25.04/25.04 NO 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 25.04/25.04 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 Confluence Problem: 25.04/25.04 (VAR vNonEmpty:S x:S) 25.04/25.04 (STRATEGY CONTEXTSENSITIVE 25.04/25.04 (a) 25.04/25.04 (b) 25.04/25.04 (f 1) 25.04/25.04 (g 1 2) 25.04/25.04 (c) 25.04/25.04 (d) 25.04/25.04 (fSNonEmpty) 25.04/25.04 (h 1 2) 25.04/25.04 ) 25.04/25.04 (RULES 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 ) 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 25.04/25.04 Inlining of Conditions Processor [STERN17]: 25.04/25.04 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 Confluence Problem: 25.04/25.04 (VAR vNonEmpty:S x:S) 25.04/25.04 (STRATEGY CONTEXTSENSITIVE 25.04/25.04 (a) 25.04/25.04 (b) 25.04/25.04 (f 1) 25.04/25.04 (g 1 2) 25.04/25.04 (c) 25.04/25.04 (d) 25.04/25.04 (fSNonEmpty) 25.04/25.04 (h 1 2) 25.04/25.04 ) 25.04/25.04 (RULES 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 ) 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 25.04/25.04 Clean CTRS Processor: 25.04/25.04 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 Confluence Problem: 25.04/25.04 (VAR x:S) 25.04/25.04 (STRATEGY CONTEXTSENSITIVE 25.04/25.04 (a) 25.04/25.04 (b) 25.04/25.04 (f 1) 25.04/25.04 (g 1 2) 25.04/25.04 (c) 25.04/25.04 (d) 25.04/25.04 (fSNonEmpty) 25.04/25.04 (h 1 2) 25.04/25.04 ) 25.04/25.04 (RULES 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 ) 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 25.04/25.04 CRule InfChecker Info: 25.04/25.04 a -> c 25.04/25.04 Rule remains 25.04/25.04 Proof: 25.04/25.04 NO_CONDS 25.04/25.04 25.04/25.04 CRule InfChecker Info: 25.04/25.04 a -> d 25.04/25.04 Rule remains 25.04/25.04 Proof: 25.04/25.04 NO_CONDS 25.04/25.04 25.04/25.04 CRule InfChecker Info: 25.04/25.04 b -> c 25.04/25.04 Rule remains 25.04/25.04 Proof: 25.04/25.04 NO_CONDS 25.04/25.04 25.04/25.04 CRule InfChecker Info: 25.04/25.04 b -> d 25.04/25.04 Rule remains 25.04/25.04 Proof: 25.04/25.04 NO_CONDS 25.04/25.04 25.04/25.04 CRule InfChecker Info: 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 Rule remains 25.04/25.04 Proof: 25.04/25.04 NO 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 25.04/25.04 Infeasibility Problem: 25.04/25.04 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 25.04/25.04 (STRATEGY CONTEXTSENSITIVE 25.04/25.04 (a) 25.04/25.04 (b) 25.04/25.04 (f 1) 25.04/25.04 (g 1 2) 25.04/25.04 (c) 25.04/25.04 (d) 25.04/25.04 (fSNonEmpty) 25.04/25.04 (h 1 2) 25.04/25.04 ) 25.04/25.04 (RULES 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S:S) -> x:S:S | x:S:S ->* c 25.04/25.04 g(x:S:S,x:S:S) -> h(x:S:S,x:S:S) 25.04/25.04 )] 25.04/25.04 25.04/25.04 Infeasibility Conditions: 25.04/25.04 x:S:S ->* c 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 25.04/25.04 Obtaining a proof using Prover9: 25.04/25.04 25.04/25.04 -> Prover9 Output: 25.04/25.04 ============================== Prover9 =============================== 25.04/25.04 Prover9 (64) version 2009-11A, November 2009. 25.04/25.04 Process 110612 was started by ubuntu on ubuntu, 25.04/25.04 Fri Jul 16 15:08:01 2021 25.04/25.04 The command was "./prover9 -f /tmp/prover9110603-0.in". 25.04/25.04 ============================== end of head =========================== 25.04/25.04 25.04/25.04 ============================== INPUT ================================= 25.04/25.04 25.04/25.04 % Reading from file /tmp/prover9110603-0.in 25.04/25.04 25.04/25.04 assign(max_seconds,20). 25.04/25.04 25.04/25.04 formulas(assumptions). 25.04/25.04 ->*_s0(x,x) # label(reflexivity). 25.04/25.04 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 25.04/25.04 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 25.04/25.04 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 25.04/25.04 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 25.04/25.04 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 25.04/25.04 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 25.04/25.04 ->_s0(a,c) # label(replacement). 25.04/25.04 ->_s0(a,d) # label(replacement). 25.04/25.04 ->_s0(b,c) # label(replacement). 25.04/25.04 ->_s0(b,d) # label(replacement). 25.04/25.04 ->*_s0(x2,c) -> ->_s0(f(x2),x2) # label(replacement). 25.04/25.04 ->_s0(g(x2,x2),h(x2,x2)) # label(replacement). 25.04/25.04 end_of_list. 25.04/25.04 25.04/25.04 formulas(goals). 25.04/25.04 (exists x2 ->*_s0(x2,c)) # label(goal). 25.04/25.04 end_of_list. 25.04/25.04 25.04/25.04 ============================== end of input ========================== 25.04/25.04 25.04/25.04 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.04/25.04 25.04/25.04 % Formulas that are not ordinary clauses: 25.04/25.04 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.04/25.04 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 3 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 4 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 5 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 6 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 7 ->*_s0(x2,c) -> ->_s0(f(x2),x2) # label(replacement) # label(non_clause). [assumption]. 25.04/25.04 8 (exists x2 ->*_s0(x2,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.04/25.04 25.04/25.04 ============================== end of process non-clausal formulas === 25.04/25.04 25.04/25.04 ============================== PROCESS INITIAL CLAUSES =============== 25.04/25.04 25.04/25.04 % Clauses before input processing: 25.04/25.04 25.04/25.04 formulas(usable). 25.04/25.04 end_of_list. 25.04/25.04 25.04/25.04 formulas(sos). 25.04/25.04 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.04/25.04 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.04/25.04 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 25.04/25.04 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 25.04/25.04 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 25.04/25.04 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 25.04/25.04 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 25.04/25.04 ->_s0(a,c) # label(replacement). [assumption]. 25.04/25.04 ->_s0(a,d) # label(replacement). [assumption]. 25.04/25.04 ->_s0(b,c) # label(replacement). [assumption]. 25.04/25.04 ->_s0(b,d) # label(replacement). [assumption]. 25.04/25.04 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 25.04/25.04 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 25.04/25.04 -->*_s0(x,c) # label(goal). [deny(8)]. 25.04/25.04 end_of_list. 25.04/25.04 25.04/25.04 formulas(demodulators). 25.04/25.04 end_of_list. 25.04/25.04 25.04/25.04 ============================== PREDICATE ELIMINATION ================= 25.04/25.04 25.04/25.04 No predicates eliminated. 25.04/25.04 25.04/25.04 ============================== end predicate elimination ============= 25.04/25.04 25.04/25.04 Auto_denials: 25.04/25.04 % copying label goal to answer in negative clause 25.04/25.04 25.04/25.04 Term ordering decisions: 25.04/25.04 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 25.04/25.04 Function symbol precedence: function_order([ c, a, b, d, g, h, f ]). 25.04/25.04 After inverse_order: (no changes). 25.04/25.04 Unfolding symbols: (none). 25.04/25.04 25.04/25.04 Auto_inference settings: 25.04/25.04 % set(neg_binary_resolution). % (HNE depth_diff=-6) 25.04/25.04 % clear(ordered_res). % (HNE depth_diff=-6) 25.04/25.04 % set(ur_resolution). % (HNE depth_diff=-6) 25.04/25.04 % set(ur_resolution) -> set(pos_ur_resolution). 25.04/25.04 % set(ur_resolution) -> set(neg_ur_resolution). 25.04/25.04 25.04/25.04 Auto_process settings: (no changes). 25.04/25.04 25.04/25.04 kept: 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.04/25.04 kept: 10 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 25.04/25.04 kept: 11 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 25.04/25.04 kept: 12 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(3)]. 25.04/25.04 kept: 13 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(4)]. 25.04/25.04 kept: 14 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(5)]. 25.04/25.04 kept: 15 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(6)]. 25.04/25.04 kept: 16 ->_s0(a,c) # label(replacement). [assumption]. 25.04/25.04 kept: 17 ->_s0(a,d) # label(replacement). [assumption]. 25.04/25.04 kept: 18 ->_s0(b,c) # label(replacement). [assumption]. 25.04/25.04 kept: 19 ->_s0(b,d) # label(replacement). [assumption]. 25.04/25.04 kept: 20 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(7)]. 25.04/25.04 kept: 21 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 25.04/25.04 kept: 22 -->*_s0(x,c) # label(goal) # answer(goal). [deny(8)]. 25.04/25.04 25.04/25.04 ============================== PROOF ================================= 25.04/25.04 25.04/25.04 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 25.04/25.04 % Length of proof is 4. 25.04/25.04 % Level of proof is 2. 25.04/25.04 % Maximum clause weight is 3.000. 25.04/25.04 % Given clauses 0. 25.04/25.04 25.04/25.04 8 (exists x2 ->*_s0(x2,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 25.04/25.04 9 ->*_s0(x,x) # label(reflexivity). [assumption]. 25.04/25.04 22 -->*_s0(x,c) # label(goal) # answer(goal). [deny(8)]. 25.04/25.04 23 $F # answer(goal). [resolve(22,a,9,a)]. 25.04/25.04 25.04/25.04 ============================== end of proof ========================== 25.04/25.04 25.04/25.04 ============================== STATISTICS ============================ 25.04/25.04 25.04/25.04 Given=0. Generated=14. Kept=14. proofs=1. 25.04/25.04 Usable=0. Sos=0. Demods=0. Limbo=13, Disabled=14. Hints=0. 25.04/25.04 Kept_by_rule=0, Deleted_by_rule=0. 25.04/25.04 Forward_subsumed=0. Back_subsumed=0. 25.04/25.04 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 25.04/25.04 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 25.04/25.04 Demod_attempts=0. Demod_rewrites=0. 25.04/25.04 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 25.04/25.04 Nonunit_fsub_feature_tests=2. Nonunit_bsub_feature_tests=0. 25.04/25.04 Megabytes=0.05. 25.04/25.04 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.04/25.04 25.04/25.04 ============================== end of statistics ===================== 25.04/25.04 25.04/25.04 ============================== end of search ========================= 25.04/25.04 25.04/25.04 THEOREM PROVED 25.04/25.04 25.04/25.04 Exiting with 1 proof. 25.04/25.04 25.04/25.04 Process 110612 exit (max_proofs) Fri Jul 16 15:08:01 2021 25.04/25.04 25.04/25.04 25.04/25.04 The problem is feasible. 25.04/25.04 25.04/25.04 25.04/25.04 CRule InfChecker Info: 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 Rule remains 25.04/25.04 Proof: 25.04/25.04 NO_CONDS 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 Confluence Problem: 25.04/25.04 (VAR x:S) 25.04/25.04 (STRATEGY CONTEXTSENSITIVE 25.04/25.04 (a) 25.04/25.04 (b) 25.04/25.04 (f 1) 25.04/25.04 (g 1 2) 25.04/25.04 (c) 25.04/25.04 (d) 25.04/25.04 (fSNonEmpty) 25.04/25.04 (h 1 2) 25.04/25.04 ) 25.04/25.04 (RULES 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 ) 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 25.04/25.04 Critical Pairs Processor: 25.04/25.04 -> Rules: 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 -> Vars: 25.04/25.04 "x", "x" 25.04/25.04 -> FVars: 25.04/25.04 "x2", "x3" 25.04/25.04 -> PVars: 25.04/25.04 "x": ["x2", "x3"] 25.04/25.04 25.04/25.04 -> Rlps: 25.04/25.04 crule: a -> c, id: 1, possubterms: a-> [] 25.04/25.04 crule: a -> d, id: 2, possubterms: a-> [] 25.04/25.04 crule: b -> c, id: 3, possubterms: b-> [] 25.04/25.04 crule: b -> d, id: 4, possubterms: b-> [] 25.04/25.04 crule: f(x2:S) -> x2:S | x2:S ->* c, id: 5, possubterms: f(x2:S)-> [] 25.04/25.04 crule: g(x3:S,x3:S) -> h(x3:S,x3:S), id: 6, possubterms: g(x3:S,x3:S)-> [] 25.04/25.04 25.04/25.04 -> Unifications: 25.04/25.04 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 25.04/25.04 R4 unifies with R3 at p: [], l: b, lp: b, conds: {}, sig: {}, l': b, r: d, r': c 25.04/25.04 25.04/25.04 -> Critical pairs info: 25.04/25.04 => Not trivial, Overlay, N1 25.04/25.04 25.04/25.04 -> Problem conclusions: 25.04/25.04 Not left linear, Not right linear, Not linear 25.04/25.04 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 25.04/25.04 CTRS Type: 1 25.04/25.04 Deterministic, Strongly deterministic 25.04/25.04 Oriented CTRS, Properly oriented CTRS, Not join CTRS 25.04/25.04 Maybe right-stable CTRS, Overlay CTRS 25.04/25.04 Maybe normal CTRS, Maybe almost normal CTRS 25.04/25.04 Maybe terminating CTRS, Maybe joinable CCPs 25.04/25.04 Maybe level confluent 25.04/25.04 Maybe confluent 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 Confluence Problem: 25.04/25.04 (VAR x:S) 25.04/25.04 (STRATEGY CONTEXTSENSITIVE 25.04/25.04 (a) 25.04/25.04 (b) 25.04/25.04 (f 1) 25.04/25.04 (g 1 2) 25.04/25.04 (c) 25.04/25.04 (d) 25.04/25.04 (fSNonEmpty) 25.04/25.04 (h 1 2) 25.04/25.04 ) 25.04/25.04 (RULES 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 ) 25.04/25.04 Critical Pairs: 25.04/25.04 => Not trivial, Overlay, N1 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 25.04/25.04 Conditional Critical Pairs Distributor Processor 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 Confluence Problem: 25.04/25.04 (VAR x:S) 25.04/25.04 (STRATEGY CONTEXTSENSITIVE 25.04/25.04 (a) 25.04/25.04 (b) 25.04/25.04 (f 1) 25.04/25.04 (g 1 2) 25.04/25.04 (c) 25.04/25.04 (d) 25.04/25.04 (fSNonEmpty) 25.04/25.04 (h 1 2) 25.04/25.04 ) 25.04/25.04 (RULES 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 ) 25.04/25.04 Critical Pairs: 25.04/25.04 => Not trivial, Overlay, N1 25.04/25.04 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 25.04/25.04 25.04/25.04 Infeasible Convergence No Conditions CCP Processor: 25.04/25.04 Infeasible convergence? 25.04/25.04 YES 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 25.04/25.04 Infeasibility Problem: 25.04/25.04 [(VAR vNonEmpty:S x:S z:S) 25.04/25.04 (STRATEGY CONTEXTSENSITIVE 25.04/25.04 (a) 25.04/25.04 (b) 25.04/25.04 (f 1) 25.04/25.04 (g 1 2) 25.04/25.04 (c) 25.04/25.04 (d) 25.04/25.04 (fSNonEmpty) 25.04/25.04 (h 1 2) 25.04/25.04 ) 25.04/25.04 (RULES 25.04/25.04 a -> c 25.04/25.04 a -> d 25.04/25.04 b -> c 25.04/25.04 b -> d 25.04/25.04 f(x:S) -> x:S | x:S ->* c 25.04/25.04 g(x:S,x:S) -> h(x:S,x:S) 25.04/25.04 )] 25.04/25.04 25.04/25.04 Infeasibility Conditions: 25.04/25.04 c ->* z:S, d ->* z:S 25.04/25.04 25.04/25.04 Problem 1: 25.04/25.04 25.04/25.04 Obtaining a model using Mace4: 25.04/25.04 25.04/25.04 -> Usable Rules: 25.04/25.04 Empty 25.04/25.04 25.04/25.04 -> Mace4 Output: 25.04/25.04 ============================== Mace4 ================================= 25.04/25.04 Mace4 (64) version 2009-11A, November 2009. 25.04/25.04 Process 110650 was started by ubuntu on ubuntu, 25.04/25.04 Fri Jul 16 15:08:01 2021 25.04/25.04 The command was "./mace4 -c -f /tmp/mace4110628-2.in". 25.04/25.04 ============================== end of head =========================== 25.04/25.04 25.04/25.04 ============================== INPUT ================================= 25.04/25.04 25.04/25.04 % Reading from file /tmp/mace4110628-2.in 25.04/25.04 25.04/25.04 assign(max_seconds,10). 25.04/25.04 25.04/25.04 formulas(assumptions). 25.04/25.04 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 25.04/25.04 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 25.04/25.04 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 25.04/25.04 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 25.04/25.04 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 25.04/25.04 ->*(x,x) # label(reflexivity). 25.04/25.04 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 25.04/25.04 end_of_list. 25.04/25.04 25.04/25.04 formulas(goals). 25.04/25.04 (exists x2 (->*(c,x2) & ->*(d,x2))) # label(goal). 25.04/25.04 end_of_list. 25.04/25.04 25.04/25.04 ============================== end of input ========================== 25.04/25.04 25.04/25.04 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 25.04/25.04 25.04/25.04 % Formulas that are not ordinary clauses: 25.04/25.04 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 2 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 3 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 4 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 5 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 25.04/25.04 6 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 25.04/25.04 7 (exists x2 (->*(c,x2) & ->*(d,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 25.04/25.04 25.04/25.04 ============================== end of process non-clausal formulas === 25.04/25.04 25.04/25.04 ============================== CLAUSES FOR SEARCH ==================== 25.04/25.04 25.04/25.04 formulas(mace4_clauses). 25.04/25.04 -->(x,y) | ->(f(x),f(y)) # label(congruence). 25.04/25.04 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 25.04/25.04 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 25.04/25.04 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 25.04/25.04 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 25.04/25.04 ->*(x,x) # label(reflexivity). 25.04/25.04 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 25.04/25.04 -->*(c,x) | -->*(d,x) # label(goal). 25.04/25.04 end_of_list. 25.04/25.04 25.04/25.04 ============================== end of clauses for search ============= 25.04/25.04 25.04/25.04 % There are no natural numbers in the input. 25.04/25.04 25.04/25.04 ============================== DOMAIN SIZE 2 ========================= 25.04/25.04 25.04/25.04 ============================== MODEL ================================= 25.04/25.04 25.04/25.04 interpretation( 2, [number=1, seconds=0], [ 25.04/25.04 25.04/25.04 function(c, [ 0 ]), 25.04/25.04 25.04/25.04 function(d, [ 1 ]), 25.04/25.04 25.04/25.04 function(f(_), [ 0, 0 ]), 25.04/25.04 25.04/25.04 function(g(_,_), [ 25.04/25.04 0, 0, 25.04/25.04 0, 0 ]), 25.04/25.04 25.04/25.04 function(h(_,_), [ 25.04/25.04 0, 0, 25.04/25.04 0, 0 ]), 25.04/25.04 25.04/25.04 relation(->*(_,_), [ 25.04/25.04 1, 0, 25.04/25.04 0, 1 ]), 25.04/25.04 25.04/25.04 relation(->(_,_), [ 25.04/25.04 0, 0, 25.04/25.04 0, 0 ]) 25.04/25.04 ]). 25.04/25.04 25.04/25.04 ============================== end of model ========================== 25.04/25.04 25.04/25.04 ============================== STATISTICS ============================ 25.04/25.04 25.04/25.04 For domain size 2. 25.04/25.04 25.04/25.04 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 25.04/25.04 Ground clauses: seen=48, kept=44. 25.04/25.04 Selections=12, assignments=12, propagations=8, current_models=1. 25.04/25.04 Rewrite_terms=76, rewrite_bools=56, indexes=7. 25.04/25.04 Rules_from_neg_clauses=1, cross_offs=1. 25.04/25.04 25.04/25.04 ============================== end of statistics ===================== 25.04/25.04 25.04/25.04 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 25.04/25.04 25.04/25.04 Exiting with 1 model. 25.04/25.04 25.04/25.04 Process 110650 exit (max_models) Fri Jul 16 15:08:01 2021 25.04/25.04 The process finished Fri Jul 16 15:08:01 2021 25.04/25.04 25.04/25.04 25.04/25.04 Mace4 cooked interpretation: 25.04/25.04 25.04/25.04 25.04/25.04 25.04/25.04 The problem is infeasible. 25.04/25.04 25.04/25.04 25.04/25.04 The problem is not joinable. 25.04/25.04 28.65user 0.76system 0:25.40elapsed 115%CPU (0avgtext+0avgdata 135892maxresident)k 25.04/25.04 8inputs+0outputs (0major+93135minor)pagefaults 0swaps