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ex10.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 6414 was started by qwang on grid01,
Wed Jun 26 22:33:07 2019
The command was "prover9 -f ex10.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file ex10.in
formulas(sos).
(all x (child(x) -> (all y (candy(y) -> love(x,y))))).
(all x ((exists y (candy(y) & love(x,y))) -> -fanatic(x))).
(all x ((exists y (pumpkin(y) & eat(x,y))) -> fanatic(x))).
(all x all y (pumpkin(y) & buy(x,y) -> carve(x,y) | eat(x,y))).
(exists x (pumpkin(x) & buy(john,x))).
candy(lifesavers).
end_of_list.
formulas(goals).
child(john) -> (exists x (pumpkin(x) & carve(john,x))).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x (child(x) -> (all y (candy(y) -> love(x,y))))) # label(non_clause). [assumption].
2 (all x ((exists y (candy(y) & love(x,y))) -> -fanatic(x))) # label(non_clause). [assumption].
3 (all x ((exists y (pumpkin(y) & eat(x,y))) -> fanatic(x))) # label(non_clause). [assumption].
4 (all x all y (pumpkin(y) & buy(x,y) -> carve(x,y) | eat(x,y))) # label(non_clause). [assumption].
5 (exists x (pumpkin(x) & buy(john,x))) # label(non_clause). [assumption].
6 child(john) -> (exists x (pumpkin(x) & carve(john,x))) # 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) | -candy(y) | love(x,y). [clausify(1)].
-candy(x) | -love(y,x) | -fanatic(y). [clausify(2)].
-pumpkin(x) | -eat(y,x) | fanatic(y). [clausify(3)].
-pumpkin(x) | -buy(y,x) | carve(y,x) | eat(y,x). [clausify(4)].
pumpkin(c1). [clausify(5)].
buy(john,c1). [clausify(5)].
candy(lifesavers). [assumption].
child(john). [deny(6)].
-pumpkin(x) | -carve(john,x). [deny(6)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating child/1
7 child(john). [deny(6)].
8 -child(x) | -candy(y) | love(x,y). [clausify(1)].
Derived: -candy(x) | love(john,x). [resolve(7,a,8,a)].
Eliminating candy/1
9 candy(lifesavers). [assumption].
10 -candy(x) | -love(y,x) | -fanatic(y). [clausify(2)].
Derived: -love(x,lifesavers) | -fanatic(x). [resolve(9,a,10,a)].
11 -candy(x) | love(john,x). [resolve(7,a,8,a)].
Derived: love(john,lifesavers). [resolve(11,a,9,a)].
Eliminating pumpkin/1
12 pumpkin(c1). [clausify(5)].
13 -pumpkin(x) | -eat(y,x) | fanatic(y). [clausify(3)].
14 -pumpkin(x) | -buy(y,x) | carve(y,x) | eat(y,x). [clausify(4)].
Derived: -eat(x,c1) | fanatic(x). [resolve(12,a,13,a)].
Derived: -buy(x,c1) | carve(x,c1) | eat(x,c1). [resolve(12,a,14,a)].
15 -pumpkin(x) | -carve(john,x). [deny(6)].
Derived: -carve(john,c1). [resolve(15,a,12,a)].
Eliminating buy/2
16 -buy(x,c1) | carve(x,c1) | eat(x,c1). [resolve(12,a,14,a)].
17 buy(john,c1). [clausify(5)].
Derived: carve(john,c1) | eat(john,c1). [resolve(16,a,17,a)].
Eliminating love/2
18 love(john,lifesavers). [resolve(11,a,9,a)].
19 -love(x,lifesavers) | -fanatic(x). [resolve(9,a,10,a)].
Derived: -fanatic(john). [resolve(18,a,19,a)].
Eliminating eat/2
20 carve(john,c1) | eat(john,c1). [resolve(16,a,17,a)].
21 -eat(x,c1) | fanatic(x). [resolve(12,a,13,a)].
Derived: carve(john,c1) | fanatic(john). [resolve(20,b,21,a)].
Eliminating carve/2
22 carve(john,c1) | fanatic(john). [resolve(20,b,21,a)].
23 -carve(john,c1). [resolve(15,a,12,a)].
Derived: fanatic(john). [resolve(22,a,23,a)].
Eliminating fanatic/1
24 fanatic(john). [resolve(22,a,23,a)].
25 -fanatic(john). [resolve(18,a,19,a)].
Derived: $F. [resolve(24,a,25,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 26.
% Level of proof is 6.
% Maximum clause weight is 0.000.
% Given clauses 0.
1 (all x (child(x) -> (all y (candy(y) -> love(x,y))))) # label(non_clause). [assumption].
2 (all x ((exists y (candy(y) & love(x,y))) -> -fanatic(x))) # label(non_clause). [assumption].
3 (all x ((exists y (pumpkin(y) & eat(x,y))) -> fanatic(x))) # label(non_clause). [assumption].
4 (all x all y (pumpkin(y) & buy(x,y) -> carve(x,y) | eat(x,y))) # label(non_clause). [assumption].
5 (exists x (pumpkin(x) & buy(john,x))) # label(non_clause). [assumption].
6 child(john) -> (exists x (pumpkin(x) & carve(john,x))) # label(non_clause) # label(goal). [goal].
7 child(john). [deny(6)].
8 -child(x) | -candy(y) | love(x,y). [clausify(1)].
9 candy(lifesavers). [assumption].
10 -candy(x) | -love(y,x) | -fanatic(y). [clausify(2)].
11 -candy(x) | love(john,x). [resolve(7,a,8,a)].
12 pumpkin(c1). [clausify(5)].
13 -pumpkin(x) | -eat(y,x) | fanatic(y). [clausify(3)].
14 -pumpkin(x) | -buy(y,x) | carve(y,x) | eat(y,x). [clausify(4)].
15 -pumpkin(x) | -carve(john,x). [deny(6)].
16 -buy(x,c1) | carve(x,c1) | eat(x,c1). [resolve(12,a,14,a)].
17 buy(john,c1). [clausify(5)].
18 love(john,lifesavers). [resolve(11,a,9,a)].
19 -love(x,lifesavers) | -fanatic(x). [resolve(9,a,10,a)].
20 carve(john,c1) | eat(john,c1). [resolve(16,a,17,a)].
21 -eat(x,c1) | fanatic(x). [resolve(12,a,13,a)].
22 carve(john,c1) | fanatic(john). [resolve(20,b,21,a)].
23 -carve(john,c1). [resolve(15,a,12,a)].
24 fanatic(john). [resolve(22,a,23,a)].
25 -fanatic(john). [resolve(18,a,19,a)].
26 $F. [resolve(24,a,25,a)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=0. Generated=1. Kept=0. proofs=1.
Usable=0. Sos=0. Demods=0. Limbo=0, Disabled=20. 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=0.04.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 6414 exit (max_proofs) Wed Jun 26 22:33:07 2019