25.047/25.047 NO 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 25.047/25.047 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 Confluence Problem: 25.047/25.047 (VAR vNonEmpty:S x:S) 25.047/25.047 (STRATEGY CONTEXTSENSITIVE 25.047/25.047 (a) 25.047/25.047 (b) 25.047/25.047 (f 1) 25.047/25.047 (g 1 2) 25.047/25.047 (h 1 2) 25.047/25.047 (c) 25.047/25.047 (d) 25.047/25.047 (fSNonEmpty) 25.047/25.047 ) 25.047/25.047 (RULES 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 ) 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 25.047/25.047 Inlining of Conditions Processor [STERN17]: 25.047/25.047 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 Confluence Problem: 25.047/25.047 (VAR vNonEmpty:S x:S) 25.047/25.047 (STRATEGY CONTEXTSENSITIVE 25.047/25.047 (a) 25.047/25.047 (b) 25.047/25.047 (f 1) 25.047/25.047 (g 1 2) 25.047/25.047 (h 1 2) 25.047/25.047 (c) 25.047/25.047 (d) 25.047/25.047 (fSNonEmpty) 25.047/25.047 ) 25.047/25.047 (RULES 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 ) 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 25.047/25.047 Clean CTRS Processor: 25.047/25.047 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 Confluence Problem: 25.047/25.047 (VAR x:S) 25.047/25.047 (STRATEGY CONTEXTSENSITIVE 25.047/25.047 (a) 25.047/25.047 (b) 25.047/25.047 (f 1) 25.047/25.047 (g 1 2) 25.047/25.047 (h 1 2) 25.047/25.047 (c) 25.047/25.047 (d) 25.047/25.047 (fSNonEmpty) 25.047/25.047 ) 25.047/25.047 (RULES 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 ) 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 25.047/25.047 CRule InfChecker Info: 25.047/25.047 a -> c 25.047/25.047 Rule remains 25.047/25.047 Proof: 25.047/25.047 NO_CONDS 25.047/25.047 25.047/25.047 CRule InfChecker Info: 25.047/25.047 a -> d 25.047/25.047 Rule remains 25.047/25.047 Proof: 25.047/25.047 NO_CONDS 25.047/25.047 25.047/25.047 CRule InfChecker Info: 25.047/25.047 b -> c 25.047/25.047 Rule remains 25.047/25.047 Proof: 25.047/25.047 NO_CONDS 25.047/25.047 25.047/25.047 CRule InfChecker Info: 25.047/25.047 b -> d 25.047/25.047 Rule remains 25.047/25.047 Proof: 25.047/25.047 NO_CONDS 25.047/25.047 25.047/25.047 CRule InfChecker Info: 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 Rule remains 25.047/25.047 Proof: 25.047/25.047 NO 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 25.047/25.047 Infeasibility Problem: 25.047/25.047 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 25.047/25.047 (STRATEGY CONTEXTSENSITIVE 25.047/25.047 (a) 25.047/25.047 (b) 25.047/25.047 (f 1) 25.047/25.047 (g 1 2) 25.047/25.047 (h 1 2) 25.047/25.047 (c) 25.047/25.047 (d) 25.047/25.047 (fSNonEmpty) 25.047/25.047 ) 25.047/25.047 (RULES 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S:S) -> x:S:S | x:S:S ->* c 25.047/25.047 g(x:S:S,x:S:S) -> h(x:S:S,x:S:S) 25.047/25.047 h(x:S:S,f(x:S:S)) -> x:S:S 25.047/25.047 )] 25.047/25.047 25.047/25.047 Infeasibility Conditions: 25.047/25.047 x:S:S ->* c 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 25.047/25.047 Obtaining a proof using Prover9: 25.047/25.047 25.047/25.047 -> Prover9 Output: 25.047/25.047 ============================== Prover9 =============================== 25.047/25.047 Prover9 (64) version 2009-11A, November 2009. 25.047/25.047 Process 50483 was started by ubuntu on ubuntu, 25.047/25.047 Wed Jul 14 10:55:24 2021 25.047/25.047 The command was "./prover9 -f /tmp/prover950474-0.in". 25.047/25.047 ============================== end of head =========================== 25.047/25.047 25.047/25.047 ============================== INPUT ================================= 25.047/25.047 25.047/25.047 % Reading from file /tmp/prover950474-0.in 25.047/25.047 25.047/25.047 assign(max_seconds,20). 25.047/25.047 25.047/25.047 formulas(assumptions). 25.047/25.047 ->*_s0(x,x) # label(reflexivity). 25.047/25.047 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 25.047/25.047 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 25.047/25.047 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 25.047/25.047 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 25.047/25.047 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 25.047/25.047 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 25.047/25.047 ->_s0(a,c) # label(replacement). 25.047/25.047 ->_s0(a,d) # label(replacement). 25.047/25.047 ->_s0(b,c) # label(replacement). 25.047/25.047 ->_s0(b,d) # label(replacement). 25.047/25.047 ->*_s0(x2,c) -> ->_s0(f(x2),x2) # label(replacement). 25.047/25.047 ->_s0(g(x2,x2),h(x2,x2)) # label(replacement). 25.047/25.047 ->_s0(h(x2,f(x2)),x2) # label(replacement). 25.047/25.047 end_of_list. 25.047/25.047 25.047/25.047 formulas(goals). 25.047/25.047 (exists x2 ->*_s0(x2,c)) # label(goal). 25.047/25.047 end_of_list. 25.047/25.047 25.047/25.047 ============================== end of input ========================== 25.047/25.047 25.047/25.047 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.047/25.047 25.047/25.047 % Formulas that are not ordinary clauses: 25.047/25.047 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.047/25.047 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 3 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 4 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 7 ->*_s0(x2,c) -> ->_s0(f(x2),x2) # label(replacement) # label(non_clause). [assumption]. 25.047/25.047 8 (exists x2 ->*_s0(x2,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.047/25.047 25.047/25.047 ============================== end of process non-clausal formulas === 25.047/25.047 25.047/25.047 ============================== PROCESS INITIAL CLAUSES =============== 25.047/25.047 25.047/25.047 % Clauses before input processing: 25.047/25.047 25.047/25.047 formulas(usable). 25.047/25.047 end_of_list. 25.047/25.047 25.047/25.047 formulas(sos). 25.047/25.047 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.047/25.047 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.047/25.047 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 25.047/25.047 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 25.047/25.047 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 25.047/25.047 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 25.047/25.047 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 25.047/25.047 ->_s0(a,c) # label(replacement). [assumption]. 25.047/25.047 ->_s0(a,d) # label(replacement). [assumption]. 25.047/25.047 ->_s0(b,c) # label(replacement). [assumption]. 25.047/25.047 ->_s0(b,d) # label(replacement). [assumption]. 25.047/25.047 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 25.047/25.047 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 25.047/25.047 ->_s0(h(x,f(x)),x) # label(replacement). [assumption]. 25.047/25.047 -->*_s0(x,c) # label(goal). [deny(8)]. 25.047/25.047 end_of_list. 25.047/25.047 25.047/25.047 formulas(demodulators). 25.047/25.047 end_of_list. 25.047/25.047 25.047/25.047 ============================== PREDICATE ELIMINATION ================= 25.047/25.047 25.047/25.047 No predicates eliminated. 25.047/25.047 25.047/25.047 ============================== end predicate elimination ============= 25.047/25.047 25.047/25.047 Auto_denials: 25.047/25.047 % copying label goal to answer in negative clause 25.047/25.047 25.047/25.047 Term ordering decisions: 25.047/25.047 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 25.047/25.047 Function symbol precedence: function_order([ c, a, b, d, h, g, f ]). 25.047/25.047 After inverse_order: (no changes). 25.047/25.047 Unfolding symbols: (none). 25.047/25.047 25.047/25.047 Auto_inference settings: 25.047/25.047 % set(neg_binary_resolution). % (HNE depth_diff=-6) 25.047/25.047 % clear(ordered_res). % (HNE depth_diff=-6) 25.047/25.047 % set(ur_resolution). % (HNE depth_diff=-6) 25.047/25.047 % set(ur_resolution) -> set(pos_ur_resolution). 25.047/25.047 % set(ur_resolution) -> set(neg_ur_resolution). 25.047/25.047 25.047/25.047 Auto_process settings: (no changes). 25.047/25.047 25.047/25.047 kept: 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.047/25.047 kept: 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.047/25.047 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 25.047/25.047 kept: 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 25.047/25.047 kept: 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 25.047/25.047 kept: 14 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 25.047/25.047 kept: 15 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 25.047/25.047 kept: 16 ->_s0(a,c) # label(replacement). [assumption]. 25.047/25.047 kept: 17 ->_s0(a,d) # label(replacement). [assumption]. 25.047/25.047 kept: 18 ->_s0(b,c) # label(replacement). [assumption]. 25.047/25.047 kept: 19 ->_s0(b,d) # label(replacement). [assumption]. 25.047/25.047 kept: 20 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 25.047/25.047 kept: 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 25.047/25.047 kept: 22 ->_s0(h(x,f(x)),x) # label(replacement). [assumption]. 25.047/25.047 kept: 23 -->*_s0(x,c) # label(goal) # answer(goal). [deny(8)]. 25.047/25.047 25.047/25.047 ============================== PROOF ================================= 25.047/25.047 25.047/25.047 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 25.047/25.047 % Length of proof is 4. 25.047/25.047 % Level of proof is 2. 25.047/25.047 % Maximum clause weight is 3.000. 25.047/25.047 % Given clauses 0. 25.047/25.047 25.047/25.047 8 (exists x2 ->*_s0(x2,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.047/25.047 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.047/25.047 23 -->*_s0(x,c) # label(goal) # answer(goal). [deny(8)]. 25.047/25.047 24 $F # answer(goal). [resolve(23,a,9,a)]. 25.047/25.047 25.047/25.047 ============================== end of proof ========================== 25.047/25.047 25.047/25.047 ============================== STATISTICS ============================ 25.047/25.047 25.047/25.047 Given=0. Generated=15. Kept=15. proofs=1. 25.047/25.047 Usable=0. Sos=0. Demods=0. Limbo=14, Disabled=15. Hints=0. 25.047/25.047 Kept_by_rule=0, Deleted_by_rule=0. 25.047/25.047 Forward_subsumed=0. Back_subsumed=0. 25.047/25.047 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 25.047/25.047 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 25.047/25.047 Demod_attempts=0. Demod_rewrites=0. 25.047/25.047 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 25.047/25.047 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. 25.047/25.047 Megabytes=0.05. 25.047/25.047 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.047/25.047 25.047/25.047 ============================== end of statistics ===================== 25.047/25.047 25.047/25.047 ============================== end of search ========================= 25.047/25.047 25.047/25.047 THEOREM PROVED 25.047/25.047 25.047/25.047 Exiting with 1 proof. 25.047/25.047 25.047/25.047 Process 50483 exit (max_proofs) Wed Jul 14 10:55:24 2021 25.047/25.047 25.047/25.047 25.047/25.047 The problem is feasible. 25.047/25.047 25.047/25.047 25.047/25.047 CRule InfChecker Info: 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 Rule remains 25.047/25.047 Proof: 25.047/25.047 NO_CONDS 25.047/25.047 25.047/25.047 CRule InfChecker Info: 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 Rule remains 25.047/25.047 Proof: 25.047/25.047 NO_CONDS 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 Confluence Problem: 25.047/25.047 (VAR x:S) 25.047/25.047 (STRATEGY CONTEXTSENSITIVE 25.047/25.047 (a) 25.047/25.047 (b) 25.047/25.047 (f 1) 25.047/25.047 (g 1 2) 25.047/25.047 (h 1 2) 25.047/25.047 (c) 25.047/25.047 (d) 25.047/25.047 (fSNonEmpty) 25.047/25.047 ) 25.047/25.047 (RULES 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 ) 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 25.047/25.047 Critical Pairs Processor: 25.047/25.047 -> Rules: 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 -> Vars: 25.047/25.047 "x", "x", "x" 25.047/25.047 -> FVars: 25.047/25.047 "x2", "x3", "x4" 25.047/25.047 -> PVars: 25.047/25.047 "x": ["x2", "x3", "x4"] 25.047/25.047 25.047/25.047 -> Rlps: 25.047/25.047 crule: a -> c, id: 1, possubterms: a-> [] 25.047/25.047 crule: a -> d, id: 2, possubterms: a-> [] 25.047/25.047 crule: b -> c, id: 3, possubterms: b-> [] 25.047/25.047 crule: b -> d, id: 4, possubterms: b-> [] 25.047/25.047 crule: f(x2:S) -> x2:S | x2:S ->* c, id: 5, possubterms: f(x2:S)-> [] 25.047/25.047 crule: g(x3:S,x3:S) -> h(x3:S,x3:S), id: 6, possubterms: g(x3:S,x3:S)-> [] 25.047/25.047 crule: h(x4:S,f(x4:S)) -> x4:S, id: 7, possubterms: h(x4:S,f(x4:S))-> [], f(x4:S)-> [2] 25.047/25.047 25.047/25.047 -> Unifications: 25.047/25.047 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 25.047/25.047 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 25.047/25.047 R7 unifies with R5 at p: [2], l: h(x4:S,f(x4:S)), lp: f(x4:S), conds: {x:S ->* c}, sig: {x4:S -> x:S}, l': f(x:S), r: x4:S, r': x:S 25.047/25.047 25.047/25.047 -> Critical pairs info: 25.047/25.047 => Not trivial, Overlay, N1 25.047/25.047 | x:S ->* c => Not trivial, Not overlay, N2 25.047/25.047 25.047/25.047 -> Problem conclusions: 25.047/25.047 Not left linear, Not right linear, Not linear 25.047/25.047 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 25.047/25.047 CTRS Type: 1 25.047/25.047 Deterministic, Strongly deterministic 25.047/25.047 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.047/25.047 Maybe right-stable CTRS, Not overlay CTRS 25.047/25.047 Maybe normal CTRS, Maybe almost normal CTRS 25.047/25.047 Maybe terminating CTRS, Maybe joinable CCPs 25.047/25.047 Maybe level confluent 25.047/25.047 Maybe confluent 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 Confluence Problem: 25.047/25.047 (VAR x:S) 25.047/25.047 (STRATEGY CONTEXTSENSITIVE 25.047/25.047 (a) 25.047/25.047 (b) 25.047/25.047 (f 1) 25.047/25.047 (g 1 2) 25.047/25.047 (h 1 2) 25.047/25.047 (c) 25.047/25.047 (d) 25.047/25.047 (fSNonEmpty) 25.047/25.047 ) 25.047/25.047 (RULES 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 ) 25.047/25.047 Critical Pairs: 25.047/25.047 => Not trivial, Overlay, N1 25.047/25.047 | x:S ->* c => Not trivial, Not overlay, N2 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 25.047/25.047 Conditional Critical Pairs Distributor Processor 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 Confluence Problem: 25.047/25.047 (VAR x:S) 25.047/25.047 (STRATEGY CONTEXTSENSITIVE 25.047/25.047 (a) 25.047/25.047 (b) 25.047/25.047 (f 1) 25.047/25.047 (g 1 2) 25.047/25.047 (h 1 2) 25.047/25.047 (c) 25.047/25.047 (d) 25.047/25.047 (fSNonEmpty) 25.047/25.047 ) 25.047/25.047 (RULES 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 ) 25.047/25.047 Critical Pairs: 25.047/25.047 => Not trivial, Overlay, N1 25.047/25.047 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.047/25.047 25.047/25.047 Infeasible Convergence No Conditions CCP Processor: 25.047/25.047 Infeasible convergence? 25.047/25.047 YES 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 25.047/25.047 Infeasibility Problem: 25.047/25.047 [(VAR vNonEmpty:S x:S z:S) 25.047/25.047 (STRATEGY CONTEXTSENSITIVE 25.047/25.047 (a) 25.047/25.047 (b) 25.047/25.047 (f 1) 25.047/25.047 (g 1 2) 25.047/25.047 (h 1 2) 25.047/25.047 (c) 25.047/25.047 (d) 25.047/25.047 (fSNonEmpty) 25.047/25.047 ) 25.047/25.047 (RULES 25.047/25.047 a -> c 25.047/25.047 a -> d 25.047/25.047 b -> c 25.047/25.047 b -> d 25.047/25.047 f(x:S) -> x:S | x:S ->* c 25.047/25.047 g(x:S,x:S) -> h(x:S,x:S) 25.047/25.047 h(x:S,f(x:S)) -> x:S 25.047/25.047 )] 25.047/25.047 25.047/25.047 Infeasibility Conditions: 25.047/25.047 c ->* z:S, d ->* z:S 25.047/25.047 25.047/25.047 Problem 1: 25.047/25.047 25.047/25.047 Obtaining a model using Mace4: 25.047/25.047 25.047/25.047 -> Usable Rules: 25.047/25.047 Empty 25.047/25.047 25.047/25.047 -> Mace4 Output: 25.047/25.047 ============================== Mace4 ================================= 25.047/25.047 Mace4 (64) version 2009-11A, November 2009. 25.047/25.047 Process 50521 was started by ubuntu on ubuntu, 25.047/25.047 Wed Jul 14 10:55:24 2021 25.047/25.047 The command was "./mace4 -c -f /tmp/mace450500-2.in". 25.047/25.047 ============================== end of head =========================== 25.047/25.047 25.047/25.047 ============================== INPUT ================================= 25.047/25.047 25.047/25.047 % Reading from file /tmp/mace450500-2.in 25.047/25.047 25.047/25.047 assign(max_seconds,20). 25.047/25.047 25.047/25.047 formulas(assumptions). 25.047/25.047 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 25.047/25.047 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 25.047/25.047 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 25.047/25.047 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 25.047/25.047 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 25.047/25.047 ->*(x,x) # label(reflexivity). 25.047/25.047 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 25.047/25.047 end_of_list. 25.047/25.047 25.047/25.047 formulas(goals). 25.047/25.047 (exists x2 (->*(c,x2) & ->*(d,x2))) # label(goal). 25.047/25.047 end_of_list. 25.047/25.047 25.047/25.047 ============================== end of input ========================== 25.047/25.047 25.047/25.047 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.047/25.047 25.047/25.047 % Formulas that are not ordinary clauses: 25.047/25.047 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 4 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 5 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.047/25.047 6 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.047/25.047 7 (exists x2 (->*(c,x2) & ->*(d,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 25.047/25.047 25.047/25.047 ============================== end of process non-clausal formulas === 25.047/25.047 25.047/25.047 ============================== CLAUSES FOR SEARCH ==================== 25.047/25.047 25.047/25.047 formulas(mace4_clauses). 25.047/25.047 -->(x,y) | ->(f(x),f(y)) # label(congruence). 25.047/25.047 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 25.047/25.047 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 25.047/25.047 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 25.047/25.047 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 25.047/25.047 ->*(x,x) # label(reflexivity). 25.047/25.047 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 25.047/25.047 -->*(c,x) | -->*(d,x) # label(goal). 25.047/25.047 end_of_list. 25.047/25.047 25.047/25.047 ============================== end of clauses for search ============= 25.047/25.047 25.047/25.047 % There are no natural numbers in the input. 25.047/25.047 25.047/25.047 ============================== DOMAIN SIZE 2 ========================= 25.047/25.047 25.047/25.047 ============================== MODEL ================================= 25.047/25.047 25.047/25.047 interpretation( 2, [number=1, seconds=0], [ 25.047/25.047 25.047/25.047 function(c, [ 0 ]), 25.047/25.047 25.047/25.047 function(d, [ 1 ]), 25.047/25.047 25.047/25.047 function(f(_), [ 0, 0 ]), 25.047/25.047 25.047/25.047 function(g(_,_), [ 25.047/25.047 0, 0, 25.047/25.047 0, 0 ]), 25.047/25.047 25.047/25.047 function(h(_,_), [ 25.047/25.047 0, 0, 25.047/25.047 0, 0 ]), 25.047/25.047 25.047/25.047 relation(->*(_,_), [ 25.047/25.047 1, 0, 25.047/25.047 0, 1 ]), 25.047/25.047 25.047/25.047 relation(->(_,_), [ 25.047/25.047 0, 0, 25.047/25.047 0, 0 ]) 25.047/25.047 ]). 25.047/25.047 25.047/25.047 ============================== end of model ========================== 25.047/25.047 25.047/25.047 ============================== STATISTICS ============================ 25.047/25.047 25.047/25.047 For domain size 2. 25.047/25.047 25.047/25.047 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.047/25.047 Ground clauses: seen=48, kept=44. 25.047/25.047 Selections=12, assignments=12, propagations=8, current_models=1. 25.047/25.047 Rewrite_terms=76, rewrite_bools=56, indexes=7. 25.047/25.047 Rules_from_neg_clauses=1, cross_offs=1. 25.047/25.047 25.047/25.047 ============================== end of statistics ===================== 25.047/25.047 25.047/25.047 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.047/25.047 25.047/25.047 Exiting with 1 model. 25.047/25.047 25.047/25.047 Process 50521 exit (max_models) Wed Jul 14 10:55:24 2021 25.047/25.047 The process finished Wed Jul 14 10:55:24 2021 25.047/25.047 25.047/25.047 25.047/25.047 Mace4 cooked interpretation: 25.047/25.047 25.047/25.047 25.047/25.047 25.047/25.047 The problem is infeasible. 25.047/25.047 25.047/25.047 25.047/25.047 The problem is not joinable. 25.047/25.047 26.65user 1.04system 0:25.47elapsed 108%CPU (0avgtext+0avgdata 136056maxresident)k 25.047/25.047 0inputs+0outputs (0major+94495minor)pagefaults 0swaps