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============================== Prover9 ===============================
Prover9 (32) version 2009-02A, February 2009.
Process 15901 was started by mccune on cleo,
Wed Feb 25 12:26:33 2009
The command was "/home/mccune/bin/prover9 -f cabbages.in".
============================== end of head ===========================

============================== INPUT =================================

% Reading from file cabbages.in

set(production).
    % set(production) -> set(raw).
    % set(raw) -> clear(auto).
    % clear(auto) -> clear(auto_inference).
    % clear(auto) -> clear(auto_setup).
    % clear(auto_setup) -> clear(predicate_elim).
    % clear(auto_setup) -> assign(eq_defs, pass).
    % clear(auto) -> clear(auto_limits).
    % clear(auto_limits) -> assign(max_weight, "1000000000000.000").
    % clear(auto_limits) -> assign(sos_limit, -1).
    % clear(auto) -> clear(auto_denials).
    % clear(auto) -> clear(auto_process).
    % set(raw) -> clear(ordered_res).
    % set(raw) -> clear(ordered_para).
    % set(raw) -> set(para_into_vars).
    % set(raw) -> set(para_from_small).
    % set(raw) -> clear(ordered_para).
    % set(raw) -> clear(back_demod).
    % set(raw) -> clear(cac_redundancy).
    % set(raw) -> assign(backsub_check, 2147483647).
    % set(raw) -> set(lightest_first).
    % set(lightest_first) -> assign(weight_part, 1).
    % set(lightest_first) -> assign(age_part, 0).
    % set(lightest_first) -> assign(false_part, 0).
    % set(lightest_first) -> assign(true_part, 0).
    % set(lightest_first) -> assign(random_part, 0).
    % set(raw) -> assign(literal_selection, none).
    % set(production) -> set(eval_rewrite).
    % set(production) -> set(hyper_resolution).
    % set(hyper_resolution) -> set(pos_hyper_resolution).
    % set(production) -> clear(back_subsume).
set(prolog_style_variables).

formulas(usable).
state(Side,W,G,C) & ok(W,G,C) -> state(otherside(Side),flip(W),flip(G),flip(C)) # answer(none).
state(Side,1,G,C) & ok(0,G,C) -> state(otherside(Side),1,flip(G),flip(C)) # answer(wolf).
state(Side,W,1,C) & ok(W,0,C) -> state(otherside(Side),flip(W),1,flip(C)) # answer(goat).
state(Side,W,G,1) & ok(W,G,0) -> state(otherside(Side),flip(W),flip(G),1) # answer(cabbage).
end_of_list.

formulas(assumptions).
state(west,1,1,1).
end_of_list.

formulas(goals).
state(east,1,1,1).
end_of_list.

formulas(demodulators).
flip(0) = 1.
flip(1) = 0.
otherside(east) = west.
otherside(west) = east.
ok(W,G,C) <-> if(W == 1 & G == 1 | G == 1 & C == 1,$F,$T).
end_of_list.

============================== end of input ==========================

============================== PROCESS NON-CLAUSAL FORMULAS ==========

% Formulas that are not ordinary clauses:
1 state(Side,W,G,C) & ok(W,G,C) -> state(otherside(Side),flip(W),flip(G),flip(C)) # answer(none) # label(non_clause).  [assumption].
2 state(Side,1,G,C) & ok(0,G,C) -> state(otherside(Side),1,flip(G),flip(C)) # answer(wolf) # label(non_clause).  [assumption].
3 state(Side,W,1,C) & ok(W,0,C) -> state(otherside(Side),flip(W),1,flip(C)) # answer(goat) # label(non_clause).  [assumption].
4 state(Side,W,G,1) & ok(W,G,0) -> state(otherside(Side),flip(W),flip(G),1) # answer(cabbage) # label(non_clause).  [assumption].
5 state(east,1,1,1) # label(non_clause) # label(goal).  [goal].

============================== end of process non-clausal formulas ===

============================== PROCESS INITIAL CLAUSES ===============

% Clauses before input processing:

formulas(usable).
-state(A,B,C,D) | -ok(B,C,D) | state(otherside(A),flip(B),flip(C),flip(D)) # answer(none).  [clausify(1)].
-state(A,1,B,C) | -ok(0,B,C) | state(otherside(A),1,flip(B),flip(C)) # answer(wolf).  [clausify(2)].
-state(A,B,1,C) | -ok(B,0,C) | state(otherside(A),flip(B),1,flip(C)) # answer(goat).  [clausify(3)].
-state(A,B,C,1) | -ok(B,C,0) | state(otherside(A),flip(B),flip(C),1) # answer(cabbage).  [clausify(4)].
end_of_list.

formulas(sos).
state(west,1,1,1).  [assumption].
-state(east,1,1,1).  [deny(5)].
end_of_list.

formulas(demodulators).
flip(0) = 1.  [assumption].
flip(1) = 0.  [assumption].
otherside(east) = west.  [assumption].
otherside(west) = east.  [assumption].
ok(W,G,C) <-> if(W == 1 & G == 1 | G == 1 & C == 1,$F,$T).  [assumption].
end_of_list.

Term ordering decisions:
Predicate symbol precedence:  predicate_order([ =, ==, ok, state ]).
Function symbol precedence:  function_order([ 1, 0, west, east, flip, otherside ]).
After inverse_order:  (no changes).

kept:      15 state(west,1,1,1).  [assumption].
kept:      16 -state(east,1,1,1).  [deny(5)].

============================== end of process initial clauses ========

============================== CLAUSES FOR SEARCH ====================

% Clauses after input processing:

formulas(usable).
6 -state(A,B,C,D) | -ok(B,C,D) | state(otherside(A),flip(B),flip(C),flip(D)) # answer(none).  [clausify(1)].
7 -state(A,1,B,C) | -ok(0,B,C) | state(otherside(A),1,flip(B),flip(C)) # answer(wolf).  [clausify(2)].
8 -state(A,B,1,C) | -ok(B,0,C) | state(otherside(A),flip(B),1,flip(C)) # answer(goat).  [clausify(3)].
9 -state(A,B,C,1) | -ok(B,C,0) | state(otherside(A),flip(B),flip(C),1) # answer(cabbage).  [clausify(4)].
end_of_list.

formulas(sos).
15 state(west,1,1,1).  [assumption].
16 -state(east,1,1,1).  [deny(5)].
end_of_list.

formulas(demodulators).
10 flip(0) = 1.  [assumption].
11 flip(1) = 0.  [assumption].
12 otherside(east) = west.  [assumption].
13 otherside(west) = east.  [assumption].
14 ok(A,B,C) <-> if(A == 1 & B == 1 | B == 1 & C == 1,$F,$T).  [assumption].
end_of_list.

============================== end of clauses for search =============

============================== SEARCH ================================

% Starting search at 0.01 seconds.

given #1 (I,wt=5): 15 state(west,1,1,1).  [assumption].

given #2 (I,wt=5): 16 -state(east,1,1,1).  [deny(5)].

given #3 (W,wt=5): 17 state(east,0,1,0) # answer(goat).  [hyper(8,a,15,a),rewrite([14,13,11]),eval(3)].

given #4 (W,wt=5): 18 state(west,1,0,1) # answer(none) # answer(goat).  [hyper(6,a,17,a),rewrite([14,12,10,11]),eval(3)].

given #5 (W,wt=5): 19 state(east,0,1,1) # answer(cabbage) # answer(none) # answer(goat).  [hyper(9,a,18,a),rewrite([14,13,11,10]),eval(3)].

given #6 (W,wt=5): 20 state(east,1,1,0) # answer(wolf) # answer(none) # answer(goat).  [hyper(7,a,18,a),rewrite([14,13,10,11]),eval(2)].

given #7 (W,wt=5): 21 state(west,1,1,0) # answer(goat) # answer(cabbage) # answer(none) # answer(goat).  [hyper(8,a,19,a),rewrite([14,12,10,11]),eval(2)].

given #8 (W,wt=5): 22 state(west,0,1,1) # answer(goat) # answer(wolf) # answer(none) # answer(goat).  [hyper(8,a,20,a),rewrite([14,12,11,10]),eval(3)].

given #9 (W,wt=5): 23 state(east,1,0,1) # answer(wolf) # answer(goat) # answer(cabbage) # answer(none) # answer(goat).  [hyper(7,a,21,a),rewrite([14,13,11,10]),eval(3)].

given #10 (W,wt=5): 24 state(west,0,1,0) # answer(none) # answer(wolf) # answer(goat) # answer(cabbage) # answer(none) # answer(goat).  [hyper(6,a,23,a),rewrite([14,12,11,10]),eval(3)].

============================== PROOF =================================

% Proof 1 at 0.01 (+ 0.00) seconds: goat # none # wolf # goat # cabbage # none # goat.
% Length of proof is 24.
% Level of proof is 9.
% Maximum clause weight is 5.
% Given clauses 10.

1 state(Side,W,G,C) & ok(W,G,C) -> state(otherside(Side),flip(W),flip(G),flip(C)) # answer(none) # label(non_clause).  [assumption].
2 state(Side,1,G,C) & ok(0,G,C) -> state(otherside(Side),1,flip(G),flip(C)) # answer(wolf) # label(non_clause).  [assumption].
3 state(Side,W,1,C) & ok(W,0,C) -> state(otherside(Side),flip(W),1,flip(C)) # answer(goat) # label(non_clause).  [assumption].
4 state(Side,W,G,1) & ok(W,G,0) -> state(otherside(Side),flip(W),flip(G),1) # answer(cabbage) # label(non_clause).  [assumption].
5 state(east,1,1,1) # label(non_clause) # label(goal).  [goal].
6 -state(A,B,C,D) | -ok(B,C,D) | state(otherside(A),flip(B),flip(C),flip(D)) # answer(none).  [clausify(1)].
7 -state(A,1,B,C) | -ok(0,B,C) | state(otherside(A),1,flip(B),flip(C)) # answer(wolf).  [clausify(2)].
8 -state(A,B,1,C) | -ok(B,0,C) | state(otherside(A),flip(B),1,flip(C)) # answer(goat).  [clausify(3)].
9 -state(A,B,C,1) | -ok(B,C,0) | state(otherside(A),flip(B),flip(C),1) # answer(cabbage).  [clausify(4)].
10 flip(0) = 1.  [assumption].
11 flip(1) = 0.  [assumption].
12 otherside(east) = west.  [assumption].
13 otherside(west) = east.  [assumption].
14 ok(A,B,C) <-> if(A == 1 & B == 1 | B == 1 & C == 1,$F,$T).  [assumption].
15 state(west,1,1,1).  [assumption].
16 -state(east,1,1,1).  [deny(5)].
17 state(east,0,1,0) # answer(goat).  [hyper(8,a,15,a),rewrite([14,13,11]),eval(3)].
18 state(west,1,0,1) # answer(none) # answer(goat).  [hyper(6,a,17,a),rewrite([14,12,10,11]),eval(3)].
19 state(east,0,1,1) # answer(cabbage) # answer(none) # answer(goat).  [hyper(9,a,18,a),rewrite([14,13,11,10]),eval(3)].
21 state(west,1,1,0) # answer(goat) # answer(cabbage) # answer(none) # answer(goat).  [hyper(8,a,19,a),rewrite([14,12,10,11]),eval(2)].
23 state(east,1,0,1) # answer(wolf) # answer(goat) # answer(cabbage) # answer(none) # answer(goat).  [hyper(7,a,21,a),rewrite([14,13,11,10]),eval(3)].
24 state(west,0,1,0) # answer(none) # answer(wolf) # answer(goat) # answer(cabbage) # answer(none) # answer(goat).  [hyper(6,a,23,a),rewrite([14,12,11,10]),eval(3)].
25 state(east,1,1,1) # answer(goat) # answer(none) # answer(wolf) # answer(goat) # answer(cabbage) # answer(none) # answer(goat).  [hyper(8,a,24,a),rewrite([14,13,10]),eval(2)].
26 $F # answer(goat) # answer(none) # answer(wolf) # answer(goat) # answer(cabbage) # answer(none) # answer(goat).  [resolve(25,a,16,a)].

============================== end of proof ==========================

============================== STATISTICS ============================

Given=10. Generated=27. Kept=11. proofs=1.
Usable=14. Sos=0. Demods=5. Limbo=0, Disabled=2. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=16. 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=0.01, System_CPU=0.00, Wall_clock=0.

============================== end of statistics =====================

============================== end of search =========================

THEOREM PROVED

Exiting with 1 proof.

Process 15901 exit (max_proofs) Wed Feb 25 12:26:33 2009

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