25.033/25.033 YES 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 25.033/25.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.033/25.033 Confluence Problem: 25.033/25.033 (VAR vNonEmpty:S x:S) 25.033/25.033 (STRATEGY CONTEXTSENSITIVE 25.033/25.033 (not 1) 25.033/25.033 (fSNonEmpty) 25.033/25.033 (false) 25.033/25.033 (true) 25.033/25.033 ) 25.033/25.033 (RULES 25.033/25.033 not(x:S) -> false | x:S ->* true 25.033/25.033 not(x:S) -> true | x:S ->* false 25.033/25.033 ) 25.033/25.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.033/25.033 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Inlining of Conditions Processor [STERN17]: 25.033/25.033 25.033/25.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.033/25.033 Confluence Problem: 25.033/25.033 (VAR vNonEmpty:S x:S) 25.033/25.033 (STRATEGY CONTEXTSENSITIVE 25.033/25.033 (not 1) 25.033/25.033 (fSNonEmpty) 25.033/25.033 (false) 25.033/25.033 (true) 25.033/25.033 ) 25.033/25.033 (RULES 25.033/25.033 not(x:S) -> false | x:S ->* true 25.033/25.033 not(x:S) -> true | x:S ->* false 25.033/25.033 ) 25.033/25.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.033/25.033 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Clean CTRS Processor: 25.033/25.033 25.033/25.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.033/25.033 Confluence Problem: 25.033/25.033 (VAR x:S) 25.033/25.033 (STRATEGY CONTEXTSENSITIVE 25.033/25.033 (not 1) 25.033/25.033 (fSNonEmpty) 25.033/25.033 (false) 25.033/25.033 (true) 25.033/25.033 ) 25.033/25.033 (RULES 25.033/25.033 not(x:S) -> false | x:S ->* true 25.033/25.033 not(x:S) -> true | x:S ->* false 25.033/25.033 ) 25.033/25.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.033/25.033 25.033/25.033 CRule InfChecker Info: 25.033/25.033 not(x:S) -> false | x:S ->* true 25.033/25.033 Rule remains 25.033/25.033 Proof: 25.033/25.033 NO 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Infeasibility Problem: 25.033/25.033 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 25.033/25.033 (STRATEGY CONTEXTSENSITIVE 25.033/25.033 (not 1) 25.033/25.033 (fSNonEmpty) 25.033/25.033 (false) 25.033/25.033 (true) 25.033/25.033 ) 25.033/25.033 (RULES 25.033/25.033 not(x:S:S) -> false | x:S:S ->* true 25.033/25.033 not(x:S:S) -> true | x:S:S ->* false 25.033/25.033 )] 25.033/25.033 25.033/25.033 Infeasibility Conditions: 25.033/25.033 x:S:S ->* true 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Obtaining a proof using Prover9: 25.033/25.033 25.033/25.033 -> Prover9 Output: 25.033/25.033 ============================== Prover9 =============================== 25.033/25.033 Prover9 (64) version 2009-11A, November 2009. 25.033/25.033 Process 38886 was started by ubuntu on ubuntu, 25.033/25.033 Wed Jul 14 10:09:54 2021 25.033/25.033 The command was "./prover9 -f /tmp/prover938877-0.in". 25.033/25.033 ============================== end of head =========================== 25.033/25.033 25.033/25.033 ============================== INPUT ================================= 25.033/25.033 25.033/25.033 % Reading from file /tmp/prover938877-0.in 25.033/25.033 25.033/25.033 assign(max_seconds,20). 25.033/25.033 25.033/25.033 formulas(assumptions). 25.033/25.033 ->*_s0(x,x) # label(reflexivity). 25.033/25.033 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 25.033/25.033 ->_s0(x1,y) -> ->_s0(not(x1),not(y)) # label(congruence). 25.033/25.033 ->*_s0(x2,true) -> ->_s0(not(x2),false) # label(replacement). 25.033/25.033 ->*_s0(x2,false) -> ->_s0(not(x2),true) # label(replacement). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 formulas(goals). 25.033/25.033 (exists x2 ->*_s0(x2,true)) # label(goal). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 ============================== end of input ========================== 25.033/25.033 25.033/25.033 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.033/25.033 25.033/25.033 % Formulas that are not ordinary clauses: 25.033/25.033 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.033/25.033 2 ->_s0(x1,y) -> ->_s0(not(x1),not(y)) # label(congruence) # label(non_clause). [assumption]. 25.033/25.033 3 ->*_s0(x2,true) -> ->_s0(not(x2),false) # label(replacement) # label(non_clause). [assumption]. 25.033/25.033 4 ->*_s0(x2,false) -> ->_s0(not(x2),true) # label(replacement) # label(non_clause). [assumption]. 25.033/25.033 5 (exists x2 ->*_s0(x2,true)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.033/25.033 25.033/25.033 ============================== end of process non-clausal formulas === 25.033/25.033 25.033/25.033 ============================== PROCESS INITIAL CLAUSES =============== 25.033/25.033 25.033/25.033 % Clauses before input processing: 25.033/25.033 25.033/25.033 formulas(usable). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 formulas(sos). 25.033/25.033 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.033/25.033 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.033/25.033 -->_s0(x,y) | ->_s0(not(x),not(y)) # label(congruence). [clausify(2)]. 25.033/25.033 -->*_s0(x,true) | ->_s0(not(x),false) # label(replacement). [clausify(3)]. 25.033/25.033 -->*_s0(x,false) | ->_s0(not(x),true) # label(replacement). [clausify(4)]. 25.033/25.033 -->*_s0(x,true) # label(goal). [deny(5)]. 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 formulas(demodulators). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 ============================== PREDICATE ELIMINATION ================= 25.033/25.033 25.033/25.033 No predicates eliminated. 25.033/25.033 25.033/25.033 ============================== end predicate elimination ============= 25.033/25.033 25.033/25.033 Auto_denials: 25.033/25.033 % copying label goal to answer in negative clause 25.033/25.033 25.033/25.033 Term ordering decisions: 25.033/25.033 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]). 25.033/25.033 Function symbol precedence: function_order([ false, true, not ]). 25.033/25.033 After inverse_order: (no changes). 25.033/25.033 Unfolding symbols: (none). 25.033/25.033 25.033/25.033 Auto_inference settings: 25.033/25.033 % set(neg_binary_resolution). % (HNE depth_diff=-3) 25.033/25.033 % clear(ordered_res). % (HNE depth_diff=-3) 25.033/25.033 % set(ur_resolution). % (HNE depth_diff=-3) 25.033/25.033 % set(ur_resolution) -> set(pos_ur_resolution). 25.033/25.033 % set(ur_resolution) -> set(neg_ur_resolution). 25.033/25.033 25.033/25.033 Auto_process settings: (no changes). 25.033/25.033 25.033/25.033 kept: 6 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.033/25.033 kept: 7 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.033/25.033 kept: 8 -->_s0(x,y) | ->_s0(not(x),not(y)) # label(congruence). [clausify(2)]. 25.033/25.033 kept: 9 -->*_s0(x,true) | ->_s0(not(x),false) # label(replacement). [clausify(3)]. 25.033/25.033 kept: 10 -->*_s0(x,false) | ->_s0(not(x),true) # label(replacement). [clausify(4)]. 25.033/25.033 kept: 11 -->*_s0(x,true) # label(goal) # answer(goal). [deny(5)]. 25.033/25.033 25.033/25.033 ============================== PROOF ================================= 25.033/25.033 25.033/25.033 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 25.033/25.033 % Length of proof is 4. 25.033/25.033 % Level of proof is 2. 25.033/25.033 % Maximum clause weight is 3.000. 25.033/25.033 % Given clauses 0. 25.033/25.033 25.033/25.033 5 (exists x2 ->*_s0(x2,true)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.033/25.033 6 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.033/25.033 11 -->*_s0(x,true) # label(goal) # answer(goal). [deny(5)]. 25.033/25.033 12 $F # answer(goal). [resolve(11,a,6,a)]. 25.033/25.033 25.033/25.033 ============================== end of proof ========================== 25.033/25.033 25.033/25.033 ============================== STATISTICS ============================ 25.033/25.033 25.033/25.033 Given=0. Generated=6. Kept=6. proofs=1. 25.033/25.033 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=6. Hints=0. 25.033/25.033 Kept_by_rule=0, Deleted_by_rule=0. 25.033/25.033 Forward_subsumed=0. Back_subsumed=0. 25.033/25.033 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 25.033/25.033 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 25.033/25.033 Demod_attempts=0. Demod_rewrites=0. 25.033/25.033 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 25.033/25.033 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. 25.033/25.033 Megabytes=0.04. 25.033/25.033 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.033/25.033 25.033/25.033 ============================== end of statistics ===================== 25.033/25.033 25.033/25.033 ============================== end of search ========================= 25.033/25.033 25.033/25.033 THEOREM PROVED 25.033/25.033 25.033/25.033 Exiting with 1 proof. 25.033/25.033 25.033/25.033 Process 38886 exit (max_proofs) Wed Jul 14 10:09:54 2021 25.033/25.033 25.033/25.033 25.033/25.033 The problem is feasible. 25.033/25.033 25.033/25.033 25.033/25.033 CRule InfChecker Info: 25.033/25.033 not(x:S) -> true | x:S ->* false 25.033/25.033 Rule remains 25.033/25.033 Proof: 25.033/25.033 NO 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Infeasibility Problem: 25.033/25.033 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 25.033/25.033 (STRATEGY CONTEXTSENSITIVE 25.033/25.033 (not 1) 25.033/25.033 (fSNonEmpty) 25.033/25.033 (false) 25.033/25.033 (true) 25.033/25.033 ) 25.033/25.033 (RULES 25.033/25.033 not(x:S:S) -> false | x:S:S ->* true 25.033/25.033 not(x:S:S) -> true | x:S:S ->* false 25.033/25.033 )] 25.033/25.033 25.033/25.033 Infeasibility Conditions: 25.033/25.033 x:S:S ->* false 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Obtaining a proof using Prover9: 25.033/25.033 25.033/25.033 -> Prover9 Output: 25.033/25.033 ============================== Prover9 =============================== 25.033/25.033 Prover9 (64) version 2009-11A, November 2009. 25.033/25.033 Process 38908 was started by ubuntu on ubuntu, 25.033/25.033 Wed Jul 14 10:09:54 2021 25.033/25.033 The command was "./prover9 -f /tmp/prover938898-0.in". 25.033/25.033 ============================== end of head =========================== 25.033/25.033 25.033/25.033 ============================== INPUT ================================= 25.033/25.033 25.033/25.033 % Reading from file /tmp/prover938898-0.in 25.033/25.033 25.033/25.033 assign(max_seconds,20). 25.033/25.033 25.033/25.033 formulas(assumptions). 25.033/25.033 ->*_s0(x,x) # label(reflexivity). 25.033/25.033 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 25.033/25.033 ->_s0(x1,y) -> ->_s0(not(x1),not(y)) # label(congruence). 25.033/25.033 ->*_s0(x2,true) -> ->_s0(not(x2),false) # label(replacement). 25.033/25.033 ->*_s0(x2,false) -> ->_s0(not(x2),true) # label(replacement). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 formulas(goals). 25.033/25.033 (exists x2 ->*_s0(x2,false)) # label(goal). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 ============================== end of input ========================== 25.033/25.033 25.033/25.033 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.033/25.033 25.033/25.033 % Formulas that are not ordinary clauses: 25.033/25.033 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.033/25.033 2 ->_s0(x1,y) -> ->_s0(not(x1),not(y)) # label(congruence) # label(non_clause). [assumption]. 25.033/25.033 3 ->*_s0(x2,true) -> ->_s0(not(x2),false) # label(replacement) # label(non_clause). [assumption]. 25.033/25.033 4 ->*_s0(x2,false) -> ->_s0(not(x2),true) # label(replacement) # label(non_clause). [assumption]. 25.033/25.033 5 (exists x2 ->*_s0(x2,false)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.033/25.033 25.033/25.033 ============================== end of process non-clausal formulas === 25.033/25.033 25.033/25.033 ============================== PROCESS INITIAL CLAUSES =============== 25.033/25.033 25.033/25.033 % Clauses before input processing: 25.033/25.033 25.033/25.033 formulas(usable). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 formulas(sos). 25.033/25.033 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.033/25.033 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.033/25.033 -->_s0(x,y) | ->_s0(not(x),not(y)) # label(congruence). [clausify(2)]. 25.033/25.033 -->*_s0(x,true) | ->_s0(not(x),false) # label(replacement). [clausify(3)]. 25.033/25.033 -->*_s0(x,false) | ->_s0(not(x),true) # label(replacement). [clausify(4)]. 25.033/25.033 -->*_s0(x,false) # label(goal). [deny(5)]. 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 formulas(demodulators). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 ============================== PREDICATE ELIMINATION ================= 25.033/25.033 25.033/25.033 No predicates eliminated. 25.033/25.033 25.033/25.033 ============================== end predicate elimination ============= 25.033/25.033 25.033/25.033 Auto_denials: 25.033/25.033 % copying label goal to answer in negative clause 25.033/25.033 25.033/25.033 Term ordering decisions: 25.033/25.033 Predicate symbol precedence: predicate_order([ ->*_s0, ->_s0 ]). 25.033/25.033 Function symbol precedence: function_order([ false, true, not ]). 25.033/25.033 After inverse_order: (no changes). 25.033/25.033 Unfolding symbols: (none). 25.033/25.033 25.033/25.033 Auto_inference settings: 25.033/25.033 % set(neg_binary_resolution). % (HNE depth_diff=-3) 25.033/25.033 % clear(ordered_res). % (HNE depth_diff=-3) 25.033/25.033 % set(ur_resolution). % (HNE depth_diff=-3) 25.033/25.033 % set(ur_resolution) -> set(pos_ur_resolution). 25.033/25.033 % set(ur_resolution) -> set(neg_ur_resolution). 25.033/25.033 25.033/25.033 Auto_process settings: (no changes). 25.033/25.033 25.033/25.033 kept: 6 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.033/25.033 kept: 7 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.033/25.033 kept: 8 -->_s0(x,y) | ->_s0(not(x),not(y)) # label(congruence). [clausify(2)]. 25.033/25.033 kept: 9 -->*_s0(x,true) | ->_s0(not(x),false) # label(replacement). [clausify(3)]. 25.033/25.033 kept: 10 -->*_s0(x,false) | ->_s0(not(x),true) # label(replacement). [clausify(4)]. 25.033/25.033 kept: 11 -->*_s0(x,false) # label(goal) # answer(goal). [deny(5)]. 25.033/25.033 25.033/25.033 ============================== PROOF ================================= 25.033/25.033 25.033/25.033 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 25.033/25.033 % Length of proof is 4. 25.033/25.033 % Level of proof is 2. 25.033/25.033 % Maximum clause weight is 3.000. 25.033/25.033 % Given clauses 0. 25.033/25.033 25.033/25.033 5 (exists x2 ->*_s0(x2,false)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.033/25.033 6 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.033/25.033 11 -->*_s0(x,false) # label(goal) # answer(goal). [deny(5)]. 25.033/25.033 12 $F # answer(goal). [resolve(11,a,6,a)]. 25.033/25.033 25.033/25.033 ============================== end of proof ========================== 25.033/25.033 25.033/25.033 ============================== STATISTICS ============================ 25.033/25.033 25.033/25.033 Given=0. Generated=6. Kept=6. proofs=1. 25.033/25.033 Usable=0. Sos=0. Demods=0. Limbo=5, Disabled=6. Hints=0. 25.033/25.033 Kept_by_rule=0, Deleted_by_rule=0. 25.033/25.033 Forward_subsumed=0. Back_subsumed=0. 25.033/25.033 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 25.033/25.033 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 25.033/25.033 Demod_attempts=0. Demod_rewrites=0. 25.033/25.033 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 25.033/25.033 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. 25.033/25.033 Megabytes=0.04. 25.033/25.033 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.033/25.033 25.033/25.033 ============================== end of statistics ===================== 25.033/25.033 25.033/25.033 ============================== end of search ========================= 25.033/25.033 25.033/25.033 THEOREM PROVED 25.033/25.033 25.033/25.033 Exiting with 1 proof. 25.033/25.033 25.033/25.033 Process 38908 exit (max_proofs) Wed Jul 14 10:09:54 2021 25.033/25.033 25.033/25.033 25.033/25.033 The problem is feasible. 25.033/25.033 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.033/25.033 Confluence Problem: 25.033/25.033 (VAR x:S) 25.033/25.033 (STRATEGY CONTEXTSENSITIVE 25.033/25.033 (not 1) 25.033/25.033 (fSNonEmpty) 25.033/25.033 (false) 25.033/25.033 (true) 25.033/25.033 ) 25.033/25.033 (RULES 25.033/25.033 not(x:S) -> false | x:S ->* true 25.033/25.033 not(x:S) -> true | x:S ->* false 25.033/25.033 ) 25.033/25.033 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.033/25.033 25.033/25.033 Critical Pairs Processor: 25.033/25.033 -> Rules: 25.033/25.033 not(x:S) -> false | x:S ->* true 25.033/25.033 not(x:S) -> true | x:S ->* false 25.033/25.033 -> Vars: 25.033/25.033 "x", "x" 25.033/25.033 -> FVars: 25.033/25.033 "x2", "x3" 25.033/25.033 -> PVars: 25.033/25.033 "x": ["x2", "x3"] 25.033/25.033 25.033/25.033 -> Rlps: 25.033/25.033 crule: not(x2:S) -> false | x2:S ->* true, id: 1, possubterms: not(x2:S)-> [] 25.033/25.033 crule: not(x3:S) -> true | x3:S ->* false, id: 2, possubterms: not(x3:S)-> [] 25.033/25.033 25.033/25.033 -> Unifications: 25.033/25.033 R2 unifies with R1 at p: [], l: not(x3:S), lp: not(x3:S), conds: {x3:S ->* false, x:S ->* true}, sig: {x3:S -> x:S}, l': not(x:S), r: true, r': false 25.033/25.033 25.033/25.033 -> Critical pairs info: 25.033/25.033 | x:S ->* false, x:S ->* true => Not trivial, Overlay, N1 25.033/25.033 25.033/25.033 -> Problem conclusions: 25.033/25.033 Left linear, Right linear, Linear 25.033/25.033 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 25.033/25.033 CTRS Type: 1 25.033/25.033 Deterministic, Strongly deterministic 25.033/25.033 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.033/25.033 Maybe right-stable CTRS, Overlay CTRS 25.033/25.033 Maybe normal CTRS, Maybe almost normal CTRS 25.033/25.033 Maybe terminating CTRS, Maybe joinable CCPs 25.033/25.033 Maybe level confluent 25.033/25.033 Maybe confluent 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 Clean Infeasible CCPs Processor: 25.033/25.033 Num of CPIs: 1 25.033/25.033 Timeout: 60 25.033/25.033 Timeout for each infeasibility problem: 60 s 25.033/25.033 | x:S ->* false, x:S ->* true => Not trivial, Overlay, N1 25.033/25.033 (PROBLEM INFEASIBILITY) 25.033/25.033 (VAR x) 25.033/25.033 (RULES 25.033/25.033 not(x) -> false | x ->* true 25.033/25.033 not(x) -> true | x ->* false) 25.033/25.033 (VAR x2) 25.033/25.033 (CONDITION x2 ->* false, x2 ->* true) 25.033/25.033 25.033/25.033 Proof: 25.033/25.033 YES 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Infeasibility Problem: 25.033/25.033 [(VAR vNonEmpty:S x:S x2:S) 25.033/25.033 (STRATEGY CONTEXTSENSITIVE 25.033/25.033 (not 1) 25.033/25.033 (fSNonEmpty) 25.033/25.033 (false) 25.033/25.033 (true) 25.033/25.033 ) 25.033/25.033 (RULES 25.033/25.033 not(x:S) -> false | x:S ->* true 25.033/25.033 not(x:S) -> true | x:S ->* false 25.033/25.033 )] 25.033/25.033 25.033/25.033 Infeasibility Conditions: 25.033/25.033 x2:S ->* false, x2:S ->* true 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Obtaining a model using Mace4: 25.033/25.033 25.033/25.033 -> Usable Rules: 25.033/25.033 not(x:S) -> false | x:S ->* true 25.033/25.033 not(x:S) -> true | x:S ->* false 25.033/25.033 25.033/25.033 -> Mace4 Output: 25.033/25.033 ============================== Mace4 ================================= 25.033/25.033 Mace4 (64) version 2009-11A, November 2009. 25.033/25.033 Process 38940 was started by ubuntu on ubuntu, 25.033/25.033 Wed Jul 14 10:09:54 2021 25.033/25.033 The command was "./mace4 -c -f /tmp/mace438925-2.in". 25.033/25.033 ============================== end of head =========================== 25.033/25.033 25.033/25.033 ============================== INPUT ================================= 25.033/25.033 25.033/25.033 % Reading from file /tmp/mace438925-2.in 25.033/25.033 25.033/25.033 assign(max_seconds,20). 25.033/25.033 25.033/25.033 formulas(assumptions). 25.033/25.033 ->(x1,y) -> ->(not(x1),not(y)) # label(congruence). 25.033/25.033 ->*(x1,true) -> ->(not(x1),false) # label(replacement). 25.033/25.033 ->*(x1,false) -> ->(not(x1),true) # label(replacement). 25.033/25.033 ->*(x,x) # label(reflexivity). 25.033/25.033 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 formulas(goals). 25.033/25.033 (exists x2 (->*(x2,false) & ->*(x2,true))) # label(goal). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 ============================== end of input ========================== 25.033/25.033 25.033/25.033 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.033/25.033 25.033/25.033 % Formulas that are not ordinary clauses: 25.033/25.033 1 ->(x1,y) -> ->(not(x1),not(y)) # label(congruence) # label(non_clause). [assumption]. 25.033/25.033 2 ->*(x1,true) -> ->(not(x1),false) # label(replacement) # label(non_clause). [assumption]. 25.033/25.033 3 ->*(x1,false) -> ->(not(x1),true) # label(replacement) # label(non_clause). [assumption]. 25.033/25.033 4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.033/25.033 5 (exists x2 (->*(x2,false) & ->*(x2,true))) # label(goal) # label(non_clause) # label(goal). [goal]. 25.033/25.033 25.033/25.033 ============================== end of process non-clausal formulas === 25.033/25.033 25.033/25.033 ============================== CLAUSES FOR SEARCH ==================== 25.033/25.033 25.033/25.033 formulas(mace4_clauses). 25.033/25.033 -->(x,y) | ->(not(x),not(y)) # label(congruence). 25.033/25.033 -->*(x,true) | ->(not(x),false) # label(replacement). 25.033/25.033 -->*(x,false) | ->(not(x),true) # label(replacement). 25.033/25.033 ->*(x,x) # label(reflexivity). 25.033/25.033 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 25.033/25.033 -->*(x,false) | -->*(x,true) # label(goal). 25.033/25.033 end_of_list. 25.033/25.033 25.033/25.033 ============================== end of clauses for search ============= 25.033/25.033 25.033/25.033 % There are no natural numbers in the input. 25.033/25.033 25.033/25.033 ============================== DOMAIN SIZE 2 ========================= 25.033/25.033 25.033/25.033 ============================== MODEL ================================= 25.033/25.033 25.033/25.033 interpretation( 2, [number=1, seconds=0], [ 25.033/25.033 25.033/25.033 function(false, [ 0 ]), 25.033/25.033 25.033/25.033 function(true, [ 1 ]), 25.033/25.033 25.033/25.033 function(not(_), [ 1, 0 ]), 25.033/25.033 25.033/25.033 relation(->*(_,_), [ 25.033/25.033 1, 0, 25.033/25.033 0, 1 ]), 25.033/25.033 25.033/25.033 relation(->(_,_), [ 25.033/25.033 1, 0, 25.033/25.033 0, 1 ]) 25.033/25.033 ]). 25.033/25.033 25.033/25.033 ============================== end of model ========================== 25.033/25.033 25.033/25.033 ============================== STATISTICS ============================ 25.033/25.033 25.033/25.033 For domain size 2. 25.033/25.033 25.033/25.033 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.033/25.033 Ground clauses: seen=20, kept=16. 25.033/25.033 Selections=1, assignments=1, propagations=11, current_models=1. 25.033/25.033 Rewrite_terms=24, rewrite_bools=26, indexes=6. 25.033/25.033 Rules_from_neg_clauses=3, cross_offs=3. 25.033/25.033 25.033/25.033 ============================== end of statistics ===================== 25.033/25.033 25.033/25.033 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.033/25.033 25.033/25.033 Exiting with 1 model. 25.033/25.033 25.033/25.033 Process 38940 exit (max_models) Wed Jul 14 10:09:54 2021 25.033/25.033 The process finished Wed Jul 14 10:09:54 2021 25.033/25.033 25.033/25.033 25.033/25.033 Mace4 cooked interpretation: 25.033/25.033 25.033/25.033 25.033/25.033 25.033/25.033 The problem is infeasible. 25.033/25.033 25.033/25.033 25.033/25.033 25.033/25.033 25.033/25.033 -> Problem conclusions: 25.033/25.033 Left linear, Right linear, Linear 25.033/25.033 Weakly orthogonal, Almost orthogonal, Orthogonal 25.033/25.033 CTRS Type: 1 25.033/25.033 Deterministic, Strongly deterministic 25.033/25.033 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.033/25.033 Maybe right-stable CTRS, Overlay CTRS 25.033/25.033 Maybe normal CTRS, Maybe almost normal CTRS 25.033/25.033 Maybe terminating CTRS, Joinable CCPs 25.033/25.033 Maybe level confluent 25.033/25.033 Maybe confluent 25.033/25.033 25.033/25.033 Resulting CCPs: 25.033/25.033 No CCPs left 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 Underlying TRS Termination Processor: 25.033/25.033 25.033/25.033 Resulting Underlying TRS: 25.033/25.033 (VAR x:S) 25.033/25.033 (STRATEGY CONTEXTSENSITIVE 25.033/25.033 (not 1) 25.033/25.033 (false) 25.033/25.033 (true) 25.033/25.033 ) 25.033/25.033 (RULES 25.033/25.033 not(x:S) -> false 25.033/25.033 not(x:S) -> true 25.033/25.033 ) 25.033/25.033 Underlying TRS terminating? 25.033/25.033 YES 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 (VAR vu95NonEmpty:S xu58S:S) 25.033/25.033 (RULES 25.033/25.033 not(xu58S:S) -> ffalse 25.033/25.033 not(xu58S:S) -> ftrue 25.033/25.033 ) 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 Dependency Pairs Processor: 25.033/25.033 -> Pairs: 25.033/25.033 Empty 25.033/25.033 -> Rules: 25.033/25.033 not(xu58S:S) -> ffalse 25.033/25.033 not(xu58S:S) -> ftrue 25.033/25.033 25.033/25.033 Problem 1: 25.033/25.033 25.033/25.033 SCC Processor: 25.033/25.033 -> Pairs: 25.033/25.033 Empty 25.033/25.033 -> Rules: 25.033/25.033 not(xu58S:S) -> ffalse 25.033/25.033 not(xu58S:S) -> ftrue 25.033/25.033 ->Strongly Connected Components: 25.033/25.033 There is no strongly connected component 25.033/25.033 25.033/25.033 The problem is finite. 25.033/25.033 25.033/25.033 25.033/25.033 -> Problem conclusions: 25.033/25.033 Left linear, Right linear, Linear 25.033/25.033 Weakly orthogonal, Almost orthogonal, Orthogonal 25.033/25.033 CTRS Type: 1 25.033/25.033 Deterministic, Strongly deterministic 25.033/25.033 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.033/25.033 Maybe right-stable CTRS, Overlay CTRS 25.033/25.033 Maybe normal CTRS, Maybe almost normal CTRS 25.033/25.033 Terminating CTRS, Joinable CCPs 25.033/25.033 Maybe level confluent 25.033/25.033 Confluent 25.033/25.033 25.033/25.033 The problem is joinable. 25.033/25.033 40.10user 1.15system 0:25.33elapsed 162%CPU (0avgtext+0avgdata 105976maxresident)k 25.033/25.033 0inputs+0outputs (0major+93609minor)pagefaults 0swaps