============================== Prover9 =============================== Prover9 (32) version 2009-11A, November 2009. Process 4306 was started by mccune on cleo, Tue Nov 3 09:37:44 2009 The command was "/home/mccune/LADR/bin/prover9 -f cancel1.in". ============================== end of head =========================== ============================== INPUT ================================= % Reading from file cancel1.in assign(max_seconds,30). formulas(sos). (x * e) * x = x. x * (x * y) = y. (x * y) * (z * u) = (x * z) * (y * u). ((x * x) * x) * x = e. end_of_list. formulas(goals). x * y = x * z -> y = z. end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 x * y = x * z -> y = z # 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). (x * e) * x = x. [assumption]. x * (x * y) = y. [assumption]. (x * y) * (z * u) = (x * z) * (y * u). [assumption]. ((x * x) * x) * x = e. [assumption]. c1 * c3 = c1 * c2. [deny(1)]. c3 != 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([ e, c1, c2, c3, * ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) Auto_process settings: (no changes). kept: 2 (x * e) * x = x. [assumption]. kept: 3 x * (x * y) = y. [assumption]. kept: 4 (x * y) * (z * u) = (x * z) * (y * u). [assumption]. kept: 5 ((x * x) * x) * x = e. [assumption]. kept: 6 c1 * c3 = c1 * c2. [deny(1)]. kept: 7 c3 != c2. [deny(1)]. ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 2 (x * e) * x = x. [assumption]. 3 x * (x * y) = y. [assumption]. 4 (x * y) * (z * u) = (x * z) * (y * u). [assumption]. 5 ((x * x) * x) * x = e. [assumption]. 6 c1 * c3 = c1 * c2. [deny(1)]. 7 c3 != c2. [deny(1)]. end_of_list. formulas(demodulators). 2 (x * e) * x = x. [assumption]. 3 x * (x * y) = y. [assumption]. 5 ((x * x) * x) * x = e. [assumption]. 6 c1 * c3 = c1 * c2. [deny(1)]. end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.01 seconds. given #1 (I,wt=7): 2 (x * e) * x = x. [assumption]. given #2 (I,wt=7): 3 x * (x * y) = y. [assumption]. given #3 (I,wt=15): 4 (x * y) * (z * u) = (x * z) * (y * u). [assumption]. given #4 (I,wt=9): 5 ((x * x) * x) * x = e. [assumption]. given #5 (I,wt=7): 6 c1 * c3 = c1 * c2. [deny(1)]. ============================== PROOF ================================= % Proof 1 at 0.01 (+ 0.00) seconds. % Length of proof is 6. % Level of proof is 3. % Maximum clause weight is 7.000. % Given clauses 5. 1 x * y = x * z -> y = z # label(non_clause) # label(goal). [goal]. 3 x * (x * y) = y. [assumption]. 6 c1 * c3 = c1 * c2. [deny(1)]. 7 c3 != c2. [deny(1)]. 23 c3 = c2. [para(6(a,1),3(a,1,2)),rewrite([3(5)]),flip(a)]. 24 $F. [resolve(23,a,7,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=5. Generated=50. Kept=22. proofs=1. Usable=5. Sos=16. Demods=13. Limbo=0, Disabled=6. Hints=0. Kept_by_rule=0, Deleted_by_rule=0. Forward_subsumed=28. Back_subsumed=0. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=13 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=401. Demod_rewrites=20. 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 4306 exit (max_proofs) Tue Nov 3 09:37:44 2009