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============================== Prover9 ===============================
Prover9 (64) version 2009-11A, November 2009.
Process 7784 was started by koen on vdheijden-arch,
Sat Jan 14 16:51:59 2017
The command was "prover9 -f logic_a.in".
============================== end of head ===========================
============================== INPUT =================================
% Reading from file logic_a.in
formulas(sos).
a(x,x) = x.
a(x,y) = a(y,x).
a(x,a(y,z)) = a(a(x,y),z).
end_of_list.
formulas(goals).
(all p all q a(p,a(q,a(p,a(q,a(p,a(q,p)))))) = a(p,q)).
end_of_list.
============================== end of input ==========================
============================== PROCESS NON-CLAUSAL FORMULAS ==========
% Formulas that are not ordinary clauses:
1 (all p all q a(p,a(q,a(p,a(q,a(p,a(q,p)))))) = a(p,q)) # 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).
a(x,x) = x. [assumption].
a(x,y) = a(y,x). [assumption].
a(x,a(y,z)) = a(a(x,y),z). [assumption].
a(c1,a(c2,a(c1,a(c2,a(c1,a(c2,c1)))))) != a(c1,c2). [deny(1)].
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([ = ]).
Function symbol precedence: function_order([ c1, c2, a ]).
After inverse_order: (no changes).
Unfolding symbols: (none).
Auto_inference settings:
% set(paramodulation). % (positive equality literals)
Auto_process settings: (no changes).
kept: 2 a(x,x) = x. [assumption].
% Operation a is commutative; C redundancy checks enabled.
kept: 3 a(x,y) = a(y,x). [assumption].
4 a(x,a(y,z)) = a(a(x,y),z). [assumption].
kept: 5 a(a(x,y),z) = a(x,a(y,z)). [copy(4),flip(a)].
6 a(c1,a(c2,a(c1,a(c2,a(c1,a(c2,c1)))))) != a(c1,c2). [deny(1)].
kept: 7 a(c1,a(c2,a(c1,a(c2,a(c1,a(c1,c2)))))) != a(c1,c2). [copy(6),rewrite([3(8)])].
============================== end of process initial clauses ========
============================== CLAUSES FOR SEARCH ====================
% Clauses after input processing:
formulas(usable).
end_of_list.
formulas(sos).
2 a(x,x) = x. [assumption].
3 a(x,y) = a(y,x). [assumption].
5 a(a(x,y),z) = a(x,a(y,z)). [copy(4),flip(a)].
7 a(c1,a(c2,a(c1,a(c2,a(c1,a(c1,c2)))))) != a(c1,c2). [copy(6),rewrite([3(8)])].
end_of_list.
formulas(demodulators).
2 a(x,x) = x. [assumption].
3 a(x,y) = a(y,x). [assumption].
% (lex-dep)
5 a(a(x,y),z) = a(x,a(y,z)). [copy(4),flip(a)].
end_of_list.
============================== end of clauses for search =============
============================== SEARCH ================================
% Starting search at 0.02 seconds.
given #1 (I,wt=5): 2 a(x,x) = x. [assumption].
given #2 (I,wt=7): 3 a(x,y) = a(y,x). [assumption].
given #3 (I,wt=11): 5 a(a(x,y),z) = a(x,a(y,z)). [copy(4),flip(a)].
% Operation a is associative-commutative; CAC redundancy checks enabled.
============================== PROOF =================================
% Proof 1 at 0.02 (+ 0.00) seconds.
% Length of proof is 10.
% Level of proof is 3.
% Maximum clause weight is 17.000.
% Given clauses 3.
1 (all p all q a(p,a(q,a(p,a(q,a(p,a(q,p)))))) = a(p,q)) # label(non_clause) # label(goal). [goal].
2 a(x,x) = x. [assumption].
3 a(x,y) = a(y,x). [assumption].
4 a(x,a(y,z)) = a(a(x,y),z). [assumption].
5 a(a(x,y),z) = a(x,a(y,z)). [copy(4),flip(a)].
6 a(c1,a(c2,a(c1,a(c2,a(c1,a(c2,c1)))))) != a(c1,c2). [deny(1)].
7 a(c1,a(c2,a(c1,a(c2,a(c1,a(c1,c2)))))) != a(c1,c2). [copy(6),rewrite([3(8)])].
9 a(x,a(x,y)) = a(x,y). [para(2(a,1),5(a,1,1)),flip(a)].
10 a(x,a(y,x)) = a(y,x). [para(2(a,1),5(a,2,2)),rewrite([3(2)])].
13 $F. [back_rewrite(7),rewrite([9(9),10(8),9(7),10(6),9(5)]),xx(a)].
============================== end of proof ==========================
============================== STATISTICS ============================
Given=3. Generated=27. Kept=9. proofs=1.
Usable=3. Sos=1. Demods=8. Limbo=4, Disabled=5. Hints=0.
Kept_by_rule=0, Deleted_by_rule=0.
Forward_subsumed=17. Back_subsumed=0.
Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0.
New_demodulators=8 (3 lex), Back_demodulated=1. Back_unit_deleted=0.
Demod_attempts=222. Demod_rewrites=33.
Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0.
Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0.
Megabytes=0.05.
User_CPU=0.02, System_CPU=0.00, Wall_clock=0.
============================== end of statistics =====================
============================== end of search =========================
THEOREM PROVED
Exiting with 1 proof.
Process 7784 exit (max_proofs) Sat Jan 14 16:51:59 2017
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