20.036/20.036 YES 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 Confluence Problem: 20.036/20.036 (VAR vNonEmpty x y) 20.036/20.036 (REPLACEMENT-MAP 20.036/20.036 (lte 1, 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 ) 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Inlining of Conditions Processor [STERN17]: 20.036/20.036 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 Confluence Problem: 20.036/20.036 (VAR vNonEmpty x y) 20.036/20.036 (REPLACEMENT-MAP 20.036/20.036 (lte 1, 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 ) 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Clean CTRS Processor: 20.036/20.036 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 Confluence Problem: 20.036/20.036 (VAR x y) 20.036/20.036 (REPLACEMENT-MAP 20.036/20.036 (lte 1, 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 ) 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 20.036/20.036 CRule InfChecker Info: 20.036/20.036 lte(0,0) -> tt 20.036/20.036 Rule remains 20.036/20.036 Proof: 20.036/20.036 NO_CONDS 20.036/20.036 20.036/20.036 CRule InfChecker Info: 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 Rule remains 20.036/20.036 Proof: 20.036/20.036 NO_CONDS 20.036/20.036 20.036/20.036 CRule InfChecker Info: 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 Rule remains 20.036/20.036 Proof: 20.036/20.036 NO_CONDS 20.036/20.036 20.036/20.036 CRule InfChecker Info: 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 Rule remains 20.036/20.036 Proof: 20.036/20.036 NO 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Infeasibility Problem: 20.036/20.036 [(VAR vNonEmpty x y vNonEmpty x y) 20.036/20.036 (STRATEGY CONTEXTSENSITIVE 20.036/20.036 (lte 1 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 )] 20.036/20.036 20.036/20.036 Infeasibility Conditions: 20.036/20.036 lte(x,y) ->*<- tt 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Obtaining a proof using Prover9: 20.036/20.036 20.036/20.036 -> Prover9 Output: 20.036/20.036 ============================== Prover9 =============================== 20.036/20.036 Prover9 (64) version 2009-11A, November 2009. 20.036/20.036 Process 84580 was started by ubuntu on ubuntu, 20.036/20.036 Wed Mar 9 10:43:56 2022 20.036/20.036 The command was "./prover9 -f /tmp/prover984571-0.in". 20.036/20.036 ============================== end of head =========================== 20.036/20.036 20.036/20.036 ============================== INPUT ================================= 20.036/20.036 20.036/20.036 % Reading from file /tmp/prover984571-0.in 20.036/20.036 20.036/20.036 assign(max_seconds,20). 20.036/20.036 20.036/20.036 formulas(assumptions). 20.036/20.036 ->_s0(x1,y) -> ->_s0(lte(x1,x2),lte(y,x2)) # label(congruence). 20.036/20.036 ->_s0(x2,y) -> ->_s0(lte(x1,x2),lte(x1,y)) # label(congruence). 20.036/20.036 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence). 20.036/20.036 ->_s0(lte(0,0),tt) # label(replacement). 20.036/20.036 ->_s0(lte(s(x1),0),ff) # label(replacement). 20.036/20.036 ->_s0(lte(s(x1),s(x2)),lte(x1,x2)) # label(replacement). 20.036/20.036 ->*<-_s0(lte(x1,x2),tt) -> ->_s0(lte(x1,s(x2)),tt) # label(replacement). 20.036/20.036 ->*_s0(x,x) # label(reflexivity). 20.036/20.036 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.036/20.036 ->*_s0(x,y) & ->*_s0(z,y) -> ->*<-_s0(x,z) # label(joinability). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(goals). 20.036/20.036 (exists x4 exists x5 ->*<-_s0(lte(x4,x5),tt)) # label(goal). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== end of input ========================== 20.036/20.036 20.036/20.036 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.036/20.036 20.036/20.036 % Formulas that are not ordinary clauses: 20.036/20.036 1 ->_s0(x1,y) -> ->_s0(lte(x1,x2),lte(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 2 ->_s0(x2,y) -> ->_s0(lte(x1,x2),lte(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 3 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 4 ->*<-_s0(lte(x1,x2),tt) -> ->_s0(lte(x1,s(x2)),tt) # label(replacement) # label(non_clause). [assumption]. 20.036/20.036 5 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.036/20.036 6 ->*_s0(x,y) & ->*_s0(z,y) -> ->*<-_s0(x,z) # label(joinability) # label(non_clause). [assumption]. 20.036/20.036 7 (exists x4 exists x5 ->*<-_s0(lte(x4,x5),tt)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.036/20.036 20.036/20.036 ============================== end of process non-clausal formulas === 20.036/20.036 20.036/20.036 ============================== PROCESS INITIAL CLAUSES =============== 20.036/20.036 20.036/20.036 % Clauses before input processing: 20.036/20.036 20.036/20.036 formulas(usable). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(sos). 20.036/20.036 -->_s0(x,y) | ->_s0(lte(x,z),lte(y,z)) # label(congruence). [clausify(1)]. 20.036/20.036 -->_s0(x,y) | ->_s0(lte(z,x),lte(z,y)) # label(congruence). [clausify(2)]. 20.036/20.036 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.036/20.036 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 ->_s0(lte(s(x),0),ff) # label(replacement). [assumption]. 20.036/20.036 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 -->*<-_s0(lte(x,y),tt) | ->_s0(lte(x,s(y)),tt) # label(replacement). [clausify(4)]. 20.036/20.036 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 -->*_s0(x,y) | -->*_s0(z,y) | ->*<-_s0(x,z) # label(joinability). [clausify(6)]. 20.036/20.036 -->*<-_s0(lte(x,y),tt) # label(goal). [deny(7)]. 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(demodulators). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== PREDICATE ELIMINATION ================= 20.036/20.036 20.036/20.036 Eliminating ->*<-_s0/2 20.036/20.036 8 -->*_s0(x,y) | -->*_s0(z,y) | ->*<-_s0(x,z) # label(joinability). [clausify(6)]. 20.036/20.036 9 -->*<-_s0(lte(x,y),tt) | ->_s0(lte(x,s(y)),tt) # label(replacement). [clausify(4)]. 20.036/20.036 Derived: -->*_s0(lte(x,y),z) | -->*_s0(tt,z) | ->_s0(lte(x,s(y)),tt). [resolve(8,c,9,a)]. 20.036/20.036 10 -->*<-_s0(lte(x,y),tt) # label(goal). [deny(7)]. 20.036/20.036 Derived: -->*_s0(lte(x,y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 20.036/20.036 ============================== end predicate elimination ============= 20.036/20.036 20.036/20.036 Auto_denials: (no changes). 20.036/20.036 20.036/20.036 Term ordering decisions: 20.036/20.036 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.036/20.036 Function symbol precedence: function_order([ 0, tt, ff, lte, s ]). 20.036/20.036 After inverse_order: (no changes). 20.036/20.036 Unfolding symbols: (none). 20.036/20.036 20.036/20.036 Auto_inference settings: 20.036/20.036 % set(neg_binary_resolution). % (HNE depth_diff=-4) 20.036/20.036 % clear(ordered_res). % (HNE depth_diff=-4) 20.036/20.036 % set(ur_resolution). % (HNE depth_diff=-4) 20.036/20.036 % set(ur_resolution) -> set(pos_ur_resolution). 20.036/20.036 % set(ur_resolution) -> set(neg_ur_resolution). 20.036/20.036 20.036/20.036 Auto_process settings: 20.036/20.036 % set(unit_deletion). % (Horn set with negative nonunits) 20.036/20.036 20.036/20.036 kept: 11 -->_s0(x,y) | ->_s0(lte(x,z),lte(y,z)) # label(congruence). [clausify(1)]. 20.036/20.036 kept: 12 -->_s0(x,y) | ->_s0(lte(z,x),lte(z,y)) # label(congruence). [clausify(2)]. 20.036/20.036 kept: 13 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.036/20.036 kept: 14 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 kept: 15 ->_s0(lte(s(x),0),ff) # label(replacement). [assumption]. 20.036/20.036 kept: 16 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 kept: 17 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 kept: 18 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 kept: 19 -->*_s0(lte(x,y),z) | -->*_s0(tt,z) | ->_s0(lte(x,s(y)),tt). [resolve(8,c,9,a)]. 20.036/20.036 kept: 20 -->*_s0(lte(x,y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 20.036/20.036 ============================== end of process initial clauses ======== 20.036/20.036 20.036/20.036 ============================== CLAUSES FOR SEARCH ==================== 20.036/20.036 20.036/20.036 % Clauses after input processing: 20.036/20.036 20.036/20.036 formulas(usable). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(sos). 20.036/20.036 11 -->_s0(x,y) | ->_s0(lte(x,z),lte(y,z)) # label(congruence). [clausify(1)]. 20.036/20.036 12 -->_s0(x,y) | ->_s0(lte(z,x),lte(z,y)) # label(congruence). [clausify(2)]. 20.036/20.036 13 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.036/20.036 14 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 15 ->_s0(lte(s(x),0),ff) # label(replacement). [assumption]. 20.036/20.036 16 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 17 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 18 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 20 -->*_s0(lte(x,y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(demodulators). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== end of clauses for search ============= 20.036/20.036 20.036/20.036 ============================== SEARCH ================================ 20.036/20.036 20.036/20.036 % Starting search at 0.00 seconds. 20.036/20.036 20.036/20.036 given #1 (I,wt=10): 11 -->_s0(x,y) | ->_s0(lte(x,z),lte(y,z)) # label(congruence). [clausify(1)]. 20.036/20.036 20.036/20.036 given #2 (I,wt=10): 12 -->_s0(x,y) | ->_s0(lte(z,x),lte(z,y)) # label(congruence). [clausify(2)]. 20.036/20.036 20.036/20.036 given #3 (I,wt=8): 13 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.036/20.036 20.036/20.036 given #4 (I,wt=5): 14 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 20.036/20.036 given #5 (I,wt=6): 15 ->_s0(lte(s(x),0),ff) # label(replacement). [assumption]. 20.036/20.036 20.036/20.036 given #6 (I,wt=9): 16 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 20.036/20.036 given #7 (I,wt=3): 17 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 20.036/20.036 given #8 (I,wt=9): 18 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 20.036/20.036 given #9 (I,wt=8): 20 -->*_s0(lte(x,y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 20.036/20.036 ============================== PROOF ================================= 20.036/20.036 20.036/20.036 % Proof 1 at 0.00 (+ 0.00) seconds. 20.036/20.036 % Length of proof is 12. 20.036/20.036 % Level of proof is 4. 20.036/20.036 % Maximum clause weight is 9.000. 20.036/20.036 % Given clauses 9. 20.036/20.036 20.036/20.036 5 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.036/20.036 6 ->*_s0(x,y) & ->*_s0(z,y) -> ->*<-_s0(x,z) # label(joinability) # label(non_clause). [assumption]. 20.036/20.036 7 (exists x4 exists x5 ->*<-_s0(lte(x4,x5),tt)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.036/20.036 8 -->*_s0(x,y) | -->*_s0(z,y) | ->*<-_s0(x,z) # label(joinability). [clausify(6)]. 20.036/20.036 10 -->*<-_s0(lte(x,y),tt) # label(goal). [deny(7)]. 20.036/20.036 14 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 17 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 18 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 20 -->*_s0(lte(x,y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 32 ->*_s0(lte(0,0),tt). [ur(18,a,14,a,b,17,a)]. 20.036/20.036 36 -->*_s0(lte(x,y),tt). [resolve(20,b,17,a)]. 20.036/20.036 37 $F. [resolve(36,a,32,a)]. 20.036/20.036 20.036/20.036 ============================== end of proof ========================== 20.036/20.036 20.036/20.036 ============================== STATISTICS ============================ 20.036/20.036 20.036/20.036 Given=9. Generated=26. Kept=26. proofs=1. 20.036/20.036 Usable=9. Sos=12. Demods=0. Limbo=3, Disabled=14. Hints=0. 20.036/20.036 Kept_by_rule=0, Deleted_by_rule=0. 20.036/20.036 Forward_subsumed=0. Back_subsumed=1. 20.036/20.036 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.036/20.036 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.036/20.036 Demod_attempts=0. Demod_rewrites=0. 20.036/20.036 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.036/20.036 Nonunit_fsub_feature_tests=4. Nonunit_bsub_feature_tests=10. 20.036/20.036 Megabytes=0.09. 20.036/20.036 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.036/20.036 20.036/20.036 ============================== end of statistics ===================== 20.036/20.036 20.036/20.036 ============================== end of search ========================= 20.036/20.036 20.036/20.036 THEOREM PROVED 20.036/20.036 20.036/20.036 Exiting with 1 proof. 20.036/20.036 20.036/20.036 Process 84580 exit (max_proofs) Wed Mar 9 10:43:56 2022 20.036/20.036 20.036/20.036 20.036/20.036 The problem is feasible. 20.036/20.036 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 Confluence Problem: 20.036/20.036 (VAR x y) 20.036/20.036 (REPLACEMENT-MAP 20.036/20.036 (lte 1, 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 ) 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 20.036/20.036 Critical Pairs Processor: 20.036/20.036 -> Rules: 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 -> Vars: 20.036/20.036 "x", "y" 20.036/20.036 20.036/20.036 -> Rlps: 20.036/20.036 crule: lte(0,0) -> tt, id: 1, possubterms: lte(0,0)-> [], 0-> [1], 0-> [2] 20.036/20.036 crule: lte(s(x),0) -> ff, id: 2, possubterms: lte(s(x),0)-> [], s(x)-> [1], 0-> [2] 20.036/20.036 crule: lte(s(x),s(y)) -> lte(x,y), id: 3, possubterms: lte(s(x),s(y))-> [], s(x)-> [1], s(y)-> [2] 20.036/20.036 crule: lte(x,s(y)) -> tt | lte(x,y) ->*<- tt, id: 4, possubterms: lte(x,s(y))-> [], s(y)-> [2] 20.036/20.036 20.036/20.036 -> Unifications: 20.036/20.036 R4 unifies with R3 at p: [], l: lte(x,s(y)), lp: lte(x,s(y)), conds: {lte(x,y) ->*<- tt}, sig: {x -> s(x'),y -> y'}, l': lte(s(x'),s(y')), r: tt, r': lte(x',y') 20.036/20.036 20.036/20.036 -> Critical pairs info: 20.036/20.036 | lte(s(x'),y') ->*<- tt => Not trivial, Overlay, NW2, N1 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Maybe right-stable CTRS, Overlay CTRS 20.036/20.036 Maybe normal CTRS, Maybe almost normal CTRS 20.036/20.036 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 Clean Infeasible CCPs Processor: 20.036/20.036 Num of CPIs: 1 20.036/20.036 Timeout: 60 20.036/20.036 Timeout for each infeasibility problem: 60 s 20.036/20.036 | lte(s(x'),y') ->*<- tt => Not trivial, Overlay, Feasible conditions, NW2, N1 20.036/20.036 (CONDITIONTYPE JOIN) 20.036/20.036 (VAR x y x1 y1) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt) 20.036/20.036 (VAR x8 x9) 20.036/20.036 (CONDITION lte(s(x8),x9) ->*<- tt) 20.036/20.036 20.036/20.036 Proof: 20.036/20.036 NO 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Infeasibility Problem: 20.036/20.036 [(VAR vNonEmpty x y x1 y1 vNonEmpty x8 x9) 20.036/20.036 (STRATEGY CONTEXTSENSITIVE 20.036/20.036 (lte 1 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 )] 20.036/20.036 20.036/20.036 Infeasibility Conditions: 20.036/20.036 lte(s(x8),x9) ->*<- tt 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Obtaining a proof using Prover9: 20.036/20.036 20.036/20.036 -> Prover9 Output: 20.036/20.036 ============================== Prover9 =============================== 20.036/20.036 Prover9 (64) version 2009-11A, November 2009. 20.036/20.036 Process 84616 was started by ubuntu on ubuntu, 20.036/20.036 Wed Mar 9 10:43:56 2022 20.036/20.036 The command was "./prover9 -f /tmp/prover984598-0.in". 20.036/20.036 ============================== end of head =========================== 20.036/20.036 20.036/20.036 ============================== INPUT ================================= 20.036/20.036 20.036/20.036 % Reading from file /tmp/prover984598-0.in 20.036/20.036 20.036/20.036 assign(max_seconds,20). 20.036/20.036 20.036/20.036 formulas(assumptions). 20.036/20.036 ->_s0(x1,y) -> ->_s0(lte(x1,x2),lte(y,x2)) # label(congruence). 20.036/20.036 ->_s0(x2,y) -> ->_s0(lte(x1,x2),lte(x1,y)) # label(congruence). 20.036/20.036 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence). 20.036/20.036 ->_s0(lte(0,0),tt) # label(replacement). 20.036/20.036 ->_s0(lte(s(x1),0),ff) # label(replacement). 20.036/20.036 ->_s0(lte(s(x1),s(x2)),lte(x1,x2)) # label(replacement). 20.036/20.036 ->*<-_s0(lte(x1,x2),tt) -> ->_s0(lte(x1,s(x2)),tt) # label(replacement). 20.036/20.036 ->*_s0(x,x) # label(reflexivity). 20.036/20.036 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity). 20.036/20.036 ->*_s0(x,y) & ->*_s0(z,y) -> ->*<-_s0(x,z) # label(joinability). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(goals). 20.036/20.036 (exists x6 exists x7 ->*<-_s0(lte(s(x6),x7),tt)) # label(goal). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== end of input ========================== 20.036/20.036 20.036/20.036 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.036/20.036 20.036/20.036 % Formulas that are not ordinary clauses: 20.036/20.036 1 ->_s0(x1,y) -> ->_s0(lte(x1,x2),lte(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 2 ->_s0(x2,y) -> ->_s0(lte(x1,x2),lte(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 3 ->_s0(x1,y) -> ->_s0(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 4 ->*<-_s0(lte(x1,x2),tt) -> ->_s0(lte(x1,s(x2)),tt) # label(replacement) # label(non_clause). [assumption]. 20.036/20.036 5 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.036/20.036 6 ->*_s0(x,y) & ->*_s0(z,y) -> ->*<-_s0(x,z) # label(joinability) # label(non_clause). [assumption]. 20.036/20.036 7 (exists x6 exists x7 ->*<-_s0(lte(s(x6),x7),tt)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.036/20.036 20.036/20.036 ============================== end of process non-clausal formulas === 20.036/20.036 20.036/20.036 ============================== PROCESS INITIAL CLAUSES =============== 20.036/20.036 20.036/20.036 % Clauses before input processing: 20.036/20.036 20.036/20.036 formulas(usable). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(sos). 20.036/20.036 -->_s0(x,y) | ->_s0(lte(x,z),lte(y,z)) # label(congruence). [clausify(1)]. 20.036/20.036 -->_s0(x,y) | ->_s0(lte(z,x),lte(z,y)) # label(congruence). [clausify(2)]. 20.036/20.036 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.036/20.036 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 ->_s0(lte(s(x),0),ff) # label(replacement). [assumption]. 20.036/20.036 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 -->*<-_s0(lte(x,y),tt) | ->_s0(lte(x,s(y)),tt) # label(replacement). [clausify(4)]. 20.036/20.036 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 -->*_s0(x,y) | -->*_s0(z,y) | ->*<-_s0(x,z) # label(joinability). [clausify(6)]. 20.036/20.036 -->*<-_s0(lte(s(x),y),tt) # label(goal). [deny(7)]. 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(demodulators). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== PREDICATE ELIMINATION ================= 20.036/20.036 20.036/20.036 Eliminating ->*<-_s0/2 20.036/20.036 8 -->*_s0(x,y) | -->*_s0(z,y) | ->*<-_s0(x,z) # label(joinability). [clausify(6)]. 20.036/20.036 9 -->*<-_s0(lte(x,y),tt) | ->_s0(lte(x,s(y)),tt) # label(replacement). [clausify(4)]. 20.036/20.036 Derived: -->*_s0(lte(x,y),z) | -->*_s0(tt,z) | ->_s0(lte(x,s(y)),tt). [resolve(8,c,9,a)]. 20.036/20.036 10 -->*<-_s0(lte(s(x),y),tt) # label(goal). [deny(7)]. 20.036/20.036 Derived: -->*_s0(lte(s(x),y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 20.036/20.036 ============================== end predicate elimination ============= 20.036/20.036 20.036/20.036 Auto_denials: (no changes). 20.036/20.036 20.036/20.036 Term ordering decisions: 20.036/20.036 Predicate symbol precedence: predicate_order([ ->_s0, ->*_s0 ]). 20.036/20.036 Function symbol precedence: function_order([ 0, tt, ff, lte, s ]). 20.036/20.036 After inverse_order: (no changes). 20.036/20.036 Unfolding symbols: (none). 20.036/20.036 20.036/20.036 Auto_inference settings: 20.036/20.036 % set(neg_binary_resolution). % (HNE depth_diff=-4) 20.036/20.036 % clear(ordered_res). % (HNE depth_diff=-4) 20.036/20.036 % set(ur_resolution). % (HNE depth_diff=-4) 20.036/20.036 % set(ur_resolution) -> set(pos_ur_resolution). 20.036/20.036 % set(ur_resolution) -> set(neg_ur_resolution). 20.036/20.036 20.036/20.036 Auto_process settings: 20.036/20.036 % set(unit_deletion). % (Horn set with negative nonunits) 20.036/20.036 20.036/20.036 kept: 11 -->_s0(x,y) | ->_s0(lte(x,z),lte(y,z)) # label(congruence). [clausify(1)]. 20.036/20.036 kept: 12 -->_s0(x,y) | ->_s0(lte(z,x),lte(z,y)) # label(congruence). [clausify(2)]. 20.036/20.036 kept: 13 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.036/20.036 kept: 14 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 kept: 15 ->_s0(lte(s(x),0),ff) # label(replacement). [assumption]. 20.036/20.036 kept: 16 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 kept: 17 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 kept: 18 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 kept: 19 -->*_s0(lte(x,y),z) | -->*_s0(tt,z) | ->_s0(lte(x,s(y)),tt). [resolve(8,c,9,a)]. 20.036/20.036 kept: 20 -->*_s0(lte(s(x),y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 20.036/20.036 ============================== end of process initial clauses ======== 20.036/20.036 20.036/20.036 ============================== CLAUSES FOR SEARCH ==================== 20.036/20.036 20.036/20.036 % Clauses after input processing: 20.036/20.036 20.036/20.036 formulas(usable). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(sos). 20.036/20.036 11 -->_s0(x,y) | ->_s0(lte(x,z),lte(y,z)) # label(congruence). [clausify(1)]. 20.036/20.036 12 -->_s0(x,y) | ->_s0(lte(z,x),lte(z,y)) # label(congruence). [clausify(2)]. 20.036/20.036 13 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.036/20.036 14 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 15 ->_s0(lte(s(x),0),ff) # label(replacement). [assumption]. 20.036/20.036 16 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 17 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 18 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 19 -->*_s0(lte(x,y),z) | -->*_s0(tt,z) | ->_s0(lte(x,s(y)),tt). [resolve(8,c,9,a)]. 20.036/20.036 20 -->*_s0(lte(s(x),y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(demodulators). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== end of clauses for search ============= 20.036/20.036 20.036/20.036 ============================== SEARCH ================================ 20.036/20.036 20.036/20.036 % Starting search at 0.00 seconds. 20.036/20.036 20.036/20.036 given #1 (I,wt=10): 11 -->_s0(x,y) | ->_s0(lte(x,z),lte(y,z)) # label(congruence). [clausify(1)]. 20.036/20.036 20.036/20.036 given #2 (I,wt=10): 12 -->_s0(x,y) | ->_s0(lte(z,x),lte(z,y)) # label(congruence). [clausify(2)]. 20.036/20.036 20.036/20.036 given #3 (I,wt=8): 13 -->_s0(x,y) | ->_s0(s(x),s(y)) # label(congruence). [clausify(3)]. 20.036/20.036 20.036/20.036 given #4 (I,wt=5): 14 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 20.036/20.036 given #5 (I,wt=6): 15 ->_s0(lte(s(x),0),ff) # label(replacement). [assumption]. 20.036/20.036 20.036/20.036 given #6 (I,wt=9): 16 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 20.036/20.036 given #7 (I,wt=3): 17 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 20.036/20.036 given #8 (I,wt=9): 18 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 20.036/20.036 given #9 (I,wt=14): 19 -->*_s0(lte(x,y),z) | -->*_s0(tt,z) | ->_s0(lte(x,s(y)),tt). [resolve(8,c,9,a)]. 20.036/20.036 20.036/20.036 given #10 (I,wt=9): 20 -->*_s0(lte(s(x),y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 20.036/20.036 given #11 (A,wt=7): 21 ->_s0(s(lte(0,0)),s(tt)). [ur(13,a,14,a)]. 20.036/20.036 20.036/20.036 given #12 (F,wt=6): 34 -->*_s0(tt,lte(s(x),y)). [resolve(20,a,17,a)]. 20.036/20.036 20.036/20.036 given #13 (F,wt=6): 36 -->*_s0(lte(s(x),y),tt). [resolve(20,b,17,a)]. 20.036/20.036 20.036/20.036 ============================== PROOF ================================= 20.036/20.036 20.036/20.036 % Proof 1 at 0.01 (+ 0.00) seconds. 20.036/20.036 % Length of proof is 14. 20.036/20.036 % Level of proof is 5. 20.036/20.036 % Maximum clause weight is 9.000. 20.036/20.036 % Given clauses 13. 20.036/20.036 20.036/20.036 5 ->_s0(x,y) & ->*_s0(y,z) -> ->*_s0(x,z) # label(transitivity) # label(non_clause). [assumption]. 20.036/20.036 6 ->*_s0(x,y) & ->*_s0(z,y) -> ->*<-_s0(x,z) # label(joinability) # label(non_clause). [assumption]. 20.036/20.036 7 (exists x6 exists x7 ->*<-_s0(lte(s(x6),x7),tt)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.036/20.036 8 -->*_s0(x,y) | -->*_s0(z,y) | ->*<-_s0(x,z) # label(joinability). [clausify(6)]. 20.036/20.036 10 -->*<-_s0(lte(s(x),y),tt) # label(goal). [deny(7)]. 20.036/20.036 14 ->_s0(lte(0,0),tt) # label(replacement). [assumption]. 20.036/20.036 16 ->_s0(lte(s(x),s(y)),lte(x,y)) # label(replacement). [assumption]. 20.036/20.036 17 ->*_s0(x,x) # label(reflexivity). [assumption]. 20.036/20.036 18 -->_s0(x,y) | -->*_s0(y,z) | ->*_s0(x,z) # label(transitivity). [clausify(5)]. 20.036/20.036 20 -->*_s0(lte(s(x),y),z) | -->*_s0(tt,z). [resolve(10,a,8,c)]. 20.036/20.036 32 ->*_s0(lte(0,0),tt). [ur(18,a,14,a,b,17,a)]. 20.036/20.036 36 -->*_s0(lte(s(x),y),tt). [resolve(20,b,17,a)]. 20.036/20.036 45 -->*_s0(lte(x,y),tt). [ur(18,a,16,a,c,36,a)]. 20.036/20.036 46 $F. [resolve(45,a,32,a)]. 20.036/20.036 20.036/20.036 ============================== end of proof ========================== 20.036/20.036 20.036/20.036 ============================== STATISTICS ============================ 20.036/20.036 20.036/20.036 Given=13. Generated=37. Kept=35. proofs=1. 20.036/20.036 Usable=13. Sos=19. Demods=0. Limbo=2, Disabled=13. Hints=0. 20.036/20.036 Kept_by_rule=0, Deleted_by_rule=0. 20.036/20.036 Forward_subsumed=2. Back_subsumed=0. 20.036/20.036 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.036/20.036 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.036/20.036 Demod_attempts=0. Demod_rewrites=0. 20.036/20.036 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.036/20.036 Nonunit_fsub_feature_tests=5. Nonunit_bsub_feature_tests=25. 20.036/20.036 Megabytes=0.10. 20.036/20.036 User_CPU=0.01, System_CPU=0.00, Wall_clock=0. 20.036/20.036 20.036/20.036 ============================== end of statistics ===================== 20.036/20.036 20.036/20.036 ============================== end of search ========================= 20.036/20.036 20.036/20.036 THEOREM PROVED 20.036/20.036 20.036/20.036 Exiting with 1 proof. 20.036/20.036 20.036/20.036 Process 84616 exit (max_proofs) Wed Mar 9 10:43:56 2022 20.036/20.036 20.036/20.036 20.036/20.036 The problem is feasible. 20.036/20.036 20.036/20.036 20.036/20.036 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Maybe right-stable CTRS, Overlay CTRS 20.036/20.036 Maybe normal CTRS, Maybe almost normal CTRS 20.036/20.036 Maybe terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 20.036/20.036 Resulting CCPs: 20.036/20.036 | lte(s(x'),y') ->*<- tt => Not trivial, Overlay, Feasible conditions, NW2, N1 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 Underlying TRS Termination Processor: 20.036/20.036 20.036/20.036 Resulting Underlying TRS: 20.036/20.036 (VAR x y x' y') 20.036/20.036 (STRATEGY CONTEXTSENSITIVE 20.036/20.036 (lte 1 2) 20.036/20.036 (ff) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt 20.036/20.036 ) 20.036/20.036 Underlying TRS terminating? 20.036/20.036 YES 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 (VAR vu95NonEmpty x y xu39 yu39) 20.036/20.036 (RULES 20.036/20.036 lte(num0,num0) -> tt 20.036/20.036 lte(s(x),num0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt 20.036/20.036 ) 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Dependency Pairs Processor: 20.036/20.036 -> Pairs: 20.036/20.036 LTE(s(x),s(y)) -> LTE(x,y) 20.036/20.036 -> Rules: 20.036/20.036 lte(num0,num0) -> tt 20.036/20.036 lte(s(x),num0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 SCC Processor: 20.036/20.036 -> Pairs: 20.036/20.036 LTE(s(x),s(y)) -> LTE(x,y) 20.036/20.036 -> Rules: 20.036/20.036 lte(num0,num0) -> tt 20.036/20.036 lte(s(x),num0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt 20.036/20.036 ->Strongly Connected Components: 20.036/20.036 ->->Cycle: 20.036/20.036 ->->-> Pairs: 20.036/20.036 LTE(s(x),s(y)) -> LTE(x,y) 20.036/20.036 ->->-> Rules: 20.036/20.036 lte(num0,num0) -> tt 20.036/20.036 lte(s(x),num0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Subterm Processor: 20.036/20.036 -> Pairs: 20.036/20.036 LTE(s(x),s(y)) -> LTE(x,y) 20.036/20.036 -> Rules: 20.036/20.036 lte(num0,num0) -> tt 20.036/20.036 lte(s(x),num0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt 20.036/20.036 ->Projection: 20.036/20.036 pi(LTE) = 1 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 SCC Processor: 20.036/20.036 -> Pairs: 20.036/20.036 Empty 20.036/20.036 -> Rules: 20.036/20.036 lte(num0,num0) -> tt 20.036/20.036 lte(s(x),num0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt 20.036/20.036 ->Strongly Connected Components: 20.036/20.036 There is no strongly connected component 20.036/20.036 20.036/20.036 The problem is finite. 20.036/20.036 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Maybe right-stable CTRS, Overlay CTRS 20.036/20.036 Maybe normal CTRS, Maybe almost normal CTRS 20.036/20.036 Terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 Confluence Problem: 20.036/20.036 (VAR x y x' y') 20.036/20.036 (REPLACEMENT-MAP 20.036/20.036 (lte 1, 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 ) 20.036/20.036 Critical Pairs: 20.036/20.036 | lte(s(x'),y') ->*<- tt => Not trivial, Overlay, Feasible conditions, NW2, N1 20.036/20.036 Terminating:YES 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Maybe right-stable CTRS, Overlay CTRS 20.036/20.036 Maybe normal CTRS, Maybe almost normal CTRS 20.036/20.036 Terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 20.036/20.036 Right Stable Processor: 20.036/20.036 Right-stable CTRS 20.036/20.036 Justification: 20.036/20.036 20.036/20.036 -> Term right-stability conditions: 20.036/20.036 Term: tt 20.036/20.036 Right-stable term 20.036/20.036 Linear constructor form 20.036/20.036 Don't know if term is a ground normal form (not needed) 20.036/20.036 Right-stability condition achieved 20.036/20.036 A call to InfChecker wasn't needed 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Right-stable CTRS, Overlay CTRS 20.036/20.036 Maybe normal CTRS, Maybe almost normal CTRS 20.036/20.036 Terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 Confluence Problem: 20.036/20.036 (VAR x y x' y') 20.036/20.036 (REPLACEMENT-MAP 20.036/20.036 (lte 1, 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 ) 20.036/20.036 Critical Pairs: 20.036/20.036 | lte(s(x'),y') ->*<- tt => Not trivial, Overlay, Feasible conditions, NW2, N1 20.036/20.036 Terminating:YES 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Right-stable CTRS, Overlay CTRS 20.036/20.036 Maybe normal CTRS, Maybe almost normal CTRS 20.036/20.036 Terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 20.036/20.036 Normal RConds Processor: 20.036/20.036 YES 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Infeasibility Problem: 20.036/20.036 [(VAR vNonEmpty x y x1 y1 vNonEmpty z) 20.036/20.036 (STRATEGY CONTEXTSENSITIVE 20.036/20.036 (lte 1 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 )] 20.036/20.036 20.036/20.036 Infeasibility Conditions: 20.036/20.036 tt -> z 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 20.036/20.036 Obtaining a model using Mace4: 20.036/20.036 20.036/20.036 -> Usable Rules: 20.036/20.036 Empty 20.036/20.036 20.036/20.036 -> Mace4 Output: 20.036/20.036 ============================== Mace4 ================================= 20.036/20.036 Mace4 (64) version 2009-11A, November 2009. 20.036/20.036 Process 84687 was started by ubuntu on ubuntu, 20.036/20.036 Wed Mar 9 10:44:16 2022 20.036/20.036 The command was "./mace4 -c -f /tmp/mace484675-2.in". 20.036/20.036 ============================== end of head =========================== 20.036/20.036 20.036/20.036 ============================== INPUT ================================= 20.036/20.036 20.036/20.036 % Reading from file /tmp/mace484675-2.in 20.036/20.036 20.036/20.036 assign(max_seconds,13). 20.036/20.036 20.036/20.036 formulas(assumptions). 20.036/20.036 ->(x1,y) -> ->(lte(x1,x2),lte(y,x2)) # label(congruence). 20.036/20.036 ->(x2,y) -> ->(lte(x1,x2),lte(x1,y)) # label(congruence). 20.036/20.036 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(goals). 20.036/20.036 (exists x6 ->(tt,x6)) # label(goal). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== end of input ========================== 20.036/20.036 20.036/20.036 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.036/20.036 20.036/20.036 % Formulas that are not ordinary clauses: 20.036/20.036 1 ->(x1,y) -> ->(lte(x1,x2),lte(y,x2)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 2 ->(x2,y) -> ->(lte(x1,x2),lte(x1,y)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 3 ->(x1,y) -> ->(s(x1),s(y)) # label(congruence) # label(non_clause). [assumption]. 20.036/20.036 4 (exists x6 ->(tt,x6)) # label(goal) # label(non_clause) # label(goal). [goal]. 20.036/20.036 20.036/20.036 ============================== end of process non-clausal formulas === 20.036/20.036 20.036/20.036 ============================== CLAUSES FOR SEARCH ==================== 20.036/20.036 20.036/20.036 formulas(mace4_clauses). 20.036/20.036 -->(x,y) | ->(lte(x,z),lte(y,z)) # label(congruence). 20.036/20.036 -->(x,y) | ->(lte(z,x),lte(z,y)) # label(congruence). 20.036/20.036 -->(x,y) | ->(s(x),s(y)) # label(congruence). 20.036/20.036 -->(tt,x) # label(goal). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== end of clauses for search ============= 20.036/20.036 20.036/20.036 % There are no natural numbers in the input. 20.036/20.036 20.036/20.036 ============================== DOMAIN SIZE 2 ========================= 20.036/20.036 20.036/20.036 ============================== MODEL ================================= 20.036/20.036 20.036/20.036 interpretation( 2, [number=1, seconds=0], [ 20.036/20.036 20.036/20.036 function(tt, [ 0 ]), 20.036/20.036 20.036/20.036 function(s(_), [ 0, 0 ]), 20.036/20.036 20.036/20.036 function(lte(_,_), [ 20.036/20.036 0, 0, 20.036/20.036 0, 0 ]), 20.036/20.036 20.036/20.036 relation(->(_,_), [ 20.036/20.036 0, 0, 20.036/20.036 0, 0 ]) 20.036/20.036 ]). 20.036/20.036 20.036/20.036 ============================== end of model ========================== 20.036/20.036 20.036/20.036 ============================== STATISTICS ============================ 20.036/20.036 20.036/20.036 For domain size 2. 20.036/20.036 20.036/20.036 Current CPU time: 0.00 seconds (total CPU time: 0.00 seconds). 20.036/20.036 Ground clauses: seen=22, kept=22. 20.036/20.036 Selections=7, assignments=7, propagations=4, current_models=1. 20.036/20.036 Rewrite_terms=42, rewrite_bools=24, indexes=2. 20.036/20.036 Rules_from_neg_clauses=0, cross_offs=0. 20.036/20.036 20.036/20.036 ============================== end of statistics ===================== 20.036/20.036 20.036/20.036 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.036/20.036 20.036/20.036 Exiting with 1 model. 20.036/20.036 20.036/20.036 Process 84687 exit (max_models) Wed Mar 9 10:44:16 2022 20.036/20.036 The process finished Wed Mar 9 10:44:16 2022 20.036/20.036 20.036/20.036 20.036/20.036 Mace4 cooked interpretation: 20.036/20.036 20.036/20.036 20.036/20.036 20.036/20.036 The problem is infeasible. 20.036/20.036 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Right-stable CTRS, Overlay CTRS 20.036/20.036 Normal CTRS, Almost normal CTRS 20.036/20.036 Terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 20.036/20.036 Problem 1: 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 Confluence Problem: 20.036/20.036 (VAR x y x' y') 20.036/20.036 (REPLACEMENT-MAP 20.036/20.036 (lte 1, 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 ) 20.036/20.036 Critical Pairs: 20.036/20.036 | lte(s(x'),y') ->*<- tt => Not trivial, Overlay, Feasible conditions, NW2, N1 20.036/20.036 Terminating:YES 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Right-stable CTRS, Overlay CTRS 20.036/20.036 Normal CTRS, Almost normal CTRS 20.036/20.036 Terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 20.036/20.036 Conditional Critical Pairs Distributor Processor 20.036/20.036 Problem 1.1: 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 Confluence Problem: 20.036/20.036 (VAR x y x' y') 20.036/20.036 (REPLACEMENT-MAP 20.036/20.036 (lte 1, 2) 20.036/20.036 (0) 20.036/20.036 (fSNonEmpty) 20.036/20.036 (ff) 20.036/20.036 (s 1) 20.036/20.036 (tt) 20.036/20.036 ) 20.036/20.036 (RULES 20.036/20.036 lte(0,0) -> tt 20.036/20.036 lte(s(x),0) -> ff 20.036/20.036 lte(s(x),s(y)) -> lte(x,y) 20.036/20.036 lte(x,s(y)) -> tt | lte(x,y) ->*<- tt 20.036/20.036 ) 20.036/20.036 Critical Pairs: 20.036/20.036 | lte(s(x'),y') ->*<- tt => Not trivial, Overlay, Feasible conditions, NW2, N1 20.036/20.036 Terminating:YES 20.036/20.036 20.036/20.036 -> Problem conclusions: 20.036/20.036 Left linear, Right linear, Linear 20.036/20.036 Not weakly orthogonal, Not almost orthogonal, Not orthogonal 20.036/20.036 CTRS Type: 1 20.036/20.036 Deterministic, Strongly deterministic 20.036/20.036 Not oriented CTRS, Not properly oriented CTRS, Join CTRS, Not semiequational CTRS 20.036/20.036 Right-stable CTRS, Overlay CTRS 20.036/20.036 Normal CTRS, Almost normal CTRS 20.036/20.036 Terminating CTRS, Maybe operational terminating CTRS, Maybe joinable CCPs 20.036/20.036 Maybe level confluent 20.036/20.036 Maybe confluent 20.036/20.036 ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 20.036/20.036 20.036/20.036 Prover9 CCP Convergence Checker Processor: 20.036/20.036 Proof: 20.036/20.036 ============================== Prover9 =============================== 20.036/20.036 Prover9 (64) version 2009-11A, November 2009. 20.036/20.036 Process 84701 was started by ubuntu on ubuntu, 20.036/20.036 Wed Mar 9 10:44:16 2022 20.036/20.036 The command was "./prover9 -t 60 -f /tmp/prover984531-18.in". 20.036/20.036 ============================== end of head =========================== 20.036/20.036 20.036/20.036 ============================== INPUT ================================= 20.036/20.036 20.036/20.036 % Reading from file /tmp/prover984531-18.in 20.036/20.036 20.036/20.036 20.036/20.036 formulas(sos). 20.036/20.036 reds(x,x). 20.036/20.036 red(x,y) & reds(y,z) -> reds(x,z). 20.036/20.036 red(x,y) -> red(lte(x,z1),lte(y,z1)). 20.036/20.036 red(x,y) -> red(lte(z,x),lte(z,y)). 20.036/20.036 red(x,y) -> red(s(x),s(y)). 20.036/20.036 red(lte(0,0),tt). 20.036/20.036 (all x red(lte(s(x),0),ff)). 20.036/20.036 (all x all y red(lte(s(x),s(y)),lte(x,y))). 20.036/20.036 (all x all y exists z (reds(lte(x,y),z) & reds(tt,z) -> red(lte(x,s(y)),tt))). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(goals). 20.036/20.036 (all x1 all y1 exists z exists z1 (reds(lte(s(x1),y1),z1) & reds(tt,z1) -> reds(lte(x1,y1),z) & reds(tt,z))). 20.036/20.036 end_of_list. 20.036/20.036 assign(max_megs,-1). 20.036/20.036 set(quiet). 20.036/20.036 20.036/20.036 ============================== end of input ========================== 20.036/20.036 20.036/20.036 % From the command line: assign(max_seconds, 60). 20.036/20.036 20.036/20.036 ============================== PROCESS NON-CLAUSAL FORMULAS ========== 20.036/20.036 20.036/20.036 % Formulas that are not ordinary clauses: 20.036/20.036 1 red(x,y) & reds(y,z) -> reds(x,z) # label(non_clause). [assumption]. 20.036/20.036 2 red(x,y) -> red(lte(x,z1),lte(y,z1)) # label(non_clause). [assumption]. 20.036/20.036 3 red(x,y) -> red(lte(z,x),lte(z,y)) # label(non_clause). [assumption]. 20.036/20.036 4 red(x,y) -> red(s(x),s(y)) # label(non_clause). [assumption]. 20.036/20.036 5 (all x red(lte(s(x),0),ff)) # label(non_clause). [assumption]. 20.036/20.036 6 (all x all y red(lte(s(x),s(y)),lte(x,y))) # label(non_clause). [assumption]. 20.036/20.036 7 (all x all y exists z (reds(lte(x,y),z) & reds(tt,z) -> red(lte(x,s(y)),tt))) # label(non_clause). [assumption]. 20.036/20.036 8 (all x1 all y1 exists z exists z1 (reds(lte(s(x1),y1),z1) & reds(tt,z1) -> reds(lte(x1,y1),z) & reds(tt,z))) # label(non_clause) # label(goal). [goal]. 20.036/20.036 20.036/20.036 ============================== end of process non-clausal formulas === 20.036/20.036 20.036/20.036 ============================== PROCESS INITIAL CLAUSES =============== 20.036/20.036 20.036/20.036 % Clauses before input processing: 20.036/20.036 20.036/20.036 formulas(usable). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(sos). 20.036/20.036 reds(x,x). [assumption]. 20.036/20.036 -red(x,y) | -reds(y,z) | reds(x,z). [clausify(1)]. 20.036/20.036 -red(x,y) | red(lte(x,z),lte(y,z)). [clausify(2)]. 20.036/20.036 -red(x,y) | red(lte(z,x),lte(z,y)). [clausify(3)]. 20.036/20.036 -red(x,y) | red(s(x),s(y)). [clausify(4)]. 20.036/20.036 red(lte(0,0),tt). [assumption]. 20.036/20.036 red(lte(s(x),0),ff). [clausify(5)]. 20.036/20.036 red(lte(s(x),s(y)),lte(x,y)). [clausify(6)]. 20.036/20.036 -reds(lte(x,y),f1(x,y)) | -reds(tt,f1(x,y)) | red(lte(x,s(y)),tt). [clausify(7)]. 20.036/20.036 reds(lte(s(c1),c2),x). [deny(8)]. 20.036/20.036 reds(tt,x). [deny(8)]. 20.036/20.036 -reds(lte(c1,c2),x) | -reds(tt,x). [deny(8)]. 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 formulas(demodulators). 20.036/20.036 end_of_list. 20.036/20.036 20.036/20.036 ============================== PREDICATE ELIMINATION ================= 20.036/20.036 20.036/20.036 ============================== end predicate elimination ============= 20.036/20.036 20.036/20.036 Auto_denials: (no changes). 20.036/20.036 20.036/20.036 Term ordering decisions: 20.036/20.036 20.036/20.036 kept: 9 reds(x,x). [assumption]. 20.036/20.036 kept: 10 -red(x,y) | -reds(y,z) | reds(x,z). [clausify(1)]. 20.036/20.036 kept: 11 -red(x,y) | red(lte(x,z),lte(y,z)). [clausify(2)]. 20.036/20.036 kept: 12 -red(x,y) | red(lte(z,x),lte(z,y)). [clausify(3)]. 20.036/20.036 kept: 13 -red(x,y) | red(s(x),s(y)). [clausify(4)]. 20.036/20.036 kept: 14 red(lte(0,0),tt). [assumption]. 20.036/20.036 kept: 15 red(lte(s(x),0),ff). [clausify(5)]. 20.036/20.036 kept: 16 red(lte(s(x),s(y)),lte(x,y)). [clausify(6)]. 20.036/20.036 kept: 17 -reds(lte(x,y),f1(x,y)) | -reds(tt,f1(x,y)) | red(lte(x,s(y)),tt). [clausify(7)]. 20.036/20.036 kept: 18 reds(lte(s(c1),c2),x). [deny(8)]. 20.036/20.036 kept: 19 reds(tt,x). [deny(8)]. 20.036/20.036 20 -reds(lte(c1,c2),x) | -reds(tt,x). [deny(8)]. 20.036/20.036 kept: 21 -reds(lte(c1,c2),x). [copy(20),unit_del(b,19)]. 20.036/20.036 20.036/20.036 ============================== PROOF ================================= 20.036/20.036 20.036/20.036 % Proof 1 at 0.00 (+ 0.00) seconds. 20.036/20.036 % Length of proof is 6. 20.036/20.036 % Level of proof is 3. 20.036/20.036 % Maximum clause weight is 5.000. 20.036/20.036 % Given clauses 0. 20.036/20.036 20.036/20.036 8 (all x1 all y1 exists z exists z1 (reds(lte(s(x1),y1),z1) & reds(tt,z1) -> reds(lte(x1,y1),z) & reds(tt,z))) # label(non_clause) # label(goal). [goal]. 20.036/20.036 9 reds(x,x). [assumption]. 20.036/20.036 19 reds(tt,x). [deny(8)]. 20.036/20.036 20 -reds(lte(c1,c2),x) | -reds(tt,x). [deny(8)]. 20.036/20.036 21 -reds(lte(c1,c2),x). [copy(20),unit_del(b,19)]. 20.036/20.036 22 $F. [resolve(21,a,9,a)]. 20.036/20.036 20.036/20.036 ============================== end of proof ========================== 20.036/20.036 20.036/20.036 ============================== STATISTICS ============================ 20.036/20.036 20.036/20.036 Given=0. Generated=12. Kept=12. proofs=1. 20.036/20.036 Usable=0. Sos=0. Demods=0. Limbo=11, Disabled=12. Hints=0. 20.036/20.036 Kept_by_rule=0, Deleted_by_rule=0. 20.036/20.036 Forward_subsumed=0. Back_subsumed=0. 20.036/20.036 Sos_limit_deleted=0. Sos_displaced=0. Sos_removed=0. 20.036/20.036 New_demodulators=0 (0 lex), Back_demodulated=0. Back_unit_deleted=0. 20.036/20.036 Demod_attempts=0. Demod_rewrites=0. 20.036/20.036 Res_instance_prunes=0. Para_instance_prunes=0. Basic_paramod_prunes=0. 20.036/20.036 Nonunit_fsub_feature_tests=1. Nonunit_bsub_feature_tests=0. 20.036/20.036 Megabytes=0.06. 20.036/20.036 User_CPU=0.00, System_CPU=0.00, Wall_clock=0. 20.036/20.036 20.036/20.036 ============================== end of statistics ===================== 20.036/20.036 20.036/20.036 ============================== end of search ========================= 20.036/20.036 20.036/20.036 THEOREM PROVED 20.036/20.036 20.036/20.036 Exiting with 1 proof. 20.036/20.036 20.036/20.036 Process 84701 exit (max_proofs) Wed Mar 9 10:44:16 2022 20.036/20.036 20.036/20.036 20.036/20.036 The problem is joinable. 20.036/20.036 20.06user 0.46system 0:20.36elapsed 100%CPU (0avgtext+0avgdata 62252maxresident)k 20.036/20.036 0inputs+0outputs (0major+40377minor)pagefaults 0swaps