25.041/25.041 NO 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 25.041/25.041 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 Confluence Problem: 25.041/25.041 (VAR vNonEmpty:S x:S) 25.041/25.041 (STRATEGY CONTEXTSENSITIVE 25.041/25.041 (a) 25.041/25.041 (b) 25.041/25.041 (f 1) 25.041/25.041 (g 1 2) 25.041/25.041 (h 1 2) 25.041/25.041 (c) 25.041/25.041 (d) 25.041/25.041 (fSNonEmpty) 25.041/25.041 ) 25.041/25.041 (RULES 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 ) 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 25.041/25.041 Inlining of Conditions Processor [STERN17]: 25.041/25.041 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 Confluence Problem: 25.041/25.041 (VAR vNonEmpty:S x:S) 25.041/25.041 (STRATEGY CONTEXTSENSITIVE 25.041/25.041 (a) 25.041/25.041 (b) 25.041/25.041 (f 1) 25.041/25.041 (g 1 2) 25.041/25.041 (h 1 2) 25.041/25.041 (c) 25.041/25.041 (d) 25.041/25.041 (fSNonEmpty) 25.041/25.041 ) 25.041/25.041 (RULES 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 ) 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 25.041/25.041 Clean CTRS Processor: 25.041/25.041 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 Confluence Problem: 25.041/25.041 (VAR x:S) 25.041/25.041 (STRATEGY CONTEXTSENSITIVE 25.041/25.041 (a) 25.041/25.041 (b) 25.041/25.041 (f 1) 25.041/25.041 (g 1 2) 25.041/25.041 (h 1 2) 25.041/25.041 (c) 25.041/25.041 (d) 25.041/25.041 (fSNonEmpty) 25.041/25.041 ) 25.041/25.041 (RULES 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 ) 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 25.041/25.041 CRule InfChecker Info: 25.041/25.041 a -> c 25.041/25.041 Rule remains 25.041/25.041 Proof: 25.041/25.041 NO_CONDS 25.041/25.041 25.041/25.041 CRule InfChecker Info: 25.041/25.041 a -> d 25.041/25.041 Rule remains 25.041/25.041 Proof: 25.041/25.041 NO_CONDS 25.041/25.041 25.041/25.041 CRule InfChecker Info: 25.041/25.041 b -> c 25.041/25.041 Rule remains 25.041/25.041 Proof: 25.041/25.041 NO_CONDS 25.041/25.041 25.041/25.041 CRule InfChecker Info: 25.041/25.041 b -> d 25.041/25.041 Rule remains 25.041/25.041 Proof: 25.041/25.041 NO_CONDS 25.041/25.041 25.041/25.041 CRule InfChecker Info: 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 Rule remains 25.041/25.041 Proof: 25.041/25.041 NO 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 25.041/25.041 Infeasibility Problem: 25.041/25.041 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 25.041/25.041 (STRATEGY CONTEXTSENSITIVE 25.041/25.041 (a) 25.041/25.041 (b) 25.041/25.041 (f 1) 25.041/25.041 (g 1 2) 25.041/25.041 (h 1 2) 25.041/25.041 (c) 25.041/25.041 (d) 25.041/25.041 (fSNonEmpty) 25.041/25.041 ) 25.041/25.041 (RULES 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S:S) -> x:S:S | x:S:S ->* c 25.041/25.041 g(x:S:S,x:S:S) -> h(x:S:S,x:S:S) 25.041/25.041 h(x:S:S,f(x:S:S)) -> x:S:S 25.041/25.041 )] 25.041/25.041 25.041/25.041 Infeasibility Conditions: 25.041/25.041 x:S:S ->* c 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 25.041/25.041 Obtaining a proof using Prover9: 25.041/25.041 25.041/25.041 -> Prover9 Output: 25.041/25.041 ============================== Prover9 =============================== 25.041/25.041 Prover9 (64) version 2009-11A, November 2009. 25.041/25.041 Process 111277 was started by ubuntu on ubuntu, 25.041/25.041 Fri Jul 16 15:10:58 2021 25.041/25.041 The command was "./prover9 -f /tmp/prover9111268-0.in". 25.041/25.041 ============================== end of head =========================== 25.041/25.041 25.041/25.041 ============================== INPUT ================================= 25.041/25.041 25.041/25.041 % Reading from file /tmp/prover9111268-0.in 25.041/25.041 25.041/25.041 assign(max_seconds,20). 25.041/25.041 25.041/25.041 formulas(assumptions). 25.041/25.041 ->*_s0(x,x) # label(reflexivity). 25.041/25.041 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 25.041/25.041 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 25.041/25.041 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 25.041/25.041 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 25.041/25.041 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 25.041/25.041 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 25.041/25.041 ->_s0(a,c) # label(replacement). 25.041/25.041 ->_s0(a,d) # label(replacement). 25.041/25.041 ->_s0(b,c) # label(replacement). 25.041/25.041 ->_s0(b,d) # label(replacement). 25.041/25.041 ->*_s0(x2,c) -> ->_s0(f(x2),x2) # label(replacement). 25.041/25.041 ->_s0(g(x2,x2),h(x2,x2)) # label(replacement). 25.041/25.041 ->_s0(h(x2,f(x2)),x2) # label(replacement). 25.041/25.041 end_of_list. 25.041/25.041 25.041/25.041 formulas(goals). 25.041/25.041 (exists x2 ->*_s0(x2,c)) # label(goal). 25.041/25.041 end_of_list. 25.041/25.041 25.041/25.041 ============================== end of input ========================== 25.041/25.041 25.041/25.041 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.041/25.041 25.041/25.041 % Formulas that are not ordinary clauses: 25.041/25.041 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.041/25.041 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 3 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 4 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 7 ->*_s0(x2,c) -> ->_s0(f(x2),x2) # label(replacement) # label(non_clause). [assumption]. 25.041/25.041 8 (exists x2 ->*_s0(x2,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.041/25.041 25.041/25.041 ============================== end of process non-clausal formulas === 25.041/25.041 25.041/25.041 ============================== PROCESS INITIAL CLAUSES =============== 25.041/25.041 25.041/25.041 % Clauses before input processing: 25.041/25.041 25.041/25.041 formulas(usable). 25.041/25.041 end_of_list. 25.041/25.041 25.041/25.041 formulas(sos). 25.041/25.041 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.041/25.041 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.041/25.041 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 25.041/25.041 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 25.041/25.041 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 25.041/25.041 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 25.041/25.041 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 25.041/25.041 ->_s0(a,c) # label(replacement). [assumption]. 25.041/25.041 ->_s0(a,d) # label(replacement). [assumption]. 25.041/25.041 ->_s0(b,c) # label(replacement). [assumption]. 25.041/25.041 ->_s0(b,d) # label(replacement). [assumption]. 25.041/25.041 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 25.041/25.041 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 25.041/25.041 ->_s0(h(x,f(x)),x) # label(replacement). [assumption]. 25.041/25.041 -->*_s0(x,c) # label(goal). [deny(8)]. 25.041/25.041 end_of_list. 25.041/25.041 25.041/25.041 formulas(demodulators). 25.041/25.041 end_of_list. 25.041/25.041 25.041/25.041 ============================== PREDICATE ELIMINATION ================= 25.041/25.041 25.041/25.041 No predicates eliminated. 25.041/25.041 25.041/25.041 ============================== end predicate elimination ============= 25.041/25.041 25.041/25.041 Auto_denials: 25.041/25.041 % copying label goal to answer in negative clause 25.041/25.041 25.041/25.041 Term ordering decisions: 25.041/25.041 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 25.041/25.041 Function symbol precedence: function_order([ c, a, b, d, h, g, f ]). 25.041/25.041 After inverse_order: (no changes). 25.041/25.041 Unfolding symbols: (none). 25.041/25.041 25.041/25.041 Auto_inference settings: 25.041/25.041 % set(neg_binary_resolution). % (HNE depth_diff=-6) 25.041/25.041 % clear(ordered_res). % (HNE depth_diff=-6) 25.041/25.041 % set(ur_resolution). % (HNE depth_diff=-6) 25.041/25.041 % set(ur_resolution) -> set(pos_ur_resolution). 25.041/25.041 % set(ur_resolution) -> set(neg_ur_resolution). 25.041/25.041 25.041/25.041 Auto_process settings: (no changes). 25.041/25.041 25.041/25.041 kept: 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.041/25.041 kept: 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.041/25.041 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 25.041/25.041 kept: 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 25.041/25.041 kept: 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 25.041/25.041 kept: 14 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 25.041/25.041 kept: 15 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 25.041/25.041 kept: 16 ->_s0(a,c) # label(replacement). [assumption]. 25.041/25.041 kept: 17 ->_s0(a,d) # label(replacement). [assumption]. 25.041/25.041 kept: 18 ->_s0(b,c) # label(replacement). [assumption]. 25.041/25.041 kept: 19 ->_s0(b,d) # label(replacement). [assumption]. 25.041/25.041 kept: 20 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 25.041/25.041 kept: 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 25.041/25.041 kept: 22 ->_s0(h(x,f(x)),x) # label(replacement). [assumption]. 25.041/25.041 kept: 23 -->*_s0(x,c) # label(goal) # answer(goal). [deny(8)]. 25.041/25.041 25.041/25.041 ============================== PROOF ================================= 25.041/25.041 25.041/25.041 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 25.041/25.041 % Length of proof is 4. 25.041/25.041 % Level of proof is 2. 25.041/25.041 % Maximum clause weight is 3.000. 25.041/25.041 % Given clauses 0. 25.041/25.041 25.041/25.041 8 (exists x2 ->*_s0(x2,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.041/25.041 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.041/25.041 23 -->*_s0(x,c) # label(goal) # answer(goal). [deny(8)]. 25.041/25.041 24 $F # answer(goal). [resolve(23,a,9,a)]. 25.041/25.041 25.041/25.041 ============================== end of proof ========================== 25.041/25.041 25.041/25.041 ============================== STATISTICS ============================ 25.041/25.041 25.041/25.041 Given=0. Generated=15. Kept=15. proofs=1. 25.041/25.041 Usable=0. Sos=0. Demods=0. Limbo=14, Disabled=15. Hints=0. 25.041/25.041 Kept_by_rule=0, Deleted_by_rule=0. 25.041/25.041 Forward_subsumed=0. Back_subsumed=0. 25.041/25.041 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 25.041/25.041 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 25.041/25.041 Demod_attempts=0. Demod_rewrites=0. 25.041/25.041 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 25.041/25.041 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. 25.041/25.041 Megabytes=0.05. 25.041/25.041 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.041/25.041 25.041/25.041 ============================== end of statistics ===================== 25.041/25.041 25.041/25.041 ============================== end of search ========================= 25.041/25.041 25.041/25.041 THEOREM PROVED 25.041/25.041 25.041/25.041 Exiting with 1 proof. 25.041/25.041 25.041/25.041 Process 111277 exit (max_proofs) Fri Jul 16 15:10:58 2021 25.041/25.041 25.041/25.041 25.041/25.041 The problem is feasible. 25.041/25.041 25.041/25.041 25.041/25.041 CRule InfChecker Info: 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 Rule remains 25.041/25.041 Proof: 25.041/25.041 NO_CONDS 25.041/25.041 25.041/25.041 CRule InfChecker Info: 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 Rule remains 25.041/25.041 Proof: 25.041/25.041 NO_CONDS 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 Confluence Problem: 25.041/25.041 (VAR x:S) 25.041/25.041 (STRATEGY CONTEXTSENSITIVE 25.041/25.041 (a) 25.041/25.041 (b) 25.041/25.041 (f 1) 25.041/25.041 (g 1 2) 25.041/25.041 (h 1 2) 25.041/25.041 (c) 25.041/25.041 (d) 25.041/25.041 (fSNonEmpty) 25.041/25.041 ) 25.041/25.041 (RULES 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 ) 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 25.041/25.041 Critical Pairs Processor: 25.041/25.041 -> Rules: 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 -> Vars: 25.041/25.041 "x", "x", "x" 25.041/25.041 -> FVars: 25.041/25.041 "x2", "x3", "x4" 25.041/25.041 -> PVars: 25.041/25.041 "x": ["x2", "x3", "x4"] 25.041/25.041 25.041/25.041 -> Rlps: 25.041/25.041 crule: a -> c, id: 1, possubterms: a-> [] 25.041/25.041 crule: a -> d, id: 2, possubterms: a-> [] 25.041/25.041 crule: b -> c, id: 3, possubterms: b-> [] 25.041/25.041 crule: b -> d, id: 4, possubterms: b-> [] 25.041/25.041 crule: f(x2:S) -> x2:S | x2:S ->* c, id: 5, possubterms: f(x2:S)-> [] 25.041/25.041 crule: g(x3:S,x3:S) -> h(x3:S,x3:S), id: 6, possubterms: g(x3:S,x3:S)-> [] 25.041/25.041 crule: h(x4:S,f(x4:S)) -> x4:S, id: 7, possubterms: h(x4:S,f(x4:S))-> [], f(x4:S)-> [2] 25.041/25.041 25.041/25.041 -> Unifications: 25.041/25.041 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 25.041/25.041 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 25.041/25.041 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 25.041/25.041 25.041/25.041 -> Critical pairs info: 25.041/25.041 => Not trivial, Overlay, N1 25.041/25.041 | x:S ->* c => Not trivial, Not overlay, N2 25.041/25.041 25.041/25.041 -> Problem conclusions: 25.041/25.041 Not left linear, Not right linear, Not linear 25.041/25.041 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 25.041/25.041 CTRS Type: 1 25.041/25.041 Deterministic, Strongly deterministic 25.041/25.041 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.041/25.041 Maybe right-stable CTRS, Not overlay CTRS 25.041/25.041 Maybe normal CTRS, Maybe almost normal CTRS 25.041/25.041 Maybe terminating CTRS, Maybe joinable CCPs 25.041/25.041 Maybe level confluent 25.041/25.041 Maybe confluent 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 Confluence Problem: 25.041/25.041 (VAR x:S) 25.041/25.041 (STRATEGY CONTEXTSENSITIVE 25.041/25.041 (a) 25.041/25.041 (b) 25.041/25.041 (f 1) 25.041/25.041 (g 1 2) 25.041/25.041 (h 1 2) 25.041/25.041 (c) 25.041/25.041 (d) 25.041/25.041 (fSNonEmpty) 25.041/25.041 ) 25.041/25.041 (RULES 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 ) 25.041/25.041 Critical Pairs: 25.041/25.041 => Not trivial, Overlay, N1 25.041/25.041 | x:S ->* c => Not trivial, Not overlay, N2 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 25.041/25.041 Conditional Critical Pairs Distributor Processor 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 Confluence Problem: 25.041/25.041 (VAR x:S) 25.041/25.041 (STRATEGY CONTEXTSENSITIVE 25.041/25.041 (a) 25.041/25.041 (b) 25.041/25.041 (f 1) 25.041/25.041 (g 1 2) 25.041/25.041 (h 1 2) 25.041/25.041 (c) 25.041/25.041 (d) 25.041/25.041 (fSNonEmpty) 25.041/25.041 ) 25.041/25.041 (RULES 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 ) 25.041/25.041 Critical Pairs: 25.041/25.041 => Not trivial, Overlay, N1 25.041/25.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.041/25.041 25.041/25.041 Infeasible Convergence No Conditions CCP Processor: 25.041/25.041 Infeasible convergence? 25.041/25.041 YES 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 25.041/25.041 Infeasibility Problem: 25.041/25.041 [(VAR vNonEmpty:S x:S z:S) 25.041/25.041 (STRATEGY CONTEXTSENSITIVE 25.041/25.041 (a) 25.041/25.041 (b) 25.041/25.041 (f 1) 25.041/25.041 (g 1 2) 25.041/25.041 (h 1 2) 25.041/25.041 (c) 25.041/25.041 (d) 25.041/25.041 (fSNonEmpty) 25.041/25.041 ) 25.041/25.041 (RULES 25.041/25.041 a -> c 25.041/25.041 a -> d 25.041/25.041 b -> c 25.041/25.041 b -> d 25.041/25.041 f(x:S) -> x:S | x:S ->* c 25.041/25.041 g(x:S,x:S) -> h(x:S,x:S) 25.041/25.041 h(x:S,f(x:S)) -> x:S 25.041/25.041 )] 25.041/25.041 25.041/25.041 Infeasibility Conditions: 25.041/25.041 c ->* z:S, d ->* z:S 25.041/25.041 25.041/25.041 Problem 1: 25.041/25.041 25.041/25.041 Obtaining a model using Mace4: 25.041/25.041 25.041/25.041 -> Usable Rules: 25.041/25.041 Empty 25.041/25.041 25.041/25.041 -> Mace4 Output: 25.041/25.041 ============================== Mace4 ================================= 25.041/25.041 Mace4 (64) version 2009-11A, November 2009. 25.041/25.041 Process 111334 was started by ubuntu on ubuntu, 25.041/25.041 Fri Jul 16 15:10:59 2021 25.041/25.041 The command was "./mace4 -c -f /tmp/mace4111294-2.in". 25.041/25.041 ============================== end of head =========================== 25.041/25.041 25.041/25.041 ============================== INPUT ================================= 25.041/25.041 25.041/25.041 % Reading from file /tmp/mace4111294-2.in 25.041/25.041 25.041/25.041 assign(max_seconds,10). 25.041/25.041 25.041/25.041 formulas(assumptions). 25.041/25.041 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 25.041/25.041 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 25.041/25.041 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 25.041/25.041 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 25.041/25.041 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 25.041/25.041 ->*(x,x) # label(reflexivity). 25.041/25.041 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 25.041/25.041 end_of_list. 25.041/25.041 25.041/25.041 formulas(goals). 25.041/25.041 (exists x2 (->*(c,x2) & ->*(d,x2))) # label(goal). 25.041/25.041 end_of_list. 25.041/25.041 25.041/25.041 ============================== end of input ========================== 25.041/25.041 25.041/25.041 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.041/25.041 25.041/25.041 % Formulas that are not ordinary clauses: 25.041/25.041 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 4 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 5 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.041/25.041 6 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.041/25.041 7 (exists x2 (->*(c,x2) & ->*(d,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 25.041/25.041 25.041/25.041 ============================== end of process non-clausal formulas === 25.041/25.041 25.041/25.041 ============================== CLAUSES FOR SEARCH ==================== 25.041/25.041 25.041/25.041 formulas(mace4_clauses). 25.041/25.041 -->(x,y) | ->(f(x),f(y)) # label(congruence). 25.041/25.041 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 25.041/25.041 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 25.041/25.041 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 25.041/25.041 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 25.041/25.041 ->*(x,x) # label(reflexivity). 25.041/25.041 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 25.041/25.041 -->*(c,x) | -->*(d,x) # label(goal). 25.041/25.041 end_of_list. 25.041/25.041 25.041/25.041 ============================== end of clauses for search ============= 25.041/25.041 25.041/25.041 % There are no natural numbers in the input. 25.041/25.041 25.041/25.041 ============================== DOMAIN SIZE 2 ========================= 25.041/25.041 25.041/25.041 ============================== MODEL ================================= 25.041/25.041 25.041/25.041 interpretation( 2, [number=1, seconds=0], [ 25.041/25.041 25.041/25.041 function(c, [ 0 ]), 25.041/25.041 25.041/25.041 function(d, [ 1 ]), 25.041/25.041 25.041/25.041 function(f(_), [ 0, 0 ]), 25.041/25.041 25.041/25.041 function(g(_,_), [ 25.041/25.041 0, 0, 25.041/25.041 0, 0 ]), 25.041/25.041 25.041/25.041 function(h(_,_), [ 25.041/25.041 0, 0, 25.041/25.041 0, 0 ]), 25.041/25.041 25.041/25.041 relation(->*(_,_), [ 25.041/25.041 1, 0, 25.041/25.041 0, 1 ]), 25.041/25.041 25.041/25.041 relation(->(_,_), [ 25.041/25.041 0, 0, 25.041/25.041 0, 0 ]) 25.041/25.041 ]). 25.041/25.041 25.041/25.041 ============================== end of model ========================== 25.041/25.041 25.041/25.041 ============================== STATISTICS ============================ 25.041/25.041 25.041/25.041 For domain size 2. 25.041/25.041 25.041/25.041 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.041/25.041 Ground clauses: seen=48, kept=44. 25.041/25.041 Selections=12, assignments=12, propagations=8, current_models=1. 25.041/25.041 Rewrite_terms=76, rewrite_bools=56, indexes=7. 25.041/25.041 Rules_from_neg_clauses=1, cross_offs=1. 25.041/25.041 25.041/25.041 ============================== end of statistics ===================== 25.041/25.041 25.041/25.041 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.041/25.041 25.041/25.041 Exiting with 1 model. 25.041/25.041 25.041/25.041 Process 111334 exit (max_models) Fri Jul 16 15:10:59 2021 25.041/25.041 The process finished Fri Jul 16 15:10:59 2021 25.041/25.041 25.041/25.041 25.041/25.041 Mace4 cooked interpretation: 25.041/25.041 25.041/25.041 25.041/25.041 25.041/25.041 The problem is infeasible. 25.041/25.041 25.041/25.041 25.041/25.041 The problem is not joinable. 25.041/25.041 27.34user 0.96system 0:25.41elapsed 111%CPU (0avgtext+0avgdata 135816maxresident)k 25.041/25.041 8inputs+0outputs (0major+94930minor)pagefaults 0swaps