============================== Prover9 =============================== Prover9 (32) version June-2007, June 2007. Process 4531 was started by zalta on mally, Sat Jul 14 15:07:46 2007 The command was "prove". ============================== end of head =========================== ============================== INPUT ================================= formulas(sos). (all x Sum(x,x) = x). (all x all y (IsIn(x,y) <-> (exists z Sum(x,z) = y))). end_of_list. formulas(goals). (all x all y (x = y -> IsIn(x,y))). end_of_list. ============================== end of input ========================== ============================== PROCESS NON-CLAUSAL FORMULAS ========== % Formulas that are not ordinary clauses: 1 (all x Sum(x,x) = x) # label(non_clause). [assumption]. 2 (all x all y (IsIn(x,y) <-> (exists z Sum(x,z) = y))) # label(non_clause). [assumption]. 3 (all x all y (x = y -> IsIn(x,y))) # 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). Sum(x,x) = x. [clausify(1)]. -IsIn(x,y) | Sum(x,f1(x,y)) = y. [clausify(2)]. IsIn(x,y) | Sum(x,z) != y. [clausify(2)]. c2 = c1. [deny(3)]. -IsIn(c1,c2). [deny(3)]. 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([ =, IsIn ]). Function symbol precedence: function_order([ c1, c2, Sum, f1 ]). After inverse_order: (no changes). Unfolding symbols: (none). Auto_inference settings: % set(paramodulation). % (positive equality literals) % set(paramodulation) -> set(back_demod). % set(hyper_resolution). % (nonunit Horn with equality) % set(hyper_resolution) -> set(pos_hyper_resolution). % set(neg_ur_resolution). % (nonunit Horn with equality) % assign(para_lit_limit, 2). % (nonunit Horn with equality) Auto_process settings: (no changes). ============================== end of process initial clauses ======== ============================== CLAUSES FOR SEARCH ==================== % Clauses after input processing: formulas(usable). end_of_list. formulas(sos). 4 Sum(x,x) = x. [clausify(1)]. 5 -IsIn(x,y) | Sum(x,f1(x,y)) = y. [clausify(2)]. 6 IsIn(x,y) | Sum(x,z) != y. [clausify(2)]. 7 c2 = c1. [deny(3)]. 9 -IsIn(c1,c1). [copy(8),rewrite([7(2)])]. end_of_list. formulas(demodulators). 4 Sum(x,x) = x. [clausify(1)]. 7 c2 = c1. [deny(3)]. end_of_list. ============================== end of clauses for search ============= ============================== SEARCH ================================ % Starting search at 0.00 seconds. given #1 (I,wt=5): 4 Sum(x,x) = x. [clausify(1)]. given #2 (I,wt=10): 5 -IsIn(x,y) | Sum(x,f1(x,y)) = y. [clausify(2)]. given #3 (I,wt=8): 6 IsIn(x,y) | Sum(x,z) != y. [clausify(2)]. ============================== PROOF ================================= % Proof 1 at 0.00 (+ 0.00) seconds. % Length of proof is 10. % Level of proof is 3. % Maximum clause weight is 8. % Given clauses 3. 1 (all x Sum(x,x) = x) # label(non_clause). [assumption]. 2 (all x all y (IsIn(x,y) <-> (exists z Sum(x,z) = y))) # label(non_clause). [assumption]. 3 (all x all y (x = y -> IsIn(x,y))) # label(non_clause) # label(goal). [goal]. 4 Sum(x,x) = x. [clausify(1)]. 6 IsIn(x,y) | Sum(x,z) != y. [clausify(2)]. 7 c2 = c1. [deny(3)]. 8 -IsIn(c1,c2). [deny(3)]. 9 -IsIn(c1,c1). [copy(8),rewrite([7(2)])]. 10 IsIn(x,x). [hyper(6,b,4,a)]. 11 $F. [resolve(10,a,9,a)]. ============================== end of proof ========================== ============================== STATISTICS ============================ Given=3. Generated=7. Kept=6. proofs=1. Usable=3. Sos=2. Demods=2. Limbo=0, Disabled=5. Hints=0. Weight_deleted=0. Literals_deleted=0. Forward_subsumed=1. Back_subsumed=0. Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. New_demodulators=2 (0 lex), Back_demodulated=0. Back_unit_deleted=0. Demod_attempts=29. Demod_rewrites=1. Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=3. Megabytes=0.02. User_CPU=0.00, System_CPU=0.00, Wall_clock=0. ============================== end of statistics ===================== ============================== end of search ========================= THEOREM PROVED Exiting with 1 proof. Process 4531 exit (max_proofs) Sat Jul 14 15:07:46 2007