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group_exercise.out
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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 64732 was started by qwang on grid01,
Fri May 31 17:37:40 2019
The command was "prover9 -f group_exercise.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file group_exercise.in
formulas(sos).
P(x,y,m(x,y)).
-P(x,y,u) | -P(y,z,v) | -P(x,v,w) | P(u,z,w).
-P(x,y,u) | -P(y,z,v) | -P(u,z,w) | P(x,v,w).
P(e,y,y).
P(i(y),y,e).
P(x,y,z) -> P(y,x,z).
P(a,b,c) & -P(c,i(a),b).
end_of_list.
formulas(goals).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 P(x,y,z) -> P(y,x,z) # label(non_clause). [assumption].
2 P(a,b,c) & -P(c,i(a),b) # label(non_clause). [assumption].
============================== end of process non-clausal formulas ===
============================== PROCESS INITIAL CLAUSES ===============
% Clauses before input processing:
formulas(usable).
end_of_list.
formulas(sos).
P(x,y,m(x,y)). [assumption].
-P(x,y,z) | -P(y,u,w) | -P(x,w,v5) | P(z,u,v5). [assumption].
-P(x,y,z) | -P(y,u,w) | -P(z,u,v5) | P(x,w,v5). [assumption].
P(e,x,x). [assumption].
P(i(x),x,e). [assumption].
-P(x,y,z) | P(y,x,z). [clausify(1)].
P(a,b,c). [clausify(2)].
-P(c,i(a),b). [clausify(2)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== PREDICATE ELIMINATION =================
No predicates eliminated.
============================== end predicate elimination =============
Auto_denials: (no changes).
Term ordering decisions:
Predicate symbol precedence: predicate_order([ P ]).
Function symbol precedence: function_order([ e, a, b, c, m, i ]).
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: 3 P(x,y,m(x,y)). [assumption].
kept: 4 -P(x,y,z) | -P(y,u,w) | -P(x,w,v5) | P(z,u,v5). [assumption].
kept: 5 -P(x,y,z) | -P(y,u,w) | -P(z,u,v5) | P(x,w,v5). [assumption].
kept: 6 P(e,x,x). [assumption].
kept: 7 P(i(x),x,e). [assumption].
kept: 8 -P(x,y,z) | P(y,x,z). [clausify(1)].
kept: 9 P(a,b,c). [clausify(2)].
kept: 10 -P(c,i(a),b). [clausify(2)].
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
% Clauses after input processing:
formulas(usable).
end_of_list.
formulas(sos).
3 P(x,y,m(x,y)). [assumption].
4 -P(x,y,z) | -P(y,u,w) | -P(x,w,v5) | P(z,u,v5). [assumption].
5 -P(x,y,z) | -P(y,u,w) | -P(z,u,v5) | P(x,w,v5). [assumption].
6 P(e,x,x). [assumption].
7 P(i(x),x,e). [assumption].
8 -P(x,y,z) | P(y,x,z). [clausify(1)].
9 P(a,b,c). [clausify(2)].
10 -P(c,i(a),b). [clausify(2)].
end_of_list.
formulas(demodulators).
end_of_list.
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.00 seconds.
given #1 (I,wt=6): 3 P(x,y,m(x,y)). [assumption].
given #2 (I,wt=16): 4 -P(x,y,z) | -P(y,u,w) | -P(x,w,v5) | P(z,u,v5). [assumption].
given #3 (I,wt=16): 5 -P(x,y,z) | -P(y,u,w) | -P(z,u,v5) | P(x,w,v5). [assumption].
given #4 (I,wt=4): 6 P(e,x,x). [assumption].
given #5 (I,wt=5): 7 P(i(x),x,e). [assumption].
given #6 (I,wt=8): 8 -P(x,y,z) | P(y,x,z). [clausify(1)].
given #7 (I,wt=4): 9 P(a,b,c). [clausify(2)].
given #8 (I,wt=5): 10 -P(c,i(a),b). [clausify(2)].
-------- Proof 1 --------
============================== PROOF =================================
% Proof 1 at 0.00 (+ 0.00) seconds.
% Length of proof is 11.
% Level of proof is 3.
% Maximum clause weight is 16.000.
% Given clauses 8.
1 P(x,y,z) -> P(y,x,z) # label(non_clause). [assumption].
2 P(a,b,c) & -P(c,i(a),b) # label(non_clause). [assumption].
5 -P(x,y,z) | -P(y,u,w) | -P(z,u,v5) | P(x,w,v5). [assumption].
6 P(e,x,x). [assumption].
7 P(i(x),x,e). [assumption].
8 -P(x,y,z) | P(y,x,z). [clausify(1)].
9 P(a,b,c). [clausify(2)].
10 -P(c,i(a),b). [clausify(2)].
42 P(i(a),c,b). [ur(5,a,7,a,b,9,a,c,6,a)].
54 -P(i(a),c,b). [resolve(10,a,8,b)].
55 $F. [resolve(54,a,42,a)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=8. Generated=79. Kept=52. proofs=1.
Usable=8. Sos=43. Demods=0. Limbo=0, Disabled=8. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=27. 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=1. Nonunit_bsub_feature_tests=7.
Megabytes=0.10.
User_CPU=0.00, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
THEOREM PROVED
Exiting with 1 proof.
------ process 64732 exit (max_proofs) ------
Process 64732 exit (max_proofs) Fri May 31 17:37:40 2019