0.013/0.013 NO 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 Confluence Problem: 0.013/0.013 (VAR vNonEmpty x) 0.013/0.013 (REPLACEMENT-MAP 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1, 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1, 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 ) 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 Inlining of Conditions Processor [STERN17]: 0.013/0.013 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 Confluence Problem: 0.013/0.013 (VAR vNonEmpty x) 0.013/0.013 (REPLACEMENT-MAP 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1, 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1, 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 ) 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 Clean CTRS Processor: 0.013/0.013 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 Confluence Problem: 0.013/0.013 (VAR x) 0.013/0.013 (REPLACEMENT-MAP 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1, 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1, 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 ) 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 0.013/0.013 CRule InfChecker Info: 0.013/0.013 a -> c 0.013/0.013 Rule remains 0.013/0.013 Proof: 0.013/0.013 NO_CONDS 0.013/0.013 0.013/0.013 CRule InfChecker Info: 0.013/0.013 a -> d 0.013/0.013 Rule remains 0.013/0.013 Proof: 0.013/0.013 NO_CONDS 0.013/0.013 0.013/0.013 CRule InfChecker Info: 0.013/0.013 b -> c 0.013/0.013 Rule remains 0.013/0.013 Proof: 0.013/0.013 NO_CONDS 0.013/0.013 0.013/0.013 CRule InfChecker Info: 0.013/0.013 b -> d 0.013/0.013 Rule remains 0.013/0.013 Proof: 0.013/0.013 NO_CONDS 0.013/0.013 0.013/0.013 CRule InfChecker Info: 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 Rule remains 0.013/0.013 Proof: 0.013/0.013 NO 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 Infeasibility Problem: 0.013/0.013 [(VAR vNonEmpty x vNonEmpty x) 0.013/0.013 (STRATEGY CONTEXTSENSITIVE 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 )] 0.013/0.013 0.013/0.013 Infeasibility Conditions: 0.013/0.013 x ->* c 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 Obtaining a proof using Prover9: 0.013/0.013 0.013/0.013 -> Prover9 Output: 0.013/0.013 ============================== Prover9 =============================== 0.013/0.013 Prover9 (64) version 2009-11A, November 2009. 0.013/0.013 Process 61067 was started by ubuntu on ubuntu, 0.013/0.013 Wed Mar 9 09:46:03 2022 0.013/0.013 The command was "./prover9 -f /tmp/prover961057-0.in". 0.013/0.013 ============================== end of head =========================== 0.013/0.013 0.013/0.013 ============================== INPUT ================================= 0.013/0.013 0.013/0.013 % Reading from file /tmp/prover961057-0.in 0.013/0.013 0.013/0.013 assign(max_seconds,20). 0.013/0.013 0.013/0.013 formulas(assumptions). 0.013/0.013 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 0.013/0.013 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 0.013/0.013 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 0.013/0.013 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 0.013/0.013 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 0.013/0.013 ->_s0(a,c) # label(replacement). 0.013/0.013 ->_s0(a,d) # label(replacement). 0.013/0.013 ->_s0(b,c) # label(replacement). 0.013/0.013 ->_s0(b,d) # label(replacement). 0.013/0.013 ->*_s0(x1,c) -> ->_s0(f(x1),x1) # label(replacement). 0.013/0.013 ->_s0(g(x1,x1),h(x1,x1)) # label(replacement). 0.013/0.013 ->*_s0(x,x) # label(reflexivity). 0.013/0.013 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 formulas(goals). 0.013/0.013 (exists x3 ->*_s0(x3,c)) # label(goal). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 ============================== end of input ========================== 0.013/0.013 0.013/0.013 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.013/0.013 0.013/0.013 % Formulas that are not ordinary clauses: 0.013/0.013 1 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 2 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 3 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 4 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 5 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 6 ->*_s0(x1,c) -> ->_s0(f(x1),x1) # label(replacement) # label(non_clause). [assumption]. 0.013/0.013 7 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 0.013/0.013 8 (exists x3 ->*_s0(x3,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.013/0.013 0.013/0.013 ============================== end of process non-clausal formulas === 0.013/0.013 0.013/0.013 ============================== PROCESS INITIAL CLAUSES =============== 0.013/0.013 0.013/0.013 % Clauses before input processing: 0.013/0.013 0.013/0.013 formulas(usable). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 formulas(sos). 0.013/0.013 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.013/0.013 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 0.013/0.013 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 0.013/0.013 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(4)]. 0.013/0.013 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(5)]. 0.013/0.013 ->_s0(a,c) # label(replacement). [assumption]. 0.013/0.013 ->_s0(a,d) # label(replacement). [assumption]. 0.013/0.013 ->_s0(b,c) # label(replacement). [assumption]. 0.013/0.013 ->_s0(b,d) # label(replacement). [assumption]. 0.013/0.013 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(6)]. 0.013/0.013 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 0.013/0.013 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.013/0.013 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 0.013/0.013 -->*_s0(x,c) # label(goal). [deny(8)]. 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 formulas(demodulators). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 ============================== PREDICATE ELIMINATION ================= 0.013/0.013 0.013/0.013 No predicates eliminated. 0.013/0.013 0.013/0.013 ============================== end predicate elimination ============= 0.013/0.013 0.013/0.013 Auto_denials: 0.013/0.013 % copying label goal to answer in negative clause 0.013/0.013 0.013/0.013 Term ordering decisions: 0.013/0.013 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 0.013/0.013 Function symbol precedence: function_order([ c, a, b, d, g, h, f ]). 0.013/0.013 After inverse_order: (no changes). 0.013/0.013 Unfolding symbols: (none). 0.013/0.013 0.013/0.013 Auto_inference settings: 0.013/0.013 % set(neg_binary_resolution). % (HNE depth_diff=-6) 0.013/0.013 % clear(ordered_res). % (HNE depth_diff=-6) 0.013/0.013 % set(ur_resolution). % (HNE depth_diff=-6) 0.013/0.013 % set(ur_resolution) -> set(pos_ur_resolution). 0.013/0.013 % set(ur_resolution) -> set(neg_ur_resolution). 0.013/0.013 0.013/0.013 Auto_process settings: (no changes). 0.013/0.013 0.013/0.013 kept: 9 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(1)]. 0.013/0.013 kept: 10 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(2)]. 0.013/0.013 kept: 11 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(3)]. 0.013/0.013 kept: 12 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(4)]. 0.013/0.013 kept: 13 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(5)]. 0.013/0.013 kept: 14 ->_s0(a,c) # label(replacement). [assumption]. 0.013/0.013 kept: 15 ->_s0(a,d) # label(replacement). [assumption]. 0.013/0.013 kept: 16 ->_s0(b,c) # label(replacement). [assumption]. 0.013/0.013 kept: 17 ->_s0(b,d) # label(replacement). [assumption]. 0.013/0.013 kept: 18 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(6)]. 0.013/0.013 kept: 19 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 0.013/0.013 kept: 20 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.013/0.013 kept: 21 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(7)]. 0.013/0.013 kept: 22 -->*_s0(x,c) # label(goal) # answer(goal). [deny(8)]. 0.013/0.013 0.013/0.013 ============================== PROOF ================================= 0.013/0.013 0.013/0.013 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 0.013/0.013 % Length of proof is 4. 0.013/0.013 % Level of proof is 2. 0.013/0.013 % Maximum clause weight is 3.000. 0.013/0.013 % Given clauses 0. 0.013/0.013 0.013/0.013 8 (exists x3 ->*_s0(x3,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.013/0.013 20 ->*_s0(x,x) # label(reflexivity). [assumption]. 0.013/0.013 22 -->*_s0(x,c) # label(goal) # answer(goal). [deny(8)]. 0.013/0.013 23 $F # answer(goal). [resolve(22,a,20,a)]. 0.013/0.013 0.013/0.013 ============================== end of proof ========================== 0.013/0.013 0.013/0.013 ============================== STATISTICS ============================ 0.013/0.013 0.013/0.013 Given=0. Generated=14. Kept=14. proofs=1. 0.013/0.013 Usable=0. Sos=0. Demods=0. Limbo=13, Disabled=14. Hints=0. 0.013/0.013 Kept_by_rule=0, Deleted_by_rule=0. 0.013/0.013 Forward_subsumed=0. Back_subsumed=0. 0.013/0.013 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 0.013/0.013 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 0.013/0.013 Demod_attempts=0. Demod_rewrites=0. 0.013/0.013 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 0.013/0.013 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. 0.013/0.013 Megabytes=0.05. 0.013/0.013 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.013/0.013 0.013/0.013 ============================== end of statistics ===================== 0.013/0.013 0.013/0.013 ============================== end of search ========================= 0.013/0.013 0.013/0.013 THEOREM PROVED 0.013/0.013 0.013/0.013 Exiting with 1 proof. 0.013/0.013 0.013/0.013 Process 61067 exit (max_proofs) Wed Mar 9 09:46:03 2022 0.013/0.013 0.013/0.013 0.013/0.013 The problem is feasible. 0.013/0.013 0.013/0.013 0.013/0.013 CRule InfChecker Info: 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 Rule remains 0.013/0.013 Proof: 0.013/0.013 NO_CONDS 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 Confluence Problem: 0.013/0.013 (VAR x) 0.013/0.013 (REPLACEMENT-MAP 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1, 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1, 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 ) 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 0.013/0.013 Critical Pairs Processor: 0.013/0.013 -> Rules: 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 -> Vars: 0.013/0.013 "x" 0.013/0.013 0.013/0.013 -> Rlps: 0.013/0.013 crule: a -> c, id: 1, possubterms: a-> [] 0.013/0.013 crule: a -> d, id: 2, possubterms: a-> [] 0.013/0.013 crule: b -> c, id: 3, possubterms: b-> [] 0.013/0.013 crule: b -> d, id: 4, possubterms: b-> [] 0.013/0.013 crule: f(x) -> x | x ->* c, id: 5, possubterms: f(x)-> [] 0.013/0.013 crule: g(x,x) -> h(x,x), id: 6, possubterms: g(x,x)-> [] 0.013/0.013 0.013/0.013 -> Unifications: 0.013/0.013 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 0.013/0.013 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 0.013/0.013 0.013/0.013 -> Critical pairs info: 0.013/0.013 => Not trivial, Overlay, NW2, N1 0.013/0.013 0.013/0.013 -> Problem conclusions: 0.013/0.013 Not left linear, Not right linear, Not linear 0.013/0.013 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 0.013/0.013 CTRS Type: 1 0.013/0.013 Deterministic, Strongly deterministic 0.013/0.013 Oriented CTRS, Properly oriented CTRS, Not join CTRS, Not semiequational CTRS 0.013/0.013 Maybe right-stable CTRS, Overlay CTRS 0.013/0.013 Maybe normal CTRS, Maybe almost normal CTRS 0.013/0.013 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 0.013/0.013 Maybe level confluent 0.013/0.013 Maybe confluent 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 Confluence Problem: 0.013/0.013 (VAR x) 0.013/0.013 (REPLACEMENT-MAP 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1, 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1, 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 ) 0.013/0.013 Critical Pairs: 0.013/0.013 => Not trivial, Overlay, NW2, N1 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 0.013/0.013 Conditional Critical Pairs Distributor Processor 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 Confluence Problem: 0.013/0.013 (VAR x) 0.013/0.013 (REPLACEMENT-MAP 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1, 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1, 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 ) 0.013/0.013 Critical Pairs: 0.013/0.013 => Not trivial, Overlay, NW2, N1 0.013/0.013 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 0.013/0.013 0.013/0.013 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 0.013/0.013 Proof: 0.013/0.013 YES 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 Infeasibility Problem: 0.013/0.013 [(VAR vNonEmpty x vNonEmpty y) 0.013/0.013 (STRATEGY CONTEXTSENSITIVE 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 )] 0.013/0.013 0.013/0.013 Infeasibility Conditions: 0.013/0.013 c -> y 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 Obtaining a model using Mace4: 0.013/0.013 0.013/0.013 -> Usable Rules: 0.013/0.013 Empty 0.013/0.013 0.013/0.013 -> Mace4 Output: 0.013/0.013 ============================== Mace4 ================================= 0.013/0.013 Mace4 (64) version 2009-11A, November 2009. 0.013/0.013 Process 61116 was started by ubuntu on ubuntu, 0.013/0.013 Wed Mar 9 09:46:03 2022 0.013/0.013 The command was "./mace4 -c -f /tmp/mace461086-2.in". 0.013/0.013 ============================== end of head =========================== 0.013/0.013 0.013/0.013 ============================== INPUT ================================= 0.013/0.013 0.013/0.013 % Reading from file /tmp/mace461086-2.in 0.013/0.013 0.013/0.013 assign(max_seconds,6). 0.013/0.013 0.013/0.013 formulas(assumptions). 0.013/0.013 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 0.013/0.013 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 0.013/0.013 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 0.013/0.013 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 0.013/0.013 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 formulas(goals). 0.013/0.013 (exists x3 ->(c,x3)) # label(goal). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 ============================== end of input ========================== 0.013/0.013 0.013/0.013 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.013/0.013 0.013/0.013 % Formulas that are not ordinary clauses: 0.013/0.013 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 4 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 5 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 6 (exists x3 ->(c,x3)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.013/0.013 0.013/0.013 ============================== end of process non-clausal formulas === 0.013/0.013 0.013/0.013 ============================== CLAUSES FOR SEARCH ==================== 0.013/0.013 0.013/0.013 formulas(mace4_clauses). 0.013/0.013 -->(x,y) | ->(f(x),f(y)) # label(congruence). 0.013/0.013 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 0.013/0.013 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 0.013/0.013 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 0.013/0.013 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 0.013/0.013 -->(c,x) # label(goal). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 ============================== end of clauses for search ============= 0.013/0.013 0.013/0.013 % There are no natural numbers in the input. 0.013/0.013 0.013/0.013 ============================== DOMAIN SIZE 2 ========================= 0.013/0.013 0.013/0.013 ============================== MODEL ================================= 0.013/0.013 0.013/0.013 interpretation( 2, [number=1, seconds=0], [ 0.013/0.013 0.013/0.013 function(c, [ 0 ]), 0.013/0.013 0.013/0.013 function(f(_), [ 0, 0 ]), 0.013/0.013 0.013/0.013 function(g(_,_), [ 0.013/0.013 0, 0, 0.013/0.013 0, 0 ]), 0.013/0.013 0.013/0.013 function(h(_,_), [ 0.013/0.013 0, 0, 0.013/0.013 0, 0 ]), 0.013/0.013 0.013/0.013 relation(->(_,_), [ 0.013/0.013 0, 0, 0.013/0.013 0, 0 ]) 0.013/0.013 ]). 0.013/0.013 0.013/0.013 ============================== end of model ========================== 0.013/0.013 0.013/0.013 ============================== STATISTICS ============================ 0.013/0.013 0.013/0.013 For domain size 2. 0.013/0.013 0.013/0.013 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.013/0.013 Ground clauses: seen=38, kept=38. 0.013/0.013 Selections=11, assignments=11, propagations=4, current_models=1. 0.013/0.013 Rewrite_terms=74, rewrite_bools=40, indexes=2. 0.013/0.013 Rules_from_neg_clauses=0, cross_offs=0. 0.013/0.013 0.013/0.013 ============================== end of statistics ===================== 0.013/0.013 0.013/0.013 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.013/0.013 0.013/0.013 Exiting with 1 model. 0.013/0.013 0.013/0.013 Process 61116 exit (max_models) Wed Mar 9 09:46:03 2022 0.013/0.013 The process finished Wed Mar 9 09:46:03 2022 0.013/0.013 0.013/0.013 0.013/0.013 Mace4 cooked interpretation: 0.013/0.013 0.013/0.013 0.013/0.013 0.013/0.013 The problem is infeasible. 0.013/0.013 YES 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 Infeasibility Problem: 0.013/0.013 [(VAR vNonEmpty x vNonEmpty x) 0.013/0.013 (STRATEGY CONTEXTSENSITIVE 0.013/0.013 (a) 0.013/0.013 (b) 0.013/0.013 (f 1) 0.013/0.013 (g 1 2) 0.013/0.013 (c) 0.013/0.013 (d) 0.013/0.013 (fSNonEmpty) 0.013/0.013 (h 1 2) 0.013/0.013 ) 0.013/0.013 (RULES 0.013/0.013 a -> c 0.013/0.013 a -> d 0.013/0.013 b -> c 0.013/0.013 b -> d 0.013/0.013 f(x) -> x | x ->* c 0.013/0.013 g(x,x) -> h(x,x) 0.013/0.013 )] 0.013/0.013 0.013/0.013 Infeasibility Conditions: 0.013/0.013 d -> x 0.013/0.013 0.013/0.013 Problem 1: 0.013/0.013 0.013/0.013 Obtaining a model using Mace4: 0.013/0.013 0.013/0.013 -> Usable Rules: 0.013/0.013 Empty 0.013/0.013 0.013/0.013 -> Mace4 Output: 0.013/0.013 ============================== Mace4 ================================= 0.013/0.013 Mace4 (64) version 2009-11A, November 2009. 0.013/0.013 Process 61143 was started by ubuntu on ubuntu, 0.013/0.013 Wed Mar 9 09:46:03 2022 0.013/0.013 The command was "./mace4 -c -f /tmp/mace461132-2.in". 0.013/0.013 ============================== end of head =========================== 0.013/0.013 0.013/0.013 ============================== INPUT ================================= 0.013/0.013 0.013/0.013 % Reading from file /tmp/mace461132-2.in 0.013/0.013 0.013/0.013 assign(max_seconds,6). 0.013/0.013 0.013/0.013 formulas(assumptions). 0.013/0.013 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 0.013/0.013 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 0.013/0.013 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 0.013/0.013 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 0.013/0.013 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 formulas(goals). 0.013/0.013 (exists x3 ->(d,x3)) # label(goal). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 ============================== end of input ========================== 0.013/0.013 0.013/0.013 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 0.013/0.013 0.013/0.013 % Formulas that are not ordinary clauses: 0.013/0.013 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 4 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 5 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 0.013/0.013 6 (exists x3 ->(d,x3)) # label(goal) # label(non_clause) # label(goal). [goal]. 0.013/0.013 0.013/0.013 ============================== end of process non-clausal formulas === 0.013/0.013 0.013/0.013 ============================== CLAUSES FOR SEARCH ==================== 0.013/0.013 0.013/0.013 formulas(mace4_clauses). 0.013/0.013 -->(x,y) | ->(f(x),f(y)) # label(congruence). 0.013/0.013 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 0.013/0.013 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 0.013/0.013 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 0.013/0.013 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 0.013/0.013 -->(d,x) # label(goal). 0.013/0.013 end_of_list. 0.013/0.013 0.013/0.013 ============================== end of clauses for search ============= 0.013/0.013 0.013/0.013 % There are no natural numbers in the input. 0.013/0.013 0.013/0.013 ============================== DOMAIN SIZE 2 ========================= 0.013/0.013 0.013/0.013 ============================== MODEL ================================= 0.013/0.013 0.013/0.013 interpretation( 2, [number=1, seconds=0], [ 0.013/0.013 0.013/0.013 function(d, [ 0 ]), 0.013/0.013 0.013/0.013 function(f(_), [ 0, 0 ]), 0.013/0.013 0.013/0.013 function(g(_,_), [ 0.013/0.013 0, 0, 0.013/0.013 0, 0 ]), 0.013/0.013 0.013/0.013 function(h(_,_), [ 0.013/0.013 0, 0, 0.013/0.013 0, 0 ]), 0.013/0.013 0.013/0.013 relation(->(_,_), [ 0.013/0.013 0, 0, 0.013/0.013 0, 0 ]) 0.013/0.013 ]). 0.013/0.013 0.013/0.013 ============================== end of model ========================== 0.013/0.013 0.013/0.013 ============================== STATISTICS ============================ 0.013/0.013 0.013/0.013 For domain size 2. 0.013/0.013 0.013/0.013 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 0.013/0.013 Ground clauses: seen=38, kept=38. 0.013/0.013 Selections=11, assignments=11, propagations=4, current_models=1. 0.013/0.013 Rewrite_terms=74, rewrite_bools=40, indexes=2. 0.013/0.013 Rules_from_neg_clauses=0, cross_offs=0. 0.013/0.013 0.013/0.013 ============================== end of statistics ===================== 0.013/0.013 0.013/0.013 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 0.013/0.013 0.013/0.013 Exiting with 1 model. 0.013/0.013 0.013/0.013 Process 61143 exit (max_models) Wed Mar 9 09:46:03 2022 0.013/0.013 The process finished Wed Mar 9 09:46:03 2022 0.013/0.013 0.013/0.013 0.013/0.013 Mace4 cooked interpretation: 0.013/0.013 0.013/0.013 0.013/0.013 0.013/0.013 The problem is infeasible. 0.013/0.013 0.013/0.013 0.013/0.013 The problem is not joinable. 0.013/0.013 0.07user 0.02system 0:00.13elapsed 77%CPU (0avgtext+0avgdata 11488maxresident)k 0.013/0.013 8inputs+0outputs (0major+9320minor)pagefaults 0swaps