3.029/3.029 NO 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 Confluence Problem: 3.029/3.029 (VAR vNonEmpty:S x:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 ) 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 Inlining of Conditions Processor [STERN17]: 3.029/3.029 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 Confluence Problem: 3.029/3.029 (VAR vNonEmpty:S x:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 ) 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 Clean CTRS Processor: 3.029/3.029 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 Confluence Problem: 3.029/3.029 (VAR x:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 ) 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 3.029/3.029 CRule InfChecker Info: 3.029/3.029 a -> c 3.029/3.029 Rule remains 3.029/3.029 Proof: 3.029/3.029 NO_CONDS 3.029/3.029 3.029/3.029 CRule InfChecker Info: 3.029/3.029 a -> d 3.029/3.029 Rule remains 3.029/3.029 Proof: 3.029/3.029 NO_CONDS 3.029/3.029 3.029/3.029 CRule InfChecker Info: 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 Rule remains 3.029/3.029 Proof: 3.029/3.029 NO 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 Infeasibility Problem: 3.029/3.029 [(VAR vNonEmpty:S vNonEmpty:S:S x:S:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S:S) -> x:S:S | x:S:S ->* c 3.029/3.029 )] 3.029/3.029 3.029/3.029 Infeasibility Conditions: 3.029/3.029 x:S:S ->* c 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 Obtaining a proof using Prover9: 3.029/3.029 3.029/3.029 -> Prover9 Output: 3.029/3.029 ============================== Prover9 =============================== 3.029/3.029 Prover9 (64) version 2009-11A, November 2009. 3.029/3.029 Process 109639 was started by ubuntu on ubuntu, 3.029/3.029 Fri Jul 16 15:05:24 2021 3.029/3.029 The command was "./prover9 -f /tmp/prover9109630-0.in". 3.029/3.029 ============================== end of head =========================== 3.029/3.029 3.029/3.029 ============================== INPUT ================================= 3.029/3.029 3.029/3.029 % Reading from file /tmp/prover9109630-0.in 3.029/3.029 3.029/3.029 assign(max_seconds,20). 3.029/3.029 3.029/3.029 formulas(assumptions). 3.029/3.029 ->*_s0(x,x) # label(reflexivity). 3.029/3.029 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 3.029/3.029 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence). 3.029/3.029 ->_s0(a,c) # label(replacement). 3.029/3.029 ->_s0(a,d) # label(replacement). 3.029/3.029 ->*_s0(x2,c) -> ->_s0(f(x2),x2) # label(replacement). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 formulas(goals). 3.029/3.029 (exists x2 ->*_s0(x2,c)) # label(goal). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 ============================== end of input ========================== 3.029/3.029 3.029/3.029 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 3.029/3.029 3.029/3.029 % Formulas that are not ordinary clauses: 3.029/3.029 1 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 3.029/3.029 2 ->_s0(x1,y) -> ->_s0(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 3.029/3.029 3 ->*_s0(x2,c) -> ->_s0(f(x2),x2) # label(replacement) # label(non_clause). [assumption]. 3.029/3.029 4 (exists x2 ->*_s0(x2,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 3.029/3.029 3.029/3.029 ============================== end of process non-clausal formulas === 3.029/3.029 3.029/3.029 ============================== PROCESS INITIAL CLAUSES =============== 3.029/3.029 3.029/3.029 % Clauses before input processing: 3.029/3.029 3.029/3.029 formulas(usable). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 formulas(sos). 3.029/3.029 ->*_s0(x,x) # label(reflexivity). [assumption]. 3.029/3.029 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 3.029/3.029 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 3.029/3.029 ->_s0(a,c) # label(replacement). [assumption]. 3.029/3.029 ->_s0(a,d) # label(replacement). [assumption]. 3.029/3.029 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(3)]. 3.029/3.029 -->*_s0(x,c) # label(goal). [deny(4)]. 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 formulas(demodulators). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 ============================== PREDICATE ELIMINATION ================= 3.029/3.029 3.029/3.029 No predicates eliminated. 3.029/3.029 3.029/3.029 ============================== end predicate elimination ============= 3.029/3.029 3.029/3.029 Auto_denials: 3.029/3.029 % copying label goal to answer in negative clause 3.029/3.029 3.029/3.029 Term ordering decisions: 3.029/3.029 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 3.029/3.029 Function symbol precedence: function_order([ a, c, d, f ]). 3.029/3.029 After inverse_order: (no changes). 3.029/3.029 Unfolding symbols: (none). 3.029/3.029 3.029/3.029 Auto_inference settings: 3.029/3.029 % set(neg_binary_resolution). % (HNE depth_diff=-2) 3.029/3.029 % clear(ordered_res). % (HNE depth_diff=-2) 3.029/3.029 % set(ur_resolution). % (HNE depth_diff=-2) 3.029/3.029 % set(ur_resolution) -> set(pos_ur_resolution). 3.029/3.029 % set(ur_resolution) -> set(neg_ur_resolution). 3.029/3.029 3.029/3.029 Auto_process settings: (no changes). 3.029/3.029 3.029/3.029 kept: 5 ->*_s0(x,x) # label(reflexivity). [assumption]. 3.029/3.029 kept: 6 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(1)]. 3.029/3.029 kept: 7 -->_s0(x,y) | ->_s0(f(x),f(y)) # label(congruence). [clausify(2)]. 3.029/3.029 kept: 8 ->_s0(a,c) # label(replacement). [assumption]. 3.029/3.029 kept: 9 ->_s0(a,d) # label(replacement). [assumption]. 3.029/3.029 kept: 10 -->*_s0(x,c) | ->_s0(f(x),x) # label(replacement). [clausify(3)]. 3.029/3.029 kept: 11 -->*_s0(x,c) # label(goal) # answer(goal). [deny(4)]. 3.029/3.029 3.029/3.029 ============================== PROOF ================================= 3.029/3.029 3.029/3.029 % Proof 1 at 0.00 (+ 0.00) seconds: goal. 3.029/3.029 % Length of proof is 4. 3.029/3.029 % Level of proof is 2. 3.029/3.029 % Maximum clause weight is 3.000. 3.029/3.029 % Given clauses 0. 3.029/3.029 3.029/3.029 4 (exists x2 ->*_s0(x2,c)) # label(goal) # label(non_clause) # label(goal). [goal]. 3.029/3.029 5 ->*_s0(x,x) # label(reflexivity). [assumption]. 3.029/3.029 11 -->*_s0(x,c) # label(goal) # answer(goal). [deny(4)]. 3.029/3.029 12 $F # answer(goal). [resolve(11,a,5,a)]. 3.029/3.029 3.029/3.029 ============================== end of proof ========================== 3.029/3.029 3.029/3.029 ============================== STATISTICS ============================ 3.029/3.029 3.029/3.029 Given=0. Generated=7. Kept=7. proofs=1. 3.029/3.029 Usable=0. Sos=0. Demods=0. Limbo=6, Disabled=7. Hints=0. 3.029/3.029 Kept_by_rule=0, Deleted_by_rule=0. 3.029/3.029 Forward_subsumed=0. Back_subsumed=0. 3.029/3.029 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 3.029/3.029 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 3.029/3.029 Demod_attempts=0. Demod_rewrites=0. 3.029/3.029 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 3.029/3.029 Nonunit_fsub_feature_tests=0. Nonunit_bsub_feature_tests=0. 3.029/3.029 Megabytes=0.04. 3.029/3.029 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 3.029/3.029 3.029/3.029 ============================== end of statistics ===================== 3.029/3.029 3.029/3.029 ============================== end of search ========================= 3.029/3.029 3.029/3.029 THEOREM PROVED 3.029/3.029 3.029/3.029 Exiting with 1 proof. 3.029/3.029 3.029/3.029 Process 109639 exit (max_proofs) Fri Jul 16 15:05:24 2021 3.029/3.029 3.029/3.029 3.029/3.029 The problem is feasible. 3.029/3.029 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 Confluence Problem: 3.029/3.029 (VAR x:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 ) 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 3.029/3.029 Critical Pairs Processor: 3.029/3.029 -> Rules: 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 -> Vars: 3.029/3.029 "x" 3.029/3.029 -> FVars: 3.029/3.029 "x2" 3.029/3.029 -> PVars: 3.029/3.029 "x": ["x2"] 3.029/3.029 3.029/3.029 -> Rlps: 3.029/3.029 crule: a -> c, id: 1, possubterms: a-> [] 3.029/3.029 crule: a -> d, id: 2, possubterms: a-> [] 3.029/3.029 crule: f(x2:S) -> x2:S | x2:S ->* c, id: 3, possubterms: f(x2:S)-> [] 3.029/3.029 3.029/3.029 -> Unifications: 3.029/3.029 R2 unifies with R1 at p: [], l: a, lp: a, conds: {}, sig: {}, l': a, r: d, r': c 3.029/3.029 3.029/3.029 -> Critical pairs info: 3.029/3.029 => Not trivial, Overlay, N1 3.029/3.029 3.029/3.029 -> Problem conclusions: 3.029/3.029 Left linear, Right linear, Linear 3.029/3.029 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 3.029/3.029 CTRS Type: 1 3.029/3.029 Deterministic, Strongly deterministic 3.029/3.029 Oriented CTRS, Properly oriented CTRS, Not join CTRS 3.029/3.029 Maybe right-stable CTRS, Overlay CTRS 3.029/3.029 Maybe normal CTRS, Maybe almost normal CTRS 3.029/3.029 Maybe terminating CTRS, Maybe joinable CCPs 3.029/3.029 Maybe level confluent 3.029/3.029 Maybe confluent 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 Confluence Problem: 3.029/3.029 (VAR x:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 ) 3.029/3.029 Critical Pairs: 3.029/3.029 => Not trivial, Overlay, N1 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 3.029/3.029 Conditional Critical Pairs Distributor Processor 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 Confluence Problem: 3.029/3.029 (VAR x:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 ) 3.029/3.029 Critical Pairs: 3.029/3.029 => Not trivial, Overlay, N1 3.029/3.029 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 3.029/3.029 3.029/3.029 InfChecker Different Ground and Normal No Conditions CCP Terms Processor: 3.029/3.029 Proof: 3.029/3.029 YES 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 Infeasibility Problem: 3.029/3.029 [(VAR vNonEmpty:S x:S y:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 )] 3.029/3.029 3.029/3.029 Infeasibility Conditions: 3.029/3.029 c -> y:S 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 Obtaining a model using Mace4: 3.029/3.029 3.029/3.029 -> Usable Rules: 3.029/3.029 Empty 3.029/3.029 3.029/3.029 -> Mace4 Output: 3.029/3.029 ============================== Mace4 ================================= 3.029/3.029 Mace4 (64) version 2009-11A, November 2009. 3.029/3.029 Process 109682 was started by ubuntu on ubuntu, 3.029/3.029 Fri Jul 16 15:05:24 2021 3.029/3.029 The command was "./mace4 -c -f /tmp/mace4109655-2.in". 3.029/3.029 ============================== end of head =========================== 3.029/3.029 3.029/3.029 ============================== INPUT ================================= 3.029/3.029 3.029/3.029 % Reading from file /tmp/mace4109655-2.in 3.029/3.029 3.029/3.029 assign(max_seconds,3). 3.029/3.029 3.029/3.029 formulas(assumptions). 3.029/3.029 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 formulas(goals). 3.029/3.029 (exists x2 ->(c,x2)) # label(goal). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 ============================== end of input ========================== 3.029/3.029 3.029/3.029 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 3.029/3.029 3.029/3.029 % Formulas that are not ordinary clauses: 3.029/3.029 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 3.029/3.029 2 (exists x2 ->(c,x2)) # label(goal) # label(non_clause) # label(goal). [goal]. 3.029/3.029 3.029/3.029 ============================== end of process non-clausal formulas === 3.029/3.029 3.029/3.029 ============================== CLAUSES FOR SEARCH ==================== 3.029/3.029 3.029/3.029 formulas(mace4_clauses). 3.029/3.029 -->(x,y) | ->(f(x),f(y)) # label(congruence). 3.029/3.029 -->(c,x) # label(goal). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 ============================== end of clauses for search ============= 3.029/3.029 3.029/3.029 % There are no natural numbers in the input. 3.029/3.029 3.029/3.029 ============================== DOMAIN SIZE 2 ========================= 3.029/3.029 3.029/3.029 ============================== MODEL ================================= 3.029/3.029 3.029/3.029 interpretation( 2, [number=1, seconds=0], [ 3.029/3.029 3.029/3.029 function(c, [ 0 ]), 3.029/3.029 3.029/3.029 function(f(_), [ 0, 0 ]), 3.029/3.029 3.029/3.029 relation(->(_,_), [ 3.029/3.029 0, 0, 3.029/3.029 0, 0 ]) 3.029/3.029 ]). 3.029/3.029 3.029/3.029 ============================== end of model ========================== 3.029/3.029 3.029/3.029 ============================== STATISTICS ============================ 3.029/3.029 3.029/3.029 For domain size 2. 3.029/3.029 3.029/3.029 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 3.029/3.029 Ground clauses: seen=6, kept=6. 3.029/3.029 Selections=3, assignments=3, propagations=4, current_models=1. 3.029/3.029 Rewrite_terms=10, rewrite_bools=8, indexes=2. 3.029/3.029 Rules_from_neg_clauses=0, cross_offs=0. 3.029/3.029 3.029/3.029 ============================== end of statistics ===================== 3.029/3.029 3.029/3.029 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 3.029/3.029 3.029/3.029 Exiting with 1 model. 3.029/3.029 3.029/3.029 Process 109682 exit (max_models) Fri Jul 16 15:05:24 2021 3.029/3.029 The process finished Fri Jul 16 15:05:24 2021 3.029/3.029 3.029/3.029 3.029/3.029 Mace4 cooked interpretation: 3.029/3.029 3.029/3.029 3.029/3.029 3.029/3.029 The problem is infeasible. 3.029/3.029 YES 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 Infeasibility Problem: 3.029/3.029 [(VAR vNonEmpty:S x:S) 3.029/3.029 (STRATEGY CONTEXTSENSITIVE 3.029/3.029 (a) 3.029/3.029 (f 1) 3.029/3.029 (c) 3.029/3.029 (d) 3.029/3.029 (fSNonEmpty) 3.029/3.029 ) 3.029/3.029 (RULES 3.029/3.029 a -> c 3.029/3.029 a -> d 3.029/3.029 f(x:S) -> x:S | x:S ->* c 3.029/3.029 )] 3.029/3.029 3.029/3.029 Infeasibility Conditions: 3.029/3.029 d -> x:S 3.029/3.029 3.029/3.029 Problem 1: 3.029/3.029 3.029/3.029 Obtaining a model using Mace4: 3.029/3.029 3.029/3.029 -> Usable Rules: 3.029/3.029 Empty 3.029/3.029 3.029/3.029 -> Mace4 Output: 3.029/3.029 ============================== Mace4 ================================= 3.029/3.029 Mace4 (64) version 2009-11A, November 2009. 3.029/3.029 Process 109720 was started by ubuntu on ubuntu, 3.029/3.029 Fri Jul 16 15:05:26 2021 3.029/3.029 The command was "./mace4 -c -f /tmp/mace4109707-2.in". 3.029/3.029 ============================== end of head =========================== 3.029/3.029 3.029/3.029 ============================== INPUT ================================= 3.029/3.029 3.029/3.029 % Reading from file /tmp/mace4109707-2.in 3.029/3.029 3.029/3.029 assign(max_seconds,3). 3.029/3.029 3.029/3.029 formulas(assumptions). 3.029/3.029 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 formulas(goals). 3.029/3.029 (exists x1 ->(d,x1)) # label(goal). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 ============================== end of input ========================== 3.029/3.029 3.029/3.029 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 3.029/3.029 3.029/3.029 % Formulas that are not ordinary clauses: 3.029/3.029 1 ->(x1,y) -> ->(f(x1),f(y)) # label(congruence) # label(non_clause). [assumption]. 3.029/3.029 2 (exists x1 ->(d,x1)) # label(goal) # label(non_clause) # label(goal). [goal]. 3.029/3.029 3.029/3.029 ============================== end of process non-clausal formulas === 3.029/3.029 3.029/3.029 ============================== CLAUSES FOR SEARCH ==================== 3.029/3.029 3.029/3.029 formulas(mace4_clauses). 3.029/3.029 -->(x,y) | ->(f(x),f(y)) # label(congruence). 3.029/3.029 -->(d,x) # label(goal). 3.029/3.029 end_of_list. 3.029/3.029 3.029/3.029 ============================== end of clauses for search ============= 3.029/3.029 3.029/3.029 % There are no natural numbers in the input. 3.029/3.029 3.029/3.029 ============================== DOMAIN SIZE 2 ========================= 3.029/3.029 3.029/3.029 ============================== MODEL ================================= 3.029/3.029 3.029/3.029 interpretation( 2, [number=1, seconds=0], [ 3.029/3.029 3.029/3.029 function(d, [ 0 ]), 3.029/3.029 3.029/3.029 function(f(_), [ 0, 0 ]), 3.029/3.029 3.029/3.029 relation(->(_,_), [ 3.029/3.029 0, 0, 3.029/3.029 0, 0 ]) 3.029/3.029 ]). 3.029/3.029 3.029/3.029 ============================== end of model ========================== 3.029/3.029 3.029/3.029 ============================== STATISTICS ============================ 3.029/3.029 3.029/3.029 For domain size 2. 3.029/3.029 3.029/3.029 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 3.029/3.029 Ground clauses: seen=6, kept=6. 3.029/3.029 Selections=3, assignments=3, propagations=4, current_models=1. 3.029/3.029 Rewrite_terms=10, rewrite_bools=8, indexes=2. 3.029/3.029 Rules_from_neg_clauses=0, cross_offs=0. 3.029/3.029 3.029/3.029 ============================== end of statistics ===================== 3.029/3.029 3.029/3.029 User_CPU=0.00, System_CPU=0.00, Wall_clock=1. 3.029/3.029 3.029/3.029 Exiting with 1 model. 3.029/3.029 3.029/3.029 Process 109720 exit (max_models) Fri Jul 16 15:05:26 2021 3.029/3.029 The process finished Fri Jul 16 15:05:26 2021 3.029/3.029 3.029/3.029 3.029/3.029 Mace4 cooked interpretation: 3.029/3.029 3.029/3.029 3.029/3.029 3.029/3.029 The problem is infeasible. 3.029/3.029 3.029/3.029 3.029/3.029 The problem is not joinable. 3.029/3.029 3.28user 0.36system 0:03.29elapsed 110%CPU (0avgtext+0avgdata 130820maxresident)k 3.029/3.029 8inputs+0outputs (0major+204962minor)pagefaults 0swaps