20.032/20.032 YES 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 Confluence Problem: 20.032/20.032 (VAR vNonEmpty x) 20.032/20.032 (REPLACEMENT-MAP 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 ) 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Inlining of Conditions Processor [STERN17]: 20.032/20.032 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 Confluence Problem: 20.032/20.032 (VAR vNonEmpty x) 20.032/20.032 (REPLACEMENT-MAP 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 ) 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Clean CTRS Processor: 20.032/20.032 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 Confluence Problem: 20.032/20.032 (VAR x) 20.032/20.032 (REPLACEMENT-MAP 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 ) 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 20.032/20.032 CRule InfChecker Info: 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 Rule remains 20.032/20.032 Proof: 20.032/20.032 NO 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Infeasibility Problem: 20.032/20.032 [(VAR vNonEmpty x vNonEmpty x) 20.032/20.032 (STRATEGY CONTEXTSENSITIVE 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 )] 20.032/20.032 20.032/20.032 Infeasibility Conditions: 20.032/20.032 x ->* true 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Obtaining a proof using Prover9: 20.032/20.032 20.032/20.032 -> Prover9 Output: 20.032/20.032 ============================== Prover9 =============================== 20.032/20.032 Prover9 (64) version 2009-11A, November 2009. 20.032/20.032 Process 10276 was started by ubuntu on ubuntu, 20.032/20.032 Wed Mar 9 09:12:53 2022 20.032/20.032 The command was "./prover9 -f /tmp/prover910266-0.in". 20.032/20.032 ============================== end of head =========================== 20.032/20.032 20.032/20.032 ============================== INPUT ================================= 20.032/20.032 20.032/20.032 % Reading from file /tmp/prover910266-0.in 20.032/20.032 20.032/20.032 assign(max_seconds,20). 20.032/20.032 20.032/20.032 formulas(assumptions). 20.032/20.032 ->_s0(x1,y) -> ->_s0(not(x1),not(y)) # label(congruence). 20.032/20.032 ->*_s0(x1,true) -> ->_s0(not(x1),false) # label(replacement). 20.032/20.032 ->*_s0(x1,false) -> ->_s0(not(x1),true) # label(replacement). 20.032/20.032 ->*_s0(x,x) # label(reflexivity). 20.032/20.032 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 formulas(goals). 20.032/20.032 (exists x3 ->*_s0(x3,true)) # label(goal). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 ============================== end of input ========================== 20.032/20.032 20.032/20.032 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.032/20.032 20.032/20.032 % Formulas that are not ordinary clauses: 20.032/20.032 1 ->_s0(x1,y) -> ->_s0(not(x1),not(y)) # label(congruence) # label(non_clause). [assumption]. 20.032/20.032 2 ->*_s0(x1,true) -> ->_s0(not(x1),false) # label(replacement) # label(non_clause). [assumption]. 20.032/20.032 3 ->*_s0(x1,false) -> ->_s0(not(x1),true) # label(replacement) # label(non_clause). [assumption]. 20.032/20.032 4 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.032/20.032 5 (exists x3 ->*_s0(x3,true)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.032/20.032 20.032/20.032 ============================== end of process non-clausal formulas === 20.032/20.032 20.032/20.032 ============================== PROCESS INITIAL CLAUSES =============== 20.032/20.032 20.032/20.032 % Clauses before input processing: 20.032/20.032 20.032/20.032 formulas(usable). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 formulas(sos). 20.032/20.032 -->_s0(x,y) | ->_s0(not(x),not(y)) # label(congruence). [clausify(1)]. 20.032/20.032 -->*_s0(x,true) | ->_s0(not(x),false) # label(replacement). [clausify(2)]. 20.032/20.032 -->*_s0(x,false) | ->_s0(not(x),true) # label(replacement). [clausify(3)]. 20.032/20.032 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.032/20.032 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(4)]. 20.032/20.032 -->*_s0(x,true) # label(goal). [deny(5)]. 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 formulas(demodulators). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 ============================== PREDICATE ELIMINATION ================= 20.032/20.032 20.032/20.032 No predicates eliminated. 20.032/20.032 20.032/20.032 ============================== end predicate elimination ============= 20.032/20.032 20.032/20.032 Auto_denials: 20.032/20.032 % copying label goal to answer in negative clause 20.032/20.032 20.032/20.032 Term ordering decisions: 20.032/20.032 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]). 20.032/20.032 Function symbol precedence: function_order([ false, true, not ]). 20.032/20.032 After inverse_order: (no changes). 20.032/20.032 Unfolding symbols: (none). 20.032/20.032 20.032/20.032 Auto_inference settings: 20.032/20.032 % set(neg_binary_resolution). % (HNE depth_diff=-3) 20.032/20.032 % clear(ordered_res). % (HNE depth_diff=-3) 20.032/20.032 % set(ur_resolution). % (HNE depth_diff=-3) 20.032/20.032 % set(ur_resolution) -> set(pos_ur_resolution). 20.032/20.032 % set(ur_resolution) -> set(neg_ur_resolution). 20.032/20.032 20.032/20.032 Auto_process settings: (no changes). 20.032/20.032 20.032/20.032 kept: 6 -->_s0(x,y) | ->_s0(not(x),not(y)) # label(congruence). [clausify(1)]. 20.032/20.032 kept: 7 -->*_s0(x,true) | ->_s0(not(x),false) # label(replacement). [clausify(2)]. 20.032/20.032 kept: 8 -->*_s0(x,false) | ->_s0(not(x),true) # label(replacement). [clausify(3)]. 20.032/20.032 kept: 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.032/20.032 kept: 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(4)]. 20.032/20.032 kept: 11 -->*_s0(x,true) # label(goal) # answer(goal). [deny(5)]. 20.032/20.032 20.032/20.032 ============================== PROOF ================================= 20.032/20.032 20.032/20.032 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.032/20.032 % Length of proof is 4. 20.032/20.032 % Level of proof is 2. 20.032/20.032 % Maximum clause weight is 3.000. 20.032/20.032 % Given clauses 0. 20.032/20.032 20.032/20.032 5 (exists x3 ->*_s0(x3,true)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.032/20.032 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.032/20.032 11 -->*_s0(x,true) # label(goal) # answer(goal). [deny(5)]. 20.032/20.032 12 $F # answer(goal). [resolve(11,a,9,a)]. 20.032/20.032 20.032/20.032 ============================== end of proof ========================== 20.032/20.032 20.032/20.032 ============================== STATISTICS ============================ 20.032/20.032 20.032/20.032 Given=0. Generated=6. Kept=6. proofs=1. 20.032/20.032 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=6. Hints=0. 20.032/20.032 Kept_by_rule=0, Deleted_by_rule=0. 20.032/20.032 Forward_subsumed=0. Back_subsumed=0. 20.032/20.032 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.032/20.032 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.032/20.032 Demod_attempts=0. Demod_rewrites=0. 20.032/20.032 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.032/20.032 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. 20.032/20.032 Megabytes=0.04. 20.032/20.032 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.032/20.032 20.032/20.032 ============================== end of statistics ===================== 20.032/20.032 20.032/20.032 ============================== end of search ========================= 20.032/20.032 20.032/20.032 THEOREM PROVED 20.032/20.032 20.032/20.032 Exiting with 1 proof. 20.032/20.032 20.032/20.032 Process 10276 exit (max_proofs) Wed Mar 9 09:12:53 2022 20.032/20.032 20.032/20.032 20.032/20.032 The problem is feasible. 20.032/20.032 20.032/20.032 20.032/20.032 CRule InfChecker Info: 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 Rule remains 20.032/20.032 Proof: 20.032/20.032 NO 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Infeasibility Problem: 20.032/20.032 [(VAR vNonEmpty x vNonEmpty x) 20.032/20.032 (STRATEGY CONTEXTSENSITIVE 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 )] 20.032/20.032 20.032/20.032 Infeasibility Conditions: 20.032/20.032 x ->* false 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Obtaining a proof using Prover9: 20.032/20.032 20.032/20.032 -> Prover9 Output: 20.032/20.032 ============================== Prover9 =============================== 20.032/20.032 Prover9 (64) version 2009-11A, November 2009. 20.032/20.032 Process 10297 was started by ubuntu on ubuntu, 20.032/20.032 Wed Mar 9 09:12:53 2022 20.032/20.032 The command was "./prover9 -f /tmp/prover910287-0.in". 20.032/20.032 ============================== end of head =========================== 20.032/20.032 20.032/20.032 ============================== INPUT ================================= 20.032/20.032 20.032/20.032 % Reading from file /tmp/prover910287-0.in 20.032/20.032 20.032/20.032 assign(max_seconds,20). 20.032/20.032 20.032/20.032 formulas(assumptions). 20.032/20.032 ->_s0(x1,y) -> ->_s0(not(x1),not(y)) # label(congruence). 20.032/20.032 ->*_s0(x1,true) -> ->_s0(not(x1),false) # label(replacement). 20.032/20.032 ->*_s0(x1,false) -> ->_s0(not(x1),true) # label(replacement). 20.032/20.032 ->*_s0(x,x) # label(reflexivity). 20.032/20.032 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 formulas(goals). 20.032/20.032 (exists x3 ->*_s0(x3,false)) # label(goal). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 ============================== end of input ========================== 20.032/20.032 20.032/20.032 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.032/20.032 20.032/20.032 % Formulas that are not ordinary clauses: 20.032/20.032 1 ->_s0(x1,y) -> ->_s0(not(x1),not(y)) # label(congruence) # label(non_clause). [assumption]. 20.032/20.032 2 ->*_s0(x1,true) -> ->_s0(not(x1),false) # label(replacement) # label(non_clause). [assumption]. 20.032/20.032 3 ->*_s0(x1,false) -> ->_s0(not(x1),true) # label(replacement) # label(non_clause). [assumption]. 20.032/20.032 4 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.032/20.032 5 (exists x3 ->*_s0(x3,false)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.032/20.032 20.032/20.032 ============================== end of process non-clausal formulas === 20.032/20.032 20.032/20.032 ============================== PROCESS INITIAL CLAUSES =============== 20.032/20.032 20.032/20.032 % Clauses before input processing: 20.032/20.032 20.032/20.032 formulas(usable). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 formulas(sos). 20.032/20.032 -->_s0(x,y) | ->_s0(not(x),not(y)) # label(congruence). [clausify(1)]. 20.032/20.032 -->*_s0(x,true) | ->_s0(not(x),false) # label(replacement). [clausify(2)]. 20.032/20.032 -->*_s0(x,false) | ->_s0(not(x),true) # label(replacement). [clausify(3)]. 20.032/20.032 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.032/20.032 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(4)]. 20.032/20.032 -->*_s0(x,false) # label(goal). [deny(5)]. 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 formulas(demodulators). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 ============================== PREDICATE ELIMINATION ================= 20.032/20.032 20.032/20.032 No predicates eliminated. 20.032/20.032 20.032/20.032 ============================== end predicate elimination ============= 20.032/20.032 20.032/20.032 Auto_denials: 20.032/20.032 % copying label goal to answer in negative clause 20.032/20.032 20.032/20.032 Term ordering decisions: 20.032/20.032 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]). 20.032/20.032 Function symbol precedence: function_order([ false, true, not ]). 20.032/20.032 After inverse_order: (no changes). 20.032/20.032 Unfolding symbols: (none). 20.032/20.032 20.032/20.032 Auto_inference settings: 20.032/20.032 % set(neg_binary_resolution). % (HNE depth_diff=-3) 20.032/20.032 % clear(ordered_res). % (HNE depth_diff=-3) 20.032/20.032 % set(ur_resolution). % (HNE depth_diff=-3) 20.032/20.032 % set(ur_resolution) -> set(pos_ur_resolution). 20.032/20.032 % set(ur_resolution) -> set(neg_ur_resolution). 20.032/20.032 20.032/20.032 Auto_process settings: (no changes). 20.032/20.032 20.032/20.032 kept: 6 -->_s0(x,y) | ->_s0(not(x),not(y)) # label(congruence). [clausify(1)]. 20.032/20.032 kept: 7 -->*_s0(x,true) | ->_s0(not(x),false) # label(replacement). [clausify(2)]. 20.032/20.032 kept: 8 -->*_s0(x,false) | ->_s0(not(x),true) # label(replacement). [clausify(3)]. 20.032/20.032 kept: 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.032/20.032 kept: 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(4)]. 20.032/20.032 kept: 11 -->*_s0(x,false) # label(goal) # answer(goal). [deny(5)]. 20.032/20.032 20.032/20.032 ============================== PROOF ================================= 20.032/20.032 20.032/20.032 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.032/20.032 % Length of proof is 4. 20.032/20.032 % Level of proof is 2. 20.032/20.032 % Maximum clause weight is 3.000. 20.032/20.032 % Given clauses 0. 20.032/20.032 20.032/20.032 5 (exists x3 ->*_s0(x3,false)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.032/20.032 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.032/20.032 11 -->*_s0(x,false) # label(goal) # answer(goal). [deny(5)]. 20.032/20.032 12 $F # answer(goal). [resolve(11,a,9,a)]. 20.032/20.032 20.032/20.032 ============================== end of proof ========================== 20.032/20.032 20.032/20.032 ============================== STATISTICS ============================ 20.032/20.032 20.032/20.032 Given=0. Generated=6. Kept=6. proofs=1. 20.032/20.032 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=6. Hints=0. 20.032/20.032 Kept_by_rule=0, Deleted_by_rule=0. 20.032/20.032 Forward_subsumed=0. Back_subsumed=0. 20.032/20.032 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.032/20.032 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.032/20.032 Demod_attempts=0. Demod_rewrites=0. 20.032/20.032 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.032/20.032 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. 20.032/20.032 Megabytes=0.04. 20.032/20.032 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.032/20.032 20.032/20.032 ============================== end of statistics ===================== 20.032/20.032 20.032/20.032 ============================== end of search ========================= 20.032/20.032 20.032/20.032 THEOREM PROVED 20.032/20.032 20.032/20.032 Exiting with 1 proof. 20.032/20.032 20.032/20.032 Process 10297 exit (max_proofs) Wed Mar 9 09:12:53 2022 20.032/20.032 20.032/20.032 20.032/20.032 The problem is feasible. 20.032/20.032 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 Confluence Problem: 20.032/20.032 (VAR x) 20.032/20.032 (REPLACEMENT-MAP 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 ) 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 20.032/20.032 Critical Pairs Processor: 20.032/20.032 -> Rules: 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 -> Vars: 20.032/20.032 "x" 20.032/20.032 20.032/20.032 -> Rlps: 20.032/20.032 crule: not(x) -> false | x ->* true, id: 1, possubterms: not(x)-> [] 20.032/20.032 crule: not(x) -> true | x ->* false, id: 2, possubterms: not(x)-> [] 20.032/20.032 20.032/20.032 -> Unifications: 20.032/20.032 R2 unifies with R1 at p: [], l: not(x), lp: not(x), conds: {x ->* false, x' ->* true}, sig: {x -> x'}, l': not(x'), r: true, r': false 20.032/20.032 20.032/20.032 -> Critical pairs info: 20.032/20.032 | x' ->* false, x' ->* true => Not trivial, Overlay, NW2, N1 20.032/20.032 20.032/20.032 -> Problem conclusions: 20.032/20.032 Left linear, Right linear, Linear 20.032/20.032 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.032/20.032 CTRS Type: 1 20.032/20.032 Deterministic, Strongly deterministic 20.032/20.032 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.032/20.032 Maybe right-stable CTRS, Overlay CTRS 20.032/20.032 Maybe normal CTRS, Maybe almost normal CTRS 20.032/20.032 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.032/20.032 Maybe level confluent 20.032/20.032 Maybe confluent 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 Clean Infeasible CCPs Processor: 20.032/20.032 Num of CPIs: 1 20.032/20.032 Timeout: 60 20.032/20.032 Timeout for each infeasibility problem: 60 s 20.032/20.032 | x' ->* false, x' ->* true => Not trivial, Overlay, NW2, N1 20.032/20.032 (CONDITIONTYPE ORIENTED) 20.032/20.032 (VAR x x1) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false) 20.032/20.032 (VAR x4) 20.032/20.032 (CONDITION x4 ->* false, x4 ->* true) 20.032/20.032 20.032/20.032 Proof: 20.032/20.032 YES 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Infeasibility Problem: 20.032/20.032 [(VAR vNonEmpty x x1 vNonEmpty x4) 20.032/20.032 (STRATEGY CONTEXTSENSITIVE 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 )] 20.032/20.032 20.032/20.032 Infeasibility Conditions: 20.032/20.032 x4 ->* false, x4 ->* true 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Obtaining a model using Mace4: 20.032/20.032 20.032/20.032 -> Usable Rules: 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 20.032/20.032 -> Mace4 Output: 20.032/20.032 ============================== Mace4 ================================= 20.032/20.032 Mace4 (64) version 2009-11A, November 2009. 20.032/20.032 Process 10347 was started by ubuntu on ubuntu, 20.032/20.032 Wed Mar 9 09:12:53 2022 20.032/20.032 The command was "./mace4 -c -f /tmp/mace410314-2.in". 20.032/20.032 ============================== end of head =========================== 20.032/20.032 20.032/20.032 ============================== INPUT ================================= 20.032/20.032 20.032/20.032 % Reading from file /tmp/mace410314-2.in 20.032/20.032 20.032/20.032 assign(max_seconds,20). 20.032/20.032 20.032/20.032 formulas(assumptions). 20.032/20.032 ->(x1,y) -> ->(not(x1),not(y)) # label(congruence). 20.032/20.032 ->*(x1,true) -> ->(not(x1),false) # label(replacement). 20.032/20.032 ->*(x1,false) -> ->(not(x1),true) # label(replacement). 20.032/20.032 ->*(x,x) # label(reflexivity). 20.032/20.032 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 formulas(goals). 20.032/20.032 (exists x4 (->*(x4,false) & ->*(x4,true))) # label(goal). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 ============================== end of input ========================== 20.032/20.032 20.032/20.032 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.032/20.032 20.032/20.032 % Formulas that are not ordinary clauses: 20.032/20.032 1 ->(x1,y) -> ->(not(x1),not(y)) # label(congruence) # label(non_clause). [assumption]. 20.032/20.032 2 ->*(x1,true) -> ->(not(x1),false) # label(replacement) # label(non_clause). [assumption]. 20.032/20.032 3 ->*(x1,false) -> ->(not(x1),true) # label(replacement) # label(non_clause). [assumption]. 20.032/20.032 4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.032/20.032 5 (exists x4 (->*(x4,false) & ->*(x4,true))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.032/20.032 20.032/20.032 ============================== end of process non-clausal formulas === 20.032/20.032 20.032/20.032 ============================== CLAUSES FOR SEARCH ==================== 20.032/20.032 20.032/20.032 formulas(mace4_clauses). 20.032/20.032 -->(x,y) | ->(not(x),not(y)) # label(congruence). 20.032/20.032 -->*(x,true) | ->(not(x),false) # label(replacement). 20.032/20.032 -->*(x,false) | ->(not(x),true) # label(replacement). 20.032/20.032 ->*(x,x) # label(reflexivity). 20.032/20.032 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.032/20.032 -->*(x,false) | -->*(x,true) # label(goal). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 ============================== end of clauses for search ============= 20.032/20.032 20.032/20.032 % There are no natural numbers in the input. 20.032/20.032 20.032/20.032 ============================== DOMAIN SIZE 2 ========================= 20.032/20.032 20.032/20.032 ============================== MODEL ================================= 20.032/20.032 20.032/20.032 interpretation( 2, [number=1, seconds=0], [ 20.032/20.032 20.032/20.032 function(false, [ 0 ]), 20.032/20.032 20.032/20.032 function(true, [ 1 ]), 20.032/20.032 20.032/20.032 function(not(_), [ 1, 0 ]), 20.032/20.032 20.032/20.032 relation(->*(_,_), [ 20.032/20.032 1, 0, 20.032/20.032 0, 1 ]), 20.032/20.032 20.032/20.032 relation(->(_,_), [ 20.032/20.032 1, 0, 20.032/20.032 0, 1 ]) 20.032/20.032 ]). 20.032/20.032 20.032/20.032 ============================== end of model ========================== 20.032/20.032 20.032/20.032 ============================== STATISTICS ============================ 20.032/20.032 20.032/20.032 For domain size 2. 20.032/20.032 20.032/20.032 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.032/20.032 Ground clauses: seen=20, kept=16. 20.032/20.032 Selections=1, assignments=1, propagations=11, current_models=1. 20.032/20.032 Rewrite_terms=24, rewrite_bools=26, indexes=6. 20.032/20.032 Rules_from_neg_clauses=3, cross_offs=3. 20.032/20.032 20.032/20.032 ============================== end of statistics ===================== 20.032/20.032 20.032/20.032 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.032/20.032 20.032/20.032 Exiting with 1 model. 20.032/20.032 20.032/20.032 Process 10347 exit (max_models) Wed Mar 9 09:12:53 2022 20.032/20.032 The process finished Wed Mar 9 09:12:53 2022 20.032/20.032 20.032/20.032 20.032/20.032 Mace4 cooked interpretation: 20.032/20.032 20.032/20.032 20.032/20.032 20.032/20.032 The problem is infeasible. 20.032/20.032 20.032/20.032 20.032/20.032 20.032/20.032 20.032/20.032 -> Problem conclusions: 20.032/20.032 Left linear, Right linear, Linear 20.032/20.032 Weakly orthogonal, Almost orthogonal, Orthogonal 20.032/20.032 CTRS Type: 1 20.032/20.032 Deterministic, Strongly deterministic 20.032/20.032 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.032/20.032 Maybe right-stable CTRS, Overlay CTRS 20.032/20.032 Maybe normal CTRS, Maybe almost normal CTRS 20.032/20.032 Maybe terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.032/20.032 Maybe level confluent 20.032/20.032 Maybe confluent 20.032/20.032 20.032/20.032 Resulting CCPs: 20.032/20.032 No CCPs left 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 Underlying TRS Termination Processor: 20.032/20.032 20.032/20.032 Resulting Underlying TRS: 20.032/20.032 (VAR x x') 20.032/20.032 (STRATEGY CONTEXTSENSITIVE 20.032/20.032 (not 1) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false 20.032/20.032 not(x) -> true 20.032/20.032 ) 20.032/20.032 Underlying TRS terminating? 20.032/20.032 YES 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 (VAR vu95NonEmpty x xu39) 20.032/20.032 (RULES 20.032/20.032 not(x) -> ffalse 20.032/20.032 not(x) -> ftrue 20.032/20.032 ) 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Dependency Pairs Processor: 20.032/20.032 -> Pairs: 20.032/20.032 Empty 20.032/20.032 -> Rules: 20.032/20.032 not(x) -> ffalse 20.032/20.032 not(x) -> ftrue 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 SCC Processor: 20.032/20.032 -> Pairs: 20.032/20.032 Empty 20.032/20.032 -> Rules: 20.032/20.032 not(x) -> ffalse 20.032/20.032 not(x) -> ftrue 20.032/20.032 ->Strongly Connected Components: 20.032/20.032 There is no strongly connected component 20.032/20.032 20.032/20.032 The problem is finite. 20.032/20.032 20.032/20.032 20.032/20.032 -> Problem conclusions: 20.032/20.032 Left linear, Right linear, Linear 20.032/20.032 Weakly orthogonal, Almost orthogonal, Orthogonal 20.032/20.032 CTRS Type: 1 20.032/20.032 Deterministic, Strongly deterministic 20.032/20.032 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.032/20.032 Maybe right-stable CTRS, Overlay CTRS 20.032/20.032 Maybe normal CTRS, Maybe almost normal CTRS 20.032/20.032 Terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.032/20.032 Maybe level confluent 20.032/20.032 Maybe confluent 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 Confluence Problem: 20.032/20.032 (VAR x x') 20.032/20.032 (REPLACEMENT-MAP 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 ) 20.032/20.032 Critical Pairs: 20.032/20.032 20.032/20.032 Terminating:YES 20.032/20.032 20.032/20.032 -> Problem conclusions: 20.032/20.032 Left linear, Right linear, Linear 20.032/20.032 Weakly orthogonal, Almost orthogonal, Orthogonal 20.032/20.032 CTRS Type: 1 20.032/20.032 Deterministic, Strongly deterministic 20.032/20.032 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.032/20.032 Maybe right-stable CTRS, Overlay CTRS 20.032/20.032 Maybe normal CTRS, Maybe almost normal CTRS 20.032/20.032 Terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.032/20.032 Maybe level confluent 20.032/20.032 Maybe confluent 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 20.032/20.032 Right Stable Processor: 20.032/20.032 Right-stable CTRS 20.032/20.032 Justification: 20.032/20.032 20.032/20.032 -> Term right-stability conditions: 20.032/20.032 Term: true 20.032/20.032 Right-stable term 20.032/20.032 Linear constructor form 20.032/20.032 Don't know if term is a ground normal form (not needed) 20.032/20.032 Right-stability condition achieved 20.032/20.032 A call to InfChecker wasn't needed 20.032/20.032 20.032/20.032 20.032/20.032 -> Term right-stability conditions: 20.032/20.032 Term: false 20.032/20.032 Right-stable term 20.032/20.032 Linear constructor form 20.032/20.032 Don't know if term is a ground normal form (not needed) 20.032/20.032 Right-stability condition achieved 20.032/20.032 A call to InfChecker wasn't needed 20.032/20.032 20.032/20.032 -> Problem conclusions: 20.032/20.032 Left linear, Right linear, Linear 20.032/20.032 Weakly orthogonal, Almost orthogonal, Orthogonal 20.032/20.032 CTRS Type: 1 20.032/20.032 Deterministic, Strongly deterministic 20.032/20.032 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.032/20.032 Right-stable CTRS, Overlay CTRS 20.032/20.032 Maybe normal CTRS, Almost normal CTRS 20.032/20.032 Terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.032/20.032 Level confluent 20.032/20.032 Confluent 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 Confluence Problem: 20.032/20.032 (VAR x x') 20.032/20.032 (REPLACEMENT-MAP 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 ) 20.032/20.032 Critical Pairs: 20.032/20.032 20.032/20.032 Terminating:YES 20.032/20.032 20.032/20.032 -> Problem conclusions: 20.032/20.032 Left linear, Right linear, Linear 20.032/20.032 Weakly orthogonal, Almost orthogonal, Orthogonal 20.032/20.032 CTRS Type: 1 20.032/20.032 Deterministic, Strongly deterministic 20.032/20.032 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.032/20.032 Right-stable CTRS, Overlay CTRS 20.032/20.032 Maybe normal CTRS, Almost normal CTRS 20.032/20.032 Terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.032/20.032 Level confluent 20.032/20.032 Confluent 20.032/20.032 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.032/20.032 20.032/20.032 Normal RConds Processor: 20.032/20.032 YES 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Infeasibility Problem: 20.032/20.032 [(VAR vNonEmpty x x1 vNonEmpty z z1) 20.032/20.032 (STRATEGY CONTEXTSENSITIVE 20.032/20.032 (not 1) 20.032/20.032 (fSNonEmpty) 20.032/20.032 (false) 20.032/20.032 (true) 20.032/20.032 ) 20.032/20.032 (RULES 20.032/20.032 not(x) -> false | x ->* true 20.032/20.032 not(x) -> true | x ->* false 20.032/20.032 )] 20.032/20.032 20.032/20.032 Infeasibility Conditions: 20.032/20.032 false -> z, true -> z1 20.032/20.032 20.032/20.032 Problem 1: 20.032/20.032 20.032/20.032 Obtaining a model using Mace4: 20.032/20.032 20.032/20.032 -> Usable Rules: 20.032/20.032 Empty 20.032/20.032 20.032/20.032 -> Mace4 Output: 20.032/20.032 ============================== Mace4 ================================= 20.032/20.032 Mace4 (64) version 2009-11A, November 2009. 20.032/20.032 Process 10404 was started by ubuntu on ubuntu, 20.032/20.032 Wed Mar 9 09:13:13 2022 20.032/20.032 The command was "./mace4 -c -f /tmp/mace410391-2.in". 20.032/20.032 ============================== end of head =========================== 20.032/20.032 20.032/20.032 ============================== INPUT ================================= 20.032/20.032 20.032/20.032 % Reading from file /tmp/mace410391-2.in 20.032/20.032 20.032/20.032 assign(max_seconds,13). 20.032/20.032 20.032/20.032 formulas(assumptions). 20.032/20.032 ->(x1,y) -> ->(not(x1),not(y)) # label(congruence). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 formulas(goals). 20.032/20.032 (exists x4 exists x5 (->(false,x4) & ->(true,x5))) # label(goal). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 ============================== end of input ========================== 20.032/20.032 20.032/20.032 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.032/20.032 20.032/20.032 % Formulas that are not ordinary clauses: 20.032/20.032 1 ->(x1,y) -> ->(not(x1),not(y)) # label(congruence) # label(non_clause). [assumption]. 20.032/20.032 2 (exists x4 exists x5 (->(false,x4) & ->(true,x5))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.032/20.032 20.032/20.032 ============================== end of process non-clausal formulas === 20.032/20.032 20.032/20.032 ============================== CLAUSES FOR SEARCH ==================== 20.032/20.032 20.032/20.032 formulas(mace4_clauses). 20.032/20.032 -->(x,y) | ->(not(x),not(y)) # label(congruence). 20.032/20.032 -->(false,x) | -->(true,y) # label(goal). 20.032/20.032 end_of_list. 20.032/20.032 20.032/20.032 ============================== end of clauses for search ============= 20.032/20.032 20.032/20.032 % There are no natural numbers in the input. 20.032/20.032 20.032/20.032 ============================== DOMAIN SIZE 2 ========================= 20.032/20.032 20.032/20.032 ============================== MODEL ================================= 20.032/20.032 20.032/20.032 interpretation( 2, [number=1, seconds=0], [ 20.032/20.032 20.032/20.032 function(false, [ 0 ]), 20.032/20.032 20.032/20.032 function(true, [ 0 ]), 20.032/20.032 20.032/20.032 function(not(_), [ 0, 0 ]), 20.032/20.032 20.032/20.032 relation(->(_,_), [ 20.032/20.032 0, 0, 20.032/20.032 0, 0 ]) 20.032/20.032 ]). 20.032/20.032 20.032/20.032 ============================== end of model ========================== 20.032/20.032 20.032/20.032 ============================== STATISTICS ============================ 20.032/20.032 20.032/20.032 For domain size 2. 20.032/20.032 20.032/20.032 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.032/20.032 Ground clauses: seen=8, kept=8. 20.032/20.032 Selections=5, assignments=5, propagations=3, current_models=1. 20.032/20.032 Rewrite_terms=16, rewrite_bools=12, indexes=9. 20.032/20.032 Rules_from_neg_clauses=0, cross_offs=0. 20.032/20.032 20.032/20.032 ============================== end of statistics ===================== 20.032/20.032 20.032/20.032 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.032/20.032 20.032/20.032 Exiting with 1 model. 20.032/20.032 20.032/20.032 Process 10404 exit (max_models) Wed Mar 9 09:13:13 2022 20.032/20.032 The process finished Wed Mar 9 09:13:13 2022 20.032/20.032 20.032/20.032 20.032/20.032 Mace4 cooked interpretation: 20.032/20.032 20.032/20.032 20.032/20.032 20.032/20.032 The problem is infeasible. 20.032/20.032 20.032/20.032 20.032/20.032 -> Problem conclusions: 20.032/20.032 Left linear, Right linear, Linear 20.032/20.032 Weakly orthogonal, Almost orthogonal, Orthogonal 20.032/20.032 CTRS Type: 1 20.032/20.032 Deterministic, Strongly deterministic 20.032/20.032 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 20.032/20.032 Right-stable CTRS, Overlay CTRS 20.032/20.032 Normal CTRS, Almost normal CTRS 20.032/20.032 Terminating CTRS, Maybe operational terminating CTRS, Joinable CCPs 20.032/20.032 Level confluent 20.032/20.032 Confluent 20.032/20.032 20.032/20.032 The problem is joinable. 20.032/20.032 40.36user 0.82system 0:20.32elapsed 202%CPU (0avgtext+0avgdata 69488maxresident)k 20.032/20.032 8inputs+0outputs (0major+48110minor)pagefaults 0swaps