0.011/0.011 NO 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 Confluence Problem: 0.011/0.011 (VAR vNonEmpty x y z) 0.011/0.011 (REPLACEMENT-MAP 0.011/0.011 (a) 0.011/0.011 (f 1, 2) 0.011/0.011 (g 1, 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1, 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 ) 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 Inlining of Conditions Processor [STERN17]: 0.011/0.011 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 Confluence Problem: 0.011/0.011 (VAR vNonEmpty x y z) 0.011/0.011 (REPLACEMENT-MAP 0.011/0.011 (a) 0.011/0.011 (f 1, 2) 0.011/0.011 (g 1, 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1, 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 ) 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 Clean CTRS Processor: 0.011/0.011 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 Confluence Problem: 0.011/0.011 (VAR x y z) 0.011/0.011 (REPLACEMENT-MAP 0.011/0.011 (a) 0.011/0.011 (f 1, 2) 0.011/0.011 (g 1, 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1, 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 ) 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 0.011/0.011 CRule InfChecker Info: 0.011/0.011 a -> t(c) 0.011/0.011 Rule remains 0.011/0.011 Proof: 0.011/0.011 NO_CONDS 0.011/0.011 0.011/0.011 CRule InfChecker Info: 0.011/0.011 a -> t(d) 0.011/0.011 Rule remains 0.011/0.011 Proof: 0.011/0.011 NO_CONDS 0.011/0.011 0.011/0.011 CRule InfChecker Info: 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 Rule remains 0.011/0.011 Proof: 0.011/0.011 NO 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 Infeasibility Problem: 0.011/0.011 [(VAR vNonEmpty x y z vNonEmpty x z) 0.011/0.011 (STRATEGY CONTEXTSENSITIVE 0.011/0.011 (a) 0.011/0.011 (f 1 2) 0.011/0.011 (g 1 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 )] 0.011/0.011 0.011/0.011 Infeasibility Conditions: 0.011/0.011 x ->* t(z) 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 Obtaining a proof using Prover9: 0.011/0.011 0.011/0.011 -> Prover9 Output: 0.011/0.011 ============================== Prover9 =============================== 0.011/0.011 Prover9 (64) version 2009-11A, November 2009. 0.011/0.011 Process 60713 was started by ubuntu on ubuntu, 0.011/0.011 Wed Mar 9 09:45:21 2022 0.011/0.011 The command was "./prover9 -f /tmp/prover960704-0.in". 0.011/0.011 ============================== end of head =========================== 0.011/0.011 0.011/0.011 ============================== INPUT ================================= 0.011/0.011 0.011/0.011 % Reading from file /tmp/prover960704-0.in 0.011/0.011 0.011/0.011 assign(max_seconds,20). 0.011/0.011 0.011/0.011 formulas(assumptions). 0.011/0.011 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 0.011/0.011 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 0.011/0.011 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 0.011/0.011 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 0.011/0.011 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 0.011/0.011 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 0.011/0.011 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence). 0.011/0.011 ->_s0(a,t(c)) # label(replacement). 0.011/0.011 ->_s0(a,t(d)) # label(replacement). 0.011/0.011 ->*_s0(x1,t(x3)) -> ->_s0(f(x1,x2),x3) # label(replacement). 0.011/0.011 ->_s0(g(x1,x1),h(x1,x1)) # label(replacement). 0.011/0.011 ->*_s0(x,x) # label(reflexivity). 0.011/0.011 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 formulas(goals). 0.011/0.011 (exists x5 exists x6 ->*_s0(x5,t(x6))) # label(goal). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 ============================== end of input ========================== 0.011/0.011 0.011/0.011 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.011/0.011 0.011/0.011 % Formulas that are not ordinary clauses: 0.011/0.011 1 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 2 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 3 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 4 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 7 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 8 ->*_s0(x1,t(x3)) -> ->_s0(f(x1,x2),x3) # label(replacement) # label(non_clause). [assumption]. 0.011/0.011 9 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.011/0.011 10 (exists x5 exists x6 ->*_s0(x5,t(x6))) # label(goal) # label(non_clause) # label(goal). [goal]. 0.011/0.011 0.011/0.011 ============================== end of process non-clausal formulas === 0.011/0.011 0.011/0.011 ============================== PROCESS INITIAL CLAUSES =============== 0.011/0.011 0.011/0.011 % Clauses before input processing: 0.011/0.011 0.011/0.011 formulas(usable). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 formulas(sos). 0.011/0.011 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 0.011/0.011 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 0.011/0.011 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 0.011/0.011 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 0.011/0.011 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.011/0.011 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.011/0.011 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(7)]. 0.011/0.011 ->_s0(a,t(c)) # label(replacement). [assumption]. 0.011/0.011 ->_s0(a,t(d)) # label(replacement). [assumption]. 0.011/0.011 -->*_s0(x,t(y)) | ->_s0(f(x,z),y) # label(replacement). [clausify(8)]. 0.011/0.011 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 0.011/0.011 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.011/0.011 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 0.011/0.011 -->*_s0(x,t(y)) # label(goal). [deny(10)]. 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 formulas(demodulators). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 ============================== PREDICATE ELIMINATION ================= 0.011/0.011 0.011/0.011 No predicates eliminated. 0.011/0.011 0.011/0.011 ============================== end predicate elimination ============= 0.011/0.011 0.011/0.011 Auto_denials: 0.011/0.011 % copying label goal to answer in negative clause 0.011/0.011 0.011/0.011 Term ordering decisions: 0.011/0.011 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 0.011/0.011 Function symbol precedence: function_order([ a, c, d, f, g, h, t ]). 0.011/0.011 After inverse_order: (no changes). 0.011/0.011 Unfolding symbols: (none). 0.011/0.011 0.011/0.011 Auto_inference settings: 0.011/0.011 % set(neg_binary_resolution). % (HNE depth_diff=-7) 0.011/0.011 % clear(ordered_res). % (HNE depth_diff=-7) 0.011/0.011 % set(ur_resolution). % (HNE depth_diff=-7) 0.011/0.011 % set(ur_resolution) -> set(pos_ur_resolution). 0.011/0.011 % set(ur_resolution) -> set(neg_ur_resolution). 0.011/0.011 0.011/0.011 Auto_process settings: (no changes). 0.011/0.011 0.011/0.011 kept: 11 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(1)]. 0.011/0.011 kept: 12 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(2)]. 0.011/0.011 kept: 13 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 0.011/0.011 kept: 14 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 0.011/0.011 kept: 15 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 0.011/0.011 kept: 16 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 0.011/0.011 kept: 17 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(7)]. 0.011/0.011 kept: 18 ->_s0(a,t(c)) # label(replacement). [assumption]. 0.011/0.011 kept: 19 ->_s0(a,t(d)) # label(replacement). [assumption]. 0.011/0.011 kept: 20 -->*_s0(x,t(y)) | ->_s0(f(x,z),y) # label(replacement). [clausify(8)]. 0.011/0.011 kept: 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 0.011/0.011 kept: 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.011/0.011 kept: 23 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(9)]. 0.011/0.011 kept: 24 -->*_s0(x,t(y)) # label(goal) # answer(goal). [deny(10)]. 0.011/0.011 0.011/0.011 ============================== PROOF ================================= 0.011/0.011 0.011/0.011 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 0.011/0.011 % Length of proof is 4. 0.011/0.011 % Level of proof is 2. 0.011/0.011 % Maximum clause weight is 4.000. 0.011/0.011 % Given clauses 0. 0.011/0.011 0.011/0.011 10 (exists x5 exists x6 ->*_s0(x5,t(x6))) # label(goal) # label(non_clause) # label(goal). [goal]. 0.011/0.011 22 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.011/0.011 24 -->*_s0(x,t(y)) # label(goal) # answer(goal). [deny(10)]. 0.011/0.011 25 $F # answer(goal). [resolve(24,a,22,a)]. 0.011/0.011 0.011/0.011 ============================== end of proof ========================== 0.011/0.011 0.011/0.011 ============================== STATISTICS ============================ 0.011/0.011 0.011/0.011 Given=0. Generated=14. Kept=14. proofs=1. 0.011/0.011 Usable=0. Sos=0. Demods=0. Limbo=13, Disabled=14. Hints=0. 0.011/0.011 Kept_by_rule=0, Deleted_by_rule=0. 0.011/0.011 Forward_subsumed=0. Back_subsumed=0. 0.011/0.011 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 0.011/0.011 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 0.011/0.011 Demod_attempts=0. Demod_rewrites=0. 0.011/0.011 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 0.011/0.011 Nonunit_fsub_feature_tests=3. Nonunit_bsub_feature_tests=0. 0.011/0.011 Megabytes=0.06. 0.011/0.011 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.011/0.011 0.011/0.011 ============================== end of statistics ===================== 0.011/0.011 0.011/0.011 ============================== end of search ========================= 0.011/0.011 0.011/0.011 THEOREM PROVED 0.011/0.011 0.011/0.011 Exiting with 1 proof. 0.011/0.011 0.011/0.011 Process 60713 exit (max_proofs) Wed Mar 9 09:45:21 2022 0.011/0.011 0.011/0.011 0.011/0.011 The problem is feasible. 0.011/0.011 0.011/0.011 0.011/0.011 CRule InfChecker Info: 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 Rule remains 0.011/0.011 Proof: 0.011/0.011 NO_CONDS 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 Confluence Problem: 0.011/0.011 (VAR x y z) 0.011/0.011 (REPLACEMENT-MAP 0.011/0.011 (a) 0.011/0.011 (f 1, 2) 0.011/0.011 (g 1, 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1, 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 ) 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 0.011/0.011 Critical Pairs Processor: 0.011/0.011 -> Rules: 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 -> Vars: 0.011/0.011 "x", "y", "z" 0.011/0.011 0.011/0.011 -> Rlps: 0.011/0.011 crule: a -> t(c), id: 1, possubterms: a-> [] 0.011/0.011 crule: a -> t(d), id: 2, possubterms: a-> [] 0.011/0.011 crule: f(x,y) -> z | x ->* t(z), id: 3, possubterms: f(x,y)-> [] 0.011/0.011 crule: g(x,x) -> h(x,x), id: 4, possubterms: g(x,x)-> [] 0.011/0.011 0.011/0.011 -> Unifications: 0.011/0.011 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: t(d), r': t(c) 0.011/0.011 0.011/0.011 -> Critical pairs info: 0.011/0.011 => Not trivial, Overlay, NW2, N1 0.011/0.011 0.011/0.011 -> Problem conclusions: 0.011/0.011 Not left linear, Not right linear, Not linear 0.011/0.011 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.011/0.011 CTRS Type: 3 0.011/0.011 Deterministic, Strongly deterministic 0.011/0.011 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 0.011/0.011 Maybe right-stable CTRS, Overlay CTRS 0.011/0.011 Maybe normal CTRS, Maybe almost normal CTRS 0.011/0.011 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 0.011/0.011 Maybe level confluent 0.011/0.011 Maybe confluent 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 Confluence Problem: 0.011/0.011 (VAR x y z) 0.011/0.011 (REPLACEMENT-MAP 0.011/0.011 (a) 0.011/0.011 (f 1, 2) 0.011/0.011 (g 1, 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1, 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 ) 0.011/0.011 Critical Pairs: 0.011/0.011 => Not trivial, Overlay, NW2, N1 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 0.011/0.011 Conditional Critical Pairs Distributor Processor 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 Confluence Problem: 0.011/0.011 (VAR x y z) 0.011/0.011 (REPLACEMENT-MAP 0.011/0.011 (a) 0.011/0.011 (f 1, 2) 0.011/0.011 (g 1, 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1, 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 ) 0.011/0.011 Critical Pairs: 0.011/0.011 => Not trivial, Overlay, NW2, N1 0.011/0.011 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.011/0.011 0.011/0.011 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 0.011/0.011 Proof: 0.011/0.011 YES 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 Infeasibility Problem: 0.011/0.011 [(VAR vNonEmpty x y z vNonEmpty y) 0.011/0.011 (STRATEGY CONTEXTSENSITIVE 0.011/0.011 (a) 0.011/0.011 (f 1 2) 0.011/0.011 (g 1 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 )] 0.011/0.011 0.011/0.011 Infeasibility Conditions: 0.011/0.011 t(c) -> y 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 Obtaining a model using Mace4: 0.011/0.011 0.011/0.011 -> Usable Rules: 0.011/0.011 Empty 0.011/0.011 0.011/0.011 -> Mace4 Output: 0.011/0.011 ============================== Mace4 ================================= 0.011/0.011 Mace4 (64) version 2009-11A, November 2009. 0.011/0.011 Process 60753 was started by ubuntu on ubuntu, 0.011/0.011 Wed Mar 9 09:45:21 2022 0.011/0.011 The command was "./mace4 -c -f /tmp/mace460729-2.in". 0.011/0.011 ============================== end of head =========================== 0.011/0.011 0.011/0.011 ============================== INPUT ================================= 0.011/0.011 0.011/0.011 % Reading from file /tmp/mace460729-2.in 0.011/0.011 0.011/0.011 assign(max_seconds,6). 0.011/0.011 0.011/0.011 formulas(assumptions). 0.011/0.011 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 0.011/0.011 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 0.011/0.011 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 0.011/0.011 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 0.011/0.011 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 0.011/0.011 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 0.011/0.011 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 formulas(goals). 0.011/0.011 (exists x5 ->(t(c),x5)) # label(goal). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 ============================== end of input ========================== 0.011/0.011 0.011/0.011 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.011/0.011 0.011/0.011 % Formulas that are not ordinary clauses: 0.011/0.011 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 3 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 4 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 7 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 8 (exists x5 ->(t(c),x5)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.011/0.011 0.011/0.011 ============================== end of process non-clausal formulas === 0.011/0.011 0.011/0.011 ============================== CLAUSES FOR SEARCH ==================== 0.011/0.011 0.011/0.011 formulas(mace4_clauses). 0.011/0.011 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 0.011/0.011 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 0.011/0.011 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 0.011/0.011 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 0.011/0.011 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 0.011/0.011 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 0.011/0.011 -->(x,y) | ->(t(x),t(y)) # label(congruence). 0.011/0.011 -->(t(c),x) # label(goal). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 ============================== end of clauses for search ============= 0.011/0.011 0.011/0.011 % There are no natural numbers in the input. 0.011/0.011 0.011/0.011 ============================== DOMAIN SIZE 2 ========================= 0.011/0.011 0.011/0.011 ============================== MODEL ================================= 0.011/0.011 0.011/0.011 interpretation( 2, [number=1, seconds=0], [ 0.011/0.011 0.011/0.011 function(c, [ 0 ]), 0.011/0.011 0.011/0.011 function(t(_), [ 0, 0 ]), 0.011/0.011 0.011/0.011 function(f(_,_), [ 0.011/0.011 0, 0, 0.011/0.011 0, 0 ]), 0.011/0.011 0.011/0.011 function(g(_,_), [ 0.011/0.011 0, 0, 0.011/0.011 0, 0 ]), 0.011/0.011 0.011/0.011 function(h(_,_), [ 0.011/0.011 0, 0, 0.011/0.011 0, 0 ]), 0.011/0.011 0.011/0.011 relation(->(_,_), [ 0.011/0.011 0, 0, 0.011/0.011 0, 0 ]) 0.011/0.011 ]). 0.011/0.011 0.011/0.011 ============================== end of model ========================== 0.011/0.011 0.011/0.011 ============================== STATISTICS ============================ 0.011/0.011 0.011/0.011 For domain size 2. 0.011/0.011 0.011/0.011 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.011/0.011 Ground clauses: seen=54, kept=54. 0.011/0.011 Selections=15, assignments=15, propagations=4, current_models=1. 0.011/0.011 Rewrite_terms=108, rewrite_bools=57, indexes=4. 0.011/0.011 Rules_from_neg_clauses=0, cross_offs=0. 0.011/0.011 0.011/0.011 ============================== end of statistics ===================== 0.011/0.011 0.011/0.011 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.011/0.011 0.011/0.011 Exiting with 1 model. 0.011/0.011 0.011/0.011 Process 60753 exit (max_models) Wed Mar 9 09:45:21 2022 0.011/0.011 The process finished Wed Mar 9 09:45:21 2022 0.011/0.011 0.011/0.011 0.011/0.011 Mace4 cooked interpretation: 0.011/0.011 0.011/0.011 0.011/0.011 0.011/0.011 The problem is infeasible. 0.011/0.011 YES 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 Infeasibility Problem: 0.011/0.011 [(VAR vNonEmpty x y z vNonEmpty x) 0.011/0.011 (STRATEGY CONTEXTSENSITIVE 0.011/0.011 (a) 0.011/0.011 (f 1 2) 0.011/0.011 (g 1 2) 0.011/0.011 (c) 0.011/0.011 (d) 0.011/0.011 (fSNonEmpty) 0.011/0.011 (h 1 2) 0.011/0.011 (t 1) 0.011/0.011 ) 0.011/0.011 (RULES 0.011/0.011 a -> t(c) 0.011/0.011 a -> t(d) 0.011/0.011 f(x,y) -> z | x ->* t(z) 0.011/0.011 g(x,x) -> h(x,x) 0.011/0.011 )] 0.011/0.011 0.011/0.011 Infeasibility Conditions: 0.011/0.011 t(d) -> x 0.011/0.011 0.011/0.011 Problem 1: 0.011/0.011 0.011/0.011 Obtaining a model using Mace4: 0.011/0.011 0.011/0.011 -> Usable Rules: 0.011/0.011 Empty 0.011/0.011 0.011/0.011 -> Mace4 Output: 0.011/0.011 ============================== Mace4 ================================= 0.011/0.011 Mace4 (64) version 2009-11A, November 2009. 0.011/0.011 Process 60786 was started by ubuntu on ubuntu, 0.011/0.011 Wed Mar 9 09:45:21 2022 0.011/0.011 The command was "./mace4 -c -f /tmp/mace460775-2.in". 0.011/0.011 ============================== end of head =========================== 0.011/0.011 0.011/0.011 ============================== INPUT ================================= 0.011/0.011 0.011/0.011 % Reading from file /tmp/mace460775-2.in 0.011/0.011 0.011/0.011 assign(max_seconds,6). 0.011/0.011 0.011/0.011 formulas(assumptions). 0.011/0.011 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 0.011/0.011 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 0.011/0.011 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 0.011/0.011 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 0.011/0.011 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 0.011/0.011 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 0.011/0.011 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 formulas(goals). 0.011/0.011 (exists x5 ->(t(d),x5)) # label(goal). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 ============================== end of input ========================== 0.011/0.011 0.011/0.011 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.011/0.011 0.011/0.011 % Formulas that are not ordinary clauses: 0.011/0.011 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 3 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 4 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 7 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 0.011/0.011 8 (exists x5 ->(t(d),x5)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.011/0.011 0.011/0.011 ============================== end of process non-clausal formulas === 0.011/0.011 0.011/0.011 ============================== CLAUSES FOR SEARCH ==================== 0.011/0.011 0.011/0.011 formulas(mace4_clauses). 0.011/0.011 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 0.011/0.011 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 0.011/0.011 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 0.011/0.011 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 0.011/0.011 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 0.011/0.011 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 0.011/0.011 -->(x,y) | ->(t(x),t(y)) # label(congruence). 0.011/0.011 -->(t(d),x) # label(goal). 0.011/0.011 end_of_list. 0.011/0.011 0.011/0.011 ============================== end of clauses for search ============= 0.011/0.011 0.011/0.011 % There are no natural numbers in the input. 0.011/0.011 0.011/0.011 ============================== DOMAIN SIZE 2 ========================= 0.011/0.011 0.011/0.011 ============================== MODEL ================================= 0.011/0.011 0.011/0.011 interpretation( 2, [number=1, seconds=0], [ 0.011/0.011 0.011/0.011 function(d, [ 0 ]), 0.011/0.011 0.011/0.011 function(t(_), [ 0, 0 ]), 0.011/0.011 0.011/0.011 function(f(_,_), [ 0.011/0.011 0, 0, 0.011/0.011 0, 0 ]), 0.011/0.011 0.011/0.011 function(g(_,_), [ 0.011/0.011 0, 0, 0.011/0.011 0, 0 ]), 0.011/0.011 0.011/0.011 function(h(_,_), [ 0.011/0.011 0, 0, 0.011/0.011 0, 0 ]), 0.011/0.011 0.011/0.011 relation(->(_,_), [ 0.011/0.011 0, 0, 0.011/0.011 0, 0 ]) 0.011/0.011 ]). 0.011/0.011 0.011/0.011 ============================== end of model ========================== 0.011/0.011 0.011/0.011 ============================== STATISTICS ============================ 0.011/0.011 0.011/0.011 For domain size 2. 0.011/0.011 0.011/0.011 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.011/0.011 Ground clauses: seen=54, kept=54. 0.011/0.011 Selections=15, assignments=15, propagations=4, current_models=1. 0.011/0.011 Rewrite_terms=108, rewrite_bools=57, indexes=4. 0.011/0.011 Rules_from_neg_clauses=0, cross_offs=0. 0.011/0.011 0.011/0.011 ============================== end of statistics ===================== 0.011/0.011 0.011/0.011 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.011/0.011 0.011/0.011 Exiting with 1 model. 0.011/0.011 0.011/0.011 Process 60786 exit (max_models) Wed Mar 9 09:45:21 2022 0.011/0.011 The process finished Wed Mar 9 09:45:21 2022 0.011/0.011 0.011/0.011 0.011/0.011 Mace4 cooked interpretation: 0.011/0.011 0.011/0.011 0.011/0.011 0.011/0.011 The problem is infeasible. 0.011/0.011 0.011/0.011 0.011/0.011 The problem is not joinable. 0.011/0.011 0.08user 0.01system 0:00.11elapsed 82%CPU (0avgtext+0avgdata 11812maxresident)k 0.011/0.011 8inputs+0outputs (0major+7353minor)pagefaults 0swaps