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ex18.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 6422 was started by qwang on grid01,
Wed Jun 26 22:33:07 2019
The command was "prover9 -f ex18.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file ex18.in
formulas(sos).
(all x (lovelottery(x) -> gambler(x))).
(all x (favorprop(x) -> lovelottery(x))).
(all x (favorprop(x) & opposeprop(x))).
(all x (baptist(x) & vote(x) & opposeprop(x) -> -propwin)).
(all x (baptist(x) & faithful(x) -> -gambler(x))).
end_of_list.
formulas(goals).
(all x (baptist(x) & vote(x))) & propwin -> (exists x (baptist(x) & -faithful(x))).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all x (lovelottery(x) -> gambler(x))) # label(non_clause). [assumption].
2 (all x (favorprop(x) -> lovelottery(x))) # label(non_clause). [assumption].
3 (all x (favorprop(x) & opposeprop(x))) # label(non_clause). [assumption].
4 (all x (baptist(x) & vote(x) & opposeprop(x) -> -propwin)) # label(non_clause). [assumption].
5 (all x (baptist(x) & faithful(x) -> -gambler(x))) # label(non_clause). [assumption].
6 (all x (baptist(x) & vote(x))) & propwin -> (exists x (baptist(x) & -faithful(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).
-lovelottery(x) | gambler(x). [clausify(1)].
-favorprop(x) | lovelottery(x). [clausify(2)].
favorprop(x). [clausify(3)].
opposeprop(x). [clausify(3)].
-baptist(x) | -vote(x) | -opposeprop(x) | -propwin. [clausify(4)].
-baptist(x) | -faithful(x) | -gambler(x). [clausify(5)].
baptist(x). [deny(6)].
vote(x). [deny(6)].
propwin. [deny(6)].
-baptist(x) | faithful(x). [deny(6)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
Eliminating lovelottery/1
7 -favorprop(x) | lovelottery(x). [clausify(2)].
8 -lovelottery(x) | gambler(x). [clausify(1)].
Derived: -favorprop(x) | gambler(x). [resolve(7,b,8,a)].
Eliminating favorprop/1
9 -favorprop(x) | gambler(x). [resolve(7,b,8,a)].
10 favorprop(x). [clausify(3)].
Derived: gambler(x). [resolve(9,a,10,a)].
Eliminating opposeprop/1
11 -baptist(x) | -vote(x) | -opposeprop(x) | -propwin. [clausify(4)].
12 opposeprop(x). [clausify(3)].
Derived: -baptist(x) | -vote(x) | -propwin. [resolve(11,c,12,a)].
Eliminating baptist/1
13 baptist(x). [deny(6)].
14 -baptist(x) | -faithful(x) | -gambler(x). [clausify(5)].
Derived: -faithful(x) | -gambler(x). [resolve(13,a,14,a)].
15 -baptist(x) | faithful(x). [deny(6)].
Derived: faithful(x). [resolve(15,a,13,a)].
16 -baptist(x) | -vote(x) | -propwin. [resolve(11,c,12,a)].
Derived: -vote(x) | -propwin. [resolve(16,a,13,a)].
Eliminating vote/1
17 -vote(x) | -propwin. [resolve(16,a,13,a)].
18 vote(x). [deny(6)].
Derived: -propwin. [resolve(17,a,18,a)].
Eliminating gambler/1
19 -faithful(x) | -gambler(x). [resolve(13,a,14,a)].
20 gambler(x). [resolve(9,a,10,a)].
Derived: -faithful(x). [resolve(19,b,20,a)].
Eliminating faithful/1
21 -faithful(x). [resolve(19,b,20,a)].
22 faithful(x). [resolve(15,a,13,a)].
Derived: $F. [resolve(21,a,22,a)].
============================== end predicate elimination =============
Auto_denials:
% assign(max_proofs, 2). % (Horn set with more than one neg. clause)
Term ordering decisions:
Predicate symbol precedence: predicate_order([ propwin ]).
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).
kept: 23 propwin. [deny(6)].
kept: 24 -propwin. [resolve(17,a,18,a)].
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 12.
% Level of proof is 5.
% Maximum clause weight is 1.000.
% Given clauses 0.
3 (all x (favorprop(x) & opposeprop(x))) # label(non_clause). [assumption].
4 (all x (baptist(x) & vote(x) & opposeprop(x) -> -propwin)) # label(non_clause). [assumption].
6 (all x (baptist(x) & vote(x))) & propwin -> (exists x (baptist(x) & -faithful(x))) # label(non_clause) # label(goal). [goal].
11 -baptist(x) | -vote(x) | -opposeprop(x) | -propwin. [clausify(4)].
12 opposeprop(x). [clausify(3)].
13 baptist(x). [deny(6)].
16 -baptist(x) | -vote(x) | -propwin. [resolve(11,c,12,a)].
17 -vote(x) | -propwin. [resolve(16,a,13,a)].
18 vote(x). [deny(6)].
23 propwin. [deny(6)].
24 -propwin. [resolve(17,a,18,a)].
25 $F. [resolve(24,a,23,a)].
============================== end of proof ==========================
============================== PROOF =================================
% Proof 2 at 0.00 (+ 0.00) seconds.
% Length of proof is 17.
% Level of proof is 5.
% Maximum clause weight is 0.000.
% Given clauses 0.
1 (all x (lovelottery(x) -> gambler(x))) # label(non_clause). [assumption].
2 (all x (favorprop(x) -> lovelottery(x))) # label(non_clause). [assumption].
3 (all x (favorprop(x) & opposeprop(x))) # label(non_clause). [assumption].
5 (all x (baptist(x) & faithful(x) -> -gambler(x))) # label(non_clause). [assumption].
6 (all x (baptist(x) & vote(x))) & propwin -> (exists x (baptist(x) & -faithful(x))) # label(non_clause) # label(goal). [goal].
7 -favorprop(x) | lovelottery(x). [clausify(2)].
8 -lovelottery(x) | gambler(x). [clausify(1)].
9 -favorprop(x) | gambler(x). [resolve(7,b,8,a)].
10 favorprop(x). [clausify(3)].
13 baptist(x). [deny(6)].
14 -baptist(x) | -faithful(x) | -gambler(x). [clausify(5)].
15 -baptist(x) | faithful(x). [deny(6)].
19 -faithful(x) | -gambler(x). [resolve(13,a,14,a)].
20 gambler(x). [resolve(9,a,10,a)].
21 -faithful(x). [resolve(19,b,20,a)].
22 faithful(x). [resolve(15,a,13,a)].
26 $F. [resolve(21,a,22,a)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=0. Generated=3. Kept=2. proofs=2.
Usable=0. Sos=0. Demods=0. Limbo=2, 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 2 proofs.
Process 6422 exit (max_proofs) Wed Jun 26 22:33:07 2019