20.041/20.041 NO 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 20.041/20.041 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 Confluence Problem: 20.041/20.041 (VAR vNonEmpty:S x:S y:S z:S) 20.041/20.041 (STRATEGY CONTEXTSENSITIVE 20.041/20.041 (a) 20.041/20.041 (f 1 2) 20.041/20.041 (k 1) 20.041/20.041 (b) 20.041/20.041 (fSNonEmpty) 20.041/20.041 (g 1 2) 20.041/20.041 (h 1) 20.041/20.041 ) 20.041/20.041 (RULES 20.041/20.041 a -> b 20.041/20.041 f(y:S,a) -> g(x:S,x:S) | h(z:S) ->* x:S, y:S ->* k(z:S) 20.041/20.041 k(x:S) -> a 20.041/20.041 k(x:S) -> b 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 ) 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 20.041/20.041 Inlining of Conditions Processor [STERN17]: 20.041/20.041 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 Confluence Problem: 20.041/20.041 (VAR vNonEmpty:S x:S y:S z:S) 20.041/20.041 (STRATEGY CONTEXTSENSITIVE 20.041/20.041 (a) 20.041/20.041 (f 1 2) 20.041/20.041 (k 1) 20.041/20.041 (b) 20.041/20.041 (fSNonEmpty) 20.041/20.041 (g 1 2) 20.041/20.041 (h 1) 20.041/20.041 ) 20.041/20.041 (RULES 20.041/20.041 a -> b 20.041/20.041 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.041/20.041 k(x:S) -> a 20.041/20.041 k(x:S) -> b 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 ) 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 20.041/20.041 Clean CTRS Processor: 20.041/20.041 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 Confluence Problem: 20.041/20.041 (VAR x:S y:S z:S) 20.041/20.041 (STRATEGY CONTEXTSENSITIVE 20.041/20.041 (a) 20.041/20.041 (f 1 2) 20.041/20.041 (k 1) 20.041/20.041 (b) 20.041/20.041 (fSNonEmpty) 20.041/20.041 (g 1 2) 20.041/20.041 (h 1) 20.041/20.041 ) 20.041/20.041 (RULES 20.041/20.041 a -> b 20.041/20.041 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.041/20.041 k(x:S) -> a 20.041/20.041 k(x:S) -> b 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 ) 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 20.041/20.041 CRule InfChecker Info: 20.041/20.041 a -> b 20.041/20.041 Rule remains 20.041/20.041 Proof: 20.041/20.041 NO_CONDS 20.041/20.041 20.041/20.041 CRule InfChecker Info: 20.041/20.041 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.041/20.041 Rule remains 20.041/20.041 Proof: 20.041/20.041 NO 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 20.041/20.041 Infeasibility Problem: 20.041/20.041 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S y:S:S z:S:S) 20.041/20.041 (STRATEGY CONTEXTSENSITIVE 20.041/20.041 (a) 20.041/20.041 (f 1 2) 20.041/20.041 (k 1) 20.041/20.041 (b) 20.041/20.041 (fSNonEmpty) 20.041/20.041 (g 1 2) 20.041/20.041 (h 1) 20.041/20.041 ) 20.041/20.041 (RULES 20.041/20.041 a -> b 20.041/20.041 f(y:S:S,a) -> g(h(z:S:S),h(z:S:S)) | y:S:S ->* k(z:S:S) 20.041/20.041 k(x:S:S) -> a 20.041/20.041 k(x:S:S) -> b 20.041/20.041 k(x:S:S) -> h(x:S:S) 20.041/20.041 )] 20.041/20.041 20.041/20.041 Infeasibility Conditions: 20.041/20.041 y:S:S ->* k(z:S:S) 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 20.041/20.041 Obtaining a proof using Prover9: 20.041/20.041 20.041/20.041 -> Prover9 Output: 20.041/20.041 ============================== Prover9 =============================== 20.041/20.041 Prover9 (64) version 2009-11A, November 2009. 20.041/20.041 Process 124678 was started by ubuntu on ubuntu, 20.041/20.041 Fri Jul 16 15:49:32 2021 20.041/20.041 The command was "./prover9 -f /tmp/prover9124669-0.in". 20.041/20.041 ============================== end of head =========================== 20.041/20.041 20.041/20.041 ============================== INPUT ================================= 20.041/20.041 20.041/20.041 % Reading from file /tmp/prover9124669-0.in 20.041/20.041 20.041/20.041 assign(max_seconds,20). 20.041/20.041 20.041/20.041 formulas(assumptions). 20.041/20.041 ->*_s0(x,x) # label(reflexivity). 20.041/20.041 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.041/20.041 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 20.041/20.041 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 20.041/20.041 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence). 20.041/20.041 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 20.041/20.041 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 20.041/20.041 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence). 20.041/20.041 ->_s0(a,b) # label(replacement). 20.041/20.041 ->*_s0(x3,k(x4)) -> ->_s0(f(x3,a),g(h(x4),h(x4))) # label(replacement). 20.041/20.041 ->_s0(k(x2),a) # label(replacement). 20.041/20.041 ->_s0(k(x2),b) # label(replacement). 20.041/20.041 ->_s0(k(x2),h(x2)) # label(replacement). 20.041/20.041 end_of_list. 20.041/20.041 20.041/20.041 formulas(goals). 20.041/20.041 (exists x3 exists x4 ->*_s0(x3,k(x4))) # label(goal). 20.041/20.041 end_of_list. 20.041/20.041 20.041/20.041 ============================== end of input ========================== 20.041/20.041 20.041/20.041 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.041/20.041 20.041/20.041 % Formulas that are not ordinary clauses: 20.041/20.041 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.041/20.041 2 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 3 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 4 ->_s0(x1,y) -> ->_s0(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 5 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 6 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 7 ->_s0(x1,y) -> ->_s0(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 8 ->*_s0(x3,k(x4)) -> ->_s0(f(x3,a),g(h(x4),h(x4))) # label(replacement) # label(non_clause). [assumption]. 20.041/20.041 9 (exists x3 exists x4 ->*_s0(x3,k(x4))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.041/20.041 20.041/20.041 ============================== end of process non-clausal formulas === 20.041/20.041 20.041/20.041 ============================== PROCESS INITIAL CLAUSES =============== 20.041/20.041 20.041/20.041 % Clauses before input processing: 20.041/20.041 20.041/20.041 formulas(usable). 20.041/20.041 end_of_list. 20.041/20.041 20.041/20.041 formulas(sos). 20.041/20.041 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.041/20.041 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.041/20.041 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 20.041/20.041 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 20.041/20.041 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(4)]. 20.041/20.041 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(5)]. 20.041/20.041 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(6)]. 20.041/20.041 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(7)]. 20.041/20.041 ->_s0(a,b) # label(replacement). [assumption]. 20.041/20.041 -->*_s0(x,k(y)) | ->_s0(f(x,a),g(h(y),h(y))) # label(replacement). [clausify(8)]. 20.041/20.041 ->_s0(k(x),a) # label(replacement). [assumption]. 20.041/20.041 ->_s0(k(x),b) # label(replacement). [assumption]. 20.041/20.041 ->_s0(k(x),h(x)) # label(replacement). [assumption]. 20.041/20.041 -->*_s0(x,k(y)) # label(goal). [deny(9)]. 20.041/20.041 end_of_list. 20.041/20.041 20.041/20.041 formulas(demodulators). 20.041/20.041 end_of_list. 20.041/20.041 20.041/20.041 ============================== PREDICATE ELIMINATION ================= 20.041/20.041 20.041/20.041 No predicates eliminated. 20.041/20.041 20.041/20.041 ============================== end predicate elimination ============= 20.041/20.041 20.041/20.041 Auto_denials: 20.041/20.041 % copying label goal to answer in negative clause 20.041/20.041 20.041/20.041 Term ordering decisions: 20.041/20.041 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.041/20.041 Function symbol precedence: function_order([ a, b, f, g, k, h ]). 20.041/20.041 After inverse_order: (no changes). 20.041/20.041 Unfolding symbols: (none). 20.041/20.041 20.041/20.041 Auto_inference settings: 20.041/20.041 % set(neg_binary_resolution). % (HNE depth_diff=-7) 20.041/20.041 % clear(ordered_res). % (HNE depth_diff=-7) 20.041/20.041 % set(ur_resolution). % (HNE depth_diff=-7) 20.041/20.041 % set(ur_resolution) -> set(pos_ur_resolution). 20.041/20.041 % set(ur_resolution) -> set(neg_ur_resolution). 20.041/20.041 20.041/20.041 Auto_process settings: (no changes). 20.041/20.041 20.041/20.041 kept: 10 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.041/20.041 kept: 11 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.041/20.041 kept: 12 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 20.041/20.041 kept: 13 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 20.041/20.041 kept: 14 -->_s0(x,y) | ->_s0(k(x),k(y)) # label(congruence). [clausify(4)]. 20.041/20.041 kept: 15 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(5)]. 20.041/20.041 kept: 16 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(6)]. 20.041/20.041 kept: 17 -->_s0(x,y) | ->_s0(h(x),h(y)) # label(congruence). [clausify(7)]. 20.041/20.041 kept: 18 ->_s0(a,b) # label(replacement). [assumption]. 20.041/20.041 kept: 19 -->*_s0(x,k(y)) | ->_s0(f(x,a),g(h(y),h(y))) # label(replacement). [clausify(8)]. 20.041/20.041 kept: 20 ->_s0(k(x),a) # label(replacement). [assumption]. 20.041/20.041 kept: 21 ->_s0(k(x),b) # label(replacement). [assumption]. 20.041/20.041 kept: 22 ->_s0(k(x),h(x)) # label(replacement). [assumption]. 20.041/20.041 kept: 23 -->*_s0(x,k(y)) # label(goal) # answer(goal). [deny(9)]. 20.041/20.041 20.041/20.041 ============================== PROOF ================================= 20.041/20.041 20.041/20.041 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.041/20.041 % Length of proof is 4. 20.041/20.041 % Level of proof is 2. 20.041/20.041 % Maximum clause weight is 4.000. 20.041/20.041 % Given clauses 0. 20.041/20.041 20.041/20.041 9 (exists x3 exists x4 ->*_s0(x3,k(x4))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.041/20.041 10 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.041/20.041 23 -->*_s0(x,k(y)) # label(goal) # answer(goal). [deny(9)]. 20.041/20.041 24 $F # answer(goal). [resolve(23,a,10,a)]. 20.041/20.041 20.041/20.041 ============================== end of proof ========================== 20.041/20.041 20.041/20.041 ============================== STATISTICS ============================ 20.041/20.041 20.041/20.041 Given=0. Generated=14. Kept=14. proofs=1. 20.041/20.041 Usable=0. Sos=0. Demods=0. Limbo=13, Disabled=14. Hints=0. 20.041/20.041 Kept_by_rule=0, Deleted_by_rule=0. 20.041/20.041 Forward_subsumed=0. Back_subsumed=0. 20.041/20.041 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.041/20.041 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.041/20.041 Demod_attempts=0. Demod_rewrites=0. 20.041/20.041 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.041/20.041 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. 20.041/20.041 Megabytes=0.06. 20.041/20.041 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.041/20.041 20.041/20.041 ============================== end of statistics ===================== 20.041/20.041 20.041/20.041 ============================== end of search ========================= 20.041/20.041 20.041/20.041 THEOREM PROVED 20.041/20.041 20.041/20.041 Exiting with 1 proof. 20.041/20.041 20.041/20.041 Process 124678 exit (max_proofs) Fri Jul 16 15:49:32 2021 20.041/20.041 20.041/20.041 20.041/20.041 The problem is feasible. 20.041/20.041 20.041/20.041 20.041/20.041 CRule InfChecker Info: 20.041/20.041 k(x:S) -> a 20.041/20.041 Rule remains 20.041/20.041 Proof: 20.041/20.041 NO_CONDS 20.041/20.041 20.041/20.041 CRule InfChecker Info: 20.041/20.041 k(x:S) -> b 20.041/20.041 Rule remains 20.041/20.041 Proof: 20.041/20.041 NO_CONDS 20.041/20.041 20.041/20.041 CRule InfChecker Info: 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 Rule remains 20.041/20.041 Proof: 20.041/20.041 NO_CONDS 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 Confluence Problem: 20.041/20.041 (VAR x:S y:S z:S) 20.041/20.041 (STRATEGY CONTEXTSENSITIVE 20.041/20.041 (a) 20.041/20.041 (f 1 2) 20.041/20.041 (k 1) 20.041/20.041 (b) 20.041/20.041 (fSNonEmpty) 20.041/20.041 (g 1 2) 20.041/20.041 (h 1) 20.041/20.041 ) 20.041/20.041 (RULES 20.041/20.041 a -> b 20.041/20.041 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.041/20.041 k(x:S) -> a 20.041/20.041 k(x:S) -> b 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 ) 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 20.041/20.041 Critical Pairs Processor: 20.041/20.041 -> Rules: 20.041/20.041 a -> b 20.041/20.041 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.041/20.041 k(x:S) -> a 20.041/20.041 k(x:S) -> b 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 -> Vars: 20.041/20.041 "y", "z", "x", "x", "x" 20.041/20.041 -> FVars: 20.041/20.041 "x4", "x5", "x6", "x7", "x8" 20.041/20.041 -> PVars: 20.041/20.041 "y": ["x4"], "z": ["x5"], "x": ["x6", "x7", "x8"] 20.041/20.041 20.041/20.041 -> Rlps: 20.041/20.041 crule: a -> b, id: 1, possubterms: a-> [] 20.041/20.041 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] 20.041/20.041 crule: k(x6:S) -> a, id: 3, possubterms: k(x6:S)-> [] 20.041/20.041 crule: k(x7:S) -> b, id: 4, possubterms: k(x7:S)-> [] 20.041/20.041 crule: k(x8:S) -> h(x8:S), id: 5, possubterms: k(x8:S)-> [] 20.041/20.041 20.041/20.041 -> Unifications: 20.041/20.041 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 20.041/20.041 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 20.041/20.041 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 20.041/20.041 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 20.041/20.041 20.041/20.041 -> Critical pairs info: 20.041/20.041 => Not trivial, Overlay, N1 20.041/20.041 => Not trivial, Overlay, N2 20.041/20.041 => Not trivial, Overlay, N3 20.041/20.041 | y:S ->* k(z:S) => Not trivial, Not overlay, N4 20.041/20.041 20.041/20.041 -> Problem conclusions: 20.041/20.041 Left linear, Not right linear, Not linear 20.041/20.041 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.041/20.041 CTRS Type: 3 20.041/20.041 Deterministic, Maybe strongly deterministic 20.041/20.041 Oriented CTRS, Properly oriented CTRS, Not join CTRS 20.041/20.041 Maybe right-stable CTRS, Not overlay CTRS 20.041/20.041 Maybe normal CTRS, Maybe almost normal CTRS 20.041/20.041 Maybe terminating CTRS, Maybe joinable CCPs 20.041/20.041 Maybe level confluent 20.041/20.041 Maybe confluent 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 Confluence Problem: 20.041/20.041 (VAR x:S y:S z:S) 20.041/20.041 (STRATEGY CONTEXTSENSITIVE 20.041/20.041 (a) 20.041/20.041 (f 1 2) 20.041/20.041 (k 1) 20.041/20.041 (b) 20.041/20.041 (fSNonEmpty) 20.041/20.041 (g 1 2) 20.041/20.041 (h 1) 20.041/20.041 ) 20.041/20.041 (RULES 20.041/20.041 a -> b 20.041/20.041 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.041/20.041 k(x:S) -> a 20.041/20.041 k(x:S) -> b 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 ) 20.041/20.041 Critical Pairs: 20.041/20.041 => Not trivial, Overlay, N1 20.041/20.041 => Not trivial, Overlay, N2 20.041/20.041 => Not trivial, Overlay, N3 20.041/20.041 | y:S ->* k(z:S) => Not trivial, Not overlay, N4 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 20.041/20.041 Conditional Critical Pairs Distributor Processor 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 Confluence Problem: 20.041/20.041 (VAR x:S y:S z:S) 20.041/20.041 (STRATEGY CONTEXTSENSITIVE 20.041/20.041 (a) 20.041/20.041 (f 1 2) 20.041/20.041 (k 1) 20.041/20.041 (b) 20.041/20.041 (fSNonEmpty) 20.041/20.041 (g 1 2) 20.041/20.041 (h 1) 20.041/20.041 ) 20.041/20.041 (RULES 20.041/20.041 a -> b 20.041/20.041 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.041/20.041 k(x:S) -> a 20.041/20.041 k(x:S) -> b 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 ) 20.041/20.041 Critical Pairs: 20.041/20.041 => Not trivial, Overlay, N2 20.041/20.041 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.041/20.041 20.041/20.041 Infeasible Convergence No Conditions CCP Processor: 20.041/20.041 Infeasible convergence? 20.041/20.041 YES 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 20.041/20.041 Infeasibility Problem: 20.041/20.041 [(VAR vNonEmpty:S x:S y:S z:S) 20.041/20.041 (STRATEGY CONTEXTSENSITIVE 20.041/20.041 (a) 20.041/20.041 (f 1 2) 20.041/20.041 (k 1) 20.041/20.041 (b) 20.041/20.041 (cx) 20.041/20.041 (fSNonEmpty) 20.041/20.041 (g 1 2) 20.041/20.041 (h 1) 20.041/20.041 ) 20.041/20.041 (RULES 20.041/20.041 a -> b 20.041/20.041 f(y:S,a) -> g(h(z:S),h(z:S)) | y:S ->* k(z:S) 20.041/20.041 k(x:S) -> a 20.041/20.041 k(x:S) -> b 20.041/20.041 k(x:S) -> h(x:S) 20.041/20.041 )] 20.041/20.041 20.041/20.041 Infeasibility Conditions: 20.041/20.041 b ->* z:S, h(cx) ->* z:S 20.041/20.041 20.041/20.041 Problem 1: 20.041/20.041 20.041/20.041 Obtaining a model using Mace4: 20.041/20.041 20.041/20.041 -> Usable Rules: 20.041/20.041 Empty 20.041/20.041 20.041/20.041 -> Mace4 Output: 20.041/20.041 ============================== Mace4 ================================= 20.041/20.041 Mace4 (64) version 2009-11A, November 2009. 20.041/20.041 Process 124750 was started by ubuntu on ubuntu, 20.041/20.041 Fri Jul 16 15:49:32 2021 20.041/20.041 The command was "./mace4 -c -f /tmp/mace4124736-2.in". 20.041/20.041 ============================== end of head =========================== 20.041/20.041 20.041/20.041 ============================== INPUT ================================= 20.041/20.041 20.041/20.041 % Reading from file /tmp/mace4124736-2.in 20.041/20.041 20.041/20.041 assign(max_seconds,10). 20.041/20.041 20.041/20.041 formulas(assumptions). 20.041/20.041 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 20.041/20.041 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 20.041/20.041 ->(x1,y) -> ->(k(x1),k(y)) # label(congruence). 20.041/20.041 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 20.041/20.041 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 20.041/20.041 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence). 20.041/20.041 ->*(x,x) # label(reflexivity). 20.041/20.041 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.041/20.041 end_of_list. 20.041/20.041 20.041/20.041 formulas(goals). 20.041/20.041 (exists x3 (->*(b,x3) & ->*(h(cx),x3))) # label(goal). 20.041/20.041 end_of_list. 20.041/20.041 20.041/20.041 ============================== end of input ========================== 20.041/20.041 20.041/20.041 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.041/20.041 20.041/20.041 % Formulas that are not ordinary clauses: 20.041/20.041 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 3 ->(x1,y) -> ->(k(x1),k(y)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 4 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 5 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 6 ->(x1,y) -> ->(h(x1),h(y)) # label(congruence) # label(non_clause). [assumption]. 20.041/20.041 7 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.041/20.041 8 (exists x3 (->*(b,x3) & ->*(h(cx),x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.041/20.041 20.041/20.041 ============================== end of process non-clausal formulas === 20.041/20.041 20.041/20.041 ============================== CLAUSES FOR SEARCH ==================== 20.041/20.041 20.041/20.041 formulas(mace4_clauses). 20.041/20.041 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 20.041/20.041 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 20.041/20.041 -->(x,y) | ->(k(x),k(y)) # label(congruence). 20.041/20.041 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 20.041/20.041 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 20.041/20.041 -->(x,y) | ->(h(x),h(y)) # label(congruence). 20.041/20.041 ->*(x,x) # label(reflexivity). 20.041/20.041 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.041/20.041 -->*(b,x) | -->*(h(cx),x) # label(goal). 20.041/20.041 end_of_list. 20.041/20.041 20.041/20.041 ============================== end of clauses for search ============= 20.041/20.041 20.041/20.041 % There are no natural numbers in the input. 20.041/20.041 20.041/20.041 ============================== DOMAIN SIZE 2 ========================= 20.041/20.041 20.041/20.041 ============================== MODEL ================================= 20.041/20.041 20.041/20.041 interpretation( 2, [number=1, seconds=0], [ 20.041/20.041 20.041/20.041 function(b, [ 0 ]), 20.041/20.041 20.041/20.041 function(cx, [ 0 ]), 20.041/20.041 20.041/20.041 function(k(_), [ 0, 0 ]), 20.041/20.041 20.041/20.041 function(h(_), [ 1, 0 ]), 20.041/20.041 20.041/20.041 function(f(_,_), [ 20.041/20.041 0, 0, 20.041/20.041 0, 0 ]), 20.041/20.041 20.041/20.041 function(g(_,_), [ 20.041/20.041 0, 0, 20.041/20.041 0, 0 ]), 20.041/20.041 20.041/20.041 relation(->*(_,_), [ 20.041/20.041 1, 0, 20.041/20.041 0, 1 ]), 20.041/20.041 20.041/20.041 relation(->(_,_), [ 20.041/20.041 0, 0, 20.041/20.041 0, 0 ]) 20.041/20.041 ]). 20.041/20.041 20.041/20.041 ============================== end of model ========================== 20.041/20.041 20.041/20.041 ============================== STATISTICS ============================ 20.041/20.041 20.041/20.041 For domain size 2. 20.041/20.041 20.041/20.041 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.041/20.041 Ground clauses: seen=52, kept=48. 20.041/20.041 Selections=14, assignments=14, propagations=8, current_models=1. 20.041/20.041 Rewrite_terms=86, rewrite_bools=60, indexes=10. 20.041/20.041 Rules_from_neg_clauses=1, cross_offs=1. 20.041/20.041 20.041/20.041 ============================== end of statistics ===================== 20.041/20.041 20.041/20.041 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.041/20.041 20.041/20.041 Exiting with 1 model. 20.041/20.041 20.041/20.041 Process 124750 exit (max_models) Fri Jul 16 15:49:32 2021 20.041/20.041 The process finished Fri Jul 16 15:49:32 2021 20.041/20.041 20.041/20.041 20.041/20.041 Mace4 cooked interpretation: 20.041/20.041 20.041/20.041 20.041/20.041 20.041/20.041 The problem is infeasible. 20.041/20.041 20.041/20.041 20.041/20.041 The problem is not joinable. 20.041/20.041 22.83user 0.75system 0:20.41elapsed 115%CPU (0avgtext+0avgdata 135992maxresident)k 20.041/20.041 8inputs+0outputs (0major+71871minor)pagefaults 0swaps