20.028/20.028 NO 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 20.028/20.028 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 Confluence Problem: 20.028/20.028 (VAR vNonEmpty:S x:S y:S z:S) 20.028/20.028 (STRATEGY CONTEXTSENSITIVE 20.028/20.028 (a) 20.028/20.028 (f 1 2) 20.028/20.028 (g 1 2) 20.028/20.028 (c) 20.028/20.028 (d) 20.028/20.028 (fSNonEmpty) 20.028/20.028 (h 1 2) 20.028/20.028 (t 1) 20.028/20.028 ) 20.028/20.028 (RULES 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 ) 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 20.028/20.028 Inlining of Conditions Processor [STERN17]: 20.028/20.028 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 Confluence Problem: 20.028/20.028 (VAR vNonEmpty:S x:S y:S z:S) 20.028/20.028 (STRATEGY CONTEXTSENSITIVE 20.028/20.028 (a) 20.028/20.028 (f 1 2) 20.028/20.028 (g 1 2) 20.028/20.028 (c) 20.028/20.028 (d) 20.028/20.028 (fSNonEmpty) 20.028/20.028 (h 1 2) 20.028/20.028 (t 1) 20.028/20.028 ) 20.028/20.028 (RULES 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 ) 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 20.028/20.028 Clean CTRS Processor: 20.028/20.028 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 Confluence Problem: 20.028/20.028 (VAR x:S y:S z:S) 20.028/20.028 (STRATEGY CONTEXTSENSITIVE 20.028/20.028 (a) 20.028/20.028 (f 1 2) 20.028/20.028 (g 1 2) 20.028/20.028 (c) 20.028/20.028 (d) 20.028/20.028 (fSNonEmpty) 20.028/20.028 (h 1 2) 20.028/20.028 (t 1) 20.028/20.028 ) 20.028/20.028 (RULES 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 ) 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 20.028/20.028 CRule InfChecker Info: 20.028/20.028 a -> t(c) 20.028/20.028 Rule remains 20.028/20.028 Proof: 20.028/20.028 NO_CONDS 20.028/20.028 20.028/20.028 CRule InfChecker Info: 20.028/20.028 a -> t(d) 20.028/20.028 Rule remains 20.028/20.028 Proof: 20.028/20.028 NO_CONDS 20.028/20.028 20.028/20.028 CRule InfChecker Info: 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 Rule remains 20.028/20.028 Proof: 20.028/20.028 NO 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 20.028/20.028 Infeasibility Problem: 20.028/20.028 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S y:S:S z:S:S) 20.028/20.028 (STRATEGY CONTEXTSENSITIVE 20.028/20.028 (a) 20.028/20.028 (f 1 2) 20.028/20.028 (g 1 2) 20.028/20.028 (c) 20.028/20.028 (d) 20.028/20.028 (fSNonEmpty) 20.028/20.028 (h 1 2) 20.028/20.028 (t 1) 20.028/20.028 ) 20.028/20.028 (RULES 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S:S,y:S:S) -> z:S:S | x:S:S ->* t(z:S:S) 20.028/20.028 g(x:S:S,x:S:S) -> h(x:S:S,x:S:S) 20.028/20.028 )] 20.028/20.028 20.028/20.028 Infeasibility Conditions: 20.028/20.028 x:S:S ->* t(z:S:S) 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 20.028/20.028 Obtaining a proof using Prover9: 20.028/20.028 20.028/20.028 -> Prover9 Output: 20.028/20.028 ============================== Prover9 =============================== 20.028/20.028 Prover9 (64) version 2009-11A, November 2009. 20.028/20.028 Process 110318 was started by ubuntu on ubuntu, 20.028/20.028 Fri Jul 16 15:06:51 2021 20.028/20.028 The command was "./prover9 -f /tmp/prover9110309-0.in". 20.028/20.028 ============================== end of head =========================== 20.028/20.028 20.028/20.028 ============================== INPUT ================================= 20.028/20.028 20.028/20.028 % Reading from file /tmp/prover9110309-0.in 20.028/20.028 20.028/20.028 assign(max_seconds,20). 20.028/20.028 20.028/20.028 formulas(assumptions). 20.028/20.028 ->*_s0(x,x) # label(reflexivity). 20.028/20.028 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.028/20.028 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence). 20.028/20.028 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence). 20.028/20.028 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence). 20.028/20.028 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence). 20.028/20.028 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence). 20.028/20.028 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence). 20.028/20.028 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence). 20.028/20.028 ->_s0(a,t(c)) # label(replacement). 20.028/20.028 ->_s0(a,t(d)) # label(replacement). 20.028/20.028 ->*_s0(x2,t(x4)) -> ->_s0(f(x2,x3),x4) # label(replacement). 20.028/20.028 ->_s0(g(x2,x2),h(x2,x2)) # label(replacement). 20.028/20.028 end_of_list. 20.028/20.028 20.028/20.028 formulas(goals). 20.028/20.028 (exists x2 exists x4 ->*_s0(x2,t(x4))) # label(goal). 20.028/20.028 end_of_list. 20.028/20.028 20.028/20.028 ============================== end of input ========================== 20.028/20.028 20.028/20.028 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.028/20.028 20.028/20.028 % Formulas that are not ordinary clauses: 20.028/20.028 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.028/20.028 2 ->_s0(x1,y) -> ->_s0(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 3 ->_s0(x2,y) -> ->_s0(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 4 ->_s0(x1,y) -> ->_s0(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 5 ->_s0(x2,y) -> ->_s0(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 6 ->_s0(x1,y) -> ->_s0(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 7 ->_s0(x2,y) -> ->_s0(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 8 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 9 ->*_s0(x2,t(x4)) -> ->_s0(f(x2,x3),x4) # label(replacement) # label(non_clause). [assumption]. 20.028/20.028 10 (exists x2 exists x4 ->*_s0(x2,t(x4))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.028/20.028 20.028/20.028 ============================== end of process non-clausal formulas === 20.028/20.028 20.028/20.028 ============================== PROCESS INITIAL CLAUSES =============== 20.028/20.028 20.028/20.028 % Clauses before input processing: 20.028/20.028 20.028/20.028 formulas(usable). 20.028/20.028 end_of_list. 20.028/20.028 20.028/20.028 formulas(sos). 20.028/20.028 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.028/20.028 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.028/20.028 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 20.028/20.028 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 20.028/20.028 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 20.028/20.028 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 20.028/20.028 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 20.028/20.028 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 20.028/20.028 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(8)]. 20.028/20.028 ->_s0(a,t(c)) # label(replacement). [assumption]. 20.028/20.028 ->_s0(a,t(d)) # label(replacement). [assumption]. 20.028/20.028 -->*_s0(x,t(y)) | ->_s0(f(x,z),y) # label(replacement). [clausify(9)]. 20.028/20.028 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.028/20.028 -->*_s0(x,t(y)) # label(goal). [deny(10)]. 20.028/20.028 end_of_list. 20.028/20.028 20.028/20.028 formulas(demodulators). 20.028/20.028 end_of_list. 20.028/20.028 20.028/20.028 ============================== PREDICATE ELIMINATION ================= 20.028/20.028 20.028/20.028 No predicates eliminated. 20.028/20.028 20.028/20.028 ============================== end predicate elimination ============= 20.028/20.028 20.028/20.028 Auto_denials: 20.028/20.028 % copying label goal to answer in negative clause 20.028/20.028 20.028/20.028 Term ordering decisions: 20.028/20.028 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.028/20.028 Function symbol precedence: function_order([ a, c, d, f, g, h, t ]). 20.028/20.028 After inverse_order: (no changes). 20.028/20.028 Unfolding symbols: (none). 20.028/20.028 20.028/20.028 Auto_inference settings: 20.028/20.028 % set(neg_binary_resolution). % (HNE depth_diff=-7) 20.028/20.028 % clear(ordered_res). % (HNE depth_diff=-7) 20.028/20.028 % set(ur_resolution). % (HNE depth_diff=-7) 20.028/20.028 % set(ur_resolution) -> set(pos_ur_resolution). 20.028/20.028 % set(ur_resolution) -> set(neg_ur_resolution). 20.028/20.028 20.028/20.028 Auto_process settings: (no changes). 20.028/20.028 20.028/20.028 kept: 11 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.028/20.028 kept: 12 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.028/20.028 kept: 13 -->_s0(x,y) | ->_s0(f(x,z),f(y,z)) # label(congruence). [clausify(2)]. 20.028/20.028 kept: 14 -->_s0(x,y) | ->_s0(f(z,x),f(z,y)) # label(congruence). [clausify(3)]. 20.028/20.028 kept: 15 -->_s0(x,y) | ->_s0(g(x,z),g(y,z)) # label(congruence). [clausify(4)]. 20.028/20.028 kept: 16 -->_s0(x,y) | ->_s0(g(z,x),g(z,y)) # label(congruence). [clausify(5)]. 20.028/20.028 kept: 17 -->_s0(x,y) | ->_s0(h(x,z),h(y,z)) # label(congruence). [clausify(6)]. 20.028/20.028 kept: 18 -->_s0(x,y) | ->_s0(h(z,x),h(z,y)) # label(congruence). [clausify(7)]. 20.028/20.028 kept: 19 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(8)]. 20.028/20.028 kept: 20 ->_s0(a,t(c)) # label(replacement). [assumption]. 20.028/20.028 kept: 21 ->_s0(a,t(d)) # label(replacement). [assumption]. 20.028/20.028 kept: 22 -->*_s0(x,t(y)) | ->_s0(f(x,z),y) # label(replacement). [clausify(9)]. 20.028/20.028 kept: 23 ->_s0(g(x,x),h(x,x)) # label(replacement). [assumption]. 20.028/20.028 kept: 24 -->*_s0(x,t(y)) # label(goal) # answer(goal). [deny(10)]. 20.028/20.028 20.028/20.028 ============================== PROOF ================================= 20.028/20.028 20.028/20.028 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.028/20.028 % Length of proof is 4. 20.028/20.028 % Level of proof is 2. 20.028/20.028 % Maximum clause weight is 4.000. 20.028/20.028 % Given clauses 0. 20.028/20.028 20.028/20.028 10 (exists x2 exists x4 ->*_s0(x2,t(x4))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.028/20.028 11 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.028/20.028 24 -->*_s0(x,t(y)) # label(goal) # answer(goal). [deny(10)]. 20.028/20.028 25 $F # answer(goal). [resolve(24,a,11,a)]. 20.028/20.028 20.028/20.028 ============================== end of proof ========================== 20.028/20.028 20.028/20.028 ============================== STATISTICS ============================ 20.028/20.028 20.028/20.028 Given=0. Generated=14. Kept=14. proofs=1. 20.028/20.028 Usable=0. Sos=0. Demods=0. Limbo=13, Disabled=14. Hints=0. 20.028/20.028 Kept_by_rule=0, Deleted_by_rule=0. 20.028/20.028 Forward_subsumed=0. Back_subsumed=0. 20.028/20.028 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.028/20.028 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.028/20.028 Demod_attempts=0. Demod_rewrites=0. 20.028/20.028 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.028/20.028 Nonunit_fsub_feature_tests=3. Nonunit_bsub_feature_tests=0. 20.028/20.028 Megabytes=0.06. 20.028/20.028 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.028/20.028 20.028/20.028 ============================== end of statistics ===================== 20.028/20.028 20.028/20.028 ============================== end of search ========================= 20.028/20.028 20.028/20.028 THEOREM PROVED 20.028/20.028 20.028/20.028 Exiting with 1 proof. 20.028/20.028 20.028/20.028 Process 110318 exit (max_proofs) Fri Jul 16 15:06:51 2021 20.028/20.028 20.028/20.028 20.028/20.028 The problem is feasible. 20.028/20.028 20.028/20.028 20.028/20.028 CRule InfChecker Info: 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 Rule remains 20.028/20.028 Proof: 20.028/20.028 NO_CONDS 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 Confluence Problem: 20.028/20.028 (VAR x:S y:S z:S) 20.028/20.028 (STRATEGY CONTEXTSENSITIVE 20.028/20.028 (a) 20.028/20.028 (f 1 2) 20.028/20.028 (g 1 2) 20.028/20.028 (c) 20.028/20.028 (d) 20.028/20.028 (fSNonEmpty) 20.028/20.028 (h 1 2) 20.028/20.028 (t 1) 20.028/20.028 ) 20.028/20.028 (RULES 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 ) 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 20.028/20.028 Critical Pairs Processor: 20.028/20.028 -> Rules: 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 -> Vars: 20.028/20.028 "x", "y", "z", "x" 20.028/20.028 -> FVars: 20.028/20.028 "x4", "x5", "x6", "x7" 20.028/20.028 -> PVars: 20.028/20.028 "x": ["x4", "x7"], "y": ["x5"], "z": ["x6"] 20.028/20.028 20.028/20.028 -> Rlps: 20.028/20.028 crule: a -> t(c), id: 1, possubterms: a-> [] 20.028/20.028 crule: a -> t(d), id: 2, possubterms: a-> [] 20.028/20.028 crule: f(x4:S,x5:S) -> x6:S | x4:S ->* t(x6:S), id: 3, possubterms: f(x4:S,x5:S)-> [] 20.028/20.028 crule: g(x7:S,x7:S) -> h(x7:S,x7:S), id: 4, possubterms: g(x7:S,x7:S)-> [] 20.028/20.028 20.028/20.028 -> Unifications: 20.028/20.028 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: t(d), r': t(c) 20.028/20.028 20.028/20.028 -> Critical pairs info: 20.028/20.028 => Not trivial, Overlay, N1 20.028/20.028 20.028/20.028 -> Problem conclusions: 20.028/20.028 Not left linear, Not right linear, Not linear 20.028/20.028 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.028/20.028 CTRS Type: 3 20.028/20.028 Deterministic, Strongly deterministic 20.028/20.028 Oriented CTRS, Properly oriented CTRS, Not join CTRS 20.028/20.028 Maybe right-stable CTRS, Overlay CTRS 20.028/20.028 Maybe normal CTRS, Maybe almost normal CTRS 20.028/20.028 Maybe terminating CTRS, Maybe joinable CCPs 20.028/20.028 Maybe level confluent 20.028/20.028 Maybe confluent 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 Confluence Problem: 20.028/20.028 (VAR x:S y:S z:S) 20.028/20.028 (STRATEGY CONTEXTSENSITIVE 20.028/20.028 (a) 20.028/20.028 (f 1 2) 20.028/20.028 (g 1 2) 20.028/20.028 (c) 20.028/20.028 (d) 20.028/20.028 (fSNonEmpty) 20.028/20.028 (h 1 2) 20.028/20.028 (t 1) 20.028/20.028 ) 20.028/20.028 (RULES 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 ) 20.028/20.028 Critical Pairs: 20.028/20.028 => Not trivial, Overlay, N1 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 20.028/20.028 Conditional Critical Pairs Distributor Processor 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 Confluence Problem: 20.028/20.028 (VAR x:S y:S z:S) 20.028/20.028 (STRATEGY CONTEXTSENSITIVE 20.028/20.028 (a) 20.028/20.028 (f 1 2) 20.028/20.028 (g 1 2) 20.028/20.028 (c) 20.028/20.028 (d) 20.028/20.028 (fSNonEmpty) 20.028/20.028 (h 1 2) 20.028/20.028 (t 1) 20.028/20.028 ) 20.028/20.028 (RULES 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 ) 20.028/20.028 Critical Pairs: 20.028/20.028 => Not trivial, Overlay, N1 20.028/20.028 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.028/20.028 20.028/20.028 Infeasible Convergence No Conditions CCP Processor: 20.028/20.028 Infeasible convergence? 20.028/20.028 YES 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 20.028/20.028 Infeasibility Problem: 20.028/20.028 [(VAR vNonEmpty:S x:S y:S z:S) 20.028/20.028 (STRATEGY CONTEXTSENSITIVE 20.028/20.028 (a) 20.028/20.028 (f 1 2) 20.028/20.028 (g 1 2) 20.028/20.028 (c) 20.028/20.028 (d) 20.028/20.028 (fSNonEmpty) 20.028/20.028 (h 1 2) 20.028/20.028 (t 1) 20.028/20.028 ) 20.028/20.028 (RULES 20.028/20.028 a -> t(c) 20.028/20.028 a -> t(d) 20.028/20.028 f(x:S,y:S) -> z:S | x:S ->* t(z:S) 20.028/20.028 g(x:S,x:S) -> h(x:S,x:S) 20.028/20.028 )] 20.028/20.028 20.028/20.028 Infeasibility Conditions: 20.028/20.028 t(c) ->* z:S, t(d) ->* z:S 20.028/20.028 20.028/20.028 Problem 1: 20.028/20.028 20.028/20.028 Obtaining a model using Mace4: 20.028/20.028 20.028/20.028 -> Usable Rules: 20.028/20.028 Empty 20.028/20.028 20.028/20.028 -> Mace4 Output: 20.028/20.028 ============================== Mace4 ================================= 20.028/20.028 Mace4 (64) version 2009-11A, November 2009. 20.028/20.028 Process 110359 was started by ubuntu on ubuntu, 20.028/20.028 Fri Jul 16 15:06:51 2021 20.028/20.028 The command was "./mace4 -c -f /tmp/mace4110335-2.in". 20.028/20.028 ============================== end of head =========================== 20.028/20.028 20.028/20.028 ============================== INPUT ================================= 20.028/20.028 20.028/20.028 % Reading from file /tmp/mace4110335-2.in 20.028/20.028 20.028/20.028 assign(max_seconds,10). 20.028/20.028 20.028/20.028 formulas(assumptions). 20.028/20.028 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence). 20.028/20.028 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence). 20.028/20.028 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence). 20.028/20.028 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence). 20.028/20.028 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence). 20.028/20.028 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence). 20.028/20.028 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 20.028/20.028 ->*(x,x) # label(reflexivity). 20.028/20.028 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.028/20.028 end_of_list. 20.028/20.028 20.028/20.028 formulas(goals). 20.028/20.028 (exists x3 (->*(t(c),x3) & ->*(t(d),x3))) # label(goal). 20.028/20.028 end_of_list. 20.028/20.028 20.028/20.028 ============================== end of input ========================== 20.028/20.028 20.028/20.028 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.028/20.028 20.028/20.028 % Formulas that are not ordinary clauses: 20.028/20.028 1 ->(x1,y) -> ->(f(x1,x2),f(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 2 ->(x2,y) -> ->(f(x1,x2),f(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 3 ->(x1,y) -> ->(g(x1,x2),g(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 4 ->(x2,y) -> ->(g(x1,x2),g(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 5 ->(x1,y) -> ->(h(x1,x2),h(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 6 ->(x2,y) -> ->(h(x1,x2),h(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 7 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 20.028/20.028 8 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.028/20.028 9 (exists x3 (->*(t(c),x3) & ->*(t(d),x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.028/20.028 20.028/20.028 ============================== end of process non-clausal formulas === 20.028/20.028 20.028/20.028 ============================== CLAUSES FOR SEARCH ==================== 20.028/20.028 20.028/20.028 formulas(mace4_clauses). 20.028/20.028 -->(x,y) | ->(f(x,z),f(y,z)) # label(congruence). 20.028/20.028 -->(x,y) | ->(f(z,x),f(z,y)) # label(congruence). 20.028/20.028 -->(x,y) | ->(g(x,z),g(y,z)) # label(congruence). 20.028/20.028 -->(x,y) | ->(g(z,x),g(z,y)) # label(congruence). 20.028/20.028 -->(x,y) | ->(h(x,z),h(y,z)) # label(congruence). 20.028/20.028 -->(x,y) | ->(h(z,x),h(z,y)) # label(congruence). 20.028/20.028 -->(x,y) | ->(t(x),t(y)) # label(congruence). 20.028/20.028 ->*(x,x) # label(reflexivity). 20.028/20.028 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.028/20.028 -->*(t(c),x) | -->*(t(d),x) # label(goal). 20.028/20.028 end_of_list. 20.028/20.028 20.028/20.028 ============================== end of clauses for search ============= 20.028/20.028 20.028/20.028 % There are no natural numbers in the input. 20.028/20.028 20.028/20.028 ============================== DOMAIN SIZE 2 ========================= 20.028/20.028 20.028/20.028 ============================== MODEL ================================= 20.028/20.028 20.028/20.028 interpretation( 2, [number=1, seconds=0], [ 20.028/20.028 20.028/20.028 function(c, [ 0 ]), 20.028/20.028 20.028/20.028 function(d, [ 1 ]), 20.028/20.028 20.028/20.028 function(t(_), [ 0, 1 ]), 20.028/20.028 20.028/20.028 function(f(_,_), [ 20.028/20.028 0, 0, 20.028/20.028 0, 0 ]), 20.028/20.028 20.028/20.028 function(g(_,_), [ 20.028/20.028 0, 0, 20.028/20.028 0, 0 ]), 20.028/20.028 20.028/20.028 function(h(_,_), [ 20.028/20.028 0, 0, 20.028/20.028 0, 0 ]), 20.028/20.028 20.028/20.028 relation(->*(_,_), [ 20.028/20.028 1, 0, 20.028/20.028 0, 1 ]), 20.028/20.028 20.028/20.028 relation(->(_,_), [ 20.028/20.028 0, 0, 20.028/20.028 0, 0 ]) 20.028/20.028 ]). 20.028/20.028 20.028/20.028 ============================== end of model ========================== 20.028/20.028 20.028/20.028 ============================== STATISTICS ============================ 20.028/20.028 20.028/20.028 For domain size 2. 20.028/20.028 20.028/20.028 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.028/20.028 Ground clauses: seen=64, kept=60. 20.028/20.028 Selections=17, assignments=19, propagations=8, current_models=1. 20.028/20.028 Rewrite_terms=121, rewrite_bools=81, indexes=21. 20.028/20.028 Rules_from_neg_clauses=1, cross_offs=1. 20.028/20.028 20.028/20.028 ============================== end of statistics ===================== 20.028/20.028 20.028/20.028 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.028/20.028 20.028/20.028 Exiting with 1 model. 20.028/20.028 20.028/20.028 Process 110359 exit (max_models) Fri Jul 16 15:06:51 2021 20.028/20.028 The process finished Fri Jul 16 15:06:51 2021 20.028/20.028 20.028/20.028 20.028/20.028 Mace4 cooked interpretation: 20.028/20.028 20.028/20.028 20.028/20.028 20.028/20.028 The problem is infeasible. 20.028/20.028 20.028/20.028 20.028/20.028 The problem is not joinable. 20.028/20.028 27.59user 1.61system 0:20.28elapsed 143%CPU (0avgtext+0avgdata 116540maxresident)k 20.028/20.028 8inputs+0outputs (0major+84321minor)pagefaults 0swaps