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ex09.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 6413 was started by qwang on grid01,
Wed Jun 26 22:33:07 2019
The command was "prover9 -f ex09.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file ex09.in
formulas(sos).
(all x (investor(x) -> (exists y ((stock(y) | bond(y)) & buy(x,y))))).
djcrash -> (all x (stock(x) & -goldstock(x) -> fall(x))).
tbrise -> (all x (bond(x) -> fall(x))).
(all x (investor(x) & (exists y (buy(x,y) & fall(y))) -> -happy(x))).
end_of_list.
formulas(goals).
djcrash & tbrise -> (all x (investor(x) & happy(x) -> (exists y (goldstock(y) & buy(x,y))))).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x (investor(x) -> (exists y ((stock(y) | bond(y)) & buy(x,y))))) # label(non_clause). [assumption].
2 djcrash -> (all x (stock(x) & -goldstock(x) -> fall(x))) # label(non_clause). [assumption].
3 tbrise -> (all x (bond(x) -> fall(x))) # label(non_clause). [assumption].
4 (all x (investor(x) & (exists y (buy(x,y) & fall(y))) -> -happy(x))) # label(non_clause). [assumption].
5 djcrash & tbrise -> (all x (investor(x) & happy(x) -> (exists y (goldstock(y) & buy(x,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).
-investor(x) | stock(f1(x)) | bond(f1(x)). [clausify(1)].
-investor(x) | buy(x,f1(x)). [clausify(1)].
-djcrash | -stock(x) | goldstock(x) | fall(x). [clausify(2)].
-tbrise | -bond(x) | fall(x). [clausify(3)].
-investor(x) | -buy(x,y) | -fall(y) | -happy(x). [clausify(4)].
djcrash. [deny(5)].
tbrise. [deny(5)].
investor(c1). [deny(5)].
happy(c1). [deny(5)].
-goldstock(x) | -buy(c1,x). [deny(5)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating investor/1
6 investor(c1). [deny(5)].
7 -investor(x) | stock(f1(x)) | bond(f1(x)). [clausify(1)].
8 -investor(x) | buy(x,f1(x)). [clausify(1)].
9 -investor(x) | -buy(x,y) | -fall(y) | -happy(x). [clausify(4)].
Derived: stock(f1(c1)) | bond(f1(c1)). [resolve(6,a,7,a)].
Derived: buy(c1,f1(c1)). [resolve(6,a,8,a)].
Derived: -buy(c1,x) | -fall(x) | -happy(c1). [resolve(6,a,9,a)].
Eliminating stock/1
10 stock(f1(c1)) | bond(f1(c1)). [resolve(6,a,7,a)].
11 -djcrash | -stock(x) | goldstock(x) | fall(x). [clausify(2)].
Derived: bond(f1(c1)) | -djcrash | goldstock(f1(c1)) | fall(f1(c1)). [resolve(10,a,11,b)].
Eliminating bond/1
12 bond(f1(c1)) | -djcrash | goldstock(f1(c1)) | fall(f1(c1)). [resolve(10,a,11,b)].
13 -tbrise | -bond(x) | fall(x). [clausify(3)].
Derived: -djcrash | goldstock(f1(c1)) | fall(f1(c1)) | -tbrise | fall(f1(c1)). [resolve(12,a,13,b)].
Eliminating happy/1
14 -buy(c1,x) | -fall(x) | -happy(c1). [resolve(6,a,9,a)].
15 happy(c1). [deny(5)].
Derived: -buy(c1,x) | -fall(x). [resolve(14,c,15,a)].
Eliminating goldstock/1
16 -djcrash | goldstock(f1(c1)) | fall(f1(c1)) | -tbrise | fall(f1(c1)). [resolve(12,a,13,b)].
17 -goldstock(x) | -buy(c1,x). [deny(5)].
Derived: -djcrash | fall(f1(c1)) | -tbrise | fall(f1(c1)) | -buy(c1,f1(c1)). [resolve(16,b,17,a)].
Eliminating buy/2
18 -buy(c1,x) | -fall(x). [resolve(14,c,15,a)].
19 buy(c1,f1(c1)). [resolve(6,a,8,a)].
Derived: -fall(f1(c1)). [resolve(18,a,19,a)].
20 -djcrash | fall(f1(c1)) | -tbrise | fall(f1(c1)) | -buy(c1,f1(c1)). [resolve(16,b,17,a)].
Derived: -djcrash | fall(f1(c1)) | -tbrise | fall(f1(c1)). [resolve(20,e,19,a)].
============================== end predicate elimination =============
Auto_denials: (non-Horn, no changes).
Term ordering decisions:
Predicate symbol precedence: predicate_order([ djcrash, tbrise, fall ]).
Function symbol precedence: function_order([ c1, f1 ]).
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: 21 djcrash. [deny(5)].
kept: 22 tbrise. [deny(5)].
kept: 23 -fall(f1(c1)). [resolve(18,a,19,a)].
24 -djcrash | fall(f1(c1)) | -tbrise | fall(f1(c1)). [resolve(20,e,19,a)].
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 25.
% Level of proof is 7.
% Maximum clause weight is 3.000.
% Given clauses 0.
1 (all x (investor(x) -> (exists y ((stock(y) | bond(y)) & buy(x,y))))) # label(non_clause). [assumption].
2 djcrash -> (all x (stock(x) & -goldstock(x) -> fall(x))) # label(non_clause). [assumption].
3 tbrise -> (all x (bond(x) -> fall(x))) # label(non_clause). [assumption].
4 (all x (investor(x) & (exists y (buy(x,y) & fall(y))) -> -happy(x))) # label(non_clause). [assumption].
5 djcrash & tbrise -> (all x (investor(x) & happy(x) -> (exists y (goldstock(y) & buy(x,y))))) # label(non_clause) # label(goal). [goal].
6 investor(c1). [deny(5)].
7 -investor(x) | stock(f1(x)) | bond(f1(x)). [clausify(1)].
8 -investor(x) | buy(x,f1(x)). [clausify(1)].
9 -investor(x) | -buy(x,y) | -fall(y) | -happy(x). [clausify(4)].
10 stock(f1(c1)) | bond(f1(c1)). [resolve(6,a,7,a)].
11 -djcrash | -stock(x) | goldstock(x) | fall(x). [clausify(2)].
12 bond(f1(c1)) | -djcrash | goldstock(f1(c1)) | fall(f1(c1)). [resolve(10,a,11,b)].
13 -tbrise | -bond(x) | fall(x). [clausify(3)].
14 -buy(c1,x) | -fall(x) | -happy(c1). [resolve(6,a,9,a)].
15 happy(c1). [deny(5)].
16 -djcrash | goldstock(f1(c1)) | fall(f1(c1)) | -tbrise | fall(f1(c1)). [resolve(12,a,13,b)].
17 -goldstock(x) | -buy(c1,x). [deny(5)].
18 -buy(c1,x) | -fall(x). [resolve(14,c,15,a)].
19 buy(c1,f1(c1)). [resolve(6,a,8,a)].
20 -djcrash | fall(f1(c1)) | -tbrise | fall(f1(c1)) | -buy(c1,f1(c1)). [resolve(16,b,17,a)].
21 djcrash. [deny(5)].
22 tbrise. [deny(5)].
23 -fall(f1(c1)). [resolve(18,a,19,a)].
24 -djcrash | fall(f1(c1)) | -tbrise | fall(f1(c1)). [resolve(20,e,19,a)].
25 $F. [copy(24),merge(d),unit_del(a,21),unit_del(b,23),unit_del(c,22)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=0. Generated=4. Kept=3. proofs=1.
Usable=0. Sos=0. Demods=0. Limbo=3, Disabled=19. 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 6413 exit (max_proofs) Wed Jun 26 22:33:07 2019