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ex21.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 6425 was started by qwang on grid01,
Wed Jun 26 22:33:07 2019
The command was "prover9 -f ex21.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file ex21.in
formulas(sos).
(all x (mall(x) -> (exists y (santa(y) & at(y,x))))).
(all x (child(x) -> (all y (visit(x,y) -> (all z (santa(z) -> talk(x,z) & at(z,y))))))).
(all x (child(x) & citychild(x) -> (exists y (mall(y) & visit(x,y))))).
(all x (child(x) & (good(x) | (exists y (santa(y) & talk(x,y)))) -> gettoy(x))).
end_of_list.
formulas(goals).
(all x (child(x) & -citychild(x) -> good(x))) -> (all y (child(y) -> gettoy(y))).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x (mall(x) -> (exists y (santa(y) & at(y,x))))) # label(non_clause). [assumption].
2 (all x (child(x) -> (all y (visit(x,y) -> (all z (santa(z) -> talk(x,z) & at(z,y))))))) # label(non_clause). [assumption].
3 (all x (child(x) & citychild(x) -> (exists y (mall(y) & visit(x,y))))) # label(non_clause). [assumption].
4 (all x (child(x) & (good(x) | (exists y (santa(y) & talk(x,y)))) -> gettoy(x))) # label(non_clause). [assumption].
5 (all x (child(x) & -citychild(x) -> good(x))) -> (all y (child(y) -> gettoy(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).
-mall(x) | santa(f1(x)). [clausify(1)].
-mall(x) | at(f1(x),x). [clausify(1)].
-child(x) | -visit(x,y) | -santa(z) | talk(x,z). [clausify(2)].
-child(x) | -visit(x,y) | -santa(z) | at(z,y). [clausify(2)].
-child(x) | -citychild(x) | mall(f2(x)). [clausify(3)].
-child(x) | -citychild(x) | visit(x,f2(x)). [clausify(3)].
-child(x) | -good(x) | gettoy(x). [clausify(4)].
-child(x) | -santa(y) | -talk(x,y) | gettoy(x). [clausify(4)].
-child(x) | citychild(x) | good(x). [deny(5)].
child(c1). [deny(5)].
-gettoy(c1). [deny(5)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating mall/1
6 -child(x) | -citychild(x) | mall(f2(x)). [clausify(3)].
7 -mall(x) | santa(f1(x)). [clausify(1)].
8 -mall(x) | at(f1(x),x). [clausify(1)].
Derived: -child(x) | -citychild(x) | santa(f1(f2(x))). [resolve(6,c,7,a)].
Derived: -child(x) | -citychild(x) | at(f1(f2(x)),f2(x)). [resolve(6,c,8,a)].
Eliminating child/1
9 child(c1). [deny(5)].
10 -child(x) | -visit(x,y) | -santa(z) | talk(x,z). [clausify(2)].
11 -child(x) | -visit(x,y) | -santa(z) | at(z,y). [clausify(2)].
12 -child(x) | -citychild(x) | visit(x,f2(x)). [clausify(3)].
13 -child(x) | -good(x) | gettoy(x). [clausify(4)].
14 -child(x) | -santa(y) | -talk(x,y) | gettoy(x). [clausify(4)].
15 -child(x) | citychild(x) | good(x). [deny(5)].
Derived: -visit(c1,x) | -santa(y) | talk(c1,y). [resolve(9,a,10,a)].
Derived: -visit(c1,x) | -santa(y) | at(y,x). [resolve(9,a,11,a)].
Derived: -citychild(c1) | visit(c1,f2(c1)). [resolve(9,a,12,a)].
Derived: -good(c1) | gettoy(c1). [resolve(9,a,13,a)].
Derived: -santa(x) | -talk(c1,x) | gettoy(c1). [resolve(9,a,14,a)].
Derived: citychild(c1) | good(c1). [resolve(9,a,15,a)].
16 -child(x) | -citychild(x) | santa(f1(f2(x))). [resolve(6,c,7,a)].
Derived: -citychild(c1) | santa(f1(f2(c1))). [resolve(16,a,9,a)].
17 -child(x) | -citychild(x) | at(f1(f2(x)),f2(x)). [resolve(6,c,8,a)].
Derived: -citychild(c1) | at(f1(f2(c1)),f2(c1)). [resolve(17,a,9,a)].
Eliminating gettoy/1
18 -good(c1) | gettoy(c1). [resolve(9,a,13,a)].
19 -gettoy(c1). [deny(5)].
Derived: -good(c1). [resolve(18,b,19,a)].
20 -santa(x) | -talk(c1,x) | gettoy(c1). [resolve(9,a,14,a)].
Derived: -santa(x) | -talk(c1,x). [resolve(20,c,19,a)].
Eliminating visit/2
21 -citychild(c1) | visit(c1,f2(c1)). [resolve(9,a,12,a)].
22 -visit(c1,x) | -santa(y) | talk(c1,y). [resolve(9,a,10,a)].
23 -visit(c1,x) | -santa(y) | at(y,x). [resolve(9,a,11,a)].
Derived: -citychild(c1) | -santa(x) | talk(c1,x). [resolve(21,b,22,a)].
Derived: -citychild(c1) | -santa(x) | at(x,f2(c1)). [resolve(21,b,23,a)].
Eliminating citychild/1
24 -citychild(c1) | santa(f1(f2(c1))). [resolve(16,a,9,a)].
25 citychild(c1) | good(c1). [resolve(9,a,15,a)].
Derived: santa(f1(f2(c1))) | good(c1). [resolve(24,a,25,a)].
26 -citychild(c1) | at(f1(f2(c1)),f2(c1)). [resolve(17,a,9,a)].
Derived: at(f1(f2(c1)),f2(c1)) | good(c1). [resolve(26,a,25,a)].
27 -citychild(c1) | -santa(x) | talk(c1,x). [resolve(21,b,22,a)].
Derived: -santa(x) | talk(c1,x) | good(c1). [resolve(27,a,25,a)].
28 -citychild(c1) | -santa(x) | at(x,f2(c1)). [resolve(21,b,23,a)].
Derived: -santa(x) | at(x,f2(c1)) | good(c1). [resolve(28,a,25,a)].
Eliminating good/1
29 santa(f1(f2(c1))) | good(c1). [resolve(24,a,25,a)].
30 -good(c1). [resolve(18,b,19,a)].
Derived: santa(f1(f2(c1))). [resolve(29,b,30,a)].
31 at(f1(f2(c1)),f2(c1)) | good(c1). [resolve(26,a,25,a)].
Derived: at(f1(f2(c1)),f2(c1)). [resolve(31,b,30,a)].
32 -santa(x) | talk(c1,x) | good(c1). [resolve(27,a,25,a)].
Derived: -santa(x) | talk(c1,x). [resolve(32,c,30,a)].
33 -santa(x) | at(x,f2(c1)) | good(c1). [resolve(28,a,25,a)].
Derived: -santa(x) | at(x,f2(c1)). [resolve(33,c,30,a)].
Eliminating santa/1
34 santa(f1(f2(c1))). [resolve(29,b,30,a)].
35 -santa(x) | -talk(c1,x). [resolve(20,c,19,a)].
Derived: -talk(c1,f1(f2(c1))). [resolve(34,a,35,a)].
36 -santa(x) | talk(c1,x). [resolve(32,c,30,a)].
Derived: talk(c1,f1(f2(c1))). [resolve(36,a,34,a)].
37 -santa(x) | at(x,f2(c1)). [resolve(33,c,30,a)].
Derived: at(f1(f2(c1)),f2(c1)). [resolve(37,a,34,a)].
Eliminating at/2
Eliminating talk/2
38 talk(c1,f1(f2(c1))). [resolve(36,a,34,a)].
39 -talk(c1,f1(f2(c1))). [resolve(34,a,35,a)].
Derived: $F. [resolve(38,a,39,a)].
============================== end predicate elimination =============
Auto_denials: (no changes).
Term ordering decisions:
Predicate symbol precedence: predicate_order([ ]).
Function symbol precedence: function_order([ ]).
After inverse_order: (no changes).
Unfolding symbols: (none).
Auto_inference settings:
% set(neg_binary_resolution). % (HNE depth_diff=0)
% clear(ordered_res). % (HNE depth_diff=0)
% set(ur_resolution). % (HNE depth_diff=0)
% set(ur_resolution) -> set(pos_ur_resolution).
% set(ur_resolution) -> set(neg_ur_resolution).
Auto_process settings: (no changes).
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 31.
% Level of proof is 7.
% Maximum clause weight is 0.000.
% Given clauses 0.
1 (all x (mall(x) -> (exists y (santa(y) & at(y,x))))) # label(non_clause). [assumption].
2 (all x (child(x) -> (all y (visit(x,y) -> (all z (santa(z) -> talk(x,z) & at(z,y))))))) # label(non_clause). [assumption].
3 (all x (child(x) & citychild(x) -> (exists y (mall(y) & visit(x,y))))) # label(non_clause). [assumption].
4 (all x (child(x) & (good(x) | (exists y (santa(y) & talk(x,y)))) -> gettoy(x))) # label(non_clause). [assumption].
5 (all x (child(x) & -citychild(x) -> good(x))) -> (all y (child(y) -> gettoy(y))) # label(non_clause) # label(goal). [goal].
6 -child(x) | -citychild(x) | mall(f2(x)). [clausify(3)].
7 -mall(x) | santa(f1(x)). [clausify(1)].
9 child(c1). [deny(5)].
10 -child(x) | -visit(x,y) | -santa(z) | talk(x,z). [clausify(2)].
12 -child(x) | -citychild(x) | visit(x,f2(x)). [clausify(3)].
13 -child(x) | -good(x) | gettoy(x). [clausify(4)].
14 -child(x) | -santa(y) | -talk(x,y) | gettoy(x). [clausify(4)].
15 -child(x) | citychild(x) | good(x). [deny(5)].
16 -child(x) | -citychild(x) | santa(f1(f2(x))). [resolve(6,c,7,a)].
18 -good(c1) | gettoy(c1). [resolve(9,a,13,a)].
19 -gettoy(c1). [deny(5)].
20 -santa(x) | -talk(c1,x) | gettoy(c1). [resolve(9,a,14,a)].
21 -citychild(c1) | visit(c1,f2(c1)). [resolve(9,a,12,a)].
22 -visit(c1,x) | -santa(y) | talk(c1,y). [resolve(9,a,10,a)].
24 -citychild(c1) | santa(f1(f2(c1))). [resolve(16,a,9,a)].
25 citychild(c1) | good(c1). [resolve(9,a,15,a)].
27 -citychild(c1) | -santa(x) | talk(c1,x). [resolve(21,b,22,a)].
29 santa(f1(f2(c1))) | good(c1). [resolve(24,a,25,a)].
30 -good(c1). [resolve(18,b,19,a)].
32 -santa(x) | talk(c1,x) | good(c1). [resolve(27,a,25,a)].
34 santa(f1(f2(c1))). [resolve(29,b,30,a)].
35 -santa(x) | -talk(c1,x). [resolve(20,c,19,a)].
36 -santa(x) | talk(c1,x). [resolve(32,c,30,a)].
38 talk(c1,f1(f2(c1))). [resolve(36,a,34,a)].
39 -talk(c1,f1(f2(c1))). [resolve(34,a,35,a)].
40 $F. [resolve(38,a,39,a)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=0. Generated=1. Kept=0. proofs=1.
Usable=0. Sos=0. Demods=0. Limbo=0, Disabled=37. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=0. Back_subsumed=0.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0.
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=0.
Megabytes=0.05.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 6425 exit (max_proofs) Wed Jun 26 22:33:07 2019