find(c1,f1(c1)) | find(c1,f2(c1)). [copy(37),merge(c)].
39 bunny(f2(c1)) | bunny(f2(c1)) | -find(c1,f1(c1)). [resolve(31,a,32,a)].
40 bunny(f2(c1)) | -find(c1,f1(c1)). [copy(39),merge(b)].
41 find(c1,f2(c1)) | find(c1,f2(c1)) | -find(c1,f1(c1)). [resolve(33,a,32,a)].
42 find(c1,f2(c1)) | -find(c1,f1(c1)). [copy(41),merge(b)].
44 find(c1,f1(c1)) | -bunny(f2(c1)). [resolve(38,b,34,b)].
45 bunny(f2(c1)). [resolve(40,b,36,a),merge(b)].
46 find(c1,f1(c1)). [back_unit_del(44),unit_del(b,45)].
47 find(c1,f2(c1)). [back_unit_del(42),unit_del(b,46)].
48 $F. [ur(34,a,45,a),unit_del(a,47)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=5. Generated=11. Kept=10. proofs=1.
Usable=2. Sos=2. Demods=0. Limbo=0, Disabled=40. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=0. Back_subsumed=4.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=2.
Demod_attempts=0. Demod_rewrites=0.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=11.
Megabytes=0.07.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 6418 exit (max_proofs) Wed Jun 26 22:33:07 2019