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ex15.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 6419 was started by qwang on grid01,
Wed Jun 26 22:33:07 2019
The command was "prover9 -f ex15.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file ex15.in
formulas(sos).
(all x ((exists y (student(y) & play(y,x))) -> tennis(x) | soccer(x) | chess(x))).
(all x (chess(x) -> -vigorous(x))).
(all x (healthy(x) -> (exists y (vigorous(y) & play(x,y))))).
(all x ((exists y (chess(y) & play(x,y))) -> -(exists z (soccer(z) & play(x,z))))).
end_of_list.
formulas(goals).
(all x (student(x) -> healthy(x))) -> (all y (student(y) -> ((exists z (chess(z) & play(y,z))) -> (exists u (tennis(u) & play(y,u)))))).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x ((exists y (student(y) & play(y,x))) -> tennis(x) | soccer(x) | chess(x))) # label(non_clause). [assumption].
2 (all x (chess(x) -> -vigorous(x))) # label(non_clause). [assumption].
3 (all x (healthy(x) -> (exists y (vigorous(y) & play(x,y))))) # label(non_clause). [assumption].
4 (all x ((exists y (chess(y) & play(x,y))) -> -(exists z (soccer(z) & play(x,z))))) # label(non_clause). [assumption].
5 (all x (student(x) -> healthy(x))) -> (all y (student(y) -> ((exists z (chess(z) & play(y,z))) -> (exists u (tennis(u) & play(y,u)))))) # 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).
-student(x) | -play(x,y) | tennis(y) | soccer(y) | chess(y). [clausify(1)].
-chess(x) | -vigorous(x). [clausify(2)].
-healthy(x) | vigorous(f1(x)). [clausify(3)].
-healthy(x) | play(x,f1(x)). [clausify(3)].
-chess(x) | -play(y,x) | -soccer(z) | -play(y,z). [clausify(4)].
-student(x) | healthy(x). [deny(5)].
student(c1). [deny(5)].
chess(c2). [deny(5)].
play(c1,c2). [deny(5)].
-tennis(x) | -play(c1,x). [deny(5)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating student/1
6 student(c1). [deny(5)].
7 -student(x) | -play(x,y) | tennis(y) | soccer(y) | chess(y). [clausify(1)].
8 -student(x) | healthy(x). [deny(5)].
Derived: -play(c1,x) | tennis(x) | soccer(x) | chess(x). [resolve(6,a,7,a)].
Derived: healthy(c1). [resolve(6,a,8,a)].
Eliminating chess/1
9 chess(c2). [deny(5)].
10 -chess(x) | -vigorous(x). [clausify(2)].
11 -chess(x) | -play(y,x) | -soccer(z) | -play(y,z). [clausify(4)].
Derived: -vigorous(c2). [resolve(9,a,10,a)].
Derived: -play(x,c2) | -soccer(y) | -play(x,y). [resolve(9,a,11,a)].
12 -play(c1,x) | tennis(x) | soccer(x) | chess(x). [resolve(6,a,7,a)].
Derived: -play(c1,x) | tennis(x) | soccer(x) | -vigorous(x). [resolve(12,d,10,a)].
Derived: -play(c1,x) | tennis(x) | soccer(x) | -play(y,x) | -soccer(z) | -play(y,z). [resolve(12,d,11,a)].
Eliminating healthy/1
13 healthy(c1). [resolve(6,a,8,a)].
14 -healthy(x) | vigorous(f1(x)). [clausify(3)].
15 -healthy(x) | play(x,f1(x)). [clausify(3)].
Derived: vigorous(f1(c1)). [resolve(13,a,14,a)].
Derived: play(c1,f1(c1)). [resolve(13,a,15,a)].
Eliminating tennis/1
16 -play(c1,x) | tennis(x) | soccer(x) | -vigorous(x). [resolve(12,d,10,a)].
17 -tennis(x) | -play(c1,x). [deny(5)].
Derived: -play(c1,x) | soccer(x) | -vigorous(x) | -play(c1,x). [resolve(16,b,17,a)].
18 -play(c1,x) | tennis(x) | soccer(x) | -play(y,x) | -soccer(z) | -play(y,z). [resolve(12,d,11,a)].
Derived: -play(c1,x) | soccer(x) | -play(y,x) | -soccer(z) | -play(y,z) | -play(c1,x). [resolve(18,b,17,a)].
Eliminating vigorous/1
19 vigorous(f1(c1)). [resolve(13,a,14,a)].
20 -vigorous(c2). [resolve(9,a,10,a)].
21 -play(c1,x) | soccer(x) | -vigorous(x) | -play(c1,x). [resolve(16,b,17,a)].
Derived: -play(c1,f1(c1)) | soccer(f1(c1)) | -play(c1,f1(c1)). [resolve(21,c,19,a)].
============================== end predicate elimination =============
Auto_denials: (no changes).
Term ordering decisions:
Predicate symbol precedence: predicate_order([ soccer, play ]).
Function symbol precedence: function_order([ c1, c2, f1 ]).
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:
% set(unit_deletion). % (Horn set with negative nonunits)
kept: 22 play(c1,c2). [deny(5)].
kept: 23 -play(x,c2) | -soccer(y) | -play(x,y). [resolve(9,a,11,a)].
kept: 24 play(c1,f1(c1)). [resolve(13,a,15,a)].
25 -play(c1,x) | soccer(x) | -play(y,x) | -soccer(z) | -play(y,z) | -play(c1,x). [resolve(18,b,17,a)].
kept: 26 -play(c1,x) | soccer(x) | -play(y,x) | -soccer(z) | -play(y,z). [copy(25),merge(f)].
27 -play(c1,f1(c1)) | soccer(f1(c1)) | -play(c1,f1(c1)). [resolve(21,c,19,a)].
kept: 28 soccer(f1(c1)). [copy(27),merge(c),unit_del(a,24)].
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
% Clauses after input processing:
formulas(usable).
end_of_list.
formulas(sos).
22 play(c1,c2). [deny(5)].
23 -play(x,c2) | -soccer(y) | -play(x,y). [resolve(9,a,11,a)].
24 play(c1,f1(c1)). [resolve(13,a,15,a)].
26 -play(c1,x) | soccer(x) | -play(y,x) | -soccer(z) | -play(y,z). [copy(25),merge(f)].
28 soccer(f1(c1)). [copy(27),merge(c),unit_del(a,24)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.00 seconds.
given #1 (I,wt=3): 22 play(c1,c2). [deny(5)].
given #2 (I,wt=8): 23 -play(x,c2) | -soccer(y) | -play(x,y). [resolve(9,a,11,a)].
given #3 (I,wt=4): 24 play(c1,f1(c1)). [resolve(13,a,15,a)].
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 25.
% Level of proof is 7.
% Maximum clause weight is 8.000.
% Given clauses 3.
1 (all x ((exists y (student(y) & play(y,x))) -> tennis(x) | soccer(x) | chess(x))) # label(non_clause). [assumption].
2 (all x (chess(x) -> -vigorous(x))) # label(non_clause). [assumption].
3 (all x (healthy(x) -> (exists y (vigorous(y) & play(x,y))))) # label(non_clause). [assumption].
4 (all x ((exists y (chess(y) & play(x,y))) -> -(exists z (soccer(z) & play(x,z))))) # label(non_clause). [assumption].
5 (all x (student(x) -> healthy(x))) -> (all y (student(y) -> ((exists z (chess(z) & play(y,z))) -> (exists u (tennis(u) & play(y,u)))))) # label(non_clause) # label(goal). [goal].
6 student(c1). [deny(5)].
7 -student(x) | -play(x,y) | tennis(y) | soccer(y) | chess(y). [clausify(1)].
8 -student(x) | healthy(x). [deny(5)].
9 chess(c2). [deny(5)].
10 -chess(x) | -vigorous(x). [clausify(2)].
11 -chess(x) | -play(y,x) | -soccer(z) | -play(y,z). [clausify(4)].
12 -play(c1,x) | tennis(x) | soccer(x) | chess(x). [resolve(6,a,7,a)].
13 healthy(c1). [resolve(6,a,8,a)].
14 -healthy(x) | vigorous(f1(x)). [clausify(3)].
15 -healthy(x) | play(x,f1(x)). [clausify(3)].
16 -play(c1,x) | tennis(x) | soccer(x) | -vigorous(x). [resolve(12,d,10,a)].
17 -tennis(x) | -play(c1,x). [deny(5)].
19 vigorous(f1(c1)). [resolve(13,a,14,a)].
21 -play(c1,x) | soccer(x) | -vigorous(x) | -play(c1,x). [resolve(16,b,17,a)].
22 play(c1,c2). [deny(5)].
23 -play(x,c2) | -soccer(y) | -play(x,y). [resolve(9,a,11,a)].
24 play(c1,f1(c1)). [resolve(13,a,15,a)].
27 -play(c1,f1(c1)) | soccer(f1(c1)) | -play(c1,f1(c1)). [resolve(21,c,19,a)].
28 soccer(f1(c1)). [copy(27),merge(c),unit_del(a,24)].
31 $F. [resolve(24,a,23,c),unit_del(a,22),unit_del(b,28)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=3. Generated=9. Kept=7. proofs=1.
Usable=3. Sos=4. Demods=0. Limbo=0, Disabled=21. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=1. 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=5.
Megabytes=0.06.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 6419 exit (max_proofs) Wed Jun 26 22:33:07 2019