20.035/20.035 NO 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 20.035/20.035 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 Confluence Problem: 20.035/20.035 (VAR vNonEmpty:S x:S z:S) 20.035/20.035 (STRATEGY CONTEXTSENSITIVE 20.035/20.035 (a) 20.035/20.035 (f 1) 20.035/20.035 (s 1) 20.035/20.035 (c) 20.035/20.035 (d) 20.035/20.035 (fSNonEmpty) 20.035/20.035 (k) 20.035/20.035 (t 1) 20.035/20.035 ) 20.035/20.035 (RULES 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 ) 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 20.035/20.035 Inlining of Conditions Processor [STERN17]: 20.035/20.035 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 Confluence Problem: 20.035/20.035 (VAR vNonEmpty:S x:S z:S) 20.035/20.035 (STRATEGY CONTEXTSENSITIVE 20.035/20.035 (a) 20.035/20.035 (f 1) 20.035/20.035 (s 1) 20.035/20.035 (c) 20.035/20.035 (d) 20.035/20.035 (fSNonEmpty) 20.035/20.035 (k) 20.035/20.035 (t 1) 20.035/20.035 ) 20.035/20.035 (RULES 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 ) 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 20.035/20.035 Clean CTRS Processor: 20.035/20.035 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 Confluence Problem: 20.035/20.035 (VAR x:S z:S) 20.035/20.035 (STRATEGY CONTEXTSENSITIVE 20.035/20.035 (a) 20.035/20.035 (f 1) 20.035/20.035 (s 1) 20.035/20.035 (c) 20.035/20.035 (d) 20.035/20.035 (fSNonEmpty) 20.035/20.035 (k) 20.035/20.035 (t 1) 20.035/20.035 ) 20.035/20.035 (RULES 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 ) 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 20.035/20.035 CRule InfChecker Info: 20.035/20.035 a -> c 20.035/20.035 Rule remains 20.035/20.035 Proof: 20.035/20.035 NO_CONDS 20.035/20.035 20.035/20.035 CRule InfChecker Info: 20.035/20.035 a -> d 20.035/20.035 Rule remains 20.035/20.035 Proof: 20.035/20.035 NO_CONDS 20.035/20.035 20.035/20.035 CRule InfChecker Info: 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 Rule remains 20.035/20.035 Proof: 20.035/20.035 NO 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 20.035/20.035 Infeasibility Problem: 20.035/20.035 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S z:S:S) 20.035/20.035 (STRATEGY CONTEXTSENSITIVE 20.035/20.035 (a) 20.035/20.035 (f 1) 20.035/20.035 (s 1) 20.035/20.035 (c) 20.035/20.035 (d) 20.035/20.035 (fSNonEmpty) 20.035/20.035 (k) 20.035/20.035 (t 1) 20.035/20.035 ) 20.035/20.035 (RULES 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S:S) -> z:S:S | s(x:S:S) ->* t(z:S:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 )] 20.035/20.035 20.035/20.035 Infeasibility Conditions: 20.035/20.035 s(x:S:S) ->* t(z:S:S) 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 20.035/20.035 Obtaining a proof using Prover9: 20.035/20.035 20.035/20.035 -> Prover9 Output: 20.035/20.035 ============================== Prover9 =============================== 20.035/20.035 Prover9 (64) version 2009-11A, November 2009. 20.035/20.035 Process 50729 was started by ubuntu on ubuntu, 20.035/20.035 Wed Jul 14 10:56:11 2021 20.035/20.035 The command was "./prover9 -f /tmp/prover950720-0.in". 20.035/20.035 ============================== end of head =========================== 20.035/20.035 20.035/20.035 ============================== INPUT ================================= 20.035/20.035 20.035/20.035 % Reading from file /tmp/prover950720-0.in 20.035/20.035 20.035/20.035 assign(max_seconds,20). 20.035/20.035 20.035/20.035 formulas(assumptions). 20.035/20.035 ->*_s0(x,x) # label(reflexivity). 20.035/20.035 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.035/20.035 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 20.035/20.035 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence). 20.035/20.035 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence). 20.035/20.035 ->_s0(a,c) # label(replacement). 20.035/20.035 ->_s0(a,d) # label(replacement). 20.035/20.035 ->*_s0(s(x2),t(x3)) -> ->_s0(f(x2),x3) # label(replacement). 20.035/20.035 ->_s0(s(c),t(k)) # label(replacement). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 formulas(goals). 20.035/20.035 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 ============================== end of input ========================== 20.035/20.035 20.035/20.035 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.035/20.035 20.035/20.035 % Formulas that are not ordinary clauses: 20.035/20.035 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.035/20.035 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 20.035/20.035 3 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 20.035/20.035 4 ->_s0(x1,y) -> ->_s0(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 20.035/20.035 5 ->*_s0(s(x2),t(x3)) -> ->_s0(f(x2),x3) # label(replacement) # label(non_clause). [assumption]. 20.035/20.035 6 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.035/20.035 20.035/20.035 ============================== end of process non-clausal formulas === 20.035/20.035 20.035/20.035 ============================== PROCESS INITIAL CLAUSES =============== 20.035/20.035 20.035/20.035 % Clauses before input processing: 20.035/20.035 20.035/20.035 formulas(usable). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 formulas(sos). 20.035/20.035 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.035/20.035 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.035/20.035 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 20.035/20.035 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.035/20.035 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(4)]. 20.035/20.035 ->_s0(a,c) # label(replacement). [assumption]. 20.035/20.035 ->_s0(a,d) # label(replacement). [assumption]. 20.035/20.035 -->*_s0(s(x),t(y)) | ->_s0(f(x),y) # label(replacement). [clausify(5)]. 20.035/20.035 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 20.035/20.035 -->*_s0(s(x),t(y)) # label(goal). [deny(6)]. 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 formulas(demodulators). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 ============================== PREDICATE ELIMINATION ================= 20.035/20.035 20.035/20.035 No predicates eliminated. 20.035/20.035 20.035/20.035 ============================== end predicate elimination ============= 20.035/20.035 20.035/20.035 Auto_denials: 20.035/20.035 % copying label goal to answer in negative clause 20.035/20.035 20.035/20.035 Term ordering decisions: 20.035/20.035 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.035/20.035 Function symbol precedence: function_order([ a, c, d, k, s, t, f ]). 20.035/20.035 After inverse_order: (no changes). 20.035/20.035 Unfolding symbols: (none). 20.035/20.035 20.035/20.035 Auto_inference settings: 20.035/20.035 % set(neg_binary_resolution). % (HNE depth_diff=-3) 20.035/20.035 % clear(ordered_res). % (HNE depth_diff=-3) 20.035/20.035 % set(ur_resolution). % (HNE depth_diff=-3) 20.035/20.035 % set(ur_resolution) -> set(pos_ur_resolution). 20.035/20.035 % set(ur_resolution) -> set(neg_ur_resolution). 20.035/20.035 20.035/20.035 Auto_process settings: (no changes). 20.035/20.035 20.035/20.035 kept: 7 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.035/20.035 kept: 8 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.035/20.035 kept: 9 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 20.035/20.035 kept: 10 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.035/20.035 kept: 11 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(4)]. 20.035/20.035 kept: 12 ->_s0(a,c) # label(replacement). [assumption]. 20.035/20.035 kept: 13 ->_s0(a,d) # label(replacement). [assumption]. 20.035/20.035 kept: 14 -->*_s0(s(x),t(y)) | ->_s0(f(x),y) # label(replacement). [clausify(5)]. 20.035/20.035 kept: 15 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 20.035/20.035 kept: 16 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(6)]. 20.035/20.035 20.035/20.035 ============================== end of process initial clauses ======== 20.035/20.035 20.035/20.035 ============================== CLAUSES FOR SEARCH ==================== 20.035/20.035 20.035/20.035 % Clauses after input processing: 20.035/20.035 20.035/20.035 formulas(usable). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 formulas(sos). 20.035/20.035 7 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.035/20.035 8 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.035/20.035 9 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 20.035/20.035 10 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.035/20.035 11 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(4)]. 20.035/20.035 12 ->_s0(a,c) # label(replacement). [assumption]. 20.035/20.035 13 ->_s0(a,d) # label(replacement). [assumption]. 20.035/20.035 15 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 20.035/20.035 16 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(6)]. 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 formulas(demodulators). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 ============================== end of clauses for search ============= 20.035/20.035 20.035/20.035 ============================== SEARCH ================================ 20.035/20.035 20.035/20.035 % Starting search at 0.00 seconds. 20.035/20.035 20.035/20.035 given #1 (I,wt=3): 7 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.035/20.035 20.035/20.035 given #2 (I,wt=9): 8 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.035/20.035 20.035/20.035 given #3 (I,wt=8): 9 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 20.035/20.035 20.035/20.035 given #4 (I,wt=8): 10 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.035/20.035 20.035/20.035 given #5 (I,wt=8): 11 -->_s0(x,y) | ->_s0(t(x),t(y)) # label(congruence). [clausify(4)]. 20.035/20.035 20.035/20.035 given #6 (I,wt=3): 12 ->_s0(a,c) # label(replacement). [assumption]. 20.035/20.035 20.035/20.035 given #7 (I,wt=3): 13 ->_s0(a,d) # label(replacement). [assumption]. 20.035/20.035 20.035/20.035 given #8 (I,wt=5): 15 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 20.035/20.035 20.035/20.035 ============================== PROOF ================================= 20.035/20.035 20.035/20.035 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 20.035/20.035 % Length of proof is 8. 20.035/20.035 % Level of proof is 3. 20.035/20.035 % Maximum clause weight is 9.000. 20.035/20.035 % Given clauses 8. 20.035/20.035 20.035/20.035 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.035/20.035 6 (exists x2 exists x3 ->*_s0(s(x2),t(x3))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.035/20.035 7 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.035/20.035 8 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 20.035/20.035 15 ->_s0(s(c),t(k)) # label(replacement). [assumption]. 20.035/20.035 16 -->*_s0(s(x),t(y)) # label(goal) # answer(goal). [deny(6)]. 20.035/20.035 28 ->*_s0(s(c),t(k)). [ur(8,a,15,a,b,7,a)]. 20.035/20.035 29 $F # answer(goal). [resolve(28,a,16,a)]. 20.035/20.035 20.035/20.035 ============================== end of proof ========================== 20.035/20.035 20.035/20.035 ============================== STATISTICS ============================ 20.035/20.035 20.035/20.035 Given=8. Generated=22. Kept=22. proofs=1. 20.035/20.035 Usable=8. Sos=9. Demods=0. Limbo=3, Disabled=11. Hints=0. 20.035/20.035 Kept_by_rule=0, Deleted_by_rule=0. 20.035/20.035 Forward_subsumed=0. Back_subsumed=1. 20.035/20.035 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.035/20.035 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.035/20.035 Demod_attempts=0. Demod_rewrites=0. 20.035/20.035 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.035/20.035 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=7. 20.035/20.035 Megabytes=0.07. 20.035/20.035 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.035/20.035 20.035/20.035 ============================== end of statistics ===================== 20.035/20.035 20.035/20.035 ============================== end of search ========================= 20.035/20.035 20.035/20.035 THEOREM PROVED 20.035/20.035 20.035/20.035 Exiting with 1 proof. 20.035/20.035 20.035/20.035 Process 50729 exit (max_proofs) Wed Jul 14 10:56:11 2021 20.035/20.035 20.035/20.035 20.035/20.035 The problem is feasible. 20.035/20.035 20.035/20.035 20.035/20.035 CRule InfChecker Info: 20.035/20.035 s(c) -> t(k) 20.035/20.035 Rule remains 20.035/20.035 Proof: 20.035/20.035 NO_CONDS 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 Confluence Problem: 20.035/20.035 (VAR x:S z:S) 20.035/20.035 (STRATEGY CONTEXTSENSITIVE 20.035/20.035 (a) 20.035/20.035 (f 1) 20.035/20.035 (s 1) 20.035/20.035 (c) 20.035/20.035 (d) 20.035/20.035 (fSNonEmpty) 20.035/20.035 (k) 20.035/20.035 (t 1) 20.035/20.035 ) 20.035/20.035 (RULES 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 ) 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 20.035/20.035 Critical Pairs Processor: 20.035/20.035 -> Rules: 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 -> Vars: 20.035/20.035 "x", "z" 20.035/20.035 -> FVars: 20.035/20.035 "x3", "x4" 20.035/20.035 -> PVars: 20.035/20.035 "x": ["x3"], "z": ["x4"] 20.035/20.035 20.035/20.035 -> Rlps: 20.035/20.035 crule: a -> c, id: 1, possubterms: a-> [] 20.035/20.035 crule: a -> d, id: 2, possubterms: a-> [] 20.035/20.035 crule: f(x3:S) -> x4:S | s(x3:S) ->* t(x4:S), id: 3, possubterms: f(x3:S)-> [] 20.035/20.035 crule: s(c) -> t(k), id: 4, possubterms: s(c)-> [], c-> [1] 20.035/20.035 20.035/20.035 -> Unifications: 20.035/20.035 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 20.035/20.035 20.035/20.035 -> Critical pairs info: 20.035/20.035 => Not trivial, Overlay, N1 20.035/20.035 20.035/20.035 -> Problem conclusions: 20.035/20.035 Left linear, Right linear, Linear 20.035/20.035 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.035/20.035 CTRS Type: 3 20.035/20.035 Deterministic, Strongly deterministic 20.035/20.035 Oriented CTRS, Properly oriented CTRS, Not join CTRS 20.035/20.035 Maybe right-stable CTRS, Overlay CTRS 20.035/20.035 Maybe normal CTRS, Maybe almost normal CTRS 20.035/20.035 Maybe terminating CTRS, Maybe joinable CCPs 20.035/20.035 Maybe level confluent 20.035/20.035 Maybe confluent 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 Confluence Problem: 20.035/20.035 (VAR x:S z:S) 20.035/20.035 (STRATEGY CONTEXTSENSITIVE 20.035/20.035 (a) 20.035/20.035 (f 1) 20.035/20.035 (s 1) 20.035/20.035 (c) 20.035/20.035 (d) 20.035/20.035 (fSNonEmpty) 20.035/20.035 (k) 20.035/20.035 (t 1) 20.035/20.035 ) 20.035/20.035 (RULES 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 ) 20.035/20.035 Critical Pairs: 20.035/20.035 => Not trivial, Overlay, N1 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 20.035/20.035 Conditional Critical Pairs Distributor Processor 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 Confluence Problem: 20.035/20.035 (VAR x:S z:S) 20.035/20.035 (STRATEGY CONTEXTSENSITIVE 20.035/20.035 (a) 20.035/20.035 (f 1) 20.035/20.035 (s 1) 20.035/20.035 (c) 20.035/20.035 (d) 20.035/20.035 (fSNonEmpty) 20.035/20.035 (k) 20.035/20.035 (t 1) 20.035/20.035 ) 20.035/20.035 (RULES 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 ) 20.035/20.035 Critical Pairs: 20.035/20.035 => Not trivial, Overlay, N1 20.035/20.035 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.035/20.035 20.035/20.035 Infeasible Convergence No Conditions CCP Processor: 20.035/20.035 Infeasible convergence? 20.035/20.035 YES 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 20.035/20.035 Infeasibility Problem: 20.035/20.035 [(VAR vNonEmpty:S x:S z:S) 20.035/20.035 (STRATEGY CONTEXTSENSITIVE 20.035/20.035 (a) 20.035/20.035 (f 1) 20.035/20.035 (s 1) 20.035/20.035 (c) 20.035/20.035 (d) 20.035/20.035 (fSNonEmpty) 20.035/20.035 (k) 20.035/20.035 (t 1) 20.035/20.035 ) 20.035/20.035 (RULES 20.035/20.035 a -> c 20.035/20.035 a -> d 20.035/20.035 f(x:S) -> z:S | s(x:S) ->* t(z:S) 20.035/20.035 s(c) -> t(k) 20.035/20.035 )] 20.035/20.035 20.035/20.035 Infeasibility Conditions: 20.035/20.035 c ->* z:S, d ->* z:S 20.035/20.035 20.035/20.035 Problem 1: 20.035/20.035 20.035/20.035 Obtaining a model using Mace4: 20.035/20.035 20.035/20.035 -> Usable Rules: 20.035/20.035 Empty 20.035/20.035 20.035/20.035 -> Mace4 Output: 20.035/20.035 ============================== Mace4 ================================= 20.035/20.035 Mace4 (64) version 2009-11A, November 2009. 20.035/20.035 Process 50785 was started by ubuntu on ubuntu, 20.035/20.035 Wed Jul 14 10:56:11 2021 20.035/20.035 The command was "./mace4 -c -f /tmp/mace450746-2.in". 20.035/20.035 ============================== end of head =========================== 20.035/20.035 20.035/20.035 ============================== INPUT ================================= 20.035/20.035 20.035/20.035 % Reading from file /tmp/mace450746-2.in 20.035/20.035 20.035/20.035 assign(max_seconds,20). 20.035/20.035 20.035/20.035 formulas(assumptions). 20.035/20.035 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 20.035/20.035 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 20.035/20.035 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence). 20.035/20.035 ->*(x,x) # label(reflexivity). 20.035/20.035 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 formulas(goals). 20.035/20.035 (exists x2 (->*(c,x2) & ->*(d,x2))) # label(goal). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 ============================== end of input ========================== 20.035/20.035 20.035/20.035 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.035/20.035 20.035/20.035 % Formulas that are not ordinary clauses: 20.035/20.035 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 20.035/20.035 2 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 20.035/20.035 3 ->(x1,y) -> ->(t(x1),t(y)) # label(congruence) # label(non_clause). [assumption]. 20.035/20.035 4 ->(x,y) & ->*(y,z) -> ->*(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.035/20.035 5 (exists x2 (->*(c,x2) & ->*(d,x2))) # label(goal) # label(non_clause) # label(goal). [goal]. 20.035/20.035 20.035/20.035 ============================== end of process non-clausal formulas === 20.035/20.035 20.035/20.035 ============================== CLAUSES FOR SEARCH ==================== 20.035/20.035 20.035/20.035 formulas(mace4_clauses). 20.035/20.035 -->(x,y) | ->(f(x),f(y)) # label(congruence). 20.035/20.035 -->(x,y) | ->(s(x),s(y)) # label(congruence). 20.035/20.035 -->(x,y) | ->(t(x),t(y)) # label(congruence). 20.035/20.035 ->*(x,x) # label(reflexivity). 20.035/20.035 -->(x,y) | -->*(y,z) | ->*(x,z) # label(transitivity). 20.035/20.035 -->*(c,x) | -->*(d,x) # label(goal). 20.035/20.035 end_of_list. 20.035/20.035 20.035/20.035 ============================== end of clauses for search ============= 20.035/20.035 20.035/20.035 % There are no natural numbers in the input. 20.035/20.035 20.035/20.035 ============================== DOMAIN SIZE 2 ========================= 20.035/20.035 20.035/20.035 ============================== MODEL ================================= 20.035/20.035 20.035/20.035 interpretation( 2, [number=1, seconds=0], [ 20.035/20.035 20.035/20.035 function(c, [ 0 ]), 20.035/20.035 20.035/20.035 function(d, [ 1 ]), 20.035/20.035 20.035/20.035 function(f(_), [ 0, 0 ]), 20.035/20.035 20.035/20.035 function(s(_), [ 0, 0 ]), 20.035/20.035 20.035/20.035 function(t(_), [ 0, 0 ]), 20.035/20.035 20.035/20.035 relation(->*(_,_), [ 20.035/20.035 1, 0, 20.035/20.035 0, 1 ]), 20.035/20.035 20.035/20.035 relation(->(_,_), [ 20.035/20.035 0, 0, 20.035/20.035 0, 0 ]) 20.035/20.035 ]). 20.035/20.035 20.035/20.035 ============================== end of model ========================== 20.035/20.035 20.035/20.035 ============================== STATISTICS ============================ 20.035/20.035 20.035/20.035 For domain size 2. 20.035/20.035 20.035/20.035 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.035/20.035 Ground clauses: seen=24, kept=20. 20.035/20.035 Selections=8, assignments=8, propagations=8, current_models=1. 20.035/20.035 Rewrite_terms=28, rewrite_bools=30, indexes=5. 20.035/20.035 Rules_from_neg_clauses=1, cross_offs=1. 20.035/20.035 20.035/20.035 ============================== end of statistics ===================== 20.035/20.035 20.035/20.035 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.035/20.035 20.035/20.035 Exiting with 1 model. 20.035/20.035 20.035/20.035 Process 50785 exit (max_models) Wed Jul 14 10:56:11 2021 20.035/20.035 The process finished Wed Jul 14 10:56:11 2021 20.035/20.035 20.035/20.035 20.035/20.035 Mace4 cooked interpretation: 20.035/20.035 20.035/20.035 20.035/20.035 20.035/20.035 The problem is infeasible. 20.035/20.035 20.035/20.035 20.035/20.035 The problem is not joinable. 20.035/20.035 40.45user 1.93system 0:20.35elapsed 208%CPU (0avgtext+0avgdata 1854884maxresident)k 20.035/20.035 0inputs+0outputs (0major+656999minor)pagefaults 0swaps