20.044/20.044 NO 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 20.044/20.044 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 Confluence Problem: 20.044/20.044 (VAR vNonEmpty:S x:S y:S z:S) 20.044/20.044 (STRATEGY CONTEXTSENSITIVE 20.044/20.044 (a) 20.044/20.044 (f 1 2) 20.044/20.044 (k 1) 20.044/20.044 (b) 20.044/20.044 (fSNonEmpty) 20.044/20.044 (g 1 2) 20.044/20.044 (h 1) 20.044/20.044 ) 20.044/20.044 (RULES 20.044/20.044 a -> b 20.044/20.044 f(y:S,a) -> g(x:S,x:S) | h(z:S) ->* x:S, y:S ->* k(z:S) 20.044/20.044 k(x:S) -> a 20.044/20.044 k(x:S) -> b 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 ) 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 20.044/20.044 Inlining of Conditions Processor [STERN17]: 20.044/20.044 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 Confluence Problem: 20.044/20.044 (VAR vNonEmpty:S x:S y:S z:S) 20.044/20.044 (STRATEGY CONTEXTSENSITIVE 20.044/20.044 (a) 20.044/20.044 (f 1 2) 20.044/20.044 (k 1) 20.044/20.044 (b) 20.044/20.044 (fSNonEmpty) 20.044/20.044 (g 1 2) 20.044/20.044 (h 1) 20.044/20.044 ) 20.044/20.044 (RULES 20.044/20.044 a -> b 20.044/20.044 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.044/20.044 k(x:S) -> a 20.044/20.044 k(x:S) -> b 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 ) 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 20.044/20.044 Clean CTRS Processor: 20.044/20.044 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 Confluence Problem: 20.044/20.044 (VAR x:S y:S z:S) 20.044/20.044 (STRATEGY CONTEXTSENSITIVE 20.044/20.044 (a) 20.044/20.044 (f 1 2) 20.044/20.044 (k 1) 20.044/20.044 (b) 20.044/20.044 (fSNonEmpty) 20.044/20.044 (g 1 2) 20.044/20.044 (h 1) 20.044/20.044 ) 20.044/20.044 (RULES 20.044/20.044 a -> b 20.044/20.044 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.044/20.044 k(x:S) -> a 20.044/20.044 k(x:S) -> b 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 ) 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 20.044/20.044 CRule InfChecker Info: 20.044/20.044 a -> b 20.044/20.044 Rule remains 20.044/20.044 Proof: 20.044/20.044 NO_CONDS 20.044/20.044 20.044/20.044 CRule InfChecker Info: 20.044/20.044 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.044/20.044 Rule remains 20.044/20.044 Proof: 20.044/20.044 NO 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 20.044/20.044 Infeasibility Problem: 20.044/20.044 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S y:S:S z:S:S) 20.044/20.044 (STRATEGY CONTEXTSENSITIVE 20.044/20.044 (a) 20.044/20.044 (f 1 2) 20.044/20.044 (k 1) 20.044/20.044 (b) 20.044/20.044 (fSNonEmpty) 20.044/20.044 (g 1 2) 20.044/20.044 (h 1) 20.044/20.044 ) 20.044/20.044 (RULES 20.044/20.044 a -> b 20.044/20.044 f(y:S:S,a) -> g(h(z:S:S),h(z:S:S)) | y:S:S ->* k(z:S:S) 20.044/20.044 k(x:S:S) -> a 20.044/20.044 k(x:S:S) -> b 20.044/20.044 k(x:S:S) -> h(x:S:S) 20.044/20.044 )] 20.044/20.044 20.044/20.044 Infeasibility Conditions: 20.044/20.044 y:S:S ->* k(z:S:S) 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 20.044/20.044 Obtaining a proof using Prover9: 20.044/20.044 20.044/20.044 -> Prover9 Output: 20.044/20.044 ============================== Prover9 =============================== 20.044/20.044 Prover9 (64) version 2009-11A, November 2009. 20.044/20.044 Process 66444 was started by ubuntu on ubuntu, 20.044/20.044 Wed Jul 14 11:53:11 2021 20.044/20.044 The command was "./prover9 -f /tmp/prover966435-0.in". 20.044/20.044 ============================== end of head =========================== 20.044/20.044 20.044/20.044 ============================== INPUT ================================= 20.044/20.044 20.044/20.044 % Reading from file /tmp/prover966435-0.in 20.044/20.044 20.044/20.044 assign(max_seconds,20). 20.044/20.044 20.044/20.044 formulas(assumptions). 20.044/20.044 ->*_s0(x,x) # label(reflexivity). 20.044/20.044 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.044/20.044 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 20.044/20.044 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 20.044/20.044 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence). 20.044/20.044 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 20.044/20.044 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 20.044/20.044 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 20.044/20.044 ->_s0(a,b) # label(replacement). 20.044/20.044 ->*_s0(x3,k(x4)) -> ->_s0(f(x3,a),g(h(x4),h(x4))) # label(replacement). 20.044/20.044 ->_s0(k(x2),a) # label(replacement). 20.044/20.044 ->_s0(k(x2),b) # label(replacement). 20.044/20.044 ->_s0(k(x2),h(x2)) # label(replacement). 20.044/20.044 end_of_list. 20.044/20.044 20.044/20.044 formulas(goals). 20.044/20.044 (exists x3 exists x4 ->*_s0(x3,k(x4))) # label(goal). 20.044/20.044 end_of_list. 20.044/20.044 20.044/20.044 ============================== end of input ========================== 20.044/20.044 20.044/20.044 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.044/20.044 20.044/20.044 % Formulas that are not ordinary clauses: 20.044/20.044 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.044/20.044 2 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 3 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 4 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 5 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 6 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 7 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 8 ->*_s0(x3,k(x4)) -> ->_s0(f(x3,a),g(h(x4),h(x4))) # label(replacement) # label(non_clause). [assumption]. 20.044/20.044 9 (exists x3 exists x4 ->*_s0(x3,k(x4))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.044/20.044 20.044/20.044 ============================== end of process non-clausal formulas === 20.044/20.044 20.044/20.044 ============================== PROCESS INITIAL CLAUSES =============== 20.044/20.044 20.044/20.044 % Clauses before input processing: 20.044/20.044 20.044/20.044 formulas(usable). 20.044/20.044 end_of_list. 20.044/20.044 20.044/20.044 formulas(sos). 20.044/20.044 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.044/20.044 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.044/20.044 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 20.044/20.044 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 20.044/20.044 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(4)]. 20.044/20.044 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(5)]. 20.044/20.044 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(6)]. 20.044/20.044 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(7)]. 20.044/20.044 ->_s0(a,b) # label(replacement). [assumption]. 20.044/20.044 -->*_s0(x,k(y)) | ->_s0(f(x,a),g(h(y),h(y))) # label(replacement). [clausify(8)]. 20.044/20.044 ->_s0(k(x),a) # label(replacement). [assumption]. 20.044/20.044 ->_s0(k(x),b) # label(replacement). [assumption]. 20.044/20.044 ->_s0(k(x),h(x)) # label(replacement). [assumption]. 20.044/20.044 -->*_s0(x,k(y)) # label(goal). [deny(9)]. 20.044/20.044 end_of_list. 20.044/20.044 20.044/20.044 formulas(demodulators). 20.044/20.044 end_of_list. 20.044/20.044 20.044/20.044 ============================== PREDICATE ELIMINATION ================= 20.044/20.044 20.044/20.044 No predicates eliminated. 20.044/20.044 20.044/20.044 ============================== end predicate elimination ============= 20.044/20.044 20.044/20.044 Auto_denials: 20.044/20.044 % copying label goal to answer in negative clause 20.044/20.044 20.044/20.044 Term ordering decisions: 20.044/20.044 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.044/20.044 Function symbol precedence: function_order([ a, b, f, g, k, h ]). 20.044/20.044 After inverse_order: (no changes). 20.044/20.044 Unfolding symbols: (none). 20.044/20.044 20.044/20.044 Auto_inference settings: 20.044/20.044 % set(neg_binary_resolution). % (HNE depth_diff=-7) 20.044/20.044 % clear(ordered_res). % (HNE depth_diff=-7) 20.044/20.044 % set(ur_resolution). % (HNE depth_diff=-7) 20.044/20.044 % set(ur_resolution) -> set(pos_ur_resolution). 20.044/20.044 % set(ur_resolution) -> set(neg_ur_resolution). 20.044/20.044 20.044/20.044 Auto_process settings: (no changes). 20.044/20.044 20.044/20.044 kept: 10 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.044/20.044 kept: 11 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.044/20.044 kept: 12 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 20.044/20.044 kept: 13 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 20.044/20.044 kept: 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(4)]. 20.044/20.044 kept: 15 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(5)]. 20.044/20.044 kept: 16 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(6)]. 20.044/20.044 kept: 17 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(7)]. 20.044/20.044 kept: 18 ->_s0(a,b) # label(replacement). [assumption]. 20.044/20.044 kept: 19 -->*_s0(x,k(y)) | ->_s0(f(x,a),g(h(y),h(y))) # label(replacement). [clausify(8)]. 20.044/20.044 kept: 20 ->_s0(k(x),a) # label(replacement). [assumption]. 20.044/20.044 kept: 21 ->_s0(k(x),b) # label(replacement). [assumption]. 20.044/20.044 kept: 22 ->_s0(k(x),h(x)) # label(replacement). [assumption]. 20.044/20.044 kept: 23 -->*_s0(x,k(y)) # label(goal) # answer(goal). [deny(9)]. 20.044/20.044 20.044/20.044 ============================== PROOF ================================= 20.044/20.044 20.044/20.044 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.044/20.044 % Length of proof is 4. 20.044/20.044 % Level of proof is 2. 20.044/20.044 % Maximum clause weight is 4.000. 20.044/20.044 % Given clauses 0. 20.044/20.044 20.044/20.044 9 (exists x3 exists x4 ->*_s0(x3,k(x4))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.044/20.044 10 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.044/20.044 23 -->*_s0(x,k(y)) # label(goal) # answer(goal). [deny(9)]. 20.044/20.044 24 $F # answer(goal). [resolve(23,a,10,a)]. 20.044/20.044 20.044/20.044 ============================== end of proof ========================== 20.044/20.044 20.044/20.044 ============================== STATISTICS ============================ 20.044/20.044 20.044/20.044 Given=0. Generated=14. Kept=14. proofs=1. 20.044/20.044 Usable=0. Sos=0. Demods=0. Limbo=13, Disabled=14. Hints=0. 20.044/20.044 Kept_by_rule=0, Deleted_by_rule=0. 20.044/20.044 Forward_subsumed=0. Back_subsumed=0. 20.044/20.044 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.044/20.044 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.044/20.044 Demod_attempts=0. Demod_rewrites=0. 20.044/20.044 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.044/20.044 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. 20.044/20.044 Megabytes=0.06. 20.044/20.044 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.044/20.044 20.044/20.044 ============================== end of statistics ===================== 20.044/20.044 20.044/20.044 ============================== end of search ========================= 20.044/20.044 20.044/20.044 THEOREM PROVED 20.044/20.044 20.044/20.044 Exiting with 1 proof. 20.044/20.044 20.044/20.044 Process 66444 exit (max_proofs) Wed Jul 14 11:53:11 2021 20.044/20.044 20.044/20.044 20.044/20.044 The problem is feasible. 20.044/20.044 20.044/20.044 20.044/20.044 CRule InfChecker Info: 20.044/20.044 k(x:S) -> a 20.044/20.044 Rule remains 20.044/20.044 Proof: 20.044/20.044 NO_CONDS 20.044/20.044 20.044/20.044 CRule InfChecker Info: 20.044/20.044 k(x:S) -> b 20.044/20.044 Rule remains 20.044/20.044 Proof: 20.044/20.044 NO_CONDS 20.044/20.044 20.044/20.044 CRule InfChecker Info: 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 Rule remains 20.044/20.044 Proof: 20.044/20.044 NO_CONDS 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 Confluence Problem: 20.044/20.044 (VAR x:S y:S z:S) 20.044/20.044 (STRATEGY CONTEXTSENSITIVE 20.044/20.044 (a) 20.044/20.044 (f 1 2) 20.044/20.044 (k 1) 20.044/20.044 (b) 20.044/20.044 (fSNonEmpty) 20.044/20.044 (g 1 2) 20.044/20.044 (h 1) 20.044/20.044 ) 20.044/20.044 (RULES 20.044/20.044 a -> b 20.044/20.044 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.044/20.044 k(x:S) -> a 20.044/20.044 k(x:S) -> b 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 ) 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 20.044/20.044 Critical Pairs Processor: 20.044/20.044 -> Rules: 20.044/20.044 a -> b 20.044/20.044 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.044/20.044 k(x:S) -> a 20.044/20.044 k(x:S) -> b 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 -> Vars: 20.044/20.044 "y", "z", "x", "x", "x" 20.044/20.044 -> FVars: 20.044/20.044 "x4", "x5", "x6", "x7", "x8" 20.044/20.044 -> PVars: 20.044/20.044 "y": ["x4"], "z": ["x5"], "x": ["x6", "x7", "x8"] 20.044/20.044 20.044/20.044 -> Rlps: 20.044/20.044 crule: a -> b, id: 1, possubterms: a-> [] 20.044/20.044 crule: f(x4:S,a) -> g(h(x5:S),h(x5:S)) | x4:S ->* k(x5:S), id: 2, possubterms: f(x4:S,a)-> [], a-> [2] 20.044/20.044 crule: k(x6:S) -> a, id: 3, possubterms: k(x6:S)-> [] 20.044/20.044 crule: k(x7:S) -> b, id: 4, possubterms: k(x7:S)-> [] 20.044/20.044 crule: k(x8:S) -> h(x8:S), id: 5, possubterms: k(x8:S)-> [] 20.044/20.044 20.044/20.044 -> Unifications: 20.044/20.044 R2 unifies with R1 at p: [2], l: f(x4:S,a), lp: a, conds: {x4:S ->* k(x5:S)}, sig: {}, l': a, r: g(h(x5:S),h(x5:S)), r': b 20.044/20.044 R4 unifies with R3 at p: [], l: k(x7:S), lp: k(x7:S), conds: {}, sig: {x7:S -> x:S}, l': k(x:S), r: b, r': a 20.044/20.044 R5 unifies with R3 at p: [], l: k(x8:S), lp: k(x8:S), conds: {}, sig: {x8:S -> x:S}, l': k(x:S), r: h(x8:S), r': a 20.044/20.044 R5 unifies with R4 at p: [], l: k(x8:S), lp: k(x8:S), conds: {}, sig: {x8:S -> x:S}, l': k(x:S), r: h(x8:S), r': b 20.044/20.044 20.044/20.044 -> Critical pairs info: 20.044/20.044 => Not trivial, Overlay, N1 20.044/20.044 => Not trivial, Overlay, N2 20.044/20.044 => Not trivial, Overlay, N3 20.044/20.044 | y:S ->* k(z:S) => Not trivial, Not overlay, N4 20.044/20.044 20.044/20.044 -> Problem conclusions: 20.044/20.044 Left linear, Not right linear, Not linear 20.044/20.044 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.044/20.044 CTRS Type: 3 20.044/20.044 Deterministic, Maybe strongly deterministic 20.044/20.044 Oriented CTRS, Properly oriented CTRS, Not join CTRS 20.044/20.044 Maybe right-stable CTRS, Not overlay CTRS 20.044/20.044 Maybe normal CTRS, Maybe almost normal CTRS 20.044/20.044 Maybe terminating CTRS, Maybe joinable CCPs 20.044/20.044 Maybe level confluent 20.044/20.044 Maybe confluent 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 Confluence Problem: 20.044/20.044 (VAR x:S y:S z:S) 20.044/20.044 (STRATEGY CONTEXTSENSITIVE 20.044/20.044 (a) 20.044/20.044 (f 1 2) 20.044/20.044 (k 1) 20.044/20.044 (b) 20.044/20.044 (fSNonEmpty) 20.044/20.044 (g 1 2) 20.044/20.044 (h 1) 20.044/20.044 ) 20.044/20.044 (RULES 20.044/20.044 a -> b 20.044/20.044 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.044/20.044 k(x:S) -> a 20.044/20.044 k(x:S) -> b 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 ) 20.044/20.044 Critical Pairs: 20.044/20.044 => Not trivial, Overlay, N1 20.044/20.044 => Not trivial, Overlay, N2 20.044/20.044 => Not trivial, Overlay, N3 20.044/20.044 | y:S ->* k(z:S) => Not trivial, Not overlay, N4 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 20.044/20.044 Conditional Critical Pairs Distributor Processor 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 Confluence Problem: 20.044/20.044 (VAR x:S y:S z:S) 20.044/20.044 (STRATEGY CONTEXTSENSITIVE 20.044/20.044 (a) 20.044/20.044 (f 1 2) 20.044/20.044 (k 1) 20.044/20.044 (b) 20.044/20.044 (fSNonEmpty) 20.044/20.044 (g 1 2) 20.044/20.044 (h 1) 20.044/20.044 ) 20.044/20.044 (RULES 20.044/20.044 a -> b 20.044/20.044 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.044/20.044 k(x:S) -> a 20.044/20.044 k(x:S) -> b 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 ) 20.044/20.044 Critical Pairs: 20.044/20.044 => Not trivial, Overlay, N2 20.044/20.044 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.044/20.044 20.044/20.044 Infeasible Convergence No Conditions CCP Processor: 20.044/20.044 Infeasible convergence? 20.044/20.044 YES 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 20.044/20.044 Infeasibility Problem: 20.044/20.044 [(VAR vNonEmpty:S x:S y:S z:S) 20.044/20.044 (STRATEGY CONTEXTSENSITIVE 20.044/20.044 (a) 20.044/20.044 (f 1 2) 20.044/20.044 (k 1) 20.044/20.044 (b) 20.044/20.044 (cx) 20.044/20.044 (fSNonEmpty) 20.044/20.044 (g 1 2) 20.044/20.044 (h 1) 20.044/20.044 ) 20.044/20.044 (RULES 20.044/20.044 a -> b 20.044/20.044 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.044/20.044 k(x:S) -> a 20.044/20.044 k(x:S) -> b 20.044/20.044 k(x:S) -> h(x:S) 20.044/20.044 )] 20.044/20.044 20.044/20.044 Infeasibility Conditions: 20.044/20.044 b ->* z:S, h(cx) ->* z:S 20.044/20.044 20.044/20.044 Problem 1: 20.044/20.044 20.044/20.044 Obtaining a model using Mace4: 20.044/20.044 20.044/20.044 -> Usable Rules: 20.044/20.044 Empty 20.044/20.044 20.044/20.044 -> Mace4 Output: 20.044/20.044 ============================== Mace4 ================================= 20.044/20.044 Mace4 (64) version 2009-11A, November 2009. 20.044/20.044 Process 66516 was started by ubuntu on ubuntu, 20.044/20.044 Wed Jul 14 11:53:11 2021 20.044/20.044 The command was "./mace4 -c -f /tmp/mace466502-2.in". 20.044/20.044 ============================== end of head =========================== 20.044/20.044 20.044/20.044 ============================== INPUT ================================= 20.044/20.044 20.044/20.044 % Reading from file /tmp/mace466502-2.in 20.044/20.044 20.044/20.044 assign(max_seconds,20). 20.044/20.044 20.044/20.044 formulas(assumptions). 20.044/20.044 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 20.044/20.044 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 20.044/20.044 ->(x1,y) -> ->(k(x1),k(y)) # label(congruence). 20.044/20.044 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 20.044/20.044 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 20.044/20.044 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence). 20.044/20.044 ->*(x,x) # label(reflexivity). 20.044/20.044 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.044/20.044 end_of_list. 20.044/20.044 20.044/20.044 formulas(goals). 20.044/20.044 (exists x3 (->*(b,x3) & ->*(h(cx),x3))) # label(goal). 20.044/20.044 end_of_list. 20.044/20.044 20.044/20.044 ============================== end of input ========================== 20.044/20.044 20.044/20.044 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.044/20.044 20.044/20.044 % Formulas that are not ordinary clauses: 20.044/20.044 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 3 ->(x1,y) -> ->(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 4 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 5 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 6 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 20.044/20.044 7 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.044/20.044 8 (exists x3 (->*(b,x3) & ->*(h(cx),x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.044/20.044 20.044/20.044 ============================== end of process non-clausal formulas === 20.044/20.044 20.044/20.044 ============================== CLAUSES FOR SEARCH ==================== 20.044/20.044 20.044/20.044 formulas(mace4_clauses). 20.044/20.044 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 20.044/20.044 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 20.044/20.044 -->(x,y) | ->(k(x),k(y)) # label(congruence). 20.044/20.044 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 20.044/20.044 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 20.044/20.044 -->(x,y) | ->(h(x),h(y)) # label(congruence). 20.044/20.044 ->*(x,x) # label(reflexivity). 20.044/20.044 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.044/20.044 -->*(b,x) | -->*(h(cx),x) # label(goal). 20.044/20.044 end_of_list. 20.044/20.044 20.044/20.044 ============================== end of clauses for search ============= 20.044/20.044 20.044/20.044 % There are no natural numbers in the input. 20.044/20.044 20.044/20.044 ============================== DOMAIN SIZE 2 ========================= 20.044/20.044 20.044/20.044 ============================== MODEL ================================= 20.044/20.044 20.044/20.044 interpretation( 2, [number=1, seconds=0], [ 20.044/20.044 20.044/20.044 function(b, [ 0 ]), 20.044/20.044 20.044/20.044 function(cx, [ 0 ]), 20.044/20.044 20.044/20.044 function(k(_), [ 0, 0 ]), 20.044/20.044 20.044/20.044 function(h(_), [ 1, 0 ]), 20.044/20.044 20.044/20.044 function(f(_,_), [ 20.044/20.044 0, 0, 20.044/20.044 0, 0 ]), 20.044/20.044 20.044/20.044 function(g(_,_), [ 20.044/20.044 0, 0, 20.044/20.044 0, 0 ]), 20.044/20.044 20.044/20.044 relation(->*(_,_), [ 20.044/20.044 1, 0, 20.044/20.044 0, 1 ]), 20.044/20.044 20.044/20.044 relation(->(_,_), [ 20.044/20.044 0, 0, 20.044/20.044 0, 0 ]) 20.044/20.044 ]). 20.044/20.044 20.044/20.044 ============================== end of model ========================== 20.044/20.044 20.044/20.044 ============================== STATISTICS ============================ 20.044/20.044 20.044/20.044 For domain size 2. 20.044/20.044 20.044/20.044 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.044/20.044 Ground clauses: seen=52, kept=48. 20.044/20.044 Selections=14, assignments=14, propagations=8, current_models=1. 20.044/20.044 Rewrite_terms=86, rewrite_bools=60, indexes=10. 20.044/20.044 Rules_from_neg_clauses=1, cross_offs=1. 20.044/20.044 20.044/20.044 ============================== end of statistics ===================== 20.044/20.044 20.044/20.044 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.044/20.044 20.044/20.044 Exiting with 1 model. 20.044/20.044 20.044/20.044 Process 66516 exit (max_models) Wed Jul 14 11:53:11 2021 20.044/20.044 The process finished Wed Jul 14 11:53:11 2021 20.044/20.044 20.044/20.044 20.044/20.044 Mace4 cooked interpretation: 20.044/20.044 20.044/20.044 20.044/20.044 20.044/20.044 The problem is infeasible. 20.044/20.044 20.044/20.044 20.044/20.044 The problem is not joinable. 20.044/20.044 23.34user 0.77system 0:20.44elapsed 117%CPU (0avgtext+0avgdata 136104maxresident)k 20.044/20.044 8inputs+0outputs (0major+70874minor)pagefaults 0swaps